Protein Adsorption on
Nanostructured Silica Surfaces
vorgelegt von
Diplom-Chemiker
Jens Meißner
geb. in Pritzwalk
von der Fakultät II – Mathematik und Naturwissenschaften
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
– Dr. rer. nat. –
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Reinhard Schomäcker
Berichter: Prof. Dr. Gerhard H. Findenegg
Berichter: Prof. Dr. Michael Gradzielski
Berichter: Prof. Dr. Bhuvnesh Bharti
Tag der wissenschaftlichen Aussprache: 12. Dezember 2017
Berlin 2018
i
Danksagung
An erster Stelle möchte ich mich ganz herzlich bei Prof. Dr. Gerhard H. Findenegg
bedanken, in dessen Arbeitskreis ich diese Dissertation anfertigen durfte. Jederzeit hatte
ich die Möglichkeit zu wissenschaftlichen Diskussionen, die die Entwicklung dieser
Arbeit ganz entscheidend voran gebracht haben.
Furthermore, I want to thank Prof. Dr. Bhuvnesh Bharti, who was helping me
during my stay at the North Carolina State University and advising me during my time as
a diploma student. I consider myself to be lucky to have met you.
Prof. Dr. Michael Gradzielski danke ich für die Möglichkeit die Labore seiner
Arbeitsgruppe zu nutzen.
Weiterhin möchte ich Prof. Dr. Reinhard Schomäcker für die Übernahme des
Vorsitzes meiner Prüfungskommission danken.
Auch möchte ich mich bei B.Sc. Albert Prause bedanken, dessen Unterstützung
als studentische Hilfskraft mir viel experimentelle Arbeit abgenommen hat. Also, I want
to thank M.Sc. Caroline Di Tommaso for her help with the SBA-15 functionalization
during her summer internship.
Für die aufopferungsvolle Hilfe und Anleitung bei Synchrotron-Messzeiten in
Triest bedanke ich mich bei Prof. Dr. Heinz Ammenitsch und seinem Team mit Dr.
Benedetta Marmiroli und Dott. Barbara Sartori. Grazie mille!
Außerdem möchte ich mich bei Jana Lutzki, Gabi Görig-Hedicke, Michaela
Dzionara sowie Petra Erdmann, Maria Bülth und Christiane Abu-Hani bedanken.
Für die Finanzierung im Rahmen des IRTG 1524 bedanke ich mich bei der
Deutschen Forschungsgemeinschaft, dem Sprecher des IRTG 1524 Prof. Dr. Martin
Schoen sowie der geschäftsführenden Direktorin Dr. Daniela Fliegner.
Ein großes Dankeschön gebührt auch allen Kommilitonen und Freunden vom
Stranski-Laboratorium, insbesondere Olli, Martin, Miriam und Lucas, Michi, Caro sowie
Sven, mit denen jeder Arbeitstag spannend wurde.
Mein besonderer Dank gilt meinen langjährigsten Freunden Micha und den
Gentlemen Alexander, Marc, Christoph, Michael, Aymeric und Jan. Durch euch konnte
ich permanent neue Motivation schöpfen!
Vom ganzen Herzen will ich mich bei meiner Familie bedanken. Auf meine
Schwester Katja mit Konstantin und Oskar kann ich mich blind verlassen. Mein größter
Dank gilt meinen wunderbaren Eltern Elke und Germut, die mich auf meinem Weg nach
allen Kräften unterstützt haben und mir in jeder meiner Entscheidungen beistanden!
ii
Zusammenfassung
Die vorliegende Dissertation ist eine Studie über die Interaktion von globulären Porteinen mit
nanostrukturierten Silika Oberflächen. Ziel der Arbeit ist es, ein besseres Verständnis für die
Einflüsse hoher Oberflächenkrümmung und räumlicher Einengung auf das Adsorptionsverhalten
und auf die Morphologie von adsorbierten Proteinen zu entwickeln.
Das Adsorptionsverhalten von Lysozyme und 𝛽-Lactoglobulin auf Silika-Nanopartikeln
wurde von pH 2 bis 11 und einer Ionenstärke bis zu 100 mM untersucht. In diesem pH Bereich
ändert sich die Ladungsverteilung auf Proteinen und Silika drastisch. So war es möglich, die
Wechselwirkungen zwischen Partikel und 𝛽- Lactoglobulin auf beiden Seiten des isoelektrischen
Punktes des Proteins zu studieren. Die erhaltenen Daten wurden mit der
Guggenheim – Anderson – de Boer Adsorptionsisotherme ausgewertet. Dieses Model lässt die
Mehrschichtadsorption aus einer flüssigen Phase zu.
Mithilfe von Neutronen Kleinwinkelstreuung wurde die Orientierung des globulären
Proteins Cytochrom c auf Silika Nanopartikeln bei verschiedenen äußeren pH Bedingungen
bestimmt. Die Streudaten wurden mit einem Formfaktor Model ausgewertet, das ‚Himbeer-
förmige‘ Strukturen beschreibt. Eine starke Veränderung in der Adsorptionsorientierung relativ
zur Partikeloberfläche wurde zwischen pH 3 und 4 gefunden. Dieses Verhalten wurde mit dem
Dipolmoment des Proteins in Verbindung gebracht. Simulationen des Dipolmoments für
verschiedene Protonierungszustände von Cytochrom c zeigen eine charakteristische Änderung
der Dipolmomentorientierung in der gleichen pH Region.
In vorangegangenen Studien wurde gefunden, dass Proteinadsorption eine Hetero-
aggregation von Silikapartikeln auslösen kann. In dieser Arbeit wurde die großräumige Struktur
der Aggregate von Silikapartikeln und fluoreszenzmarkiertem Lysozym mit konfokaler
Laserrastermikroskopie untersucht. Die 3D Aggregatstruktur wurde aus Stapeln einzelner 2D
Aufnahmen rekonstruiert. Die globale Struktur wurde mithilfe des Verhältnisses aus der
Oberfläche und dem Volumen der Aggregate abgeschätzt.
Die Aufnahme von Proteinen in nanometerkleinen Poren hängt vom zugänglichen
Porenvolumen und von den Wechselwirkungen zwischen Protein und Porenwand ab. Die
Adsorption von Lysozym in mesoporösen SBA-15 mit nativen und chemisch modifizierten
Porenwänden wurde über einen weiten pH Bereich untersucht. Um die beobachteten Unterschiede
zu erklären, wurde ein geometrisches Model für die Porenauffüllung entwickelt, welches die
Porengrößenverteilung einbezieht.
Die Schmelzpunktserniedrigung von elf wässrigen Alkalihalogenidlösungen in den
Mesoporen von SBA-15 und MCM-41 wurde mit DSC untersucht. Es wurde gefunden, dass die
eutektische Temperatur vom Volumenbruch der Salzkristalle in der Pore abhängt. Die
Unterschiede waren am größten für Salze, die Oligohydrat Kristalle formen. Salzspezifische
Effekte spielen dabei nur eine untergeordnete Rolle.
iii
Abstract
This Ph.D. thesis presents a study of the interaction of globular proteins with nanostructured silica
surfaces. It aims to gain a better understanding of the consequences of a high surface curvature
and confinement on the adsorption behavior and morphology of the adsorbed protein.
The adsorption behavior of lysozyme and 𝛽-lactoglobulin on silica nanoparticles was
studied from pH 2 to 11 and ionic strength until 100 mM. Within this pH range the surface charge
distribution on proteins and silica changes drastically. Specifically it was possible to study the
interactions between particles and 𝛽-lactoglobulin on both sides of the isoelectric point of the
protein. Resulting data were evaluated with the Guggenheim – Anderson – de Boer adsorption
isotherm equation which accounts for multilayer adsorption from liquid phases.
The orientation of the globular protein cytochrome c adsorbed on silica nanoparticles was
determined as a function of solution pH using small angle neutron scattering. The scattering data
was evaluated with a form factor model accounting specifically for 'raspberry-shaped' structures.
A pronounced shift in the adsorption orientation relative to the particle surface was detected
between pH 3 and 4. This behavior was correlated with the dipole moment of the protein.
Simulations of the dipole moment for different protonation states of cytochrome c show a
distinctive change in the dipole moment orientation for the same pH region.
In preceding studies it was found that protein adsorption can cause hetero-aggregation of
the silica nanoparticles. Here, the large-scale structure of these aggregates was studied by confocal
laser scanning microscopy with fluorescently labeled lysozyme. Stacks of 2D images were used
to reconstruct the 3D aggregate structure and estimate the global structural properties in terms of
their surface-area-to-volume ratio.
Protein uptake in nanometer-sized pores depends on the accessible pore space and the
interaction of the protein with the pore wall. The adsorption of lysozyme in mesoporous SBA-15
silica materials with native and chemically modified pore walls was studied over a wide pH range.
To assess the observed differences in the protein uptake capacity of the materials, a geometrical
pore filling model was developed that takes into account the different pore-size distribution of the
materials.
The melting point depression of eleven aqueous alkali halide systems confined in the
mesopores of SBA-15 and MCM-41 silica was studied by DSC. It was found that the eutectic
temperature in the pores is mainly dependent of the fraction of volume occupied by the salt
crystallites, i.e. largest for salts forming oligohydrates in the pores. Salt-specific adsorption effects
at the pore wall are only of minor importance.
iv
Publications
Parts of this thesis are based on the publications listed below.
Chapter 3:
J. Meissner, A. Prause, B. Bharti and G. H. Findenegg: Characterization of protein
adsorption onto silica nanoparticles: influence of pH and ionic strength", Colloid Polym
Sci 2015, 293, 3381 – 3391. Reproduced with permission. Published open access under
the Creative Commons Attribution 4.0 International license.
http://dx.doi.org/10.1007/s00396-015-3754-x
Chapter 6:
J. Meissner, A. Prause, C. Di Tommaso, B. Bharti and G. H. Findenegg: Protein
Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from
the Pore Structure, J. Phys. Chem. C 2015, 119, 2438 – 2446. Copyright 2015 American
Chemical Society. Reproduced with permission.
http://dx.doi.org/10.1021/jp5096745
Chapter 7:
J. Meissner, A. Prause and G. H. Findenegg: Secondary Confinement of Water Observed
in Eutectic Melting of Aqueous Salt Systems in Nanopores, J. Phys. Chem. Lett. 2016, 7,
1816 – 1820. Copyright 2016 American Chemical Society. Reproduced with permission.
http://dx.doi.org/10.1021/acs.jpclett.6b00756
v
Contents
CHAPTER 1 INTRODUCTION ....................................................................................................... 1
1.1 PROTEIN ADSORPTION AT HIGHLY CURVED HYDROPHILIC SURFACES ..................... 1
1.2 PROTEIN-INDUCED AGGREGATION OF SILICA NANOPARTICLES ............................... 3
1.3 ORIENTATION OF ADSORBED PROTEIN MOLECULES ................................................. 4
1.4 FREEZING/MELTING OF CONCENTRATED SALT SOLUTIONS IN NANOPORES ............. 5
CHAPTER 2 METHODS AND MODELS ....................................................................................... 7
2.1 FLUORESCENCE MICROSCOPY .................................................................................. 7
2.1.1 Confocal Laser Scanning Microscopy................................................................ 7
2.1.2 Fluorescence Correlation Spectroscopy ............................................................. 9
2.2 SMALL ANGLE NEUTRON SCATTERING .................................................................. 10
2.2.1 Technical Background...................................................................................... 11
2.2.2 Raspberry Form Factor Model ......................................................................... 13
2.3 PROTEIN DIPOLE MOMENT ..................................................................................... 15
2.4 DIFFERENTIAL SCANNING CALORIMETRY .............................................................. 17
CHAPTER 3 CHARACTERIZATION OF PROTEIN ADSORPTION ONTO SILICA
NANOPARTICLES: INFLUENCE OF PH AND IONIC STRENGTH ............... 19
3.1 INTRODUCTION ....................................................................................................... 19
3.2 MATERIALS AND METHODS .................................................................................... 21
3.2.1 Materials ........................................................................................................... 21
3.2.2 Protein Adsorption Measurements ................................................................... 21
3.2.3 Adsorption Isotherm Equation ......................................................................... 22
3.3 RESULTS ................................................................................................................. 23
3.3.1 Nanoparticle and Protein Characteristics ......................................................... 23
3.3.2 Lysozyme Adsorption ....................................................................................... 25
3.3.3 𝛽-Lactoglobulin Adsorption ............................................................................. 27
3.4 DISCUSSION ............................................................................................................ 29
3.5 CONCLUSION .......................................................................................................... 33
CHAPTER 4 EVOLUTION OF HETERO-AGGREGATE STRUCTURE AT DIFFERENT
PROTEIN LOADINGS ............................................................................................. 35
4.1 INTRODUCTION ....................................................................................................... 35
4.2 MATERIALS AND METHODS .................................................................................... 36
4.2.1 Materials ........................................................................................................... 36
vi
4.2.2 Protein Labeling ............................................................................................... 36
4.2.3 Adsorptions Measurements .............................................................................. 36
4.2.4 Fluorescence Correlation Spectroscopy ........................................................... 37
4.2.5 Confocal Laser Scanning Microscopy.............................................................. 37
4.3 RESULTS ................................................................................................................. 38
4.3.1 Adsorptions Comparison .................................................................................. 38
4.3.2 Fluorescence Correlation Spectroscopy ........................................................... 40
4.3.3 Confocal Laser Scanning Microscopy.............................................................. 41
4.4 DISCUSSION AND OUTLOOK.................................................................................... 43
4.4.1 Adsorptions Comparison .................................................................................. 43
4.4.2 Fluorescence Methods ...................................................................................... 44
CHAPTER 5 ORIENTATION OF CYTOCHROME C ADSORBED ON SILICA
PARTICLES............................................................................................................... 49
5.1 INTRODUCTION ....................................................................................................... 49
5.2 MATERIALS AND EXPERIMENTAL TECHNIQUES ...................................................... 50
5.3 THE ‘RASPBERRY–LIKE’ FORM FACTOR ................................................................. 51
5.4 CHARGE DISTRIBUTION ON CYTOCHROME C .......................................................... 56
5.5 DISCUSSION AND CONCLUSIONS ............................................................................. 58
5.6 APPENDIX ............................................................................................................... 60
5.6.1 Characterization of Silica Particles and Cytochrome c .................................... 60
5.6.2 Fitting of SANS Data with the RB-model ........................................................ 61
5.6.3 Adsorption Isotherms and Calculation of Expected Surface Coverage ............ 62
5.6.4 Instrumental Details SANS .............................................................................. 63
CHAPTER 6 PROTEIN IMMOBILIZATION IN SURFACE-FUNCTIONALIZED SBA-15:
PREDICTING THE UPTAKE CAPACITY FROM THE PORE STRUCTURE 65
6.1 INTRODUCTION ....................................................................................................... 65
6.2 PORE FILLING MODEL ............................................................................................. 66
6.3 RESULTS ................................................................................................................. 68
6.3.1 Functionalized SBA-15 Materials .................................................................... 68
6.3.2 Analysis of Porosity ......................................................................................... 70
6.3.3 Lysozyme Adsorption ....................................................................................... 73
6.3.4 Protein Immobilization Capacity of the Materials ........................................... 74
6.4 DISCUSSION ............................................................................................................ 77
6.4.1 Protein Uptake Capacity ................................................................................... 77
6.4.2 Influence of Surface Functionalization ............................................................ 78
6.5 CONCLUSION .......................................................................................................... 79
6.6 APPENDIX ............................................................................................................... 80
6.6.1 Preparation of Mesoporous Materials .............................................................. 80
vii
6.6.2 Sample Characterization Methods .................................................................... 81
6.6.3 Calculation of Matrix Porosity ......................................................................... 82
6.6.4 Normalized Pore Size Distribution Function ................................................... 85
6.6.5 Protein Adsorption Measurements ................................................................... 87
6.6.6 Adsorption Data and Langmuir Fits for Lysozyme in the OMS Materials ...... 88
6.6.7 Protein pore filling model ................................................................................ 89
CHAPTER 7 SECONDARY CONFINEMENT OF WATER OBSERVED IN EUTECTIC
MELTING OF AQUEOUS SALT SYSTEMS IN NANOPORES ........................ 93
7.1 INTRODUCTION ....................................................................................................... 93
7.2 RESULTS AND DISCUSSION ..................................................................................... 94
7.3 CONCLUSION .......................................................................................................... 99
7.4 APPENDIX ............................................................................................................. 100
7.4.1 Characterization of silica materials ................................................................ 100
7.4.2 Eutectic point of bulk systems........................................................................ 100
7.4.3 Systems Forming Salt Hydrates ..................................................................... 102
7.4.4 Volume fraction of Salt in Solid Eutectic Mixtures ....................................... 102
7.4.5 Information from DSC Cooling Scans ........................................................... 104
7.4.6 Information from in situ XRD ........................................................................ 107
7.4.7 Summarized DSC Pore Melting Results ........................................................ 109
CHAPTER 8 CONCLUSIONS AND OUTLOOK ....................................................................... 113
8.1 PROTEIN ADSORPTION ON SILICA NANOPARTICLES ON ABOVE AND BELOW THE
ISOELECTRIC POINT .............................................................................................. 113
8.2 HETERO-AGGREGATION OF SILICA NANOPARTICLES WITH A PROTEIN: OBSERVING
THE AGGREGATE STRUCTURE WITH FLUORESCENCE METHODS ........................... 114
8.3 ORIENTATION OF ADSORBED PROTEIN ON BULK PH CONDITIONS AS A
CONSEQUENCE OF THE DIPOLE ORIENTATION ...................................................... 116
8.4 PREDICTION OF PROTEIN ADSORPTION IN NATIVE AND CHEMICALLY MODIFIED
MESOPOROUS SILICA MATERIALS .......................................................................... 117
8.5 FREEZING/MELTING OF AQUEOUS SALT SYSTEMS IN SILICA MESOPORES ........... 119
REFERENCES ................................................................................................................................ 121
ABBREVIATIONS AND SYMBOLS ............................................................................................. 139
Protein Adsorption at Highly Curved Hydrophilic Surfaces
1
Chapter 1 Introduction
Adsorption and immobilization of proteins at solid surfaces play an important role in the
environment and in many fields of technology. While protein adsorption at flat surfaces has
been studied for many decades, the interaction with nanoparticles and immobilization in
nanoporous matrices represents a relatively new field of research. In this thesis I present the
results obtained during my Ph.D. research. The major topic is adsorption of proteins onto
nanostructured surfaces e.g. inorganic nanoparticles and porous materials. The first chapter
gives a brief introduction in the field of colloidal physics and establishes a general
understanding of the research field.
1.1 Protein Adsorption at Highly Curved Hydrophilic Surfaces
In the last two decades colloidal science grew into a technology with lots of applications in
various fields and disciplines. Today nanoscopic materials can be found in all parts of the
everyday life, reaching from quantum dots used in modern displays1 over silver nanoparticles
in antibacterial products and cleansers2,3 up to medical devices for targeted drug delivery.4,5 In
the near future, nanomaterials will be omnipresent in the human environment and therefore
exposed to the biological media containing salts, proteins and polymers. Adsorption of these
compounds on nanoparticles and nanostructured surfaces is a ubiquitous process and is
observed on hydrophobic as well as on hydrophilic surfaces. It is obvious that this has an
influence on both, the particles and the protein. Hence, the intended functionality of surfaces
can be affected. For this reasons a general and in-depth understanding of the interactions of
nanomaterials with biological matter and the resulting consequences is vital.
Maybe the most fundamental question in this field is for the nature and strength of the
interaction of proteins with the respective surface. At this point it is important to differentiate
between hydrophobic and hydrophilic surfaces. The main driving force for adsorption of
proteins on hydrophobic surfaces is of entropic nature. In the case of hydrophobic surfaces
immersed in aqueous solutions, water molecules form a structured network (hydrophobic
effect) in the close vicinity of the surface. During the process of adsorption these ordered water
molecules are liberated from the surface. The adsorption force caused by this entropic gain can
be big enough to even bypass electrostatic repulsion.6,7
In contrast to that the interactions between soft matter and hydrophilic surfaces are
dominated by electrostatic forces and adsorption is almost exclusively limited to situations
when protein and surface are oppositely charged.7 This holds for structurally stable and
inflexible (“hard”) proteins (e.g. lysozyme and cytochrome c). On the other hand “soft” proteins
2
Introduction
can deform easily as a consequence of lacking disulfide bonds and fewer hydrogen bonds. Such
instable proteins can lose their secondary structure to a certain extend upon adsorption. In this
case entropy contributes to the overall adsorption energy.
In order to quantitatively describe the protein adsorption on nanostructured surfaces
different isotherm models have been discussed. The most fundamental model is the Langmuir
isotherm developed by Irving Langmuir in the early 20th century.8 It assumes that all adsorption
sites are equivalent, only one monolayer is adsorbed and molecules adsorbed on neighboring
sites do not interact with each other. For many situations these assumptions are not valid as
proteins usually carry a net charge and adsorbed on neighboring sites the proteins will
experience a strong repulsive interaction. Alternatively, the Hill model was considered to
describe such materials better.9 This model was in its first form developed to describe the
dissociation curves of hemoglobin and assumes a cooperative adsorption behavior. In the case
of non-cooperative behavior this isotherm model reduces to the Langmuir model. This means
multilayer adsorption is not natively described by this model. In contrast to that, the GAB-
model (Guggenheim-Anderson-de Boer) accounts for multilayer adsorption and describes three
states for the adsorbate molecule.10,11 A first layer with direct contact to the substrate is strongly
bound. In every further layer the adsorbate molecules are equally strong bound but different
from the first layer and the bulk phase. The GAB-model was used for the evaluation of the
adsorption experiments presented in Chapter 3, where differently charged proteins (lysozyme
and 𝛽-lactoglobulin) were adsorbed to the anionic surface of silica particles.
A special case of nanostructured surfaces are nanopores, i.e. pore with a uniform
diameter in the nanometer range. Such pores are found in the ordered mesoporouse silicates
such as SBA-15 or MCM-41. These materials are often considered as suitable support materials
for immobilized enzymes in order to stabilize the proteins against polar solvents or heat12–14
and as carriers for targeted protein release.15–17 The microenvironment in these pores can be
specifically tailored for each application by adjusting the pore size and manipulating the surface
chemistry.18,19 By adequately choosing the parameters it is possible to enhance the stability and
enzymatic activity of an enzyme compared to the native, free protein.20–24 On the other hand, it
is also possible to avoid protein adsorption on surfaces by modifying the surface chemistry. It
is reported that zwitterionic and polyethylene glycol grafted surfaces are protein repellant.25
This effect can be utilized to protect exposed surfaces from biofouling. In Chapter 6 this thesis
the loading capacity of such porous materials was analyzed and described with a general pore
filling model, accounting for irregularities of the pore-size distribution.
Protein-Induced Aggregation of Silica Nanoparticles
3
1.2 Protein-Induced Aggregation of Silica Nanoparticles
The behavior of colloidal dispersions is often determined by the interplay of van der Waals and
electrostatic double layer forces, as described by the classical DLVO theory (after Derjaguin,
Landau, Verwey and Overbeek).26,27 Accordingly, in a stable colloidal dispersion the short range
van der Waals attraction is compensated by electrostatic repulsion between equally charged
particles. This interplay can be disturbed by changes in the solution composition. For example
an addition of salt (increase in ionic strength, IS) screens the repulsive electrostatic force which
in turn lowers the barrier for a close contact of the particles. In close proximity the attractive
van der Waals force dominates and causes a strong attraction between single particles,
ultimately causing aggregation. Despite its ability to describe the stability of colloidal
dispersions, the DLVO theory does not include all forces acting between colloidal particles.
These non-DLVO forces, such as steric interactions, hydration forces, hydrophobic interactions
and depletion forces,28 can also define the state of a system containing proteins and silica
particles.29,30
In order to discuss systems containing proteins and nanoparticles it is important to
briefly look at the surface charge of proteins. Proteins are polyelectrolytes with different
cationic or anionic groups, each with a different dissociation constant. Depending on the
solution pH these groups are either charged (positively or negatively) or uncharged and thus
the net charge of the entire protein varies with pH. At a protein-specific pH the number of
positive and negative charges are equal leading to a situation where the protein is
electrostatically neutral although it still carries local charges. This point is called isoelectric
point (IEP). Below this pH value the protein is positively charged, at pH exceeding the IEP the
protein is negatively charged.
When added to a dispersion of charged particles, an oppositely charged protein will
readily adsorb at the particle surface as a consequence of electrostatic attraction. In this case
the adsorption of proteins can cause a destabilization of the colloidal dispersion. This behavior
is explained with bridging aggregation of the particles by the protein (see Chapter 3 and 4), i.e.
simultaneous binding of a protein molecule to two particles, leading to large-scale aggregates
and flocculation of the system. Often even visible to the bare eye, as the stable dispersion
immediately turns turbid upon protein addition.
In our earlier work we reported a study of bridging aggregation of silica nanoparticles
by lysozyme.31,32 Protein adsorption was found between the IEP of silica and lysozyme and the
adsorption capacity increased towards the IEP of lysozyme as the electrostatic repulsion
between individual adsorbed molecules decreases. In the same pH interval the increased
turbidity indicated strong aggregation between the particles. Zeta potential measurements
showed qualitatively a behavior which is expected for particles with a certain number of
adsorbed proteins.
4
Introduction
The aggregate structure was further investigated by a detailed analysis with small-angle
x-ray scattering (SAXS) under different pH and salinity conditions.31 The structure factor of
the SAXS intensity profiles was modeled with a short-range square-well pair potential.32 The
analysis showed a pronounced influence of pH on the aggregate structure. At low pH (pH < 6)
the aggregates were small and dense and the structure was not affected by changes in the ionic
strength of the surrounding solution. With increasing pH the aggregate structure opened up to
a looser network of large, branched aggregates. At pH values beyond pH 9 a distinct salt effect
was found. Without additional salt the aggregate structure remained open and loose up to the
maximum pH of the study. In this pH regime the addition of salt led to an increased attractive
force between the particles as the electrostatic repulsion is shielded by the high IS.
As the structural studies of the protein-silica aggregates had been performed only for
fixed protein to silica ratios, it was of interest to specifically investigate the evolution of
aggregate sizes as the number ratio of protein to silica particles was changed. Such a study was
now performed with the help of fluorescence techniques. In Chapter 4 a study using a
combination of fluorescence laser scanning microscopy (CLSM) and fluorescence correlation
spectroscopy (FCS) is shown. In this work the early stages of the aggregation process (i.e. low
protein to silica ratios) were investigated with FCS whereas later stages (i.e. high protein to
silica ratios) were studied with CLSM. With this combination of techniques it was possible to
observe the structural evolution of hetero-aggregates over several decades of protein to silica
ratios and visualize the large-scale structures by direct optical methods.
1.3 Orientation of Adsorbed Protein Molecules
For the development of useful industrial application of enzyme/nanoparticle systems details of
the adsorption of protein molecules, including adsorption-induced changes of tertiary and
secondary structure, and the orientation of the molecule relative to the surface need to be
understood, as the stability and function crucially depend on these parameters.33
One useful method to probe the internal structure of a protein either in solution or
adsorbed on nanoparticles is circular dichroism spectroscopy (CD spectroscopy). With this
technique the content of ordered sequences in the protein is analyzed by measuring the
absorption of circular polarized UV-light. Differences in the secondary structure between native
and adsorbed protein can be traced back to different content of alpha-helices, beta-sheets and
coiled segments of the peptide backbone. Many of these studies found a significant change in
the secondary structure34–36 for a variety of protein-particle combinations. Other studies show
a contrary picture and report only minor changes in the secondary structure of the protein.37 For
example human serum albumin is structurally influenced when contacted to silver particles but
is not affected by gold particles.38 Comparing the structure of different proteins adsorbed on the
Freezing/Melting of Concentrated Salt Solutions in Nanopores
5
same particles revealed that “soft” proteins (BSA, hemoglobin) are more susceptible to
perturbation than “hard” proteins (cytochrome c, RNase).39 Solely differences in the size of
particles with otherwise identical composition are known to cause a completely different
behavior of adsorbed proteins.40,41 Remarkably, studies imply that the protein structure and
activity is best maintained when it is adsorbed on smaller particles. This behavior is explained
with a smaller contact patch and a lower electrostatic potential for smaller particles.40 This lead
to less perturbation of the protein conformation by electrostatic influences as seen in CD
spectroscopy.41 This multitude of scientific results show a picture where the conformational
integrity of a protein is vastly depending on individual properties of the protein:nanoparticle
system.
The spatial orientation of individual proteins is difficult to analyze. Indirect methods
have been used to probe the orientation of adsorbed protein molecules, including studies with
fluorescence markers42 and molecular simulations.43 In the latter case explicit-solvent
molecular dynamics simulations were used to predict the adsorption orientation of
chymotrypsin and lysozyme on amorphous silica from DLVO forces. Based on the main
assumption that the adsorption on charged hydrophilic surfaces is dominated by electrostatic
forces the electrical dipole moment was found to dominate the adsorption orientation. The
protein orients in such a way that its electrical dipole moment is aligned perpendicular to the
silica surface with the positive pole pointing towards the negatively charged surface. Results
were most clear for chymotrypsin which has a significantly larger dipole moment.
In this thesis neutron small-angle scattering (SANS) was used as an alternative method
for probing the orientation of adsorbed protein molecules. Cytochrome c was used as a model
protein for structurally “hard” proteins with a large electric dipole moment. It was adsorbed
onto silica particles and the pH was changed to understand the spatial response to a change in
the dipole moment orientation. The scattering data is analyzed with a recently developed form
factor model44 and the results are compared with simulations of the spatial orientation of the
protein dipole moment vector. The results are presented in Chapter 5.
1.4 Freezing/Melting of Concentrated Salt Solutions in Nanopores
As discussed in Section 1.1, the adsorption of proteins at solid surfaces is strongly affected by
the ionic strength, as the electrostatic interactions are screened by added salt. Salt-specific
effects may also be important, as small ions of the electrolyte may compete in different ways
for adsorption sites at the surface.45,46 In order to study the relevance of such ion-specific
effects, a comparative study of properties of concentrated electrolyte solutions in the pores of
SBA-15 was performed.
6
Introduction
As a sensitive way to monitor salt-specific or ion-specific effects, the melting behavior
of the salt solutions in SBA-15 was investigated. Within the strong confinement of silica pores
smaller than 10 nm the melting of water is observed at temperatures more the 50 K below the
bulk melting point.47 This implies that in narrow pores liquid water is stable down to
temperatures below the homogeneous nucleation temperature of bulk ice (ca. 235 K). On
hydrophilic surfaces a layer of a non-freezable water is located directly at the surface. In small
pores the volume fraction of this layer becomes substantial and affects the properties of the total
pore water to a significant extent.
This weathering of buildings stones and historical monuments is of great economic and
cultural importance. This manifests in the amount of work which has been done on the field of
pore crystallization induced deterioration of natural stone and concrete.48–50 From this research,
it is known that different salt solutions cause vastly different damage pattern to limestone with
moderately large pores (> 30 nm).51 Furthermore, the uptake of salts into the pores of stones
increases the damage induced by halotolerant microbial populations found in aged walls.52
Regarding the processes of weathering damage, the research has been focused on understanding
the mechanisms on the micron-sized pores of natural stone.
For this reason Chapter 7 of this thesis presents a comparative study of the depression
of the eutectic temperature of a series of alkali halides in nanometer-sized pores of SBA-15 and
MCM-41 silica. Large shifts of the eutectic temperature were found for salt solutions
crystallizing in oligohydrates. Those bulky crystallites require a significant larger fraction of
the pore volume and therefore, act as an additional or secondary confinement for the water ice.
The results were evaluated as a function of the volume fraction of solid salt crystals in the frozen
solution and modeled using a modified Gibbs-Thomson equation.
Fluorescence Microscopy
7
Chapter 2 Methods and Models
This chapter gives a more in depth overview about four important characterization techniques
used in this work. Other experimental methods were used as routine experiments. A complete
overview about all used methods and synthesis including the precise instrumentation and
references can be found in the respective chapter.
2.1 Fluorescence Microscopy
In order to study the global structure of lysozyme-silica hetero-aggregates a combination of two
complementary techniques has been used. The overall macroscopic aggregate structure of the
flocculates has been studied using confocal laser scanning microscopy (CLSM). With this
technique aggregate sizes from 200 nanometre to a few hundred micrometre are assessable.
Properties of smaller structures where probed using fluorescence correlation spectroscopy
(FCS). With this combination of experiments makes it possible to study the exact same systems
over length scales of 4 orders of magnitude.
2.1.1 Confocal Laser Scanning Microscopy
Confocal laser scanning microscopy (CLSM) is a technique readily applied to visualize small
specimen and is often used in the medical field but also other scientific divisions benefit from
its capabilities. The fundamental base for this technique was pioneered by Marvin Minsky in
1957 with the US patent 3013467,53 where he reported the principle working mechanism for a
confocal microscope. Figure 2.1 shows the beam path of a confocal microscope setup with all
important components.53,54 In this concept the use of a pinhole limits the light entering the
detector to one specific focal plane in the sample providing a superior resolution in the z-
direction (parallel to the beam path). Therefore the confocal microscope reduces the field of
view to a small spot in the sample and the use of a movable sample stage gives the opportunity
to scan through the sample in all three spatial dimensions. This specific setup provide many
advantages over normal light microscopes. Just to name a few:
Increased signal-to-noise ratio
Reduced blurring of the image
Higher effective resolution
Images of “unusually thick and highly-scattered specimens”53
xyz-scanning trough the sample
8
Methods and Models
With the wider availability of laser systems the first confocal laser scanning microscope was
developed by Davidovits and Eggers and the first images of cells were published in 1971.55 In
1983 Åslund and co-workers constructed the first CLSM, where a stack of pictures where taken
and later visualized in 3D.56
In the following decades the popularity of this technique grew and ultimately it evolved
to a standard in biomedical research and related fields. Its latest improvement was pioneered
by Hell and Wichmann, who developed the idea for a microscope, which is capable of a
resolution below the diffraction limit.57,58 Such an STED-microscope (stimulated emission
depletion) has a resolution far below the diffraction limit up to a molecular level.59 The
resolutions of a conventional fluorescence CLSM is defined as:60
𝑟lateral=0.4𝜆
𝑁𝐴 and 𝑟axial=1.4𝜆𝑛
𝑁𝐴2
(2.1)
Where 𝜆 the wavelength, 𝑛 is the refractive index and NA is the numerical aperture of the used
objective. For typical conditions (as used for experiments presented in Chapter 4) it gives a
lateral resolution of 163 nm.
