polymers
Article
Insights into Nano-Scale Physical and Mechanical
Properties of Epoxy/Boehmite Nanocomposite
Using Different AFM Modes
Media Ghasem Zadeh Khorasani 1,2,* , Dorothee Silbernagl 1, Daniel Platz 3and
Heinz Sturm 1,4
1Bundesanstalt für Materialforschung und -prüfung (BAM), Div. 6.6, D-12205 Berlin, Germany;
2Department Polymertechnik/Polymerphysik, Technical University of Berlin, D-10587 Berlin, Germany
3TU Wien, Institute of Sensor and Actuator Systems, A-1040 Vienna, Austria; [email protected]
4Department Mechanical Engineering and Transport Systems, Technical University of Berlin,
D-10587 Berlin, Germany
*Correspondence: [email protected]
Received: 27 December 2018; Accepted: 29 January 2019; Published: 1 February 2019
Abstract:
Understanding the interaction between nanoparticles and the matrix and the properties
of interphase is crucial to predict the macroscopic properties of a nanocomposite system. Here,
we investigate the interaction between boehmite nanoparticles (BNPs) and epoxy using different
atomic force microscopy (AFM) approaches. We demonstrate benefits of using multifrequency
intermodulation AFM (ImAFM) to obtain information about conservative, dissipative and van der
Waals tip-surface forces and probing local properties of nanoparticles, matrix and the interphase.
We utilize scanning kelvin probe microscopy (SKPM) to probe surface potential as a tool to visualize
material contrast with a physical parameter, which is independent from the mechanics of the surface.
Combining the information from ImAFM stiffness and SKPM surface potential results in a precise
characterization of interfacial region, demonstrating that the interphase is softer than epoxy and
boehmite nanoparticles. Further, we investigated the effect of boehmite nanoparticles on the bulk
properties of epoxy matrix. ImAFM stiffness maps revealed the significant stiffening effect of
boehmite nanoparticles on anhydride-cured epoxy matrix. The energy dissipation of epoxy matrix
locally measured by ImAFM shows a considerable increase compared to that of neat epoxy. These
measurements suggest a substantial alteration of epoxy structure induced by the presence of boehmite.
Keywords:
nanomechanical properties; boehmite; epoxy nanocomposites; atomic force microscopy;
intermodulation; interphase
1. Introduction
Epoxy materials are used as a matrix in carbon-fiber reinforced polymers to produce light-weight
constructions for applications in such industries as automotive, aerospace and construction. Despite
excellent properties such as high strength, high modulus, good adhesion, high chemical and heat
resistance [
1
], the main challenge to overcome is the brittleness and low fracture toughness of cured
epoxy matrix [
2
]. Among commercially available inorganic nanoparticles, boehmite nanoparticles
(BNPs) have shown enhancements of mechanical properties of matrix in several polymer-based
nanocomposites [
3
–
7
]. Particularly, BNPs show significant reinforcing effects on epoxy matrices,
including increasing shear strength, shear modulus and compressive strength while improving
the fracture toughness [
4
,
8
,
9
]. The underlying mechanism of toughening effect of BNPs on epoxy
matrix is hypothesized to be due to formation of a soft interphase between epoxy and boehmite.
Polymers 2019,11, 235; doi:10.3390/polym11020235 www.mdpi.com/journal/polymers
Polymers 2019,11, 235 2 of 19
However, the direct investigations on interphase properties of such a nanocomposite system has not
yet been addressed.
The interfacial region between a filler and bulk matrix, which exhibits different chemical, physical
and mechanical properties compared to bulk, is referred as interphase. It is widely accepted that the
mechanical properties of composites are strongly influenced by the properties of their interphase [
10
].
The nature of interphase in thermoplastic and thermosetting matrices are substantially different.
In thermoplastics, the interphase consists of immobilized polymer chains which exhibit less flexibility
than the bulk. In thermosetting matrices however, the crosslinking chemistry at the interphase as
well as in the bulk can be altered by the presence of particles. The interphase can have sizes from few
nanometers up to few microns [
11
–
13
]. It may exhibit a property gradient or may be homogeneous [
12
].
Determination of interphase properties using experimental approaches is challenging due to
resolution limitations in conventional mechanical characterization methods. Formation of interphases
has been investigated widely in different studies using numerical methods [
14
–
17
] and or with
experimental methods, for instance with temperature modulated differential scanning calorimetry
(TMDSC) [
18
]. A direct approach to investigate mechanical properties of interphases is atomic
force microscopy (AFM). AFM force–distance curve (FDC) is the most common approach to probe
mechanical properties of small volumes. Especially, the ability to apply well-known models
from contact mechanics (Hertz, DMT and JKR) [
19
] makes this method suitable for quantitative
measurements of polymers. This method, has a high spatial resolution and is, therefore, suitable for
probing the interphase between heterogeneous layers of material [
20
]. However, FDC substantially
lacks the lateral resolution required to probe nano-scale domains of interphase in nanocomposites.
For probing smaller volumes and resolving single nanoparticles, dynamic AFM-based approaches are
required. The most common dynamic AFM mode is tapping mode which is mostly used to obtain high
resolution surface topography images with additional compositional information in the tip oscillation
phase image. Some studies demonstrated that the phase shift is correlated to surface stiffness [
21
].
However, in most cases, quantitative determination of mechanical properties is not possible with
tapping mode phase image. A novel dynamic AFM technique is intermodulation AFM (ImAFM)
in which a multi-frequency method provides more information about the tip-surface interaction
forces than aforementioned approaches. Besides providing force curves which are equivalent to
conventional FDCs, ImAFM yields information about energy dissipated by the tip-sample interaction
giving insight to the viscous behavior of the material. ImAFM provides high resolution stiffness maps
which makes it suitable for visualizing and for the quantitative probing of nanoscale heterogeneous
phases in polymer nanocomposites. Along with stiffness maps, a second channel of information are
required to distinguish the heterogenous phases (e.g., polymer and nanoparticles) and assign the
mechanical properties to them. Using topography images for this purpose is not sufficiently precise
particularly when the dispersed phase is too small. Moreover, mechanical approaches can be affected
by topographic changes, therefore affecting the accuracy in distinguishing the border between the
phases [
10
]. Therefore, along with ImAFM, another information channel which probes a material
property independent from its mechanics, can provide higher reliability of data analysis. Scanning
kelvin probe microscopy (SKPM) is commonly applied to semiconductors and conducting systems in
order to determine the work function. So far, SKPM has been widely used to characterized electrical
contacts, semiconductors, devices such as transistors for purposes such as determination of work
function [
22
]. It has been also used to localize corrosion in metal alloys [
23
] or to measure electrical
surface charges of biological samples [
24
]. In recent years, this method is used to probe embedded
materials with different physical properties in insulating polymer matrices [
25
]. The electrical surface
potential obtained from SKPM can be used as an information channel to visualize heterogeneous
phases, even with sub-surface sensitivity [25].
In the present work, we aim to study the effect of BNPs on anhydride-cured epoxy resin.
First, we focus on visualizing and mechanical characterization of interphase by combining different
information channels of ImAFM together with SKPM. Second, we investigate the effect of BNPs on
Polymers 2019,11, 235 3 of 19
bulk matrix (away from particles) including stiffness, and dissipating energy. Finally, we compare the
results with macroscopic mechanical analysis of these nanocomposites reported in other works and
propose a describing model.
2. Materials and Methods
2.1. Materials and Sample Preparation
The epoxy system used in this study is bisphenol-A-diglycidyl ether (DGEBA, Araldite
®
LY 556,
Huntsman, Inc.) cured with an anhydride curing agent methyl tetrahydrophtalic acid anhydride
(MTHPA, Aradur
®
HY 917, Huntsman, Inc.) and accelerated by an amine, 1-methyl-imidazole (DY070,
Huntsman). The mixture of epoxy, hardener and accelerator is 100:90:1 parts per weight, respectively.
BNPs used in this study are commercially available spray-dried nanoparticles with orthorhombic
shape and primary particle size of approx.14 nm based on the manufacturer’s datasheet (DISPERAL
HP14, SASOL, Germany). First, suspensions of 30 wt % boehmite were provided and blended with
DGEBA and further the hardener and accelerator are added to the blend. The concentrations used
in this study is 0, 5 and 15 wt % BNP in 100:90:1 ratio of DGEBA, MTHPA and DY070, respectively.
