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Physical Aging and Glass Transition of Hairy Nanoparticle Assemblies
H. Koerner1, E. Opsitnick1, C.A. Grabowski1, L. F. Drummy1, M-S. Hsiao1, J. Che1, M. Pike1, V. Person2, M.R.
Bockstaller3, J. S. Meth4, R. A. Vaia1
1
Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright Patterson Air Force
Base, Ohio 45433-7750
2
Dept. of Chemistry, Clark Atlanta University, SW Atlanta, GA 30314,
3
Dept. of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213,
4
DuPont Central Research & Development, E.I. DuPont de Nemours & Co., Inc., Wilmington, Delaware
19803
Table of Contents:
S1. Morphology
2
S2. Thermal Properties: Tg
11
S3. Thermal Properties: Physical Aging
11
S4. Very long time aging of 50 vol% PS-aHNP
13
S5. References
14
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S1. Morphology
Figure S1.1 illustrates the general difference between nanoparticle arrangement in blended
nanocomposites and aHNPs. In general for a random dispersion of spheres such as in a blended
nanocomposite,S1 the structural arrangements of nanoparticles at volume fractions below 0.3 ideally
corresponds to a disordered liquid, while volume fractions between 0.3 and 0.46 may be considered an
ordered liquid based on an increase in next neighbor spatial correlation. Above 0.46 to 0.49 the system
may be described as random closed packed and above 0.5 as a disordered crystalline lattice. For
reference, we define Lideal as the center-center distance between lattice points in a hexagonal array for a
given lattice density (LIdeal = l+2r0=2r0-1/3). A hexagonal array of spheres has 12 equivalent near
neighbors in the first coordination sphere and yields the maximum packing efficiency. Recall that a
hexagonal lattice (mathematical construct) is separate from the basis (physical units that occupy a
lattice point). The volume fraction of spheres can be less than the maximum packing fraction of the
lattice if the sphere’s radius is less than half the distance along the close packed lattice direction (hcp:
<100>; fcc: <110>).
Figure S1.1: Schematic of dispersion state of HNPs (left) and blends (right) with estimates to
q(1)/q(ideal).
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Overall, the scattering intensity at low and intermediate loadings for blend-PS-X (Fig 2E) is governed
mostly by the form factor of the silica. The scattering peak intensities at q> 0.04 A-1 scale linearly with
total silica concentration, and are dominated by the Bessel oscillations of a spherical form factor with a
relatively narrow size distribution. The structure factor (S(q), Fig 2G) contains oscillations that only shift
marginally with silica loading and are in the range of the nanoparticle diameter (q ~ 2/d). These arise
from a fraction of silica whose surfaces are in contact. As denoted in Figure S1, a fraction of silica with
such close spacing is characteristic of a random lattice arrangement and consistent with a single phase
blend. This single phase is reflected in the finite value of S(0) (Fig 2), and the almost non-existent
intensity increase at ultralow q (USAX Fig. S1.2). These scattering features have been extensively
discussed in Reference S2, and are consistent with a random arrangement of spheres with a minor
fraction of small aggregates, clusters and chains of silica particles.S2 This can be visualized in the low
magnification, large TEM in Fig. S1.3. As the number density of silica increases, the average particleparticle spacing within the random dispersion decreases. The scattering feature at S(q1) however
increases since the relative population of particles in close contact increases, consistent a denser
random lattice with a constant size spherical basis. In otherwords, the random arrangement converges
to a distorted (disordered) lattice as noted above. Therefore for a single phase, L/L ideal, where L is the
distance between lattice points (or center of silica), approaches 1 as the volume fraction approaches the
maximum packing volume fraction. Concomitantly, the intensity of S(q1) is near 1 implying that the long
range near-neighbor correlations of this fraction of the population are weak.
In contrast, the scattering curves of aHNP-PS-X systems are mainly governed by interference between
the dispersed silica (Fig 2 F, H). The intensity and position (q) of these features (Table S1, Fig S1.1)
increase with increased loading approximately as the cube root of the volume fraction of PS and
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consistent with the simple packing arguments. Fig. S1.1A shows that the ratio of L/LIdeal for aHNPs is
close to unity over a broad volume fraction range. This implies the emergence of large domains of silica
with a narrow distribution of particle separation. Figure 2B & D and Fig. S1.3 D-F show HAAD FST
micrographs of HNP-PS-1 and HNP-PS-18 revealing this uniform distribution.