Figure 2.1: (a): Principle beam path of a confocal microscope working in the epi-illuminating mode (one lens is
used simultaneously as objective and condenser lens). With the sample S, the objective O2, a dichromatic mirror
M, the pin hole B, the detector D, the objective O1 and the light source (laser) L. (b): Beam path for a FCS
experiment with the light source (laser) L, the sample S, dichromatic mirrors M1 and M2, a filter F and 2 detectors
D1 and D2. In the sample the specimen x diffuses through the confocal volume C and emits a fluorescent signal.
Fluorescence Microscopy
9
In the here reported experiments a Leica TSC SP5 II equipped with an HCX PL APO
CS 63.0 × 1.20 water UV immersion objective was used to collect stacks of images with
different focal planes. The total confocal volume was 123×123×123 µm3 with a voxel
resolution of 0.5×0.5×0.5 µm3. Detailed experimental parameters and information about the
data treatment are given in Chapter 4.
2.1.2 Fluorescence Correlation Spectroscopy
FCS measures the fluctuation of a fluorescence signal from a small volume of the sample as a
function of time. This technique uses a confocal microscope (see Section 2.1.1) and its
opportunity to imaging a very small volume. The first application published in literature dates
from 1972, where Magde et al. reported a data for the binding of ethidium bromide to DNA.61
The principle beam path of a FCS experiment is given in Figure 2.1b.
The fluorescence correlation spectroscopy (FCS) was used to assess objects which were
too small for imaging with the afore mentioned CLSM. With this combination it was possible
to keep the experimental parameter largely unchanged and also to gain information about
different stages of the aggregation process for a broad range of length scales.
In a FCS experiment the size is not measured directly but derived indirectly via the
diffusions kinetic of the individual components in the observation volume. Stokes-Einstein
equation (Eq. 2.2) was used to calculate the hydrodynamic radius 𝑅ℎ from the diffusion
coefficient 𝐷f.
𝑅h=𝑘𝐵𝑇
6𝜋𝜂𝐷f
(2.2)
Where 𝑘𝐵 is the Boltzmann constant, 𝑇 the temperature and 𝜂 the viscosity of the surrounding
solution. All parameters are known or kept constant within an experiment except the diffusion
constant. In order to obtain the diffusion constant from the time resolved fluorescent signal the
autocorrelation function 𝐺(𝜏) needs to be derived with Equation 2.3.62
𝐺(𝜏)=〈𝛿𝐼(𝑡)∙𝛿𝐼(𝑡+𝜏)〉
〈𝐼(𝑡)〉2
(2.3)
𝐼(𝑡) is the fluorescence intensity at the time t, 𝛿𝐼(𝑡) and 𝛿𝐼(𝑡+𝜏) are the intensity fluctuations
at the time 𝑡 or 𝑡+𝜏 around 𝐼(𝑡),𝜏 is the lag time and 〈𝐼(𝑡)〉 is the time averaged intensity,
equivalent to:
10
Methods and Models
〈𝐼(𝑡)〉= (1𝑡
⁄)∫𝐼(𝑡)
d
𝑡
𝑡
0
(2.4)
The characteristic lag times for each diffusing component were extracted from the experimental
autocorrelation function 𝐺(𝜏) using a fitting function derived for a free diffusing object in a 3d-
Gaussian profile.63
𝐺(𝜏)=∑𝜌𝑖(1+𝜏
𝜏D,𝑖)−1(1+ 𝜏
𝜉2∙𝜏D,𝑖)−12
⁄
𝑖
mit
𝜌𝑖=𝑄𝑖2∙𝑁𝑖
(∑𝑄𝑗∙𝑁𝑗𝑗 )2
(2.5)
With 𝜏D,𝑖 beeing the characteristic lag time of the component 𝑖 and 𝜉 the aspect ratio of the
Gaussian profile (𝑉𝐺=𝜋32
⁄∙𝑤03∙𝜉). With the help of the weighting parameter 𝜌𝑖 and the
quantum yield 𝑄𝑖 it is possible to calculate the number ratio of each component 𝑖. Assuming an
equal quantum yield for all components leads to:
〈𝑁〉=1
∑𝜌𝑖𝑖
(2.6)
In many cases the experimental autocorrelation function shows a significant intensity signal at
small lag times, usually related to fast transitions from a triplet state. To account for this process
an additional factor was introduced.
𝐺(𝜏)=1−𝛩+𝛩∙𝑒−𝜏𝜏𝛩
⁄
1−𝛩 ∑𝜌𝑖(1+ 𝜏
𝜏D,𝑖)−1(1+ 𝜏
𝜉2∙𝜏D,𝑖)−12
⁄
𝑖
(2.7)
Here 𝛩 is the proportion of fluorophores in a triplet state and 𝜏𝛩 the respective lag time. Finally,
the arising lag times can be converted to the diffusion constants via Equation 2.8.
𝜏D,𝑖=𝑤02
4𝐷f
(2.8)
2.2 Small Angle Neutron Scattering
Some of the most valuable tools to study the shape and interaction at the nanoscale are scattering
methods. Modern colloidal and surface science is vitally dependent on those experimental
techniques to determine particle size, dispersion stability or particle mobility. Especially, small
angle X-ray scattering (SAXS) has proven to be a capable tool to characterize the interactions
between the particles in the presence of proteins.29,31
Small Angle Neutron Scattering
11
One of the model system treated in this theses, silica and lysozyme, was examined using
X-ray scattering in great detail. In particular, the pH modulated interaction of the protein silica
particle aggregates was deduced to a sticky hard sphere potential.31 In the following work this
finding was further specified to a range of salinities.32 Combining these results with data from
other methods Bharti et al. was able to identify specific interaction stages of the silica particles
with attached lysozyme, depending on the external conditions. These findings could be
generalized to cytochrome c, another hard protein with a similar isoelectric point than
lysozyme.64
These results were made possible by the fact that the silica particles and the surrounding
medium have a large difference in the electron density. This ensures a strong X-ray scattering
signal which can be easily detected with modern laboratory equipment. As the protein shows
only a small contrast difference, the resulting intensity curve originate nearly entirely form the
particles in the system. This circumstance almost intrinsically neglects the information about
the state of the used protein. That the information about the protein adsorbed on the particles
are anything but negligible has been shown by several studies. Vertegel et al. presented circular
dichroism (CD) spectroscopy results of adsorbed lysozyme indicating a particle size sensitive
nature of the protein adsorption. A similar effect on the conformational structure of human
carbonic anhydrase was published in the same year by Lundqvist et al. (for details see
Section 1.1).40,41
2.2.1 Technical Background
Small angle neutron scattering (SANS) was used to expand the capabilities of scattering
experiments so the information about both, the particles and the protein, can be retained. In
contrast to X-rays neutrons are scattered by the nuclei. This gives rise to entirely different
contrast scenarios compared to SAXS. A system consisting of cytochrome c adsorbed on silica
particles in deuterium oxide (D2O) was chosen. Cytochrome c and silica show a very similar
difference in the scattering length density (SLD) from D2O towards neutrons. This ensures that
the resulting scattering signal arises from the complete ensemble of silica particle and adsorbed
protein.
In a neutron scattering experiment the sample is irradiated by a beam of neutrons
(Fig. 2.2 a). These neutrons are produced in research neutron sources, typically an atomic
reactor or a spallation source. These sources produce free neutrons with a distribution of wave
length and propagation directions. For a successful SANS experiment it is a prerequisite to
know these two parameters. To select one wavelength from the spectrum a velocity selector is
used. This form of monochromator made use of the particle character of neutron matter waves
and let only pass neutrons of a certain velocity. Collimation of the beam is typically ensured by
12
Methods and Models
a set of slits placed at variable distances depending on the necessary beam quality. The
collimated and monochromatic neutron beam is then scattered at the sample. After that, the
scattered beam is passing through an evacuated chamber towards the neutron detector. As
neutrons do not readily interact with matter it takes special materials to efficiently detect the
neutron flux. Often 3He or BF3 proportional detectors are used. The detector can be placed at
variable distances to increase the accessible angular range. When the detector is placed close to
the sample, it is possible to measure larger angels and long distances between the sample and
detector allow very small angles.
In scattering experiments it is useful to represent the scattering intensity curves as a
function of the scattering vector q. The scattering vector q is dependent on the wavelength λ of
the incident beam and the scattering angle 𝜃. Equation 2.9 gives the mathematical expression
of relation of these three measures.
𝑞=4∙𝜋∙sin𝜃
𝜆
(2.9)
Considering an elastic scattering process, without energy transfer during that scattering event,
the scattering vector can be described as the difference between the incoming wave vector 𝑘𝑖
and the scattered wave vector 𝑘𝑓
(Eq. 2.10). This relation is depicted as a scheme in Figure 2.2b.
𝑞 =𝑘𝑓
−𝑘𝑖
(2.10)
A scattering intensity curve 𝐼(𝑞) contains information about the size and shape of the scatterer
(form factor) as well as about the interactions between the individual scatterers (structure
factor). These properties can be extracted from the data by fitting with an appropriate analytical
Figure 2.2: (a): Schematic view of a SANS setup. The incident beam (IB) of neutrons is generated in the neutron
source (NS) and passed through a monochromator (M) to select the desired wavelength. Followed by a number of
collimation slits (C) and the sample (S). The intensity of the scattered beam (SB) is measured with the detector
(D). (b): Schematic view of the geometry of an elastic scattering event. The wave vector of the incoming neutron
𝑘𝑖
and of the (at an angle 𝜃) scattered neutron 𝑘𝑓
sum up to the scattering vector 𝑞 according to Equation 2.10.
𝑞
→
Small Angle Neutron Scattering
13
model or comparing with numerical simulations. In the presented case of cytochrome c
adsorbed on silica beads a ‘raspberry-type’ model was used to fit the intensity profile. Further
details on this very model are given in Section 2.2.2 and the data analysis and the detailed
results are presented in Chapter 5.
2.2.2 Raspberry Form Factor Model
The scattering intensity 𝐼(𝑞) can be described as a product of different factors by the following
equation (Eq. 2.11)
𝐼(𝑞)=𝜑∙∆𝜌2∙𝑉∙𝑃(𝑞)∙𝑆(𝑞)
(2.11)
Where 𝜑 is the volume fraction of the scattering entities, 𝑉 is the volume of the single scatterer,
∆𝜌 is the scattering length density (SLD) difference of the scatterer and the surrounding
medium, 𝑃(𝑞) is the form factor and 𝑆(𝑞) is the structure factor. The difference of the scattering
length density ∆𝜌 is often called the scattering contrast and can be calculated with the following
equation.
𝜌=∑𝑏𝑖𝛿𝑁A
𝑚
𝑖=𝑁∑𝑏𝑖
𝑖
(2.12)
Where 𝛿 is the bulk density of the material, 𝑚 is the relative molar mass, 𝑁 is the number
density of the scatterers and 𝑏𝑖 is the scattering length of the nucleus 𝑖.
The structure factor 𝑆(𝑞) in Equation 2.11 describes the global arrangement of the
scattering particles in the sample and mathematically relates to the Fourier transform of the pair
correlation function. Therefore, an analysis of the structure factor can be used to investigate the
interaction and the structure formation inside the dispersion. This has been done in great detail
in earlier works31,32 and is briefly summarized in the introduction.
The form factor 𝑃(𝑞) in Equation 2.11 contains information about the individual
scattering particle. Generally, the form factor is the Fourier transform of the pair distribution
function. For the analysis in Chapter 5 a specific form factor was used to account for the special
‘raspberry-like’ shape of the cytochrome c/silica composite. This model was developed by
Kjersta Larson-Smith, Andrew Jackson and Danilo C. Pozzo to describe the scattering signal
from Pickering emulsions.44 Starting from the work of Pederson65 for the scattering signal from
polymer micelles they evolved the model to account for differently sized small particles placed
at the interface of an bigger spherical particle. This complex particle shape is sketched in
Figure 2.3. The derived equation for ‘raspberry-like’ particles is given in Equation 2.13.
14
Methods and Models
𝐼(𝑞)=(𝜙s𝑉s∆𝜌s2+𝜙p2𝜙pa2𝑉s
𝜙s∆𝜌p2)Pps(𝑞)+(𝜙p(1−𝜙p𝑎)𝑉p∆𝜌p2)Ψp2(𝑞)
(2.13)
Where 𝜙p and 𝜙s are the total volume fractions of smaller and bigger central particle
respectively, 𝜙pa is the fraction of small particles bound to the surface of the bigger particle, 𝑉p
and 𝑉s are the volumes of the particles, ∆𝜌p, and ∆𝜌s are the scattering length density contrasts
of the particles and 𝛹p2(𝑞) is the form factor of the smaller particles. Pps(𝑞) is the form factor
of the entire ‘raspberry-like’ particle (Eq. 2.14).
Pps(𝑞)= 1
M2[(𝛥𝜌s)2𝑉s2Ψs2+𝑁p(∆𝜌p)2𝑉p2𝛹p2+𝑁p(𝑁p−1)(∆𝜌p)2𝑉p2Spp
+2𝑁p∆𝜌s∆𝜌p𝑉s𝑉p𝑆ps]
(2.14)
with
M=∆𝜌s𝑉s+𝑁p∆𝜌p𝑉p
Where 𝑁p is the average number of small particles at the surface of the large particle, M is a
prefactor taking into account the total scattering length density of the complete ‘raspberry-like’
composite, Sps and Spp are the large-small and small-small particle correlation terms (Eq. 2.15
and 2.16).
Figure 2.3: Schematic visualization of a ‘raspberry-like’ particle composite with a central large particle and several
smaller particles attached to its surface. The central particle has the diameter 𝐷s and the smaller particles have the
diameter 𝐷p.
Protein Dipole Moment
15
Sps=ΨsΨpsin(𝑞(𝑅s+𝛿𝑅p))
𝑞(𝑅s+𝛿𝑅p)
(2.15)
Spp=Ψ𝑝2[sin(𝑞(𝑅s+𝛿𝑅p))
𝑞(𝑅s+𝛿𝑅p)]2
(2.16)
Ψs=3[sin(𝑞𝑅s)−𝑞𝑅scos(𝑞𝑅s)]
(𝑞𝑅s)2
(2.17)
𝛹p=3[sin(𝑞𝑅p)−𝑞𝑅pcos(𝑞𝑅p)]
(𝑞𝑅p)2
(2.18)
Were 𝑅s and 𝑅p are the radii of the central larger particle and the smaller particles sitting at its
surface. The factor 𝛿 relates to the fraction of 𝑅p being outside of the central particle. This is
important for Pickering emulsions, where the small particles immersed in the central droplet to
some extent. In the presented case of proteins adsorbing at solid silica particles this does not
apply and the factor 𝛿 was kept at the value 1, as the protein cannot penetrate the central silica
particle.
This form factor also accounts for free smaller particles in the dispersion and not
attached in the interface of the bigger sphere. It need to be mentioned that the smaller particles
are treated as monodisperse particles. However, the polydispersity of the bigger particle can be
analyzed.
2.3 Protein Dipole Moment
The main backbone of a protein is a polymer consisting of single 𝛼-amino acids bound together
by a condensation reaction forming a peptide bond. Every amino acid carries a residue at the
𝛼-carbon atom which can range from a simple hydrogen atom (glycine) to more complex side
chains like an imidazole group (histidine). Some of the amino acids found in proteins carry
ionizable side chains like carboxy acids (aspartic acid) or amino groups (lysine). Depending on
the pH these groups are in a specific protonation state and thus differently charged. This leads
to different net charges of the protein and to a different charge distribution on its surface. As a
16
Methods and Models
consequence of this asymmetric electric charge distribution proteins possess an electric dipole
moment. The dipole moment vector 𝜇 is defined according to Equation 2.14 as the vector sum
of all charges 𝑞𝑖 at the distance 𝑟𝑖 from a constant reference point 𝑟r. Typically the center of
mass is chosen as reference point and the resulting vector is pointing from the negative towards
the positive charge.
𝜇 =∑𝑞𝑖(𝑟 𝑖−𝑟 r)
𝑖
(2.19)
In the case of protein molecules this is not straight forward as several charges and hundreds of
atoms need to be considered. A combination of different software packages were used in order
to calculate the electric dipole moment vector for cytochrome c. This section gives a summary
of the process needed to calculate the dipole moment vector and the final results are shown in
Chapter 5.
The foundation of the calculation are the protein structure and the precise atomic
positions of cytochrome c. For all calculations the solution structure 2GIW from reduced horse
heart cytochrome c was used as provided by the RCSB protein data bank (PDB).66 This structure
includes the main protein backbone for cytochrome c as well as the heme c group.
In order to assign the correct charges for a series of solution pH the software PDB2PQR
was used.67,68 This package assigns the titration state of each ionizable group in the structure
for a chosen pH value. The pKa values were predicted by PROPKA69,70 on the basis of the
proteins 3-dimensional structure. This step is crucial as the pKa value of a side chain in close
vicinity to other groups can vary significantly.71,72 At the end of this process a single .pqr file
was generated containing both the atomic positions and the correct protonation state of each
functional group.
The electric dipole moment at the given pH is calculated with a python code written by
Miguel Ortiz-Lombardia.73 This code calculates the magnitude and the direction of the dipole
moment vector from the position of each charge relative to the center of mass. Results were
visualized with the program UCSF Chimera.74
In a final step the electrostatic potential on the surface of the protein was visualized
using the Adaptive Poisson-Boltzmann Solver (APBS) plugin for UCSF Chimera. APBS is a
software designed to solve the equations of continuum electrostatics for large molecules such
as proteins.75 The full documentation of the software can be found online.76
Differential Scanning Calorimetry
17
2.4 Differential Scanning Calorimetry
As explained in Section 1.4 the phase behavior of binary mixtures was investigated as part of
this thesis (results are presented in Chapter 7). One of the best tools do experimentally
determine the phase transition temperatures inside narrow pores is differential scanning
calorimetry (DSC). This technique has been used in the past to study the phase behavior of pure
liquids in silica pores of different size.
In a DSC experiment the difference in heat flow between a sample and a reference is
measured while both are heated to the same temperature. The principle setup scheme is shown
in Figure 2.4. The experimental setup consist of two identical heatable sample chambers which
are placed in thermal contact to a liquid nitrogen cooled heat sink. Both sample chambers are
heated to a programmed temperature higher than the temperature of the heat sink. The power
needed to maintain/increase the sample temperature is measured for each sample cell.
Difference in heat flow between sample and reference cell are detected as a function of the
sample temperature and provide the information about phase transitions in the sample. This
type of DCS technique is also known as power-compensated DSC.77
For one typical experiment approximately 50 mg of mesoporous silica material were
contacted with 100 µL of an aqueous solution of the desired salt and placed in a sealed
aluminum sample container. During the measurement it is crucial that the scan speed is chosen
correctly. A DSC experiment provides the best signal to noise ratio at high scan speeds but very
Figure 2.4: Schematic drawing of a power-compensated DSC. Two identical furnaces (Reference and Sample)
with individual heating (H1 and H2) and temperature sensors (T1 and T2) are placed in an insulated chamber and
cooled (in the present case with liquid nitrogen). The temperature of each furnace cell is controlled by a computer-
aided data-acquisition and controlling unit. The power difference between reference and sample is measured and
converted into the heat flow.
18
Methods and Models
high scan speeds are prone to a smearing of the signals. Most experiments were conducted with
a temperature scan speed of 0.5 K min-1. This value was experimentally determined in earlier
studies in the group of Prof. Findenegg.78 For a few samples a variety of scan speeds (0.5, 1,
3 K min-1) were used in order to combine both, good temperature resolution and sensitivity.
Introduction
19
Chapter 3 Characterization of Protein Adsorption onto Silica
Nanoparticles: Influence of pH and Ionic Strength
1
3.1 Introduction
Globular proteins are strongly adsorbed to hydrophobic as well as hydrophilic interfaces due to
the patchwise hydrophobic/hydrophilic character of their surface. The 'multipolar' nature of
proteins – as distinct from 'bipolar' surfactants – leads to specific phenomena in the adsorption
onto nanoparticles and emulsion droplets;79 whereas surfactants cause a stabilization of
dispersions and emulsions, adsorption of proteins makes the particles/droplets 'sticky', when
attractive patches exist on opposite sides of the protein molecule. In such cases, the adsorption
of the protein can cause bridging aggregation and flocculation of the particles.31,32,79,80 This
chapter presents a study of protein adsorption onto silica nanoparticles under the influence of
this protein-induced flocculation.
The interaction of proteins with nanoparticles (NPs) plays an important role in
biotechnology and biomedical applications. In a biological environment, the NPs are exposed
to a variety of proteins which may or may not be adsorbed to the particle surface, depending on
the strength of protein-particle interaction.81 In the past decade, many aspects of protein
interaction with NPs have been investigated.82 It has been found that the strength of protein –
surface interaction and the secondary structure of adsorbed proteins is affected by the NP
size40,41,83,84 and the hydrophilic or hydrophobic nature of the NPs.84–87 Electrostatic interactions
play an important role in the adsorption of proteins at hydrophilic/charged surfaces. It is thought
that conformationally stable ('hard') proteins are adsorbed at charged surfaces only under
electrostatically attractive conditions.6 Specifically, at a negatively charged surface, only
proteins with a net positive charge should be adsorbed, i.e., proteins having an isoelectric point
IEP higher than the pH of the solution. However, recent studies of protein adsorption into
polyelectrolyte brushes have shown that a protein can be strongly adsorbed into a brush having
the same charge as the protein, i.e., adsorption takes place at the 'wrong side' of its isoelectric
point.88–90 It was proposed that this is a consequence of the 'patchy' charge distribution on the
protein surface, which implies that a protein of net negative charge can still have patches of
positive charge. When a protein near the surface is oriented such that a positive patch points
toward the negatively charged surface, an attractive interaction of entropic origin can arise as a
result of the release of counter-ions.88,91 In fact, it has long been recognized that the binding
1
Reproduced with permission from J. Meissner, A. Prause, B. Bharti, G. H. Findenegg, Colloid Polym
Sci 2015, 293, 3381. Published open access under the Creative Commons Attribution 4.0 International license
(https://creativecommons.org/licenses/by/4.0/).
http://dx.doi.org/10.1007/s00396-015-3754-x
20
Characterization of Protein Adsorption onto Silica Nanoparticles: Influence of pH and Ionic Strength
strength of a protein is determined by a small number of charged groups located in the contact
region on the surface of the protein.92 An alternative explanation for protein adsorption at the
wrong side of the isoelectric point is based on the charge regulation effect. Since the ionizable
groups on the protein represent weak acids and bases, their charge is dependent on pH, and
thus, their degree of dissociation will be influenced by the local electrostatic field near the
surface. Next to a negatively charged surface, the pH is lower and the protein charge more
positive than in the bulk solution.93,94
The role of electrostatic interactions in protein adsorption onto silica and metal oxide
surfaces has been considered in many studies.95–98 Commonly, it is found that the adsorbed
amount as a function of pH reaches a maximum near IEP of the protein.95,97 Since the net charge
is zero at IEP, the electrostatic repulsion between adsorbed protein molecules is at a minimum,
and thus, the molecules can attain a closer packing at the surface than when carrying a net
charge. Van der Veen et al.97 performed a comparative adsorption study of two proteins of
different IEP at a macroscopic silica surface. It was found that added electrolyte affects the
protein adsorption at the two sides of IEP in opposite ways, which indicates the importance of
electrostatic protein – protein and protein – surface interactions. Here, we present a similar
comparative study for the adsorption of proteins at silica nanoparticles (SiNP). In this case, the
adsorption behavior may also be affected by the surface curvature and the protein-induced
aggregation of the particles, which in turn is also dependent on pH and ionic strength.31,32
Protein adsorption onto SiNP can be determined either by measuring the depletion of the
solution after equilibration with the SiNP, or indirectly from the increase in size of the SiNP
due to the formation of a protein layer. The latter method avoids errors in the measurement of
protein concentration, but it is indirect, as it relies on a suitable adsorption isotherm equation.9
A variety of isotherm equations for protein adsorption have been discussed in the literature,
from classical ligand-binding models developed in biochemistry99,100 to models derived from
modern statistical mechanics.101 Most of the models assume that adsorption is limited to some
maximum level, usually a monolayer of protein molecules. Although this will be a reasonable
assumption in many circumstances, weaker adsorption beyond a monolayer has also been
reported, particularly in a pH range close to the isoelectric point of the protein.31
Lysozyme (Lyz) and 𝛽-lactoglobulin (𝛽-Lg) were chosen for this comparative
adsorption study. The two proteins have similar size and molar mass but a widely different
isoelectric point. Important characteristics of the two proteins are given in Table 3.1. Lyz is a
conformationally stable (“hard”) protein due to 4 intramolecular disulfide bonds, and no
significant association of the protein occurs at concentrations relevant in the present context.
𝛽-Lg has only two intramolecular disulfide bonds and is less stable than Lyz toward partial
unfolding. It represents a mixture of two generic variants (A and B) differing only in two
positions along the chain.102 Depending on pH, temperature, ionic strength, and concentration,
𝛽-Lg is present in different oligomeric forms.103 It was of interest to find out how these
Materials and Methods
21
differences in surface charge distribution and aggregation behavior affect the adsorption of the
two proteins at SiNP.
3.2 Materials and Methods
3.2.1 Materials
Ludox TMA colloidal silica (Sigma-Aldrich) was used as the adsorbent in this study. The Ludox
dispersion was dialyzed for 5 days against DI water (water changed 3 times per day) to remove
remaining salt. Its mean particle diameter 𝐷S was 21 nm (determined by dynamic light
scattering). Its specific surface area 𝑎S was 128 m2/g (value from the manufacturer), in
agreement with the geometric surface area derived from the particle diameter, 𝑎geom=
6𝜌S𝐷=130m2g
⁄⁄ , based on a mass density of silica 𝜌S=2.20gcm3
⁄. The value of
𝑎S𝑎geom=1.02
⁄ indicates a low surface roughness of the particles.104 The electrophoretic
mobility of the Ludox particles was determined by electrophoretic light scattering of a 1 wt%
dispersion as described elsewhere,31 using a Nano-Zetasizer (Malvern Instruments, UK). Three
measurements, each consisting of at least 50 runs, were performed for each sample.
Lysozyme from chicken egg white lyophilized powder (Sigma-Aldrich, ≥40,000
units/mg protein, lot SLBH9534V, purity ≥90 %) and 𝛽-lactoglobulin from bovine milk (Sigma
Aldrich, lot SLBC4958V, purity ≥90 %) were used in this study.
3.2.2 Protein Adsorption Measurements
The amount of protein adsorbed on the SiNP was determined by measuring the depletion of the
supernatant solution after equilibration of the sample. For each adsorption isotherm at given pH
and salt concentration, a stock solution of buffer (10 mM formiate, MES, BICINE, or CAPS)
was freshly prepared and adjusted to the desired pH with aqueous HCl or NaOH solution (1 M).
Stock solutions of protein (10 mg/mL) and NaCl (250 mM) were then prepared in the buffer
Table 3.1: Characteristic parameters of the proteins.
Protein
Dimensions
Molar weight 𝑀𝑊
Isoelectric point IEP
nm
kDa
-
Lysozyme
3 × 3 × 4.5
14.3
11.123
𝛽-lactoglobulin
3.6 × 3.6 × 3.6
18.4
5.230
22
Characterization of Protein Adsorption onto Silica Nanoparticles: Influence of pH and Ionic Strength
solution. A portion of dialyzed Ludox TMA dispersion (about 30 wt%) was diluted in a volume
ratio 1:2 with buffer solution to obtain the Ludox TMA stock solution (about 10 wt%). The
mass fraction of silica in this stock solution was checked gravimetrically for each adsorption
isotherm. The three stock solutions (SiNP, protein, and buffer) were then mixed in known
proportions to arrive at eight different protein concentrations (0.5 – 5 mg/mL), three different
NaCl concentrations (0, 25, and 100 mM), and a constant mass fraction of Ludox TMA (about
1 wt%). The samples were equilibrated for 20 h at 20 °C in closed vials using a thermo-mixer.
After equilibration, the samples were centrifuged for 3 h at 15,000 rpm (21,000g) to separate
the supernatant from the silica. The possibility of systematic errors caused by sedimentation of
non-adsorbed protein during centrifugation was checked by determining sedimentation
isotherms of 𝛽-Lg in the absence of SiNP but under otherwise the same conditions (protein
concentration, pH, salt concentration and centrifugation time) as in the adsorption
measurements. It was found that this error was negligibly small under the experimental
conditions.
Protein concentration in the supernatant solution was determined by UV-vis
spectrometry. Sample spectra were compared to a protein standard (1 mg/mL), prepared from
the same protein stock solution, in the wavelength range 265 – 300 nm. The best-fit value of
the concentration was obtained by minimizing the sum of square deviation in absorbance from
the concentration standard in the chosen wavelength range.105 The surface concentration 𝛤 of
adsorbed protein (mass per unit surface area) was calculated from the depletion of the
supernatant solution by the relation
𝛤=𝑉(𝑐0−𝑐eq)
𝑚s𝑎s
(3.1)
where 𝑉 is the volume of protein solution of initial mass concentration 𝑐0 and final
concentration 𝑐eq after equilibration with a mass 𝑚S of silica of specific surface area 𝑎S. The
adsorbed amount was also expressed by the number of protein molecules per silica particle,
𝑁=𝛤𝑁A𝜌S𝑎S𝐷3𝜋
6𝑀P
(3.2)
where 𝑀P is the molar weight of the protein and 𝑁A the Avogadro constant.
3.2.3 Adsorption Isotherm Equation
The liquid-phase version of the Guggenheim – Anderson – De Boer (GAB) model was used to
represent the protein adsorption data. Similar to the BET relation, the GAB multilayer gas
Results
23
adsorption model10 assumes that the state of adsorbate molecules in the second and all higher
adsorption layers is the same, but different from that in the first layer. A further assumption of
the GAB model is that the state of adsorbed molecules in the second and higher layers is also
different from the bulk liquid state. The liquid-phase version of the GAB model takes up the
concept of two distinct adsorption states: There are 𝑁m equivalent adsorption sites per unit area
to which adsorbate molecules bind strongly, and each occupied site can accommodate
successively further adsorbate molecules in a weaker sorption state. This three-parameter
adsorption isotherm has the form11
𝛤=𝛤m𝐾S𝑐eq
(1−𝐾L𝑐eq)(1+𝐾S𝑐eq−𝐾L𝑐eq)
(3.3)
where 𝛤m=𝑁m𝑀P𝑁A
⁄ is the surface concentration of strongly adsorbed protein, 𝐾S is the
adsorption constant for molecules in the strong adsorption state, and 𝐾L the adsorption constant
of the weak adsorption state. Equation 3.3 reduces to the Langmuir equation when 𝐾L=0, but
it yields values of 𝛤 greater than 𝛤m at high concentrations 𝑐eq when 𝐾𝐿>0. The familiar BET
equation for vapor adsorption is recovered from Equation 3.3 by setting 𝐾L𝑐eq=𝑝𝑝0
⁄>0 and
introducing the parameter 𝐶=𝐾S𝐾L
⁄.
3.3 Results
3.3.1 Nanoparticle and Protein Characteristics
The electrophoretic mobility 𝜇e of the Ludox TMA NPs was determined at several pH values
in the absence of salt and in 100 mM NaCl, and the zeta potential 𝜁 was calculated from the
Figure 3.1: (a) Zeta potential of Ludox TMA silica particles as a function of pH for two different ionic strengths
(see Table 3.1). (b) Estimated net charge of lysozyme and 𝛽-lactoglobulin as a function of pH.
24
Characterization of Protein Adsorption onto Silica Nanoparticles: Influence of pH and Ionic Strength
mobility by the Henry equation. The electrokinetic surface charge density 𝜎0 of the particles
was estimated from the zeta potential using the Gouy-Chapman relation.106 Results for 𝜇e, 𝜁
and 𝜎0 for several pH values are collected in Table 3.1. The dependence of the zeta potential on
pH is shown in Figure 3.1a. Note that the zeta potential of the Ludox TMA particles is negative
in the entire pH range, i.e., no isoelectric point is observed down to pH 2.
The net charge of the proteins was estimated from the numbers of the individual acidic
and basic amino acids and their respective acidity constants.107 The dependence of the estimated
net charge on pH is shown in Figure 3.1b. Both proteins have a high positive net charge at pH 2,
but for 𝛽-Lg, the net charge falls of steeply with increasing pH and becomes negative above
pH 5.2 = IEP. Lyz contains a larger number of basic amino acids than 𝛽-Lg; hence, its net
charge falls off less steeply, and its isoelectric point is reached only at pH 11. Accordingly, in
the case of lysozyme the protein and the silica particles are oppositely charged from pH 2 to
pH 11. In the case of 𝛽-Lg the protein and silica particles are oppositely charged up to pH 5.2
but equally charged at higher pH.
Table 3.1: Electrophoretic mobility, zeta potential, and electrokinetic charge density of Ludox TMA silica
nanoparticles as a function of pH without added salt and with 100 mM NaCl.