The epoxy mixture ratio used is the standard stoichiometric ratio (suggested by the manufacturer).
The mixture is cured for 4 h at 80
◦
C to reach gelation and 4 h at 120
◦
C for post-curing. Dispersion and
curing process was performed by Jux and coworker and described in details elsewhere [
8
,
9
]. Please
note that the samples used in this study are identical to those in the above-mentioned publications.
There, the reader can find more information about the dispersion and other properties in those articles,
specifically that which is not mentioned in this work.
The surface of cured samples is cut with ultramicrotome to obtain a smooth surface. Before AFM
measurements the surfaces of samples are ion-polished to reduce the contaminations and residues
from microtome cutting.
2.2. Intermodulation AFM
Recently, dynamic AFM methods including usage of multi-frequency have been developed in
nanomechanical studies of surfaces. In this work, we use one such multi-frequency method called
Intermodulation AFM (ImAFM). In ImAFM the cantilever is excited with not only one frequency
such as in tapping mode but with two frequencies close to a resonance of the cantilever. Here, we
choose frequencies 0.5 kHz above and below the frequency of the first flexural eigenmode of the
cantilever. Away from the surface, the cantilever performs a beating motion. Engaged to the surface,
the cantilever motion is distorted by the nonlinear tip-sample interaction which creates additional
frequency components in the cantilever motion spectrum as shown in Appendix A. These frequency
components are called intermodulation products (IMPs), or mixing products, since they appear at
frequencies which are linear integer combinations of the drive frequencies. The amplitudes and
phases of IMPs are measured during scanning with a multi-frequency lock-in amplifier. At each
pixel, hundreds of oscillations are carried out starting from low amplitudes, reaching a maximum and
decreased to zero. As this cycle takes less than few milli-seconds, ImAFM has the advantage of being
much faster, as compared to the conventional force–distance curves (FDC).
The IMPs are directly correlated to the tip-surface force. For a single pixel, we can visualize
this correlation with force quadrature curves which show the in-phase and out-of-phase component
of the force with respect to the tip motion for each oscillation cycle [
26
]. The in-phase component
F
I
corresponds to the conservative part of the force describing the elastic behavior of the surface.
The out-of-phase quadrature F
Q
measures the dissipated energy during a single oscillation cycle.
Examples of F
I
and F
Q
curves are presented in Figure 1.F
I
(A) looks similar to those conventional
force–distance curves: it consists of an attractive and repulsive regime. The amplitude in the beginning
of the measuring cycle is low therefore there is no tip-surface interaction. By increasing the amplitude,
tip and sample spends more time closer and the tip gets into attractive regime (positive values of F
I
)
Polymers 2019,11, 235 4 of 19
which is due to van der Waals forces. With further increase of the amplitude, the tip makes contact
with the surface and penetrates into it. In this region the tip experiences a net repulsive force (negative
values of F
I
). However, at this stage F
I
(A) cannot be treated directly as FDC curves since the force
is plotted as a function of oscillation amplitude rather than tip position. Amplitude-dependence
force spectroscopy (ADFS) uses the inverse Abel transform to converts FI(A) to a traditional force-tip
position curves [
27
,
28
]. The ADFS curves can be treated as FDC curves: the slope of the curve in the
repulsive regime gives a quantitative measure of the stiffness describing the purely elastic responds of
the measured sample volume. The force in attractive regime mainly originates from van der Waals
forces which are caused by dipole–dipole and dipole-induced dipole interactions between the tip and
surface. Therefore, the work of attractive forces includes information about material changes which is
independent from the surface mechanics.
Polymers 2019, 11, 235 4 of 21
values of FI). However, at this stage FI(A) cannot be treated directly as FDC curves since the force is
plotted as a function of oscillation amplitude rather than tip position. Amplitude-dependence force
spectroscopy (ADFS) uses the inverse Abel transform to converts FI(A) to a traditional force-tip
position curves [27,28]. The ADFS curves can be treated as FDC curves: the slope of the curve in the
repulsive regime gives a quantitative measure of the stiffness describing the purely elastic responds
of the measured sample volume. The force in attractive regime mainly originates from van der Waals
forces which are caused by dipole–dipole and dipole-induced dipole interactions between the tip and
surface. Therefore, the work of attractive forces includes information about material changes which
is independent from the surface mechanics.
Figure 1. Reconstructed conservative FI (a) and dissipative FQ (b) forces on a polymer substrate. the
red and green lines present the approach and retract curves, respectively.
The FQ(A) describes the dissipative part of tip-surface interaction, which originates from viscous
nature of the material [29].
For the analysis of spatially varying features, we create surface maps of the ADFS stiffness, the
attractive force and the total energy dissipated during in a single pixel. It is noteworthy that the force
quadrature curves shown in Figure 1 are measurements of single pixels whereas the maps show the
measurement of a complete surface. Details about calculation of energy dissipation from
multifrequency data can be found in Appendix B
ImAFM measurements were carried out using MFP3D microscope (Asylum Research, Santa
Barbara, CA, USA). A multi-frequency lock-in amplifier (Intermodulation Products, Segersta,
Sweden) is used to generate the drive signals and measure the intermodulation spectra. The probes
are HQ:NSC35 (Mikromasch, Wetzlar, Germany) with resonance frequency of 190 kHz (for
measurements shown in section 3.1) and 202 kHz (for measurements shown in section 3.2), with tip
radius lower than 20 nm.
2.3. Scanning Kelvin Probe Microscopy
The vibrating capacitor or kelvin probe is a method to measure the contact potential difference
(CPD) between a sample and tip also called surface potential Vsp [30]. The sample and probe behave
as a capacitor plate with air as the dielectric in between. Vsp depends mainly on difference between
work functions of probe and the sample. To obtain high lateral resolution surface potential maps,
scanning kelvin probe microscopy (SKPM) is used. In this method, an AC signal excites the cantilever
Figure 1.
Reconstructed conservative F
I
(
a
) and dissipative F
Q
(
b
) forces on a polymer substrate. the
red and green lines present the approach and retract curves, respectively.
The F
Q
(A) describes the dissipative part of tip-surface interaction, which originates from viscous
nature of the material [29].
For the analysis of spatially varying features, we create surface maps of the ADFS stiffness,
the attractive force and the total energy dissipated during in a single pixel. It is noteworthy that
the force quadrature curves shown in Figure 1are measurements of single pixels whereas the maps
show the measurement of a complete surface. Details about calculation of energy dissipation from
multifrequency data can be found in Appendix B.
ImAFM measurements were carried out using MFP3D microscope (Asylum Research, Santa
Barbara, CA, USA). A multi-frequency lock-in amplifier (Intermodulation Products, Segersta, Sweden)
is used to generate the drive signals and measure the intermodulation spectra. The probes are
HQ:NSC35 (Mikromasch, Wetzlar, Germany) with resonance frequency of 190 kHz (for measurements
shown in Section 3.1) and 202 kHz (for measurements shown in Section 3.2), with tip radius lower
than 20 nm.
2.3. Scanning Kelvin Probe Microscopy
The vibrating capacitor or kelvin probe is a method to measure the contact potential difference
(CPD) between a sample and tip also called surface potential V
sp
[
30
]. The sample and probe behave
as a capacitor plate with air as the dielectric in between. V
sp
depends mainly on difference between
Polymers 2019,11, 235 5 of 19
work functions of probe and the sample. To obtain high lateral resolution surface potential maps,
scanning kelvin probe microscopy (SKPM) is used. In this method, an AC signal excites the cantilever
electrostatically at its resonance frequency. The potential difference between probe and the surface
results in the mechanical oscillation of cantilever. The feedback loop nulls the oscillation by applying a
bias voltage to the cantilever. This bias voltage is then collected as a contact potential difference (CPD).
