Document [original]

Comparison of Conventional and Super-Glassy

Polymers– Molecular Mobility, Gas Transport and

Influence of Nanofiller

vorgelegt von

Dipl. - Chem.

Nora Magdalena Konnertz

geboren in Viersen

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

1. Gutachterin: Prof. Dr. Regine von Klitzing

2. Gutachter: Prof. Dr. Andreas Schönhals

3. Gutachter: Prof. Dr. Klaus Rätzke

Tag der wissenschaftlichen Aussprache: 16. Februar 2017

Berlin 2017

Acknowledgements

I would like to express my gratitude to all who helped me complete my dissertation

with their professional and especially personal support.

My sincere thanks goes out to Prof. Dr. Andreas Schönhals and Dr. Martin Böhning

for giving me the opportunity to work at their laboratories at BAM Federal Institute

for Materials Research and Testing Berlin. Thank you for your helpful advices,

interesting discussions and the trust in me.

I have furthermore to thank Prof. Dr. Regine von Klitzing for undertaking the first

correction.

Additionally, I would like to thank my colleagues from BAM for their personal and

scientific support. I am deeply indebted to Thomas Ryback for supporting me signif-

icantly in technical and scientific questions.

I warmly thank my students Yi Ding, Laura Geoffroy and Vinicius Viana de Souza

Duarte. Especially, Yi Ding made significant contributions to my work.

In addition, I would like to thank Dr. Stefan Wellert (TU Berlin) for the WAXS

measurements, Dr. Wayne Harrison for the PIM-1 synthesis, Petra Fengler for

dynamic mechanical analysis, Michael Morys for the SEM images and Patrick Klack

as well as Dietmar Neubert for FTIR and TGA measurements. Furthermore, I express

my gratitude to the BAM mechanics for realizing all technical wishes.

For the financial support I gratefully thank the BAM PhD program.

A special thank goes to my family and good friends for their support, patience and

love.

Abstract

In the field of gas separation, polymeric membranes are favorable materials. Polymers

are inexpensive compared to ceramics and metals, offer a good processability, and

possess the ability to operate at large scale. The most important fact about polymeric

membranes is their good selectivity. Nevertheless, most of the polymeric membranes

show a strong tendency to physical aging and plasticization, which lead to changes

in their performance with time. Up to know, it is not fully understood how these

drawbacks are connected to the internal molecular mobility. In this study, a commonly

used non-porous polyimide for gas separation applications, Matrimid, was compared

to a microporous, high performance polymer, PIM-1. PIMs are Polymers with Intrinsic

Microporosity and were firstly introduced by Budd and McKoewn in the early 2000s.

PIM-1 was the first synthesized PIM and, even if many more PIMs followed , PIM-

1 shows the most promising gas transport properties. The molecular mobility of

the solution casted Matrimid and PIM-1 was investigated by Broadband Dielectric

Spectroscopy (BDS). For both polymers, one relaxation process, denoted as β∗, and

a conductivity contribution were found. Due to a very high activation energy for

this β∗–relaxation (86 kJ/mol for PIM-1 and 99 kJ/mol for Matrimid) and the high

temperature range where the peak appeared, it was concluded that the β∗–relaxation

has to be of cooperative nature. A sandwich like structure, formed by π−π–stacking,

was assumed. The conductivity, observed for both polymers quite well below their

glass transition temperatures, was attributed to the π−π–stacked structure as well.

One approach to reduce and/or overcome plasticization and physical aging is the

incorporation of nanofiller. In this study, PhenethylPOSS was embedded in PIM-

1 and Matrimid due to an expected interaction of the phenyl substituents of POSS

with the π–systems of the polymers and thus probably stabilizing the polymer matrix.

Therefore, concentrations of 0 to 20 wt% (0 to 40 wt%) were mixed in Matrimid (PIM-

1). A miscibility on a molecular level was observed up to 4 wt% for Matrimid, whereas

up to 10 wt% for PIM-1. For higher POSS contents, a phase separation was found,

while the size and distribution within the polymers strongly differed from one another.

Enhanced permeability for PIM-1 and Matrimid was achieved with embedding 1 wt%

of POSS. Furthermore, the phase separated Matrimid composites yielded a reduced

plasticization effect for CO2.

Zusammenfassung

Auf dem Gebiet der Gastrennung sind polymere Membranen favorisierte Materi-

alien, da sie im Vergleich zu Keramiken und Metallen preiswert sind, eine gute

Verarbeitbarkeit bieten und eine hohe Selektivität aufweisen. Allerdings zeigt ein

Großteil der Polymermembranen eine starke Tendenz zur physikalischen Alterung

und/oder Weichmachung, die im Laufe der Zeit zur Änderungen ihrer Permeabilität

und/oder Selektivität führen kann. Inwiefern die molekulare Beweglichkeit mit der

physikalischen Alterung und der Weichmachung zusammenhängt, ist bis jetzt aller-

dings noch nicht vollständig verstanden. Diesen Punkt greift diese Arbeit auf, indem

ein kommerziell gebräuchliches, nicht-poröses Polyimid für die Gastrennung, Matri-

mid, mit einem mikroporösen Hochleistungspolymer, PIM-1, verglichen wird. PIMs

sind Polymere mit intrinsischer Mikroporösität und wurden erstmals von Budd und

McKoewn in den frühen 2000er Jahren vorgestellt. PIM-1 ist das erste synthetisierte

PIM und bringt vielversprechende Gastransporteigenschaften mit. Die molekulare

Beweglichkeit der gegossenen Matrimid- und PIM-1-Filme wurde mittels Dielek-

trischer Relaxationsspektroskopie (BDS) untersucht. Für beide Polymere wurde ein

Relaxationsprozess, bezeichnet als β∗, und Leitfähigkeit unterhalb der Glasüber-

gangtemperatur gefunden. Die Aktivierungsenergie für diesen β∗–Relaxationsprozess

(86 kJ/mol für PIM-1 und 99 kJ/mol für Matrimid) und der Temperaturbereich, in

dem der Peak auftrat, waren sehr hoch. Aus diesen Gründen wurde für die β∗–

Relaxation von einem kooperativen Prozess ausgegangen. Es wurde eine "sand-

wichartige" Struktur angenommen, die sich durch π−π–Stacking der Polymerket-

ten und/oder -segmenten bildet. Des Weiteren wurde für beide Polymere unter-

halb ihrer Glasübergangstemperaturen eine Leitfähigkeit beobachtet, die ebenfalls

durch die besondere π−πWechselwirkungen erklärt wurde. Ein Ansatz zur Reduk-

tion und/oder Überwindung von Weichmachung und physikalischer Alterung ist der

Einsatz von Nanofillern eingebettet in der Polymermatrix. In dieser Arbeit wurde

PhenethylPOSS in PIM-1 und Matrimid gemischt, weil eine Wechselwirkung der

Phenylsubstituenten von POSS mit den π–Systemen der Polymere angenommen

wurde und somit die Polymermatrix gegebenenfalls stabilisiert werden kann. Die

Konzentrationen wurden von 0 bis 20 Gew.-% für Matrimid (0 bis 40 Gew.-% für

PIM-1) variiert. Für Matrimid wurde eine molekulare Mischbarkeit bis zu 4 Gew.-%

beobachtet, während bis zu 10 Gew.-% für PIM-1. Bei höheren POSS Konzentra-

tionen kam es zu einer Phasentrennung, während sich die Größe und Verteilung

der POSS Agglomerate innerhalb der Polymere stark voneinander unterschieden.

Durch Einbringen von 1 Gew.-% POSS in Matrimid und PIM-1 Matrix wurde die

Permeabilität deutlich erhöht. Des Weiteren wurde die CO2Weichmachung in den

Matrimid Kompositen reduziert.

Contents

1 Motivation 1

2 Introduction 5

2.1 Glass Transition Phenomena . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Thermal Glass Transition . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Dynamic Glass Transition . . . . . . . . . . . . . . . . . . . . . 9

2.2 GlassyDynamics............................... 11

2.2.1 Models for the Glass Transition . . . . . . . . . . . . . . . . . . 11

2.3 Gas Separation Membranes . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.1 Diffusion Mechanism of Gases in Porous and Non-Porous

Membranes.............................. 14

2.3.2 Gas Separation in Non-Porous Polymers . . . . . . . . . . . . 15

2.3.3 Sorption in Glassy Polymers: Dual Mode Behavior . . . . . . 21

2.3.4 Effects of Permeant . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.5 Effects of Temperature . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.6 Challenges and Limits of Technology . . . . . . . . . . . . . . . 24

3 Methods 27

3.1 Broadband Dielectric Spectroscopy (BDS) . . . . . . . . . . . . . . . . 27

3.1.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.2 Dielectric Response . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1.3 Analysis of Dielectric Spectra . . . . . . . . . . . . . . . . . . . 31

3.1.4 Dielectric Measurements . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Permeation: Time-Lag Method . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Density..................................... 38

3.4 Differential Scanning Calorimetry . . . . . . . . . . . . . . . . . . . . . 38

3.5 Dynamic Mechanical Analysis . . . . . . . . . . . . . . . . . . . . . . . 38

3.6 FTIRSpectroscopy.............................. 39

3.7 Scanning Electron Microscopy . . . . . . . . . . . . . . . . . . . . . . . 39

3.8 Thermogravimetric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 40

4 Materials and Sample Preparation 41

4.1 Materials ................................... 41

4.2 SamplePreparation ............................. 43

5 Matrimid and Matrimid/POSS Nanocomposites 45

5.1 Introduction .................................. 46

5.2 RelaxationBehavior ............................. 46

5.2.1 Characterization........................... 47

5.2.2 Relaxation Behavior of Pure Matrimid . . . . . . . . . . . . . . 50

5.2.3 Properties of Matrimid/POSS Nanocomposites . . . . . . . . . 59

5.2.4 Conclusions.............................. 70

5.3 Gas Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.3.1 GasPermeability .......................... 71

5.3.2 Conclusions.............................. 78

6 PIM-1 and PIM-1/POSS Nanocomposites 79

6.1 Introduction .................................. 79

6.2 PIM-1 ..................................... 80

6.2.1 Conclusions.............................. 86

6.3 PIM-1/POSS Nanocomposites . . . . . . . . . . . . . . . . . . . . . . . 87

6.3.1 Characterization........................... 87

6.3.2 Relaxation Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.3.3 Gas Transport Properties . . . . . . . . . . . . . . . . . . . . . . 99

6.3.4 Conclusions.............................. 105

7 Conclusions and Outlook 107

7.1 Conclusions .................................. 107

7.2 Outlook .................................... 113

A Further Experimental Details I

A.1 Materials and Sample Preparation . . . . . . . . . . . . . . . . . . . . I

A.2 Dielectric Investigations: PIM-1 and Matrimid . . . . . . . . . . . . . V

B Abbreviations VII

C Publications XI

C.1 Paper...................................... XI

C.2 Contributions to Conferences . . . . . . . . . . . . . . . . . . . . . . . . XII

C.2.1 Oral Presentations . . . . . . . . . . . . . . . . . . . . . . . . . XII

C.2.2 Poster Presentations . . . . . . . . . . . . . . . . . . . . . . . . XII

D Bibliography XIII

1 Motivation

Membrane technology is one of the key technologies to reduce the energy consump-

tion of chemical separation processes and of renewable energy fields because a phase

change is not required.

Industrial gas separation membranes are mainly used for hydrogen recovery, air

separation and natural gas purifications. Hydrogen recovery is important for ammonia

purge gas recovery, oxo-chemical synthesis and refinery gas purification.1–4 In the

field of air separation, nitrogen enrichment applications have the largest market.1,2,5

It is essential to remove carbon dioxide and acidic gases from natural gas to avoid

pipeline corrosion, during natural gas transport.6

In the last decades, polymer membranes were successfully used in industrial gas

separations.6This is due to the fact that they are inexpensive compared to metal

or ceramic materials, they show good processability and their ability to operate at

large scale.7Besides polysulfones, polycarbonates and aramides, polyimides are

now commonly used as gas separation membranes.6

In general, the separation properties of a polymer are essential for the performance

of a polymeric membrane. Several studies concentrating on structure/property rela-

tionships regarding their membrane performances were conducted8–12 and have iden-

tified structural features, offering desirable gas separation properties.11,12 Mostly,

glassy polymers with rigid polymer backbones provided the best combination of good

separation properties (selectivity) and high performance (permeability), because the

frozen-in structure of dense polymers below their glass transition temperature (Tg)

offers additional free volume, which is essential for the gas transport through poly-

mers.12

Nevertheless, some challenges in membrane science and limitations of membrane

technology still remain. Several studies have shown that there is a trade-off relation

between permeability and selectivity, which complicates the development of new

1 Motivation

materials with high performance and good separation properties. Furthermore, due

to the glassy state, polymeric membranes are in a non-equilibrium state, which leads

to a continuous change of their internal structure, trying to reach equilibrium. This

results in loss of the good performance of glassy polymers with time. This effect is

called physical aging.

Another challenge to improve and/or overcome is plasticization. Increasing the con-

centration of gas within a polymer can lead to a swelling of the polymeric structure.

This would lead to increased free volume as well as increased molecular mobility,

thus enhancing diffusivity but strongly reducing selectivity.

Up to now, it is not fully understood how the challenging phenomenons of plasti-

cization and physical aging are related to the internal structure of the polymers and

thus, hindering large scale applications of various promising polymers. This study is

performed to gain a more detailed comprehension on how molecular mobility and gas

transport properties are related to the internal structure of a polymer respectively

of a polymer nanocomposite. Therefore, the commonly used, non-porous polyimide

Matrimid is compared to a high performance polymer, a polymer of intrinsic micro-

porosity (PIM, here PIM-1). Whereas, the used commercially available Matrimid is

frequently used for gas separation applications,13–15 PIMs were firstly introduced by

Budd and McKeown in 2004.16,17 The first synthesized PIM, PIM-1, is still of huge

interest because it offers extraordinary gas transport properties.

In contrast to other polymers with very high fractional free volume and extremely high

gas permeabilities like polyacetylenes (e.g. PTMSP), PIMs offer high permeabilities

and high selectivities representing the current state-of-the-art in air separation and

hydrogen recovery.18,19 Due to the rigid polymer backbone PIMs provide a high ad-

ditional free volume, which is essential for their high performance. A major drawback

for practical membrane applications of PIMs is their tendency to physical aging.20,21

One approach to reduce or even overcome the phenomenon of physical aging and of

plasticization as well as improving gas transport properties, is to introduce fillers to

the polymer matrix. These composites are often called "mixed matrix membranes" The

filler can either be large, small or even nano sized and porous or non-porous. Due

to their high surface to volume ratio, nanofiller are especially suited to influence the

interface between the matrix and filler. This can either lead to an increase of the free

volume, indicating an increase in molecular mobility and sorption abilities or, if the

1 Motivation

interaction between filler and matrix is good, to a stabilization of the polymer ma-

trix. Eventually, filler addition to the polymer matrix enhances performance through

improving permeability and/or selectivity, as well as reducing or suppressing aging

effects and plasticization.20,22–24 So this approach can address both important issues

of glassy membrane polymers.

Current research for mixed matrix membranes have used e.g. metal-organic frame-

works (MOFs),25,26 zeolites27–29 or silica30,31 as nanofiller. In the case of silica

nanofillers Polyhedral Oligomeric Silsesquioxanes (POSS) are of huge interest in

the field of gas separation.32–37 POSS composites, as potential materials for gas

separation, were investigated by Rahman et al.38,39 POSS may be regarded as

the smallest possible silica particle and is composed of a silica cage with organic

substituents (R) at the edges (Rn(SiO1.5)n(n≥6), n is the number of silica atoms).

Octa-silsequioxanes are the major product of a typical synthesis route and are mostly

investigated. The main advantage of using POSS as filler is that their solubil-

ity,40 miscibility, thermal stability and mechanical properties are easily influenced

by chemical variation of the substituents.32,41–43 Besides its good solubility in many

solvents, PhenethylPOSS (PhE-POSS) is miscible with different polymers. In this

study, PhE-POSS was used as nanofiller for Matrimid and PIM-1 because it is

expected that the phenyl–substituent of POSS interacts with the π–system of the

polymer, respectively and thus, stabilize the polymer matrix to probably reduce plas-

ticization, aging and improve the gas transport properties.

A correlation between molecular motions of the polymer matrix and the diffusion of

gas molecules through the matrix can be observed for conventional glassy polymers.

This correlation is in agreement with fundamental transport models44,45 as well as

simulations of molecular dynamics,46,47 which was further discussed for experimental

data on ref.48,49 The solubility of a gas in a polymer depends on its condensability,

the free volume distribution and on the molecular interactions within the polymer ma-

trix.50 Furthermore, the already mentioned challenges left in membrane science and

limitation of technology permeability/selectivity trade-off, physical aging and plas-

ticization strongly depends on the molecular mobility of the polymer. Additionally,

the film formation during casting, i.e. the solidification of the polymer by solvent

evaporation, is predominantly governed by the molecular mobility of the polymer

matrix. Thus, investigations addressing molecular mobility combined with gas trans-

port experiments are realized in this study for Matrimid as well as PIM-1 and the

composites with PhE-POSS as nanofiller, respectively.

2 Introduction

At high temperatures amorphous polymers are in a rubbery, liquid like state. With

decreasing temperature they undergo a glass-rubber transition and the polymer be-

comes glassy. From the temperature range at which the amorphous polymer changes

from the highly viscous, rubbery to the glassy, brittle state the glass transition tem-

perature Tgcan be estimated. In the following section this phenomenon is discussed

in more detail.

2.1 Glass Transition Phenomena

2.1.1 Thermal Glass Transition

When an amorphous glass forming polymer is cooled, without crystallization, the

density and viscosity increases while the molecular mobility decreases.51 At a certain

temperature range, the segmental mobility for structural rearrangements becomes too

low over experimentally accessible time scales. The liquid is then no longer in an

equilibrium state. A glass is then formed, which is in a non-equilibrium state, without

any long-range order.52 This process is called the thermal glass transition whereby

this transition takes place in a given temperature range. The glass transition is a

kinetic phenomenon and not a thermodynamic phase transition, which is explained

by discontinuous changes in any physical property, in contrast to first and second

order transitions.53,54

Depending on the temperature, a polymeric system in the bulk could behave like

an elastic solid, rubber-like, as a viscoelastic, highly deformable material or as a

melt. The shear modulus G versus the temperature demonstrates this behavior as it

is shown in Figure 2.1.

2 Introduction

Liquid like

behavior

Viscoeleastic

behavior

Glass like

behavior

G~10 Pa

Glass

transition

G~10 Pa

Temperature

log(Shear modulus G)

M1M2

Figure 2.1 – Sketch of the shear modulus vs. the temperature for an amorphous polymer.

Solid line represents a polymer with a molecular weight of M1>MCand

the dashed line a polymer with M2>M1(based on ref.55).

At low temperatures, the shear modulus is in the range of 109Pa and the polymer

shows an elastic-solid-like behavior. At the glass transition temperature Tg, the

shear modulus rapidly decreases by ca. 3 orders of magnitude. For temperatures

higher than Tg, the behavior of the polymer changes from glassy to viscoelastic and

rubbery. Entanglements (topological interactions), which are formed for molecular

weights Mwhigher than the critical molecular weight MC(for very flexible polymers

about 104g/mol) are responsible for this rubber-like plateau. With further increase

of the temperature, the polymer behaves like an ordinary liquid, which indicates the

shear modulus to be 0. As it can be seen from Figure 2.1 the viscoelastic behavior

of a glassy polymer strongly depends on the molecular weight.

The glass transition temperature is a characteristic phenomenon for polymers. Be-

sides the specific volume (see Figure 2.4), the typical temperature dependence (for a

constant cooling rate) for a glassy polymer around Tgcan also be observed for other

thermodynamic quantities like the enthalpy and entropy (see Figure 2.2).

2 Introduction

Temperature

Volume, Ethalpy, Entropy

Tg,2

Tg,1

Figure 2.2 – Thermodynamic quantities like volume, enthalpy and entropy vs. temper-

ature around the glass transition temperature Tg. Tg,1and Tg,2are for

different cooling rates where T1>T2. Tmcharacterizes a hypothetical

melting point and TKthe Kautzmann temperature. (based on ref.55)

With decreasing temperature down to Tg, the slope of the temperature dependence

of the volume, entropy and enthalpy changes. At the same time, a step-like change

can be observed for material properties like specific heat cp=(∂H/∂T )por thermal

expansion coefficient α=(1/V ) (∂V /∂T )p(Figure 2.3), which is denoted as the

thermal glass transition temperature.

Temperature

Specific heat, expansion coeff., etc

Glass Glass

transition

Supercooled

melt

Figure 2.3 – Scheme of the temperature dependence of different material properties like

specific heat and expansion coefficient for a glassy polymer.55

In order to measure the thermal Tgmethods like Differential Scanning Calorimetry

(DSC),56,57 ellipsometry,58,59 etc. can be used.

2 Introduction

The reduced molecular mobility below the glass transition temperature Tgleads to

excess properties e.g. free volume, enthalpy, etc.. Figure 2.4 shows a scheme of the

specific volume of a polymer as a function of the temperature above and below Tg.

Figure 2.4 – The temperature dependence of the specific volume of a glassy polymer

(based on ref.60).

The specific volume Vspec decreases with decreasing temperature corresponding to

the thermal expansion coefficient of the liquid state αl. By passing Tg, cooperative

movements freeze while smaller units of the polymer structure are still mobile and the

liquid turns into a glass, retaining the internal structure of the rubbery state above

Tg. In this temperature range, changes of the volume follow the thermal expansion

coefficient of the solid αsand due to the frozen-in segmental mobility additional free

volume results. In general, the free volume is defined as the difference of the specific

volume Vspec and the extrapolated volume of an undercooled liquid Vlas well as the

matrix volume Vmatrix. Non-relaxed free volume is characterized by the difference of

the specific volume and Vl. Several occupied volumes may be subtracted from the

specific volume Vspec to obtain the free volume:

1. Vspec - VvdW : the van der Waals volume gives the free volume at 0 K.

2. Vspec - Vc: the volume of the hypothetical crystal (closed packed) gives the

excess free volume.

3. Vspec -Vl: the extrapolated volume of an undercooled liquid gives the amount

of unrelaxed free volume.

2 Introduction

By calculating the so called fractional free volume ΦFV , described by Bondi,61 the

free volume of common glassy polymers is determined as:

ΦFV =Vfree

Vspec

= 1 −1.3·VvdW

Vspec

(2.1)

2.1.2 Dynamic Glass Transition

Molecular mobility is an important part of the glass formation process. In order to

measure those segmental dynamics different techniques e.g. Dynamic Mechanical

Analysis (DMA),51 neutron scattering62 and in a extremely wide frequency range by

Broadband Dielectric Spectroscopy (BDS)63 could be applied.

During the glass formation, different changes related to dynamical processes can be

observed which are schematically shown in Figure 2.5 with the dielectric loss ε“as

an example.

2 Introduction

log ɛ´´

log (f /Hz)

-1

-2

-3

-2

-4

-6 2468

log (f /Hz)

-4

β-Relaxation

α-Relaxation

β-Relaxation

1000/T

1000/T 1000/T

Δcp

<T2

Figure 2.5 – Sketch of dynamics for glassy polymers around Tg. First, dielectric loss

ε“vs. frequency for two different temperature T1<T2. Second, relaxation

rate vs. inverse temperature for αand β-relaxation. Third, specific heat

capacity vs. the inverse temperature (based on ref.55).

Many polymers show processes at higher frequencies, for instance the β–relaxation.