Added salt
pH
Ionic strength
𝜇e
𝜁
𝜎0
mM
10-8m2s-1V-1
mV
E nm-2
0 mM
2.0
10
-1.84
-37
-0.01
3.0
1
-2.03
-41
-0.03
4.1
7
-2.41
-47
-0.06
5.0
1
-2.77
-57
-0.03
6.0
4
-2.72
-54
-0.06
7.0
9
-2.83
-55
-0.09
8.0
3
-3.01
-60
-0.06
9.0
8
-3.22
-62
-0.10
10.0
3
-3.36
-67
-0.07
11.0
8
-3.24
-63
-0.10
100 mM
2.0
110
-0.27
-13
-0.06
2.9
101
-1.00
-17
-0.08
4.0
106
-1.12
-19
-0.09
5.2
101
-1.24
-21
-0.10
6.2
106
-1.51
-25
-0.12
6.9
109
-1.65
-27
-0.14
8.2
104
-2.23
-37
-0.19
9.1
108
-2.52
-42
-0.22
10.2
104
-2.65
-44
-0.23
11.0
108
-2.47
-41
-0.22
Results
25
3.3.2 Lysozyme Adsorption
The adsorption of Lyz on Ludox TMA SiNPs was studied in a pH range 3.5 to 11.2 in the
absence of salt and in 25 and 100 mM NaCl solutions. Figure 3.2 shows adsorption isotherms
(20 °C) for a series of pH values up to the isoelectric point in the absence of added salt.
Adsorption is expressed by the surface concentration 𝛤 (mg/m2) and by the average number of
protein molecules per silica particle (𝑁) and is plotted against the concentration 𝑐eq of protein
in the equilibrated solution. The isotherms are of high-affinity type, i.e., sharply increasing at
low concentrations and leveling off at higher concentrations. The adsorption level attained in
the experimental concentration range is below 0.5 mg/m2 at pH 3.5, but strongly increasing
with pH to a value close to 4 mg/m2 at pH 11.2 (not shown in Fig. 3.2). From the cross-sectional
area of Lyz adsorbed side-on (𝐴0 ≈ 4.5 nm × 3 nm = 13.5 nm2), the monolayer capacity is about
1.8 mg/m2, as indicated by the dashed line in Figure 3.2. It can be seen that this adsorption level
is nearly reached at pH 7.5, but higher values are attained closer to IEP. A higher monolayer
capacity (about 2.6 mg/m2) would result from head-on adsorption of the Lyz molecules.
However, molecular simulation studies indicate that side-on adsorption is the preferred
orientation of Lyz on negatively charged silica surfaces.43,108 Hence, the results in Figure 3.2
indicate that adsorption exceeding a monolayer of protein molecules occurs at pH > 8.
Figure 3.3 illustrates the influence of added NaCl on the adsorption isotherm of Lyz at
a low and a high pH. In both cases, the high-affinity character of adsorption isotherms is lost
when salt is added, but the influence on the adsorption level at higher protein concentrations is
Figure 3.2: Adsorption isotherms of lysozyme on Ludox TMA for several pH values without added salt:
Experimental data (symbols) and fits by the GAB model (lines). The adsorbed amount is expressed as protein
mass per unit area ( 𝛤) and by the mean number of protein molecules per silica particle (N). The monolayer
capacity based on a dense packing of protein molecules in side-on orientation (𝐴0 = 13.5 nm2) is indicated by the
dashed line.
26
Characterization of Protein Adsorption onto Silica Nanoparticles: Influence of pH and Ionic Strength
different in the two pH regimes: At pH 4.5 (Fig. 3.3a), when the protein is highly charged,
adsorption continues to increase in the presence of salt, becoming higher than the plateau value
reached in the absence of salt. At pH 9.5 (Fig. 3.3b), when the adsorption level exceeds one
nominal monolayer, added salt causes a significant decrease of the adsorption level at all protein
concentrations studied in this work.
The experimental adsorption data can be represented by the GAB isotherm equation
(Eq. 3.3), as shown by the full curves in Figures 3.2 and 3.3. Values of the parameters 𝛤m, 𝐾S
and 𝐾L obtained by fitting the adsorption data with Equation 3.3 are presented as a function of
pH in Figure 3.4. The limiting surface concentration 𝛤m of strongly adsorbed protein (Fig. 3.4a)
is increasing with pH and reaches values above 3 mg/m2 near IEP. Hence, in this pH region, the
surface concentration of strongly bound protein clearly exceeds a monolayer of closely packed
molecules. The adsorption constant 𝐾S for the strongly bound protein (Fig. 3.4b), which relates
to the high-affinity region of the adsorption isotherms, exhibits no systematic dependence on
pH, but a systematic decrease with increasing salt concentration. The adsorption constant 𝐾L of
Lyz in the weakly bound state (Fig. 3.4c) is smaller by 2 – 3 orders of magnitude than 𝐾S . Like
𝐾S, it shows no systematic dependence on pH but some increase with the ionic strength. To
quantify the contribution of the weak adsorption state to the overall adsorption, we introduce
the adsorption ratio 𝛤(𝑐∗)𝛤m
⁄, where 𝛤(𝑐∗) represents the adsorbed amount at a reference
concentration, 𝑐∗in the flat region of the isotherms as calculated by Equation 3.3. Values of
𝛤(𝑐∗)𝛤m
⁄<1 indicate that at the chosen reference concentration, the adsorbed amount is lower
than the limiting concentration 𝛤m of strongly adsorbed protein, while 𝛤(𝑐∗)𝛤m
⁄>1 implies
that the weak adsorption state contributes to the overall adsorption. Figure 3.4d shows the
adsorption ratio as a function of pH for a reference concentration 𝑐∗=2 mg/mL. Values of
Figure 3.3: Adsorption isotherms of lysozyme on Ludox TMA: Influence of added salt at pH 4.5 (a) and pH 9.5
(b): filled square, no added salt; filled circle, 25 mM NaCl; filled triangle, 100 mM NaCl, and fits by the GAB
model; see caption of Figure 3.2 for details.
Results
27
𝛤(𝑐∗)𝛤m
⁄ close to 1 are found in the absence of salt, indicating that in this case all adsorbed
Lyz is strongly bound. At pH > 7, where added salt causes a decrease of the adsorbed amount
(Fig. 3.3), values of 𝛤(𝑐∗)𝛤m
⁄>1 indicate that the salt-induced decrease of adsorption
involves the participation of weak adsorption sites. These findings will be discussed in
Section 4.4.
3.3.3 𝛽-Lactoglobulin Adsorption
Adsorption isotherms of 𝛽-Lg on Ludox TMA for a series of pH values in the absence of salt
are shown in Figure 3.5. It can be seen that adsorption sharply increases from pH 2 to pH 4
(Fig. 3.5a) and sharply decreases from pH 4 to pH 7 (Fig. 3.5b). All isotherms for pH < 7
exhibit a high-affinity adsorption regime, even at pH 2, where the limiting adsorption is only
0.2 mg/m2.Beyond this high-affinity regime, a further increase of adsorption with protein
concentration is observed at pH values near IEP. This effect is most pronounced at pH 4. A
monolayer of densely packed 𝛽-Lg molecules (cross-sectional area
𝐴0 ≈ 3.6 nm × 3.6 nm ≈ 13 nm2) corresponds to a surface concentration of ca. 2.3 mg/m2
(dashed line in Fig. 3.5). This adsorption level is well exceeded at pH 4 but not at pH 5 (i.e.,
close to IEP = 5.2). At pH 6, when the net charge of the protein has changed from positive to
weakly negative, there is still significant adsorption of the protein, but at pH 7 and higher, no
adsorption of 𝛽-Lg is detected in the absence of salt.
The influence of salt on the adsorption of 𝛽-Lg at different pH values is shown in
Figure 3.6, where the four panels demonstrate a reversal of the influence of salt on the protein
adsorption in the range from pH 4 to 7: At pH 4 (Fig. 3.6a), the highest adsorption is found in
the absence of salt and the lowest adsorption at 100 mM salt. Changing from pH 4 to pH 5
Figure 3.4: Lysozyme adsorption: Fit values of the GAB parameters as a function of pH for three ionic strengths
(no salt, 25 mM, 100 mM NaCl): (a) limiting surface concentration 𝛤m of strongly bound protein; (b) adsorption
constant 𝐾S; (c) adsorption constant 𝐾L; (d) adsorption ratio 𝛤(𝑐∗)𝛤m
⁄ for 𝑐∗ = 2 mg/mL (see text).
28
Characterization of Protein Adsorption onto Silica Nanoparticles: Influence of pH and Ionic Strength
(Fig. 3.6b) causes a drastic decrease of adsorption in the absence of salt, but no significant
decrease at 25 or 100 mM salt; as a consequence, the adsorption at no salt is now intermediate
between that at 25 and 100 mM salt. Changing from pH 5 to pH 6 (Fig. 3.6c) causes further
strong decrease in adsorption at no salt, and also a strong decrease at 25 mM salt, but again, no
decrease of adsorption at 100 mM salt. Finally, at pH 7 (Fig. 3.6d), the adsorption in the absence
of salt has fallen to zero, and the adsorption at 25 mM salt has fallen below the adsorption at
100 mM salt, thus completing the inversion of the protein adsorption level as a function of salt
concentration.
The adsorption data for 𝛽-Lg can again be represented by the GAB equation (Eq. 3.3),
as shown by the full curves in Figures 3.5 and 3.6. The parameters 𝛤m, 𝐾S and 𝐾L obtained from
fits of the adsorption data and values of the adsorption ratio 𝛤(𝑐∗)𝛤m
⁄ at the reference
concentration 𝑐∗ = 2 mg/mL are shown as a function of pH in Figure 3.7. The limiting surface
concentration 𝛤m of strongly bound protein (Fig. 3.7a) increases sharply at low pH, reaching a
maximum at pH 4–5 and falls off more or less steeply at higher pH values, depending on the
salt concentration. The highest values of 𝛤m, attained at pH 4–5 and low salt concentration
correspond to nearly a monolayer of densely packed 𝛽-Lg monomers (2.3 mg/m2). At pH above
IEP = 5.2, the values of 𝛤m demonstrate the inversion of the influence of salt on the protein
adsorption in this pH range. Unlike 𝛤m, the adsorption constant 𝐾S of strongly bound protein
(Fig. 3.7b) decreases in a monotonic way from low to high pH, without any singular behavior
near IEP. It also decreases with increasing salt concentration, though to a lesser extent than in
the case of Lyz. Remarkably, values of 𝐾S well above 1 mL/mg are still found in a pH range
where both the surface and the protein are negatively charged. In contrast to 𝐾S , the adsorption
constant 𝐾L of 𝛽-Lg in the weakly bound state (Fig. 3.7c) exhibits a pronounced maximum at
Figure 3.5: Adsorption isotherms of 𝛽-lactoglobulin on Ludox TMA for several pH values without added salt: (a)
pH ≤ pH 4; (b) pH ≥ pH 4. Experimental data (symbols) and fits by the GAB model (lines). The monolayer
capacity based on a dense packing of monomeric protein (𝐴0 = 13 nm2) is indicated by the dashed line; see also
caption of Fig. 3.2.
Discussion
29
pH 4 in the absence of salt, which disappears on addition of salt. In the presence of salt, 𝐾L
gradually decreases from pH 3 to pH 6 but appears to increase again at higher pH. The graphs
of the adsorption ratio 𝛤(𝑐∗)𝛤m
⁄ for 𝛽-Lg as a function of pH (Fig. 3.7d) again show the
singular role of the weak adsorption state of 𝛽-Lg at pH 4 in the absence of salt, where a
pronounced maximum, 𝛤(𝑐∗)𝛤m
⁄ ≈ 2, is observed, implying that 50% of the protein is adsorbed
in the weakly bound state. Except for this singular point, 𝛤(𝑐∗)𝛤m
⁄ values in a range 1.1 to 1.3
are found for the pH range 3 – 5 and values close to 1 at higher pH. This indicates that protein
in the weakly bound state plays a significant role in the neighborhood of the isoelectric point,
but not elsewhere.
3.4 Discussion
Because Lyz and 𝛽-Lg have greatly different values of IEP, electrostatic interactions with the
negative silica surface are causing a different dependence of adsorption on pH. A comparison
of the adsorption of the two proteins at the SiNP is shown in Figure 3.8, where the surface
concentration 𝛤(𝑐∗) of adsorbed protein at a common concentration 𝑐∗ = 2 mg/mL is plotted as
a function of pH. For Lyz, where weak adsorption states play no major role, the values of 𝛤(𝑐∗)
are similar to those of 𝛤m at given pH and ionic strength (see Fig. 3.4d). In the case of 𝛽-Lg, for
which weak adsorption states are significant in the neighborhood of IEP, values of 𝛤(𝑐∗) are
higher than 𝛤m at pH values close to IEP (see Fig. 3.7d).
For Lyz in the absence of salt, the surface concentration 𝛤(𝑐∗) increases with pH in a
nearly linear manner in the entire experimental pH range up to pH 11.2 ≈ IEP.
Figure 3.6: Adsorption isotherms of 𝛽-lactoglobulin on Ludox TMA at (a) pH 4; (b) pH 5; (c) pH 6; (d) pH 7.
Experimental data: filled square, no salt; filled circle, 25 mM NaCl; filled triangle, 100 mM NaCl; full lines: fit
by the GAB equation. The estimated monolayer capacity is indicated by a dashed line. See caption to Fig. 3.2 for
further details.
30
Characterization of Protein Adsorption onto Silica Nanoparticles: Influence of pH and Ionic Strength
At pH < 7, the surface concentration is less than a complete monolayer. In this regime,
added salt reduces the initial high-affinity adsorption but promotes further adsorption at higher
protein concentrations (Fig. 3.3a). The salt-induced reduction of high-affinity adsorption can
be attributed to a screening of the attractive electrostatic interaction between protein and the
surface (lowering of the binding constant 𝐾S), and the salt-induced promotion of adsorption at
higher protein concentrations can be attributed to a screening of the repulsive electrostatic
interactions between protein molecules in the adsorbed layer. The interplay of these two effects
causes the observed change in isotherm shape (Fig. 3.3a) and a weak increase in 𝛤(𝑐∗) with salt
concentration in the region below pH 7, as shown in Figure 3.8.
At pH > 8 the adsorbed amount of Lyz exceeds the amount corresponding to a densely
packed monolayer. In this pH regime, added salt causes a weaker increase of 𝛤(𝑐∗) with pH
than in the absence of salt, and a maximum in 𝛤(𝑐∗) appears at a pH near IEP. With increasing
salt concentration, this maximum becomes more shallow, but we are unable to decide whether
it is located at or somewhat below IEP, due to the limited precision of our data and the lack of
data for pH > IEP. Our results do not confirm the existence of a sharp adsorption maximum at
a pH < IEP reported for the adsorption of Lyz on a flat silica surface in the absence of salt,97 but
except for this point, our results are consistent with those reported in the literature.97 In
particular, we also find that added salt causes a decrease in the adsorbed amount in a range of
pH < IEP, in which the adsorbed amount exceeds one monolayer of protein molecules. This
finding is surprising at first sight in view of the notion that higher ionic strength reduces the
repulsive protein – protein interaction and thus enhances adsorption. Presumably, the formation
of a second adsorbed protein layer in the pH region near IEP involves attractive electrostatic
interactions between oppositely charged patches on protein molecules in the first and second
Figure 3.7: 𝛽-Lactoglobulin adsorption: Fit values of the GAB parameters as a function of pH for three ionic
strengths (no salt, 25 mM, 100 mM NaCl): (a) limiting surface concentration 𝛤m of strongly bound protein; (b)
adsorption constant 𝐾S; (c) adsorption constant 𝐾L; d adsorption ratio 𝛤(𝑐∗)𝛤m
⁄ for 𝑐∗ = 2 mg/mL (see text).
Discussion
31
layer. An increase of ionic strength will screen these interactions and thus cause a reduction of
the adsorbed amount, as it is observed for Lyz in this study. Indeed, at 100 mM NaCl, the
maximum adsorption of Lyz near IEP has been reduced to hardly more than one nominal
monolayer (Fig. 3.8).
In our earlier work,31,32 we found that pH and added salt has a pronounced influence on
the protein-induced aggregation of SiNP near the isoelectric point. In the absence of salt, large-
scale aggregation occurs over a wide pH range, but the aggregates re-disperse at pH 10. Hence,
at pH ≥ 10, in the absence of salt, the observed adsorbed amount represents the adsorption onto
isolated (non-aggregated) SiNP. On the other hand, in the presence of 100 mM NaCl salt, the
silica-protein hetero-aggregates do not redisperse near IEP,31,32 and thus, the measured adsorbed
amount represents the amount adsorbed in the confined geometry between silica particles.
Presumably, part of the observed salt-induced decrease in the adsorbed amount near pH 11 is
caused by this transition from adsorption onto free particles to adsorption between silica
particles in the large-scale aggregates.
For 𝛽-Lg, we could characterize the adsorption behavior for pH values on both sides of
the isoelectric point (Fig. 3.8). In the pH regime below IEP, the dependence of 𝛤(𝑐∗) on pH and
salt concentration qualitatively resembles the behavior of Lyz, although the variation of 𝛤(𝑐∗)
with pH is occurring in a narrow pH region due to the low value of IEP. Since the SiNP used in
this study are negatively charged down to pH 2 (cf. Fig. 3.1a and Table 3.1), the similar pH and
salt dependence of 𝛤(𝑐∗) of the two proteins at pH < IEP indicates that in both cases, the
behavior is dominated by electrostatic interactions. The low level of adsorption up to pH 3
indicates that in this regime, the attractive protein – surface interactions are nearly balanced by
repulsive protein – protein interactions. Both of these interactions are screened by added salt,
so that the adsorption level is only weakly affected by salt. The very strong increase in
adsorption from pH 3 to pH 4 in the absence of salt, to values much beyond one nominal
monolayer, may again be attributed to a transition from repulsive to attractive protein – protein
Figure 3.8: Comparison of lysozyme and 𝛽-lactoglobulin adsorption onto silica nanoparticles: Adsorbed amount
𝛤(𝑐∗) at the reference concentration 𝑐∗ = 2 mg/mL plotted against pH: filled square, no salt; filled circle, 25 mM
NaCl; filled triangle, 100 mM NaCl. The isoelectric points (IEP) of the proteins are indicated by vertical dashed
lines.
32
Characterization of Protein Adsorption onto Silica Nanoparticles: Influence of pH and Ionic Strength
interactions in the pH range near IEP. This interpretation is supported by the salt-induced
reduction of adsorption at this pH. Interestingly, the adsorbed amount at pH 5 (closest to IEP)
is much lower than this maximum value and less dependent on the ionic strength. In an earlier
study of 𝛽-Lg adsorption onto silica surfaces, Elofsson et al.103 reported that the pH dependence
of adsorption was caused mainly by the pH dependent variation in self-association of the protein
in solution. At room temperature and pH values below 4 and above 5.2, the protein exists
predominantly in form of dimers and monomers, with an increasing tendency for the dimer to
dissociate into monomers at lower and higher pH, respectively. The dissociation of the dimer is
the strongest in the absence of salt, due to a higher (less screened) electrostatic repulsion
between the monomeric units.104 In a narrow pH region near pH 4.6, the dimers aggregate to a
larger oligomeric unit (presumably an octamer), and this secondary aggregation is enhanced by
a decrease in ionic strength.103,104 It is tempting to attribute the very high adsorption of 𝛽-Lg at
pH 4 in the absence of salt, and its strong dependence on the ionic strength at this pH, to the
adsorption of this higher oligomer. However, in this case, one would expect a high value of
𝛤(𝑐∗) not only at pH 4 but also at pH 5 in the absence of salt, which is not the case. In this
context, we also have to consider that according to a recent report,83 the monomer – dimer
association equilibrium of 𝛽-Lg in the adsorbed state is affected by curvature of the adsorbing
surface. In a study of 𝛽-Lg adsorption at a nanoscale hydrophobic surface, it was found83 that
the association is weakened by surface curvature, to the extent that no adsorbed dimers were
detectable on particles of 25 nm diameter. It would be of interest to find out if such a curvature
dependence of protein association also prevails in the adsorption onto hydrophilic NP.
The adsorption behavior of 𝛽-Lg at pH > IEP, where the protein has a negative net
charge and is electrostatically repelled by the equally charged surface, confirms that adsorption
of globular proteins on the 'wrong side' of the isoelectric point is not limited to polyelectrolyte
brushes88–91 but can also occur on charged inorganic surfaces.94,97 Adsorption of 𝛽-Lg at pH >
IEP may involve electrostatic interactions with the negative silica surface, either due to the
persistence of positive patches at the protein surface, or due to charge regulation effects.93,94
Non-electrostatic contributions to the adsorption energy must also play a significant role in the
adsorption of this protein on the SiNP. At pH 7 and 8, the repulsive electrostatic
protein – surface and protein – protein interaction can over-compensate this attractive non-
electrostatic adsorption energy in the absence of salt, so that no adsorption occurs. In the
presence of salt, the repulsive electrostatic interactions are screened and the non-electrostatic
adsorption energy dominates, causing increasing adsorption with increasing salt concentration.
Hence, the observed inversion of the salt dependence of the adsorption at pH > IEP can be
attributed to the competition of electrostatic and non-electrostatic contributions to the
adsorption energy.
As a final remark, we have to point out that the adsorption of the proteins will be affected
by the surface chemistry of the SiNP. This applies particularly to the adsorption behavior at low
Conclusion
33
pH. As shown in Figure 3.1a, the Ludox TMA particles used in the present work have a negative
zeta potential down to pH 2. In contrast, the SiNP of our earlier work,31 which were prepared
by a different route than Ludox TMA, had a zeta potential near zero below pH 4, and no
adsorption of Lyz was found on these particles below pH 4. This difference in adsorption
behavior at low pH can again be rationalized by electrostatic interactions as outlined above.
3.5 Conclusion
The present study has highlighted the important role of electrostatic interactions in the
adsorption of the globular proteins Lyz and 𝛽-Lg onto negatively charged silica nanoparticles.
For both proteins, two adsorption regimes as a function of pH were identified for pH < IEP: At
low pH, the competition of attractive protein – surface interactions with the repulsive
protein – protein interactions causes adsorption limited to one monolayer of protein molecules.
At pH values closer to IEP, repulsive interactions between protein molecules become less
important and attractive protein – protein interactions resulting from oppositely charged
patches on two proteins become relevant, leading to adsorption well above one monolayer of
protein at low ionic strength. In the case of 𝛽-Lg (IEP ≈ 5), for which the adsorption behavior
could be studied on both sides of IEP, a pronounced maximum in adsorption was observed
somewhat below IEP in the absence of salt, and an inversion of the salt effect on the adsorption
level was found in the pH region around IEP. This inversion is attributed to a competition of
electrostatic and non-electrostatic contributions to the adsorption energy. The role of protein
association to dimers and higher oligomers appears to dominate the adsorption behavior near
IEP, but further work is needed to clarify details of this behavior.
Introduction
35
Chapter 4 Evolution of Hetero-Aggregate Structure at
Different Protein Loadings
2
4.1 Introduction
In preceding work the structural properties of hetero-aggregates formed by silica nanoparticles
(SiNP) and adsorbed protein were studied by small angle X-ray scattering (SAXS).31,32 Similar
to the findings explained in the previous Chapter 3 a strong pH and salinity dependence of these
structural parameters was found. The structure of the hetero-aggregates is governed by the pH
and salinity via the interaction strength between the Lyz and the SiNP.
SAXS experiments require moderate particle and protein concentrations. For very low
concentrations the sensitivity is too weak for reliably experimental scattering data. At very high
concentrations of particles and proteins the samples tend to multiple scattering, which makes
the evaluation of the resulting data impossible as the general scattering theory is not valid for
multiple scattering. In addition, the spatial resolution of the used laboratory scale SAXS
apparatuses was limited by the assessable q-range. Due to these experimental limitations these
studies left open the question how the particles are aggregating when either a very small number
or a very large number of protein molecules are available.
In order to overcome the limitations of SAXS in the extreme protein loading scenarios
fluorescence correlation spectroscopy (FCS) and confocal laser scanning microscopy (CLSM)
was used. This combination of techniques allowed to study a very broad loading range from 0.1
to 5,000 Lyz per particle, and also offered the opportunity to monitor the aggregates with direct
optical methods. The aggregate sizes for low protein loadings were investigated with FCS. The
dense and turbid samples obtained for higher concentrations were observed with CLSM and a
3D reconstructions of these micrographs were made. The surface-are-to-volume ratio of the
found aggregates was used as a measure for the structural properties.
The FCS and CLSM techniques require that the probed sample is fluorescent. This was
achieved by labeling lysozyme with a fluorescein dye. Additionally, the adsorption parameter
(Chapter 3) for labeled and native lysozyme were compared, to ensure the general relevance of
the results obtained with the labeled protein.
2
The experiments presented in this chapter were performed by Albert Prause in his Bachelor thesis which was
supervised by Prof. Findenegg and myself. In particular, I was strongly involved in the planning of the
experimental program and day-to-day supervision of the experiments, as well as the data evaluation and
interpretation.
36
Evolution of Hetero-Aggregate Structure at Different Protein Loadings
4.2 Materials and Methods
4.2.1 Materials
Commercial Ludox TMA (Sigma Aldrich) silica particle dispersions (SiNP) were used for the
studies presented in this chapter. The particles had an average particle size of 27 nm and a
polydispersity of 𝑠=0.13 (SAXS). To remove possible impurities and additives the stock
solution was dialyzed (using a membrane with a molecular weight cutoff of 14.000 kDa)
against water which was changed three times per day. According to the manufacturer data sheet,
the specific surface area of the material was aS=128 m2g−1. For the experiments Milli-Q
water from MilliPore QPAC was used (18 MΩ cm).
Lyophilized hen egg white lysozyme (Lyz, Sigma Aldrich, 𝑀𝑊=14,388 Da, ≥ 90 %),
fluorescein-5-isothiocyanat (FITC), Merck and Sigma Aldrich), acetic acid (AcOH, Th. Geyer,
≥ 99.5 %), 2-(bis(2-hydroxyethyl)-amino)-acetic acid (BICINE, Sigma-Aldrich, ≥ 99 %),
3-(cyclohexyl-amino)-1-propane sulfonic acid (CAPS, Sigma-Aldrich, ≥ 98 %) was used
without purification.
4.2.2 Protein Labeling
301 mg of lysozyme (Lyz) was dissolved in 6.92 mL BICINE buffer (10mM pH 8.3) and the
pH was adjusted to 8.3 again. Under stirring 8.15 mL of a FITC stock solution (1 mg/mL, in
BICINE, pH 8.3) was slowly added to the native lysozyme (Lyznative) solution. The mixture was
stirred at 20 °C for 15 h. The pH was adjusted to pH = 4 (HCl, 1 M) and the mixture was stirred
for additional 30 min. The labeled Lyz (LyzFTC) was purified by size exclusion chromatography
(PD-10 column, GE Health Care, Matrix: Sephadex G-25) using the gravity protocol. The
collected orange solution was lyophilized and the solid orange product (LyzFTC) was stored at -
30 °C.109,110
4.2.3 Adsorptions Measurements
Adsorption experiments were performed as described in Chapter 3. In a typical experiment,
samples of 2 mL where prepared by mixing aliquots of stock solutions of SiNP dispersion,
LyzFTC and NaCl to achieve the desired compositions. The SiNP with the adsorbed protein
where sedimented by centrifugation (21,000g) and the supernatant was collected. The
concentrations of protein and dye in the supernatant was determined by UV-vis spectroscopy
Materials and Methods
37
of the protein backbone (280 nm) and the dye (491 nm). The adsorbed amount was calculated
according to the method described in Chapter 3.
4.2.4 Fluorescence Correlation Spectroscopy
A Leica TCS SP5 II confocal microscope equipped with a HCX PL APO CS 63.0 × 1.20 water
UV immersion objective and an argon-laser (488 nm) was used for the FCS and CLSM
experiments. The samples were prepared on cover slides (Zeiss, 18 mm x 18 mm, thickness:
170 ± 5 µm). The pinhole aperture was set to 111.48 µm. The confocal volume (0.23 fL) and
its aspect ratio (𝜉=6) was measured after every restart of the instrument with an aqueous
Rhodamine 6G solution (5 nM). A fresh reference sample of LyzFTC and FITC solution was
measured for new day of instrument use.
For FCS experiments 3 sets of TMA dispersions (0.01, 0.10 and 1.00 wt%, CAPS
10 mM, pH 9.6) were prepared. To those dispersions aliquots of LyzFTC were added to achieve
the desired concentrations (1, 5, 10 and 20 µg mL-1). A sample (20 µL) was measured three
times for 10 min with a low laser intensity (< 2 mW in the confocal volume). The sample was
covered during the experiment to avoid evaporation of the solvent or possible parasitic light
incidence. The theory is described in more detail in Chapter 2.
4.2.5 Confocal Laser Scanning Microscopy
The same microscope setup was used as for the FCS experiments. For the CLSM experiments
3 sets of TMA dispersions (0.01, 0.10 and 1.00 wt%, CAPS 10 mM, pH 9.6) were prepared and
mixed with aliquots of LyzFTC to achieve the desired concentrations (10, 20, 50, 100, 150, 200,
300, 400 and 500 µg mL-1) of LyzFTC. A sample (20 µL) was pipetted on a cover slide and
allowed to rest for 5 min. Signal gain of the detector was set to 500 V. Ever measurement gave
a three-dimensional (3D) stack of micrographs with a volume of 246×246×123.4 µm with
a lateral resolution of 0.48 µm/pixel and a height resolution of 0.50 µm/pixel.
The 3D-stacks were analyzed with the Fiji111 software package using the 3D-obeject
counter.112 In a first step the contrast was normalized and the intensity threshold for the object
analysis was set to 75. The object analysis gave values for the surface and the volume of all
objects in the sample volume. From the sum of all object surfaces ∑𝐴𝑖𝑖 and the total object
volume ∑𝑉𝑖𝑖 the surface-area-to-volume ratio 𝐴𝑉
⁄ was calculated according to Equation 4.1
for further interpretation of the data. The theory is described in more detail in Chapter 2.
38
Evolution of Hetero-Aggregate Structure at Different Protein Loadings
A𝑉
⁄=∑𝐴𝑖𝑖
∑𝑉𝑖𝑖
(4.1)
4.3 Results
4.3.1 Adsorptions Comparison
Adsorption isotherms for FTC-labeled lysozyme (LyzFTC) on TMA particles and fits of the data
with the GAB model are shown in Figure 4.1. The isotherms shown are taken at high pH close
to the IEP of Lyz to match the conditions in the fluorescence experiments. For the case of no
added salt (orange data points and solid lines in Fig. 4.1) the adsorbed amount rises steeply and
reaches a maximum value already for low equilibrium concentrations of LyzFTC (<0.5 mg/mL).
Under these conditions the adsorbed protein amount is well beyond the value for one monolayer
of protein which is indicated by the black dashed line in the diagrams. The limiting adsorbed
amount at pH 10.5 without added salt was beyond the experimental concentration range.
The addition of salt changes the steepness of the isotherms drastically (green data points
and solid lines in Fig. 4.1). The limiting adsorbed amount is reached at higher equilibrium
concentrations >1 mg/mL) in the case of pH 9.6.
The adsorption isotherms were analyzed by a fit to the GAB adsorption model (Eq. 3.3)
for adsorption from liquid phases (cf. Chap. 3). The resulting best fit values for the model
parameters are displayed as a function of the bulk pH in Figure 4.2. Panel 4.2a shows the
limiting adsorption 𝛤𝑚 which is increasing with increasing pH. When no salt is added to the
Figure 4.1: Experimental adsorption isotherms for 𝑝𝐻=9.6 (a) and 𝑝𝐻=10.5 (b). Shown are the data for
samples with added salt (green symbols) and without added salt (orange symbols). The solid lines represent the
fits using the GAB-adsorption model, the dashed line corresponds to one close-packed layer of protein molecules
at the particle surface. This figure is modified from the Bachelor thesis of Albert Prause.
Results
39
system this behavior continues for the experimental pH range. However, the value of the
maximum adsorbed amount for this sample shows a large error which can be rationalized by
the experimental concentration range. The other GAB-model parameters show no significant
change within the experimental pH range. The adsorption constant 𝐾𝑆 peaks around pH 8 and
drops for higher pH values. Constant 𝐾𝐿 is for the entire pH low and decreases with higher pH.
All best fit values for the parameters of the GAB-adsorption model are summarized in
Table 4.1.
Figure 4.2: Best fit values of the GAB-model parameters for LyzFTC/SiNP as a function of the bulk pH. The
limiting adsorption (a), adsorption constants 𝐾𝑆 (b) and 𝐾𝐿 (c) and the adsorption ratio 𝛤(𝑐∗)𝛤m
⁄ for 𝑐∗ = 2 mg/mL
(d) are shown.
Table 4.1: Comparison of the GAB model parameters for the adsorption of FTC-labeled and native lysozyme
(LyzFTC and Lyznative) on Ludox TMA nanoparticles presented in Figure 4.2.
LyzFITC
Lyznative
pH
4.6
8.3
9.6
10.5
4.5
8.5
9.5
10.5
𝛤𝑚mg m-2
⁄
0.6
2.1
3.4
4.0
0.5
2.4
3.1
3.5
𝐾𝑆mL mg-1
⁄
34
140
49
10
134
46
62
72
𝐾𝐿mL mg-1
⁄
0.06
0.04
0
0
0
0
0
0
40
Evolution of Hetero-Aggregate Structure at Different Protein Loadings
4.3.2 Fluorescence Correlation Spectroscopy
All correlation functions gathered for the three sets of samples are displayed in Figure 4.3.
Every experimental correlation function was normalized to the total number of fluorophores
〈N〉 in the sample. Experimental correlation functions were fitted with Equation 2.7 (cf.
Chapter 2). The mean number of fluorophores in the confocal volume was calculated with
Equation 2.6.
The analysis was done with 2 or 3 components for every correlation function. A small
amount of free fluorescein dye (FTC) was found in most samples. Its characteristic time
constant was determined in a separate experiment and kept constant during the fitting process.
Using Equation 2.8 the fitted characteristic diffusions times were converted into the diffusion
constants 𝐷f. The corresponding hydrodynamic radius (𝑅h) of each component was calculated
via the Stokes-Einstein equation (Eq. 4.2).