The corresponding equations and technical considerations are described in detail elsewhere [
31
]. SKPM
is usually carried out as a dual-pass approach, performing two scans per line on the selected scan
area. The first pass which includes the mechanical excitation of the cantilever (tapping mode) obtains
the topography of the line. In the second pass, which is known as lift or nap mode, the topography
information is used to maintain a defined distance from the surface which is known as nap height.
Choosing a suitable nap height is crucial for increasing the resolution of SKPM while avoiding touching
the surface during the second pass.
In this work we used MFP3D microscope (Asylum Research, Santa Barbara, CA, USA) in SKPM
mode. The gold-coated silicon probes with resonance frequency of 190.130 kHz, radius lower than
20 nm provided by Mikromasch (Wetzlar, Germany) was used. During all SKPM measurements nap
height is chosen to be 50 nm as the suitable height according to topographic features of the surface.
The resulted scans shown in this article are corrected by offset plane with the purpose of enhancing
the visibility of the contrast. Therefore, the scale shown in SKPM images are different than the actual
values. The measurements were carried out in air, at room temperature, using the first eigenmode
frequency. Therefore no major subsurface sensitivity is expected, since this would mainly be the case
when using the second eigenmode [32].
3. Results
In Section 3.1, we focus on distinguishing particles, visualization of the interphase and
determination of its stiffness. We use an epoxy/boehmite nanocomposite with 5 wt % nanoparticles
(EP/BNP5) as this weight percentage is high enough to show mechanical improvements in the
macroscale meanwhile not so high that the particle agglomerations become dominant over the
scanned surface [
9
]. We obtain the ImAFM stiffness and attractive forces of different phases of the
nanocomposite including particles, interphase and matrix, meanwhile using potential map obtained
by the SKPM mode as a complementary tool to verify the presence of particles.
In Section 3.2, we quantify the effect of nanoparticles on the bulk matrix. The stiffness, work of
attractive forces, and energy dissipation of the matrix phase in a high concentration nanocomposite
with 15 wt % BNPs are derived from ImAFM measurements and compared to those of neat epoxy.
15 wt % concentration was specifically chosen since this nanocomposite has the highest Young’s
modulus among other concentrations measured in our previous study, meanwhile the epoxy matrix in
this nanocomposite possesses the lowest crosslinking density [
33
]. Hence, it is hypothesized that with
this filler concentration the properties of the epoxy matrix are strongly altered by BNPs.
3.1. ImAFM and SKPM Studies on Epoxy with 5 wt % BNP
Figure 2shows AFM data acquired from a region located on the surface of EP/BNP5. The overview
of a larger scan area is provided in Appendix C. The topography image (Figure 2a) shows protrusions
with different sizes. The main challenge is to distinguish the features related to presences of BNPs
from nodular structures which are commonly observed in cured epoxy systems [
34
]. For this purpose,
potential map obtained by the SKPM mode is used as a complementary tool to verify the presence of
BNPs. Generally speaking, the potential values are related to the work function and electronic state of
the surface which is actually a signal to measure the material contrast [
24
]. In Figure 2b, the surface
potential map shows contrast between the protrusions and the rest of the surface which verifies the
presence of BNPs within these areas. Please note that in most conductive cantilevers, the entire bottom
side of cantilever is coated with a conductive layer (here, gold). Therefore, the signal is not limited
to the capacitance formed between the tip apex and the sample, but the entire cone is participating
Polymers 2019,11, 235 6 of 19
in producing the signal. Despite such limitations in the lateral resolution, SKPM clearly identifies
compositional contrasts with the precision required in this work.
Polymers 2019, 11, 235 6 of 21
Figure 2. (a) The 3-dimensional tapping mode topography; (b) Surface potential; (c) Work of attractive
forces Wattr and (d) stiffness maps of epoxy/boehmite nanocomposite with 5 wt % nanoparticles. The
scan sizes in all images are 860 nm × 860 nm. White pixels in Wattr show error.
Figure 2c and d show the work of attractive forces Wattr and stiffness maps, respectively,
generated from ADFS curves. In a single ADFS curve obtained for each pixel, Wattr is calculated from
the net attractive regime and the slope of the curve is proportional to stiffness. The Wattr map shows
a clear contrast between the protrusions and the surrounding with a well-defined border. The area
with sudden decrease in Wattr is located where the potential maps shows the presence of boehmite.
Considering the van der Waals forces as the main driving force for net attractive regime, the low
Figure 2.
(
a
) The 3-dimensional tapping mode topography; (
b
) Surface potential; (
c
) Work of attractive
forces W
attr
and (
d
) stiffness maps of epoxy/boehmite nanocomposite with 5 wt % nanoparticles.
The scan sizes in all images are 860 nm ×860 nm. White pixels in Wattr show error.
Figure 2c,d show the work of attractive forces W
attr
and stiffness maps, respectively, generated
from ADFS curves. In a single ADFS curve obtained for each pixel, W
attr
is calculated from the
net attractive regime and the slope of the curve is proportional to stiffness. The W
attr
map shows
a clear contrast between the protrusions and the surrounding with a well-defined border. The area
with sudden decrease in W
attr
is located where the potential maps shows the presence of boehmite.
Considering the van der Waals forces as the main driving force for net attractive regime, the low values
of W
attr
is an indication for a weaker van der Waals forces between the tip (gold) and BNPs than the
epoxy. Van der Waals forces which are mainly originated from dipole–dipole and dipole-induced
Polymers 2019,11, 235 7 of 19
dipole interactions between tip and the surface, can be used as an additional information channel
about the surface composition independent from its mechanics. Thus, when measuring the mechanical
response with ImAFM, Wattr signal can also be used to visualize material contrast.
Despite the existence of two distinguishable phases in Figure 2c, the contrast in stiffness map
(Figure 4) shows a variety of stiffness values in different distances from the protrusions. The area
related to protrusions shows two phases, an area close to the center of protrusions with higher stiffness
surrounded by an extremely low stiffness area (shown in black color). It is noteworthy that the soft area
is located at an immediate distance from nanoparticles located by potential and W
attr
maps. Therefore,
the soft area relates to the particle-polymer interphase.
It is noteworthy that the bulk matrix shows variations in stiffness in the scanned area. Blocks with
high (yellow) and low (red) stiffnesses in bulk epoxy indicate the inhomogeneous nature of the matrix.
Since sudden height changes affect the force measurements, it is crucial to investigate the roll
of topography artifacts. Detailed analysis of topography-stiffness relation for the scanned surface is
presented in Appendix D. This analysis demonstrates that except minor points with sudden changes
of height and groove-like topographic features, most of topography changes and the stiffness values
are independent from each other. Thus, by excluding the affected points of the scanned areas as error
points, the remaining ADFS curves are independent from topography artifacts.
To precisely distinguish the stiffness of particles, interphase and polymer, several areas with the
presence of nanoparticles are selected and analyzed separately (Appendix E). One of the selected areas
is shown in the topography image (Figure 3a), and the corresponding maps of surface potential and
stiffness are presented in Figure 3b,c, respectively. The surface potential distinguishes the nanoparticles
from matrix however the interfacial region is not resolved in the potential map. Meanwhile, in the
stiffness map, the existences of a soft region in the vicinity of particles is clearly observable. In Figure 3d,
single ADFS curves of selected points with different distances from the particle are presented compared.
Here, it is also shown that the stiffness (slope) of the point in the interfacial region is drastically low.
To precisely relate all the measured stiffness in the scanned area to different phase of the nanocomposite
(particle, matrix and interphase), we use the material contrast shown in surface potential map together
with the stiffness map. For this purpose, we combine two information channels of stiffness and surface
potential—and plot a two-dimensional histogram as shown in Figure 4. It is noteworthy that the
measured points which were affected by sudden topographic changes are considered as error and
excluded from the 2D histogram cloud.
Polymers 2019, 11, 235 7 of 21
values of W
attr
is an indication for a weaker van der Waals forces between the tip (gold) and BNPs
than the epoxy. Van der Waals forces which are mainly originated from dipole–dipole and dipole-
induced dipole interactions between tip and the surface, can be used as an additional information
channel about the surface composition independent from its mechanics. Thus, when measuring the
mechanical response with ImAFM, W
attr
signal can also be used to visualize material contrast.