The temperature of this process can usually be described by an Arrhenius relation:

f(T) = 1

2πτβ(T)=f∞·exp −EA

kBT(2.2)

where EArepresents the activation energy, kBthe Boltzmann constant and f∞de-

notes the frequency in the high temperature limit (f∞= (2πτ∞)−1). Mostly, the

β-process can be assigned to rotational fluctuations of side groups or other inter-

and intramolecular fluctuations.55

The α-relaxation (structural (primary) relaxation or dynamic glass transition) appears

in the low frequency range (see Figure 2.5).55 For polymers, this transition is due

to segmental fluctuations and can be described by the empirical Vogel-Fulcher-

2 Introduction

Tammann equation (VFT):64–66

f(T) = 1

2πτα(T)=f∞·exp −A·T0

T−T0(2.3)

where A characterizes the fragility parameter, which can be taken as a classification

parameter for glassy polymers.67,68 When f(T) deviates strongly from the Arrhenius

type behavior, the polymer is called "fragile". While for temperature dependence

similar to the latter the polymer is considered "strong". T0represents the Vogel or

ideal glass transition temperature, which is found to be 30 to 70 K below the thermal

glass transition temperature. The relaxation rate fmax (f(Tg)) reaches typical values

of 10−2-10−3Hz at Tg(see Figure 2.5).

2.2 Glassy Dynamics

2.2.1 Models for the Glass Transition

Up to now, there is no generally accepted theoretical approach describing all as-

pects of the glass transition.55 In this section, the cooperativity approach by Adam

and Gibbs69 as well as the free volume theory by Doolittle70 and Cohen71,72 are

introduced, which justify the empirical VFT dependence, respectively.63

2.2.1.1 Cooperativity Approach

The theory of Adam and Gibbs is based on the assumption of the existence of "Co-

operatively Rearranging Regions (CRR)", which are defined as the smallest volume

changing its configuration independently from neighboring regions.63 The relaxation

time is related to the number of particles as follows:

τ∼exp −z(T)·∆E

kBT(2.4)

where z(T) characterizes the number of segments per CRR and ∆E denotes the free

energy barrier for one molecule. z(T) is related to the total configurational entropy

2 Introduction

Sc(T) by:

z(T) = Sc

NkBln2(2.5)

where N is the total number of segments and kBln2 characterizes the minimum of

entropy of a CRR assuming a two state model. Sc(T) can be related to the change

of specific heat capacity ∆cpat Tgas follows:

Sc(T) =

∆cp

TdT (2.6)

The VFT dependence can be obtained with the assumptions of T2=T0and ∆cp≈C/T

from eq. 2.4 and 2.6. When the size of a CRR diverges as z(T) ∼(T−T0)−1the

configurational entropy at T0, Sc(T0), disappears. Nevertheless, this cooperativity

approach does not give any information about the absolute size for the CRR at Tg.

Donth developed a fluctuation approach54,73,74 where the height of the step in cp

and the temperature fluctuation ∂T of a CRR at Tgis connected with the correlation

length ξby:

ξ3∼VCRR =

kBT2

g∆1

cp

ρ(∂T )2(2.7)

where ∆(1/cp) characterizes the step of the reciprocal specific heat (when cV≈cp

is assumed), ρthe density and ∂T can be extracted experimentally from the width

of the glass transition.75,76 Recently, broadband heat capacity spectroscopy enabled

the estimation of ∂T.77,78 The size of a CRR for different polymers is about 1 -

3 nm (corresponding to 10 - 200 segments55), which was estimated by Differential

Scanning Calorimetry (DSC)79 and Specific Heat Spectroscopy (SHS)80,81

2.2.1.2 Free Volume Theory

The free volume theory (see also Figure 2.4) is based on four assumptions:55,63

•Every segment of a polymer chain is assigned to a local volume V

2 Introduction

•If V is larger than a critical value Vc, the surplus could be considered as free

Vfree =V−Vc

•Molecular transport is realized by a jump over a distance corresponding to the

size of a molecule VM(≈VvdW ) when Vfree >V∗≈VMwhere V∗is the minimal

free volume required for a jump of a segment (or molecule) between two sites

•The free volume can redistribute without any "cost" of energy

The statistics of this redistribution is assumed to follow the Boltzman statistic and

Vfree to be the total free volume of the system. Thus, the jump rate 1/τ is defined

by:

τ∼

∞

V∗

exp −Vfree

Vfree dVfree ∼exp −V∗

Vfree (2.8)

where Vfree denotes the average free volume. With a linear temperature dependence

of the fractional free volume f=Vfree/V , where V is the total volume:

f=fg+αf(T−Tg)(2.9)

and temperature independence of f∗=V∗/V the VFT equation can be obtained. fg

characterizes the fractional free volume at Tgand αfdenotes the thermal expansion

coefficient. With the VFT equation (eq. 2.3) follows:

AT0=f∗

αf

·T0=Tg−fg

αf

(2.10)

In this model T0is the temperature where the free volume disappears. The free

volume model is able to describe the temperature dependence relaxations close to

Tgbut the fractional free volume cannot be obtained separately.

2.2.1.3 Dynamic and Free Volume Models related to Gas Transport Models

It has to be noted that the free volume model was used by Fujita82 as well as the

cooperative approach by Schaefer et al.83 in a similar way to describe the diffusion

of low molecular penetrants through a membrane.

2 Introduction

Whereas, Brandt‘s model84 is based on the assumption that an intramolecular acti-

vation energy is required for bending two polymer chains away from each other and

intermolecular energy to overcome the repulsion of the bending segments by their

neighbors. For more details of those and more gas transport models see ref.85

2.3 Gas Separation Membranes

Membranes in general offer high potential to reduce the energy consumption of sep-

aration processes because a phase change is often not required compared to conven-

tional material separation techniques like destillation, crystallization, absorption or

adsorption which are all thermal driven processes. Membrane technology is widely

used for the separation of various mixtures variating in molecular or particle size,

charge or affinity for the membrane. They find applications in medicine, power engi-

neering, chemical industry and more.85 Some membrane processes were established

in the last decades, e.g. microfiltration (MF), ultrafiltration (UF), reverse osmoses

(RO), electrodialysis (ED), pervaporation (PV) and gas separation (GS).

In the field of gas separation membranes diverse materials; organic, inorganic, porous,

non-porous, find notable application. So why polymeric materials are of such a great

interest? Porous materials offer a high permeability due to the pore flow but at the

same time a bad selectivity. Inorganic solids like ceramics or metals show low solu-

bilities and low diffusion because of their internal structure binding the penetrants.

Whereby liquids provide high gas solubilities but low selectivities. Beside its good

processability and low costs, compared to ceramics and metals, polymers offer high

selectivity and permeability. For these reasons, polymeric membranes emerge as the

favorable material for gas separation applications.

In general, the transport mechanism of a gas through a membrane depends on the

internal structure of the membrane material, porous or non-porous membranes.

2.3.1 Diffusion Mechanism of Gases in Porous and Non-Porous

Membranes

When the material is porous, the gas transport occurs by Poiseuille flow, Knudsen

diffusion or molecular sieving (see Figure 2.6) depending on the ratio of pore diameter

2 Introduction

and the mean free path of the gas molecules λ.

Figure 2.6 – Sketch of different gas transport mechanism through porous membranes

(adapted from ref.86).

When the pore diameter dpore in membranes is larger than the mean free path λof

the gas molecules, Poiseuille flow takes place. If the pore size of the membranes is

smaller than 50 – 100 Å, this diffusion is called Knudsen diffusion.87 In the case of

molecular sieving, the difference between pore diameter and gas molecule has to be

less than 7 Å.

2.3.2 Gas Separation in Non-Porous Polymers

Diffusion in non-porous membranes occurs according to the solution-diffusion mech-

anism, where the driving force is a concentration gradient across the membrane. The

solution-diffusion mechanism is divided into 3 steps (Figure 2.7):88

•Sorption of the gas molecules at the so called upstream side (higher pressure

= higher equilibrium concentration)

•Diffusion of the gas through the dense polymer across the concentration gra-

dient

•Desorption of the gas molecules from the so called downstream side (lower

pressure = lower equilibrium concentration)

2 Introduction

Figure 2.7 – Sketch of the Solution-Diffusion mechanism.

The diffusion in (isotropic) material is generally described by the first Fick‘s law:

J=−D·∂c

∂x (2.11)

where J denotes the net flux of diffusing material across unit area of a reference

plane,51 x defines the space coordinate measured normal to the section, c is the

concentration of diffusing substance and D characterizes the diffusion coefficient∗.

Eq. 2.11 is only valid for an isotropic medium where diffusion and structure proper-

ties are the same at any point within the material, which means that the diffusion

coefficient is independent from the concentration and the position in the material,

D = constant.

When the diffusion coefficient is constant and one dimensional (gradient of concentra-

tion only in x direction) but due to the mass transport time-dependent, Equation 2.11

becomes the second Fick‘s law:

∂c

∂t =−D·∂2c

∂x2(2.12)

Plane Sheet

In case of diffusion into a plane sheet of material which is as thin as the effective

diffusion of the substances enter only through the plane faces and negligible amounts

through the edges89 (see Figure2.8).

∗In this work, "diffusion coefficient" is equal to the mutual diffusion where the driving force is a

concentration gradient. Whereas, the tracer diffusion describes the statistical motion of a single

particle.

2 Introduction

Figure 2.8 – Scetch of gas diffusion through a plane sheet with a thickness of l in the

steady state. c1, p1and c2, p2are gas concentration and gas pressure at

the upstream and downstream side of the membrane, respectively.

Steady State

After a certain time the concentration remains constant at any point of the sheet, the

steady state (see Figure 2.8). With a membrane thickness of l (surfaces: x = 0 and

x = l), with constant diffusion coefficient D and constant concentrations (c1(upstream)

and c2(downstream)) the diffusion equation in one dimension (eq. 2.12) reduces to:89

0 = d2c

dx2(2.13)

By integrating to x:

dx =constant (2.14)

and with x = 0 and x = l and with further integration:

c−c1

c2−c1

l(2.15)

Eq. 2.14 and 2.15 show that the concentration gradient from c1to c2is linear, thus

the molar flux in the steady state is given by:

Jst =−D·dc

dx =D·c1−c2

l(2.16)

The permeability coefficient P at a pressure difference of ∆p=p1−p2through a

2 Introduction

membrane of a thickness l analog to eq. 2.16 is given by:

Jst =P·p1−p2

l(2.17)

where p1is the pressure of the upstream and p2the pressure of the downstream (see

Figure 2.8).

If the diffusion coefficient is constant and the concentration c is proportional to the

applied gas pressure (sorption isotherm is linear, Henry‘s law):

c=S·p(2.18)

eq. 2.16 and 2.17 are equivalent. S is the solubility and c denotes the concentration

within the membrane which is in equilibrium with the external pressure p. With

eq. 2.16 and 2.17 eq. 2.18 changes to:

P=D·S(2.19)

Transient State

When the initial concentration c0= 0, the upstream concentration c1(= S·p1) is

constant and the downstream pressure p2=c2= 0, the concentration profile in the

material changes until it is constant (see Figure 2.9).

Figure 2.9 – Concentration gradient within a material for a transient to steady state

diffusion.

The time until the steady state is reached depends on the diffusion coefficient which

determines the speed. If the diffusion coefficient is constant and independent from

2 Introduction

the concentration the concentration gradient can be calculated as a function of x and

t.89 The amount of permeated gas is given by:

Qt=

0 dV 0

gas

dt !dt =V0

m,gas

0dn

dt dt =F·V0

m,gas

Jstdt (2.20)

=⇒Qt

l·c1

=D·t

l2−1

6−2

π2

∞

(−1)n

n2exp −D·n2·π2·t

l2(2.21)

where V0

gas characterizes the volume of a gas under standard conditions (STP:

TST P = 273.15 K and pST P = 1.013 bar) and V0

m,gas = 22.4 cm3/mol denotes the

molar volume for an ideal gas. With t−→ ∞ (steady state) eq. 2.21 reduces to:

Qt=D·c1

l·t−l2

6·D(2.22)

and Qtchanges to the steady state region (Figure 2.10).

Time-Lag Experiment

Figure 2.10 presents a schematic time-lag experiment curve including additional

boundary conditions which are maintained for a time-lag experiment:

t<0 0≤x≤lc=0

t = 0 x = 0 c = S·p1

t = 0 x = l c = 0

t>0 0≤x≤lc = f(x,t)

2 Introduction

Figure 2.10 – Schematic time-lag measurement curve.

With the boundary conditions eq.2.17 is reduced to:

Jst =P·p1

l(2.23)

and thus, the permeability is described by:

P=Jst ·l

(2.24)

With Qt= 0 and t = τT L Eq. 2.22 becomes to: :

τT L =l2

6·D(2.25)

where the so called time-lag τT L describes the intersection of the extrapolated

steady-state line with the x-axis (Figure 2.10), which can be used to determine

the diffusion coefficient:

D=l2

6τT L

(2.26)

Below Tgthe segmental mobility of a glassy polymer is limited (section 2.1) and thus,

full thermodynamic equilibration after the gas sorption is not possible. This leads to

a pressure-dependence of P and D where τT L is not only correlated to the diffusion

coefficient while the concentration must be constant. Thus, the diffusion coefficient

2 Introduction

D, determined from the time-lag τT L, is an effective diffusion coefficient Deff :

Deff =l2

6τT L

(2.27)

In the following the effective diffusion coefficient Deff is denoted even below Tg

simplified as D.

2.3.3 Sorption in Glassy Polymers: Dual Mode Behavior

In order to describe sorption of gas molecules in glassy polymers several models were

developed, whereas none is able to explain all phenomena observed experimentally

(like gas-induced swelling and plasticization), completely and satisfactorily. How-

ever, due to its easy applicability the Dual Mode sorption model is commonly used

for various polymer gas systems.90,91 This model is a combination of a Henry solution

and a Langmuir adsorption (see Figure 2.11).

Figure 2.11 – Sorption isotherms for Henry, Langmuir and Dual-Mode.

The idea of the Dual-Mode model is based on the specific internal structure of a

glassy polymer (see Figure 2.4). Below Tgthe reduced segmental mobility lead

to accessible unrelaxed free volume (see Figure 2.4) providing "micro holes". Thus,

additionally to the Henry sorption (like in elastomers and rubbers), a hole-filling

mechanism described by a Langmuir mechanism is assumed. Consequently, this

leads to two different kinds of sorbed gas molecules: cD(issolved)and cH(oles).

2 Introduction

cD(issolved)is linear relation to the pressure where the solubility coefficient is constant

(Henry-constant kD). This behavior is described by Henry‘s law:

cD(p)=kD·p(2.28)

where cDis the concentration of the penetrant in the polymer, kDcharacterizes the

Henry-constant and p denotes the pressure. The Langmuir sorption cH(oles)can be

regarded as a hole-filling mechanism in the additional unrelaxed free volume and is

described by Langmuir isotherm:

cH(p)=c0

H·b·p

1 + b·p(2.29)

where c’His the saturation capacity and b the affinity constant (quotient of ad- and

desorption rate).

In conclusion, the total concentration of a sorbed gas in a glassy polymer follows a

combination of equation 2.28 and 2.29, the Dual-Mode model:90,92

c(p)=cD+cH=kD·p+c0

H·b·p

1 + b·p(2.30)

Whereupon, this sorption isotherm for glassy polymers is dominated for low p by the

hole filling mechanism (Langmuir) and for higher p by Henry sorption because the

Langmuir term reached already its saturation level (see Figure 2.11).

2.3.4 Effects of Permeant

Size and Shape

Glassy polymers offer high selectivities due to their high diffusivity selectivity. The

diffusion coefficient depends on the size and the shape of the penetrant. The gas

molecule "jumps" through the polymer matrix when the size of the gas molecule is

practicable with the polymer gaps. In general, the diffusion coefficient increases

with decreasing size of the penetrant. Furthermore, the shape of the gas molecules

is an important factor. The kinetic diameter σkin is calculated from the minimum

equilibrium cross-sectional diameter of the gas molecule93 and is a parameter used

for a comparison of different gases. Rod-like molecules such as CO2show increased

2 Introduction

diffusion coefficients compared to spherical molecules such as CH494 which can be

explained by the smaller kinetic diameter of CO2compared to CH4.

Table 2.1 – Kinetic diameter and critical temperature of H2, N2, O2, CH4and CO2.

H2N2O2CH4CO2

Kinetic diameter σkin /Å 2.89 3.64 3.46 3.80 3.30

Critical temperature Tc/K 33.3 126.2 154.6 190.7 304.2

Condensability

The condensability of the gas influences the solubility because the van der Waals

interaction depends on the polarizability of the gas molecules. The gas solubility

increases with increasing gas condensability, which is related to the critical temper-

ature Tc(Table 2.1); the higher Tc, the higher is the solubility. The condensability

(solubility) is competitive to the size of the penetrant (diffusivity) in separation pro-

cesses. One example is the challenging separation of CO2and H2. On the one hand,

H2has a higher diffusivity than CO2. But on the other hand, the solubility of CO2is

higher compared to H2. Due to those two competitive driving forces the separation

of CO2and H2is difficult.

2.3.5 Effects of Temperature

The temperature dependence of the sorption process is described by the van‘t Hoff

equation:

S(T) = S0·exp −∆HS

RT (2.31)

where S0is a constant (S(T→ ∞) = S0) and ∆HSis the partial molar enthalpy

of sorption. The temperature dependence the diffusion can be described by the

Arrhenius relation:

D(T) = D0·exp −EA,D

RT (2.32)

2 Introduction

where D0is a constant (D(T→ ∞) = D0) and EA,D characterizes the activation energy

of the diffusion. R denotes the universal gas constant (R = 8.314 J/(mol K)).

2.3.6 Challenges and Limits of Technology

The flux, permeability and selectivity are key factors of the transport performance of

polymeric membranes.6The flux can be influenced by the type (permeability) and the

effective thickness of the polymer. However, the selectivity (eq. 2.33) depends on the

choice of the polymer but also on the producibility of- preferably very thin- "pinhole-

free" membranes. Permeability and selectivity are key material properties to be

considered for the applicability of a polymer as a potential gas separation material,

whereas the thickness is a fabrication parameter. From all those structure/property

relationship studies, a trade-off relationship between selectivity and permeability

emerged. A concept named "upper bound" was identified by Robeson based on a

large amount of collected experimental data. This model includes plots of log of the

selectivity versus log permeability (of the gas with the higher permeability); where all

data points seem to be located below a well defined limiting line.11,12,95 Figure 2.12

shows an example of such upper bound (also called Robeson plot) for CO2/CH4. The

ideal selectivity is defined as the quotient of the pure gas permeabilities:

αid

i,j =Pi

(2.33)

where Piand Pjare the permeabilities of pure gases i and j, respectively. It has to

be noted that the real selectivity can differ strongly from the ideal one.

2 Introduction

1E-4 0.01 1 100 10000 1000000

0.1

100

1000

10000

P(CO

) / P(CH

)

Polycarbonates

Polyarylates

Polynorbonenes

Polysulfones

PIMs

P(CO

)

Figure 2.12 – Selectivity of CO2against CH4vs. permeability of CO2plotted in a so

called Robeson plot. The data was provided by ref.96

Besides the permeability/selectivity trade-off as a "widely recognized challenge",6

physical aging is a significant material property compromising the industrial viability

of many potentially effective membrane polymers. Glassy polymers are often used

as gas separation materials.97,98 Glassy polymers offer excess free volume due to

decreased polymer segmental mobility below the glass transition temperature Tg

(see section 2.1). Due to their non-equilibrium state, the polymer undergoes slow,

localized segmental motions towards the equilibrium leading to a higher density.99

Hence, a reduced free volume causing a decrease in the gas permeability. Besides

the permeability, other physical properties e.g. specific volume, enthalpy, entropy,

etc. are altered (section 2.1).

This aging effect can also be induced or intensified by highly soluble gases such as

CO2. Those gases lead to a plasticization effect where the polymer structure swells

with increasing gas concentration and the molecular mobility of the polymer matrix

is enhanced.

In order to handle these described challenges it is important to understand the

mechanism of gas transport through polymeric membranes as well as dynamics in

polymers. For these reasons in this study gas transport experiments are combined

with measurements of the molecular mobility.

3 Methods

3.1 Broadband Dielectric Spectroscopy (BDS)

Broadband Dielectric Spectroscopy (BDS) probes the interaction of an electrical

field with matter (liquids and solids), in a non-destructive way, in a broad frequency

range (10−6Hz to 1012 Hz). In this frequency range, relaxation phenomena caused

by fluctuations of dipoles and drift motion of mobile charge carriers can be observed.

3.1.1 Theoretical Background

Detailed discussion of the following considerations can be found in ref.63

When an electrical field is applied to a material, a dielectric displacement in the

material is the result. For small electric field strengths E, the dielectric displacement

Ddiel is defined as:

Ddiel =ε∗·ε0·E(3.1)

where ε∗denotes the complex dielectric function or dielectric permittivity, ε0charac-

terizes the dielectric permittivity of the vacuum (8.854 ·10−12 A·s·V−1·m−1) and E

the applied electric field. The resulting dielectric displacement within the material

due to the application of an electrical field is described by the polarization:

P=Ddiel −Ddiel.,0=(ε∗−1)·ε0·E(3.2)

where Ddiel.,0denotes the dielectric displacement of the free space. Furthermore,

(ε∗−1) defines the dielectric susceptibility χ∗of the material. When a periodic

3 Methods

electrical field (eq. 3.3) is applied to the system

E(t) = E0exp(−iωt)(3.3)

where E(t) characterizes the outer electrical field, t the time, E0denotes the alternat-

ing electric field amplitude, ωthe angular frequency and, i2= -1, the permittivity of

the material is expressed by a complex function ε∗consisting of a real part (in-phase

response) proportional to the reversible stored energy and an imaginary part (90◦

out-of-phase response) related to the energy loss per cycle. This complex dielectric

function ε∗is given by:

ε∗(ω) = ε0(ω)−iε00(ω)(3.4)

where ε0is the real part, ε00 the imaginary part and ωthe radial frequency (f=ω/2π).

Conductivity contributions could be analyzed with the complex conductivity σ∗is

defined as:

σ∗=σ0(ω) + iσ00(ω) = iωε0ε∗(ω)(3.5)

where σ0(ω)and σ00(ω)are the real and imaginary part of σ∗. The real and imaginary

part are described as:

σ0(ω) = ωε0ε00(ω)(3.6)

σ00(ω) = ωε0ε0(ω)(3.7)

3.1.2 Dielectric Response

Different relaxation phenomena contribute to the total dielectric response. Those

phenomena could be related either to molecular fluctuations of dipoles or mobile

charge carriers within the whole matrix or at interfaces (conductivity contributions).

Each of them shows a characteristic frequency and temperature dependence of the

real and imaginary part.

Macroscopic polarization refers to microscopic dipole moments piof molecules or

particles within a volume V. Whereby, the microscopic dipoles can either be perma-

3 Methods

nent or induced. Induced dipole moments caused by a local electric field can be

distinguished by the shift of the electron cloud respecting to the nuclei. Depending

on the time scale, electronic (10−12 s) or atomic polarizations (longer time scales)

are examples which are not considered here.

When an electrical field is applied to a system dipoles try to orientate along the direc-

tion of the field E which is called orientation polarization. At low frequencies, almost

all molecular dipoles can follow the outer electrical field with the same frequency or

time constant. Whereupon, with increasing frequency the fluctuation is retarded to

fluctuate with the same frequency as the dipoles are attached to molecules or are

hindered by the surrounding matrix. A characteristic time– the relaxation time τ–

refers to each of theses two phenomena. All these processes depend on temperature.