𝑅h=𝑘B𝑇
6𝜂𝜋𝐷f
(4.2)
The resulting values for the diameter of the diffusing species and the corresponding
number fractions of fluorescent particles are plotted in Figure 4.4 against the number of proteins
per nanoparticle in the sample (Lyz/SiNP). Over the entire experimental range small clusters
with a 𝐷=2𝑅ℎ=33±5 nm are found. This size is close to the diameter of the primary TMA
Figure 4.3: Normalized experimental correlation functions from the investigated Lyz/SiNP samples. The panels
correspond to SiNP concentrations of (a) 0.01 wt%, (b) 0.1 wt%, (c) 1 wt%. The correlation functions in the
individual panels represent different concentrations, as indicated in panel (a); the same concentrations are show
in the panels (b) and (c). For clarity the correlation functions are shifted relative to each other by a constant
increment of 0.75. This figure is modified from the Bachelor thesis of Albert Prause.
Results
41
SiNP(𝐷s=27 nm). Starting at a loading of 1 Lyz/SiNP, a second fraction of particles with a
larger but varying diameter 𝐷 become detectable. At a protein loading of 1 Lyz/SiNP these
larger aggregates have a diameter of 𝐷≈1 µm, but the size of these larger aggregates decreases
as the protein loading is further increased. At a loading of 10-20 Lyz/SiNP 𝐷 is found to be
close to 100 nm. For even higher loadings the diameter increases again to 𝐷 close to 1 µm. For
the sample with the highest protein loading (Lyz/SiNP = 200) a third component appeared in
the FCS data. This indicates that the population of larger aggregates is polydispers.
Over the entire range of Lyz/SiNP the number fraction of small particles in the confocal
volume is high (Fig. 4.4b). Here it is important to note that one large aggregate, consisting of
many bridged SiNP is detected as one diffusing entity. Therefore, number fraction is dominated
by the small clusters.
4.3.3 Confocal Laser Scanning Microscopy
The long-range structure of the large aggregates was studied with CLSM, as this technique
provides information in the micrometer length scale. The set of the reconstructed 3D images is
Figure 4.4: (a) Average diameters of diffusing species in Lyz/SiNP samples as calculated from the characteristic
diffusing times (see text) obtained by FCS. The parameters are plotted versus Lyz/SiNP. (b) Number fraction of
the different diffusing species in the samples. The colors of the bars indicate the size of the species corresponding
to the colors given panel (a). This figure is partially reproduced from the Bachelor thesis of Albert Prause.
42
Evolution of Hetero-Aggregate Structure at Different Protein Loadings
Figure 4.5: 3D reconstructions of 2D CLSM micrographs of the samples of SiNP with Lyz. The visible structures
are formed by hetero-aggregation of individual SiNP (depiction in false color). Every panel shows one 3D stack
for one specific loading ratio (Lyz/SiNP) after normalization and image processing. (a) Lyz/SiNP =9.4, (b)
Lyz/SiNP =28.3, (c) Lyz/SiNP =142, (d) Lyz/SiNP =377, (e) Lyz/SiNP =953, (f) Lyz/SiNP = 4715. Every 3D
stack has a box size of 123 x 123 x 123 µm3. This figure is reproduced from the Bachelor thesis of Albert Prause.
Discussion and Outlook
43
displayed in Figure 4.5 where the panels (a) and (b) correspond to 0.01 wt% of SiNP, (c) and
(d) to 0.1 wt% of SiNP and (e) and (f) to 1 wt% of SiNP. The LyzFTC concentration was adjusted
accordingly to achieve a wide range of protein loadings from 9.4 Lyz/SiNP in panel (a) going
up to nominal 4715 Lyz/SiNP in panel (f).
At low loadings (Fig. 4.5a) only very few and small aggregates are visible. The number
of these small aggregates increases when the amount of added protein is increased (Fig. 4.5b).
When the loading is further increased the aggregates grow in size and number. Near the bottom
of the observed sample volume larger aggregates are found due to sedimentation. Figure 4.5d
shows a dense network, filling the entire observation volume. This space-filling network breaks
up into smaller elongated aggregates for even higher loadings (Fig. 4.5e) and finally (Fig. 4.5f)
relatively small and compact aggregated at very high loadings.
The surface-area-to-volume ratio 𝐴𝑉
⁄ was extracted from the data by the method
described in Section 4.2.4 and the results are displayed as a function of the nominal protein
loading in Figure 4.6. For low protein loadings up to 20 Lyz/SiNP, 𝐴𝑉
⁄ is found to be constant
within the error margin (𝐴𝑉
⁄≈10±0.5 µm-1). As the protein loading increases 𝐴𝑉
⁄ drops
slowly to 𝐴𝑉
⁄≈8±0.7 µm-1. Exceeding the nominal monolayer capacity of 170 Lyz/SiNP,
𝐴𝑉
⁄ drops sharply to approximately 3 µm-1. This drop is followed by a gradual increase of 𝐴𝑉
⁄
for higher protein loadings until reaching 𝐴𝑉
⁄=6.5±1.2 µm-1 at the end of the experimental
protein loading range of 4715 Lyz/SiNP.
4.4 Discussion and Outlook
4.4.1 Adsorptions Comparison
The results of the adsorption measurements for LyzFTC on Ludox TMA are compared with
results for native Lyz in Table 4.1. The limiting adsorption 𝛤m of LyzFTC is systematically higher
than for Lyznative and most significant for high pH values (beyond the IEP of Lyz). For lower
pH values the differences are within the error margin of the measurement. Nevertheless, this
can indicate a minor difference in the adsorption behavior of LyzFTC and Lyznative. One possible
explanation for this observation can be found in the manipulated chemical composition of
LyzFTC. The hydrophobic dye could cause the formation of a fraction of dimers adsorbing to the
SiNP and thus increasing the 𝛤m. At low pH conditions Lyz carries a high positive charge.
Hence, the formation of dimers is prohibited by charge stabilization. At pH values close to the
IEP the net charge of Lyz might not be sufficient to stabilize the modified LyzFTC.
The interaction strength of the first strongly adsorbed layer of protein is characterized
by 𝐾S (cf. Chap. 3). The values of 𝐾S for LyzFTC are comparable within the error margin to the
44
Evolution of Hetero-Aggregate Structure at Different Protein Loadings
values of 𝐾𝑆 for Lyznative. Therefore, it is valid to assume the adsorption strength of native and
modified Lyz towards the silica surface to be similar. The third GAB-model parameter, 𝐾L, is
a measure for any further than one adsorbed layer. In both cases, LyzFITC and Lyznative, 𝐾L is
nearly zero. This implies a monolayer adsorption. However, the adsorption of dimers, formed
by bridging between the FTC groups would not show up in this measure, as the dimer adsorbs
as one single particle.
Summarizing the adsorption quantification we see a very similar behavior for LyzFTC
and Lyznative on Ludox TMA SiNP. Significant differences are measurable at pH values higher
than the IEP of the protein. Regarding the FCS/CSLM experiments, which were conducted at
lower pH (pH=9.6) no major differences in adsorption behavior due to the functionalization
with FTC are expected.
4.4.2 Fluorescence Methods
The aggregation behavior on short length scales was investigated by FCS and the results are
summarized in Figure 4.4. The correlation curves obtained by FCS experiments were fitted
assuming two or three diffusing species inside the confocal volume (additionally to free FTC).
One of the species, which was found in all samples, had a hydrodynamic diameter of 33 nm
Figure 4.6: Nominal surface to volume ratio of Lyz/SiNP aggregates for different loading ratios. The concentration
of SiNP in the samples is indicated by the color and the symbol shape. Red diamonds: 1 %; blue triangles: 0.1 %,
green circles: 0.01 %. Surface and volume of the aggregates are analyzed from CLSM scans by the software Fiji.62
The marked data points correspond to the respective 3D graphic in Figure 4.5. This figure is modified from the
Bachelor thesis of Albert Prause.
Discussion and Outlook
45
(Fig. 4.4, red points). This diameter conforms roughly to the diameter of one SiNP with two
adsorbed Lyz. This supports earlier findings of individual particles with adsorbed protein close
to pH 10.31 These clusters are charge stabilized by the negative charge of the central SiNP not
compensated by the adsorbed Lyz.
A second population of larger objects is detectable in the FCS data from Lyz/SiNP
samples (Fig. 4.4, blue points). Judging on this, already one Lyz per SiNP is enough to form
larger networks of connected particles. The error bars for these aggregates are large which is
not surprising, as these large aggregates are not spherical and not monodisperse, as CLSM
micrographs show (Fig. 4.5). Of course, such an irregular population of objects is expected to
produce a broad distribution in the diffusion times leading to a large uncertainty in the
calculated sizes. FCS is not suited for the analysis of irregular aggregates, further information
is obtained with CLSM.
Comparing the number ratios of the small and large species in the confocal volume
(Fig. 4.4) it seems that the small particles are the majority. But this a mathematical artifact, as
one large aggregate, consisting of thousands of SiNP, is counted as one single diffusing particle.
A more useful value is the mass fraction but a conversion is not possible as the exact volume
of the large aggregates is not precisely known.
For a better understand the structure and its evolution with increasing protein loading a
3D images were reconstructed from stacks of 2D CLSM micrographs. In order to investigate a
broad range of protein loadings the samples were prepared with different initial particle
concentrations. Therefore, the overall amount of aggregates is different between some of the
samples. For a comparable analysis of the 3D structures the surface-area-to-volume ratio 𝐴𝑉
⁄
was calculated using Equation 4.1. The results of this analysis are displayed in figure 4.6 as a
function of the nominal protein loading Lyz/SiNP. A plot of 𝐴𝑉
⁄ versus a mutual Lyz/SiNP
axis shows a general trend and merges together without further normalization. This is an
indication for the applicability of this analysis. A low 𝐴𝑉
⁄ for a given volume of aggregates is
expected for spherical and large structures. When the aggregates are small or show an irregular
network structure 𝐴𝑉
⁄ increases.
The effect of sedimentation was evaluated by analyzing the 𝐴𝑉
⁄ for the upper and lower
half of one sample (377 Lyz/SiNP, Fig. 4.5d). The calculation resulted in 𝐴𝑉
⁄=4 for the
upper half, compared to 𝐴𝑉
⁄=3 for the lower half of the sample. This result is expected, as
the larger and most compact aggregates (with a lower 𝐴𝑉
⁄) should sediment faster than the
smaller branched ones. Nevertheless, the found differences are nearly within the error margin
of the used method. Therefore, the effect of sedimentation is not further discussed in this study.
Final results of 𝐴𝑉
⁄ analysis are displayed in Figure 4.6, following the evolution of the
aggregate structure as a function Lyz loading. At low Lyz loadings (Lyz/SiNP < 10) the 𝐴𝑉
⁄
remains constant on a high value. The aggregates found in this regime are compact in shape.
Beginning with Lyz/SiNP = 10 the 𝐴𝑉
⁄ drops, first slightly then sharply, until a minimum at
46
Evolution of Hetero-Aggregate Structure at Different Protein Loadings
protein loadings around the monolayer capacity of Lyz/SiNP = 170. This implies that the
aggregates become denser and more compact. It is interesting, that the start of the drop in
Figure 4.6 coincides with the appearance of larger objects in the FCS results (Fig. 4.4). The
SiNP repel each other because the negative charges on the particles are not fully compensated
by the adsorbed Lyz. This results in a sponge-like network structure. At loadings beyond the
monolayer capacity 𝐴𝑉
⁄ increases again until the end of the experimental Lyz/SiNP range, the
network structure breaks up into smaller and more compact parts. The excess of Lyz in the
system lead to charge compensation of the SiNP, even though the single Lyz are only weakly
charged at this pH. The network structure contracts and reduces its external surface.
These results are comparable with earlier findings for pH titrations by Bharti et al. This
is unsurprising as both effects (pH and Lyz concentration) relay on the same influence factors:
Residual charge on the SiNP. During a pH titration the net charge of the aggregates is regulated
by the protonation state of SiNP. In the current experiment a similar effect is achieved by
regulating the charge on the SiNP by the amount of Lyz in the system. This reproducibility
strengthens the assumption that the adsorption of Lyz is dominated by electrostatic forces and
proves that 𝐴𝑉
⁄ is a useful parameter for the analysis of CLSM data.
For future work the analysis of the 3D CLSM data should be extended to the fractal
dimension. This would enhance the comparability and wide spread use of this method even
further.113 The software package used for this analysis includes a method for calculating the 2D
fractal dimension, which can be transferred to 3D fractal dimensions via 𝐷frac, 3D=𝐷frac,2D+
1.114–116 Strictly this approach is limited to particle sizes larger than the experimental resolution.
It would be necessary to compare the results from this method with an independent experiment,
like static light scattering (SLS). Hence, fractal dimensions can be derived from a Porod fit.
However, turbid samples, like Lyz/SiNP, are notoriously difficult to measure with SLS
Figure 4.7: Static light scattering (SLS) profile I(q) for Lyz/SiNP (1 wt% Ludox TMA, 3 mg/mL Lyznative).
Courtesy of Dr. Heinz Amenitsch (TU Graz). The experiment was performed with a flat cell SLS apparatus
capable of measuring turbid samples.64 The blue line represents a Porod fit resulting in a power law of 2.38
indicating a fractal dimension of 2.38.
Discussion and Outlook
47
techniques because their tendency for multiple scattering. The effect of multiple scattering can
be minimized by maintaining a high transmission (T > 0.9) with a small sample cell thickness.
To test the feasibility of this approach one sample was send to Dr. Heinz Amenitsch at the
TU Graz (Fig. 4.7). The custom SLS apparatus at the TU Graz is equipped with a special flat
geometry sample cell with variable thickness. Making it possible to maintain a high
transmission and reduce the influence of multiple scattering. The data was fitted with a Porod
fit resulting in a fractal dimension of 𝐷frac=2.38. This example shows that SLS is a potential
addition to the presented experiments and can contribute to the structure evaluation of Lyz/SiNP
composites.
Introduction
49
Chapter 5 Orientation of Cytochrome c Adsorbed on Silica
Particles
3
5.1 Introduction
In the past decade nanoscience has found its way into numerous biomedical applications, such
as targeted molecular delivery, in-vivo imaging, sensing, and gene therapy.117–119 In all these
application the nanosized particles come in direct contact with the biomolecular environments
containing various proteins. The efficiency and biocompatibility of the functional
nanomaterials is strongly influenced by their interaction and binding with surrounding
proteins.120,121 Hence, developing a fundamental understanding on how proteins interact with
nanoparticles is of eminent importance. The binding of proteins onto nanoparticles is a net result
of convoluted surface and bulk effects, such as electrostatics, van der Waals, hydrophobic, and
steric interactions.120,122,123 The contribution of each force in the surface self-assembly of
protein is governed by physiochemical characteristics of the protein, particle, and surrounding
medium.124 Several recent studies have been focused on developing a better understanding of
these bio-nano interactions. While most of the reports investigate the change in the secondary
structure of proteins upon adsorption,125,126 less attention was paid to the determination of their
spatial orientation on the surface.
Proteins are biopolymers with a highly complex composition and anisotropic shape. The
anisotropic nature of proteins leads to the possibility to bind a substrate in numerous
configurations. However, only a few orientations are thermodynamically favorable.30,42 For
example, cytochrome c forms a macroscopically ordered film when a non-covalent high-
affinity binding occurs between the protein and the substrate. Whereas the film is disordered
when the substrate has sites with variable binding energies.127 These binding characteristics not
only influence the assembly of the protein on surfaces, but also impact its biochemical
properties, including enzymatic activity.40,128,129
The spatial organization of the proteins can be investigated using methods such as,
labelling proteins with probes to determine local surface binding sites,42 and via measuring
protein redox potentials. The labelling of proteins with fluorescent probes significantly alter the
binding energy of the specific site,130 and not all proteins show redox behavior limiting the
practical applicability. Accordingly, complementary methods for determining protein
orientation at surfaces are highly desirable.
3
The work presented in Chapter 5 is a draft of a manuscript which is in preparation and will be submitted for
publication in the near future. J. Meissner, J. Justin, Z. Di, G. H. Findenegg, B. Bharti, in preparation.
50
Orientation of Cytochrome c Adsorbed on Silica Particles
5.2 Materials and Experimental Techniques
In this chapter small angle neutron scattering (SANS) was used to investigate the effect of
surface charge distribution on the orientation of cytochrome c onto silica nanoparticles. The
primary structure of cytochrome c consists of 104 amino acids, two of which are connected to
a heme c group via thioether bonds. The outer shape of the folded cytochrome c protein can be
approximated as an ellipsoid of dimensions 2.6 × 3.0 × 3.2 nm3.131 Silica dispersions were used
as model nanoparticles to study the binding of the protein. The particles were synthesized using
previously reported methods,132,133 and their diameter was fine-tuned by adjusting the reaction
temperature and stirring speed. The physical characteristics of the nanoparticle dispersion
synthesized are provided in Table 5.1 (corresponding SANS profiles in Fig. 5.6).
The shape and size of the protein in D2O without any silica nanoparticles was
determined using SANS. The experimental SANS profiles were measured in the pH range
2 – 11, and were fitted using the form factor of randomly oriented oblate ellipsoids.134 The
SANS intensity curves and the resulting fit values of equatorial (𝐷peq) and axial (𝐷pax) diameters
are displayed in the Appendix (Fig. 5.7). We find that the diameter of cytochrome c remained
constant within the experimental error margin over the studied pH range, with 𝐷peq ~ 3.7 nm
and 𝐷pax ~ 2.1 nm. The observed protein size and its independence on the solution pH is in
agreement with previous reports.135,136 Structural changes between the two redox states of
cytochrome c are small.135,137
The focus of the present study is the determination of the spatial orientation of
cytochrome c on silica nanoparticles. To access information about the orientation of the protein
it is necessary to measure scattering originating from the cytochrome c adsorbed onto silica
nanoparticles. From neutron scattering profiles a lot information about the surface-bound
protein can be obtained, as the contrast of proteins and particles to deuterated water (D2O) is
high (i.e. its neutron scattering length densities are very different). In order to suppress
incoherent scattering from hydrogen to a minimum the nanoparticles dispersions were
synthesized directly in D2O. The experiments were performed on 1 wt% (3.2 wt% for SiNP41)
silica particle dispersions containing a fixed amount of cytochrome c. The amount of
Table 5.1: The particle size, its polydispersity and the experimental volume fraction determined by fitting
experimental SANS profiles of the silica particle dispersions. The curve fitting was performed using the from-
factor of spheres, randomly distributed in D2O, with a log-normal size distribution. The respective SANS intensity
curves I(q) are displayed in Figure 5.6.
Sample
Diameter DSiNP /nm
Polydispersity
Volume fraction
SiNP7
7
0.17
0.0051
SiNP13
13
0.14
0.0051
SiNP41
41
0.13
0.0164
The ‘Raspberry–like’ Form Factor
51
cytochrome c was chosen in such a way that at pH 8.3 basically all protein was adsorbed on the
particles, and no free protein remained in solution. The pH of the dispersion was varied in the
range 2-11, by the addition of minimum amount of 0.1N HCl or 0.1N NaOH. The resulting
SANS profiles were then analyzed using SasView software package.138
5.3 The ‘Raspberry–like’ Form Factor
A SANS profile of a dispersion is obtained by radially averaging the corresponding 2D
scattering pattern. The scattered intensity, 𝐼(𝑞), is related to the shape, size, concentration,
composition and spatial distribution of the scattering objects as139
𝐼(𝑞)=𝑁∆𝜌2𝑃(𝑞)𝑆(𝑞)
(5.1)
where 𝑁 is the number of the scattering objects, ∆𝜌 scattering length density contrast of the
particles against the matrix (here D2O), and q is the scattering vector related to neutron
wavelength (λ) and angle of scattering (θ) as 𝑞=4𝜋𝜆
⁄sin𝜃2
⁄. In Equation 5.1, P(q) and S(q),
respectively, are form factor and structure factor. The form factor, P(q), is a function of particle
shape, and size; and S(q) is the measure of spatial correlation between these particles. For
particle dispersions, the characteristic interparticle separation (center-to-center distance) are
always larger than the single particle diameter, hence the S(q) selectively affects the I(q) at low
scattering vectors. Whereas the P(q) selectively influences the scattering intensity at higher
scattering vectors. In this article, we focus on the model dependent analysis of the form factor
P(q), and ignore contributions from structure factor i.e. S(q) = 1, which have been addressed in
previous reports.32,140
A typical SANS profile obtained for a silica dispersion with 𝐷𝑆 = 7 nm, containing
4.68 mg/mL of cytochrome c at pH 8.3 is shown in Figure 5.1a. The smeared oscillation
observed at q ~ 1 nm-1 is the signature of form factor of silica nanoparticles with adsorbed
protein. The oscillation at q ~ 0.2 nm-1 is the result of structure factor originating from high
concentration of repulsive silica particles in the dispersion. Since we are interested in
determining the orientation of cytochrome c on silica nanospheres, we specifically focus on the
range 0.2 < q < 3 nm-1.
Accessing a detailed picture of nanoscaled structures by the application of scattering
techniques relies on an appropriate form factor model which represents the geometrical
conditions of the sample. In Figure 5.1 three different form factor models representing three
possible scenarios for the assembly of cytochrome c and silica nanoparticles are compared with
an experimental scattering profile. These are: (a) A mixture of non-interacting spheres and
ellipsoids; (b) particles with a uniform shell of discrete thickness, and (c) particles decorated
with individual spherical objects (‘raspberry-like’ particles).
52
Orientation of Cytochrome c Adsorbed on Silica Particles
The composite form factor of a mixture of non-interacting spheres and ellipsoids,
representing the silica NPs and cytochrome c, respectively, is shown in Figure 5.1a. In this case,
the theoretical scattering intensity was calculated by the linear combination of two form factors.
The parameter values used to simulate the scattering profile are given in Table 5.2. As can be
seen in Figure 5.1a, this model prediction of the scattering intensity gives a poor representation
of the experimental scattering profile in the q-range between 0.5 and 1.5 nm-1. This clearly
shows that the model of coexisting independent species is not appropriate for the present
system. Earlier studies have shown that at this pH and protein concentration, cytochrome c is
strongly bound to the surface of the silica nanoparticles.64 Hence the model of independent non-
interacting silica and cytochrome c is unrealistic, and linear combination of the individual form-
factors for spheres and ellipsoids does not reproduce the experimental scattering profile
(Fig. 5.1a).
The model describing the adsorbed protein as a uniform shell around the central silica
particle is shown in Figure 5.1b (parameters in Table 5.2). The details of the analytical
expression used to simulate the core-shell particle scattering profile are provided elsewhere.141
Figure 5.1: (a), (b) and (c): Neutron scattering profiles I(q) of 1 wt% SiNP7 and 4.68 mg/mL cytochrome c in D2O
at pH 8.3 (points). In panel (a), (b) and (c) the solid line represents a simulation of different scenarios based on
the experimental parameters. The inset sketches illustrate the conceptual picture of the model used for the
respective simulation. (a) The silica particles and the protein molecules are modeled as separate, non-interacting
entities. (b): The silica particles are surrounded by an effective shell of proteins with a homogeneous SLD. (c):
Silica particles and protein are modeled as composite consisting of a central silica particle decorated with
individual cytochrome c molecules, each with its individual SLD. The solid red and black lines represent
simulation results for 2 different sizes for the attached cytochrome c. Tabulated simulation parameters are given
in Table 5.2. (d) The sketch depicting the ’raspberry-like’ scattering model used for the simulations in (c).
The ‘Raspberry–like’ Form Factor
53
The fraction of SiNP surface covered with protein was calculated as 𝜙p
a=
(𝑁protein𝐴protein)𝐴SiNP
⁄ where 𝐴protein and 𝐴SiNP are the surface area of protein and SiNP
respectively and 𝑁protein the number of proteins on the surface. As can be observed in
Figure 5.1b, this simple core-shell model fails to represent the scattering intensity variation at
q > 0.5 nm-1, where it underestimates the scattered intensity. One major drawback of the core-
shell model is the assumption of uniform protein layer (shell) formation around the particles,
which ignores the discrete nature of adsorbed protein molecules separated from each other by
the dispersing medium. Moreover, the higher experimental scattering intensity at q > 0.5 nm-1,
is a signature of larger surface area probed by the incident neutrons. This observation is
reminiscent of adsorption of non-ionic surfactants onto silica surface, where similar decrease
in scattering profile indicated the formation of discrete micelles on nanocurved surfaces.142,143
A scattering model accounting for such scatterers was reported by Larson-Smith et al.44
The authors derived an analytical model for interpreting the scattering profiles from Pickering
emulsions as ‘raspberry-like’ particles (RB-model). The model assumes a random distribution
of small particles on a larger central spherical particle (Fig. 5.1d). The form factor of the
raspberry-like particles can be calculated by solving Debye equations.44,144 The net scattering
intensity from a ‘raspberry-like’ particle is given as
Table 5.2: Model parameters of the simulations in Figure 5.1. Simulations were based on the assumption of (a)
individual, non-interacting SiNP and cytochrome c particles; (b) a core-shell particle consisting of a central silica
sphere and a uniform shell of cytochrome c molecules; (c) a central silica sphere decorated with individual
cytochrome c molecules.
Parameter
(a) Individual
scattering spheres
and ellipsoids
(b) Core-shell
model
(c)‘raspberry-like’
particles
𝐷SiNP nm
⁄
7.2
7.2
7.2
PDISiNP −
⁄
0.171
0.171
0.171
𝜑SiNP −
⁄
0.0050
0.0231 )1
0.0050
𝐷protein nm
⁄
𝐷pax=2.4
𝐷peq=3.6
2.4 )2
2.4/3.6
𝜑protein −
⁄
0.0041
0.0041
0.0041
𝑆𝐿𝐷SiNP Å2
⁄
3.48∙10−6
3.48∙10−6
3.48∙10−6
𝑆𝐿𝐷protein Å2
⁄
3.07∙10−6
5.64∙10−6
3.07∙10−6
𝑆𝐿𝐷solvent Å2
⁄
6.09∙10−6
6.09∙10−6
6.09∙10−6
𝜙pa−
⁄)3
- )4
- )4
0.54/0.35
)1 volume fraction of the complete core-shell particle; )2 corresponds to the shell thickness in the core-shell model;
)3 fraction of SiNP surface covered with protein was calculated as 𝜙pa=(𝑁protein𝐴protein)𝐴SiNP
⁄; )4 this parameter is not
necessary in this model
54
Orientation of Cytochrome c Adsorbed on Silica Particles
𝐼(𝑞)=(𝜙s𝑉s∆𝜌s2+𝜙p2𝜙pa2𝑉s
𝜙s∆𝜌p2)𝑃ps(𝑞)+(𝜙p(1−𝜙pa)𝑉p∆𝜌p2)Ψp2(𝑞)
(5.2)
where 𝜙p and 𝜙s are the total volume fraction of protein and silica respectively, 𝜙pa is the
fraction of protein bound to silica surface, 𝑉p and 𝑉s are respective volumes of a cytochrome c
molecule and a silica nanoparticle, ∆𝜌p=|𝜌protein−𝜌D2O|, and ∆𝜌s=|𝜌silica−𝜌D2O| are the
neutron scattering length density contrasts of protein and silica against the dispersing medium
(here D2O); 𝑃ps(𝑞) and 𝛹p2(𝑞) are the form factors of ‘raspberry-like’ particles, and protein
molecules. This model accounts for the scattering from the protein molecules bound to the silica
nanoparticles as well as the unbound protein in the dispersion. In this experimental study, all
parameters of Equation 5.2 are known, except the cytochrome c diameter (𝐷p), and the
fractional surface coverage of the central particle (𝜙pa). Hence, the experimental SANS profiles
of cytochrome c bound to silica nanoparticles can be fitted using the RB-model with only 𝐷p
and 𝜙pa as free parameters.
Analytical simulations of the RB-model using two protein radii and experimental SANS
data for SiNP7 are shown in Figure 5.1c. The simulation with 𝐷p = 2.4 nm represents well the
experimental SANS profile whereas a simulation with 𝐷p = 3.6 nm shows major deviations
from the experimental data around 1 nm-1. The high-q region (q > 0.4 nm-1), which corresponds
to shorter length scales, sensitive to the local orientation of protein, is well reproduced by the
RB-model. This simple example shows the applicability of the RB-model to the present
experimental system of protein bound silica nanospheres. The sensitivity of the RB-model to
small differences in 𝐷p (Fig. 5.1c), offer a unique possibility to precisely determine the radius
of adsorbed proteins.
The SANS experiments were performed for dispersions of SiNP of three different sizes
containing cytochrome c at different pH values. The amount of protein was kept constant for
all silica dispersions. The RB-form factor model was used to fit the experimental SANS profiles
in the pH range 2-11. The corresponding fits for SiNP7, and SiNP13 dispersion containing the
protein are shown in Figure 5.2, and the fits for SiNP41 are shown in the Appendix (Fig. 5.7).
All the parameter values used in the fitting process are provided in Table 5.3 and 5.4 in the
Appendix. As can be seen from Figure 5.2a and 5.2b, the RB-model gives an excellent fit of
the experimental scattering curves. Specifically, the model is able to reproduce the high-q
scattering observed in Porod’s regime, which can be attributed to surface roughness induced by
the adsorbed protein on silica surface. The discrepancies between the model and experimental
scattering at low-q regime can be attributed to the formation of protein bridged silica
aggregates. The aggregation of SiNP is observed only in the pH range 4.5 – 7.0, and greatly
influences the scattering intensity profile at q < 0.6 nm-1. This can also be observed in the
photographs of the samples shown in Figure 5.2c and 5.2d. A detailed study of silica particle
The ‘Raspberry–like’ Form Factor
55
aggregation induced by the adsorption of lysozyme and cytochrome c has been reported
previously.31,32 In addition, a difference in color of the silica-cytochrome c dispersion was
observed at different pH values which can be attributed to the change in the oxidation state of
the iron in the heme c group of the adsorbed cytochrome c.
It is important to note that the protein binds onto the silica surface due to local
electrostatic attraction, and a change in pH modulates these surface charge driven interactions.31
It was previously shown that the amount of cytochrome c bound to the silica surface changes
significantly with change in pH.64 Hence, in the dispersions used for the SANS experiments in
Figure 5.2 not the same fraction of protein was bound to the silica surface. However, the
fractional surface coverage of silica at a given pH can be estimated using protein binding
isotherms (Fig. 5.9, Appendix), which can be compared with the surface coverage values
estimated using RB-model based curve fittings. The fractional silica surface covered with
protein as obtained by RB-model fitting and the estimated coverage from adsorption isotherms
for SiNP7 are shown in Figure 5.3b (data for SiNP13 and SiNP41 are shown in the Appendix
Fig. 5.10). As can be observed, the experimentally calculated silica surface coverage and the
RB-model fit values are in good agreement. This further ascertains the applicability of the
fitting model to this specific experimental dispersion.
The RB-model allows a precise determination of the diameter of protein adsorbed onto
the nanoparticle surface. The apparent diameter (𝐷p) of the adsorbed protein obtained by model
fitting shows a decrease with increasing pH for all three silica particle dispersions. The fit value
of 𝐷p decreases from 3.5 nm in acidic pH to 2.2 nm for neutral and basic pH. In the case of
Figure 5.2: Small angle neutron scattering intensity profiles I(q) for (a) SiNP7 and (b) SiNP13 particles in D2O
with a fixed amount of cytochrome c at different bulk pH values as indicated in the graph. Solid lines represent
fits with the RB-model. Tabulated fit parameter are given in Table 5.3 in the Appendix. The curves are shifted by
a constant factor of 10 for better visualization. The photographs show the samples for (c) SiNP7 and (d) SiNP13
silica particles, as measured in the SANS experiments. Only the sample at pH 4.5 – 7.0 showed pronounced bulk
aggregation, all other dispersions remained stable upon protein addition.
56
Orientation of Cytochrome c Adsorbed on Silica Particles
SiNP7 and SiNP13, the apparent size change begins at pH > 4, and is completed at pH 7.
Whereas in the case of SiNP41, apparent size transition begins at much lower pH (~2), and
completes at pH < 6 (Fig. 5.3a). The average equatorial diameter of the oblate cytochrome c
molecule has been determined by SANS measurements (Fig. 5.7, Appendix), and are
represented by dashed lines in Figure 5.3a. It is important to remember that the diameters of
native unabsorbed cytochrome c were found to be stable over the entire experimental pH range.
A pH induced deformation of the shape of protein is therefore not expected in the adsorbed
state. This assumption is confirmed by Kondo et al.39, where the authors compared CD spectra
of different proteins in their native and adsorbed state and concluded that hard proteins (e.g.
cytochrome c) undergo only minor changes upon adsorption on small silica nanoparticles.
Baring the values for the equatorial and axial diameter of native cytochrome c in mind, it can
be hypothesized that the protein adsorbs onto silica in a ‘head-on’ configuration at low pH, and
a ‘side-on’ state at higher pH values (Fig. 5.3a). This change in configuration of cytochrome c
is in agreement with previous report on the pH driven re-orientation of human carbonic
anhydrase II on silica surface, where the similar effect was observed.42
5.4 Charge Distribution on Cytochrome c
To gain insight into the origin of the reorientation of protein on silica nanoparticles, the pH
induced change in the surface charge distribution on cytochrome c was estimated. Depending
upon the amino acid composition of a protein and their local physiochemical environment, the
ionization state of functional group varies significantly. This results into a non-uniform
distribution of charges on a protein, which further induces a net non-zero dipole moment, 𝜇 , in
the protein. Here the dipole moment was used as a quantitative measure of asymmetry in the
Figure 5.3: (a) Protein diameter as derived from neutron scattering experiments by fitting the scattering intensity
profiles with a form factor model for ‘raspberry-like’ particles. Three different particle sizes were evaluated. All
dispersions show a drop in the diameter of adsorbed cytochrome c with increasing pH. Solid lines indicate the
equatorial (semi-major axis) and axial (semi-minor axis) diameter of native cytochrome c derived from neutron
scattering experiments. (b) Comparison of the fractional surface covered with cytochrome c as obtained from the
RB model fitting of the SANS data (points) with the expected coverage derived from adsorption isotherms (solid
line) for the SiNP7.
Charge Distribution on Cytochrome c
57
surface charge distribution, and was correlated with the pH dependent binding of cytochrome c
on silica nanoparticles.