Despite the existence of two distinguishable phases in Figure 2c, the contrast in stiffness map
(Figure 4) shows a variety of stiffness values in different distances from the protrusions. The area
related to protrusions shows two phases, an area close to the center of protrusions with higher
stiffness surrounded by an extremely low stiffness area (shown in black color). It is noteworthy that
the soft area is located at an immediate distance from nanoparticles located by potential and W
attr
maps. Therefore, the soft area relates to the particle-polymer interphase.
It is noteworthy that the bulk matrix shows variations in stiffness in the scanned area. Blocks
with high (yellow) and low (red) stiffnesses in bulk epoxy indicate the inhomogeneous nature of the
matrix.
Since sudden height changes affect the force measurements, it is crucial to investigate the roll of
topography artifacts. Detailed analysis of topography-stiffness relation for the scanned surface is
presented in Appendix D. This analysis demonstrates that except minor points with sudden changes
of height and groove-like topographic features, most of topography changes and the stiffness values
are independent from each other. Thus, by excluding the affected points of the scanned areas as error
points, the remaining ADFS curves are independent from topography artifacts.
To precisely distinguish the stiffness of particles, interphase and polymer, several areas with the
presence of nanoparticles are selected and analyzed separately (Appendix E). One of the selected
areas is shown in the topography image (Figure 3a), and the corresponding maps of surface potential
and stiffness are presented in Figure 3b,c, respectively. The surface potential distinguishes the
nanoparticles from matrix however the interfacial region is not resolved in the potential map.
Meanwhile, in the stiffness map, the existences of a soft region in the vicinity of particles is clearly
observable. In Figure 3d, single ADFS curves of selected points with different distances from the
particle are presented compared. Here, it is also shown that the stiffness (slope) of the point in the
interfacial region is drastically low. To precisely relate all the measured stiffness in the scanned area
to different phase of the nanocomposite (particle, matrix and interphase), we use the material contrast
shown in surface potential map together with the stiffness map. For this purpose, we combine two
information channels of stiffness and surface potential—and plot a two-dimensional histogram as
shown in Figure 4. It is noteworthy that the measured points which were affected by sudden
topographic changes are considered as error and excluded from the 2D histogram cloud.
Figure 3. (a) 9AFM tapping mode topography with the selected region of analysis marked with a
square box; (b) surface potential map and histogram and (c) amplitude-dependence force
spectroscopy (ADFS) stiffness map and histogram of the selected area; (d) ADFS curves related to
Figure 3.
(
a
) 9AFM tapping mode topography with the selected region of analysis marked with a
square box; (
b
) surface potential map and histogram and (
c
) amplitude-dependence force spectroscopy
(ADFS) stiffness map and histogram of the selected area; (
d
) ADFS curves related to three points shown
with circle markers on the maps with the approximation of the location of boehmite nanoparticles
(BNPs) (dark blue), epoxy matrix (green) and interphase (light blue).
Polymers 2019,11, 235 8 of 19
Polymers 2019, 11, 235 8 of 21
three points shown with circle markers on the maps with the approximation of the location of
boehmite nanoparticles (BNPs) (dark blue), epoxy matrix (green) and interphase (light blue).
Figure 4. Two-dimensional histogram of stiffness vs. surface potential of the selected area (shown in
Figure 3) of the scanned surface of EP/BNP 5. The dashed lines are used to help the eyes to distinguish
between three different regions of the histogram.
In the 2D histogram, the stiffness values are sorted based on the corresponding surface potential
values and three distinguishable regions (marked with dashed circle lines in Figure 4) are clearly
observable on the histogram cloud. In the following, each region is discussed separately:
1) Dark blue points are related to pure BNP particles as they exhibit negative surface potential
values (from −0.3 V to −0.5 V). They have large distributions of stiffness varying from 5 up to
22. The variation of stiffness values in the area related to pure BNPs can be due to following
reasons: i) Due to anisotropic nature of boehmite crystals, force curves obtained from
different orientations show different stiffness values. ii) Particles which are present in the
nanocomposites are in fact secondary particles which are formed by aggregation of several
primary particles with the size of 14 nms. Therefore, while in contact with the tip, several
intra and inter-slippage between layers can occur which helps the deformation and results
in apparent stiffness values which may be lower than the actual values.
2) Green points are related to the pure matrix, far from the particle, according to their surface
potential values. In this area, potential values are mostly positive and have a narrower
distribution (between −0.05 and 0.2 V) compared to that of BNPs. The stiffness variation in
epoxy matrix is high the values are distributed between 5 to 50. The broad distribution of
stiffness in epoxy phase is due to following reasons: i) Inhomogeneous phases in epoxy-
anhydride cured systems which has been already reported in several studies [35,36]. ii) Local
changes in stoichiometric ratio which results in changes in the chemical structure of the
network density and thus affect the mechanical properties of the epoxy [33].
3) The light blue cloud is related to the matrix in the immediate proximity of particles. This
interfacial region has a gradient potential, but no gradient in stiffness is observed. The
Figure 4.
Two-dimensional histogram of stiffness vs. surface potential of the selected area (shown in
Figure 3) of the scanned surface of EP/BNP 5. The dashed lines are used to help the eyes to distinguish
between three different regions of the histogram.
In the 2D histogram, the stiffness values are sorted based on the corresponding surface potential
values and three distinguishable regions (marked with dashed circle lines in Figure 4) are clearly
observable on the histogram cloud. In the following, each region is discussed separately:
(1)
Dark blue points are related to pure BNP particles as they exhibit negative surface potential
values (from
−
0.3 V to
−
0.5 V). They have large distributions of stiffness varying from 5 up to
22. The variation of stiffness values in the area related to pure BNPs can be due to following
reasons: (i) Due to anisotropic nature of boehmite crystals, force curves obtained from different
orientations show different stiffness values.( ii) Particles which are present in the nanocomposites
are in fact secondary particles which are formed by aggregation of several primary particles
with the size of 14 nms. Therefore, while in contact with the tip, several intra and inter-slippage
between layers can occur which helps the deformation and results in apparent stiffness values
which may be lower than the actual values.
(2)
Green points are related to the pure matrix, far from the particle, according to their surface
potential values. In this area, potential values are mostly positive and have a narrower distribution
(between
−
0.05 and 0.2 V) compared to that of BNPs. The stiffness variation in epoxy matrix
is high the values are distributed between 5 to 50. The broad distribution of stiffness in epoxy
phase is due to following reasons: i) Inhomogeneous phases in epoxy-anhydride cured systems
which has been already reported in several studies [
35
,
36
]. ii) Local changes in stoichiometric
ratio which results in changes in the chemical structure of the network density and thus affect the
mechanical properties of the epoxy [33].
(3)
The light blue cloud is related to the matrix in the immediate proximity of particles. This
interfacial region has a gradient potential, but no gradient in stiffness is observed. The potential
values start from low values in vicinity of particles (
−
0.3 V) increasing up to 0.05 V when getting
Polymers 2019,11, 235 9 of 19
close to the pure matrix. In all distances from the particle, the interphase shows stiffness values
between 1 to 5. The homogenous interphase is unlike commonly reported interphase formation in
which there was a gradient in property changes were observed [
12
]. The soft interphase appears
as a phase segregation which can be due to several effects. One is the preferential absorption
of one of epoxy components (DGEBA monomers or anhydride curing agents) on the surface of
BNPs. This hypothesis is discussed further in Section 4.
One surprising observation is the average stiffness of BNP particles which is lower than that
of epoxy phase. Contrary to the structural stiffness of boehmite calculated by simulation which
suggest a modulus value between 136 and 267 GPa with respect to plane orientation, Fankhänel and
coworkers reported an experimental average modulus of 10 GPa [
37
]. This behavior is suggested
to be due to the slippage behavior between the layers and weak interlayer bonding. Nevertheless,
knowing that the neat anhydride-cured epoxy has a Young’s modulus of approx. 3.3 GPa [
4
,
38
], it is
expected that in our nanocomposite system, particles exhibit higher stiffness values than the polymer
matrix. To understand this unexpected inversion of stiffness between filler and matrix, in the next
section, properties of the matrix phase of EP/BNP nanocomposites are investigated and compared
with neat cured-epoxy.