For dielectrics, the response of a system to a disturbance (here the time-dependent

external electrical field E(t)) is the polarization and can be characterized by a linear

equation:63

P(t) = ˆ

P∞+ε0

−∞

ε(t−t‘)dE(t‘)

dt‘dt‘(3.8)

where ˆ

P∞characterizes all contributions arising from induced polarization and ε(t)

denotes the time dependent dielectric function. By applying a periodical disturbance

E(ω) = E0exp(−iωt)with ωas the angular frequency, the polarization as response

is described by:

P(ω) = ε0·(ε∗(ω)−1)·E(ω)(3.9)

The time dependent dielectric function ε(t) and the complex dielectric function ε∗(ω)

are correlated by an one-sided Fourier transformation.

Molecular fluctuations arises from localized, segmental and/or cooperative motion of

the whole polymer chain100 (see Figure 3.1).

3 Methods

Figure 3.1 – Different molecular motions within a polymer (adapted from ref.101).

Localized fluctuations can take place within a monomeric unit or arise from rotation

of a short side of the chain on a length scale of ξ < 1nm. Usually, those secondary

processes are named as βand γ–relaxations and take place at high frequencies or

low temperatures. In contrast, segmental motions are observed at lower frequencies

and higher temperatures and on length scales of ξ≈1−2nm. They are related to

the glass transition temperature. This primary process is called α–relaxation. With

increasing temperature, this relaxation process shifts to higher frequencies.

Besides the molecular fluctuations, separation or motion of charge carriers contribute

to the total dielectric response as well. Mobile charge carriers such as electrons,

ions or charged defects can migrate through the material leading to conductivity

contributions.

In phase separated morphologies, charge carriers can be separated on a mesoscopic

length scale at the phase boundaries, leading to an interfacial polarization– the

Maxwell-Wagner-Sillars (MWS) polarization. The relaxation time of the Maxwell-

Wagner-Sillars polarization is inverse proportional to the conductivity of the mate-

rial. The relaxation time decreases with increasing conductivity. Thus, the process

is shifted to lower temperatures respectively higher frequencies. In some cases, the

analysis of the MWS polarization is complicate, as sometimes this process arises in

a similar temperature/frequency range with other relaxation processes.63,102,103 Fur-

thermore, charge carriers can be separated at the external electrodes on a macro-

scopic scale– the electrode polarization.63

3 Methods

3.1.3 Analysis of Dielectric Spectra

Each of the processes contributing to the total dielectric response show specific tem-

perature and frequency dependencies of the real and imaginary part of the complex

dielectric function (eq. 3.4). In the following section, the analysis and the dielectric

spectra of isothermal frequency scans are discussed.

log ω

log ɛ´´

ɛ`

Conductivity

contribution

ωπmax = 2 fmax

εs

ε∞

∞

Δε ε ε= -s∞

Figure 3.2 – Real ε‘(ω)(blue) and imaginary part ε“(ω)(black) of the complex dielectric

function (eq. 3.4) for a Debye relaxation process. (based on ref.63)

A peak in the imaginary part (loss part) ε“(ω)and a step-like decrease in the real part

ε‘(ω)indicates a relaxation process (Figure 3.2). MWS polarization and conductivity

phenomena are identified by an increase of the imaginary part ε“(ω)with decreasing

frequency. Real and imaginary parts are connected by the Kramers/Kronig rela-

tions.104,105

The shape of the imaginary part gives information about the distribution of relaxation

times. The dielectric strength ∆εcould be calculated from the step in the real

part ε‘(ω)and/or the area under the imaginary part ε“(ω). The relaxation rate

ωmax = 2πfmax or relaxation time τp= 1/ωmax is characterized by the position of the

maximal loss (see Figure 3.2).

Several model functions were developed to analyze dielectric spectra. The simplest

model was introduced by Debye106 where non-interacting dipoles are assumed, lead-

ing to an ideal relaxation behavior. In frequency domain, the Debye function is given

as follows:

ε∗(ω) = ε∞+∆ε

1 + iωτD

(3.10)

3 Methods

where ∆ε=εS−ε∞denotes the dielectric strength with εS= lim

ωτ<<1ε‘(ω)corre-

sponding to the static permittivity and ε∞= lim

ωτ>>1ε‘(ω)characterizing the unrelaxed

permittivity. ε∞is identified by a plateau in the real part. The Debye relaxation

time (τD) is determined by ωmax = 2πfmax = 1/τD.

In general, the dielectric behavior of polymers cannot be described by the Debye

function. Typically, the peaks for polymeric materials are much broader and of an

asymmetric shape. This is named as non-Debye or non-ideal relaxation behavior.

A number of model functions have been developed to describe the broadening of

the loss peaks, for instance the Cole/Cole function.107 Compared to eq. 3.10, the

Cole/Cole model describes symmetric broadening of the dielectric function:

ε∗(ω) = ε∞+∆ε

1 + (iωτCC )β(3.11)

where 0< β ≤1characterizes the symmetric broadening of ε∗for β= 1, the Debye

function is obtained again. The Cole/Cole relaxation time τCC is connected to the

maximum of ε“by τCC = 1/ωmax = 1/(2πfmax).

The Havriliak-Negami function (HN function) is used to describe both asymmetry

and the broadening of the dielectric function:63,108,109

ε∗

HN =ε∞+∆ε

h1 + (iωτHN )βiγ(3.12)

where τHN denotes the Havriliak-Negami relaxation time related to the frequency of

maximal loss fmax.ε∞characterizes the value of the real part ε‘for f >> 1/τHN ,∆ε

is the dielectric strength, ωthe radial frequency (ω= 2π), and β,γ(0 < β;βγ ≤

1) represents the asymmetry and broadening of the spectra compared to the Debye

function.63 The maximal loss fmax is related to the HN relaxation time by:108,110

fmax =ω

2π=1

2πτHN

sin πβ

2 + 2γ

βsin πβγ

2 + 2γ−1

β(3.13)

The temperature dependence of fmax can be described either by Arrhenius (eq. 2.2)

or the empirical Vogel-Fulcher-Tammann equation (VFT) (eq. 2.3).

3 Methods

Conductivity effects are treated in the usual way by adding a power law:

ε“

cond =a·σ0

ωs·ε0

(3.14)

with (0< s ≤1) to the dielectric loss (see Fig. 3.3). Where ε0is the permittivity

of the free space (= 8.854 x 10−12 As V−1m−1). σ0is the DC conductivity of the

sample. For dimensional reason the factor a has the unit (rad·s−1)s−1. The parameter

s (0< s ≤1) describes for s = 1 Ohmic and for s <1 non-Ohmic effects in the

conductivity.111,112

12345

-3.0

-2.8

-2.6

-2.4

-2.2

Conductivity

log (f /Hz)

log ´´

HN function

´´

cond

Figure 3.3 – Dielectric loss vs. frequency for PIM-1 (PIM-1-00) for 494 K. The line is

a fit of the HN function to the data.

The frequency dependence of the real part of the complex conductivity spectra for

a typical behavior expected for semi-conducting polymeric materials is shown in

Figure 3.4.

3 Methods

-1 0 1 2 3 4 5 6

-14

-12

-10

-8

-6

log(

/S cm

-1

)

log (f /Hz)

Figure 3.4 – Real part of the complex conductivity σ‘vs. frequency for the second cooling

run for pure Matrimid (MI-00) at 570 K.

For high frequencies, the real part σ0decreases with decreasing frequency with a

power law down to a characteristic frequency fc, where a plateau value is reached.

The plateau value corresponds to the DC conductivity.111 In literature, there are

several models available to describe the frequency dependence of the real part of

the complex conductivity quantitatively. One example is the Dyre model, where the

conductivity is considered as a hopping process in a random free energy landscape.113

In a more simplified approach, the data can be approximated by the well-known

Jonscher power law:114

σ0(f) = σDC 1 + f

fcn(3.15)

The critical frequency fccharacterizes the onset of the dispersion and the exponent n

has values between 0.5 and 1. σDC can be obtained by fitting the Jonscher equation

to the data.

3.1.4 Dielectric Measurements

For a capacitor with a dielectric within, the complex dielectric function is defined as:

ε∗(ω)=C∗(ω)

(3.16)

where C∗denotes the complex capacitance of the filled capacitor and C0the geo-

metrical capacitance (vacuum capacitance). The complex dielectric function can be

3 Methods

obtained by the measurement of the complex impedance Z∗of the sample:

ε∗(ω)=1

i·ω·Z∗(ω)·C0

(3.17)

A high resolution ALPHA analyzer interfaced to an active sample head (Novocontrol,

Montabaur, Germany) was used to measure the complex dielectric function in a

frequency range from 10−1to 106Hz. The samples were measure in parallel plate

geometry (see Figure 3.5).

Figure 3.5 – Sketch of the sample holder of a Broadband Dielectric Spectroscopy set

up.

In order to ensure a good electrical contact, gold-electrodes with a diameter of 20 mm

were thermally deposited on both sites of the sample. The measurements were car-

ried out by isothermal frequency scans at selected temperatures. To determine the

influence of the temperature treatment on the structure of the sample, a detailed

temperature program with several heating and cooling cycles from 173 K to 573 K

(∆T=3 K) for the Matrimid samples (Figure 3.6a) and from 173 K to 523 K (∆T=3 K

or 5 K) for the PIM-1 samples (Figure 3.6b) was used. The temperature was con-

trolled by a Quatro Novocontrol cryo-system with a stability of 0.1 K. For more

details see ref.63 During the whole temperature program the sample was kept in a

dry nitrogen atmosphere.

3 Methods

200

300

400

500

600

700

573 K

173 K

T /K

Time of the measurement

cooling

heating

cooling

heating

298 K

473 K

200

300

400

500

600

523 K

473 K

173 K

cooling

Time of the Measurement

heating

T /K

heating

298 K

Figure 3.6 – Heating/cooling cycles of the dielectric measurements on a) Matrimid and

Matrimid/POSS and b) PIM-1 and PIM-1/POSS.

3.2 Permeation: Time-Lag Method

In order to measure the gas permeability of different gases for Matrimid, PIM-1

and their composites the time-lag method was applied (details can be found in sec-

tion 2.3). Figure 3.7 shows a flow sheet of the used time-lag set up.

Figure 3.7 – Flow sheet of the used time-lag method.

The dense, defect free polymer film (diameter 38 mm) is placed in a permeation

cell on a porous metal support in a temperature-controlled set-up and subsequently

3 Methods

sealed by a Viton O-ring. Before the measurements (start by feeding the probe gas

p1to the upstream part of the permeation cell) the whole permeation cell and the film

are carefully degassed. The downstream pressure increase, due to accumulation of

permeating gas in the closed downstream volume, is measured with a temperature-

controlled MKS Baratron gauge (128 A, 10 mbar range) and recorded as function of

time.115 Figure 3.8 gives an example curve of the downstream pressure p2vs. the

time for Matrimid.

0 10000 20000 30000

Time /s

/mbar

s t

Time-lag

Figure 3.8 – Example curve of Matrimid at a CH4pressure of 10 bar and 35 ◦C.

In a time-lag experiment the permeability coefficient P is estimated from the slope

of the steady state with the general definition of the molar flux through a membrane

J = 1/F ·(dn/dt) and with eq. 2.23:90,92,115,116

P=V·l·TST P

F·T·p1·pST P dp2

dt st

(3.18)

where V denotes the constant downstream volume, F the effective sample area, T

the temperature, l the sample film thickness, p1characterizes the upstream pressure,

TST P is 273.15 K, pST P is 1.013 bar and (dp2/dt)st the steady state downstream

pressure increase. The permeability coefficients are given in Barrer, which is defined

as:

1Barrer = 10−10 cm3(ST P)cm

cm2cmHg s (3.19)

Diffusion coefficients can be estimated by the time-lag τT L as it was shown in eq. 2.26.

3 Methods

3.3 Density

Method 1

The density of the Matrimid and Matrimid/PhenethylPOSS samples was measured

by the immersion method (ISO 1183-1:2004(E)). A MC410 S analytical balance

(Satorius, Göttingen, Germany) and the associated YDK 01 LP density determination

kit were used. The samples were weighed in air and n-heptane at room temperature.

Method 2

For the determination of the density of PIM-1 and PIM-1/PhenethylPOSS sample

a density gradient column (DGC) was used according to DIN 53479 at 296.15 K.

Solutions of calcium nitrate Ca(NO3)2in ethanol were prepared to obtain a density

range of 1.1 to 1.4 cm3/g. For the calibration of the DGC glass floats with defined

densities were used. The correlation of position (height) in the density gradient

column with density was linear and interpolation was performed by linear regression.

For each material sample two specimens were measured.

3.4 Differential Scanning Calorimetry

Differential scanning calorimetry (DSC) was applied for the thermal analysis (DSC

204 F1 Phoenix, Netzsch). The samples were measured in the temperature range

from 223 K to 673 K with a heating rate of 10 K/min under nitrogen.

3.5 Dynamic Mechanical Analysis

For dynamic mechanical analysis (DMA), a DMA 242 D (Netzsch) was used in tensile

mode. The complex elastic modulus E∗and the complex strain compliance D∗were

measured, with a temperature rate of 1 K/min, in the frequency sweep mode between

0.1 – 10 Hz and in the temperature range of 263 K to 573 K first and then twice

from 263 K to 673 K, under nitrogen atmosphere.

3 Methods

In the case of the DMA measurements in tensile mode, the complex modulus of

elasticity E∗is obtained, which is given by:

E∗(T , f)=E‘(T , f)+iE“(T , f)(3.20)

where E‘ is the real part (storage modulus) and E“ the imaginary part (loss modulus).

From the thermodynamic point of view the complex dielectric function is a gener-

alized compliance.63 In order to compare the dielectric with the mechanical data

the mechanical compliance should be therefore considered instead of the modulus.

The compliance is defined as the inverse modulus of elasticity. The so called strain

compliance D∗is given by:

D∗(T , f)=D‘(T , f)−iD“(T , f)(3.21)

where D‘ is the real part and D“ the imaginary part (strain compliance).

3.6 FTIR Spectroscopy

A Vertex70 FTIR spectrometer (Bruker Optics) equipped with a FTIR600 Linkam cell

(Linkam Scientific Instruments Ltd., Chilworth, UK) was used to obtain FTIR spectra.

The samples were measured in transmission mode at room temperature and in a

wavenumber range of 450 to 4500 cm−1, accumulating 32 scans with a resolution of

4 cm−1.

3.7 Scanning Electron Microscopy

Scanning electron microscopy (SEM) was performed with a Zeiss EVO MA10 device.

The samples were broken with prior cooling using liquid nitrogen, to analyze the cross

sections. Afterwards, the samples were sputtered with a thin gold layer.

3 Methods

3.8 Thermogravimetric Analysis

Thermogravimetric analysis (TGA) was conducted to monitor the drying/annealing

process of the cast films and to estimate the PhE-POSS content within the PIM-1

and Matrimid composites. A TG/DTA 220 instrument (Seiko, THASS Germany) was

used in a temperature range from 312 to 1168 K with a heating rate of 10 K/min

and with synthetic air as flow gas.

4 Materials and Sample Preparation

4.1 Materials

4.1.1 Gases

Nitrogen N2, oxygen O2, methane CH4and carbon dioxide CO2were purchased from

Air Liquide and Linde with a purity of 99.9995 %.

4.1.2 Polymer Matrix

Matrimid

Matrimid is an amorphous polymer with a density of 1.24 g/cm3and a glass tran-

sition temperature Tgof about 321 ◦C (see Fig. 4.2). Matrimid 5218 (Fig. 4.1), a

BTDA-DAPI polyimide consisting of 3,3’-4,4’-benzophenone tetra-carboxylic dianhy-

dride and diaminophenylindane was acquired from Huntsman International LLC. This

polyimide is marketed as full-imidized polymer during manufacturing. The material

was used without further purification.

Figure 4.1 – Structure of Matrimid 5218.

4 Materials and Sample Preparation

0 100 200 300 400 500

0.0

0.1

0.2

0.3

0.4

0.5

= 321 °C

PIM-1

W /mW mg

-1

T /°C

exo

Matrimid

Figure 4.2 – DSC measurements for pure Matrimid and pure PIM-1 for the second

heating (heating rate 10 K/min).

PIM-1

PIM-1 (Fig. 4.3) was synthesized by Wayne J. Harrison (The University of Manch-

ester) according to ref.117 (see appendix A.1). The density of PIM-1 is 1.15 g/cm3.

For PIM-1 no glass transition temperature can be observed before decomposition

(see Fig. 4.2).

Figure 4.3 – Structure of PIM-1.

4.1.3 Nanofiller: Phenethyl-POSS

Phenethyl-POSS (PhE-POSS) was used as nanofiller due to good solubility/ mis-

cibility and expected interactions of the phenyl substituents and the π–system of the

used polymers (POSS is a trademark of Hybrid Plastics Inc. (Hattiesburg, MS). See

also www.hybridplastics.com.). PhE-POSS was purchased from Hybrid Plastics, Inc.

A detailed characterization of PhE-POSS is given in reference.118,119 The material

4 Materials and Sample Preparation

was used without further purification. MALDI-TOF was used to characterize PhE-

POSS. As discussed in ref.,119 the spectra showed a mixture of octa- (T8, n = 8),

deca- (T10, n = 10) PhE-POSS and small amounts of larger cage sizes as well. It

is generally known from the synthesis of POSS that the main fraction of the product

consists of octa-cages.120,121

Figure 4.4 – Structure of PhenethylPOSS.

4.2 Sample Preparation

The polymer films were prepared by solution casting. The used temperature treat-

ments are compromises of temperatures which are high enough to remove the residual

solvent but preferably low to reduce previous physical aging effects.

4.2.1 Matrimid and Matrimid/PhE-POSS Composites

In the first step, 0.7 g of Matrimid and different amounts of PhE-POSS were dissolved

in 12 ml dichloromethane (DCM) and mixed for 4 h. Afterwards, the solution was

casted on a Teflon-plate in a closed chamber to ensure a slow first evaporation of

DCM. In the next step, the samples were dried in vacuum at 100 ◦C for 6 days.

The obtained Matrimid/PhenethylPOSS films were transparent and yellowish. With

increasing PhE-POSS concentration, the films became less transparent. For high

PhE-POSS concentrations, small areas of high cloudiness were formed (see Fig-

ure 4.5).

4 Materials and Sample Preparation

Figure 4.5 – Images of cast Matrimid/PhE-POSS films with 1 wt%and with 7 wt% PhE-

POSS.

4.2.2 PIM-1 and PIM-1/PhE-POSS Composites

Here, 1 g of PIM-1 and different amounts of PhE-POSS were dissolved in 12 ml

chloroform and stirred for 4 hours. Afterwards, the solution was filtered (5 µm PTFE-

filter) and then cast on a Teflon plate. In order to ensure slow evaporation of the sol-

vent, the films were dried in chloroform atmosphere at room temperature for 2 days.

Based on thermogravimetric analysis (TGA), the samples were then heated up to

348 K (75 ◦C) for 3 days, all giving transparent, yellowish films (see Figure 4.6). For

more details to the finding of the temperature treatment see appendix A.1. With in-

creasing PhE-POSS content the films tend to become more brittle. As for pure PIM-

1, no glass transition could be measured before the decomposition of the nanocom-

posites.

Figure 4.6 – Image of cast PIM-1 film and with 30 wt% of PhE-POSS.

5 Matrimid and Matrimid/POSS

Nanocomposites∗

Abstract

The dielectric properties of Matrimid and Matrimid/ PhE-POSS nanocomposites

were investigated using BDS in combination with standard techniques. Matrimid

shows one relaxation process assigned as β∗–relaxation and a conductivity contri-

bution. The relaxation process has a high activation energy of 99 kJ/mol. Thus, this

process is assumed to be of cooperative nature due to a π−π–stacking of the phenyl

rings of Matrimid. The influence of the thermal history on Matrimid was analysed

with BDS as well, where an annealing effect is found. The Matrimid/PhenethylPOSS

nanocomposites show a miscibility on a molecular level up to a concentration of about

4 wt% PhenethylPOSS. For higher concentrations, a phase separated structure was

indicated. The conductivity of both systems is explained by π−π–stacking of the

phenyl rings, which enhances charge transport.

Furthermore, gas transport properties were investigated for Matrimid and Matrimid/

PhenethylPOSS composites for N2, O2, CH4and CO2at 35 ◦C. The permeability of

Matrimid was enhanced by 1 wt% embedded in the polymer matrix for all analyzed

gases. In addition, the plasticization effect of Matrimid was reduced for high POSS

contents in the composites. Permeability, selectivity and diffuion coefficients evi-

denced a phase separated structure for the Matrimid/PhE-POSS composites above

8 wt%.

∗Similar content (section 5.1 and 5.2) was published in Konnertz, N.; Böhning, M.; Schönhals, A.,

Polymer, 2016, 90, 89 - 101.

5 Matrimid and Matrimid/POSS Nanocomposites

5.1 Introduction

Sánchez-Soto et al. studied the morphology and properties of polycarbonate Phen-

ethylPOSS nanocomposites which were prepared by melt blending.122 A good misci-

bility up to a PhenethylPOSS concentration of 5 wt% was found. At higher concentra-

tions, micron-sized aggregates of POSS are observed with scanning and transmission

electron microscopy. Furthermore, wide angle X-ray diffraction revealed a crystalline

structure comparable to pure PhenethylPOSS but with lower crystal sizes and less

ordered structure within the POSS-rich domains compared to pure PhenethylPOSS.

Miscibility, specific interactions, and thermomechanical properties of a novolac resin

PhenethylPOSS nanocomposite were studied by Wu et al.123 Here, a good miscibil-

ity up to a concentration of 20 wt% was observed. The high miscibility was explained

by hydrogen bonds between the hydroxyl groups of the phenolic resin and the POSS

siloxane groups which was evidenced by FTIR. At higher POSS concentrations an

aggregation of the nanofiller was also verified by polarized optical spectroscopy,

differential scanning calorimetry, and wide angle X-ray diffraction.

Hao et al. investigated polystyrene/PhenethylPOSS118 and poly(bisphenol A car-

bonate) (PBAC)/PhenethylPOSS systems by broadband dielectric spectroscopy119

and gas transport measurements.115 For polystyrene a molecular miscibility up to

40 wt% of POSS was found. In contrast, PBAC/PhenethylPOSS showed a phase

separation at a concentration of ca. 7 wt%. Due to π−πstacking of the phenyl

rings of POSS and polystyrene,123 the miscibility for the polystyrene/POSS system

is enhanced compared to polycarbonate.118,119,122

Li et al. successfully incorporated octa amid acid POSS (up to 20 wt%) with sub-

sequent embedding of Zn2+ in Matrimid by solution casting124 to improve the gas

transport properties.125 A good miscibility of POSS and Matrimid due to inter-

molecular hydrogen bonds between the carboxylic groups of POSS and Matrimid

was found.

5.2 Relaxation Behavior

Recently, Comer et al. investigated the dielectric and mechanical relaxation be-

havior of Matrimid in a temperature range from 123 K to 573 K (one run, steps of

5 Matrimid and Matrimid/POSS Nanocomposites

∆T = 10 K).126 The prepared solution-casted Matrimid film was dried after casting

seven days at room temperature at ambient conditions, four days under vacuum at

373 K, at 473 K for one day and then in a nitrogen purge at 603 K for 30 min. Using

mechanical spectroscopy (DMA), a γ-relaxation was observed at low temperatures

(f = 1 Hz, T ≈153 K) for their Matrimid sample. At higher temperatures than the

γ-relaxation, a β-relaxation (f = 1 Hz, T ≈348 K) and an α-relaxation was observed.