The atomic coordinates of the solution structure 2GIW66 of cytochrome c in the protein
data base (PDB) were used to perform the calculations. The correct protonation state of
cytochrome c was calculated for each pH with PDB2PQR software tool.67,68 The net dipole
moment was calculated using the vector sum, as71
𝜇 =∑𝑞𝑖(𝑟 𝑖−𝑟 r)
𝑖
(5.3)
where the i-th charge 𝑞𝑖 is at the distance 𝑟𝑖 from a constant reference point 𝑟r. This procedure
neglects any conformational changes of cytochrome c induced by changing the pH.
Electrostatic surface maps of cytochrome c were generated using the software Adaptive
Poisson – Boltzmann Solver75 in combination with the protonation data given by PDB2PQR.
Further details on the procedure are provided in Chapter 2.3.
The calculations performed assisted in the construction of detailed 3D surface
electrostatic maps of the protein at different pH and corresponding dipole moment was
calculated using Equation 5.3. The magnitude of the dipole moment remains nearly constant
around 300 Debye over the entire pH range (Fig. 5.4b). This value is in good agreement with
the experimentally measured dipole moment values for horse heart cytochrome c.145 However,
the orientation of the dipole moment relative to the protein changes greatly with pH (Fig. 5.4a).
The electrostatic surface maps for cytochrome c at different pH are shown in Figure 5.4c, the
viewing perspective is such that imaging plane remains parallel to dipole moment vector. Hence
Figure 5.4: (a) Left ordinate: End-to-end distances of cytochrome c (circles) measured along the dipole moment
axes for different pH values. Each point is an average of at least 6 interatomic distances between the point where
the dipole moment vector intersects the protein surface and the opposite side. (b) Magnitude of the dipole moment
(squares) of cytochrome c as a function of pH. (c) Electrostatic surface maps for the 2GIW structure of
cytochrome c for different pH as indicated below the structure. The dipole moment vector is represented as a line,
with its length proportional to the magnitude of the dipole moment vector. Here the protein is visualized such that
the dipole moment vector remains parallel to the viewing plane.
58
Orientation of Cytochrome c Adsorbed on Silica Particles
the rotation of cytochrome c (Fig. 5.4c), is a signature of the changes in surface charge
distribution patterns. The calculations show a change in the direction of dipole moment vector
at pH 4. This behavior can be rationalized by measuring the end-to-end distance of the
cytochrome c along the direction of dipole moment vector. The variation of this distance with
pH is displayed in Figure 5.4a. The figure clearly shows that the dipole moment for pH < 4 is
oriented parallel to the equatorial axis (longer) of cytochrome c. At higher pH the dipole
moment becomes parallel to the shorter axis of cytochrome c.
5.5 Discussion and Conclusions
Comparing the results of the SANS experiments with the calculations of the dipole moment of
cytochrome c it stands out that the observed changes in the protein orientation are occurring at
similar pH values. This implies a connection between the reduction of 𝐷P and the shift of the
dipole moment of cytochrome c. Since the dipole moment vector points towards the positive
side of separated charges, in the present case this refers to the larger positive patch on
cytochrome c. At low pH the dipole moment points along the semi-major axis thus the protein
molecule is forced to align in a way that the dipole moment points towards the negatively
charged silica surface. For higher the bulk pH the dipole moment reorients along the semi-
minor axis and consequently the orientation of the entire protein relative to the surface will
change accordingly (Fig. 5.5). Such preferential protein binding via its positive patch has been
shown experimentally for human carbonic anhydrase II42 and simulated for lysozyme on
amorphous silica surfaces.43 In all these cases the interaction resulting into the binding of
protein to silica surfaces is primarily electrostatic. Fraaje et al.146 concluded on the basis of total
internal reflection fluorescence microscopy, that the orientation of cytochrome c on a planar
SnO2 electrode (positively charged at pH 4) can be affected by the interfacial potential during
the adsorption process. More complex situation arise when the binding of protein occurs with
hydrophobic or entropy driven interactions which are beyond the scope of the present study.
However, the SANS based experimental methodology of determining the protein orientation on
Figure 5.5: Schematic view of the proposed pH-dependent adsorption behavior for cytochrome c (green ellipsoids)
on silica nanoparticles (yellow spheres). A shift in pH leads to a change in the orientation of the adsorbed
cytochrome c molecule.
Discussion and Conclusions
59
surfaces developed here can be applied to understand non-electrostatic complex bio-nano
interactions, and corresponding effects on the protein functionality.
In conclusions, the equilibrium orientation of ellipsoidal shaped protein, cytochrome c,
on the surface of silica nanoparticles was studied. Small angle neutron scattering technique was
used to determine the local orientation of the protein on silica nanoparticles of 7, 13, and 41 nm
diameter. A ‘raspberry-like’ particle model was used to analyze the experimental scattering
profiles in the pH regime 2 – 11. For all three silica nanoparticle sizes, it was found that at
pH < 4, the protein adsorbs with a ‘head-on’ configuration. Whereas at higher pH values, the
protein reorients on the silica surface with a ‘side-on’ configuration as a preferential binding
state. The experimental observation were interpreted based on the change in the surface charge
distribution on protein molecules. On the basis of electrostatic surface mapping and the
end-to-end distance of cytochrome c along the dipole moment vector, it was concluded that the
observed reorientation of the protein molecule on silica surface is due to the reorganization of
the surface charges on the protein. The experimental findings, and their theoretical
interpretation provide a new methodology of investigating and predicting protein orientations
on nanocurved surfaces. This approach may assist in better understanding of bio-nano
interactions, which would further help in developing new platforms for advanced biomedical
applications.
60
Orientation of Cytochrome c Adsorbed on Silica Particles
5.6 Appendix
5.6.1 Characterization of Silica Particles and Cytochrome c
Figure 5.6: Small angle neutron scattering intensity profiles I(q) for SiNP7, SiNP13 and SiNP41 particles in D2O
without any added of cytochrome c at pH 8.3. Solid lines represent fits with a form factor model accounting for
non-interacting solid spheres. Tabulated fit parameter are given in Table 5.1. The curves are shifted by a constant
factor of 100 for better visualization.
Figure 5.7: (a) Small angle neutron scattering intensity profiles I(q) for cytochrome c in D2O in the absence of
nanoparticles at different bulk pH values as indicated in the graph. Solid lines represent fits with a form factor
model accounting for non-interacting ellipsoid. The curves are shifted by a constant factor of 10 for better
visualization. (b) The resulting fit values for the equatorial and axial axis of the ellipsoidal model for different pH
conditions. The dashed line represent the mean value of the displayed data points.
Appendix
61
Table 5.3: Values of the fixed general parameters used for the RB-model fitting of the SANS intensity curves
Figure 5.2 and 5.8. With the diameter of the silica particle 𝐷SiNP, its polydispersity 𝑠SiNP, volume fractions of silica
𝜑SiNP and cytochrome c 𝜑protein, scattering length densities SLD of silica, solvent and cytochrome c and ∆
parameter accounting for penetration of the central particle by the outer particles.
SiNP7
SiNP13
SiNP41
𝐷SiNP nm
⁄
7.2
12.9
40.8
sSiNP −
⁄
0.17
0.14
0.13
𝜑SiNP −
⁄
0.0051
0.0051
0.0164
𝜑protein −
⁄
0.0041
0.0012
0.0032
𝑆𝐿𝐷SiNP Å2
⁄
3.48∙10−6
𝑆𝐿𝐷solvent Å2
⁄
6.09∙10−6
𝑆𝐿𝐷protein Å2
⁄
2.90∙10−6
∆−
⁄
1.00
5.6.2 Fitting of SANS Data with the RB-model
Figure 5.8: Small angle neutron scattering intensity profiles I(q) for SiNP41 particles in D2O with a fixed amount
of cytochrome c at different bulk pH values as indicated in the graph. The curves are shifted by a constant factor
of 10 for better visualization.
Table 5.4: Best fit values of the open parameters for the RB-model fitting of the SANS intensity curves Figure 5.2
and 5.8 at different pH. The diameter of the adsorbed cytochrome c, 𝐷prot, and the fraction of the nanoparticle
surface covered with protein 𝜑surf, p.
SiNP7
SiNP13
SiNP41
pH
𝐷prot
nm
𝜑surf, p
pH
𝐷prot
nm
𝜑surf, p
pH
𝐷prot
nm
𝜑surf, p
3.0
3.4
0.14
4.0
3.2
0.03
2.3
2.9
0.40
4.5
3.4
0.28
5.0
3.4
0.06
3.3
2.7
0.47
6.5
3.1
0.40
7.0
2.2
0.41
5.3
2.1
0.49
8.3
2.4
0.55
8.3
1.9
0.47
7.3
2.0
0.90
9.6
2.6
0.54
10.0
2.2
0.32
8.3
2.0
0.70
11.3
2.0
0.85
62
Orientation of Cytochrome c Adsorbed on Silica Particles
5.6.3 Adsorption Isotherms and Calculation of Expected Surface Coverage
In order to estimate the surface coverage of cytochrome c on the silica particles during the
SANS measurements a series of adsorption isotherms were collected at different pH conditions.
The results are displayed in Figure 5.9 together with the respective GAB model fits
(cf. Chap. 3), best fit values for GAB parameter are tabulated in Table 5.5. As the GAB
parameter are highly pH dependent the individual values of each sample were interpolated for
the respective pH conditions. Together with the knowledge of the starting concentration of
cytochrome c in the SANS sample it is possible to calculate the adsorbed amount. Fractional
surface coverages are calculated based on the assumption of a side-on footprint of the
cytochrome c molecule. Figure 5.10 shows the fractional surface coverage for the SANS
samples as deduced by the isotherms together with the fitting results by the RB-model. It is
important to compare these values, as this parameter was used to judge about the quality of the
fit. Although, some minor deviations between the expected and the fitted fractional surface
coverage the values are in good agreement.
Figure 5.9: Adsorption isotherms for cytochrome c on silica nanoparticles (Ludox TMA, 𝐷𝑆𝑖𝑁𝑃=27 nm) at
different pH conditions (as indicated in the legend). Solid lines are fits with the GAB model introduced in
Chapter 3. Best fit values are given in Table 5.5. Experiments were performed according to the established
methods, for details see Chapter 3.
Table 5.5: Best fit values of the GAB parameters for the experimental adsorption isotherms in Figure 5.9.
pH
3.1
6.0
8.3
11.2
𝛤m
0.34
0.71
1.52
1.98
𝐾S
16.3
45.1
36.4
28.0
𝐾L
0
0.08
0.10
0
Appendix
63
5.6.4 Instrumental Details SANS
For the SANS experiments presented here two sets of SANS data were used, collected at two
different neutron sources. The data for native cytochrome c and the 40 nm silica particles with
adsorbed cytochrome c were collected at the instrument PAXY at the Laboratoire Léon
Brillouin (LLB) in Saclay (France). During a second beam time, the data for 7 nm and 14 nm
silica particles with adsorbed cytochrome c were collected. These experiments were done at the
KWS 1 instrument at the Forschungsreaktor München II (FRM II) neutron source in Garching,
Germany. The experimental details on the used instrumental setups at the respective instruments
are summarized in Table 5.6.
Figure 5.10: Comparison of the fractional surface coverages as deduced from the adsorption isotherms (Fig 5.9)
and the best fit values from the RB-model from the SANS measurement for (a) SiNP7, (b) SiNP13 and (c) SiNP41.
The points represent the data points form the RB-model, the solid lines are connecting the calculated points from
the adsorption data at the respective pH.
Table 5.6: Best fit values of the GAB parameters for the experimental adsorption isotherms in Figure 5.9.
Setup
K1
K2
K3
Paxy
Wavelength 𝜆 / nm
5.00
5.00
17.00
Collimation length / m
)*
)*
)*
Detector distance / m
1.1
5.0
5.0
Beam size / mm2
10×10
10×10
10×10
KWS 1
Wavelength 𝜆 / nm
4.50
4.50
4.50
Collimation length / m
8.0
20.0
20.0
Detector distance / m
2.0
4.0
20.0
Beam size / mm2
30×30
30×30
30×30
)* At this instrument the collimation length was automatically optimized according to the sample/detector distance.
Introduction
65
Chapter 6 Protein Immobilization in Surface-Functionalized
SBA-15: Predicting the Uptake Capacity from the
Pore Structure
4
6.1 Introduction
Ordered mesoporous silica (OMS) materials have attracted much attention as hosts for the
immobilization and thermal stabilization of enzymes,12–14 and as delivery systems for proteins
and peptides.14–16 Favorable properties of OMS materials include their large internal surface
area combined with high mechanical strength,147 the possibility to adjust the size and
arrangement of the pores, and the ability to modify the surface properties to match the targeted
enzyme.12,16 In addition, recent studies indicate that immobilization at the walls of nanosized
pores can cause enhanced thermal stability and enzymatic activity compared to the free
protein.21–24 This trend has been attributed to the high surface curvature of the pore wall and the
resulting crowded microenvironment of the protein in the pores, which may provide stability
against unfolding.
The protein immobilization capacity of OMS materials depends on their specific pore
volume and pore size distribution.17,148,149 SBA-15 and other materials prepared with block
copolymer surfactants as the structure-directing template exhibit a complex pore structure with
irregular intrawall micro- and mesopores in addition to the regular main channels. The level of
secondary porosity depends on the synthesis temperature, the postsynthesis heat treatment, and
the procedure of template removal. The pore structure of SBA-15 has been studied by state-of-
the-art gas adsorption analysis 150,151 and structure-sensitive methods including small-angle
XRD152–154 and neutron scattering,155 and electron tomography.156 Surface-functionalized
SBA-15 materials prepared by co-condensation of the silica precursor with functional
siloxanes19 can exhibit even higher degrees of structural complexity. In the past, these structural
features have not been taken into account in the assessment of the protein uptake capacity.
Usually it is inferred that the amount of immobilized protein is directly proportional to the
specific pore volume of the sample. However, this assumption is not justified for samples
exhibiting secondary porosity, when part of the pore volume is not accessible for the protein.
It is well-established that the adsorption of conformationally stable (“hard”) proteins
like lysozyme to silica surfaces is dominated by electrostatic interactions.31,32,157 Accordingly,
the protein binding strength and limiting adsorption are strongly dependent on pH and on the
ionic strength of the solution.158–160 Globular proteins can fill the pore space of OMS most
efficiently at a pH corresponding to their isoelectric point (IEP),149,161 because the repulsive
4
Reproduced with permission from J. Meissner, A. Prause, C. Di Tommaso, B. Bharti, G. H. Findenegg, J. Phys.
Chem. C. 2015, 119 (5), 2438. Copyright 2015 American Chemical Society.
http://dx.doi.org/10.1021/jp5096745
66
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
electrostatic interaction between the protein molecules is minimal at this point. Many reports in
the literature suggest that the immobilization capacity of OMS for proteins can be enhanced by
surface-functionalization with acidic or basic groups, to promote stronger electrostatic
interaction between the host and guest.12–15,24,148,162–164 Hence, to promote the adsorption of the
positively charged lysozyme (IEP = 11) the negative charge density of the pore walls can be
increased, either by partial replacement of Si by Al atoms,161 or by surface functionalization
with negatively charged groups.19,24,165
In this chapter we show how the secondary porosity of chemically functionalized
SBA-15 materials can be characterized quantitatively and taken into account in the assessment
of the protein immobilization capacity. Our method for estimating the protein uptake capacity
extends the geometrical model of Sang, Vinu, and Coppens,149 by taking into account the
nonideal pore-size distribution of the matrix. The application of the new predictive tool is
demonstrated by a comparative study of the uptake of the globular protein lysozyme in native
and surface-functionalized SBA-15 materials. Functionalization with propylsulfonic acid was
chosen to find out if the adsorption of the positively charged protein can be enhanced by
increasing the negative surface charge density at the pore walls. Since the surface of protein
molecules exhibits both positively and negatively charged patches, the availability of positive
and negative charges at the pore walls might favor protein binding. In order to probe this
possibility, SBA-15 was functionalized with a zwitterionic sulfobetaine. Zwitterionic coatings
at free surfaces are known to reduce nonspecific adsorption of biomolecules.25,166 It was of
interest to find out if the protein-repellent nature of zwitterionic coatings is preserved in the
confined geometry of nanometer-sized pores, or if the crowded microenvironment in the pores
might even cause enhanced binding of the protein. The broader question about the influence of
surface-functionalization on the thermal stability or enzymatic activity of the immobilized
protein is outside the scope of this article.
6.2 Pore filling Model
A model for estimating the maximum uptake of globular proteins in the cylindrical channels of
OMS materials was presented by Sang, Vinu, and Coppens (SVC).149 This model assumes that
the entire pore volume 𝑣p consists of cylindrical pores of uniform diameter 𝐷. This can be a
good approximation for MCM-41 but not for SBA-15, where secondary (intrawall) porosity
makes a significant contribution to the pore volume (see Section 6.3.2). For materials having a
distribution of pore sizes the SVC model can be generalized by adding up the number of protein
molecules in pores of different sizes. For the maximum amount of protein in the pore space we
obtain (see Appendix)
Pore filling Model
67
𝑛pore=1
𝑁A𝑣prot∫𝜙prot(𝐷)𝑓(𝐷)d𝐷
(6.1)
where 𝑁A is the Avogadro constant and 𝑣prot the volume of a protein molecule; 𝜙prot(𝐷)
represents the protein packing fraction (maximum volume fraction of protein) in pores of
diameter 𝐷, and 𝑓(𝐷)=𝑑𝑣p𝑑𝐷
⁄ is the pore-size distribution function. Following SVC149 we
assume that prolate-shaped proteins like lysozyme are adsorbed side-on to the pore wall, and
we neglect packing effects of molecules in the direction of the pore axis. This is equivalent to
assuming that the protein molecules represent cylinders with 𝑣prot=(𝜋4
⁄)𝜎2𝛿, where 𝜎 and
𝛿 denote the minor and major cross-sectional diameters. The protein packing fraction then
becomes (see Appendix)
𝜙m(𝐷)=𝑁(𝐷)
(𝐷𝜎
⁄)2
(6.2)
where 𝑁(𝐷) is the maximum number of circles (diameter 𝜎 ) that can be accommodated inside
a circle of diameter 𝐷. Depending on the size ratio 𝐷𝜎
⁄ this number is given by
𝑁(𝐷𝜎
⁄)={ 01
𝑁1
𝑁1+1 𝐷𝜎
⁄<1
1<𝐷𝜎
⁄<2
2<𝐷𝜎
⁄<3
3<𝐷𝜎
⁄<4
(6.3)
with149
Figure 6.1: Protein packing fraction 𝜙m in cylindrical pores as a function of the reduced pore diameter 𝐷𝜎
⁄. For
hard protein molecules (diameter 𝜎) only discrete values of 𝑁 are possible (top scale), and sharp changes in 𝜙m
appear at integer values of 𝐷𝜎
⁄, as indicated by the sketched pores, where the red circles represent protein
molecules.
68
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
𝑁1=π(arcsin 𝜎
𝐷−𝜎)−1
(6.4)
Figure 6.1 shows 𝜙m(𝐷) plotted as a function of the reduced pore diameter 𝐷𝜎
⁄. The maximum
number of particles N that can be accommodated in the cross-section of the pore for given 𝐷𝜎
⁄
is also indicated. The steps in 𝜙m(𝐷) at integer values of 𝐷𝜎
⁄ represent the diameters at which
it becomes possible to place one more protein molecule along a pore diameter. When only a
single layer of protein molecules is formed at the pore wall while the pore center remains vacant,
𝜙m(𝐷) becomes a smoothly varying function above 𝐷𝜎
⁄ = 2, with a shallow maximum near
𝐷𝜎
⁄ = 2.5. For lysozyme in the cylindrical pore channels of the present SBA-15 materials, 𝐷𝜎
⁄
is between 2.5 and 3.0, i.e., close to this local maximum in 𝜙m(𝐷), but adsorption into
secondary pores of diameters 𝐷 > 𝜎 will also contribute to the overall protein uptake. Hence a
characterization of the secondary porosity of OMS materials is important for the assessment of
their protein immobilization capacity.
6.3 Results
6.3.1 Functionalized SBA-15 Materials
Three OMS materials were used in this work: native SBA-15, sulfonic-acid functionalized
SBA-15 (SO3-SBA) and zwitterionic functionalized SBA-15 (Zwi-SBA) (see Appendix). The
materials were characterized by powder XRD, nitrogen adsorption, TEM, and TGA. The XRD
profiles (Fig. 6.2a) confirm the 2D-hexagonal pore lattice of the materials and give the lattice
constant 𝑎0 (Table 6.1). The nitrogen sorption isotherms (Fig. 6.2b) exhibit the characteristic
type IV behavior with a H1 hysteresis loop. The pore size distribution of the three samples
(shown as inset in the panels of Fig. 6.2b) exhibits a narrow peak corresponding to the main
Table 6.1: Characterization of Pore Texture of the SBA-15 Materials: Lattice parameter 𝑎0, mesopore diameter
𝐷 (KJS method, adsorption branch), specific surface area 𝑎𝑆 (BET method), single point pore volume 𝑣𝑃
(extrapolation of linear region to 𝑝𝑝0=1
⁄), micropore volume 𝑣Pmicro (t-plot method), mass ratio of functional
organic group to silica 𝑚F𝑚S
⁄ (from TGA), and mean particle diameter 𝐷𝑝𝑎𝑟𝑡 of the samples.
𝑎0
𝐷
𝑎S
𝑣P
𝑣Pmicro
𝑚F𝑚S
⁄
𝐷part
sample
nm
nm
m2/g
cm3/g
cm3/g
-
nm
SBA-15
11.1
7.7
780
0.93
0.05
0
350
SO3-SBA
11.8
8.0
660
0.81
0.02
0.23
120
Zwi-SBA
11.8
8.0
345
0.48
0.02
0.30
300
Results
69
cylindrical channels and different levels of intrawall porosity at the lower end of the mesopore
range.150 The SO3-SBA sample shows, in addition, a satellite peak with pores of 6 – 7 nm next
to the peak of the main 8 nm channels. For this sample the hysteresis loop extends down to
𝑝𝑝0
⁄ = 0.5, reminiscent of the behavior of plugged SBA-15 materials.167 The pronounced
increase of the adsorption isotherm at 𝑝𝑝0
⁄ > 0.9 found for this sample is attributed to
condensation of nitrogen in voids between silica particles. This interparticle pore volume was
neglected in the further analysis. Parameters derived from the nitrogen adsorption isotherm are
included in Table 6.1. The mean particle diameter of the OMS materials, 𝐷part, which is needed
to estimate the protein adsorption at the external surface of the particles, was determined from
TEM images. Values of 𝐷part are also included in Table 6.1. Representative TEM images are
presented in the Appendix.
TGA scans for the three samples are shown in Figure 6.3, and results derived from TGA
are summarized in Table 6.4 of the Appendix. The weight loss of the samples below 100 °C
(5 ± 0.5% for native SBA-15; 9 ± 0.5% for the two functionalized materials) is due to the
evaporation of adsorbed water. The weight loss above 300 °C can be attributed to the
decomposition of the functional organic group and any remaining (nonextracted) template.
From the relative mass of the dry samples below the decomposition step (𝑚𝑆+𝑚𝐹=0.91 at
100 °C) and above this step (𝑚S = 0.74 for SO3-SBA; 𝑚S = 0.69 for Zwi-SBA, at 500 °C) we
obtain the mass ratio of functional organic material to silica, 𝑚F𝑚S
⁄ = 0.23 ± 0.02 (SO3-SBA)
and 0.30 ± 0.02 (Zwi-SBA). These values are consistent with the concentration of functional
siloxane chosen in the synthesis: For SO3-SBA (1 mol% of the silicon atoms added as functional
Figure 6.2: Characterization of the three SBA-15 materials: (a) small-angle powder XRD showing the 10, 11, and
20 Bragg reflections; (b) nitrogen adsorption/desorption isotherms and resulting pore size distribution (inset).
70
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
siloxane) the observed 𝑚F𝑚S
⁄ corresponds to 75% incorporation, for Zwi-SBA (10 mol% of
silicon atoms added as functional siloxane) to 86% incorporation of the functional siloxane.
6.3.2 Analysis of Porosity
The data in Table 6.1 form the basis for a determination of the secondary porosity of the SBA-
15 materials which is needed in our analysis of the protein adsorption. To derive this relation
we focus on a unit cell of the 2D hexagonal pore lattice having unit length in the direction of
the channel axis (see Fig. 6.4). The volume of this unit cell (𝑉cell) is made up of the cylindrical
pore (𝑉P), the functional organic layer that surrounds the pore as a cylindrical shell (𝑉𝐹), and
the silica matrix (𝑉M), that contains the secondary pores. Secondary porosity 𝜀 is defined as the
volume fraction of pores in the matrix. As explained in the Appendix, it can be calculated from
the parameters in Table 6.1 using the relation (Eq. 6.24 in Appendix)
𝜀=𝑣P𝑎𝜌S𝑉a−(1+𝑏)𝑉P
(𝑣P𝑎𝜌S+1)𝑉A−𝑏𝑉P
(6.5)
where 𝑣P is the total specific pore volume as determined by nitrogen adsorption, 𝜌S is the bulk
density of silica, 𝑎=1+𝑚F𝑚S
⁄, and 𝑏=𝑚F𝜌S𝑚S𝜌F
⁄, where 𝜌F represents the density of the
organic film at the pore wall. The volumes 𝑉A and 𝑉P in Equation 6.5 are given by 𝑉A=𝑉cell−
𝑉P, with 𝑉cell=(√32
⁄)𝑎02, and 𝑉P=(𝜋4
⁄)𝐷2. All quantities except the densities 𝜌S and 𝜌F
can be obtained from Table 6.1. For the evaluation of our data we take 𝜌𝑆 = 2.2 g/cm3 and
𝜌F = 1 g/cm3. Once the secondary porosity of the sample is known from Equation 6.5, the
contributions of the cylindrical and the secondary pores to the total specific pore volume𝑣P can
be calculated as (see Appendix)
Figure 6.3: TGA and DTA scans of native SBA-15 (SBA), propylsulfonic acid functionalized SBA-15
(SO3-SBA), and sulfobetaine functionalized SBA-15 (Zwi-SBA).
Results
71
𝑣Pcyl=𝑉𝑃1+𝑏(1−𝜀)
𝑎𝜌S(1−𝜀)𝑉A
(6.6)
𝑣Psec=𝜀
𝑎𝜌S(1−𝜀)
(6.7)
and the corresponding specific volumes of silica matrix and functional organic layer are given
by 𝑣S=1(𝑎𝜌S(1−𝜀))
⁄, and 𝑣F=𝑏𝑎𝜌S
⁄. For native SBA-15 samples, i.e., in the absence of
an organic layer, Equations 6.5 − 6.7 apply with 𝑎 = 1 and 𝑏 = 0. The importance of accounting
for the secondary porosity of SBA-15 materials is illustrated by the fact that a model without
secondary porosity (𝜀 = 0) drastically underestimates the specific pore volume, which in this
case is given by 𝑣𝑃=𝑣Pcyl=(𝑉P𝜌S𝑉A
⁄ ). For our native SBA-15 sample with the parameters 𝑎0
and 𝐷 given in Table 6.1 and 𝜌S = 2.2 g/cm3, this gives 𝑣P = 0.36 cm3/g, i.e., a value much
smaller than the experimental total pore volume (𝑣P = 0.93 cm3/g). A similar discrepancy is
found for SBA-15 samples reported in the literature, including those used by SVC.149 This
implies that the matrix of SBA-15 contains a significant degree of secondary porosity, which
affects the overall specific pore volume in two ways: (i) directly, by increasing the pore volume;
(ii) indirectly, by decreasing the mass of the matrix.
Results of an analysis of the porosity of our samples on the basis of Equations 6.5 − 6.7
are presented in Figure 6.4. The graph in Figure 6.4a shows the total specific pore volume 𝑣P
and the specific volume resulting from the primary cylindrical pores 𝑣Pcyl plotted as a function
Figure 6.4: Pore structure analysis of the three OMS materials: (a) total specific pore volume 𝑣P and volume of
cylindrical pores 𝑣Pcyl vs mass ratio 𝑚F𝑚S
⁄; (b) volume fraction of cylindrical and secondary pores, functional
organic layer, and silica matrix in the three materials vs 𝑚F𝑚S
⁄. The sketch shows a 2D unit cell of OMS with
the cylindrical primary pore (P), the functional organic layer (F), and the silica matrix (M) which contains the
secondary pores.
72
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
of the mass ratio 𝑚F𝑚S
⁄ of the samples. The specific volume of secondary pores (micro- and
mesopores) is given by 𝑣Psec=𝑣P−𝑣Pcyl. For our native SBA-15 we find that secondary pores
make a substantial contribution to the total mesopore volume (𝑣Pcyl = 0.61; 𝑣Psec = 0.27), in
agreement with values reported in the literature.154–156 In the SO3 -SBA sample, secondary pores
also make a substantial contribution (𝑣Pcyl = 0.57; 𝑣Psec = 0.22), while for Zwi-SBA the
contribution of 𝑣Psec is very small (𝑣Pcyl = 0.44; 𝑣Psec = 0.02). The low secondary porosity of
Zwi-SBA conforms with earlier findings168 that surface- functionalized SBA-15 materials
synthesized by the co-condensation route and template removal by solvent extraction exhibit
low secondary porosity. The high value of v p sec found for SO3-SBA is believed to be of a
different origin than in the native SBA-15. It can be attributed to the lower degree of structural
order of this sample, as manifested by the appearance of a satellite peak in the pore-size
distribution (inset in Fig. 6.2b). These somewhat smaller cylindrical pores are believed to
constitute a major part of the secondary porosity of this sample. Figure 6.4b characterizes the
three OMS materials by showing the relative contributions of cylindrical and secondary pores,
organic layer, and silica to the volume of the samples.
Figure 6.5: Adsorption isotherms of lysozyme in SO3-SBA (20 °C) at pH 4.0, 7.0, 9.4, and 10.5, without added
salt (left panels) and in 100 mM NaCl (right panels). The curves represent fits with the Langmuir equation.
Results
73
6.3.3 Lysozyme Adsorption
Adsorption isotherms of lysozyme in the native and surface-functionalized SBA-15 materials
were measured at pH values from 4 to 10.5, without and with added salt (100 mM NaCl). The
isotherms for the sulfonic acid modified material are presented in Figure 6.5. The respective
results for native and zwitterionized SBA-15 are shown in the Appendix. The adsorption
isotherms are of the high-affinity type, reaching a limiting adsorption value at equilibrium
concentrations well below 1 mg/mL. Notable exceptions are the isotherms at pH 4 and those at
pH 10.5 in the presence of salt. All adsorption isotherms can be represented by the Langmuir
equation, from which we extract the parameters limiting adsorption m max and adsorption
equilibrium constant 𝐾. The error in 𝑚max is <5% in most cases (up to 10% at pH 4 and pH 10).
The error in 𝐾 is <20% in most cases but up to 100% for the high-affinity isotherms at high pH.
Numerical values of 𝑚max and 𝐾 for the three systems are given in Table 6.5 of the Appendix.
The influence of surface modification on the adsorption affinity of the protein is
expressed by the Henry’s law adsorption constant 𝐾H=(𝛿𝛤𝛿𝑐
⁄ )c=0=𝐾𝛤m, where 𝛤=
𝑚lyz 𝑎S
⁄ is the adsorption per unit area and 𝛤m=𝑚max 𝑎S
⁄ is the limiting adsorption per unit
area. 𝐾H is a measure of the interaction of isolated adsorbed protein molecules with the surface.
Results for 𝐾H as a function of pH are given in Table 6.2. At pH 4, surface functionalization
Figure 6.6: Limiting specific adsorption m max of lysozyme as a function of pH at two ionic strengths (without
salt and 100 mM NaCl): native SBA-15 (top); SO3 -SBA (middle); Zwi-SBA (bottom).
74
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
with sulfonic acid causes a marked increase of the adsorption affinity 𝐾H of lysozyme relative
to native SBA-15, but the enhancement factor 𝐾H(funct)𝐾H(nat)⁄ decreases with increasing
pH. Functionalization with zwitterionic sulfobetaine shows an opposite trend, namely an
increase of the enhancement factor as pH increases. In all systems the addition of electrolyte
causes some increase of the adsorption affinity at low pH, but a pronounced decrease of the
affinity at high pH. In the presence of electrolyte the maximum adsorption affinity of lysozyme
is not found near its isoelectric point (pH 10.5), but at a lower pH.
The limiting adsorption 𝑚max of lysozyme as a function of pH is presented in Figure 6.6.
In all cases 𝑚max strongly increases with pH, reaching high values at pH 10.5. The limiting
adsorption is also affected by the addition of salt: At low pH a salt-induced increase of 𝑚max is
found, but a salt-induced decrease of 𝑚max is observed at high pH. These trends are parallel to
those observed in the adsorption affinity (Table 6.2).
6.3.4 Protein Immobilization Capacity of the Materials
As shown in Figure 6.6 the highest values of the limiting adsorption of lysozyme are found at
pH 10.5, i.e., near the IEP of the protein. Hence, the values of m max at pH 10.5 (without added
salt) may be taken as the maximum loading for lysozyme in the three OMS materials. Here we
compare these experimental values of 𝑚max with the maximum uptake 𝑚total expected on the
basis of our porefilling model.