3.2. ImAFM Studies on Neat Epoxy and Epoxy with 15 wt % BNP
In Figure 5topography images of neat cured epoxy and epoxy/BNP nanocomposite with
15 wt %
particle content (EP/BNP15), respectively are compared. Moreover, an overview of the particle
distribution in EP/BNP15 is provided by operating scanning electron microscopy in transmission
mode (Appendix F). Although larger agglomerates were scarcely observed, the majority of surface
contains particles in form of agglomerates with the size of less than 100 nm similar to what is observed
in Figure 5b. The area shown here in Figure 5b was carefully selected so as to avoid large agglomerates.
In Figure 6, the W
attr
of neat epoxy and EP/BNP15 are compared. As previously discussed,
W
attr
data channel shows contrast between BNPs and epoxy phase independent from the mechanical
properties. Here as well, in the inset image of Figure 5, the W
attr
image of EP/BNP15 shows contrast
between BNP and polymer phase. The W
attr
of neat epoxy also contains inhomogeneities which is
due to well-known nodular structures of epoxy. Nevertheless, the surprising observation is that in
EP/BNP15, the pure matrix phase in presence of BNPs has higher values of W
attr
compared to neat
epoxy. The comparison of W
attr
histograms shown in Figure 5demonstrates 100% increase in W
attr
for
the matrix. This is a clear indication that BNPs induces physical/chemical alteration in epoxy which is
worthwhile for further investigations.
Polymers 2019, 11, 235 9 of 21
potential values start from low values in vicinity of particles (−0.3 V) increasing up to 0.05 V
when getting close to the pure matrix. In all distances from the particle, the interphase shows
stiffness values between 1 to 5. The homogenous interphase is unlike commonly reported
interphase formation in which there was a gradient in property changes were observed [12].
The soft interphase appears as a phase segregation which can be due to several effects. One
is the preferential absorption of one of epoxy components (DGEBA monomers or anhydride
curing agents) on the surface of BNPs. This hypothesis is discussed further in Section 4.
One surprising observation is the average stiffness of BNP particles which is lower than that of
epoxy phase. Contrary to the structural stiffness of boehmite calculated by simulation which suggest
a modulus value between 136 and 267 GPa with respect to plane orientation, Fankhänel and
coworkers reported an experimental average modulus of 10 GPa [37]. This behavior is suggested to
be due to the slippage behavior between the layers and weak interlayer bonding. Nevertheless,
knowing that the neat anhydride-cured epoxy has a Young’s modulus of approx. 3.3 GPa [4,38], it is
expected that in our nanocomposite system, particles exhibit higher stiffness values than the polymer
matrix. To understand this unexpected inversion of stiffness between filler and matrix, in the next
section, properties of the matrix phase of EP/BNP nanocomposites are investigated and compared
with neat cured-epoxy.
3.2. ImAFM Studies on Neat Epoxy and Epoxy with 15 wt % BNP
In Figure 5 topography images of neat cured epoxy and epoxy/BNP nanocomposite with 15 wt
% particle content (EP/BNP15), respectively are compared. Moreover, an overview of the particle
distribution in EP/BNP15 is provided by operating scanning electron microscopy in transmission
mode (Appendix F). Although larger agglomerates were scarcely observed, the majority of surface
contains particles in form of agglomerates with the size of less than 100 nm similar to what is observed
in Figure 5b. The area shown here in Figure 5b was carefully selected so as to avoid large
agglomerates.
In Figure 6, the Wattr of neat epoxy and EP/BNP15 are compared. As previously discussed, Wattr
data channel shows contrast between BNPs and epoxy phase independent from the mechanical
properties. Here as well, in the inset image of Figure 5, the Wattr image of EP/BNP15 shows contrast
between BNP and polymer phase. The Wattr of neat epoxy also contains inhomogeneities which is due
to well-known nodular structures of epoxy. Nevertheless, the surprising observation is that in
EP/BNP15, the pure matrix phase in presence of BNPs has higher values of Wattr compared to neat
epoxy. The comparison of Wattr histograms shown in Figure 5 demonstrates 100% increase in Wattr for
the matrix. This is a clear indication that BNPs induces physical/chemical alteration in epoxy which
is worthwhile for further investigations.
(a) (b)
Figure 5.
Tapping mode topography of 350 nm
×
350 nm scan area of neat epoxy (
a
) and epoxy with
15 wt % BNPs (EP/BNP15) (b).
Polymers 2019,11, 235 10 of 19
Polymers 2019, 11, 235 10 of 21
Figure 6. The comparison of the histograms of work of attractive forces Wattr in neat epoxy and
EP/BNP15. The left-side inset image is Wattr map of neat epoxy and the right-side is Wattr map of
EP/BNP15.
Figure 7 compares the stiffness of neat epoxy with epoxy matrix in EP/BNP15. The histograms
show that the stiffnesses of nanoparticles are slightly higher than of neat epoxy, as expected.
However, this relationship is inversed in EP/BNP15 in which matrix is stiffer than the particles. The
inversed situation with particles softer than the epoxy matrix has been also observed in section 3.1.
The comparison between the stiffness of matrix in EP/BNP15 and neat epoxy reveals a 100% to 400%
increase in matrix stiffness which occurs in the presence of boehmite. This is a significant change
property of epoxy.
Figure 6.
The comparison of the histograms of work of attractive forces W
attr
in neat epoxy and
EP/BNP15. The left-side inset image is W
attr
map of neat epoxy and the right-side is W
attr
map of
EP/BNP15.
Figure 7compares the stiffness of neat epoxy with epoxy matrix in EP/BNP15. The histograms
show that the stiffnesses of nanoparticles are slightly higher than of neat epoxy, as expected.
However, this relationship is inversed in EP/BNP15 in which matrix is stiffer than the particles.
The inversed situation with particles softer than the epoxy matrix has been also observed in Section 3.1.
The comparison between the stiffness of matrix in EP/BNP15 and neat epoxy reveals a 100% to 400%
increase in matrix stiffness which occurs in the presence of boehmite. This is a significant change
property of epoxy.
Polymers 2019, 11, 235 11 of 21
Figure 7. Comparison of stiffness histograms of neat epoxy and EP/BNP15. The left-side inset image
related to stiffness map of neat epoxy and the right-side to EP/BNP15.
Figure 8 compares the energy dissipation maps of neat epoxy with EP/BNP15. It is observed that
in EP/BNP15, the energy dissipation of particles is lower than of epoxy matrix. Clearly, long chains
of polymer can dissipate the energy more than BNPs with crystal structures. However, comparing
the peak values of energy dissipation histograms, it is observed that epoxy matrix in EP/BNP15 shows
an approx. 10% increase of energy dissipation compared to neat epoxy. This also indicates physical
alteration of epoxy matrix as an effect of boehmite nanoparticles.
Figure 7.
Comparison of stiffness histograms of neat epoxy and EP/BNP15. The left-side inset image
related to stiffness map of neat epoxy and the right-side to EP/BNP15.
Polymers 2019,11, 235 11 of 19
Figure 8compares the energy dissipation maps of neat epoxy with EP/BNP15. It is observed that
in EP/BNP15, the energy dissipation of particles is lower than of epoxy matrix. Clearly, long chains of
polymer can dissipate the energy more than BNPs with crystal structures. However, comparing the
peak values of energy dissipation histograms, it is observed that epoxy matrix in EP/BNP15 shows
an approx. 10% increase of energy dissipation compared to neat epoxy. This also indicates physical
alteration of epoxy matrix as an effect of boehmite nanoparticles.
Polymers 2019, 11, 235 12 of 21
Figure 8. Comparison of energy dissipation histograms in neat epoxy and EP/BNP15. The top inset
image related to energy dissipation map of neat epoxy and the bottom image to EP/BNP15.
4. Discussion
The analysis of ADFS curves in EP/BNP5 presented in Section 3.1 demonstrated the formation
of an interfacial region which has a significantly low stiffness. This region appears mostly as a block
of homogeneously soft material in the vicinity of particles rather than a region with stiffness gradient.