The β-relaxation was claimed to be of “localized, relatively non-cooperative molecu-

lar origin”,126 while the α-relaxation was assigned to segmental fluctuation. The γ-

and β-relaxation were also confirmed by Comer et al. using dielectric spectroscopy.

The quantitative analysis of both processes yields activation energies which were

further analyzed by the Starkweather approach.127

This section focuses on the relaxation behavior of pure Matrimid and Matrimid/

PhenethylPOSS composites. Here, in contrast to Comer et al.,126 the dielectric mea-

surements of Matrimid and the Matrimid/PhenethylPOSS composites were carried

out with a specific sample conditioning to study the influence of the temperature

treatment on the molecular mobility of Matrimid and the nanocomposites.

5.2.1 Characterization

The thermal glass transition temperatures (Tg) of the samples were determined by

means of DSC. Sample specifications, thermal glass transition temperatures, den-

sities (ρ), and film thicknesses of the samples are given in Table 1. The sample

designations include the concentration of PhE-POSS within the composites. The

results for the concentration dependence of the density and Tgof the samples are

discussed in detail in paragraph 5.2.3.

5 Matrimid and Matrimid/POSS Nanocomposites

Table 5.1 – Sample codes with the corresponding PhE-POSS concentrations, glass

transition temperatures for the first and second heating, their densities,

and the film thickness of MI and the MI/PhE-POSS composites.

Sample wt% Tg/K Tg/K ρ/g cm−3Thickness /µm

(1st heating) (2nd heating)

MI-00 0 575 594 1.24 90.5

MI-006 0.6 574 593 1.22 93.1

MI-01 1 573 590 1.25 94.2

MI-02 2 573 589 1.27 90.4

MI-03 3 567 587 1.28 107.0

MI-04 4 566 586 1.25 104.7

MI-07 7 557 582 1.26 103.1

MI-10 10 557 583 1.26 107.1

MI-15 15 558 583 1.25 110.5

MI-20 20 557 583 1.24 116.5

PhE-POSS 100 - 517119 1.22119 -

It was attempted to adjust the film thickness to around 100 µm. Due to an increasing

viscosity with increasing PhE-POSS concentration, the thickness of the composites

films increases slightly with the POSS amount.

Thermogravimetric analysis (TGA) was applied to prove the PhE-POSS content

within the Matrimid-PhE-POSS composites. Figure 5.1 gives example curves of

the TGA measurements, and the inset provides a detailed view on the TGA curves

at high temperatures for MI-00 and selected MI/PhE-POSS composites. The inset

presents a detailed view on the TGA curves above 900 K.

5 Matrimid and Matrimid/POSS Nanocomposites

400 600 800 1000 1200

100

T /K

Weight loss /%

900 1000 1100 1200 1300

7 wt%

2 wt%

Weight loss /%

T /K

20 wt%

Figure 5.1 – TGA curves of MI-00 (dashed-dotted line), MI-02 (solid line), MI-07

(dashed line) and MI-20 (dotted line). The inset gives a detailed view

of the TGA curves at high temperatures.

The polymer matrix and the POSS are completely oxidized during heating. It is

assumed that only Si as SiO2remains in the residue as it can be seen from the

plateaus of the TGA curves at high temperatures (Figure 5.1). This plateau value

increases with increasing POSS content (see inset of Figure 5.1). For this reason

it is concluded that the residual weight can be regarded as measure of the POSS

concentration.

In Figure 5.2 the remaining weight percent is plotted versus the nominal PhE-POSS

concentration used for the preparation.

0 5 10 15 20

c(PhE-POSS) /wt%

Remaining weight percent /%

Figure 5.2 – Remaining weight percent vs. c(PhE-POSS). The solid line is a linear fit

to the data.

5 Matrimid and Matrimid/POSS Nanocomposites

The relation between residual weight and POSS concentration is linear, supporting

this approach, to estimate the POSS content by TGA.

5.2.2 Relaxation Behavior of Pure Matrimid

5.2.2.1 Broadband Dielectric Spectroscopy

As discussed above, Comer et al. investigated the dielectric relaxation behavior of

Matrimid in a temperature range from 123 K to 573 K with temperature steps of

10 K.126 In that work the casted Matrimid film was dried seven days at ambient

conditions, four days under vacuum at 373 K, at 473 K for one day, and finally

in a nitrogen purge at 603 K for 30 min. Two relaxation processes were observed

below Tg. A first relaxation mode was observed in the temperature range from 153 K

to 263 K and was denoted γ–relaxation. A further process was found at higher

temperatures (370 K – 500 K) than the γ–process and is assigned to a β–relaxation.

Figure 5.3 shows our measurement of the dielectric loss of pure Matrimid (MI-00)

in dependence on frequency and temperature in a 3D representation for the second

heating cycle.

Figure 5.3 – Dielectric loss logε“vs. frequency and temperature for pure Matrimid (MI-

00) in a 3D presentation for the second heating cycle (compare Figure 3.6).

In contrast to the work of Comer et al., only one relaxation process is observed,

indicated as a peak in the dielectric loss ε“. The γ–relaxation described by Comer et

al. at low temperatures is not observed here. The reason is not known and requires

5 Matrimid and Matrimid/POSS Nanocomposites

further investigations. One reason might be the different sample preparation and

annealing procedure.

The observed relaxation peak is rather broad. With increasing temperature, the

process shifts to higher frequencies as expected. The relaxation mode is located in

a temperature range similar to the β–process of Comer et al.126 Here, the process

is called β∗–relaxation for reasons discussed below. In the temperature range above

the β∗–process, a strong increase in ε“is observed, which increases with decreasing

frequency. This effect is due to conductivity phenomena related to drift motions of

mobile charge carriers. Surprisingly, conductivity is observed at temperatures well

below the glass transition temperature of Matrimid. This effect will be discussed in

detail in the section 5.2.2.2 below.

The HN-function (eq. 3.12) was fitted to the data leading to the relaxation rate fmax

and the dielectric strength ∆ε. Examples for the fit are given in Figure 5.4.

-1 0 1 2 3 4 5 6

-2.2

-2.0

-1.8

-1.6

-1.4

390 K

465 K

max

Conductivity

max

log (f /Hz)

log

´´

Figure 5.4 – Dielectric loss vs. frequency for MI-00 at 390 K and 465 K. The lines

are fits of the HN function to the data. The dashed lines represent the

contribution of the respective relaxation process.

The temperature dependence relaxation rates fmax for the β∗–relaxation for all heat-

ing and cooling runs are plotted vs. inverse temperature in Figure 5.5 (relaxation

map). For comparison, the data of Comer et al. are included too. At first glance,

the temperature dependence of the relaxation rates seems to follow the Arrhenius

equation (see eq. 2.2).

5 Matrimid and Matrimid/POSS Nanocomposites

1.75 2.00 2.25 2.50 2.75

Heating

Cooling

Heating

Cooling

Comer et al.

log

(

max,

/Hz

)

1000/T /K

-1

Figure 5.5 – Relaxation rate fmax,β∗vs. inverse temperature for pure Matrimid (MI-00)

including the complete temperature treatment (1st heating, 1st cooling,

2nd heating, 2nd cooling), whereas first cooling and second heating are

superposed. Furthermore, the results for pure Matrimid from Comer et

al. are included.126 The lines are fits of the Arrhenius equation to the

corresponding data.

Obviously, the apparent activation energy changes with the thermal treatment of

the sample. The first change in the apparent activation energy is observed between

the first heating and the first cooling cycle, where for the first cooling run a higher

apparent activation energy is found than for the heating cycle. This might be due

to the evaporation of traces of residual solvent and/or the formation of a densified

structure during the temperature treatment. The apparent activations energies for

the first cooling and the second heating run are more or less identical. This leads

to the conclusion that the cooling process does not further affect the structure of

Matrimid. The thermal treatment during the second heating up to 573 K results in

a decrease of EAof the β∗–relaxation. This indicates a loosening of the structure or

a change in the packing of the polymer segments, leading to an enhanced mobility.

This assumption is in agreement with the results for the activation energy of Comer

et al.126 They heated the Matrimid film before the BDS measurements up to 603 K

leading to a similar apparent activation energy of the β∗–relaxation.

The activation energies estimated for the β∗–relaxation are relatively high and not

characteristic for a solely β–process. The activation energy of true β–processes

for polymers is expected to be in the range of 40 kJ/mol to 60 kJ/mol. Here, the

activation energies are found in the range of 100 kJ/mol (see Figure 5.6). Moreover,

the β∗–relaxation is found at relatively high temperatures close to the glass transition

temperature. This is also untypical for a β–process.

5 Matrimid and Matrimid/POSS Nanocomposites

A process with similar properties to the β∗–relaxation reported here was also ob-

served for Poly(ethylene 2,6 naphtalene dicarboxylate) (PEN).128–130 The reported

activation energies for the β∗–relaxation of PEN are in a range similar to the values

found here for the β∗–relaxation observed for Matrimid. Hardy et al. assigned the β∗–

relaxation of PEN to fluctuations of agglomerated naphthalene groups. Spies/Gehrke

and Jones et al. evidenced such an agglomeration of naphthalene groups in solu-

tion131 as well as in solid state132 with optical spectroscopy. These arguments lead

to the assumption that the β∗–relaxation observed for Matrimid might also be due

to molecular fluctuations of agglomerated phenyl groups. Wide angle X-ray mea-

surements evidence such aggregates with a molecular spacing of 3.2 Å and 5.3 Å

(Appendix A.4).133 Such molecular fluctuations require a certain cooperativity of the

underlying molecular motions, which was also evidenced by the Starkweather anal-

ysis given in ref.126 This analysis indicates a relatively high value of the activation

entropy which is characteristic for cooperative processes as well.

The strong increase in the imaginary part ε“at low frequencies is attributed to

conductivity effects (see Figure 5.4). This indicates a high mobility of charge car-

riers within Matrimid even below the thermal glass transition temperature which is

discussed in detail in paragraph 5.2.2.2.

A Matrimid film was prepared as described in 4.2 to verify that the structure of

Matrimid is stable after heating the sample up to 573 K. Afterwards, the sample

was measured using BDS as previously accomplished with an additional heating (up

to 573 K) and cooling (down to 173 K) (sample code: MI-3Heat). Furthermore, a

Matrimid film was prepared as described in section 4.2, then dried additionally at

473 K for one day in vacuum and afterwards, heated to 573 K in air for 30 minutes

(sample code: MI-00-300) to compare the influence of the film preparation with the

results of Comer et al. This film was measured with BDS using the temperature

program as described in section 3.1. The activation energies of the β∗–relaxation for

the different heating (H) and cooling (C) runs of MI-00, MI-00-300 and MI-3Heat

as well as the EA,β of Comer et al. are shown in Figure 5.6.

5 Matrimid and Matrimid/POSS Nanocomposites

100

120

140

160

MI-00

MI-00-300

MI-3Heat

Comer et al.

/kJ mol

-1

Temperature ramp

Figure 5.6 – Activation energy EA,β∗for the different heating (H) and cooling runs (C)

for MI-00, MI-00-300, and MI-3Heat. Furthermore, the value of Comer et

al. is included.126 The lines are guide for the eyes.

MI-00-300 shows an opposite behavior of EA,β∗compared to the other Matrimid films.

The activation energy of the β∗–relaxation for MI-00-300 decreases after heating up

to 473 K, increases afterwards and finally strongly increases after heating the sample

up to 573 K.

The observed changes of the activation energy with the heat treatment cannot be

attributed to chemical alterations within the samples, especially because it is con-

sidered as fully imidized. The material is still completely soluble even after the

strongest thermal impact. Also, the FTIR spectra for the untreated and the treated

samples are identical (see Figure 5.7). Therefore, it is concluded that the observed

changes are due to changes of the packing density of the polymer segments.

3500 3000 2500 2000 1500 1000

MI-00-300

MI-00

wavenumber /cm

-1

MI-00-300

after BDS

N N

Figure 5.7 – FTIR spectra of MI-00, MI-00-300 and the sample MI-00-300 after BDS

measurement.

5 Matrimid and Matrimid/POSS Nanocomposites

5.2.2.2 Conductivity

As discussed above, Matrimid as well as the corresponding composites show a strong

conductivity contribution at temperatures well below their thermal glass transition

temperatures. This is an unusual behavior because for most conventional polymers

conductivity effects are observed above Tgbecause charge transport is related to

segmental dynamics in these systems.63 Therefore, it is concluded that for the Ma-

trimid systems charge transport is due to a different mechanism. This conductivity

effect is quantified by the complex conductivity given by equation 3.5.

-1 0 1 2 3 4 5 6

-14

-12

-10

-8

-6

570 K

513 K

462 K

log(

/S cm

-1

)

log (f /Hz)

Figure 5.8 – Real part of the complex conductivity σ0versus frequency for the second

cooling run for pure Matrimid MI-00 at different temperatures (T = 570 K;

T = 513 K; T = 46 K).

The frequency dependence of the real part of the complex conductivity spectra shows

the typical behavior, which is expected for semi-conducting polymeric materials (see

section 3.1.3). The data is approximated by the Jonscher power law (eq. 3.15) and

σDC is obtained by fitting the Jonscher equation to the data.

Figure 5.9 depicts the DC conductivity σDC as a function of inverse temperature for

pure Matrimid. The temperature dependence of the DC conductivity can be described

by the Arrhenius equation (eq. 2.2). For conventional amorphous polymers, the con-

ductivity is related to segmental dynamics and its temperature follows the Vogel-

Fulcher-Tammann equation (eq. 2.3). For Matrimid, the temperature dependence is

Arrhenius–like (EA,σDC = 115 kJ/mol) and is observed at temperatures below the glass

transition temperature. Therefore, it is concluded that for Matrimid the conductivity

is not directly related to segmental dynamics. As discussed above, agglomerates

5 Matrimid and Matrimid/POSS Nanocomposites

formed by stacked phenyl groups by π−π–interaction were found with wide angle

X-ray scattering measurements. Due to the overlapping π–systems, charge transport

in Matrimid is enhanced.

1.7 1.8 1.9 2.0 2.1 2.2

-14

-13

-12

-11

log

(

/S cm

-1

)

1000/T /K

-1

Figure 5.9 – Direct current conductivity (σDC ) for the second cooling run vs. inverse

temperature for MI-00. The line is a fit of the Arrhenius equation to the

data.

5.2.2.3 Dynamic Mechanical Analysis

The dynamic-mechanical properties of Matrimid were determined by DMA. The loss

modulus E“ and the strain compliance D“ vs. temperature are compared for pure

Matrimid for the third heating at 1 Hz in Figure 5.10. The loss modulus shows the

β∗– relaxation at lower and an α–relaxation (dynamic glass transition) at higher

temperatures. The dynamic glass transition is related to segmental fluctuations. A

similar behavior is reported by Comer et al.126 Compared to the loss modulus, the

imaginary part of the compliance shows also a β∗–relaxation at lower temperatures.

For higher temperatures in the region, where the α–relaxation is observed in the

modulus, the onset of flow is evidenced in the loss part of the compliance by a strong

increase of D“ with increasing temperature.

5 Matrimid and Matrimid/POSS Nanocomposites

200 300 400 500 600

1.5

2.0

2.5

log(E´´ /MPa)

T /K

-5

-4

-3

-2

-1

-Relaxation

log

(

D´´ / 10

-3

MPa

-1

)

Figure 5.10 – Loss modulus E“ (solid line) and loss part of the strain compliance D“

(dashed line) for Matrimid (MI-00) vs. temperature for the third heating

run at 1 Hz (DMA).

Figure 5.11 compares the temperature dependence of the dielectric loss ε“and loss

part of the mechanical compliance D“ at the same frequency.

200 300 400 500 600

0.00

0.05

0.10

0.15

Flow

Conductivity

D´´ /GPa

-1

T /K

-Relaxation

0.00

0.02

0.04

0.06

0.08

´´

Figure 5.11 – Loss part of the strain compliance D“ (DMA) (dashed line) and dielectric

loss ε“(solid line) vs. temperature of Matrimid (MI-00) for the second

cooling run at a frequency of 1 Hz.

In principle, a similar behavior is observed for dielectric and mechanical properties.

Compared to the dielectric data the loss peak for the compliance is shifted a bit to

higher temperatures. This effect is commonly observed for polymers.134 Both methods

are sensitive to different molecular probes. While dielectric relaxation is related to

dipole fluctuations, the mechanical compliance senses the fluctuations of the shear

angle. This means both methods monitor the same process but through a different

window.

5 Matrimid and Matrimid/POSS Nanocomposites

Figure 5.12 gives the loss part of the elastic modulus versus temperature for two

different frequencies.

250 300 350 400 450 500

1.8

1.9

2.0

2.1

Process II

log(E´´ /MPa)

T /K

Process I

Figure 5.12 – Loss modulus E“ for Matrimid (MI-00) vs. temperature for the third heat-

ing run at 0.3 Hz (solid line) and 10 Hz (dashed line).

While for high frequencies 10 Hz and 1 Hz (see Figure 5.10) only one broad peak

is observed, this peak splits into two processes for lower frequencies. Also a closer

inspection of the dielectric loss gives evidences that the β∗–relaxation consist of two

processes (see Figure 5.13) which merge together for higher frequencies or temper-

atures.

-2 -1 0 1 2 3 4 5 6 7

-2.2

-2.0

-1.8

-1.6

-1.4

374.1 K

431.1 K

Process II

log ´´

log (f /Hz)

Process I

Figure 5.13 – Dielectric loss vs. frequency for MI-00 at 431.1 K and 374.1 K for the

first cooling run.

Unfortunately, due to the close overlapping the processes cannot be separated un-

ambiguously. Bearing in mind that WAXS pattern shows two different spacings for

stacks and the assignment of the β∗–relaxation to molecular fluctuations to these

5 Matrimid and Matrimid/POSS Nanocomposites

aggregates, it is concluded that the observed two modes of the β∗–relaxation are

due to these different aggregates.

5.2.3 Properties of Matrimid/POSS Nanocomposites

Before the dielectric properties are discussed in detail, DSC and density measure-

ments are considered.

5.2.3.1 Differential Scanning Calorimetry

In Figure 5.14, DSC measurements of pure Matrimid MI-00 for the first and second

heating run are shown. The peak at low temperatures of the first heating run is

attributed to water. When the sample is exposed to normal atmosphere after the

second heating run, the DSC measurements show this peak for the first heating run

again.

300 400 500 600 700

0.0

0.1

0.2

0.3

0.4

heating

= 594 K

DSC /mW mg

-1

T /K

exo

= 575 K

heating

Figure 5.14 – DSC measurements for pure Matrimid MI-00 for the 1st and the 2nd

heating run.

The glass transition temperatures Tgwere taken from the step in the heat flow

(Figure 5.14). Tgof pure Matrimid and the corresponding nanocomposites with

POSS for the first and second heating run are presented in Figure 5.15.

5 Matrimid and Matrimid/POSS Nanocomposites

0 4 8 12 16 20

550

560

570

580

590

600

heating

c(PhE-POSS) /wt%

heating

Figure 5.15 – Dependence of the thermal glass transition temperature Tgon the con-

centration of PhE-POSS for the 1st and the 2nd heating run for pure

Matrimid MI-00 and the MI/PhE-POSS composites. The DSC measure-

ments were carried out up to 670 K with a heating rate of 10 K/min. The

lines are guides for the eyes.

Tgis shifted to higher temperatures for the second heating compared to the first run.

For the first heating run, Tgdecreases with increasing concentration of PhE-POSS

up to about 8 wt%. For higher PhE-POSS concentrations, Tgbecomes independent

of the amount of POSS. A comparable dependence of the glass transition temper-

ature on the concentration of PhE-POSS was observed for polycarbonate/POSS

nanocomposites.119 In that case, the decrease in Tgwith increasing POSS concen-

tration was explained by a plasticization effect where the plateau value of Tgfor

higher concentrations of POSS evidenced a (nano)phase separation. Compared to

polycarbonate, Matrimid is a stiff polymer with a high amount of free volume. In

the case of low concentrations of POSS, PhE-POSS can be dissolved on a molec-

ular level, probably in the free volume sites where the phenyl rings of POSS can

interact with that of Matrimid. This assumption is further supported by the results

for the densities which are discussed below. By that mechanism the densed packed

structure of Matrimid is partially disturbed and the molecular mobility of the poly-

mer segments (or parts of it) is enhanced which leads to a decrease of Tg. For ca.

8 wt% of PhE-POSS, all available free volume sites are filled up and with increas-

ing POSS concentration PhE-POSS cannot be dissolved in the Matrimid structure

and (nano)phase separation takes place with further increase of the concentration of

POSS. This also means when the saturation of PhE-POSS in the Matrimid matrix

is reached the composition of the mixed phase remains constant. Thus, the molecu-

lar interaction between Matrimid and POSS does not change further, leading to a

5 Matrimid and Matrimid/POSS Nanocomposites

constant Tgindependent of the concentration of POSS. This is in good agreement

with a prediction of Tgfor partially miscible systems by Brostow et al.135 Like for

pure Matrimid, the thermal glass transition is shifted to higher temperatures for the

second heating. The observed increase of Tgis caused by structural changes and

a densification of the Matrimid matrix due to a partial collapse of the free volume

sites. Compared to the first heating run, the transition from the decrease of Tgto the

plateau value is shifted from ca. 8 wt% of PhE-POSS to 4 wt%. This is in agreement

with the picture developed above that PhE-POSS is solved in the free volume sites.

Due to the thermal treatment, the free volume sites are partially collapsed and the

miscibility limit is shifted to lower concentrations of PhE-POSS. Moreover, this is

also in agreement with the dielectric experiments discussed below where the second

heating run is considered as well and nanophase separation is observed at around

4 wt% of PhE-POSS.

5.2.3.2 Density

The densities of the composites are plotted versus POSS concentration in Fig-

ure 5.16.

0 20 40 60 80 100

1.20

1.22

1.24

1.26

1.28

1.30

Ideal 2 phase behavior

/g cm

-3

c(PhE-POSS) /wt%

Critical concentration

for phase separation

Figure 5.16 – Density of the MI/PhE-POSS composites vs. the PhE-POSS concen-

tration. The solid line is a guide for the eyes. The dotted-dashed line

indicates the behavior of an ideal two component system.

Surprisingly, for low POSS concentrations the density of the composites is higher

than the densities of both compounds. It increases with the POSS concentration for

low c(PhE-POSS). After the maximum between ca. 5 wt% and ca. 8 wt%, ρdecreases

5 Matrimid and Matrimid/POSS Nanocomposites

with further increase of the POSS concentration and approaches the behavior which

is characteristic for an ideal two component system (Figure 5.16).

Hao et al. investigated the molecular mobility of Poly(bisphenol A carbonate)

(PBAC)/ PhE-POSS nanocomposites by BDS.119 They observed an opposite depen-

dence of the density on the POSS concentration. In that case, the density decreases

with increasing concentration of POSS in the miscible state. This was explained by

the assumption that the adding of POSS molecules leads to an increase of the free

volume and therefore to a decrease of the density. Compared to PBAC, Matrimid has

a larger free volume.136 In the case of low concentrations PhE-POSS is dissolved

due to this free volume in the Matrimid matrix leading to an increase of the density.

With increasing concentration, molecules saturate the free volume of the Matrimid

matrix and an aggregation of PhE-POSS molecules occurs, leading to a (nano)phase

separated structure. Thus, with further increasing POSS concentration an ideal two

phase behavior can be observed for the density.