For OMS samples with cylindrical pores of nearly uniform size and a distribution of
smaller-sized secondary pores, the expression for the maximum protein uptake in the pore space
per gram of OMS (Eq. 6.1) can be written in the form
𝑚pore=𝐶𝜙m(𝐷)𝑣Pcyl+𝐶∫ 𝜙m(𝐷)𝑓(𝐷) d𝐷
𝐷−𝜗
𝜎
(6.8)
Table 6.2: Henry’s Law constant 𝐾H (adsorption affinity) of lysozyme adsorption on the three OMS materials at
different pH values and two ionic strengths.
sample
𝑐NaCl/mM
pH 4
pH 7
pH 9.4
pH 10.5
SBA-15
0
0.03
2.0
11
39
SO3-SBA
0
1.5
11
52
32
Zwi-SBA
0
0.02
4.5
61
(260)
SBA-15
100
0.10
6.5
5.9
3.1
SO3-SBA
100
2.0
11
23
6
Zwi-SBA
100
0.03
1.5
26
3.6
Results
75
with 𝐶=4𝑀𝑁A𝜋𝜎2𝛿
⁄, where 𝑀𝑊 is the molar mass of the protein. The first term on the right-
hand side of Equation 6.8 represents 𝑚cyl, the specific mass of protein adsorbed in the
cylindrical pores of mean diameter 𝐷. The second term gives 𝑚max, the specific mass of protein
adsorbed in secondary pores. The integral is taken from a pore size corresponding to the
diameter of the protein (𝜎) to a pore size 𝐷−𝜗, where 𝜗 represents the half-width of the
distribution of primary cylindrical pore channels. To apply Equation 6.8 to the present OMS
materials a normalized distribution function 𝑓(𝐷) was derived from the experimental pore size
distribution (inset in the panels in Fig. 6.2b) by subtracting a baseline, to account for multilayer
adsorption.150 The baseline was chosen in such a way that the ratio of pore volumes 𝑣Psec 𝑣Pcyl
⁄
extracted from the pore size distribution conforms to the respective ratio given by Equations 6.6
and 6.7. Details of this procedure are explained in Supporting Information.
An analysis of the uptake capacity of the present SBA-15 materials on the basis of
Equation 6.8 is given in Table 6.3. For lysozyme (𝑀𝑊 = 14.3 kg/mol), using 𝜎 = 3.0 nm,
𝛿 = 4.5 nm, the prefactor in Equation 6.8 becomes 𝐶 = 0.75 g/cm3. Values of the mean pore size
𝐷 and specific pore volumes (𝑣Pcyl and 𝑣Psec) are taken from Sections 6.3.1 and 6.3.2, and the
protein packing function 𝜙m(𝐷) is determined by Equations 6.2 − 6.4. The evaluation of
Equation 6.8 is exemplified for native SBA-15 and SO3-SBA in Figure 6.7. In both cases the
normalized pore size distribution function 𝑓(𝐷) exhibits a sharp peak representing the primary
pore channels (pore sizes 𝐷±𝜗, with 𝜗 ≈ 0.5 nm) and a distribution of smaller secondary
pores. Since the protein packing function 𝜙m(𝐷) for lysozyme (𝜎 = 3 nm) is nearly constant in
the size range of the primary pores, this part of the integral can be replaced by 𝜙m(𝐷)𝑣Pcylas in
Equation 6.8.The protein uptake in secondary pores is evaluated by numerical integration.
Resulting values of 𝑚cyl, 𝑚sec, and the total uptake capacity of pores, 𝑚pore, are given in
Table 6.3.
The amount of protein adsorbed at the outer surface of OMS particles depends on the
size and shape of the particles and can be estimated only in an approximate way. For elongated
cylindrical particles the amount adsorbed at the outer surface is related to the amount adsorbed
inside the pore channels approximately by149
Table 6.3: Uptake Capacity of OMS Materials for Lysozyme (σ = 3 nm) Estimated by Equations 6.8 and 6.9 and
Comparison of the Total Uptake Capacity with the Prediction of the SVC Model. )*
sample
cylindrical
secondary
𝑣Pcyl
𝑚cyl
𝑣Psec
𝑚sec
𝑚pore
𝑚ext
𝑚total
𝑚SVC
SBA-15
0.61
314
0.32
96
410
39
449
517
SO3-SBA
0.57
295
0.24
95
390
106
496
521
Zwi-SBA
0.44
225
0.04
10
235
25
260
271
)* Specific pore volumes in cm3/(g OMS); specific protein uptake in mg/(g OMS).
76
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
𝑚ext
𝑚pore=(𝑎0
𝐷part)2𝑁ext
𝑁1
(6.9)
where 𝐷part is the mean particle diameter (see Table 6.1) and 𝑁ext is the number of protein
molecules that can be accommodated along the external perimeter of the cylindrical particles.
It can be estimated as149 𝑁ext=𝜋[arcsin(𝜎(𝐷part+𝜎)
⁄)]−1. According to Equation 6.9, 𝑚ext
depends strongly on the mean particle diameter, and its contribution to the total protein uptake
becomes important for 𝐷part < 200 nm. Values of 𝑚ext estimated by Equation 6.9 (with 𝑚pore
given by the SVC model) are included in Table 6.3. The error in 𝑚ext (resulting mostly from
the uncertainty in 𝐷part) is estimated to be <20% for native SBA-15 and Zwi-SBA, and <40%
for SO3-SBA. For this latter sample the uncertainty in the estimated total uptake 𝑚total=
𝑚pore+𝑚ext is dominated by the uncertainty of 𝑚ext.
Values of 𝑚total estimated by Equation 6.8 and 6.9 are given in Table 6.3 and compared
with the respective values obtained by the SVC model, in which the uptake in the pores is
estimated as 𝑚pore=𝐶𝜙m(𝐷)𝑣p. Figure 6.8 compares the predicted uptake capacity with the
experimental limiting uptake of lysozyme in the three OMS materials at pH 10.5. The uptake
capacity estimated by the SVC model is also shown for comparison.
Figure 6.7: Determination of the protein uptake capacity from the normalized pore size distribution 𝑓(𝐷) and the
protein packing fraction function 𝜙m(𝐷) for lysozyme in native SBA-15 (upper graph); SO3-SBA (lower graph).
The parts of 𝑓(𝐷) which contribute to the protein uptake are color-coded.
Discussion
77
6.4 Discussion
6.4.1 Protein Uptake Capacity
Figure 6.8 shows that the new model gives lower values of the protein uptake than the SVC
model, providing a better prediction of the experimental maximum uptake of lysozyme in the
OMS materials. For native SBA-15, where the uncertainty in m total caused by adsorption at
the external surface is small (<1%), the value of mtotal estimated by Equations 6.8 and 6.9 is
still about 15% higher than the experimental maximum uptake. This may be due to an
overestimate of the protein uptake in secondary pores as a result of using an incorrect
normalization of the PSD (cf. Fig. 6.7a and Appendix). The SVC model overestimates the
uptake capacity of native SBA-15 by more than 30%, as it assumes that the total pore volume
is fully accessible to the protein. For SO3-SBA the new model predicts the experimental
maximum uptake very well. The contribution of 𝑚sec to the total uptake is again rather high
(Table 6.3). Figure 6.7b shows that in this case most of the secondary porosity comes from the
satellite peak in the pore size distribution and a significant part of these pores have diameters
𝐷 > 2 𝜎 and allow for a high protein packing fraction. Accordingly, the SVC model gives a
better prediction of the uptake capacity of this sample than for native SBA-15 (Fig. 6.8). For
Zwi-SBA the experimental maximum uptake 𝑚max in the presence of salt (100 mM) agrees
with the predicted total uptake capacity 𝑚total, but the value of 𝑚max in the absence of salt is
significantly higher (Fig. 6.8). This disagreement might be due to an error in the experimental
pore volume of Zwi-SBA (cf. Table 6.1) and thus to a wrong prediction of 𝑚total. More likely,
the disagreement is caused by errors in the experimental adsorption isotherm at pH 10.5 in the
absence of salt (see Fig. 6.11 in the Appendix) which also lead to an exceedingly high value of
𝐾H (see Table 6.2). Unfortunately, we could not resolve this question by repeat measurements
due to a lack of sample material.
The analysis presented above confirms the widely accepted view that native SBA-15
materials prepared by the classical protocol,18 and using calcination for template removal,
contain a high level of wall porosity.150,154–156 Since a large part of these pores are too small for
the protein to enter, the SVC model overestimates the uptake capacity of classical SBA-15
materials. In the work of SVC,149 materials of mean pore diameter from 7.6 to 15 nm were
obtained by microwave-assisted hydro-thermal aging at temperatures from 100 to 240 ° C. It is
well-known that aging at high temperatures (>100 °C) leads not only to an increase in size of
the primary pores of SBA-15, but also to the disappearance of microporosity and formation of
secondary pores bridging the primary pores, so that the materials transform to a 3D mesopore
system.169 The temperature-induced transformation of narrow to wider secondary pores
78
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
explains why the lysozyme uptake in these samples was found to conform to the original SVC
model.149
Our functionalized SBA-15 materials both have a very low micropore volume, possibly
due to incomplete removal of PEO chains of the template which protrude into the pore
walls.150,169 The structurally well-ordered Zwi-SBA also has a very low level of secondary
mesoporosity, so that the protein uptake capacity is determined almost solely by the volume of
cylindrical pores, as in the SVC model. The structurally less ordered SO3-SBA material
contains a high proportion of disordered pores in a size range in which the protein molecules
can pack nearly as well as in the main cylindrical channels (see Fig. 6.7). Accordingly, the
protein uptake capacity estimated by the new model is again not much lower than the SVC
value (see Table 6.3). These results suggest that the SVC model might be better applicable to
functionalized SBA-15 rather than standard native SBA-15 materials, but further work is
needed to confirm this conjecture.
6.4.2 Influence of Surface Functionalization
Table 6.2 shows that surface functionalization with sulfonic acid increases the adsorption
affinity 𝐾H of lysozyme at low pH, when lysozyme molecules are highly charged,31,159 while
the bare silica surface is nearly uncharged.45 Presumably, this is due to the higher negative
surface charge density of SO3-SBA relative to the native silica surface at this low pH. This view
is supported by the observed decrease of the enhancement factor 𝐾H(funct)𝐾H(nat)⁄ with
increasing pH, as the surface charge density of the bare silica surface becomes similar to (or
even higher than) the SO3-functionalized surface. Functionalization with zwitterionic
sulfobetain has little influence on the adsorption affinity of lysozyme at low pH, but causes an
Figure 6.8: Comparison of the experimental maximum uptake of lysozyme by the three OMS materials (pH 10.5
without salt, and with 100 mM NaCl, indicated by the pair of columns) with the estimated uptake capacity of the
pore space (𝑚pore ) and total uptake capacity (𝑚total=𝑚pore+𝑚ext) of the samples (indicated by horizontal bars).
The dashed line indicates the total uptake capacity estimated by the SVC model.
Conclusion
79
enhancement of 𝐾H at higher pH. This indicates that the mechanisms of antifouling action of
zwitterionic groups166 are not effective in strongly confined geometries. Further work is needed
to better understand this interesting finding. The observation that the adsorption affinity 𝐾H
decreases when the ionic strength is increased to 100 mM (Table 6.2) is expected for the ion
exchange mechanism of protein adsorption at charged surfaces.170 This trend is also observed
with Zwi-SBA (though to a lesser extent than with the other substrates), which indicates a
relatively low zwitterion efficiency of Zwi-SBA.166
6.5 Conclusion
This study has shown that the porefilling model introduced in Section 6.2 can form a rational
basis for assessing the protein immobilization capacity of native and surface-functionalized
OMS materials. Whereas in earlier studies of protein immobilization it was assumed that the
entire pore volume 𝑣P is made up of cylindrical pores of uniform size, the new model makes a
distinction between the volume of primary cylindrical pores (𝑣Pcyl) and the pore volume due to
secondary porosity (𝑣Psec), which may or may not be accessible to the protein, depending on the
pore size distribution. We propose a procedure to normalize the experimental pore size
distribution in such a way that the ratio (𝑣Psec 𝑣Pcyl
⁄) determined from the pore size distribution
is consistent with the values of 𝑣Pcyl and 𝑣Psec determined independently from the total specific
pore volume (𝑣P), the diameter of the cylindrical pores (𝐷), the lattice constant of the pore
lattice (𝑎0), and the mass ratio of the organic functional layer and silica matrix (𝑚F𝑚S
⁄). In
Section 6.3.4 it is shown that the amount of protein immobilized in the pores can be estimated
from the normalized pore size distribution 𝑓(𝐷) of the OMS and the packing fraction function
𝜙m(𝐷) of the protein. The new model gives an improved prediction of the uptake capacity for
lysozyme in native SBA-15 by accounting for the uptake capacity of the secondary pores in a
realistic manner. For the two functionalized materials the prediction of the uptake capacity by
the two models is nearly equally good. This can be rationalized by the fact that for one of them
(Zwi-SBA) the secondary pore volume is very small, while for the other material (SO3-SBA)
the secondary pore volume is made up mostly of pores in which the protein can pack nearly as
well as in the primary pores. Finally, we stress that the new model can be applied not only to
OMS materials, but also to the protein uptake in any mesoporous material, if the pore size
distribution of the material is known.
80
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
6.6 Appendix
6.6.1 Preparation of Mesoporous Materials
Chemicals: Pluronic P-123 (EO20PO70EO20 triblockcopolymer), (3-mercaptopropyl)-
trimethoxysilane (MPTMS), (N,N-dimethyl-3-aminopropyl)trimethoxysilane, propane sultone,
hydrogen peroxide (35wt%), hydrochloric acid (analytical grade), sodium hydroxide (≥98%),
NaCl (≥98%), all from Sigma-Aldrich, and tetraethoxysilane (TEOS) from ABCR (≥98%) were
used in the synthesis of the OMS materials or the protein adsorption measurements. Milli-Q
water from MilliPore QPAC was used for all the experiments.
Native SBA-15 was prepared by the method reported by Zhao et al.,18 using Pluronic P123 as
the template and TEOS as the silica precursor. The precipitated composite material was aged at
95 °C for 24 h and calcined in air at 500 °C for 6 h.
Sulfonic-acid functionalized SBA-15 (SO3-SBA) was prepared by co-condensation of the
silica precursor with the thiol-precursor MPTMS, as reported by Margolese et al.19 The molar
composition for 4 g of copolymer was 0.0348TEOS : 0.0062MPTMS : 0.0123H2O2 : 0.24HCl
: 6.7H2O, so that 15 % of the silicon atoms were present in form of the thiol precursor. A TEOS
prehydrolysis time of 45 min prior to the addition of MPTMS and H2O2 was chosen. According
to this protocol,19 quantitative conversion of the thiol to sulfonate groups is achieved when the
oxidant H2O2 is added simultaneously with MPTMS. The reaction mixture was stirred for 20 h
at 40°C and aged for 24 h at 100°C without stirring. The white precipitate was collected, washed
with Milli-Q water and dried at room temperature. The template was then removed by extraction
with ethanol (24 h under reflux).
Zwitterion-functionalized SBA-15 (Zwi-SBA) was prepared by a similar protocol as SO3-
SBA, using 3-(dimethyl(3-(trimethoxysilyl)propyl)-ammonio)propane-1-sulfonate
(abbreviated SBS) as the sulfobetain precursor.170,171 4 g of Pluronic P123 was dissolved in
125 g of 1.9 M hydrochloric acid. After equilibration at 40 C, 7.26 g TEOS were added and
prehydrolyzed under stirring at 40°C for 45 min. 1.21 g of SBS was then added. The molar
composition for 4 g of copolymer was 0.0348TEOS : 0.0037SBS : 0.24HCl : 6.7H2O, so that
10% of the silicon atoms were present in form of the sulfobetaine precursor. The reaction
mixture was stirred for 20 h at 40 °C and aged for 24 h at 100 °C without stirring. The white
precipitate was collected and treated as in the case of the sulfonic acid functionalized material.
The sulfobetaine precursor (SBS) was synthesized as described by Litt et al.171 A solution of
2.23 g of 1,3-propane sultone in 18 mL of dried acetone was prepared and 3.75 g of N,N-
dimethyl-amino-propyl-trimethoxysilane were added in a dry nitrogen atmosphere. The
reaction mixture was stirred at 20 °C for 5 h. The resulting white precipitate was collected and
Appendix
81
washed with acetone, dried and stored in a desiccator under vacuum. Reaction yield was 81%.
The product was characterized by 1H NMR.
6.6.2 Sample Characterization Methods
Transmission electron microscopy (TEM). Images were obtained with a JEM-2100
instrument (JEOL) operating at 200 kV. Cu grids with a carbon film (thickness 20-10 nm,
200 mesh) were used. The images were processed using the ImageJ software.172
Powder XRD with a SAXSess mc2 instrument (Anton Paar) was used to record small-angle
powder XRD profiles of the OMS materials. The instrument was equipped with a slit collimated
Cu Kα X-ray source (0.1542 nm) operated at 40 kV (50 mA). The powder samples were held in
the beam path with adhesive tape. The software package Saxsquant 3.50 was used for data
reduction.
Nitrogen adsorption isotherms at 77 K were determined on a Gemini III 2375 volumetric
surface analyser (Micromeritics). The samples were outgassed at 120 °C for 1h before the
measurement and reweighed in air at ambient humidity conditions afterwards (sample weight
𝑚W). The specific surface area and pore volume of the samples was calculated on the basis of
𝑚W by applying a correction for the water content based on the TGA measurements.
In the analysis of the nitrogen adsorption isotherms the mean diameter of the primary
pores was determined from the inflection point of the pore condensation step by the generalized
KJS relation173 which (unlike the NLDFT method) is applicable to the functionalized as well as
the native SBA-15 materials. The single-point total pore volume 𝑣p was determined by
extrapolation of the linear region in the adsorption isotherm above pore condensation to
𝑝𝑝0=0
⁄. The micropore volume 𝑣p,micro was determined by the t-plot method.
Thermogravimetric analysis (TGA) of the OMS materials was done using a TGA1 STARe
system (MettlerToledo). The heating rate was 10 K/min in the temperature range from 25 to
800 °C.
Figure 6.9: TEM images of the three OMS materials: (a) native SBA-15; (b) SO3-SBA; (c) Zwi-SBA.
82
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
Analysis of TG scan:
𝑚W=𝑚H2O+𝑚F+𝑚S=1
𝑚0=𝑚F+𝑚S
where
𝑚W = unit mass of sample equilibrated in the lab atmosphere
𝑚H2O = relative mass of adsorbed water vapor
𝑚F = relative mass of functional organic layer
𝑚S = relative mass of silica
(6.10)
6.6.3 Calculation of Matrix Porosity
In this section we derive expressions for the specific pore volumes contributed by the ordered
cylindrical pore channels and the disordered secondary pores embedded in the matrix of
SBA-15. (Eq. 6.2 and 6.3). We consider a unit cell of the 2D hexagonal lattice (see Fig. 6.3).
The total volume per unit length of the pore (𝑉cell) is made up of the cylindrical pore (𝑉P), the
functional organic layer that surrounds the pore as a cylindrical shell (𝑉F), and the silica matrix
(𝑉M),
𝑉cell=𝑉P+𝑉F+𝑉M
(6.11)
with
𝑉cell=√3
2𝑎02
(6.12)
Table 6.4: Analysis of TGA dataa)
sample
𝑀F
gmol
⁄
𝑚H2O
𝑚sample
𝑚F
𝑚0
𝑚F
𝑚S
𝑛F𝑚s
⁄
mmolg
⁄
𝑛F𝑎s
⁄
µmolm2
⁄
SBA-15
-
0.05
0
0
0
0
SO3-SBA
123.15
0.09
0.17
0.23
1.9
2.9
Zwi-SBA
209.3
0.09
0.21
0.30
1.4
4.2
a) 𝑀F, molar mass of functional organic group; 𝑚0, mass of dry sample; 𝑚F, mass of functional organic group; 𝑛F,
amount of functional organic groups; 𝑎𝑠 specific surface area of the sample.
Appendix
83
𝑉P=𝜋4𝐷2
(6.13)
In the equations below we also use the volume difference
𝑉A≡𝑉cell−𝑉P=√3
2𝑎02−𝜋4𝐷2
(6.14)
Note that the symbol 𝑉 represents volumes per unit pore length (i.e., areas). The subscripts P,
F, and M refer to the space occupied by the cylindrical pore, the functional layer and the matrix.
The quantities 𝑎0 and 𝐷 represent the lattice parameter and the mean pore diameter as defined
in Figure 6.3.
Native SBA-15. For native (unfunctionalized) SBA-15 silica (𝑉F=0) without any secondary
porosity (“ideal SBA-15”) the mass of a unit cell per unit pore length is given by 𝑀M=𝜌S𝑉M=
𝜌S(𝑉cell−𝑉P), where 𝜌S is the bulk density of silica. The specific pore volume (i.e., volume per
unit mass) of such an ideal sample is
𝑣𝑝id=𝑉𝑃
𝑀𝑀=𝑉𝑃
𝜌𝑆𝑉𝐴
(6.15)
For our native SBA-15 material, with the parameters given in Table 6.1 (𝑎0=11.1 nm, 𝐷=
7.7 nm) and the density of nonporous silica (𝜌S=2.2gcm3
⁄), this gives 𝑣pid=0.36cm3g
⁄,
i.e. drastically smaller than the experimental total specific pore volume of this sample (𝑣p=
0.93cm3g
⁄). Such a large deviation is typical for SBA-15 materials when the template was
removed by calcinations. It implies that in addition to the ordered cylindrical pores the material
must contains pores distributed in the matrix in a random manner. The secondary porosity 𝜀 is
defined as the fraction of matrix volume taken up by these secondary pores. Below we show
how 𝜀 can be calculated from the parameters 𝑎0, 𝐷, and the specific pore volume of the sample,
𝑣𝑝, again with the density of nonporous silica as an additional input parameter.
When a fraction 𝜀 of the silica matrix is taken up by secondary pores, then the mass per
unit cell is 𝑀M=𝜌S(1−𝜀)𝑉M and the specific volume of cylindrical pores becomes
𝑣pcyl=𝑉P
𝜌S(1−𝜀)𝑉A
(6.16)
which is larger by a factor 1(1−𝜀)
⁄ than 𝑣pid (Eq. 6.15). In addition, the secondary porosity
contributes a volume 𝜀𝑉M=𝜀(𝑉cell−𝑉P) per unit cell, i.e., a specific pore volume
𝑣psec=𝜀𝑉A
𝜌S(1−𝜀)𝑉A=𝜀
𝜌S(1−𝜀)
(6.17)
84
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
The total specific pore volume then becomes
𝑣𝑝=𝑣pcyl+𝑣psec
(6.18)
When the quantities 𝑎0, 𝐷, 𝑣𝑝, and 𝜌S are known, the secondary porosity 𝜀 can be calculated
from Equations 6.15 – 6.17
𝜀=𝑣p𝜌S𝑉A−𝑉P
(𝑣p𝜌S+1)𝑉A
(6.19)
with 𝑉P and 𝑉A given by Equations 6.13 and 6.14. The resulting value of 𝜀 can be used to
determine 𝑣pcyl and 𝑣psec by Equations 6.16 and 6.17.
Functionalized SBA-15. The formalism outlined above can be applied to SBA-15 materials
functionalized by an organic layer which forms a cylindrical shell around the pores of mean
diameter 𝐷 (see Fig. 6.3). The unit cell volume 𝑉cell is made up of the volumes 𝑉P, 𝑉F, and 𝑉M
(Eq. 6.11) and the expressions for 𝑉cell, 𝑉𝑃, and 𝑉𝐴 (Eq. 6.12 – 6.14) still apply. 𝑉𝐹 is related to
the volume of silica matrix 𝑉M via the mass ratio of organic film and silica, 𝑚𝐹𝑚𝑆
⁄, and the
respective ratio of mass densities, 𝜌F𝜌S
⁄,
𝑉F=𝑀F
𝜌F=1
𝜌F𝑚F
𝑚S𝑀M=1
𝜌F𝑚F
𝑚S𝜌S(1−𝜀)𝑉M=𝑏(1−𝜀)𝑉M
(6.20)
where 𝑏=𝜌S𝑚F𝜌F𝑚S
⁄. From Equation 6.20, and 𝑉A=𝑉M+𝑉F, we obtain
𝑉M=𝑉A
1+𝑏(1−𝜀)
(6.21)
The mass per unit cell is now given by the contributions of the silica matrix and the organic
layer as
𝑀cell=𝑀M+𝑀F=(1+𝑚F
𝑚S)𝑀𝑀=(1+𝑚F
𝑚S)𝜌S(1−𝜀)𝑉M
=𝑎𝜌S(1−𝜀)𝑉A
1+𝑏(1−𝜀)
(6.22)
where 𝑎=1+𝑚F𝑚S
⁄. As earlier, the specific pore volume is obtained by referring the volume
per unit cell to the mass per unit cell. By analogy with Equation 6.15 we thus obtain
𝑣p=𝑉P+𝜀𝑉M
𝑀M=𝑉P[1+𝑏(1−𝜀)]+𝜀𝑉A
𝑎𝜌S(1−𝜀)𝑉A
(6.23)
This relation can again be used to calculate the secondary porosity 𝜀, for which we find
Appendix
85
𝜀=𝑣p𝑎𝜌S𝑉A−(1+𝑏)𝑉P
(𝑣p𝑎𝜌S+1)𝑉A−𝑏𝑉P
(6.24)
Finally, the specific volumes of ordered cylindrical pores, secondary pores and the functional
organic layer become
𝑣pcyl= 𝑉P
𝑀M=𝑉P1+𝑏(1−𝜀)
𝑎𝜌S(1−𝜀)𝑉A
(6.25)
𝑣psec=𝜀𝑉M
𝑀M=𝜀
𝑎𝜌S(1−𝜀)
(6.26)
𝑣F=𝑉F
𝑀M=𝑏
𝑎𝜌S
(6.27)
𝑣M=𝑉M
𝑀M=1
𝑎𝜌S(1−𝜀)
(6.28)
The volumes 𝑣pcyl, 𝑣psec, 𝑣F, and 𝑣M add up to the total volume per unit mass of the sample.
By normalization to this specific sample volume we obtain the corresponding volume fractions
of cylindrical and secondary pores, functional organic layer and silica matrix, which are shown
in graphical form in Figure 6.3.
6.6.4 Normalized Pore Size Distribution Function
To estimate the protein uptake capacity by Equation 6.8, we need to determine the normalized
pore size distribution 𝑓(𝐷) of the OMS materials. Starting from the pore size distribution (PSD)
as obtained by nitrogen adsorption, the determination of 𝑓(𝐷) involves two steps: (1) Setting
the borderline between primary cylindrical pores and secondary pores at a pore size 𝐷−𝜗,
where 𝐷 is the mean pore diameter of the cylindrical pores and 𝜗 the half width of the main
peak in the psd.19 And (2) applying a correction to the PSD to account for multilayer adsorption
of nitrogen in the primary pore channels and at the external surface of the particles.150 This is
achieved by subtracting a baseline from the experimental PSD. This baseline is higher at pore
diameters 𝐷<𝐷 than at 𝐷>𝐷, because multilayer adsorption in the primary pores contributes
only at 𝐷<𝐷. The position of the baseline in this regime was determined using the criterion
that the ratio of secondary to primary pore volume determined by integration of the two regimes
86
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
of the normalized PSD must be equal to 𝑣psec 𝑣pcyl
⁄ as determined by Equations 6.25 and 6.26.
Since 𝑣psec represents the total secondary pore volume (including micropores) while the
experimental PSD covers only the mesopore range (𝐷>2 nm) a correction to include the
micropore volume was applied as follows: Using the symbols 𝑉cyl and 𝑉meso
sec for the volume of
cylindrical and secondary pores resulting from the integration of the normalized PSD in the
mesopore range, and 𝑉meso=𝑉cyl+𝑉meso
sec for the respective overall mesopore volume, the
corresponding total pore volume (including micropores), 𝑉total, is estimated from the
experimental specific pore volume 𝑣𝑝 and the specific mesopore volume of the sample,
𝑣p,meso=𝑣p−𝑣p,micro, as
𝑉total=𝑣𝑝
𝑣p,meso𝑉meso
(6.29)
and the overall secondary pore volume (including micropores) is
𝑉sec=𝑉total−𝑉cyl
(6.30)
Hence the criterion for the baseline of the PSD at 𝐷<𝐷 is
Figure 6.10: Determination of the normalized pore size distribution function 𝑓(𝐷) by subtraction of a background
from the PSD raw data (see text): (a) native SBA-15; (b) SO3-SBA.
Appendix
87
𝑉sec
𝑉cyl=𝑣psec
𝑣pcyl
(6.31)
Figure 6.10 illustrates the baseline correction of the PSD for native SBA-15 and SO3-SBA. In
the case of native SBA-15 the procedure outlined above can be applied in a straightforward
way. For the less well-ordered sample of SO3-SBA it was not possible to meet the criterion of
Equation 6.31 with a constant baseline, as this always leads to a ratio 𝑉sec 𝑉cyl
⁄ greater than the
experimental value. In order to meet the criterion of Equation 6.31 for this system it had to be
assumed that the baseline increases toward the lower limit of the mesopore range. This leads to
a low level of pore sizes near the lower limit of the mesopore range, which is in line with the
low micropore volume of this sample (see Fig. 6.4b). Since for lysozyme only pores of diameter
>3 nm are accessible, the pore size distribution of smaller pores is of no relevance. Nevertheless,
a reliable determination of the normalized PSD remains a challenge for future work.
6.6.5 Protein Adsorption Measurements
Lysozyme from chicken egg white (lyophilized powder, protein ≥90%, ≥40.000 units/mg
protein) was received from Sigma-Aldrich (lot 061M1329 V) and stored at −30 °C. Adsorption
isotherms of lysozyme onto the OMS materials were determined in unbuffered solutions at
controlled pH in the absence and presence of salt (100 mM NaCl). For each set of experiments,
stock solutions of lysozyme (10 mg/mL), NaCl (300 mM), and OMS (20 mg/mL) were freshly
prepared in water at the desired pH by addition of known aliquots of HCl or NaOH. Samples
with 1.5−15 mg protein were prepared from the protein and salt stocks, and 0.5 mL of the stirred
OMS stock was added to reach the sample volume of 3 mL. The samples were equilibrated at
20 °C for 20 h in a closed vial, using a Thermomixer. After readjustment of the pH the silica
was separated from the supernatant by centrifugation at 15.000 rpm for 45 min, and the residual
concentration of protein in the supernatant was determined by UV-vis spectrometry. The spectra
of the samples were compared with a concentration standard at several wavelengths in the 265-
300 nm range, and the concentration was obtained by minimizing the variance of the deviations
from this concentration standard. The amount of adsorbed protein was calculated by a mass
balance. A correction for adsorbed water was applied to the weight 𝑚0 of all samples
equilibrated in the laboratory atmosphere, on the basis of the water weight loss of the three
materials found by TGA. In preliminary experiments it was found that the adsorption
equilibrium of lysozyme in the OMS materials was established on a time scale of a few hours,
even at a pH near the IEP. Hence, the lysozyme uptake after 20 h was taken as the equilibrium
adsorbed amount.
88
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
6.6.6 Adsorption Data and Langmuir Fits for Lysozyme in the OMS Materials
Adsorption isotherms for lysozyme in native SBA-15 and Zwi-SBA-15 at pH from 4 to 10.5 in
the absence and presence of salt are shown in Figure 6.11 and 6.12.
The adsorption data can be represented within experimental error limits by the Langmuir
equation,
𝑚Lyz=𝑚max 𝐾𝑐
1+𝐾𝑐
(6.32)
where 𝑚Lyz is the mass of adsorbed lysozyme per unit mass of the sample, and 𝑐 is the
equilibrium concentration of protein in the supernatant solution. The parameters 𝑚max (limiting
adsorption per unit mass) and 𝐾 (Langmuir adsorption constant) were determined from the
Langmuir equation in the form
𝑐
𝑚Lyz=1
𝑚max𝐾+𝑐
𝑚max
(6.33)
The resulting values of the parameters 𝑚max and 𝐾 are given in Table 6.5. The adsorption
affinity (Henry’s law adsorption constant 𝐾H) represents the initial slope of the adsorption
isotherm and is related to these parameters as 𝐾H=𝐾𝑚max.
Figure 6.11: Adsorption isotherms of lysozyme in native SBA-15 at four different pH values in the absence of
salt (left panels) and with 100 mM NaCl (right panels).
Appendix
89
6.6.7 Protein pore filling model
To relate the protein uptake into OMS to the specific pore volume of the sample we generalize
the geometric model of Sang, Vinu and Coppens (SVC)149 to the situation of materials having
a distribution of pore sizes. In the SVC model the maximum amount of protein that can be
accommodated in pores of cross-sectional area 𝐴p=(𝜋4
⁄)𝐷2 is given by
𝑛max=𝑁
𝑁A𝐴p𝛿prot𝑣p
(6.34)
where 𝑁 is the number of molecules that can be accommodated side-by-side in a cross-section
of the pore, 𝑁A is the Avogadro constant, 𝛿prot is the longest dimension of a protein molecule,
and 𝑣p is the specific pore volume of the sample. In Equation 6.34 the factor 𝑁𝐴p
⁄𝛿 represents
the number of protein molecules in a volume element of length 𝛿prot of the pore. The volume
fraction of protein in this element is then
𝜑m=𝑁𝑣prot
(𝜋4
⁄)𝐷2𝛿prot
(6.35)
Figure 6.12: Adsorption isotherms of lysozyme in Zwi-SBA-15 at four different pH values in the absence of salt
(left panels) and with 100 mM NaCl (right panels).
90
Protein Immobilization in Surface-Functionalized SBA-15: Predicting the Uptake Capacity from the
Pore Structure
where 𝑣prot is the volume of a protein molecule. Equation 6.35 is strictly a 2D model of protein
packing without consideration of packing effects in the direction of the pore axis. Elongated
protein molecules are treated as cylinders of diameter 𝜎 and length 𝛿prot, so that 𝑣prot=
(𝜋4
⁄)𝜎2𝛿. Inserting this into Equation 6.35 and combining with 6.34 gives
𝑛max=4
𝑁A𝜋𝜎2𝛿prot𝜑m𝑣p
(6.36)
with
𝜑m=𝑁
(𝐷𝜎
⁄)2
(6.37)
For a sample containing cylindrical pores of different diameters 𝐷, Equation 6.36 can be
generalized by introducing the pore size distribution function 𝑓(𝐷)=(𝑑𝑣p𝑑𝐷
⁄)D
𝑛max=4
𝑁A𝜋𝜎2𝛿prot∫𝜑m(𝐷)𝑓(𝐷)d𝐷
(6.38)
where the integral extends over the relevant pore sizes.