As we have reported elsewhere, BNPs induce changes in epoxy matrix which result in different
thermomechanical behavior and a significant decrease of crosslinking density [33]. One hypothesis is
that a disturbed crosslink density near the particles results in formation of a soft interphase. However,
it has been demonstrated in several works on epoxy systems that the glassy state modulus does not
reflect the crosslinking properties of the material, but exhibits the noncovalent bonding and inter and
intra-molecular packing [39,40]. It was demonstrated that a low crosslinking density system can
exhibit higher modulus at glassy state. Therefore, the disturbed crosslink density cannot explain the
formation of a soft interphase. Another hypothesis is the accumulation of one component of epoxy
mixture (either DGEBA or anhydride hardener or both) on the surface of particles due to preferential
absorption, covalent or noncovalent bonding with boehmite, leading to a local phase segregation.
This effect was observed in an epoxy-copper layered composite that a hard interphase was formed
due to formation of regions with different amount of amine hardener as an effect of preferential
absorption of the copper layer [12]. In our case, the local stoichiometric ratio of epoxy and hardener
can also vary in bulk matrix and thus resulting in alteration of chemical and physical properties of
the matrix. For further investigations on the chemical composition of the interphase we use high
resolution infrared-AFM in order to verify this hypothesis.
In Section 3.2, the effect of BNPs on epoxy matrix was investigated. The significant increase in
stiffness, attractive forces and energy dissipation in bulk matrix compared to neat epoxy
demonstrated that boehmite induces physical, mechanical and chemical property alteration in
Figure 8.
Comparison of energy dissipation histograms in neat epoxy and EP/BNP15. The top inset
image related to energy dissipation map of neat epoxy and the bottom image to EP/BNP15.
4. Discussion
The analysis of ADFS curves in EP/BNP5 presented in Section 3.1 demonstrated the formation of
an interfacial region which has a significantly low stiffness. This region appears mostly as a block of
homogeneously soft material in the vicinity of particles rather than a region with stiffness gradient.
As we have reported elsewhere, BNPs induce changes in epoxy matrix which result in different
thermomechanical behavior and a significant decrease of crosslinking density [
33
]. One hypothesis is
that a disturbed crosslink density near the particles results in formation of a soft interphase. However,
it has been demonstrated in several works on epoxy systems that the glassy state modulus does not
reflect the crosslinking properties of the material, but exhibits the noncovalent bonding and inter
and intra-molecular packing [
39
,
40
]. It was demonstrated that a low crosslinking density system can
exhibit higher modulus at glassy state. Therefore, the disturbed crosslink density cannot explain the
formation of a soft interphase. Another hypothesis is the accumulation of one component of epoxy
mixture (either DGEBA or anhydride hardener or both) on the surface of particles due to preferential
absorption, covalent or noncovalent bonding with boehmite, leading to a local phase segregation.
This effect was observed in an epoxy-copper layered composite that a hard interphase was formed
due to formation of regions with different amount of amine hardener as an effect of preferential
absorption of the copper layer [
12
]. In our case, the local stoichiometric ratio of epoxy and hardener
Polymers 2019,11, 235 12 of 19
can also vary in bulk matrix and thus resulting in alteration of chemical and physical properties of
the matrix. For further investigations on the chemical composition of the interphase we use high
resolution infrared-AFM in order to verify this hypothesis.
In Section 3.2, the effect of BNPs on epoxy matrix was investigated. The significant increase in
stiffness, attractive forces and energy dissipation in bulk matrix compared to neat epoxy demonstrated
that boehmite induces physical, mechanical and chemical property alteration in anhydride-cured
epoxy matrix. It was demonstrated that these property alterations in epoxy are not only limited
to the interfacial region, but the bulk epoxy is affected significantly. The changes in epoxy matrix
can affect the macroscopic properties of the composite significantly, even more so than more than
what the interphase can do. Therefore, when applying models, such as Halpin–Tsai [
41
,
42
], also the
increased modulus of the matrix must be taken into account. It is noteworthy that the stiffening effect
of nanoparticles in crosslinked matrices has already been reported. Using the ImAFM approach, they
observed an increase of stiffness in PDMS matrix in the presence of silica nanoparticles.
We were also able to show that, although BNPs themselves exhibit a lower energy dissipation
than polymer matrix (as seen in Figure 7), they induce changes in the matrix structure which result
in the increase of energy dissipation in bulk polymer. The fracture toughness and critical energy
release rate increase in epoxy-boehmite nanocomposites which was reported previously verifies this
observation [9].
5. Conclusions
In this article, we applied different AFM-based methods to visualize property contrast and
probe mechanical properties of nanoparticles, polymer matrix and the interphase in epoxy-boehmite
nanocomposite systems. Multi-frequency intermodulation AFM (ImAFM) was used as a tool to
measure forces together with scanning kelvin probe macroscopy (SKPM) as an additional information
channel to show material contrast independent from the mechanics of the surface. ImAFM maps
demonstrated stiffness contrast between polymer, particle and the interphase. SKPM shows potential
contrast between boehmite nanoparticles and epoxy matrix. Combination of mechanical and surface
potential values led to a more precise determination of the location and stiffness of interphase.
The results demonstrated the presence of a soft block of polymer near the interfacial region with
no visible stiffness gradient. The stiffness of this region is considerably lower than both particles and
polymer phase.
Moreover, the effect of boehmite on the matrix properties was investigated by focusing on
stiffness and energy dissipation during the tip-surface interaction obtained from ImAFM force curves.
A significant stiffening effect of boehmite nanoparticles on anhydride-cured DGEBA was demonstrated.
Meanwhile, the presence of boehmite resulted in increase of energy dissipation. We suggest that
boehmite cause structural alteration of matrix by inducing local changes in stoichiometric ratio of the
epoxy and hardener due to preferential surface absorption, covalent or non-covalent bonding between
boehmite particles and mixture components.
Author Contributions:
Conceptualization, H.S. and D.S.; Methodology, M.G.Z.K., D.S., D.P. and H.S.;
Software, D.S. and D.P.; Validation, M.G.Z.K., D.S., D.P. and H.S.; Formal Analysis, M.G.Z.K., D.S. and D.P.;
Investigation, M.G.Z.K. and D.S.; Resources, H.S.; Data Curation, D.S. and M.G.Z.K. and Writing-Original Draft
Preparation, M.G.Z.K.; Writing-Review & Editing, M.G.Z.K., D.S., D.P. and H.S.; Visualization, M.G.Z.K.; Project
Administration, D.S.; Funding Acquisition, H.S.
Funding:
The work was funded by Deutsche Forschungsgemeinschaft (DFG) in the frame of a research
unit FOR2021: “Acting principles of nano-scaled matrix additives for composite structures” with project
number 232311024.
Acknowledgments:
The authors gratefully acknowledge Maximilian Jux at Technical University of Braunschweig
for providing the nanocomposite samples. We further thank Mr. Nathanael Jöhrmann, TU Chemnitz, for ion
polishing. The authors especially wish to thank to Mrs. Sigrid Benemann and Dr. Vasile-Dan Hodoroaba for the
SEM measurements.
Conflicts of Interest: The authors declare no conflict of interest.
Polymers 2019,11, 235 13 of 19
Appendix A
Polymers 2019, 11, 235 14 of 21
Appendix A
Figure A1. Free oscillation (a) and oscillation in intermittent contact (b) of a cantilever with ω0 = 299.6
kHz on a polymer surface.
Appendix B
Energy dissipation in multifrequency AFM:
In conventional dynamic atomic force microscopy (AFM) a sharp tip at the end of a micro-
cantilever oscillates sinusoidally close to a surface of a sample. The phase difference between the tip
oscillation and the drive force or the tip motion far away from the surface is can be related to the
energy or power dissipated by the tip-surface interaction. Thus, the (oscillation) phase signal is often
considered as a valuable channel of information giving compositional contrast between different
surface materials.