5.2.3.3 Broadband Dielectric Spectroscopy

Due to the strong effect of the thermal treatment on the properties of Matrimid dis-

cussed before the dielectric properties of the composites are discussed for the second

cooling run in the following part. In Figure 5.17 the dielectric loss for the samples

MI-00, MI-02, MI-15, and PhE-POSS is given as a function of the temperature at

a frequency of 1 kHz as an example of the dielectric spectra for the composites.

200 300 400 500 600

-3.0

-2.5

-2.0

-1.5

-1.0

MI-00

MI-02

MI-15

PhE-POSS

Process IV

Process I

log

´´

T /K

Process II + III

Figure 5.17 – Dielectric loss vs. temperature for the second cooling for pure Matrimid

MI-00, for MI/PhEPOSS with 2 wt% MI-02, 15 wt% PhEPOSS MI-15,

and pure PhE-POSS at a frequency of 1 kHz.

5 Matrimid and Matrimid/POSS Nanocomposites

The peak in the dielectric loss ε“ at around 250 K for PhE-POSS indicates the

dynamic glass transition or α–relaxation of POSS (process I). For a more detailed

discussion see also ref.119 As discussed in section 5.2.2, a β∗–relaxation (process II)

and a conductivity phenomenon (process IV) is observed for Matrimid. For MI-02,

one broad peak which is similar to Matrimid is present. This behavior indicates

that PhE-POSS is miscible in Matrimid on a molecular level. The dielectric loss

of MI-15 has, besides the one broad peak at high temperatures which is related to

Matrimid, one additional peak at temperatures which is close to the α–relaxation

of pure PhE-POSS. Obviously, the latter process belongs to bulk-like PhE-POSS

in a (nano)phase separated state. The conductivity contribution is observed for all

samples while its strength increases with increasing PhE-POSS concentration.

The dielectric loss log ε“is plotted vs. frequency log f for MI-00, MI-02 and MI-15

at a fixed temperature of 423 K in Figure 5.18 to analyze the broad peak at high

temperatures (process II and III, Figure 5.17).

0 2 4 6

-2.0

-1.5

-1.0

-0.5

MI-00

MI-02

MI-15

log

´´

log (f /Hz)

MWS

-Relaxation

Figure 5.18 – Dielectric loss for the second cooling vs. frequency at 423 K for Matrimid,

MI-02, and MI-15.

For MI-00 and MI-02 only one broad peak is observed which indicates miscibil-

ity on a molecular level. In case of MI-15, an additional relatively sharp peak is

visible which is related to interfacial polarization effects (Maxwell-Wagner-Sillars

polarization, MWS), supporting the assumption of a phase separation for high PhE-

POSS concentrations. The following parts discuss the different relaxation processes

belonging to Matrimid and PhE-POSS, respectively.

5 Matrimid and Matrimid/POSS Nanocomposites

Relaxation Process Belonging to Matrimid: β∗–Relaxation

In this part, the influence of the PhE-POSS concentration on the β∗–relaxation

is discussed. The dielectric spectra of the composites are analyzed by fitting the

Havriliak-Negami function (eq. 3.12) to the data. The relaxation rates of the β∗–

relaxation fmax,β∗are shown exemplary for MI-00, MI-02, and MI-07 plotted versus

inverse temperature (Figure 5.19).

1.8 2.1 2.4 2.7 3.0

MI-00

MI-02

MI-07

log

(

max,

/Hz

)

1000/T /K

-1

Figure 5.19 – Relaxation rate fmax,β∗for the second cooling vs. inverse temperature for

Matrimid, MI-02, and MI-07. The lines are fits of the Arrhenius equation

to the corresponding data.

The temperature dependence of the relaxation rates is Arrhenius-like (eq. 2.2). The

activation energies EA,β∗are extracted and discussed for PhE-POSS concentrations

up to 7 wt% (Table 5.2).

5 Matrimid and Matrimid/POSS Nanocomposites

Table 5.2 – Activation energy EA,β∗determined by Arrhenius of different MI/PhE-POSS

composites.

Sample EA,β∗/kJ mol−1

MI-00 99.2

MI-006 102.5

MI-01 118.7

MI-02 101.5

MI-03 101.9

MI-04 96.1

MI-07 79.0

EA,β∗seems to be almost independent of the POSS content up to a PhE-POSS

concentration of 4 wt%. The Matrimid matrix is only slightly influenced by the PhE-

POSS molecules, which are incorporated in or close to the free volume sites, and

by the proposed aggregates. Since the β∗–relaxation is assigned to the aggregates,

EA,β∗is almost independent of c(PhE-POSS). With further increasing PhE-POSS

concentration, EA,β∗seems to decrease slightly. For POSS concentrations higher

than 7 wt%, the β∗–relaxation overlaps with the MWS polarization peak (see be-

low). For those nanocomposites, the analysis of the β∗–relaxation cannot be done

unambiguously.

Relaxation of Bulk-Like PhE-POSS

For PhE-POSS concentrations higher than 4 wt%, an additional peak in the imagi-

nary part of ε“ (about T = 270 K) close to the α–relaxation of PhE-POSS is observed

(Figure 5.17 and Figure 5.20). Its dielectric strength increases with increasing POSS

concentration.

5 Matrimid and Matrimid/POSS Nanocomposites

200 240 280 320

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

MI-00

MI-10

MI-15

PhE-POSS

log

´´

T /K

Figure 5.20 – Dielectric loss for the second cooling vs. temperature for pure PhE-POSS,

MI-00, MI-10, and MI-15 at a frequency of 1 kHz.

The peak is directly related to the dynamic glass transition of bulk-like PhE-POSS

which indicates a (nano)phase separation of PhE-POSS and Matrimid. This is in

agreement with the results described above. The increase of the dielectric strength

of this peak with increasing PhE-POSS concentration directly evidences the α–

relaxation of PhE-POSS-rich domains which grow and/or increase in numbers with

increasing POSS content. Compared to the α–relaxation of bulk POSS, the observed

peak for the composites shifts slightly to higher temperatures. This shift can be due to

two different origins. Firstly, the deeply frozen Matrimid matrix can be considered as

a confinement to the POSS-rich domains which may constrain the mobility in these

domains and thus increase its glass transition temperature. Secondly, if Matrimid is

dispersed in the POSS-rich domains to a marginal extent, this can also lead to an

increase of its glass transition temperature. Unfortunately, on the basis of the given

experimental data, one cannot discriminate between both possibilities.

Dielectric Process due to the Phase Separated Structure: Maxwell-Wagner-Sillars Polar-

ization

As discussed above, in addition to the broad peak of the β∗–relaxation an addi-

tional process can be observed in the same temperature range for higher POSS

concentrations (see Figure 5.16). Its intensity increases with increasing PhE-POSS

concentration. In phase separated morphologies, charges carriers can be separated

on a mesoscopic length scale at the phase boundaries, leading to an interfacial polar-

ization (MWS63). The proposed structure of the POSS/Matrimid composites consists

5 Matrimid and Matrimid/POSS Nanocomposites

of PhE-POSS domains and a Matrimid matrix (Figure 5.21). The Tgof PhE-POSS

is low compared to Tgof Matrimid (Table 5.1). In the temperature range of the

β∗–relaxation of Matrimid, the POSS molecules are in the liquid state and thus the

mobility of the charge carriers within the PhE-POSS rich domains is much higher

than in the Matrimid matrix, but their drift motion movement is blocked at the inter-

faces to the Matrimid matrix. This leads to an interfacial polarization - the MWS

polarization process. The high mobility of the charge carries in the POSS rich do-

mains is the molecular reason that the MWS process is observed at temperatures

which are below the glass transition temperature of Matrimid. A similar behavior

was observed for PhE-POSS/PBAC composites.119 The HN-function (eq. 3.12) is

also employed to analyze this MWS interfacial polarization process. The resulting

characteristic rates fmax,MW S are given versus inverse temperatures in Figure 5.21.

2.0 2.4 2.8 3.2

-1

MI-07

MI-15

MI-20

max, MWS

1000/T /K

-1

Figure 5.21 – Characteristic rate fmax,MW S of the Maxwell-Wagner-Sillars polarization

for the second cooling vs. inverse temperature for MI-07, MI-15, and

MI-20. The lines are fits of the VFT-equation to the corresponding data.

The scheme shows the proposed phase separated structure within the

composites for high PhE-POSS concentrations.119

The temperature of the rate fmax,MW S is curved when plotted versus 1/T and can be

described by Vogel-Fulcher-Tammann (eq. 2.3). The estimated VFT parameters are

listed in Table 5.3.

5 Matrimid and Matrimid/POSS Nanocomposites

Table 5.3 – VFT parameters for the MWS polarization of different MI/PhE-POSS com-

posites.

Sample VFT parameters of MWS polarization

A /K logf∞/Hz T0/K

MI-07 762.3 4.1 170.3

MI-10 341.1 2.6 236.1

MI-15 418.8 3.0 218.9

MI-20 535.8 3.2 200.5

The temperature dependence of the relaxation rates of the β∗–relaxation of Matrimid

follows the Arrhenius equation while the rate of the MWS polarization process are

described by the VFT-relation. This is a further proof that the MWS process is due

to the PhE-POSS rich domains. It is well accepted that for molecular or polymeric

systems the temperature dependence of the conductivity is related to the α–relaxation

in these materials. A characteristic feature of the α–relaxation is VFT-dependence of

their relaxation rates. As discussed above, the MWS process is related to the mobility

of the charge carriers and therefore to the conductivity. For that reason, the VFT-like

temperature dependence of the rate of the MWS process in the PhE-POSS/Matrimid

composites evidences that the MWS is due to the POSS rich domains. Moreover,

the estimated Vogel temperature for this process is close to the Vogel temperature

of the α–relaxation of bulk PhE-POSS (218 K).

With increasing POSS concentration, the rate of the MWS process decreases (see

Figure 5.21). As discussed in ref.,119 the rate of the MWS process is related to the

size d of the POSS rich domain fmax,MW S ∼d−1. This means that the decrease of

fmax,MWS with increasing POSS concentration is related to the growing of the size

of the POSS rich domains. But compared to the PhE-POSS/PBAC, the increase

of the size of the domains is much weaker. Therefore, it must be concluded that

with increasing POSS amount the number of POSS rich domains increases stronger

than their size. This behavior might be related to the stiffer structure of Matrimid

compared to polycarbonate.

5 Matrimid and Matrimid/POSS Nanocomposites

5.2.3.4 Scanning Electron Microscopy

These assumptions are further supported by SEM images of cross-sections of different

MI/PhE-POSS composites (Figure 5.22).

Figure 5.22 – SEM images of cross sections of different MI/PhE-POSS composites MI-

04, MI-10, and MI-20.

With increasing PhE-POSS concentration, the number and the size of the “holes”

visible in the cross sections of the composites (Figure 5.22) increases as well. It

is assumed that those holes occur during the cryogenic fracture where the POSS

aggregates are detached from the Matrimid matrix. Therefore, those “holes” are

considered to represent the phase-separated PhE-POSS domains originally present

in the composite matrix. Sánchez-Soto et al. observed this effect for a polycarbonate-

PhE-POSS matrix as well.122 A first analysis using simple image processing indicate

that the area fraction of the holes corresponds roughly to the concentration of PhE-

POSS. Note that the weight fractions are almost equal to the volume fractions as

the densities of the both components are approximately similar (Figure 5.16).

As it was already mentioned, the MI/PhE-POSS composites show a strong conduc-

tivity distribution at temperatures well below their thermal glass transition temper-

atures as well. Due to the MWS polarization which occurs in a similar temperature

range, this conductivity cannot be analyzed quantitatively for the composites.

5 Matrimid and Matrimid/POSS Nanocomposites

5.2.4 Conclusions

Dielectric properties of pure Matrimid and the nanocomposites were analyzed by

Broadband Dielectric Spectroscopy. Pure Matrimid displayed one relaxation process

pointed as β∗–relaxation and a conductivity contribution. The activation energy of

the β∗–relaxation was relatively high (EA,β∗= 99 kJ/mol) compared to solely β–

processes for other glassy polymers. Furthermore, the β∗–relaxation was found at

comparatively high temperatures close to the glass transition temperature which

is also not characteristic for beta processes. Thus, it was assumed that the β∗–

relaxation has to be of a cooperative nature due to π−π–stacking of the phenyl rings

of Matrimid. The influence of the thermal history on Matrimid was analyzed with

BDS as well. Those results and Differential Scanning Calorimetry measurements

indicated an annealing effect, leading to a more dense packing of the polymer chains

and thus to higher activation energies and higher Tg.

The conductivity contribution of Matrimid and the nanocomposites were found to

be well below their glass transition temperature. This led to the conclusion that,

for Matrimid, the conductivity is not directly related to segmental dynamics. As

discussed above, agglomerates of stacked phenyl groups by π−π–interaction were

found with wide angle X-ray scattering. Due to this π−π–stacking, charge transport

in Matrimid is enhanced as well.

Additionally, dynamic-mechanical properties were investigated using DMA. Basi-

cally, the dielectric and mechanical properties of Matrimid showed similar results.

For the loss modulus, a β∗–relaxation at lower and an α–relaxation (dynamic glass

transition) at higher temperatures was observed. In this high temperature range,

a strong increase for the loss part of the compliance was observed, proving the

onset of flow. Dynamic-mechanic and dielectric measurements evidenced that the

β∗–relaxation consists of two processes which merge together for higher frequen-

cies (loss modulus) or temperature (dielectric loss). This was further manifested by

WAXS pattern displaying two different spacings for stacks. It was concluded that

the observed two modes of the β∗–relaxation are due to different aggregates.

Up to a PhE-POSS concentration of 4 wt%, POSS was dissolved on a molecular

level in Matrimid. For higher PhE-POSS concentrations, BDS results evidenced a

Maxwell-Wagner-Sillars polarization, indicating a phase separated structure. This

5 Matrimid and Matrimid/POSS Nanocomposites

assumed structure was further evidenced by SEM images, where, after prior breaking

with liquid nitrogen, cavities on the surface of the fracture edge were observed.

5.3 Gas Transport Properties

Compared to polystyrene and polycarbonate used in previous studies115,118,119 Matri-

mid has a more rigid structure, which leads to a higher free volume and thus, improved

gas transport properties. A main disadvantage of Matrimid is a strong tendency to

plasticization.15,137

Bos et al. observed reduced plasticization (CO2) for heat-treated Matrimid/Thermid

FA-700 blends compared to a pure Matrimid film.137

Recently, several groups analyzed the influence of different nanofillers such as car-

bons,25 metal-organic frameworks (MOFs),25 zeolites27–29 and silicas30 in Matrimid

on its gas transport properties. Kanehashi et al. observed improved gas permeabil-

ities as well as selectivities for mixed matrix membranes of Matrimid and different

carbon nanoparticles.25

In this study PhenethylPOSS was mixed in Matrimid because an interaction of the

phenyl substituents of POSS with the π–system of Matrimid is expected and thus,

probably stabilizes the Matrimid matrix to reduce e.g. plasticization, as discussed

above.

5.3.1 Gas Permeability

N2, O2, CH4and CO2–permeability was measured for MI-00, MI-01, MI-02, MI-

04, MI-07, MI-10 and MI-15 (table 5.1) with the time-lag method (1 to 20 bar at

308 K (35 ◦C)). In the following discussion, permeability, diffusion coefficients and

selectivity for Matrimid and Matrimid/PhE-POSS are discussed.

5 Matrimid and Matrimid/POSS Nanocomposites

5.3.1.1 Permeability

Figure 5.23 presents a 3D representation of the CO2–permeability versus upstream

pressure p1and c(PhE-POSS) at 308 K for Matrimid and selected Matrimid/PhE-

POSS composites.

Figure 5.23 – CO2permeability vs. upstream pressure p1and c(PhE-POSS) at 308 K

for the investigated MI/PhE-POSS composites.

The CO2–permeability of MI-00 and low concentrations of POSS up to 4 wt% show a

“minimum” at 10 bar and increases with further increase of pressure. On a first sight,

this behavior is different for 10 wt% of POSS. The permeability of MI-10 remains

constant after the first decrease of the permeability. So it seems that for POSS

concentrations above 10 wt% the CO2–induced plasticization at higher pressures

(>10 bar) is suppressed.

In Figure 5.24 the permeability for all analyzed samples are shown in its pressure

dependence and were moreover compared to data from Bos et al.15

5 Matrimid and Matrimid/POSS Nanocomposites

0 5 10 15 20

MI-00

MI-01

MI-04

MI-10

Bos et al.

P /Barrer

/bar

Figure 5.24 – CO2permeability vs. upstream pressure p1at 308 K for MI-00, MI-01,

MI-02, MI-04, MI-07, MI-10 and MI-15. Furthermore, data for Matrimid

from Bos et al. is included.15

The permeability of MI-00 first decreases with increasing CO2pressure to a “mini-

mum” at about 10 bar and then increases with further increase of the pressure due

to CO2–induced plasticization. For concentrations up to 4 wt% a slight “minimum” is

visible as well, however, for higher POSS concentrations the permeability remains

constant after 10 bar. MI-01 shows a slight increased permeability compared to pure

Matrimid (MI-00). In contrast, higher POSS concentration leads to overall decreased

permeabilities compared to MI-00.

The decrease of the permeability below 10 bar can be explained by the Dual-Mode

behavior, where an increase of pressure leads to a decrease of the solubility. In case

of highly soluble gases, like CO2, plasticization occurs, leading to an increase of the

permeability at higher pressures. Bos et al.15 have shown such a plasticization effect

for Matrimid as well (see Figure 5.24). In contrast to the used sample preparation

procedure used in this study, Bos et al. removed the film after drying from the used

glass plate with a small amount of water dried their Matrimid film at 150 ◦C for

4 days. These differences in film preparation can be the reason for the differences of

the absolute values of their permeabilities.

The Dual-Mode behavior is present for all composites shown in Figure 5.24 up to

10 bar. In contrast to 1 wt% of POSS, the permeability for the other composites is

lower compared to pure Matrimid (MI-00). This effect supports the assumption made

in the previous section for the density and determined Tgs, that POSS is dissolved in

the free volume sides of Matrimid. This leads to a hindered gas transport through the

5 Matrimid and Matrimid/POSS Nanocomposites

polymer matrix and thus, decreased permeabilities with increasing POSS content.

The internal structure of MI-01 is assumed to be more open compared to MI-00 and

thus, the permeability is slightly enhanced.

In section 5.2 a phase separated structure was assumed for POSS concentrations

higher than 8 wt%, which was evidenced by DSC (Fig. 5.15) and density measure-

ments (Fig. 5.16). In contrast, the BDS results, shown in the previous section, show

a phase separation already at about 4 wt%, which was also evidenced by the second

heating cycle of DSC measurements. The analyzed BDS data was taken from the

second cooling cycle. Here, in contrast to the gas transport measurements the sam-

ples were heated up once to 473 K and to 573 K, leading to a more dense structure

and thus, to phase separation at about 4 wt%.

For low POSS concentrations, POSS is dissolved on a molecular level in the free

volume sites of Matrimid. At about 8 wt%, the free volume is filled up and phase

separation occurs, POSS agglomerates are formed. It is assumed that the POSS

molecules join somehow the postulated π−π–stacking and thus, with increasing

POSS concentration the polymer matrix is more and more stabilized. Thus, plasti-

cization is reduced with increasing POSS concentration (see Figure 5.24) but at the

same time the permeability is decreased because the POSS domains are assumed

to be impermeable.115

In Figure 5.25 the permeability of N2, O2, CH4and CO2versus the PhE-POSS

concentration is shown for 10 bar and 308 K.

5 Matrimid and Matrimid/POSS Nanocomposites

0 5 10 15

0.3

0.4

0.5

0.6

Phase Separation

P /Barrer

c (PhE-POSS) /wt%

0 5 10 1 5

Phase Separation

P /Barrer

c (PhE-POSS) /wt%

0 5 10 15

0.2

0.3

0.4

0.5

P /Barrer

c (PhE-POSS) /wt%

Phase Separation

0 5 10 15

P /Barrer

c (PhE-POSS) /wt%

Phase Separation

Figure 5.25 – Permeability of N2, O2, CH4and CO2vs. c(PhE-POSS) at 308 K and

10 bar. Lines are guides to the eyes. The gray background indicates the

phase separation range observed for BDS/density in section 5.2.

The permeability decreases with increasing POSS concentration for all analyzed

gases. After the assumed phase separation at about 8 wt%, the permeability remains

almost constant. Furthermore, the permeability of MI-01 is higher compared to MI-00

for all analyzed gases.

With increasing POSS concentration up to the assumed phase separation at about

8 wt% the free volume of Matrimid is filled up. This assumption was already sup-

ported by the increase of the density with increasing POSS concentration, shown in

Figure 5.16. The permeability of a penetrating gas is related to the free volume as it

jumps from "hole" to "hole". Thus, the permeability decreases with increasing POSS

concentration. When the phase separation sets in, POSS agglomerates are formed

and the free volume sites are filled up. Thus, the composition of the Matrimid/PhE-

POSS matrix remains constant, means the interaction between polymer and filler

does not change with further increasing POSS concentration. For these reasons, the

permeability is constant for higher POSS concentrations.

It is known that high concentrations of silicon atoms incorporated in a polymer matrix

5 Matrimid and Matrimid/POSS Nanocomposites

can lead to an increase of the O2solubility.138–141 Thus, here with increasing POSS

content within Matrimid the O2–permeability is enhanced as well. However, this

effect becomes less for the phase separated samples, the O2permeability is almost

constant with a further increase of the POSS concentration.

The increased permeability (for all gases) of MI-01 may be ascribed to a looser chain

packing in the cast film compared to pure Matrimid MI-00. Thus, small amounts of

POSS lead to enhanced gas transport properties, which was also observed for other

polymer matrices like PIM-1 (see section 6.3 and ref.22).

5.3.1.2 Diffusion Coefficients

The diffusion coefficients D were obtained by eq. 2.26 and are shown for N2, O2, CH4

and CO2vs. the PhE-POSS concentration for 10 bar and 308 K in Figure 5.26.

0 5 10 15

D /10

-9

-1

c (PhE-POSS) /wt%

Phase Separation

0 5 10 15

c (PhE-POSS) /wt%

D /10

-9

-1

Phase Separation

0 5 10 15

1.0

1.5

2.0

4Phase Separation

c (PhE-POSS) /wt%

D /10

-9

-1

0 5 10 15

c (PhE-POSS) /wt%

D /10

-9

-1

Phase Separation

Figure 5.26 – Diffusion coefficients of N2, O2, CH4and CO2vs. c(PhE-POSS) at 308 K

and 10 bar. Lines are guides to the eyes. The gray background indicates

the phase separation range observed for BDS/density in section 5.2.

For all analyzed gases the diffusion coefficient shows the same dependence on the

PhE-POSS concentration. For the phase separated as well as the non-phase sepa-

5 Matrimid and Matrimid/POSS Nanocomposites

rated samples D increases with increasing POSS content. When the phase separa-

tion sets in, the diffusion coefficient changes significantly.

The incorporation of POSS leads a facilitated diffusion even though it is assumed that

the free volume sites are filled up. The significant change of the diffusion coefficients

at the assumed critical concentration for phase separation, indicates a considerable

change of the internal structure. Interestingly, with further increase of the POSS

concentration, the diffusion coefficients increases again for the already phase sep-

arated structure. This indicates a decrease of the solubility as the permeability is

almost constant for the phase separated samples.

5.3.1.3 Selectivity

In addition, the selectivities of O2/N2and CO2/CH4versus the concentration of POSS

within the composites are presented in Figure 5.27.

0 5 10 15

Phase Separation

)

c (PhE-POSS) /wt%

0 5 10 15

(CO

/CH

)

Phase Separation

c (PhE-POSS) /wt%

Figure 5.27 – Selectivity of O2/N2and CO2/CH4vs. c(PhE-POSS) at 308 K and 10 bar.