These images are
representative of the entire HNP-Y-X series, and are comparable to prior reports of HNP morphology
using similar preparation.S3 Note that even though the center-center distance corresponds to lattice
packing concepts the long range correlations of the silica basis is less than what is considered the
threshold for crystalline order. The Hansen-Verlet criterionS3 classifies a material with S(q1) values
greater than 2.85 as crystalline, whereas S(q1) < 2.85 corresponds to disordered, liquid-like
morphologies. This apparent contradiction – HNP core spacing corresponding to lattice but local order
between silica being disordered, liquid like - reflects the hybrid nature of the HNP. The silica core
defines the initial size disparity of the HNP; however the synthesis of the polymeric canopy introduces a
second size disparity.
During film formation or annealing, the polymeric canopy is “soft.”
This
malleability appears to accommodate these disparities resulting in a semblance of a lattice, but with
HNPs of different core-canopy ratio occupying different sites to ensure space filling. This can be seen in
the TEM micrographs (Fig 2B,D, Fig S1.3 D-F) as well as in prior reports, such as Reference S3. As silica
volume fraction increases, ordering increases as S(q1) approaches 2.85 (Fig. S1.1B), but then decreases
above intermediate loading. This is likely due to the broad size distribution of the silica cores and
inadequate relative volume of grafted polymer at these high silica fractions to accommodate space
filling constraints.
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Table S1: Morphological characteristics of aHNPs and blended nanocomposites.
aHNP
r0=8nm ±35%
aHNP-PS-1
L,
nm
>35#
Lideal
nm
34.5
aHNP-PS-4
22.4
21.7
19.5
aHNP-PS-6
aHNP-PS-18
aHNP-PS-50
12.1
13.3
10.1
10.3
aHNP-PS-62‡
nd
aHNP-PS-57‡
nd
aHNP-PS-54‡
nd
Blend
ro=13nm ±10%

blend-PS-1
8.8
54.5
9
28
9.1
22
blend-PS-40
11.8
16
blend-PS-50
12
15
blend-PS-7p5 
blend-PS-15
#

=outside measuring window. Values for blends are from a minor fraction of clusters only.
2.0
1.0
B
A
S(q=q1)
L / Lideal
0.8
0.6
0.4
0.2
1.5
1.0
0
10
20
30
40
50
0
20
40
, %

Figure S1.1: A) center-center distance (L) from structure factor peak q(1) normalized by ideal effective particle
center-center distance (LIdeal) for HNP (spheres) and blended nanocomposites (circles). B) Structure factor intensity
at first peak S(q(1)) for HNP (spheres) and blended nanocomposites (circles). According to Hansen-Verlet
criterion,S3 these are all generally disordered with aHNP-PS-18 exhibiting the highest level of long-range
correlations.
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aHNP-PS-4
aHNP-PS-6
aHNP-PS-18
aHNP-PS-50
HS30
A
105
103
102
101
PNC-PS-7p5
PNC-PS-15
PNC-PS-40
HS30
105
intensity, a.u.
intensity, a.u.
104
B
106
104
103
102
101
10-3
10-2
q, A
10-1
10-3
-1
10-2
q, A
10-1
-1
Figure S1.2: Ultra small angle X-ray scattering on aHNP and blended nanocomposite samples. Ultra small angle
scattering data was collected on representative samples to determine larger scale agglomerates in the system that
would contribute to scattering at angles not captured in conventional SAX experiments. A) aHNP-PS-X, B) blendPS-X. For comparison, HS30 (Sigma Aldrich, average particle size 26nm) shows the scattering curve of a 17 v% silica
nanoparticle solution in isopropanol with no aggregate formation. The scattering of aHNP-PS system shows a flat
plateau at low q up to 750nm in real space, evidence that there are no agglomerates up to 1micron in this system.
Traditional blended nanocomposites show weak features and q-dependent scattering at very low q consistent with
the presence of small clusters.
A
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B
C
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D
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E
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F
Figure S1.3: Transmission Electron Microscopy (TEM) comparing blended nanocomposites to aHNPs ( A) blend-PS1; B) blend-PS-7.5; C) blend-PS-15; D) aHNP-PS-1; E) aHNP-PS-18; F) aHNP-PS-50). Note that the Bright Field
images of blends are of two-dimensional projections of the three-dimensional arrangement of silica (ro=13 nm)
within a 90 nm thick microtome section, and thus volume fractions may appear higher than from a true
monolayer. Images of aHNPs (ro=8 nm) were taken in High-Angle Annular Dark-Field Scanning Transmission mode
on nanoparticle monolayers (see Experimental).