Recently, a variety of multifrequency AFM methods have been developed giving detailed
insight into the tip-surface interaction. However, the in multifrequency AFM the tip motion is no
longer purely sinusoidal and thus the equations relating dissipated energy and phase signal in
conventional dynamic AFM do not hold for multifrequency AFM methods such as Intermodulation
AFM. Here, we show how similar relations can be derived for general multifrequency techniques
allowing for simple computation of the energy dissipated directly from the measured tip motion
spectrum. Generally, the energy Edis dissipated by the tip-surface force Fts is given by the integral
𝐸 = 𝐹
(𝑧)𝑑𝑧 (1)
Where C is the trajectory of the tip in the z coordinate. This expression can be written as a parametric
integral,
𝐸 =𝐹
(𝑡)𝑧𝑑𝑡 (2)
Where T is the period of the tip motion and the dot denotes derivation with respect to time t. We
introduce the time-reversed velocity which is defined as 𝑧−𝑡= 𝑧(−𝑡) which yields
𝐸 =𝐹
(𝑡)𝑧−(0−𝑡)𝑑𝑡 (3)
This integral can be identified as a convolution and allows by the Fourier convolution theorem
us to establish a relation between the dissipated energy Edis and the spectrum of the tip motion,
𝐸 = Ғ−𝑖𝜔𝐹
. 𝑧
∗ (0) (4)
Figure A1.
Free oscillation (
a
) and oscillation in intermittent contact (
b
) of a cantilever with
ω0= 299.6 kHz
on a polymer surface.
Appendix B
Energy dissipation in multifrequency AFM:
In conventional dynamic atomic force microscopy (AFM) a sharp tip at the end of a
micro-cantilever oscillates sinusoidally close to a surface of a sample. The phase difference between
the tip oscillation and the drive force or the tip motion far away from the surface is can be related to
the energy or power dissipated by the tip-surface interaction. Thus, the (oscillation) phase signal is
often considered as a valuable channel of information giving compositional contrast between different
surface materials.
Recently, a variety of multifrequency AFM methods have been developed giving detailed insight
into the tip-surface interaction. However, the in multifrequency AFM the tip motion is no longer
purely sinusoidal and thus the equations relating dissipated energy and phase signal in conventional
dynamic AFM do not hold for multifrequency AFM methods such as Intermodulation AFM. Here, we
show how similar relations can be derived for general multifrequency techniques allowing for simple
computation of the energy dissipated directly from the measured tip motion spectrum. Generally,
the energy Edis dissipated by the tip-surface force Fts is given by the integral
Edis =ZCFts(z)dz (A1)
where Cis the trajectory of the tip in the zcoordinate. This expression can be written as a parametric
integral,
Edis =ZT
CFts(t).
zdt (A2)
where Tis the period of the tip motion and the dot denotes derivation with respect to time t. We
introduce the time-reversed velocity which is defined as .
z−t=.
z(−t)which yields
Edis =ZT
CFts(t).
z−(0−t)dt (A3)
This integral can be identified as a convolution and allows by the Fourier convolution theorem us
to establish a relation between the dissipated energy Edis and the spectrum of the tip motion,
Edis =
Polymers 2019, 11, 235 15 of 21
Where Ғ is the Fourier operator, i is the complex unit, ω is the frequency variable, the hat denotes a
Fourier transformed quantity and the star the complex conjugate. In the last step we have used that
the Fourier transform of the time-reversed velocity can be expressed as
𝑧−(𝜔)=−𝑖𝜔𝑧
∗(𝜔) (5)
With the cantilever transfer function 𝐺
, we can determine the spectrum of the tip-surface force
𝐹
from the measured tip-motion spectrum close to the surface 𝑧 and far away from the surface 𝑧,
𝐹
=𝐺
(𝑧
−𝑧
) (6)
In case of a linear single mode cantilever, the transfer function is given by
𝐺
(𝜔)=𝜔
/𝑘
𝜔
−𝜔+𝑖𝜔𝜔
𝑄
(7)
Where 𝜔 is the angular resonance frequency, k is the spring constant and Q is the quality factor of
the cantilever. The dissipated energy Edis now becomes
𝐸 =Ғ−𝑖𝜔𝐺
|𝑧
| (0)−Ғ−𝑖𝜔𝐺
𝑧
𝑧
∗ (0) (8)
With this relation we can determine the energy dissipated by the tip-surface force during one
period of the tip motion directly from the measured free and engaged tip motion spectra.
Appendix C: Overview of Nanoparticle Distribution in EP/BNP5
Based on the contrasts observed in Figure C2, particles tend to form agglomerates in the average
size 100 nms. since the primary particle size is 14 nm, what we refer here as particles as actually
secondary particles in the form of aggregation of few 10 primary particles.
Figure C2. Tapping mode topography (top) and SKPM surface potential map (bottom) of a 10µm ×
6µm scan area of EP/BNP5.
−1{−iωˆ
Fts.ˆ
z∗}(0)(A4)
Polymers 2019,11, 235 14 of 19
where
Polymers 2019, 11, 235 15 of 21
Where Ғ is the Fourier operator, i is the complex unit, ω is the frequency variable, the hat denotes a
Fourier transformed quantity and the star the complex conjugate. In the last step we have used that
the Fourier transform of the time-reversed velocity can be expressed as
𝑧−(𝜔)=−𝑖𝜔𝑧
∗(𝜔) (5)
With the cantilever transfer function 𝐺
, we can determine the spectrum of the tip-surface force
𝐹
from the measured tip-motion spectrum close to the surface 𝑧 and far away from the surface 𝑧,
𝐹
=𝐺
(𝑧
−𝑧
) (6)
In case of a linear single mode cantilever, the transfer function is given by
𝐺
(𝜔)=𝜔
/𝑘
𝜔
−𝜔+𝑖𝜔𝜔
𝑄
(7)
Where 𝜔 is the angular resonance frequency, k is the spring constant and Q is the quality factor of
the cantilever. The dissipated energy Edis now becomes
𝐸 =Ғ−𝑖𝜔𝐺
|𝑧
| (0)−Ғ−𝑖𝜔𝐺
𝑧
𝑧
∗ (0) (8)
With this relation we can determine the energy dissipated by the tip-surface force during one
period of the tip motion directly from the measured free and engaged tip motion spectra.
Appendix C: Overview of Nanoparticle Distribution in EP/BNP5
Based on the contrasts observed in Figure C2, particles tend to form agglomerates in the average
size 100 nms. since the primary particle size is 14 nm, what we refer here as particles as actually
secondary particles in the form of aggregation of few 10 primary particles.
Figure C2. Tapping mode topography (top) and SKPM surface potential map (bottom) of a 10µm ×
6µm scan area of EP/BNP5.
is the Fourier operator, iis the complex unit,
ω
is the frequency variable, the hat denotes a
Fourier transformed quantity and the star the complex conjugate. In the last step we have used that
the Fourier transform of the time-reversed velocity can be expressed as
.
z−(ω)=−iωˆ
z∗(ω)(A5)
With the cantilever transfer function
ˆ
G
, we can determine the spectrum of the tip-surface force
ˆ
Fts
from the measured tip-motion spectrum close to the surface ˆ
zand far away from the surface ˆ
zfree,
ˆ
Fts =ˆ
G−1(ˆ
z−ˆ
z0)(A6)
In case of a linear single mode cantilever, the transfer function is given by
ˆ
G(ω)=ω2
0/k
ω2
0−ω2+iω0ω
Q
(A7)
where
ω0
is the angular resonance frequency, kis the spring constant and Qis the quality factor of the
cantilever. The dissipated energy Edis now becomes
Edis =
Polymers 2019, 11, 235 15 of 21
Where Ғ is the Fourier operator, i is the complex unit, ω is the frequency variable, the hat denotes a
Fourier transformed quantity and the star the complex conjugate. In the last step we have used that
the Fourier transform of the time-reversed velocity can be expressed as
𝑧−(𝜔)=−𝑖𝜔𝑧
∗(𝜔) (5)
With the cantilever transfer function 𝐺
, we can determine the spectrum of the tip-surface force
𝐹
from the measured tip-motion spectrum close to the surface 𝑧 and far away from the surface 𝑧,
𝐹
=𝐺
(𝑧
−𝑧
) (6)
In case of a linear single mode cantilever, the transfer function is given by
𝐺
(𝜔)=𝜔
/𝑘
𝜔
−𝜔+𝑖𝜔𝜔
𝑄
(7)
Where 𝜔 is the angular resonance frequency, k is the spring constant and Q is the quality factor of
the cantilever. The dissipated energy Edis now becomes
𝐸 =Ғ−𝑖𝜔𝐺
|𝑧
| (0)−Ғ−𝑖𝜔𝐺
𝑧
𝑧
∗ (0) (8)
With this relation we can determine the energy dissipated by the tip-surface force during one
period of the tip motion directly from the measured free and engaged tip motion spectra.