Lines are guides to the eyes. The gray background indicates the phase

separation range observed for BDS/density in section 5.2.

By incorporation of POSS within the Matrimid matrix the O2/N2selectivity is im-

proved for all composites compared to pure Matrimid. In contrast, the CO2/CH4

selectivity is debased significantly with the incorporation of POSS until the phase

separation occurs. For the phase separated composites, both selectivities changes

dramatically and then, with further increasing POSS concentration αis almost con-

stant.

5 Matrimid and Matrimid/POSS Nanocomposites

As it was already discussed the POSS molecules are dissolved in the free vol-

ume sites of Matrimid, leading to a densified structure and thus, to a hindered gas

transport through the Matrimid matrix especially for the bulky gases CO2and CH4.

However, α(O2/N2) is improved by the incorporation of POSS within the Matrimid

matrix, which can be explained by the already mentioned special interaction of the

O2molecules with the silicon atoms of POSS.

5.3.2 Conclusions

Gas transport properties of Matrimid and Matrimid/PhE-POSS composites were

investigated by the time-lag method for N2, O2, CH4and CO2at 308 K (35 ◦C).

The assumed phase separation at about 8 wt% was in evidence for permeability,

diffusion coefficients as well as the selectivities of the Matrimid/PhE-POSS com-

posites. Furthermore, an enhanced permeability for all analyzed gases was observed

for 1 wt% of POSS (MI-01), indicating a more open structure compared to pure

Matrimid. In addition, the plasticization effect of CO2was reduced for the phase

separated composites.

6 PIM-1 and PIM-1/POSS

Nanocomposites∗†

Abstract

Molecular dynamics and conductivity of PIM-1 and PIM-1/PhE-POSS were investi-

gated by BDS. For pure PIM-1 one relaxation process denoted as β∗–relaxation and

a conductivity contribution was found. Due to a high activation energy of 86 kJ/mol

the β∗–relaxation was assigned to agglomerates formed by π−π–stacking of the

phenyl rings of PIM-1. The PIM-1/PhE-POSS showed a miscibility up to 15 wt%.

For higher POSS concentrations a phase separated structure was observed. The

conductivity phenomena was explained by π−π–stacking as well.

Furthermore, gas permeability was determined with the time lag method (0 – 20

bar upstream pressure) at 35 ◦C for N2, O2, CH4and CO2for PIM-1 and depicted

PIM-1/PhE-POSS composites. For 1 wt% of POSS, an enhanced permeability was

found for all gases compared to pure PIM-1.

6.1 Introduction

While previously studied polymers with very high fractional free volume and ex-

tremely high gas permeabilities, e.g., polyacetylenes such as PTMSP, show only

poor selectivities, most PIMs exhibit an attractive combination of almost as high

permeabilities with reasonable permselectivities. Therefore, PIMs today represent

∗Similar content (section 6.1 and 6.2) was published in Konnertz, N.; Ding, Y.; Harrison, W. J.; Budd,

P. M.; Schönhals, A.; Böhning, M., ACS Macro Letters, 2016, 5, 528-532.

†Similar content (section 6.3) submitted to Konnertz, N.; Ding, Y.; Harrison, W. J.; Budd, P. M.;

Schönhals, A.; Böhning, M. Journal of Membrane Science

6 PIM-1 and PIM-1/POSS Nanocomposites

the current state-of-the-art in air separation and hydrogen recovery.18,19 All these

superglassy polymers share a distinct tendency to physical aging, which is the ma-

jor drawback with regard to practical membrane applications. After formation of the

dense film (or thin selective layer) sometimes followed by a nonsolvent treatment in

order to exchange residual casting solvent the initial permeability decreases signif-

icantly with time.20,21 Therefore, one of the current research topics in the field aims

at the suppression of physical aging either by optimizing the chemical architecture

of the polymers or by adding suitable (nano)fillers which stabilize their structural

arrangement in the glassy state.20,22–24

For conventional glassy polymers, a correlation between certain molecular motions

of the solid polymeric matrix and the diffusion of small molecules within can be ob-

served. This follows from fundamental transport models44,45 and molecular dynamics

simulations46,47 and is also discussed based on experimental data.48,49 For the super-

glassy high free volume polymers such a correlation no longer holds as the transport

mechanism is obviously different. Distinct differences are found in terms of the cor-

responding activation energies.142,143 This is also in agreement with a continuous

free volume phase, found, e.g., in detailed atomistic molecular dynamics simulations

of such polymers.144,145

An investigation addressing the molecular mobility of PIMs is of great importance,

as two major phenomena which determine the practical performance in membrane

application, i.e., the physical aging and the plasticization induced by highly sorbing

penetrants, are directly related. Furthermore, the film formation during casting, i.e.,

the solidification of the polymer by solvent evaporation, is predominantly governed

by the molecular mobility of the polymer matrix. Thus, systematic studies of various

PIMs as well as corresponding nanocomposites will substantially contribute to fur-

ther developments toward practical applications of PIMs in membrane separations

especially as BDS is complementary to investigations using X-ray scattering146,147

or addressing electronic properties of PIMs.148

6.2 Dielectric Investigations: PIM-1

In this chapter the first synthesized and most representative PIM-1 (Figure 4.3) is

investigated by Broadband Dielectric Spectroscopy (BDS).

6 PIM-1 and PIM-1/POSS Nanocomposites

It has to be noted that for PIMs in general no thermal glass transition is observed

below the decomposition.16 A DSC measurement of PIM-1 is shown in Fig. 4.2.

The decomposition starts at about 640 K (370 ◦C), so we do not expect to find a

related dynamic glass transition (segmental dynamics, α-relaxation) in the applied

temperature range.

In Figure 6.1 the temperature-dependent dielectric loss logε“at a fixed frequency

of 1000 Hz is plotted for the two heating runs and the cooling run between them.

200 300 400 500

-3.0

-2.8

-2.6

Heating

Cooling

Heating

log

´´

Temperature /K

Figure 6.1 – Comparison of dielectric spectra (logε“vs. temperature) at a fixed fre-

quency of 1 kHz for the different heating and cooling runs.

A significant difference between first heating and the two subsequent runs is re-

vealed. The dielectric loss curve of the first heating shows one distinct peak and a

shoulder. The peak at higher temperatures, around 460 K (187 ◦C), can be assigned

to a molecular relaxation process which is found similarly during the first cooling

and second heating. It has to be noted that the dielectric loss in the first heating

run, up to about 400 K (127 ◦C), is in general significantly higher than in the sub-

sequent measurements. This is probably caused by the remaining solvent molecules.

Together with the adumbrated shoulder around 313 K (40 ◦C) this indicates rather

the evaporation process than a higher molecular mobility due to plasticization by

traces of solvent. Also the influence of water, sorbed from the atmosphere, might be

taken into account, for which a strong effect on the gas transport properties due to

partial blocking of the accessible free volume is well-known.142,149

The curves of the dielectric loss measured during first in this temperature range —

and also show the distinct relaxation peak around 460 K (187 ◦C). The observed

onset at lower temperature points at a second relaxation peak below 200 K (-73 ◦C),

6 PIM-1 and PIM-1/POSS Nanocomposites

but this can unfortunately not be fully characterized within the temperature range

accessible for the BDS measurements.

Figure 6.2 shows a three-dimensional representation of the BDS measurement, i.e.,

the dielectric loss logε“versus frequency log f and temperature T.

Figure 6.2 – 3D representation of the dielectric loss logε00 of PIM-1 vs. frequency and

temperature for the second heating run.

The peak of the molecular relaxation of PIM-1 is clearly seen, and as expected it

shifts to higher frequencies with increase of temperature. The increase of dielectric

loss with decreasing frequency (and increasing temperature) is due to conductivity,

which is related to the drift motion of charge carriers in the film. For further analysis

of the relaxation process, the Havriliak–Negami function (eq. 3.12) was fitted to the

data, according to Figure 5.4.

In Figure 6.3 the determined frequencies of maximal dielectric loss are plotted in

Arrhenius coordinates.

6 PIM-1 and PIM-1/POSS Nanocomposites

1.8 2.0 2.2 2.4 2.6 2.8

log (f

max,

/Hz)

1000/T /K

-1

Figure 6.3 – Plot of the frequency of maximal dielectric loss fmax,β∗in Arrhenius coor-

dinates.

At first glance, the linear behavior seems to indicate a localized molecular relaxation

process, usually denoted as β–relaxation, which is typically found for most poly-

mers. In contrast to that, cooperative segmental relaxation processes usually follow

a Vogel–Fulcher–Tammann (VFT) law, distinctly deviating from the linear Arrhenius

behavior An activation energy of EA= 86.1 kJ/mol is obtained for the PIM-1 under

investigation. This value is relatively high for commonly observed local β–processes

in polymers. For that, usually activation energies between 40 and 60 kJ/mol are

expected. A similar phenomenon was also found for example in poly(ethylene naph-

talate) (PEN). The activation energy of the β∗–relaxation (EA,β∗) for PEN is in the

similar range as the value obtained for PIM-1. For PEN this is ascribed to the

formation of intermolecular sandwich–like agglomerates of aromatic moieties of the

polymer chain with strong interaction of the respective π–systems.129–131

This leads to higher activation energies and a more cooperative character of the

molecular relaxation process. Moreover, a similar behavior was found for Matrimid,

discussed in section 5.2.2.

Although for PIMs generally a limited molecular mobility is assumed due to their

rigid structure, which leads to the low packing density and the exceptional gas trans-

port properties, a somewhat similar reason for the higher activation energy should

be considered. Preliminary wide-angle X-ray measurements of our film sample show

several broad reflections which evidence such aggregates with a molecular spac-

ing of about 3.4 and 10 Å133 (see Figure A.4), which is in agreement with earlier

investigations of PIM-1 reported in refs.,146.147 Due to the resulting partial cooper-

ative character, the observed molecular relaxation process of PIM-1 is denoted as

6 PIM-1 and PIM-1/POSS Nanocomposites

β∗–relaxation.

For a further analysis of the dielectric behavior of PIM-1, also the conductivity is

considered – especially because of the postulated π−πstacking of the aromatic

moieties of the polymer chain, which may have a distinct influence on the conductivity

mechanism.

The frequency dependence of the real part of the complex conductivity σ0(Figure 6.4)

shows the typical behavior expected for semiconducting polymeric materials.

-1 0 1 2 3 4 5 6

-14

-12

-10

-8

523 K = 250 °C

502 K = 229 °C

484 K = 211 °C

log

(

/S cm

-1

)

log (f /Hz)

Figure 6.4 – Frequency dependence of the real part of the complex conductivity σ0at

the indicated temperature.

For high frequencies the real part σ0decreases with decreasing frequency with a

power law down to a characteristic frequency fc, where a plateau value is reached.

The plateau value corresponds to the DC conductivity σDC .150 As can be seen from

Figure 6.4, this DC conductivity increases with increasing temperature. Figure 6.5

shows a linear behavior for the plateau values σDC in dependence of the reciprocal

temperature; i.e., the DC conductivity follows an Arrhenius relation. An apparent

activation energy of EA,σDC = 101 kJ/mol was estimated, which is significantly higher

than the activation energy of the β∗-relaxation.

6 PIM-1 and PIM-1/POSS Nanocomposites

1.9 2.0 2.1 2.2 2.3

-15.5

-15.0

-14.5

-14.0

-13.5

-13.0

log

(

/S cm

-1

)

1000/T /K

-1

Figure 6.5 – DC conductivity σDC for PIM-1 in dependence of the inverse temperature.

The lines are fits of the Arrhenius equation to the data.

It is necessary to note that the conductivity contribution was observed in the glassy

state. For most conventional polymers the transport mechanism of charge carriers is

due to mobility of charge carriers (impurities) connected with segmental dynamics

of the polymer matrix above the glass transition, and therefore the DC conductivity

follows VFT-behavior.

For PIM-1 no glass transition is observed before decomposition. Therefore, it is con-

cluded that for PIM-1 the conductivity is not directly related to segmental dynamics.

As discussed above wide-angle X-ray scattering measurements show evidence of ag-

glomerates probably of stacked phenyl groups by π−πinteraction. Due to the

overlapping π-systems charge transport in PIM-1 is enhanced.

It has to be noted that the PIM-1 sample shows a distinct change in color after the

temperature cycle of the BDS measurement (Figure 3.6). As can be seen from the

photographs in Figure 6.6, the color changes from yellow to brownish.

Figure 6.6 – Photographs of the freshly cast PIM-1 film (approx. 70 mm diameter) (A)

and of the sample after the BDS measurements (B) — here the outer ring

represents the real colour as the central part of about 20 mm diameter

is covered with a thin gold layer. (C) shows the PIM-1 from (B) after

re-dissolving in chloroform.

6 PIM-1 and PIM-1/POSS Nanocomposites

A comparison of FTIR spectra for the virgin and the BDS-measured sample (Fig-

ure 6.7) does not show any changes. Furthermore, the strongly annealed material

regains its original yellow color after being redissolved in chloroform. So, no in-

dications for changes in the chemical structure were found, and an only reversible

change of the amorphous packing in the solid film may be concluded.

3000 2500 2000 1500 1000

C=N

Absorbance /a.u.

Wavenumber /cm

-1

C-O

ar.

C=C

C-H C-H

before

after

Figure 6.7 – FTIR spectra of PIM-1 before and after the temperature cycle up to 573 K

(300 ◦C).

6.2.1 Conclusions

In conclusion, a molecular relaxation process with Arrhenius behavior and an unusu-

ally high activation energy, denoted β∗, has been observed in PIM-1, together with a

significant conductivity in the glassy state. As expected, no α-relaxation (related to

a glass transition) was found. Both the β∗-relaxation as well as the conductivity are

explained with the formation of local intermolecular agglomerates due to interaction

of π-electrons in aromatic moieties of the polymer backbone (π−π- stacking). Up to

now, this has not been taken into account when film formation, chain dynamics, free

volume, and especially gas transport properties of PIMs were discussed. Although

the reported findings have to be further investigated — also considering more PIMs

in a systematic manner — they represent a new important aspect of this innovative

class of polymers.

6 PIM-1 and PIM-1/POSS Nanocomposites

6.3 PIM-1/POSS Nanocomposites: Molecular Mobility and

Gas Transport Properties

Yong et al. reported a study on the suppression of physical aging and plasticization

of PIM-1 by incorporation of different POSS nanoparticles with various aliphatic

substituents.22

As it was already mentioned in section 5.1, PhE-POSS was already successfully

embedded in novolac resin,123 polystyrene118 and polycarbonate.49,115,119

In this study, PhE-POSS was incorporated within PIM-1. Investigations on molec-

ular mobility and gas transport properties of the PIM-1/PhE-POSS composites are

discussed in this section and compared to the results found for the Matrimd compos-

ites (section 5.2.3).

6.3.1 Characterization

In Table 6.1, sample codes of the nanocomposites as well as pure PIM-1 are given

including the PhE-POSS content, the thickness of the films and the measured den-

sity.

6 PIM-1 and PIM-1/POSS Nanocomposites

Table 6.1 – Sample codes with the corresponding PhE-POSS concentration, the film

thickness of PIM-1, and the PIM-1/PhE-POSS nanocomposites and the

density.

Sample wt% Thickness /µmρ/g cm−3

PIM-1-00 0 217 1.150

PIM-1-01 1 215 1.149

PIM-1-05 5 119 1.151

PIM-1-075 7.5 238 1.153

PIM-1-10 10 170 1.155

PIM-1-15 15 207 1.157

PIM-1-20 20 193 1.160

PIM-1-30 30 187 1.164

PIM-1-40 40 155 -

PhE-POSS 1.22119 - 100

In order to verify the PhE-POSS content, in the nanocomposites TGA was applied

under oxidative conditions. Example curves of the residual mass above 900 K for

different PhE-POSS concentrations are shown in Figure 6.8a.

6 PIM-1 and PIM-1/POSS Nanocomposites

900 1000 1100

PIM-1-01

PIM-1-10

Weight /%

Temperature /K

PIM-1-40

0 10 20 30 40

Remaining weight percent /%

c(PhE-POSS) /wt%

Figure 6.8 – a) TGA curves of PIM-1-01 (solid line), PIM-1-10 (dashed line) and PIM-

1-40 (dotted line). b) Remaining weight percent vs. c(PhE-POSS). The

solid line is a linear fit to the data.

During heating in the TGA, the polymer matrix and the POSS filler are completely

oxidized. Thereby, only Si is assumed to remain in the residue as SiO2, as is

identified by the plateaus of the TGA curves at high temperatures (Figure 6.8a).

With increasing PhE-POSS content, the plateau value increases. Thus, the residual

weight is regarded as a measure of the PhE-POSS content. Figure 6.8b shows

the final remaining weight vs. the nominal PhE-POSS concentration used for the

corresponding formulation. The resulting linear relation confirms this approach. In

the following text the samples are identified by their nominal PhE-POSS content.

6.3.2 Relaxation Behavior

A detailed discussion of the dielectric behavior of pure PIM-1 (PIM-1-00) is already

included in our previous section 6.2. For PIM-1-00, a significant difference between

the first heating and the subsequent runs was observed. This was attributed to

remaining solvent and/or absorbed water in the initial state of the sample. During

the first heating, these volatile components are lost by evaporation. For this reason,

here only the second heating runs of the composites, after heating the samples up

to 473 K, are discussed.

In Figure 6.9a, the dielectric loss vs. temperature for the second heating run for PIM-

1-00, pure PhE-POSS, and selected composites at 1 kHz are shown. Figure 6.9b

presents a stacked overview of the dielectric loss vs. the temperature for all samples.

6 PIM-1 and PIM-1/POSS Nanocomposites

200 300 400 500

-3.0

-2.5

-2.0

-1.5

PIM-1-00

PIM-1-01

PIM-1-075

PIM-1-30

PhE-POSS

log

Temperature /K

200 300 400 500 600

15 wt%

20 wt%

30 wt%

10 wt%

7.5 wt%

5 wt%

1 wt%

log

/arbitrary units

Temperature /K

0 wt%

Figure 6.9 – a) Dielectric loss vs. temperature for the second heating of pure PIM-1

(PIM-1-00), of PIM-1 with 1 wt% PhE-POSS (PIM-1-01), 7.5 wt% PhE-

POSS (PIM-1-075), 30 wt% PhE-POSS (PIM-1-30) and pure PhE-POSS

at a frequency of 1 kHz. b) Stacked dielectric loss vs. temperature for the

second heating of pure PIM-1 (PIM-1-00), pure PhE-POSS and of PIM-

1/PhE-POSS composites at a frequency of 1 kHz.

200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0

1.2

PhE-POSS

PIM-1-00

PIM-1-01

PIM-1-05

PIM-1-075

PIM-1-10

PIM-1-15

PIM-1-30

´´/ ´´

max

T /K

Figure 6.10 – Dielectric loss normalized by the maximum value of the peak vs. temper-

ature for the second heating of PIM-1-00, PIM-1-01, PIM-1-05, PIM-1-

075, PIM-1-15, PIM-1-30 and pure PhE-POSS at a frequency 1 kHz

For pure PIM-1, one distinct relaxation process is observed, which is called the β∗–

relaxation. This process is assigned to coordinated fluctuations of aggregates caused

by π−π–stacking (see section 6.2). For pure PhE-POSS, also one relaxation process

is observed, which is due to the dynamic glass transition (α–relaxation) of PhE-POSS

(for a more detailed discussion see ref.119). For concentrations of PhE-POSS up to

10 wt%, only the β∗–relaxation related to the PIM-1 matrix is observed as a peak,

which indicates miscibility on a molecular level at first glance. However, for PIM-1-

15 and PIM-1-30, a weak but distinct second relaxation process becomes apparent.

6 PIM-1 and PIM-1/POSS Nanocomposites

This second peak can be attributed to the α–relaxation of PhE-POSS located in

PhE-POSS rich domains formed by phase separation, because this relaxation process

is observed in a temperature range similar to the α–relaxation of pure PhE-POSS.

This peak is shifted slightly to higher temperatures compared to the dynamic glass

transition of pure PhE-POSS as indicated in Fig. 6.10. This is most probably due to

the restricting and/or confining effects of the rigid glassy PIM-1 matrix on the soft

PhE-POSS domains. Unfortunately, the nanocomposite with 40 wt% of PhE-POSS

(PIM-1-40) was too brittle to perform BDS measurements.

A closer inspection of the normalized dielectric loss curves for PhE-POSS in Fig. 6.10

shows further a significantly rising level of ε“between 220 and 400 K for the inter-

mediate PhE-POSS concentrations up to about 10 wt%. This indicates, according to

the fluctuation dissipation theorem, an enhanced molecular mobility in this tempera-

ture range. Also, a change in shape of the dielectric loss curves in this temperature

range becomes obvious: For pure PIM-1 and the nanocomposites at low PhE-POSS

concentrations, the curves exhibit a shape concave to the temperature-axis which

disappears above 5 wt% (Fig. 6.9b).

Based on these observations, three concentration ranges may be distinguished for

the nanocomposite materials: At low concentrations of PhE-POSS up to about 5 wt%

(here denoted as range I), a single, clearly discernible relaxation peak (related to

the β∗–relaxation of PIM-1) dominates the dielectric spectrum. In the intermediate

concentration range II, i.e. between 5 and 10 wt%, the overall dielectric loss rises

significantly with increasing PhE-POSS content. From the normalized dielectric

loss curves in Fig. 6.10, it can be seen that the β∗–peak remains nearly unchanged

while on both sides the ε“–curve is on a higher level and exhibits slight changes in

shape, as mentioned above.

At concentrations above 10 wt% (denoted as range III), the appearance of a second

relaxation peak related to the α–relaxation of PhE-POSS is a clear indicator of a

phase separation.

From this behavior and the fact that PIM-1 has an extremely high fractional free

volume and most probably forms a continuous free volume phase,151 the following

(simplified) picture of the investigated nanocomposites is suggested:

At low concentrations, i.e. in concentration range I (characterized by complete mis-

cibility), the PhE-POSS incorporated into the nanocomposite is entirely accommo-

6 PIM-1 and PIM-1/POSS Nanocomposites

dated in the free volume of PIM-1 in a more or less isolated state. Within these

free volume sites, the POSS molecules can fluctuate, causing an increased dielectric

loss. As these fluctuations are restricted or constrained by the surrounding PIM-1

matrix, the molecular fluctuations are slowed down compared to the bulk and thus

the dielectric loss is also increased at higher temperatures (e.g. compared to the

glass transition of pure PhE-POSS). One possible molecular mechanism of the re-

striction of the molecular PhE-POSS can be the incorporation of one or more phenyl

rings of PhE-POSS into the proposed stack-like structure of aromatic moieties of

the PIM-1 matrix due to interactions of the π–systems.152 It seems obvious that for

the restriction of the PhE-POSS molecules in the PIM-1 matrix, a broad variety of

possibilities exists due to the amorphous structure of PIM-1 and different options to

incorporate the phenyl groups of PhE-POSS into the structure of PIM-1. Therefore,

the molecular fluctuations become heterogeneous, resulting in a broad relaxation

time spectra, which thus lead to a broadly distributed loss ε“(instead of a distinct

peak) also in the temperature domain (see Figure 6.10).

As stated above, at low concentrations PhE-POSS exist individually and separately

in the free volume sites. With increasing concentration of PhE-POSS, the free

volume sites are increasingly filled-up, the PhE-POSS molecules start to recognize

each other and the related molecular mobility may be regarded as a pre-stage of the

co-operative α–relaxation. In this intermediate concentration range II, this behavior

manifests itself as a change in shape of the dielectric loss curves.