Table 6.5: Langmuir parameters for lysozyme adsorbed in the OMS materials at four different pH values without
added salt and in 100 mM NaCl.
without salt
100 mM NaCl
System
pH
𝑚max
mg/g
𝐾
mLmg
⁄
𝑚max
mg/g
𝐾
mL mg
⁄
SBA-15
4.0
31
0.70
113
0.70
7.0
210
7.4
281
18
9.4
257
35
272
17
10.5
386
78
333
7.2
SO3-SBA
4.0
61
16
145*
9.0*
7.0
252
29
303
25
9.4
345
100
345
45
10.5
489
43
453
8.7
Zwi-SBA
4.0
11
0.77
66
0.16
7.0
211
7.4
186
2.9
9.4
225
93
188
48
10.5
343
265
249
5.0
* Values for 50 mM NaCl
Appendix
91
Pore size dependence of the protein packing factor 𝛗𝐦. In the approximation underlying the
SVC model150 the determination of 𝑁 as a function of the reduced pore diameter 𝐷𝜎
⁄ (Eq. 6.37)
becomes equivalent to calculating the number of circular objects (diameter 𝜎) that can be
arranged in a series of non-overlapping concentric rings (‘layers’) of width 𝜎 and outer diameter
𝑑𝑛=𝐷−2(𝑛−1)𝜎. Treating the number of objects 𝑁𝑛 in layer 𝑛 as a continuous variable it
becomes
𝑁𝑛=𝜋(arcsin 𝜎
𝑑𝑛−𝜎)−1
(6.39)
For the outermost layer (𝑛=1), 𝑑1 represents the pore diameter 𝐷. A second layer (𝑛=2) with
𝑑2=𝐷−2𝜎 can form when 𝐷≥4𝜎. Generally, a maximum of 𝑚 layers can form when
2𝑚𝜎<𝐷<(2𝑚+1)𝜎, and the total number of molecules becomes
𝑁𝑚=𝜋∑(arcsin 𝜎
𝐷−(2𝑛−1)𝜎)−1
𝑚
𝑛=1
(6.40)
If the pore diameter is in the range (2𝑚+1)𝜎<𝐷<2(𝑚+1)𝜎, a further particle fits in at
the center of the pore, so that the total number of particle becomes 𝑁𝑚+1. For 𝑚=1 this is
the situation when 𝐷 is between 3𝜎 and 4𝜎. Here, 6 particles form the outer layer in contact
with the pore wall and one further particle is near the center of the pore.
As mentioned above, the approximation for calculating 𝑁 as a function of 𝐷𝜎
⁄ assumes
that the protein molecules are arranged in non-overlapping concentric rings. Accordingly, the
limiting value of 𝜑𝑚 for large 𝐷𝜎
⁄ calculated with this relation is lower than the packing
fraction of a 2D hexagonal lattice, which is 𝜑2D=𝜋2√3
⁄≈0.907.
Introduction
93
Chapter 7 Secondary Confinement of Water Observed in
Eutectic Melting of Aqueous Salt Systems in
Nanopores
5
7.1 Introduction
Phase transitions at the nanoscale, such as the condensation of vapors or the freezing of liquids
in narrow pores, are of fundamental interest for the understanding of competing interactions in
strongly confined systems.174–176 Systems of interest cover a wide variety of host materials of
well-defined pore geometry, such as graphene nanocapillaries,177 metal-organic frameworks,178
cryo-cooled protein crystals,179 zeolites,180 and ordered mesoporous silica.181–183 Water confined
in the cylindrical pore channels of MCM-41 or SBA-15 silica exhibits a large freezing point
depression, increasing with decreasing pore diameter. Water molecules at the pore wall are
strongly interacting with surface silanol groups and do not participate in this phase transition.
The density of water in the central part of the pore strongly decreases below the normal freezing
temperature. Accordingly, the density increment of the solid/liquid transition becomes quite
small in pores of diameter less than 3.5 nm,184 and freezing/melting as a first-order phase
transition disappears below a pore diameter of ca. 2.5 nm.185,186
In contrast with the extensive work devoted to pure water, little attention has been paid
to phase transitions of aqueous solutions in pores. Aqueous salt systems are of particular
interest, since the nature and range of the dominating interactions are strongly dependent on the
salt concentration, and because the two components undergo different processes at the
solid/liquid transition: while water is melting, the salt dissolves in ionic form and thus requires
the presence of liquid water. In addition, novel volumetric effects may come into play with salts
crystallizing in form of hydrates, which may take up significantly more space in the pores than
anhydrous salts. Generally, a shift of the solid/liquid phase transition of salt solutions in pores
occurs as a combination of confinement and colligative187 effects (see Fig. 7.1): The melting
temperature of pure water in the pores is shifted by an increment ∆𝑇p0=𝑇0−𝑇p0 that depends
on the pore diameter 𝐷 (Fig. 7.1a). When salt is added, the freezing point of water is lowered
proportional to the salt concentration (liquidus line L in Fig. 7.1b). The liquidus line of ice and
the solubility line of the salt intersect at the eutectic point (temperature 𝑇E, salt molality 𝑚E).
The eutectic temperature in the pore, 𝑇E,p, is shifted against the bulk eutectic temperature by an
increment ∆𝑇p=𝑇E−𝑇E,p.
In this work we determined ∆𝑇p for several aqueous alkali halide systems in the pore
channels of SBA-15 and MCM-41 materials. At the eutectic point some of these salts crystallize
5
Reproduced with permission from J. Meissner, A. Prause, G. H. Findenegg, J. Phys. Chem. Lett. 2016, 7 (10),
1816. Copyright 2016 American Chemical Society.
http://dx.doi.org/10.1021/acs.jpclett.6b00756
94
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
as oligohydrates, others in anhydrous form. We find a remarkable increase of ∆𝑇p with the
fraction of volume occupied by salt in the solid eutectic mixture. We attribute this effect to a
stronger confinement of water/ice in the pores due to the precipitated salt. To the best of our
knowledge such an effect, which we call secondary confinement (as distinct from confinement
in pristine pores), has not been reported previously.
7.2 Results and Discussion
Well-characterized SBA-15 and MCM-41 silica materials, designated as SBA-A (𝐷=7.1 nm),
SBA-B (8.5 nm) and MCM (4.4 nm) were used in this study (see Appendix). For the DSC
measurements the materials were overfilled with salt solution, such that about 25 percent of the
solution was confined in the pores and a threefold excess remained unconfined (external
reservoir; Fig. 7.1c). No salt exclusion from the pores is expected at the present high salt
concentrations, at which the Debye length 𝜆D is typically 0.1 nm and the condition 𝐷𝜆D
⁄≫
1 applies for all samples studied.188 Figure 7.1a shows the DSC cooling/heating scan of a
10 wt% NaCl solution in SBA-A. The endothermic peaks on the heating scan result from
eutectic melting in the pores (𝑃) and from eutectic melting (𝐸) and melting of ice along the
liquidus line (𝐿) in the external reservoir. The corresponding exothermic peaks on the cooling
scan are labeled as 𝑃f, 𝐸f and 𝐿f. Here we focus on the results from the heating scans which
yield phase transition temperatures close to thermodynamic equilibrium. A phase diagram
Figure 7.1: (a) Sketch of melting temperature vs. pore diameter 𝐷 for pure water; (b) melting lines and eutectic
temperature of salt solution in bulk and in a pore of diameter 𝐷; (c) aqueous eutectic mixture in pores and external
reservoir for three temperature ranges of a cooling scan: (1) between the freezing temperature of pure water (𝑇0)
and the bulk eutectic temperature (𝑇E); (2) between 𝑇E and the pore eutectic temperature (𝑇E,p); (3) below 𝑇E,p.
Note that the external reservoir has a thickness in the µm range while the pore width is in the nm size range.
Results and Discussion
95
derived from samples with salt concentrations up to the eutectic composition is shown in
Figure 7.2b. Notably, no pore freezing/melting liquidus line (𝐿pore in Fig. 7.1b) is observed in
the cooling/heating scans. The absence of this transition in the pores is a signature of overfilled
samples and can be rationalized from the sample geometry (Fig. 7.1c): During cooling,
precipitation of ice in the reservoir causes a gradual increase of the salt concentration in the
external solution and in the pores, since the salt concentration in the pores can equilibrate with
the reservoir down to the (undercooled) eutectic freezing temperature of the reservoir. At this
temperature the pore liquid of all samples has attained the eutectic composition, irrespective of
their initial composition, and only eutectic freezing/melting occurs in the pores. DSC
cooling/heating scans reveal that the hysteresis of the eutectic phase transition in the pores (𝑃
vs. 𝑃f) is weaker than in the external sample, suggesting that the transition in the pores is
nucleated by the external solid:182: As sketched in Figure 7.1c, ice bulges into the pore entrance
at 𝑇<𝑇E and propagates into the pore at the temperature at which the thermodynamic Gibbs-
Thomson equation is fulfilled for the diameter of the pore entrance.186,189Salt nano-crystals will
precipitate from the oversaturated solution in the region next to the ice front and may
accumulate near the pore walls as the ice front moves ahead (Fig. 7.1c).
We now turn to a comparison of the confinement-induced shift of the eutectic
temperature, ∆𝑇𝑝=𝑇E−𝑇E.p, for a series of alkali halides. Eutectic pore melting peaks for
NaCl, KCl, RbCl and CsCl in SBA-A are shown in Figure 7.3a, where for each salt the
temperature scale is normalized to the onset of the bulk eutectic melting peak. Also shown is
the pore melting peak of pure water normalized to the melting peak of bulk water. Note that
∆𝑇p can be greater or smaller than ∆𝑇p0, the melting point depression of pure water. The highest
∆𝑇p value in this series of alkali chlorides is found for NaCl, the salt that crystallizes in form of
a dihydrate at the eutectic point, while the others crystallize in anhydrous form.190
For two of the salts studied (NaBr and KF) more than one DSC signal appears below
the bulk eutectic transition. Heating scans from repeated cooling-heating cycles performed at
different scan rates are presented in Fig. 7.3b and 7.3c. For both these salts two oligohydrates
Figure 7.2: (a) DSC cooling/heating scans of a 10 wt% aqueous NaCl solution in SBA-A. Peaks on the heating
scan are labeled P (pore), E and L (external sample), peaks on the cooling scan Pf (pore), Ef and Lf (external
sample); (b) phase diagram NaCl + water derived from DSC heating scans: Data for the liquidus line (L) and
eutectic temperature (E) of external sample and pore eutectic temperature (P).
96
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
appear in the phase diagram: a dihydrate and a tetrahydrate for KF (abbreviated as KF2 and
KF4), a dihydrate and a pentahydrate for NaBr (abbreviated as NaBr2 and NaBr5). In both
cases the higher hydrate represents the stable form at the eutectic temperature (see Appendix).
DSC scans for NaBr + H2O without the silica matrix indicate that metastable NaBr2 is formed
in eutectic freezing, which transforms to NaBr5 on heating in a separate transition below
eutectic melting (Appendix, Fig. 7.7). This transition (marked 𝐵2→5 in Fig. 7.3b) was confirmed
by temperature-scanning XRD measurements (Appendix, Fig. 7.10). On the assumption that
the same sequence of transitions as in bulk samples also occurs in the pores, we attribute the
three peaks below bulk eutectic melting of the NaBr + H2O system (Fig. 7.3b) to the transition
from NaBr2 to NaBr5 (𝑃2→5) and eutectic melting of NaBr5 (𝑃E) in the pores, and to the
transition from NaBr2 to NaBr5 in the excess sample (𝐵2→5). For the KF + H2O system
(Fig. 7.3c) DSC cooling scans indicate that both metastable KF2 and stable KF4 are formed in
eutectic freezing (Appendix, Fig.7.8), but in this case no transition from KF2 to KF4 can be
detected in the heating scans. Hence the two transitions observed in the pores are attributed
tentatively to eutectic melting of the tetrahydrate (𝑃E4) and dihydrate (𝑃E2).
For the set of alkali halides studied we find that the values of ∆𝑇p increase in a similar
sequence in the three silica materials. For the two SBA materials this is shown in Figure 7.2d,
where the ∆𝑇p values for SBA-B are plotted against the values for SBA-A. The data can be
represented by a line through the origin having a slope 𝑠=0.87, consistent with the ratio of
the melting point depression values ∆𝑇p0 of pure water in the two materials (13.1/15.1 = 0.87).
Figure 7.3: (a) DSC heating scans for eutectic salt systems confined in SBA-A, monitoring transitions below the
bulk eutectic temperature 𝑇E: (a) pore melting of NaCl, KCl, RbCl, CsCl and pure H2O (scan rate 0.5 K/min); (b)
and (c): multiple peaks detected for NaBr and KF at three different scan rates (2, 1 and 0.5 K/min) (see text for
explanation); (d) comparison of eutectic melting point depression ∆𝑇p of all salts in pores of SBA-A and SBA-B.
Results and Discussion
97
Higher values of ∆𝑇𝑝 are found for all salts in MCM, as expected from its smaller pore size. A
diagram of ∆𝑇p values in MCM vs. SBA-A similar to Figure7.3d is shown in the Appendix
(Fig. 7.12). The similar sequence of the ∆𝑇p values in the three materials suggests a genuine
salt-specific behavior for the eutectic melting in pores. Notably, for all three matrices the largest
∆𝑇p values are found for those salts for which the stable form at the eutectic temperature is a
higher oligohydrate, viz., KF (tetrahydrate), NaBr (pentahydrate) and NaI (pentahydrate) (see
Appendix). It is revealing to correlate ∆𝑇𝑝 with the volume fraction of the salt phase in the solid
eutectic mixture, 𝜙E=𝑥E𝑉S[𝑉I+𝑥E(𝑉S−𝑉I)]⁄ , where 𝑉S and 𝑉I represent the molar volumes
of the salt phase and ice, and 𝑥𝐸 is the mole fraction of salt (hydrate) given by 𝑥E=
𝑛S(𝑛W+𝑛S−ℎE𝑛S)
⁄, where ℎE is the number of water molecules in the hydrate. Values of 𝜙E
for the present alkali halide systems range from 0.015 (NaF) to 0.64 (NaBr ∙5H2O) (Appendix,
Table 7.3). Figure 7.4 shows the ∆𝑇p values in SBA-A and MCM plotted against 𝜙E. For both
pore sizes we observe a pronounced increase of∆𝑇p with increasing 𝜙E. The deviating behavior
of NaF and KF will be discussed later.
The observed increase of ∆𝑇p with the fraction of pore volume occupied by solid salt
(Fig. 7.4) suggests that precipitated salt causes a secondary confinement (SC) for water/ice in
the pores. A simple expression for the salt-induced melting-point depression is obtained for the
case when the precipitated salt forms a layer of crystallites near the pore wall, as sketched in
Figure 7.1c. In this case the effective core radius within which crystallization of water occurs
is reduced from 𝑅c to a smaller value 𝑅sc. From the concomitant decrease of the cross-sectional
core area one finds191 𝑅sc 𝑅c=
⁄√1−𝜙E. We infer that the melting point depression of water
in the core of the salt-containing pores conforms to a Gibbs-Thomson relation ∆𝑇SC=𝐶GT/𝑅SC,
as in the absence of salt, when ∆𝑇p0=𝐶GT 𝑅C
⁄.174,182 Hence, the salt-induced melting point
Figure 7.4: Depression of the eutectic temperature ∆𝑇p of aqueous alkali halide systems plotted as a function of
the volume fraction 𝜙E of salt in the solid eutectic mixture. Experimental data (symbols; red for salts crystallizing
as oligohydrates, blue for anhydrates), and fit of the data by Equation 7.2 (full line). (a) Confinement in SBA-A;
(b) in MCM.
98
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
depression will be related to the melting point depression of water/ice in the absence of salt,
∆𝑇p0, by
∆𝑇sc
∆𝑇p0=1
√1−𝜙E
(7.1)
According to this relation we expect ∆𝑇sc=∆𝑇p0 for 𝜙E= 0 and an increase of ∆𝑇sc proportional
to (1−𝜙E)−12
⁄ with increasing 𝜙E. Figure 7.4 shows, however, that for salts with low 𝜙E the
melting point depression ∆𝑇p is somewhat smaller than ∆𝑇p0. Hence, salt-induced confinement
alone does not account for the depression of the eutectic temperature in the pores, but a further
effect must exist that causes this negative contribution to ∆𝑇p. We surmise that this contribution
arises from salt-specific or ion-specific influences on the non-freezing layer (nfl) at the pore
wall. Denoting this by a (positive) term ∆𝑇nfl we obtain
∆𝑇p=∆𝑇sc(𝜙𝐸)−∆𝑇nfl=∆𝑇p0(1−𝜙E)−12
⁄−∆𝑇nfl
(7.2)
For a test of Equation 7.2 we adopt the experimental melting point depression of pure water in
the silica matrix (∆𝑇p0 values in Fig. 7.4) and take ∆𝑇nfl as an adjustable parameter. The curves
in Figure 7.4 represent Equation 7.2 with ∆𝑇nfl = 1.5 K for SBA-A and ∆𝑇nfl = 6.1 K for MCM.
The corresponding graph for SBA-B is shown in the Appendix (Fig. 7.13). It is remarkable that
a relation based on a simple model with a single adjustable parameter reproduces the main trend
of the eutectic point depression data of the alkali halide systems in the nanopores.
For NaF in MCM and for KF4 in all matrices we find higher values of ∆𝑇p than expected
on the basis of Equation 7.2 (Fig. 7.4). One possible cause for this is the strong hydrogen bond
interaction of fluoride ions with water and surface silanol groups, which may lead to a larger
thickness of the nonfreezing layer at the pore wall and a concomitant greater ∆𝑇p.182 For salts
composed of large, weakly hydrated (chaotropic) ions we generally find low ∆𝑇p values but no
hint at size dependent adsorption effects of cations at the negatively charged silica surface, as
reported in the literature.192 Changing from pH 5 (at which the present results were obtained)
to pH 9 had no noticeable effect on ∆𝑇p for the NaCl system, where we expected stronger
adsorption of the cations at higher pH. These findings show that ion-specific surface charge
effects45 are screened to a length scale of the ionic diameter at the high ionic strength of the
present systems. On the other hand, the trends emerging from Figure 7.4 are in line with the
concept of matching water affinities of the ions forming a salt,193 in the sense that salts formed
by ions of similar size (NaF, CsI) are weakly soluble (low 𝜙E and ∆𝑇p) while salts formed by
ions of strongly different size (NaBr, NaI) are highly soluble (high 𝜙E and ∆𝑇p).
We have estimated the size of salt crystallites in the pores by X-ray diffraction from the
width of Bragg reflexes, using the Scherrer equation.194 For dried samples at room temperature
this yields a typical crystallite size of about 1 nm (Appendix, Fig. 7.9). Although the Scherrer
Conclusion
99
equation is not applicable to such small crystals we adopt this value in the following geometric
consideration. If in pores of diameter 𝐷 the salt crystallites form a layer of thickness 𝑑 at the
pore wall, the mean volume fraction 𝜙E can be expressed by the reduced density 𝜌salt of salt
particles in this layer and the fraction of the pore volume 𝜑 making up the layer, i.e., 𝜙E=
𝜌salt𝜑, where 𝜑=1−(1−2𝑑𝐷
⁄ )2. Hence for a monolayer of 1 nm sized crystallites
(𝑑 = 1 nm) and an assumed maximum packing density 𝜂max = 0.5 in the layer we find that salt
up to a maximum 𝜙E of 0.24 (for SBA-A, 𝐷 = 7.1 nm) and 0.35 (for MCM, 𝐷 = 4.4 nm) can
be accommodated. For higher values of 𝜙E, as they are found for the oligohydrate salts
(Fig. 7.4), the thickness of the salt layer will exceed a monolayer. In the case of MCM this
implies that the free core of the pores available for ice will have a thickness of less than 2.5 nm.
In this context it is of interest that exceptionally broad DSC pore melting peaks were found for
the salts with the highest 𝜙E and ∆𝑇p (NaBr, NaI and KF) in MCM (Appendix, Fig. 7.11). We
suspect that in these cases, in which the pore eutectic temperature is below 210 K, no first-order
freezing/melting of water occurs in the pores of MCM, similar to the situation of pure water in
pores of diameter below 2.5 nm.185,186 An experimental test of the geometrical model discussed
above by temperature-scanning small-angle X-ray scattering is currently in progress.
7.3 Conclusion
In conclusion, we have found that the shift of the eutectic melting temperature of aqueous salt
systems in nanosized pores depends on the fraction of volume occupied by the solid salt. Salts
crystallizing as voluminous hydrates at the eutectic temperature cause a stronger depression of
the eutectic temperature than salts crystallizing in anhydrous form. We model this effect by
assuming that solid salt represents a secondary confinement for water/ice in the pores. The
different role played by the two solid phases in the eutectic phase transition can be rationalized
by recalling that melting of ice is pre-requisite for the dissolution of salt. Secondary
confinement may play a role in many technologically relevant fields, whenever nanoporous
materials are impregnated with salts or related substances, e.g., for supported metal oxide
catalysts,195,196 trapping of radioactive waste,197 advanced adsorbents,198 or adsorption heat
transformation devices.199 In addition, salt crystallization in the pores of stone and brick is
believed to be a major reason for the destruction of building materials by salt weathering. The
existence of different hydration states of the crystals appears to play an important role in these
processes.200,201
100
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
7.4 Appendix
7.4.1 Characterization of silica materials
The MCM-41 and SBA-15 silica materials used in this study were prepared by the methods
described previously.186,202 The specific surface area, the pore volume, and the pore size
distribution (PSD) of the materials was characterized by nitrogen adsorption at 77 K and argon
adsorption at 87 K. Figure 7.5 shows the adsorption-desorption isotherms for the samples MCM
and SBA-A and their PSD as derived from the desorption branch of the isotherms on the basis
of the nonlocal density functional theory (NLDFT) with the kernel for cylindrical silica pores.151
Values of the specific surface area (BET), the total pore volume and the mean diameter
of the cylindrical pore channels of the materials are summarized in Table 7.1. Also included are
values of the pore lattice parameter determined from the 10 reflection of the 2D pore lattice. A
further sample, denoted as SBA-B, was characterized only by nitrogen adsorption.
7.4.2 Eutectic point of bulk systems
Literature data for the eutectic point of the alkali halide + water systems studied in this work
are given in Table 7.2. Here, 𝑇E represents the eutectic temperature and 𝑤E the eutectic
composition expressed as weight fraction of salt. The salt concentration expressed as molality
𝑚𝐸 (mol per kg water) is obtained from 𝑤E by the relation 𝑚E=𝑤E𝑀S
⁄(1−𝑤E), where 𝑀S
is the molar mass of salt (kg/mol). In four of the eleven systems a salt hydrate coexists with ice
and solution at the eutectic point. The respective hydration number ℎE (number of water
molecules per unit salt) is also given in Table 7.2.
Table 7.1: Specific surface area 𝑎s, total specific pore volume 𝑣p, mean pore diameter 𝐷 and pore lattice parameter
𝑎0 of the MCM-41 and SBA-15 silica samples.
sample
gas
𝑎s
m2 g−1
𝑣p
cm3g−1
𝐷
nm
𝑎0
nm
MCM
N2
811
0.79
4.45 ±0.03
5.13 ± 0.01
Ar
686
0.75
4.38 ±0.03
SBA-A
N2
786
0.85
7.12 ±0.05
10.89 ± 0.03
Ar
655
0.82
6.86 ± 0.05
SBA-B
N2
582
0.87
8.5±0.2
Appendix
101
In the present DSC study the eutectic temperature of the bulk system is defined as the onset
temperature of the eutectic melting peak of the excess sample. A comparison of these values,
𝑇E(exp), with literature data of 𝑇E(Lit) (Table 7.2) is shown in Figure 7.6.
Figure 7.5: Adsorption/desorption isotherms of nitrogen and argon (left) and pore size distribution derived from
the desorption branch (right) for the samples (a) MCM; (b) SBA-A.
Table 7.2: Eutectic point data of alkali halide + water systems.
Salt
𝑇E
K
𝑤E
𝑚E
mol kg−1
ℎE
reference
𝑎0
nm
NaF
269.9
0.039
0.97
0
167
NaCl
251.90
0.232
5.17
2
168
NaBr
245.15
0.403
6.47
5
169
NaI
241.65
0.471
5.94
5
170
KF
251.5
0.219
4.83
4
167
KCl
262.50
0.196
3.27
0
168
KBr
260.55
0.313
3.83
0
169
KI
250.10
0.522
6.58
0
169
RbCl
256.75
0.398
5.46
0
168
CsCl
249.45
0.569
7.84
0
171
CsI
269.15
0.274
1.45
0
172
102
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
7.4.3 Systems Forming Salt Hydrates
NaCl: The dihydrate NaCl ∙2H2O is the only hydrate formed in the NaCl + water system at
normal pressure. It represents the stable phase in equilibrium with the aqueous solution from
the eutectic temperature (251.9 K) to 271.9 K. Anhydrous NaCl is the stable form at higher
temperatures.203
NaBr: Two hydrates are formed in the NaBr + water system. The pentahydrate NaBr ∙5H2O is
the stable form in equilibrium with aqueous solution from the eutectic temperature (245.2 K)
to 248.8 K. The dihydrate NaBr ∙2H2O is the stable form from 248.8 K to 324.4 K, and
anhydrous NaBr is the stable form at higher temperatures. Note that the pentahydrate represents
the stable form only in a rather narrow range.204
NaI: Two hydrates are formed in the NaI + water system. The pentahydrate NaI ∙5H2O is the
stable form in equilibrium with aqueous solution from the eutectic temperature (241.7 K) to
260.9 K, followed by the dihydrate NaI ∙2H2O, which is the stable form up to at least 313 K.205
KF: Two hydrates are also formed in the KF + water system. The tetrahydrate KF ∙4H2O is the
stable form in equilibrium with aqueous solution from the eutectic temperature (251.5 K) to
290.9 K. The dihydrate KF ∙2H2O is the stable form from 290.9 K to approximately 318 K, and
anhydrous KF is the stable form at higher temperatures.206
7.4.4 Volume fraction of Salt in Solid Eutectic Mixtures
The volume fraction of the salt phase in the solid eutectic mixture is given by
Figure 7.6: Experimental values of the bulk eutectic temperature 𝑇E(exp) of the alkali halide + water systems
correlated with literature values of 𝑇E(𝐿𝑖𝑡) (Table 7.2). The 𝑇E(𝑒𝑥𝑝) values represent values for the excess phase
with the three silica materials.
Appendix
103
𝜙E=𝑥E𝑉S
𝑉I+𝑥E(𝑉S−𝑉I)
(7.3)
where 𝑉S and 𝑉I denote the molar volumes of the salt phase and ice, respectively, and 𝑥E is the
mole fraction of salt in the mixture. In the case of salt hydrates we have to take into account
that the amount of free (unbound) water is reduced and given by 𝑛W−ℎE𝑛S, where 𝑛W and 𝑛S
represent the overall amounts of water and salt, and ℎE is the number of water molecules per
unit salt in the hydrate. Accordingly, a general expression for the mole fraction 𝑥E is187
𝑥E=𝑛S
𝑛W+𝑛S−ℎE𝑛S
(7.4)
which can be expressed in terms of the molality 𝑚E as
𝑥E=𝑚E
55.51+(1−ℎE)𝑚E
(7.5)
Values of the volume fraction 𝜙E estimated on the basis of Equation 7.3 and 7.5 for the present
systems are summarized in Table 7.3. A value 𝑉I = 19.5 cm3/mol was adopted for the molar
volume of ice from its density at 233.15 K.207 The molar volume of the anhydrous salts was
taken from their density.208 For salts crystallizing as hydrates, 𝑉S was obtained either from
crystal structure data (sodium chloride dihydrate,209 potassium fluoride dihydrate210 and
tetrahydrate,211 sodium bromide dihydrate212), or estimated by assuming volume additivity of
anhydrous salt and water (pentahydrates of NaBr and NaI). This assumption causes an
overestimate of the composite volume of typically 5-7%, which for the given salt hydrates
translates into an error in 𝜙E of 2-3%. The overall error in 𝜙E resulting from the uncertainty of
the molar volumes of salt and ice and the composition of the mixture in the pores is estimated
to be less than 5%.
104
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
7.4.5 Information from DSC Cooling Scans
Much information about phase transitions in the pores was obtained from successive DSC
cooling-heating cycles performed at different scan rates. High rates provide high sensitivity,
subsequent scans at lower rate probe rate-dependent shifts of the peak position. Heating scans
resulting from such cycles are shown in Figure 7.2b and 7.2c. Here we present complementary
information gained from the cooling scans of successive cooling-heating cycles.
NaBr + water. Figure 7.7a shows the cooling scans from repeated cooling-heating cycles for
an eutectic NaBr + H2O mixture imbibed in SBA-A. The large exothermic feature between 240
and 230 K results from supercooled eutectic freezing of the excess sample. At the higher scan
rates (2 K/min, 1 K/min) it consists of two sharp signals which we attribute to the formation of
NaBr dihydrate (NaBr2) and pentahydrate (NaBr5), in view of the fact that NaBr2 represents
the stable form down to nearly the eutectic temperature (see Section 7.4.3). The broad features
below the bulk eutectic transition result from transitions in the pores. The two overlapping
peaks marked as P1 and P2 may be caused, by analogy with the bulk system, from eutectic
freezing involving the formation of NaBr2 and NaBr5. More likely, P1 results from eutectic
Table 7.3: Molar volume 𝑉S of alkali halides and volume fraction 𝜙E in solid eutectic mixture based on Equation
7.3 and 7.5. The salts are listed in ascending order of 𝜙E. For salts for which two hydrates exist, 𝜙E values for
both phases are given.
Salt
𝑚E
mol kg−1
ℎE
𝑉S
cm3mol−1
𝜙E
NaF
0.97
0
16.4
0.015
CsI
1.45
0
57.6
0.072
KCl
3.27
0
37.6
0.102
KBr
3.83
0
43.3
0.133
RbCl
5.46
0
43.2
0.179
CsCl
7.84
0
42.4
0.235
KI
6.58
0
53.0
0.244
NaCl ∙2H2O
5.17
2
63.0
0.271
KF ∙2H2O
4.83
2
55.8
0.232
KF ∙4H2O
4.83
4
90.3
0.395
NaI ∙2H2O
5.94
2
75.9
0.346
NaI ∙5H2O
5.94
5
130.9
0.607
NaBr ∙2H2O
6.47
2
64.4
0.335
NaBr ∙5H2O
6.47
5
122.2
0.637
Appendix
105
freezing with formation of NaBr2, and P2 from the transition from metastable NaBr2 to stable
NaBr5 in the pores.
Indirect evidence for this solid-state transition in the pores comes from DSC of the NaBr
+ H2O bulk system (without the silica matrix). A cooling-heating cycle of the eutectic bulk
mixture (scan rate 0.5 K/min) is shown in Figure 7.7b. Supercooled eutectic freezing occurs
near 233 K and no further transition takes place down to 200 K. In the subsequent heating scan
a smaller endothermic peak, marked as B2→5, appears at 233 K. Importantly, this peak does not
re-appear, neither on cooling nor heating, as long as the temperature is cycled below eutectic
melting. This finding indicates that eutectic freezing of the sample leads – at least in part – to
the metastable form NaBr2, which then transforms to the stable form NaBr5 on heating in the
transition B2→5. This assignment is in accordance with the Ostwald rule of stages, according to
which crystallization from solution often starts in such a way that the thermodynamically
unstable form appears first, followed by re-crystallization to the thermodynamically stable
phase.200,213 The presence of two hydrate forms in the NaBr + H2O system was also confirmed
by low-temperature XRD (see Section 7.4.5).
Based on these complementary findings we attribute the three signals observed in the
heating scans of the NaBr + H2O system below the bulk eutectic temperature (Fig. 7.2b of the
main text) to the conversion of dihydrate to pentahydrate (P2→5) and eutectic melting in the
pore (PE), and to the conversion of dihydrate to pentahydrate in the excess (bulk) sample
(B2→5).
KF + H2O. In the KF + H2O system, the tetrahydrate (KF4) represents the stable form in a
broader temperature range above the eutectic point (see Section 7.4.3). DSC measurements of
the bulk system (without silica) indicate that no phase transitions take place below the eutectic
Figure 7.7: DSC of eutectic aqueous NaBr: (a) cooling scans for the solution imbibed in SBA-A at cooling rates
2.0, 1.0 and 0.5 K/min; the broad overlapping signals shown in the inset are attributed to the transitions in the
pores; (b) cooling-heating cycle of the bulk sample without silica matrix (see text for explanation).
106
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
temperature. Yet DSC heating scans in the presence of SBA-A show that two transitions are
occurring in the pores below bulk eutectic melting (Fig. 7.2c).
Figure 7.8a presents cooling scans from a sequence of cooling-heating cycles taken at
different scan rates for KF + H2O imbibed in SBA-A. In each of the scans the sharp signal at
the highest temperature represents supercooled eutectic freezing of the excess sample.
Supercooling of this transition is most pronounced in the first scan (taken at 2 K/min) and
smallest in the last scan (0.5 K/min).
The two smaller and rounded peaks at temperatures below supercooled freezing of the
bulk sample, shown at enlarged scale in Figure 7.8b, correspond to phase transitions in the
pores. By analogy with the NaBr + H2O system and again based on Ostwald’s rule of stages we
infer that the larger peak at higher temperature (marked as P1 represents (nucleated) eutectic
freezing in the pores with formation of the metastable KF dihydrate (KF2), and the small peak
at lower temperature (marked as P2) to a partial conversion of KF2 to the stable form KF4.
Unlike the case of NaBr, we have to infer that at temperatures below P2 part of the salt in the
pores still exists in form of metastable KF2, and the rest as the stable form KF4.
Based on this assignment we attribute the two signals observed in the heating scans of
the KF + H2O system below the bulk eutectic temperature (see Fig. 7.2c) to pore eutectic
melting with KF4 as the salt phase (PE4) and pore eutectic melting with KF2 as the salt phase
(PE2). Eutectic melting with KF4 as the salt phase is believed to occur at a lower temperature
than pore eutectic melting with KF2, in line with our model of secondary confinement, since
KF4 occupies a larger fraction of the pore volume than KF2. However, this assignment of the
two phase transitions in the pores is only tentative, as an independent proof is still missing.