Appendix C: Overview of Nanoparticle Distribution in EP/BNP5
Based on the contrasts observed in Figure C2, particles tend to form agglomerates in the average
size 100 nms. since the primary particle size is 14 nm, what we refer here as particles as actually
secondary particles in the form of aggregation of few 10 primary particles.
Figure C2. Tapping mode topography (top) and SKPM surface potential map (bottom) of a 10µm ×
6µm scan area of EP/BNP5.
−1{−iωˆ
G|ˆ
z|2}(0)−
Polymers 2019, 11, 235 15 of 21
Where Ғ is the Fourier operator, i is the complex unit, ω is the frequency variable, the hat denotes a
Fourier transformed quantity and the star the complex conjugate. In the last step we have used that
the Fourier transform of the time-reversed velocity can be expressed as
𝑧−(𝜔)=−𝑖𝜔𝑧
∗(𝜔) (5)
With the cantilever transfer function 𝐺
, we can determine the spectrum of the tip-surface force
𝐹
from the measured tip-motion spectrum close to the surface 𝑧 and far away from the surface 𝑧,
𝐹
=𝐺
(𝑧
−𝑧
) (6)
In case of a linear single mode cantilever, the transfer function is given by
𝐺
(𝜔)=𝜔
/𝑘
𝜔
−𝜔+𝑖𝜔𝜔
𝑄
(7)
Where 𝜔 is the angular resonance frequency, k is the spring constant and Q is the quality factor of
the cantilever. The dissipated energy Edis now becomes
𝐸 =Ғ−𝑖𝜔𝐺
|𝑧
| (0)−Ғ−𝑖𝜔𝐺
𝑧
𝑧
∗ (0) (8)
With this relation we can determine the energy dissipated by the tip-surface force during one
period of the tip motion directly from the measured free and engaged tip motion spectra.
Appendix C: Overview of Nanoparticle Distribution in EP/BNP5
Based on the contrasts observed in Figure C2, particles tend to form agglomerates in the average
size 100 nms. since the primary particle size is 14 nm, what we refer here as particles as actually
secondary particles in the form of aggregation of few 10 primary particles.
Figure C2. Tapping mode topography (top) and SKPM surface potential map (bottom) of a 10µm ×
6µm scan area of EP/BNP5.
−1{−iωˆ
Gˆ
z0ˆ
z∗}(0)(A8)
With this relation we can determine the energy dissipated by the tip-surface force during one
period of the tip motion directly from the measured free and engaged tip motion spectra.
Appendix C Overview of Nanoparticle Distribution in EP/BNP5
Based on the contrasts observed in Figure A2, particles tend to form agglomerates in the average
size 100 nms. since the primary particle size is 14 nm, what we refer here as particles as actually
secondary particles in the form of aggregation of few 10 primary particles.
Polymers 2019, 11, 235 15 of 21
Where Ғ is the Fourier operator, i is the complex unit, ω is the frequency variable, the hat denotes a
Fourier transformed quantity and the star the complex conjugate. In the last step we have used that
the Fourier transform of the time-reversed velocity can be expressed as
𝑧−(𝜔)=−𝑖𝜔𝑧
∗(𝜔) (5)
With the cantilever transfer function 𝐺
, we can determine the spectrum of the tip-surface force
𝐹
from the measured tip-motion spectrum close to the surface 𝑧 and far away from the surface 𝑧,
𝐹
=𝐺
(𝑧
−𝑧
) (6)
In case of a linear single mode cantilever, the transfer function is given by
𝐺
(𝜔)=𝜔
/𝑘
𝜔
−𝜔+𝑖𝜔𝜔
𝑄
(7)
Where 𝜔 is the angular resonance frequency, k is the spring constant and Q is the quality factor of
the cantilever. The dissipated energy Edis now becomes
𝐸 =Ғ−𝑖𝜔𝐺
|𝑧
| (0)−Ғ−𝑖𝜔𝐺
𝑧
𝑧
∗ (0) (8)
With this relation we can determine the energy dissipated by the tip-surface force during one
period of the tip motion directly from the measured free and engaged tip motion spectra.
Appendix C: Overview of Nanoparticle Distribution in EP/BNP5
Based on the contrasts observed in Figure C2, particles tend to form agglomerates in the average
size 100 nms. since the primary particle size is 14 nm, what we refer here as particles as actually
secondary particles in the form of aggregation of few 10 primary particles.
Figure C2. Tapping mode topography (top) and SKPM surface potential map (bottom) of a 10µm ×
6µm scan area of EP/BNP5.
Appendix D
Analysis of Topography Artifacts in Measured Stiffness
Figure A2.
Tapping mode topography (
top
) and SKPM surface potential map (
bottom
) of a
10 µm×6µm
scan area of EP/BNP5.
Polymers 2019,11, 235 15 of 19
Appendix D
Analysis of Topography Artifacts in Measured Stiffness
Sudden height changes can cause artefacts in topography and force measurements, known
convolution effect [
43
]. Here we study the effect of topography changes on force measurements
including stiffness and attractive forces. The first derivative of the topography is calculated and plotted
over the force measurement values. Figure A3 shows the histogram of stiffness and work of attractive
forces versus the histogram of topography (first derivative). For both highly negative and positive
values of height derivative which indicates areas of with extreme up and downhills in topography,
W
attr
shows low values, however in flat areas (where the derivative is zero or close to zero) W
attr
exhibit both low and high values. It can be concluded that expect the highly extreme topography
changes, the values of W
attr
are not affected by topography changes. The same can be observed for
stiffness: Zero values of stiffness which we take as error occur all over the surface from flat to sharply
angled. Also, in flat areas the stiffness can vary from 0 to 100.
Topography features rarely cause artifacts in Potential measurement as in SKPM the tip is kept far
from the surface and does not come into contact with the surface.
Polymers 2019, 11, 235 17 of 21
Figure D3. the effect of topography changes on ImAFM force measurement. (a) histogram of ImAFM
stiffness and (b) work of attractive force Wattr versus the histogram first derivative of height obtained
from tapping mode.
Appendix E
Analysis of stiffness-potential relationship of a selected area
Figure A3.
The effect of topography changes on ImAFM force measurement. (
a
) histogram of ImAFM
stiffness and (
b
) work of attractive force W
attr
versus the histogram first derivative of height obtained
from tapping mode.
Polymers 2019,11, 235 16 of 19
Appendix E
Analysis of stiffness-potential relationship of a selected area.
Polymers 2019, 11, 235 18 of 21
(a)
(b)
(c)
(d)
(e)
(f)
Figure E4. (a) Surface potential; (b) work of attractive forces Wattr and (c) the stiffness map of a selected
area from Figure 2 scans. (d) The corresponding topography of the scanned area where the domains
of particle, interphase and pure matrix are distinguished by traces with dark blue, light blue and
green color, respectively. (e) 2D histogram of stiffness vs. potential. (f) typical ADFS curves related
to particles (dark blue), interphase (light blue) and pure matrix(green). White pixels in (b) and (c)
indicate error pixels
Figure A4.
(
a
) Surface potential; (
b
) work of attractive forces W
attr
and (
c
) the stiffness map of a selected
area from Figure 2scans. (
d
) The corresponding topography of the scanned area where the domains
of particle, interphase and pure matrix are distinguished by traces with dark blue, light blue and
green color, respectively. (
e
) 2D histogram of stiffness vs. potential. (
f
) typical ADFS curves related
to particles (dark blue), interphase (light blue) and pure matrix(green). White pixels in (
b
,
c
) indicate
error pixels.
Polymers 2019,11, 235 17 of 19
Appendix F
Polymers 2019, 11, 235 19 of 21
Appendix F
Figure F5. T-SEM micrograph of a 100 nm thick microtome cut of the EP/BNPT5.
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