At high concentrations (15 wt% and above), a phase separated morphology is observed

in which domains of pure PhE-POSS are formed, which enable the fully co-operative

motion giving rise to the observed α–relaxation and to the corresponding separate

peak in ε“. The small “holes” (<300 nm), visible in the SEM images of PIM-1-30

and even more pronounced in PIM-1-40 (Figure 6.11), may be taken as an addi-

tional indicator of the phase separated structure. During breaking of the previously

cooled nanocomposites, PhE-POSS domains are “broken out” of the PIM-1 matrix,

leaving holes in the cross section. This effect was described in the previous section

for Matrimid/PhE-POSS (5.2.3) and Polycarbonate/PhE-POSS122 composites and

found by other investigators as well.123

6 PIM-1 and PIM-1/POSS Nanocomposites

Figure 6.11 – SEM images of the cross sections of a)PIM-1-00, b) PIM-1-10, c) PIM-

1-30 and d) PIM-1-40.

For the detailed analysis of the β∗–relaxation of the PIM-1 matrix in the nanocom-

posites, the model function of Havriliak-Negami (HN-function) (eq. 3.12) was fitted

to the data.

Conductivity effects are treated in the usual manner by adding a power law (eq. 3.14)

to the dielectric loss. By fitting the HN-function (for examples see Figure 5.4) to the

data, the relaxation rate fmax (eq. 3.13) is obtained. The relaxation rate corresponds

to the frequency of the maximum of the dielectric loss and is given in eq. 2.3. The

temperature dependence of the relaxation rate of the β∗–relaxation log(fmax,β∗) obeys

the Arrhenius equation (see Figure 6.12b).

6 PIM-1 and PIM-1/POSS Nanocomposites

1.6 1.8 2.0 2.2 2.4 2.6 2.8

PIM-1-00

PIM-1-05

PIM-1-10

log

(

max,

/Hz

)

1000/T /K

-1

Figure 6.12 – Relaxation rate fmax,β∗for the second heating vs. inverse temperature of

PIM-1-00, PIM-1-05, and PIM-1-10. The lines are fits of the Arrhenius

equation to the corresponding data.

The determined activation energies of the β∗–relaxation EA,β∗for all samples are

given in Figure 6.13 as function of the PhE-POSS concentration.

0 10 20 30

100

/kJ mol

-1

c(PhE-POSS) /wt%

typical values for the activation energy

of the

relaxation of polymers

Figure 6.13 – Activation energy EA,β∗for the second heating cycle determined by Ar-

rhenius vs. the PhE-POSS concentration.

As already discussed for pure PIM-1 (section6.2), the activation energy EA,β∗for the

β∗–relaxation is ca. 86 kJ/mol. This value is relatively high compared to β–processes

typical for localized fluctuations in conventional polymers (40 to 60 kJ/mol). There-

fore, it is assumed that sandwich-like agglomerates are formed due to the interaction

between the π–systems of the polymer backbones. For a detailed discussion, see

section 6.2 and ref.129–131 At first, EA,β∗increases with increasing POSS concentra-

tion. Taking into account the simple picture for the nanocomposites derived from the

phenomenological analysis of the ε“–spectra, the changes of the activation energies

6 PIM-1 and PIM-1/POSS Nanocomposites

can be discussed as follows: At low concentrations, the aromatic phenyl moieties

of the organic POSS-substituents interact with π–systems of PIM-1 as discussed

above. Thus, some of the fluctuating aggregates are interconnected compared to pure

PIM-1, resulting in an increased value of the activation energy of the β∗–relaxation.

This coincides with concentration range I.

A further increase of the filler concentration leads to formation of small agglomerates

of PhE-POSS (concentration range II). In contrast to the individual PhE-POSS

molecules, these agglomerates can no longer be completely accommodated within

the undisturbed free volume elements of PIM-1. Therefore, they cause a subtle

distortion of the surrounding PIM-1 matrix.

This effect still leads to a further increase of the activation energy of the β∗–relaxation

for which a maximum value is observed around 10 wt% of PhE-POSS. For concen-

trations higher than that, phase separation occurs (range III). Here, a part of the

constraints and distortions superimposed to the aggregates are removed resulting in

a decreasing EA,β∗. Moreover, the PhE-POSS-rich domains of the phase-separated

structure will weaken the stack-like arrangement of the phenyl rings of PIM-1. This

effect also explains the increasing brittleness of the prepared films above 10 wt%

PhE-POSS: the thereby weakened cohesive energy leads to an immediate decline

of the mechanical properties, as the formation of entanglements seems unlikely for

the rigid PIM-1 and therefore has no stabilizing effect.

The weakened π−π–interaction of PIM-1 by the disturbed arrangement of its aro-

matic moieties finally leads to a constant level for EA,β∗which is – rather coinciden-

tally - comparable to that of pure PIM-1.

For composites based on Matrimid and PhE-POSS a different concentration de-

pendence of the activation energy of the β∗–relaxation in dependence was observed

(section 5.2.3). EA,β∗(Matrimid/PhE-POSS) was constant up to the phase separation

at about 4 wt% PhE-POSS and then decreased compared to the pure polymer. This

effect was ascribed to incorporation of small amounts of PhE-POSS molecules within

the free volume sites of Matrimid only slightly affecting the internal structure of the

polymer. In contrast, PIM-1 has a more rigid structure with a higher free volume.

For that reason, even the small distortion due to agglomeration of PhE-POSS within

the free volume of PIM-1 weakens the π−π–interaction, resulting in a decrease of

EA,β∗. With further increasing PhE-POSS concentration, phase separation occurs

6 PIM-1 and PIM-1/POSS Nanocomposites

and the mobility of the PIM-1 chains is enhanced and thus EA,β∗levels off at the

value for pure PIM-1.

In order to verify the simplified phenomenological picture, the density of the PIM-

1/PhE-POSS composites was investigated in dependence of the nanofiller concen-

tration (see Figure 6.14).

0 20 40 60 80 100

1.14

1.16

1.18

1.20

1.22

c(PhE-POSS) /wt%

/g cm

-3

Ideal two phase behavior

0 10 20 30

1.150

1.155

1.160

1.165

Figure 6.14 – Density of the PIM-1/PhE-POSS nanocomposites vs. c(PhE-POSS). The

solid line is a linear fit of all data points and the dashed line sketches

the behavior of an ideal two phase system. The inset gives a detailed

view on the PhE-POSS concentrations up to 30 wt%. The error bars were

estimated based on at least two values.

At first glance, density increases approximately linear with increasing PhE-POSS

content. A detailed view on the density of the composites shows that, up to a concen-

tration of 10 wt%, the densities almost follow the ideal behavior – only a slight trend

to lower densities seems discernible. This behavior is in agreement with the assump-

tion that PhE-POSS is dissolved in the free volume of PIM-1. When approaching

the critical concentration for the occurrence of a phase separated morphology, around

15 wt%, the dependency of the density on the POSS concentration is changed and

deviates more clearly from the ideal two-phase behavior. As discussed above, it is

assumed that in some regions within the PIM-1 matrix the formation of PhE-POSS

aggregates starts to distort the internal structure and meanwhile the free volume

is further filled with individual PhE-POSS molecules. At very low concentrations,

the second process dominates and thus the density increases further with increasing

POSS content. When phase separation sets in, the negative deviation in the density

change becomes more pronounced.

6 PIM-1 and PIM-1/POSS Nanocomposites

It should be noted that the prepared composites of PIM-1 and PhE-POSS are trans-

parent up the highest concentration of the nanofiller. This means that the domain-

size of the phase-separated structure must be smaller than half of the wave length

of visible light. Taking blue light as the visible light with the shortest wavelength,

the phase-separated domains should have a maximum size of ca. 200 nm. This is

supported by the SEM pictures shown in Fig. 6.11.

This is different to the discussed Matrimid/PhE-POSS composites, where the sam-

ples become increasingly turbid for POSS concentration above 4 wt% (see Fig. 4.5).

This line of argumentation is also in agreement with the observation that in the

dielectric spectra of PIM-1/PhE-POSS nanocomposites no pronounced Maxwell/

Wagner/Sillars (MWS) polarization effects have been observed, indicating also that

the phase-separated domains should be small and the corresponding MWS polar-

izations will be observed at higher frequencies than considered here. In contrast

to that, the Matrimid/PhE-POSS composites showed pronounced MWS phenomena

(see section 5.2.3).

Conductivity

Besides the discussed relaxation processes, conductivity effects are observed sur-

prisingly for the PIM-1/PhE-POSS composites although no glass transition could

be measured before decomposition. For most conventional polymers, the mobility of

charge carriers is related to segmental dynamics of the polymer and thus conductivity

effects in general are observed above Tg.63 As already discussed in section 6.2, it

is assumed that conductivity effects of PIM-1 are related to the postulated π−π–

stacking of the polymer segments which supports the charge transport.

In order to analyze this effect in detail, the complex conductivity is used (eq. 3.5). In

Figure 6.15a, the real part of the complex conductivity σ‘is depicted for PIM-1-075

as function of frequency for different temperatures. In Figure 6.15b, the real part

of the complex conductivity σ‘versus frequency is shown for different PhE-POSS

concentrations at the same temperature.

6 PIM-1 and PIM-1/POSS Nanocomposites

-1 0 1 2 3 4 5 6

-14

-12

-10

-8

463 K

493 K

523 K

log

(

/S cm

-1

)

log (f /Hz)

-1 0 1 2 3 4 5 6

-14

-12

-10

-8

PIM-1-01

PIM-1-05

PIM-1-30

log (f /Hz)

log

(

/S cm

-1

)

c,30wt%

c,5wt%

c,1wt%

Figure 6.15 – Real part of the complex conductivity σ‘vs. frequency for the second

heating run of a) PIM-1-075 at different temperatures (T = 463 K, T =

493 K, T = 523 K) and b) for PIM-1-01, PIM-1-05 and PIM-1-30 at

499 K.

The real part of the complex conductivity σ‘shows the typical frequency dependence

expected for a semi-conducting polymer: σ‘decreases with decreasing frequency

until a critical frequency fcis reached where this dependence changes to a plateau

(see section 3.1.3). This plateau corresponds to the DC conductivity. The value for

the DC conductivity increases with increasing temperature (Figure 6.15a) as well as

increasing PhE-POSS content (Figuree 6.15b).

The data is approximated by the Jonscher power law (eq. 3.15) and σDC is obtained

by fitting the Jonscher equation to the data.

The DC conductivity σDC vs. inverse temperature is shown in Figure 6.16a for different

PhE-POSS concentrations. The data follow an Arrhenius behavior similar to pure

PIM-1 (discussed in section 6.2). The concentration dependence of the activation

energy of the conductivity EA,σDC is given in Figure 6.16b.

6 PIM-1 and PIM-1/POSS Nanocomposites

1.9 2.0 2.1 2.2

-14.5

-14.0

-13.5

-13.0

-12.5

PIM-1-01

PIM-1-05

PIM-1-20

PIM-1-30

log

(

/S cm

-1

)

1000/T /K

-1

0 10 20 30

100

110

120

c(PhE-POSS) /wt%

A, DC

/kJ mol

-1

Figure 6.16 – a) Direct current conductivity σDC for the second heating vs. the in-

verse temperature of PIM-1-01, PIM-1-05, PIM-1-20 and PIM-1-30 .

The lines are an Arrhenius fit to the data. b) Activation energy of the

conductivity EA,σDC vs. PhE-POSS concentration.

The observed activation energies for the conductivity are larger than those for the

β∗–relaxation, as already discussed for pure PIM-1 in section 6.2. This indicates

that the conductivity is not directly related to the β∗–relaxation. Up to a PhE-

POSS concentration of about 5 wt%, EA,σDC is independent of c(PhE-POSS). This

corresponds to region I, as identified for the β∗–relaxation. As already discussed,

here small amounts of PhE-POSS can participate in motional processes of the sur-

rounding PIM-1 matrix. For the conductivity, it is assumed that the phenyl rings of

PhE-POSS join the π−π–stacking of the PIM-1 matrix and thus almost not affect

the conductivity. With increasing PhE-POSS concentration, the activation energy

increases step-like up to about 10 wt% (see Figure 6.16b). This corresponds to con-

centration range II, where small PhE-POSS agglomerates are formed and the PIM-1

matrix is slightly distorted. This results in a distinct increase of EA,σDC because the

stack-like arrangement of the phenyl rings, which supports the charge transport, is

disturbed. Above the critical concentration for the phase-separation, i.e. concen-

tration range III, EA,σDC shows a further, but less pronounced, linear increase with

increasing POSS concentration due to the further weakening of the π−π–stacking,

as discussed above.

6.3.3 Gas Transport Properties

The gas transport properties of PIM-1 and selected composites were analyzed for

N2, O2, CH4, and CO2at 35 ◦C. For a first orientation of the influence of PhE-POSS

6 PIM-1 and PIM-1/POSS Nanocomposites

on the gas transport properties of PIM-1, small POSS concentration was chosen,

where individual filler molecules are completely accommodated in the fractional free

volume of the polymer matrix: PIM-1-01 with 1 wt% PhE-POSS. For comparison,

a somewhat higher POSS loading, still below the critical concentration of phase

separation, was included, where significant changes of the matrix can be expected:

PIM-1-075 with 7.5 wt% PhE-POSS.

6.3.3.1 Permeability and Diffusion Coefficients

The effect of PhE-POSS loadings on the permeability (a) and diffusion coefficients

(b) of N2versus the upstream pressure p1is shown in Figure 6.17.

0 5 10 15 20

250

300

P /Barrer

/bar

0 5 10 15 20

D /10

-7

-1

/bar

Figure 6.17 – a) N2–permeability and b) diffusion coefficients vs. upstream pressure p1

for PIM-1-00, PIM-1-01 and PIM-1-075 at 35 ◦C.

In all cases, a decrease of permeability with increasing upstream pressure is observed,

while the diffusion coefficients increase slightly. This behavior is in agreement with

the dual-mode behavior expected for glassy polymers and was reported earlier by Li

et al. for pure PIM-1.153 A similar pressure dependence was also found for oxygen

and methane, while for carbon dioxide its plasticizing effect seems to dominate – see

more detailed discussion below.

Overall, for nitrogen the permeability is increased by a factor of three and the diffu-

sion coefficients by two for PIM-1-01 compared to pure PIM-1, whereas loadings of

7.5 wt% lead to a reduction of the permeability as well as the diffusion coefficients

compared to PIM-1-00. In Figure 6.18, the effect of PhE-POSS loadings on the

100

6 PIM-1 and PIM-1/POSS Nanocomposites

permeability (a) and diffusion coefficients (b) of O2versus the upstream pressure p1

is shown.

0 5 10 15 20

100

200

300

700

800

900

P /Barrer

/bar

0 5 10 15 20

D /10

-7

-1

/bar

Figure 6.18 – a) O2–permeability and b) diffusion coefficients vs. upstream pressure p1

for PIM-1-00, PIM-1-01 and PIM-1-075 at 35 ◦C.

As was observed for N2(Figure 6.17), the O2–permeability and the diffusion co-

efficients are significantly increased as well by loadings of 1 wt% of PhE-POSS

(PIM-1-01), whereas higher loadings of 7.5 wt% (PIM-1-075) lead to decreased per-

meability and diffusion coefficients. The same trend was found also for methane as

shown in Figure 6.19.

0 5 10 15 20

100

200

300

400

P /Barrer

/bar

0 5 10 15 20

D /10

-7

-1

/bar

Figure 6.19 – a) CH4–permeability and b) diffusion coefficients vs. upstream pressure

p1for PIM-1-00, PIM-1-01 and PIM-1-075 at 35 ◦C.

The CO2-permeability (a) and the diffusion coefficients (b) versus the upstream pres-

sure p1are shown in Figure 6.20.

101

6 PIM-1 and PIM-1/POSS Nanocomposites

0 5 10 15 20

1000

2000

3000

4000

5000

P /Barrer

/bar

0 5 10 15 20

D /10

-7

-1

/bar

Figure 6.20 – a) CO2–permeability and b) diffusion coefficients vs. upstream pressure

p1for PIM-1-00, PIM-1-01 and PIM-1-075 at 35 ◦C.

As for N2, O2, and CH4, permeability and diffusion coefficients of CO2in PIM-1-

01 are significantly higher compared to PIM-1-00 and PIM-1-075. Moreover, for

pure PIM-1 (PIM-1-00) and 7.5 wt% (PIM-1-075) a distinct plasticization effect of

CO2 is observed, i.e. not only the diffusivity but also the permeability increases

with increasing upstream pressure. In contrast, the CO2-permeability of PIM-1-01

(1 wt% PhE-POSS) decreases drastically with increasing pressure. The initially

much higher permeability of CO2in PIM-1-01 may be ascribed to a looser chain

packing in the cast film compared to pure PIM-1. It should be noted that the per-

meation experiments were performed in the order of increasing gas solubility, i.e.

N2, O2, CH4, CO2. So the distinctly increased permeability of PIM-1-01 compared

to PIM-1-00 observed for the low solubility gases N2, O2and CH4and also for

CO2at 1 bar is related to this initial state of the film. The plasticizing effect of

carbon dioxide is well known and mainly due to its much higher solubility compared

to the other gases used in this study. This plasticization effect leads obviously to a

collapse of the loosened structure of PIM-1-01 at higher carbon dioxide pressures

corresponding to higher concentrations in the polymer. This enhanced physical ag-

ing dominates the permeability in this case. In contrast, PIM-1-00 and PIM-1-075

show a significant increase of CO2-permeability with upstream pressure due to the

plasticizing effect of CO2, as their more stable structure in the polymer film is less

prone to physical ageing. Interestingly, this behavior of the gas transport properties

is not directly reflected by the density or BDS data discussed in the first part of

this work, indicating that already subtle changes in the structure of a solid film may

have a strong impact on the gas transport properties, especially for PIMs.

102

6 PIM-1 and PIM-1/POSS Nanocomposites

Nevertheless, for all analyzed gases the permeability and the diffusion coefficients of

PIM-1-01 are found to be much higher than for PIM-1-00 and PIM-1-075. Therefore,

it may be assumed that PIM-1-01 has a loose, more open structure – also after the

partial collapse induced by CO2at higher pressures – compared to pure PIM-1,

which was also reported by Yong et al. for a PIM-1/POSS composite.22 Thus, small

amounts of PhE-POSS generally lead to enhanced gas transport properties of the

PIM-1 matrix.

For PIM-1-075, it is assumed that PhE-POSS agglomerates are formed, which oc-

cupy the free volume to an extent that they start to distort the surrounding polymer

matrix. Consequently, it seems reasonable that this is connected with a reduction

in diffusivity and permeability as parts of the free volume may be blocked thereby.

Furthermore, these agglomerates may also lead to a rigidification of the adjacent

matrix polymer as previously observed for other mixed matrix materials.124,154

Although the findings concerning the gas transport in PIM-1/PhE-POSS nanocom-

posites are in agreement with the simplified picture developed based on the BDS

measurements, the distinct effects of small loadings on diffusivity and permeability

are not reflected to the same extent by the BDS data. In view of this complex

behavior, a straightforward connection between the two is not expected.

The pronounced tendency to physical ageing of PIM-1-01 and its irreversibility were

proven by repeated measurements at the end of our measurement series, including

also some experiments at elevated temperatures up to 338 K not shown in this work.

Here, the permeability decreased for CO2at 1 bar from initially 4920 Barrer (see

Fig. 6.20) to 1430 Barrer. Although more detailed investigations concerning the

ageing behavior might be necessary, it becomes clear that the potential improvement

of the membrane performance cannot be directly utilized in practical applications. A

possible approach to stabilize the loosened structure of the PIM-1 matrix could be

a covalent crosslinking within the formed solid film, e.g. by partially functionalized

POSS fillers.

6.3.3.2 Selectivity

The selectivity of the three materials is examined, taking the technically relevant

gas pair CO2/CH4as an example for natural gas upgrading to assess the potential

improvement of the nanocomposite system under investigation.

103

6 PIM-1 and PIM-1/POSS Nanocomposites

In Figure 6.21 the CO2/CH4selectivity versus CO2permeability of PIM-1-00, PIM-

1-01 and PIM-1-075 at 35 ◦C and 1 bar are shown in comparison to the 2008 upper

bound.12

0.001 0.1 10 1000 100000

100

1000

P(CO

) /Barrer

/CH

selectivity

Robeson upper bound

Figure 6.21 – CO2/CH4selectivity vs. CO2permeability of PIM-1-00, PIM-1-01 and

PIM-1-075 at 35 ◦C and 1 bar. The line is the Robeson upper bound

published in 2008.12

By blending 1 wt% PhE-POSS into PIM-1 the gas separation performance is im-

proved – as the permeability is distinctly increased without losing selectivity, the

Robeson upper bound is touched by PIM-1-01. In contrast, the loss in CO2–

permeability observed for PIM-1-075 is not accompanied by an equivalent gain in

selectivity. So the potential membrane performance drops significantly for the higher

PhE-POSS concentration.

It should be noted at this point that the PIM-1 film investigated here might be

somewhat different from that of other investigators with respect to pre-treatment,

thickness, casting solvent, and thermal history.142 Specifically, no solvent treatment

of the film with methanol or ethanol was performed in this study, which is known

to result in significantly higher permeability values. In contrast, a treatment at

elevated temperatures and a thorough degassing was applied before permeability

measurements for all materials under investigation.

Thus, the permeability of PIM-1 may be lower than reported elsewhere and therefore

not situated directly on the 2008 upper bound, as one might expect. Nevertheless,

Figure 6.21 demonstrates the distinct relative effect of PhE-POSS on the permea-

bility of the nanocomposites.

104

6 PIM-1 and PIM-1/POSS Nanocomposites

6.3.4 Conclusions

As reported in the previous section, Broadband Dielectric Spectroscopy (BDS) re-

veals some important features of PIM-1, such as the unusually high activation energy

of the localized relaxation process (β∗) due to π−π–stacking as well as significant

conductivity in the glassy state below Tg, which may be relevant for a deeper un-

derstanding of the film formation process and resulting membrane performance as

well as for other applications of polymers of intrinsic microporosity. Furthermore,

BDS results help to characterize the effects of the nanoscaled fillers with respect to

miscibility, phase behavior and free volume of PIM-1/PhE-POSS nanocomposites.

Investigations of the gas transport properties show drastic increases of diffusivity and

permeability for very low filler concentrations, demonstrating that particularly subtle

changes lead to effects on the membrane performance of PIM-1 based materials.

Changes observed for 1 wt% PhE-POSS in PIM-1 point towards the Robeson upper

bound indicating a substantial improvement in membrane performance. But the pro-

nounced trend to physical aging prevents a direct utilization of these improvements.

So the stabilization of such a modified structure of the polymer in the solid state

remains the key challenge for further developments in this field.

105

7 Conclusions and Outlook

7.1 Conclusions

Polymeric membranes are increasingly used in industrial gas separation applications.

However, novel polymers demonstrate much better gas transport properties than cur-

rent state of the art membrane materials. One negative effect of today’s polymeric

membranes is the tendency to plasticization for certain gas separation processes.

In this thesis a detailed structure/property study is performed on the commercially

available and commonly used Matrimid, compared to the high performance poly-

mer PIM-1. Both polymers exhibit good gas transport properties but show strong

tendencies to physical aging and plasticization. Furthermore, this work comprises

the impact of a nanofiller embedded into both polymers on the structure/property

relationship.

Films of Matrimid and PIM-1 as well as their variations with PhenethylPOSS (PhE-

POSS) as nanofiller, respectively, were prepared by solution casting. The PhE-

POSS concentration varied from 0 - 20 wt% for Matrimid and from 0 - 40 wt% for

PIM-1.