Figure 7.8: DSC of eutectic aqueous KF imbibed in SBA-A: (a) cooling scans at different cooling rate (2 K/min,
1 K/min, 0.5 K/min); (b) enlarged view of the scan at 2 K/min. The rounded peaks P1 and P2 below the bulk
eutectic freezing transition are attributed to transitions in the pores, namely eutectic freezing with formation of
metastable KF2 (P1) and partial conversion of KF2 to PF4 (P4).
Appendix
107
7.4.6 Information from in situ XRD
Estimation of salt crystallite size. The size of salt crystallites in the pores was estimated by
XRD from the width of the Bragg reflections, based on the Scherrer equation. Samples were
prepared by imbibition of eutectic solution of NaBr into SBA-A and subsequent drying at room
temperature. During the drying process of the slurry the concentration of salt in the pores
increased due to diffusion from the external excess, but part of the excess salt crystallizes
outside the pore space. Nitrogen adsorption measurements showed that about 30% of the pore
volume was occupied by the dry salt.
Powder XRD profiles of the dry samples were recorded in a 2θ range of 15 – 50°
(Cu 𝐾𝛼,𝜆=1.54 Å) (Fig. 7.9). After subtraction of the silica background (Fig. 7.9a) the
remaining signal was modeled by a sum of six Lorentzians, each two centered at the position
of the first three leading Bragg reflections (Fig. 7.9b).
Figure 7.9: Scherrer analysis of a dried sample of NaBr in SBA-A: (a) subtraction of the background of pure SBA-
A from the sample containing salt; (b) the signal after background subtraction is simulated by a superposition of
three narrow and three broad Lorentzians.
Table 7.4: Peak height and peak width parameters I and ∆𝜃 of the Lorentzian functions used to represent the three
leading Bragg reflections for NaBr outside and inside the pores of SBA-A.
hkl
2𝜃
𝐼b
𝐼p
∆𝜃b
∆𝜃p
°
a.u.
a.u.
°
°
111
25.92
3244
202
0.1215
6.801
220
30.00
5921
846
0.1215
6.801
200
42.91
3947
52
0.1215
6.801
108
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
𝐼total=𝐼bg+∑ [ℒbulk(𝜃𝑖,∆𝜃b,𝐼𝑖,b)+ℒpore(𝜃𝑖,∆𝜃p,𝐼𝑖,p)]
3𝑖=1
(7.6)
By allowing for two width parameters, ∆𝜃𝑏 and ∆𝜃𝑝, we obtain a narrow and a broad peak for
each reflection, assigned to the external salt and the small salt crystallites inside the pores,
respectively. Values of the parameters 𝐼𝑖,b,𝐼𝑖,p,∆𝜃b, and ∆𝜃p are given in Table 7.4.
On the basis of the Scherrer equation194 the volume averaged crystallite size is given by
𝐿hkl=𝑘𝜆
𝛽cos𝜃hkl
(7.7)
with 𝑘: Scherrer constant, 𝜆: wavelength, 𝛽: integral peak width, and 𝜃: angular peak position.
From the integral width of the broad peaks, 𝛽=(𝜋2
⁄)∆𝜃𝑝=10.7, and with 𝑘=0.94 we find
𝐿=0.9(4)±0.1 nm. This value represents only a rough estimate, since the Scherrer equation
breaks down for very small crystals. We conclude that the salt crystallites in the pores have a
size not greater than approximately 1 nm.
Evidence for different salt hydrates. Combined in situ X-ray diffraction and small-angle
scattering measurements on the present samples were carried out at the Elettra synchrotron
facility (Trieste, Italy). XRD data were recorded in a q-range of 16–27 nm-1 (𝜆=1.54 Å) with
a 2D PILATUS 100k detector in the temperature range 130–290 K. Due to experimental
limitations only samples having a high excess of external salt solution could be studied.
Accordingly, the observed XRD profiles result mainly from salt and ice crystals in the excess
phase outside the pores. In addition, the resulting XRD profiles were affected by spurious ice
formation at the outside of the sample capillary. Figure 7.10 shows the XRD profile for a
eutectic sample of NaBr + H2O (in contact with MCM) during a cooling/heating cycle (290–
130–290 K). Bragg reflections assigned to hexagonal ice are marked with arrows. One observes
a sharp change in the Bragg pattern at a temperature 231 K on the heating scan, indicating a
phase transition of the salt in the excess sample. Within experimental accuracy this solid-state
transition occurs at the same temperature as the small endothermic peak in the DSC heating
scan marked as B2→5 in Figure 7.7b, which was attributed to a transition from NaBr dihydrate
to pentahydrate. Hence, the XRD scan provides independent support for this conjecture, which
also implies that in the cooling scan, part of the salt crystallizes as NaBr2 instead of the stable
form NaBr5, in agreement with Ostwald’s rule of stages.
Appendix
109
7.4.7 Summarized DSC Pore Melting Results
Peak width of pore melting peaks. The width of eutectic melting peaks in the pores was
defined as the difference between the peak maximum and onset temperatures, 𝛿𝑇= 𝑇max−
𝑇ons. Mean values for the individual salts in each of the three matrices are given in Figure 7.11.
To differentiate between the individual salts, Figure 7.11a shows 𝛿𝑇 plotted as a function of the
eutectic temperature 𝑇E of the systems (𝑇E values from Table 7.2). We find 𝛿𝑇=2±1 K for
most salts in the pores of SBA-A and SBA-B, but higher values of 𝛿𝑇, ranging from 3 to 10 K,
in the more narrow pores of MCM. Figure 7.11b shows that as a general trend the peak width
𝛿𝑇 increases as the pore eutectic temperature 𝑇E,p decreases. A related trend has been reported
in the literature for the freezing/melting of water in MCM-41 materials, where it was found that
the width of the pore melting peak increases with decreasing pore diameter, i.e., lower pore
melting temperature.186 Hence, the trends of 𝛿𝑇 shown in Figure 7.11b are consistent with the
concept of secondary confinement, since low values of 𝑇E,p (i.e., high values of ∆𝑇p) are
Figure 7.10: XRD profile of the eutectic NaBr + water system in contact with MCM during a cooling/heating cycle
(290-130-290 K). Bragg reflections assigned to hexagonal ice are marked with arrows. A sharp change in the
Bragg pattern appearing at 231 K in the heating scan is marked by a dashed line. The top panel shows the spectra
for two selected temperatures, one below and one above the transition, as marked with lines in the lower panel.
110
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
expected for a small effective pore width as it results from secondary confinement of water/ice
by the precipitated salt.
Tabulated ∆𝐓𝐩 results and complementary figures. Experimental data of the eutectic melting
point depression ∆𝑇p=𝑇E−𝑇E,p of the aqueous alkali halide systems confined in the pore
channels of the three silica matrices are given in Table 7.5. These data represent mean values
from a series of independent DSC measurements.
Figure 7.11: Half width 𝛿𝑇 of DSC pore melting peaks for the alkali halide salts in the pores of the three silica
materials as indicated in the graph: (a) 𝛿𝑇 data plotted as a function of the eutectic temperature 𝑇E; (b) the same
data plotted as a function of the pore eutectic temperature 𝑇E,p. For KF4 in MCM the half width is greater than
12 K and cannot be determined accurately.
Appendix
111
Table 7.5: Eutectic temperature increment ∆𝑇E=𝑇0−𝑇E of the external (bulk) samples and shift of the eutectic
temperature in the pores, ∆𝑇p=𝑇E−𝑇E,p for the alkali halide systems in MCM, SBA-A and SBA-B. Values of
the melting point depression of water in the three materials are also included.
Salt
𝜙E
∆𝑇p
K
𝛥𝑇p
K
𝛥𝑇p
K
𝛥𝑇p
K
external
MCM
SBA-A
SBA-B
H2O
0
0.28
33.2
15.1
13.1
NaF
0.015
2.78
38.9
14.8
14.6
NaCl
0.271
21.33
34.0
17.1
14.6
NaBr
0.637
27.18
47.7
23.1
19.7
NaI
0.601
29.81
49.2
23.0
19.9
KF2
0.232
21.46
30.1
17.5
13.9
KF4
0.395
21.46
49.7
25.2
21.2
KCl
0.101
11.12
29.1
14.3
12.5
KBr
0.133
13.12
28.6
14.5
12.5
KI
0.243
22.15
30.2
15.4
13.3
RbCl
0.177
16.89
30.8
14.4
13.3
CsCl
0.235
23.05
31.7
16.3
14.0
CsI
0.072
4.65
29.9
14.7
12.5
Figure 7.12: Eutectic melting point depression ∆𝑇𝑝 of the salt systems in MCM and in SBA-B plotted as a function
of the corresponding ∆𝑇𝑝 values in SBA-A. The lines show linear regression of the data by regression lines through
the origin.
112
Secondary Confinement of Water Observed in Eutectic Melting of Aqueous Salt Systems in
Nanopores
A correlation graph for the ∆𝑇p values of all salt systems in SBA-B and in SBA-A is shown in
Figure 7.2d. Figure 7.12 presents a related correlation graph for the ∆𝑇p data of the salts in
MCM and SBA-A. The correlation graph for SBA-B is also shown for comparison. Linear
regression of the ∆𝑇𝑝 values in MCM vs. the ∆𝑇𝑝 values in SBA-A by a line through the origin
yields a slope 𝑠 = 2.04. This value is somewhat lower than the value expected from the melting
point depression of ice/water in the two materials, 33.2/15.1 = 2.20. The deviation of 𝑆 from
this value can be attributed mostly to the exceptionally high value of ∆𝑇p for NaF in MCM.
Graphs for the eutectic melting point depression ∆𝑇p as a function of the volume fraction
𝜙E of salt in the solid eutectic mixture for the salts in SBA-A and MCM are presented in
Figure 7.3. A graph with the corresponding results for the salts in SBA-B is shown in
Figure 7.13c. The graphs for SBA-A and MCM are also shown for comparison. The curves in
Figure 7.13 represent Equation 7.2 with ∆𝑇nfl = 6.1 K (MCM), 1.5 K (SBA-A) and 1.4 K
(SBA-B).
Figure 7.13: Depression of eutectic melting point in pores ∆𝑇pof the aqueous alkali halide systems plottet as a
function of the volume fraction 𝜙E of salt in the solid eutectic mixture for (a) MCM; (b) SBA-A; (c) SBA-B.
Experimental data (symbol) and fit of the data by Equation 7.2 (full line). The dashed line gives the melting point
of water in the respective material. Red data points refer to salts crystallizing as oligohydrate, symbols to salts
crystallizing in anhydrous form.
Protein Adsorption on Silica Nanoparticles on Above and Below the Isoelectric Point
113
Chapter 8 Conclusions and Outlook
In this concluding Chapter the main achievements of this Ph.D. thesis are summarized and
discussed in the context of the existing research and its impact to recent literature. Additionally,
new developments in the presented projects are outlined and an outlook to future work is given.
8.1 Protein Adsorption on Silica Nanoparticles on Above and Below the
Isoelectric Point
In Chapter 3 experimental data for the adsorption of lysozyme (Lyz) and 𝛽-lactoglobulin (𝛽-Lg)
on silica nanoparticles were presented for a wide pH range. An important difference between
these two proteins is their different IEP. While Lyz has its IEP at pH 11, the IEP of 𝛽-Lg is close
to pH 5. The Lyz/SiNP system was chosen as it was used extensively in earlier experiments to
investigate the structural characteristics of the hetero-aggregates formed in a wide pH range.
This system represents an ideal model system for protein nanoparticle interaction studies, but
the high IEP of Lyz limits the accessible pH range to a regime where the net charge of Lyz is
opposite to that of the silica surface. 𝛽-Lg was chosen in order to extend this study to systems
where the net charge of the protein is the same as that of the SiNP.
Qualitatively the two proteins show a similar adsorption behavior below their IEP (net
charge of protein is opposite to that of the silica surface). The adsorbed amount increases with
increasing pH and reaches a maximum close to the IEP. This is explained with the fact that
close to the IEP the net charge of the proteins is neutral and thus the repulsive interactions
between adsorbed protein molecules are small which allows a more dense packing on the silica
surface. On the other hand, positively charged groups still exist by which the protein is anchored
to the negatively charged surface. Because attractive electrostatic interactions are screened by
electrolytes, it is expected that the adsorption of the protein is weakened by the addition of salt,
which was confirmed by measurements. The observed salt effect gives strong evidence that the
adsorption behavior is dominated by electrostatic forces while non-electrostatic and protein-
specific interactions play a minor role in this regime.
In the case of 𝛽-Lg the regime of equal net charge of the protein and the silica particles
was also accessible. Without added salt the adsorption capacity of 𝛽-Lg on the SiNPs drops
sharply beyond the IEP, but in the presence of salt this drop becomes less pronounced and
adsorption is still observed at a pH 9, i.e., well above the IEP. This salt-induced enhancement
of adsorption may be partly due to the screening of the (negative) net charge on the adsorbed
protein, but the origin of adsorption must be of a non-electrostatic nature. This was tentatively
attributed to a different interplay of the single contributions to the overall adsorption energy.
114
Conclusions and Outlook
Van-der-Waals forces and hydrophobic interactions may contribute more to the adsorption
energy in this regime, and the addition of salt promotes the close approach of the equally
charged proteins and particles.
Whereas in the literature, adsorption of proteins is commonly analyzed on the basis of
the Langmuir or the Hill equation, in this work the liquid-phase variant of the
Guggenheim – Anderson – de Boer (GAB) model10 was used for the quantitative analysis of
the collected adsorption data. This isotherm model assumes two independent adsorption states:
a more strongly bound state is attributed to adsorption in the first layer, and an additional weaker
state to adsorption in any further layers. This model is similar to the well-known BET model
for gas-phase adsorption. Like the BET model the GAB model reduces to the Langmuir
isotherm in case the second (weaker) adsorption-constant reaches zero. For both proteins the
Langmuir model underestimates the adsorbed amount of adsorbed protein at higher 𝑐eq in large
regions of bulk pH. The contribution of non-monolayer adsorption could be efficiently modeled
by the use of the the GAB model. The total adsorbed amount 𝛤max could be precisely predicted
and the adsorption constants were estimated.
8.2 Hetero-Aggregation of Silica Nanoparticles with a Protein: Observing the
Aggregate Structure with Fluorescence Methods
The hetero-aggregation of SiNPs with protein was previously investigated by small-angle
scattering and analytical ultracentrifugation. In Chapter 4 of this thesis a study is presented in
which fluorescence microscopy techniques are used to directly visualize the structures over a
wide range of protein-to-particles number ratios (over 3 orders of magnitude). In order to
achieve a high resolution and to enhance the contrast between aggregates and the surrounding
medium a fluorescence confocal laser scanning microscope (CLSM) was used. Stacks of 2-
dimensional micrographs were combined to achieve a 3-dimensional depiction of the
aggregates. In order to compare the results of different protein-to-particle number ratios on a
quantitative basis the surface-area-to-volume ratio (𝐴𝑉
⁄) was calculated for every 3D stack. A
low 𝐴𝑉
⁄ is characteristic for a large compact aggregate while a high A/V is typical for a loose
network structure and finely dispersed particles. It was found that 𝐴𝑉
⁄shows a minimum when
the protein loading reaches a monolayer. For even higher protein loadings a gradual increase in
𝐴𝑉
⁄ was detected. These results indicate that initially (at low protein-to-particle ratios, below
a complete monolayer) a network-like structure is formed but only a limited number of adsorbed
protein molecules is available as connecting nodes. Also, the high negative charge of the silica
surface is not fully compensated by the adsorbed positively charged protein which leads to a
strong repulsion between the single network components. With more adsorbed proteins more
connecting points are generated and the complete network becomes electrostatically neutral.
Hetero-Aggregation of Silica Nanoparticles with a Protein: Observing the Aggregate Structure with
Fluorescence Methods
115
Ultimately, the fine network collapses to a dense structure. This behavior is similar to findings
of our earlier study32 where the limitation of connection points was achieved by limiting the
protein adsorption by pH variation.
To extend this study to even lower protein-to-particle number ratios, this system was
also studied by fluorescence correlation spectroscopy (FCS). This technique it superior to
CLSM in detecting small aggregates and particles and therefore lower protein/particles ratios
became measurable. The most remarkable result of the FCS experiment is the appearance of
very small structures over the entire experimental protein-to-particle number ratio range. These
small aggregates have a diameter of approximately one particle radius plus one protein radius.
It stands to reason that single building blocks of aggregates are present, even when larger
aggregates dominate the dispersion.
In future studies, the results of the CLSM experiments could be analyzed even further
in order to calculate the fractal dimension of the aggregates. Fractal dimensions are frequently
used to test structures for self-similarities and its structural complexity. In the context of this
work this would allow us to compare the aggregate structure across the vastly different length
scales probed in this CLSM experiment. The fractal dimension of the 3D CLSM data can be
derived from the fractal dimension of the single 2D slices of each z-stack by 𝐷frac, 3D=
𝐷frac,2D+1.114–116 This method is valid until the size of the primary particle is smaller than the
resolution of the microscope which is not the case for the studied system. More experiments
are needed in order to verify whether fractal dimensions offer a way to compare the results
extracted from the microscopy data with future light scattering studies and thus ensure its
reliability.
Fractal dimensions derived from CLSM measurements can be compared with non-
classical DLS methods which provide the opportunity to measure the opaque and non-
transparent samples. In Chapter 4 (Fig. 4.7) the feasibility of modern DLS techniques was tested
for aggregated Lyz/SiNP samples. This exemplary measurement yielded an intensity curve
typical for mass fractal structures as was expected for this sample. It was concluded that
non-classical DLS is a valuable technique for future studies and synergizes well with the 3D-
analysis of CLSM micrographs.
Furthermore, it would be interesting to replace the labeled protein by intrinsically
fluorescent proteins like GFP. This would avoid the problems of altering the native protein with
an attached fluorescent dye. Unfortunately the fluorescent properties of those proteins are
sensitive to its structure and therefore susceptible to deformations during the adsorption.
Nevertheless, this is difficult to predict, and an experimental test is necessary to explore the
feasibility of such studies.
A study on the kinetics of the protein mediated aggregation process was attempted in
collaboration with H. Amenitsch at the Austrian SAXS beam line at the Elettra synchrotron in
Trieste. In a first experiment standard stopped flow methods with SAXS detection showed that
116
Conclusions and Outlook
the aggregation process is completed within the dead time of the system. In a second
experiment, a free jet micromixer was used to access sub millisecond time scales.214 It was
found, that the process of particle aggregation is faster than a few milliseconds.215 Although the
data did not allow the determination of a precise rate constant for the flocculation process, it is
clear that the aggregation is comparably fast. This is a hint that the kinetics of the system
Lyz/SiNP obey the predictions of a diffusion limited aggregation process216,217 in which
diffusion is the rate-limiting factor for the aggregate growth. This process typically generates
mass fractal structures as they found them in the CLSM micrographs.
8.3 Orientation of Adsorbed Protein on bulk pH Conditions as a Consequence
of the Dipole Orientation
In Chapter 5 an experimental method is presented which allows to test the predictions of protein
binding sites to surfaces as obtained by simulations.43 This method could help to find better
surface supports for proteins planned for an industrial application.
The apparent diameter of cytochrome c adsorbed on the surface of differently sized
silica particles has been followed over a wide pH range with small angle neutron scattering
(SANS). Attempts to analyze the scattering intensity curves with a spherical shell model or
individual non-interacting protein molecules and particles failed, as these simplistic models
were unable to reproduce the individual high-q pattern caused by the shape of the scattering
object. Ultimately, the scattering data was analyzed with an analytical form factor model
accounting for the special shape of scatters in the sample. This model was originally developed
for Pickering emulsions where smaller particles are situated at the surface of a bigger droplet
resembling a ‘raspberry-like’ shape.44 Most of the model parameter were known (e.g.
concentrations) or determined independently (e.g. SiNP size) so that the complexity of the
analysis was reduced to two free parameters.
A significant change in the apparent protein diameter was found between pH 4 and 5.
This apparent reduction in diameter was observed for all studied particles sizes but shifted
slightly towards higher pH for larger particles. This change in the apparent diameter was
attributed to the change of the orientation of the ellipsoidal cytochrome c relative to the surface.
Rationally, this means that cytochrome c is adsorbed in a ‘head-on’ configuration when exposed
to low pH conditions and turns into a ‘side-on’ arrangement beyond pH 5. In order to rule out
that the observed change is an intrinsic pH effect on the structure of the protein, a separate series
of SANS measurements was performed in the absence of SiNPs. It was found that cytochrome c
is pH-stable in the entire experimental range. This finding is in agreement with studies of the
literature.39
Prediction of protein adsorption in native and chemically modified mesoporous silica materials
117
The experimentally found shift in the protein orientation was attributed tentatively to a
major change in the dipole moment vector of cytochrome c happening in the same pH-region.
To verify this conjecture, the distribution of charges in the structure of cytochrome c was
modeled based on the PDB structure 2GIW. A combination of programs were used to assign
the protonation state of each side chain and compute the dipole moment vector. It was shown
that for the low pH-region the dipole moment vector is almost aligned parallel to the longer
polar axis of the ellipsoidal structure of cytochrome c. When the pH is increased over pH 4 the
dipole moment vector points perpendicular to the equatorial plane of the protein. This result
supports our conclusion that the change in orientation of the adsorbed protein is closely linked
with a change in the orientation of its dipole moment.
It is remarkable that even for the smallest tested particles (7 nm) whose size was
comparable to the size of the protein (≈ 3 nm) the dipole moment seems to dictate the
adsorption orientation. Smaller particles carry fewer charges and due to the curvature the
neighboring charges would be further apart from the attached protein. Therefore it was not
strictly expected to see such a clear behavior for the smallest particles.
Combining the experimental SANS data and the electrostatic modeling of the protein
structure provides a strong tool to understand the adsorption on a microscopic scale. It might
even be possible to predict the adsorption site of pH-stable proteins from its solution structure.
Nevertheless, this method fails when adsorption is not electrostatically dominated or the net
dipole moment is very small.
Although the results for the specific case of cytochrome c are convincing further testing
is needed. One limitation is, that the protein solution structure was kept constant for all pH and
only the protonation state was altered according to the pKa of every side chain. Even when the
overall shape of the protein remains the same it is still possible that the internal structure
changes slightly. When ionic side chains are affected this would affect the dipole moment, too.
Therefore a more sophisticated way of modeling the protein structure, its protonation state and
even containing ions and cofactors is desirable.
8.4 Prediction of protein adsorption in native and chemically modified
mesoporous silica materials
A model to estimate the protein loading capacity of a mesoporous solid with cylindrical pores
of uniform size was published in literature (SVC model).149 In Chapter 6 an extension of this
model is presented which accounts for a distribution of pore sizes and which is also applicable
to materials with chemically modified pore walls.
In order to test the validity of the new model a set of mesoporous materials (SBA-15)
with chemically modified surfaces were synthesized. The materials were characterized with
118
Conclusions and Outlook
nitrogen sorption, x-ray diffraction and thermogravimetric analysis. Based on this information,
the pore size distribution and the degree of chemical modification of the pore walls were
estimated. The materials differed significantly in the relative proportions of cylindrical pores,
secondary pores and of the functional layer. It was possible to estimate the contributions of the
cylindrical pores, secondary pores, silica matrix and functional layer to the total volume of the
material. Protein adsorption experiments were carried out with lysozyme at two salinities and
over a wide range of pH. Similar to the adsorption on spherical nanoparticles (cf. Chapter 3)
the adsorbed amount increases towards the IEP of the protein independent from the chemical
functionality presented on the surface of the solid material. Analogous to the situation for
lysozyme adsorption at SiNPs, added salt was again found to cause a reduction of adsorption
in the pores.
Comparing the proposed model with the existing model for protein adsorption showed
an improvement especially for materials with a high content of secondary porosity. Often a
significant fraction of such secondary porosity is not assessable to the protein as the pore size
is smaller than the protein diameter. It was shown that it is important to account for such
excluded pore space to correctly calculate the protein loading on porous solids. The formalism
presented here can help to efficiently identify suitable support materials for industrially used
proteins. It synergizes well with the results explained in Chapter 5 about protein orientation on
particle surfaces. Considering the non-spherical shape of most proteins in is vital to know the
apparent protein diameter. Combining the presented formalisms the protein loading capacity
could be predicted on a micro- and mesoscopic scale, just by knowing the individual properties
of each material.
One of the tested SBA-15 was modified with a zwitterionic surface. Generally such
surfaces are considered as protein repellant. Remarkably, a significant adsorption of lysozyme
was found for this material. It is not clear why the protein repelling effect is lacking in the
confined space and further work is needed to understand this finding.
Another interesting future option is to expand the fluorescent experiments presented in
Chapter 4 to porous materials. With the use of FCS it could be possible to quantify the kinetics
of the protein diffusion inside the porous matrix. This is particularly interesting when the pore
diameter becomes smaller than two times the protein diameter. Under these circumstances the
diffusion processes should be described by single file diffusion (diffusion limited to one spatial
dimension).218,219 In this case proteins in the pore matrix cannot pass each other making such
systems interesting for controlled and sequential drug release.
Freezing/Melting of Aqueous Salt Systems in Silica Mesopores
119
8.5 Freezing/Melting of Aqueous Salt Systems in Silica Mesopores
In Chapter 7 the eutectic melting and freezing of aqueous salt solutions within the confinement
of nanometer sized pores was studied. Differential scanning calorimetry (DSC) was used to
determine the melting temperature for a number of aqueous salt solutions in three different pore
sizes. Such results might have an impact in industrial applications to avoid weathering of
buildings and monuments48–51 but also for the production of supported metal oxide catalysts.220
It was found that the confinement-induced shift of the eutectic temperature in the pores
can be significantly greater than the shift of the melting temperature of pure water. This effect
was explained by the additional confinement introduced by the precipitated salt crystals in the
pores. More or less bulky salt crystals within the pore reduce the available pore volume for
water and thus lead to an additional (secondary) confinement of ice/water in the pores. This
effect is most dramatic for bulky oligohydrates which occupy a significant part of the pore
volume, in some cases more than half of the available pore volume. The existence of such
oligohydrate crystals in the external bulk solution could be proven with synchrotron
SAXS/WAXS experiments performed at the Austrian SAXS beamline at the Elettra
synchrotron in Trieste. From these assumptions a one-parameter model based on a modified
version of the Kelvin equation was developed.182 This model is in good agreement with the
general trend found in the experimental data for the depression of the eutectic temperature for
all tested pore sizes and salt solutions. For a few samples more than one pore melting signal
was detected. This was explained with a delayed transition of the one hydrate form to another
one.
The water-rich region of the eutectic phase diagram for NaCl in the pores of SBA-15
and MCM-41 was measured in the presence of excess liquid phase. The fact that inside the
pores only the eutectic phase transition could be observed was attributed to a diffusive exchange
of salt from the excess liquid into the pore during cooling. Meanwhile we succeeded to prepare
samples without excess phase by a two-solvent technique.221 It was found that under these
circumstances the complete phase diagram including the liquidus line in the pore could be
detected by DSC.
It was also attempted to determine the size of salt crystals precipitated in the pore.
Laboratory scale XRD experiments provided evidence that the crystals are much smaller than
the pore diameter (4-7 nm) but the application of the Scherrer equation to such small crystals is
problematic. Typically, the broadened Bragg peaks become indistinguishable from the
background and a reliable analysis of the peak width fails. In this point more experiments
including different techniques are needed to determine the size of precipitated salt in the pores.
During the synchrotron SAXS/WAXS measurements at Elettra it was also possible to
collect precise data of the pore lattice deformation of SBA-15 during the freezing/melting
temperature scans. Currently, the analysis is still ongoing and they might lead a way towards a
120
Conclusions and Outlook
better understanding of the processes during the phase transition within the pores and the crystal
size.
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121
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Abbreviation and Symbols
139
Abbreviations and Symbols
2D
:
Two-dimensional
3D
:
Three-dimensional
A/V
:
Surface-area-to-volume ratio
𝐴0
:
Footprint area of Lyz in side-on orientation
a0
:
Lattice parameter
AcOH
:
Acetic acid
𝑎geom
:
Geometric surface area
APBS
:
Adaptive Poisson Boltzmann solver
𝑎s
:
Specific surface area
BET
:
Brunauer – Emmett – Teller
𝑏𝑖
:
Scattering length of the nucleus i
BICINE
:
2-(bis(2-hydroxyethyl)-amino)-acetic acid
C
:
𝐾S𝐾L
⁄
𝑐∗
:
Reference concentration of lysozyme (2 mg/mL)
CAPS
:
3-(cyclohexyl-amino)-1-propane sulfonic acid
CD
:
Circular dichroism
𝑐eq
:
Equilibrium concentration
CGT
:
Gibbs-Thomson constant
CLSM
:
Confocal laser scanning microscopy
D
:
pore diameter
DSiNP
:
Diameter of silica nanoparticle
𝐷𝜎
⁄
:
Reduced pore diameter
𝐷f
:
Diffusion coefficient
DLVO
:
Derjaguin, Landau, Verwey and Overbeek
𝐷pax
:
Axial diameter of an ellipsoid
𝐷peq
:
Equatorial diameter of an ellipsoid
Dpart
:
Diameter of an OMS particle
DSC
:
Differential scanning calorimetry
E
:
Peak from eutectic melting
Ef
:
Peak from eutectic freezing
f(D)
:
Normalized pore size distribution
FCS
:
Fluorescence correlation spectroscopy
FITC
:
Fluorescein-5-isothiocyanat
FTC
:
Fluorescein dye
𝐺(𝜏)
:
Autocorrelation function
GAB
:
Guggenheim - Anderson - de Boer
hE
:
Hydration number
𝐼(𝑞)
:
Scattered intensity as a function of q
IEP
:
Isoelectric point
IS
:
Ionic strength
K
:
Langmuir adsorption constant
k
:
Scherrer constant
140
Abbreviation and Symbols
𝑘B
:
Boltzmann constant
KH
:
Henry`s law adsorption constant
KJS
:
Kruk – Jaroniec – Sayari
𝐾L
:
Adsorption constant for weakly bound protein
𝐾S
:
Adsorption constant for strongly bound protein
L
:
Melting along the liquidus line (bulk)
Lf
:
Freezing along the liquidus line (bulk)
Lpore
:
Freezing/melting along the liquidus line in pores
Lyz
:
Lysozyme
LyzFTC
:
FTC labeled lysozyme
Lyznative
:
Native lysozyme
M
:
Prefactor accounting for total SLD of 'raspberry-like' particles
mE
:
Molality at eutectic point
mF/mS
:
Mass ratio of functional organic group to silica
mmax
:
Limiting adsorbed amount of Lyz in pores
𝑚S
:
Mass of silica
mtotal
:
Maximum uptake of Lzy as expected from porefilling model
MW
:
Molecular weight
N
:
Number of proteins per SiNP
𝑛
:
Refractive index
NA
:
Numerical aperture
NA
:
Avogadro constant
Next
:
Number of protein molecules adsorbed at the external surface of
OMS
nfl
:
Non-freezing layer
NLDFT
:
Nonlocal density functional theory
Nm
:
number of adsorption sites per unit area
𝑁p
:
Average number of small particles
NP
:
Nanoparticle
nS
:
Amount of salt
nW
:
Amount of water
OMS
:
Ordered mesoporous silica
P
:
Peak from eutectic melting in pores
P(q)
:
Form factor
PDB
:
Protein data base
Pf
:
peak from eutectic freezing in pores
pKa
:
Logarithmic acid dissociation constant
PSD
:
Pore size distribution function
𝑞
:
Scattering vector
𝑄𝑖
:
Quantum yield
RB
:
Raspberry-like
RC
:
Effective core radius of a pore for freezing
𝑅ℎ
:
Hydrodynamic radius
RSC
:
Effective core radius considering secondary confinement
s
:
Polydispersity
S(q)
:
Structure factor
Abbreviation and Symbols
141
SANS
:
Small-angle neutron scattering
SAXS
:
Small-angle x-ray scattering
SC
:
Secondary confinement
SiNP
:
Silica nanoparticle
SLD
:
Scattering length density
SLS
:
Static light scattering
STED
:
Stimulated emission depletion
SVC
:
Sang, Vinu, Coppens
T0
:
Melting temperature of bulk water
TE
:
Eutectic temperature
TEM
:
Transmission electron microscopy
TEOS
Tetraethoxysilane
TE,p
:
Eutectic temperature in pores
TGA
:
Thermogravimetry
Tmax
:
Temperature at DSC peak maximum
Tons
:
Temperature at DSC peak onset
𝑇p0
:
Melting temperature of confined water
𝑉G
:
Volume of Gaussian profile
wE
:
Eutectic composition as weight fraction of salt
xE
:
Mole fraction of salt at eutectic point
XRD
:
X-ray diffraction
𝛽-Lg
:
𝛽-lactoglobulin
𝛤
:
Surface concentration of adsorbed protein
𝛿
:
Penetration factor for the 'raspberry-like' model
∆𝑇nfl
:
Increment from ion specific influences on the non-freezing layer
∆𝑇p
:
Increment between TE and TEp
∆𝑇0
:
Increment between T0 and Tp0
𝜀
:
Secondary porosity
∆𝜌
:
Scattering length density difference
𝜁
:
Zeta potential
𝜂
:
Viscosity
𝜃
:
Scattering angle
𝜆
:
Wavelength
𝜆D
:
Debye length
𝜇
:
Dipole moment vector
𝜇e
:
Electrophoretic mobility
𝜉
:
Aspect ratio of the Gaussian profile
𝜌F
:
Density of organic functionalization
𝜌𝑖
:
Weighing parameter
𝜌S
:
Density of silica
𝜎
:
Protein diameter
𝜎0
:
Electrokinetic surface charge density
𝜏D,𝑖
:
Characteristic lag time of the component i
𝜙E
:
Volume fraction of salt in the solid eutectic mixture
𝜙m(𝐷)
:
Protein packing fraction as function of pore diameter
142
Abbreviation and Symbols