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S2. Thermal Properties: Tg
Tg, oC
105
100
95
0.1
1
10
/Rg
Figure S2.1: Tg as function of separation between particle surfaces, l, over Rg for blends (gray circles) and aHNP
(black spheres) systems. Although trends at l/Rg >1 are visible, more data for l/Rg <1 are necessary for further
interpretation.
S3. Thermal Properties: Physical aging
The structural relaxation rate is typically described via the Kohlrausch-Williams-Watts equation Eq
S1S4,S5.
 (t a )  exp[ (t a /  )  ]
(Eq S1)
Where (t) is the normalized relaxation function,  is the characteristic structural relaxation time and 
is a measure of the distribution of relaxation times. Values of  close to 1 indicate a homogeneous
system with narrow relaxation time distribution, while values of  close to 0 indicate a system with very
broad distribution of relaxation times. Enthalpy relaxation values as a function of aging time are
obtained from DSC experiments and are analyzed using the Cowie-Ferguson equation Eq S2. H data is
obtained by integral difference between unaged and aged sample trace S6:
H (Ta , t a )  H  [1  (t a )]
Koerner et al Aging aHNPs, 2015
(Eq S2)
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where H is the maximum enthalpic relaxation reached at infinite aging time.
Figure S3.1 provides additional calorimetric traces of PS aHNP and blended nanocomposites at
intermediate silica loading. Fits of EqS2 to enthalpy recovery for a series of aging times ta at a given
aging temperature Ta (Figure S3.2) can be used to obtain the characteristic structural relaxation time 
(figure 5) and the distribution parameter  (Figure S3.3). Finally, the estimated H is summarized in
Figure S3.4.
aHNP-PS-18
PNC-PS-15
1.5
1.5
c (J/gK)
1.8
c (J/gK)
1.8
1
p
p
1
0.5
0.5
0
80
100
120
o
140
0
80
100
120
140
Temperature (oC)
Temperature ( C)
3
3
2
2
Ha, J/g
Ha, J/g
Figure S3.1. Comparison of enthalpy relaxation experiment between aHNP-PS-18 (left) and blend-PS-15
system (right) at intermediate silica volume fractions.
1
1
0
0
2
3
4
log ta, s
5
2
3
4
5
log ta, s
Figure S3.2. Enthalpic relaxation H with annealing time ta for left: aHNP-PS-6 (purple spheres) and
blend-PS-7.5 (grey circles) and right: aHNP-PS-18 (red spheres) and blend-PS-18 (black circles); and
associated fits (dashed line) to the KWW7 model following the Cowie methodS6.
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4
H, J/g
3
2
1
0
-35
-30
-25
-20
-15
-10
-5
0
o
Ta-Tg, C
Figure S3.3. Equilibrium enthalpy H∞ is obtained from fitting KWW to the Ha data from physical aging studies
of aHNPs, blends and neat polystyrene samples (symbols are listed in Table 1 and Experimental).
S4. Long time aging of 50 vol% PS-aHNP
cp, J/g K
0.6
0.4
0.2
0.0
90
100
110
120
130
140
Temperature, oC
Figure S4.1 DSC trace of physically aged aHNP-PS-50. A Tg step is only visible after 2 weeks of physical aging at TaTg=-20oC.
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S5. References
S1.
S2.
S3.
S4.
S5.
S6.
S7.
Percus, J. K.; Yevick, G. J. J. Phys. Rev. 1958, 110, 1.
Meth, J. S.; Zane, S. G.; Chi, C. Z.; Londono, J. D.; Wood, B. A.; Cotts, P.; Keating, M.; Guise, W.;
Weigand, S. Macromolecules 2011, 44, (20), 8301-8313.
Goel, V.; Pietrasik, J.; Dong, H.; Sharma, J.; Matyjaszewski, K.; Krishnamoorti, R. Macromolecules
2011, 44, 8129-8135.
Kohlrausch, F. Annalen der Physik und Chemie 1866, 128, 1.
Williams, G.; Watts, D. C. Trans. Faraday Soc. 1970, 66, 80.
Cowie, J. M. G.; Ferguson, R. Polymer 1993, 34, 2135.
Williams, G.; Watts, D. C. Transactions of the Faraday Society 1970, 66, (0), 80-85.
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