The molecular mobility of Matrimid, PIM-1 and of both nanocomposite systems were

investigated by Broadband Dielectric Spectroscopy (BDS). Pure Matrimid and PIM-

1 displayed one broad relaxation process, denoted as β∗–relaxation, and a conduc-

tivity contribution. For both polymers the relaxation process occurred at higher

temperatures as it is expected for solely β–processes. Furthermore, the activation

energies for this β∗–relaxation (EA,β∗,Matrimid = 99 kJ/mol, EA,β∗,PIM−1= 86 kJ/mol)

are relatively high compared to β–processes of comparable glassy polymers (40 -

60 kJ/mol). Concluding the specific β∗–relaxation and high activation energies ob-

served for Matrimid and PIM-1, the β∗–relaxation has to be of cooperative nature.

7 Conclusions and Outlook

It was assumed that the cooperative relaxation is caused by agglomerates which are

formed by π−π–stacking of the phenyl rings of Matrimid (or PIM-1).

The assumption of such agglomerates were evidenced by preliminary wide-angle X-

ray (WAXS) measurements of Matrimid and PIM-1 (Fig. 7.1). The measurements

showed several broad reflections with spacings of 3.2 and 5.3 Åfor Matrimid and 3.4

and 10 Åfor PIM-1 while 10 Åcan be attributed to the micropores.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

2500

5000

7500

10000

PIM-1

(Å

-1

)

Intensity

Matrimid

Figure 7.1 – X-ray curve of the freshly cast Matrimid and PIM-1 films.

Furthermore, dynamic mechanical properties of Matrimid were determined using Dy-

namic Mechanical Analysis (DMA). Performing DMA on PIM-1 film was not possible

because of the brittleness of the film which broke during measurement. For Matrimid,

basically, the same processes as for BDS were observed with DMA. At higher tem-

peratures an α–relaxation, the dynamic glass transition, and at lower temperatures

aβ∗–relaxation was found for the loss modulus. In addition, the dynamic-mechanic

and the dielectric properties showed that the β∗–relaxation consists of two pro-

cesses, merging together either with increasing frequency (DMA) or temperature

(BDS). Combined with the results of two spacings measured by WAXS, the sep-

aration of the β∗–relaxation into two processes was explained by the existence of

different agglomerates.

A conductivity contribution well below the glass transition temperature was observed

for Matrimid and PIM-1. The temperature dependence was Arrhenius like, which is

untypical for conventional amorphous polymers, where the Vogel-Fulcher-Tammann

equation describes the temperature dependence well. The estimated activation en-

ergies are EA,σDC ,Matrimid = 115 kJ/mol and EA,σDC ,PIM−1= 101 kJ/mol. Therefore,

108

7 Conclusions and Outlook

and with the results of the WAXS measurements and the β∗–relaxation, the observed

conductivity was ascribed to the π−π–stacking, which enhances charge transport.

For Matrimid/PhE-POSS and PIM-1/PhE-POSS composites a β∗–relaxation as

well as a conductivity contribution were found with BDS. For Matrimid/PhE-POSS

at a POSS concentration of about 4 wt% and for PIM-1/PhE-POSS of about 10 wt%

an additional peak at lower temperature appeared. It was concluded that this ob-

served peak belongs to the α–relaxation of pure PhE-POSS, which takes place in the

same temperature range and thus, a phase separated structure above the respective

POSS concentration was assumed for both composites.

Additionally, this assumed phase separated structure was further supported by a

Maxwell-Wagner-Sillars polarization, which was clearly visible for the Matrimid

composites and only slightly present for the PIM-1 composites.

An overview of the main results for Matrimid and PIM-1 as well as their PhE-POSS

composites are listed in Table 7.1.

Table 7.1 – Pure Matrimid and pure PIM-1 measurement results overview.

Polymer TgρThickness EA,β∗EA,σDC Spacings ccrit

◦C g cm−3µm kJ/mol kJ/mol Åwt%

Matrimid 320 1.24 91 99 115 3.2/5.3 4

PIM-1 - 1.15 217 86 101 3.4 10

In general, Matrimid and PIM-1 have shown similar results regarding their inter-

nal molecular mobility. Due to their π–systems, both polymers form sandwich like

structures by π−π–stacking. However, the activation energies for the motion of the

formed agglomerates are slightly different, 99 kJ/mol for Matrimid and 86 kJ/mol for

PIM-1. This is attributed to a higher free volume in PIM-1, which is formed due

to the rigid structure (see Figure 7.2), leading to a slightly enhanced mobility of

the agglomerates compared to Matrimid. One interesting aspect is that the differ-

ence of EA,β∗and EA,σDC for Matrimid and PIM-1 is about 15 kJ/mol, which might be

accidentally but should be further investigated.

109

7 Conclusions and Outlook

PIM-1 Matrimid

Figure 7.2 – Structures of Matrimid and PIM-1.

After the incorporation of PhenethylPOSS into Matrimid and PIM-1, the difference

of the amount of free volume is still present. The composites of Matrimid and PIM-1

differ strongly with respect to their optical transparency for high POSS concentra-

tions (see Fig. 7.3).

Figure 7.3 – Images of cast Matrimid/PhE-POSS (7 wt%) and PIM-1/PhE-POSS

(30 wt%).

With increasing POSS concentration, the Matrimid composites became less transpar-

ent and for high POSS concentrations small areas of high cloudiness were formed. In

contrast, the PIM-1 composites were transparent even at high POSS concentrations.

It was concluded that the maximum size of the POSS domains in the phase-separated

structure, has to be about 200 nm because the domains must be smaller than half

110

7 Conclusions and Outlook

of the wave length of visible light. This assumption was further supported by SEM

images of the fracture edge of the Matrimid and PIM-1 composites. Cavities on the

surface of the fracture edge were observed for both composites at high POSS con-

centrations which were attributed to broken out POSS agglomerates. For Matrimid

composites cavities appear with concentrations higher than 4 wt%, whereas for PIM-1

the concentration must be higher than 30 wt%.

Figure 7.4 – SEM images of fracture edge of Matrimid and PIM-1 composites with

POSS concentrations of 20 wt% and 40 wt%.

In Figure 7.4 the fracture edges of Matrimid and PIM-1 composites are shown, each

with the maximum investigated concentration of POSS. The size of the observed

cavities in Matrimid strongly differs from the cavities in PIM-1 composites. The

POSS agglomerates formed in PIM-1 are much smaller than the POSS agglomerates

formed in the Matrimid composites. This result is in line with the BDS results for

the PIM-1/PhE-POSS composites where no pronounced Maxwell/Wagner/Sillars

(MWS) polarization effects was observed, however, Matrimid/PhE-POSS composites

showed pronounced MWS phenomena.

Besides the smaller size of the POSS domains in PIM-1 compared to Matrimid,

the rigidity is strongly different, indicated by the difference in brittleness of fresh

cast films. Furthermore, the concentration dependence of the normalized density is

an additional indication for a more rigid structure of PIM-1 compared to Matrimid

(Figure 7.5).

111

7 Conclusions and Outlook

0 20 40 60 80 100

1.00

1.05

pure polymer

c(PhE-POSS) /wt%

Figure 7.5 – Normalized density of Matrimid (circles) and PIM-1 (squares) composites

vs. PhE-POSS concentration.

For both polymers it was assumed that small amounts of POSS are dissolved in the

free volume sites of the polymer matrix. For small POSS concentrations, the density

of Matrimid and PIM-1 composites increases, supporting the assumption of the filling

of the free volume sites. When the phase separation occurs and POSS agglomerates

are formed, ρof the Matrimid composites decreases towards the ideal two phase

behavior. In contrast, ρof the PIM-1 composites starts to deviate from the ideal two

phase behavior. This was assigned to two competitive processes. Besides the filling

of the free volume sites, the formation of POSS agglomerates starts to distort the

internal structure while the free volume is further filled up.

Furthermore, gas transport experiments showed strong interactions of the POSS

molecules with the surrounding polymer matrix. The permeability of PIM-1 and Ma-

trimid was enhanced by only 1 wt% of POSS embedded in polymers. In case of PIM-1

this enhancement indicated a substantial improvement of the membrane performance

as the selectivity/permeability was improved towards the Robeson upper bound. Un-

fortunately, pronounced trend to physical aging prevents a direct utilization of these

improvements.

In addition, the interaction of the POSS agglomerates with the Matrimid matrix, in

the phase separated structure, led to a reduced plasticization effect for CO2.

In conclusion, this work proves the existence of agglomerates formed by π−π–

stacking in Matrimid and in PIM-1. Up to the present this fact was not taken into

account when film formation, free volume, chain dynamics and especially gas trans-

port properties were discussed. The expected interaction of the phenyl ring of the

substituents of POSS with the π–system of the polymers was proved. However,

112

7 Conclusions and Outlook

this strong interaction either leads to significant improvements for small POSS con-

centrations (especially for PIM-1) or reduces plasticization (for Matrimid) for high

POSS contents.

7.2 Outlook

In general, the observed π−πinteractions provide a high potential on the one hand

for the stabilization of the polymer itself and on the other hand for a better inter-

action between polymer and filler in a mixed matrix membrane and thus, improve

gas transport properties and/or reduce plasticization effects. Due to the indicated

physical aging effect observed for 1 wt% of POSS in PIM-1, another additional sta-

bilization has to be found, e.g. additional crosslinking. Nevertheless, the discussed

findings in this study have to be further investigated and extended to more PIMs as

well as nanofillers.

113

A Further Experimental Details

A.1 Materials and Sample Preparation: PIM-1∗

Material

Synthesis

The synthesis of PIM-1 was carried out according to the procedure below, based on

that reported by Du et al:117

To a dry 500 ml three-necked round bottom flask equipped with a Dean-Stark trap,

5,5’,6,6’-tetrahydroxy-3,3,3’,3’-tetramethyl-1,1’-spirobisindane (TTSBI) (17.021 g,

0.05 mol), tetrafluoroterephthalonitrile (TFTPN) (10.005 g, 0.05 mol), anhydrous

potassium carbonate (20.730 g, 0.15 mol), dimethylacetamide DMAc (100 ml), and

toluene (50 ml) were added under an atmosphere of nitrogen gas. The monomers

were allowed to dissolve before the reaction mixture was refluxed during rapid stirring

at 200 rpm at 160 ◦C for 40 min. Heating was carried out using a IKA hot-plate

together with a DrySyn aluminium heating block. After 40 min, the viscous solution

was poured into methanol. To purify the polymer, the sample was dissolved in 500 ml

of chloroform and re-precipitated in methanol while stirring. After washing with

∗Similar content was published in Konnertz, N.; Ding, Y.; Harrison, W. J.; Budd, P. M.; Schönhals,

A.; Böhning, M., ACS Macro Letters, 2016, 5, 528-532; Supporting Information.

A Further Experimental Details

acetone, the product was stirred in 1,4-dioxane for 30 min to remove low molecular

weight oligomers and cyclic products, before washing again with acetone. The sample

was then refluxed overnight in deionized water, stirred in methanol for 20 min and

then dried at 100 ◦C for two days. The final yield of PIM-1 obtained was 22.06 g

(95.9 %).

It has to be noted that for PIM-1 very different casting/ drying protocols can be

found in the literature, which lead to different states of the solid film (as revealed,

e.g., by different gas permeabilities). Drying temperatures in the range from 40 ◦C

up to 100 ◦C have been reported20,153,155 the strong tendency to physical aging of

PIMs suggests as low as possible temperatures as long as complete solvent removal

is ensured. Furthermore, it is known that a methanol treatment for solvent exchange

results in lower packing density (and high gas permeabilities), while contact with

water (e.g., for removing the film from the casting plate) has an opposite effect.

Characterization

Gel Permeation Chromatography (GPC)

Gel Permeation Chromatography (GPC) measurements were carried out using a Vis-

cotek GPC max VE 2001 instrument with two PL mixed B columns and a Viscotek

TDA 302 Triple Detector Array which employs a viscometer, refractive index and

light scattering detectors. Chloroform was used as solvent at a flow rate of 1 cm−3

min−1and the injection volume was 100 µl. A PIM-1 solution in filtered chloroform

was used at a concentration of 1.00 mg/ml. A calibration curve constructed from

polystyrene standards of known molar mass was used to calculate a comparative

value of molar mass from the refractive index detector. For light scattering, a refrac-

tive index increment value for PIM-1 in chloroform of 0.196 g/ml was used in the

calculation of molar mass. An absolute value of molar mass and polydispersity of

the PIM-1 was then calculated using data from all three detectors. The results are

listed in table A.1.

Table A.1 – Results from Gel Permeation Chromatography of PIM-1.

Polymer MWMnMW/MnMp

PIM-1 82800 29300 2.8 55900

A Further Experimental Details

SEC in chloroform against polystyrene standards gave MW= 82800 g/mol and a

polydispersity index of PDI = 2.8.

1H Nuclear Magnetic Resonance (NMR)

1H Nuclear Magnetic Resonance (NMR) spectroscopy was carried out using a Bruker

400 MHz spectrometer. For sample preparation, PIM-1 was dissolved in deuterated

chloroform (CDCl3, Aldrich 99.8% atom D) to make a concentrated solution which

was then transferred into a 5 mm NMR tube. Results from 1H-NMR can be found in

Figure A.1.

The typical peaks attributed to PIM-1 can be seen in the 1H-NMR spectra:

a– aromatic hydrogens, peaks 6.36 and 6.74 ppm

b– hydrogens on the five membered ring, peaks 2.1 and 2.26 ppm

c– hydrogens from methyl groups, peaks 1.24 and 1.29 ppm

Additional peak suggesting presence of residual solvent: Peak at 3.63 ppm– at-

tributed to 1,4-dioxane. This was used to purify the polymer by removing oligomers/

cyclic PIM-1 species.

The 1H-Nuclear Magnetic Resonance spectra are shown below in Figure A.1 and

A.2.

III

A Further Experimental Details

7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

Chemical Shift (ppm)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Normalized Intensity

1.24

1.29

2.08

2.10

2.26

3.63

6.35

6.74

7.19

Figure A.1 –1H-NMR of PIM-1 before washing with methanol.

7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

Chemical Shift (ppm)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Normalized Intensity

0.79

0.81

0.83

1.14 1.19 1.24

1.29

1.56

1.81

1.97

2.08

2.26

3.87

3.94

4.04

6.20

6.35

6.60

6.74

7.19

Figure A.2 –1H- NMR after washing with methanol – the 1,4-dioxane peak at 3.63 ppm

is no longer visible.

Sample Preparation

Thermogravimetric Analysis

In order to obtain a representative PIM-1-film, a protocol without methanol treatment

and without direct water contact was chosen. An optimal annealing temperature

was determined by several casting/drying steps (temperature, time) with subsequent

thermogravimetric analysis (TGA), respectively. After drying for 1 day in vacuum at

40 ◦C in the TGA, a remaining mass loss of about 2.6% at 200 ◦C was observed, which

after 5 days at 40 ◦C was still 1.3%. For the second series of films, temperatures

A Further Experimental Details

above the boiling point of the solvent used (chloroform, bp = 61 ◦C) were chosen:

75 and 100 ◦C. After 3 days, at 75 ◦C there was a mass loss at 200 ◦C of 0.44% in

the TGA, which was the same as for 1 day at 100 ◦C. After 3 days at 100 ◦C only a

further reduction to 0.33% was achieved. Therefore, 3 days at 75 ◦C was chosen for

the film used in this study. Selected TGA curves are given in Figure A.3.

100 °C 200 °C 300 °C 400 °C

0.96

0.97

0.98

0.99

1.00

Powder

40 °C /1 d

40 °C /5 d

75 °C /1 d

75 °C /3 d

75 °C /7 d

100 °C /1 d

100 °C /3 d

Weight /%

300 350 400 450 500 550 600 650 700

Temperature /K

Figure A.3 – Selected TGA curves of PIM-1 films after the indicated drying/annealing

protocols.

A.2 Dielectric Investigations: PIM-1 and Matrimid

X-Ray Measurements

A SAXSess mc2 small angle scattering system (Anton Paar, Graz, Austria) operated in

wide angle modus was applied for X-ray measurements. Line-collimation operational

mode and Cu-Kα-radiation (λ= 0.154 nm) were used. The polymer samples were

placed between two small copper plates and mounted to a solid sample holder in an

evacuated sample chamber (1 mbar). The illuminated area was 20 mm x 1 mm. Data

were recorded with an imaging plate and an exposition time of 15 min at constant

temperature of 20 ◦C. The OptiQuant Image Analysis Software (Perkin Elmer) was

utilized to read out the imaging plate and subsequent, treated with the SAXS Quant

Software (Anton Paar).

A Further Experimental Details

0.0 0.5 1.0 1.5 2.0 2.5 3.0

2500

5000

7500

10000

(Å

-1

)

Intensity

0.0 0.5 1.0 1.5 2.0 2.5 3.0

2500

5000

7500

10000

Intensity

(Å

-1

)

Figure A.4 – X-ray curves of the freshly cast Matrimid (a) and PIM-1 (b) film.

B Abbreviations

A a factor with unit rad ·s−1s−1

A fragility parameter

αthermal expansion coefficient

αsthermal expansion coefficient of a solid

αlthermal expansion coefficient of a liquid

αid

i,j ideal selectivity

B b affinity constant

BDS Broadband Dielectric Spectroscopy

C c concentration

C∗complex capacitance

C0vacuum capacitance

c1concentration upstream

c2concentration downstream

cDconcentration of the penetrant in the polymer

cHLangmuir sorption

c’Hsaturation capacity

cpspecific heat

CRR Cooperatively Rearranging Regions

D D diffusion coefficient

Ddiel dielectric displacement

Ddiel.,0dielectric displacement of the free space

Deff effective diffusion coefficient

D∗complex strain compliance

D‘ real part of the complex strain compliance

D“ imaginary part of the complex strain compliance

DC direct current

DMA Dynamic Mechanical Analysis

DSC Differential Scanning Calorimetry

B Abbreviations

E E electric field

E∗complex elastic modulus

E‘ storage modulus

E“ loss modulus

∆E free energy barrier for one molecule or segments

∆εdielectric strength

EA,D activation energy of the diffusion

EA,β∗activation energy of the β∗–relaxation

EA,cond activation energy of the conductivity

E0alternating electric field amplitude

E(t) outer electrical field

εpermittivity

ε∗complex dielectric function

ε‘ real part of ε∗

ε“ imaginary part of ε∗

ε0dielectric permittivity of vacuum (8.854 x 10−12 As V−1m−1)

εsstatic permittivity

ε∞unrelaxed permittivity

ε(t) time dependent dielectric function

F f frequency

fccharacteristic frequency

fgfractional free volume at Tg

fmax relaxation rate

f∞frequency in the high temperature limit

F effective sample area

G G shear modulus

J J molar flux

Jst molar flux in the steady state

H∆HSpartial molar enthalpy of the sorption

HN Havriliak Negami

K kBBoltzmann constant (1.38 10−23 J/K)

kDHenry-constant

L l membrane thickness

λmean free path

M MWmolecular weight

Mccritical molecular weight

VIII

B Abbreviations

MWS Maxwell-Wagner-Sillars

N N total number of particles

P p pressure

p1pressure upstream

p2pressure downstream

P permeability coefficient

P polarization

P∞contributions arising from induced polarization

pimicroscopic dipole moments

ΦFV fractional free volume

Q Qttotal amount of permeated gas

R R universal gas constant (8.314 J mol−1K−1)

ρdensity

S s parameter describing ohmic and non-ohmic effects

S solubility coefficient

Sctotal configurational entropy

σ∗complex conductivity

σ‘real part of σ∗

σ“imaginary part of σ∗

σ0DC (direct current) conductivity

σDC DC (direct current) conductivity

σkin kinetic diameter

ST steady state

STP standard conditions TST P = 273.15 K and pST P = 1.013 bar

SEM Scanning Electron Microscopy

T t time

τrelaxation time

τ∞relaxation time in the high temperature limit

τT L time-lag

T temperature

T0Vogel or ideal glass transition temperature

Tccritical temperature

Tgglass transition temperature

TKKautzmann temperature

Tmmelting temperature

TGA Thermogravimetric Analysis

B Abbreviations

TL time lag

V V volume

V∗minimal free volume required for a jump of a segment (or molecule)

between two sites

Vccritical volume

gas volume of a gas at standard conditions STP

m,gas molar volume for an ideal gas (22.4 cm3mol−1)

Vfree total free volume

Vfree average free volume

Vlvolume of an undercooled liquid

VMvolume of molecule (VM≈VvdW )

VMatrix matrix volume

Vspec specific volume

VvdW van der Waals volume

VCRR volume of "Cooperatively Rearranging Regions (CRR)"

VFT Vogel-Fulcher-Tammann

Wωangular frequency

X x space coordinate measured normal to the section

χ∗dielectric susceptibility

ξlength

Z Z∗complex impedance

z(T) number of segments per CRR

C Publications

C.1 Paper

Related Work

1. N. Konnertz, M. Böhning and A. Schönhals, Dielectric investigations of nanocom-

posites based on matrimid and polyhedral oligomeric phenethyl-silsesquioxanes

(POSS), Polymer, 2016, 90, 89-101.

2. N. Konnertz, Y. Ding, W. J. Harrison, P.M. Budd, A. Schönhals, M. Böhning,

Molecular mobility of the high performance membrane polymer PIM-1 as in-

vestigated by dielectric spectroscopy, ACS Macro Letters, 2016, 5, 528-532.

3. N. Konnertz, Y. Ding, W. J. Harrison, P.M. Budd, A. Schönhals, M. Böhning,

Molecular Mobility and Gas Transport Properties of Nanocomposites based on

PIM-1 and Polyhedral Oligomeric Phenethyl-Silsesquioxanes (POSS), Journal

of Membrane Science, 2017, 529, 274-285.

Other Publications

4. D. Becker, N. Konnertz, M. Böhning, J. Schmidt, A. Thomas, Light-Switchable

Polymers of Intrinsic Microporosity, Chemistry of Materials, 2016, 28, 8523-

8529.

C Publications

C.2 Contributions to Conferences

C.2.1 Oral Presentations

1. N. Konnertz, A. Schönhals and M. Böhning, Gas Transport Properties and

Molecular Mobility of Matrimid/PhenethylPOSS Nanocomposites, 15th Net-

work Young Membrains, Aachen, September 2015.

2. N. Konnertz, A. Schönhals and M. Böhning, Gas Transport Properties and

Molecular Mobility of Matrimid/PhenethylPOSS Nanocomposites, EUROMEM-

BRANE, Aachen, September 2015.

3. N. Konnertz, M. Böhning and A. Schönhals, Dielectric Investigations of the high

Performance Polymer PIM-1 and Nanocomposites containing PhenethylPOSS,

9th International Conference on Broadband Dielectric Spectroscopy and its

Applications, Pisa, Italy, September 2016.

C.2.2 Poster Presentations

1. N. Konnertz, M. Böhning and A. Schönhals, Gastransport Properties and Molec-

ular Mobility of Matrimid/PhenethylPOSS Nanocomposites, DPG Frühjahrsta-

gung, Berlin, March 2015.

2. N. Konnertz and M. Böhning, QCM System for the Characterization of Gas

Sorption and Physical Aging on Membrane Polymers and Nanocomposites for

Gas Separation Applications, DPG Frühjahrstagung, Berlin, March 2015.

3. N. Konnertz and M. Böhning, QCM System for the Characterization of Gas

Sorption and Physical Aging on Membrane Polymers and Nanocomposites for

Gas Separation Applications, EUROMEMBRANE, Aachen, September 2015.

XII

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