Supplemental Material
The Moisture Outgassing Kinetics of a Silica
Reinforced Polydimethylsiloxane
H. N. Sharma, W. McLean II, R. S. Maxwell, L. N. Dinh*
Lawrence Livermore National Laboratory,
7000 East Ave, Livermore, California 94550, United States
Corresponding Author
*[email protected]
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S1. Polynomial fitting of isoconversional parameters
The variation in activation energy and pre-exponential factor with conversion obtained from
the isoconversional analysis can be expressed in terms of a polynomial fit (eg. 𝑝(𝑥) = 𝑐0 +
𝑐1 𝑥+. .. + 𝑐𝑛 𝑥 𝑛 , where 𝑝, 𝑐, 𝑥, and 𝑛 are the kinetic parameters, polynomial constants,
variables, and polynomial power respectively). The polynomial expression can be useful for the
kinetic parameters prediction at a known conversion level. Fig. S1 shows the polynomial fit for
the kinetic parameters obtained from the isoconversional analysis of vacuum heat-treated M9787
samples. We considered a range of 0.05-0.85 (5 % - 85 %) in this demonstration. Choice of the
polynomial order is based on the goodness of fit. Polynomial coefficients from the fit are given
in Table S1.
Table S1: Polynomial coefficients for the fit of isoconversional parameters. 9th order and 8th
order polynomial fits were used for the kinetics parameters extracted from the vacuum heattreated samples and the first peak from the 30 ppm moisture re-exposed samples, respectively.
Vacuum heat-treated
Coefficients
Moisture re-exposed
𝐸𝑎 fit
ln[𝜈𝑓(𝛼)] fit
𝐸𝑎 fit
ln[𝜈𝑓(𝛼)] fit
C0
1.1214E+02
1.7205E+01
8.0775E+01
2.0361E+01
C1
8.6663E+02
1.4252E+02
-2.8594E+01
4.7893E+00
C2
-1.2892E+04
-2.1693E+03
1.1128E+03
1.6219E+02
C3
1.1163E+05
1.8853E+04
-1.0688E+04
-2.3474E+03
C4
-5.6037E+05
-9.5471E+04
4.6304E+04
1.1309E+04
C5
1.7078E+06
2.9394E+05
-1.0849E+05
-2.7789E+04
C6
-3.1726E+06
-5.5136E+05
1.4185E+05
3.7284E+04
C7
3.4849E+06
6.1068E+05
-9.7511E+04
-2.6035E+04
C8
-2.0722E+06
-3.6554E+05
2.7494E+04
7.4171E+03
C9
5.1318E+05
9.0976E+04
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Fig. S1: Polynomial fit of activation energy (in kJ/mol) vs conversion (panel a) and ln[𝜈𝑓(𝛼)] vs
conversion (panel b) of vacuum heat-treated M9787 samples.
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Fig. S2 shows polynomial fits of the kinetic parameters from the isoconversional analysis of
low temperature peaks (< 500 K) from TPD spectra of 30 ppm moisture re-exposed samples.
Eighth order polynomial fitting was performed for the activation energy and ln[𝜈𝑓(𝛼)] vs.
𝛼 curves. Polynomial coefficients from the fit are given in Table S1.
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Fig. S2: Polynomial fit of activation energy (in kJ/mol) vs. conversion (panel a) and n[𝜈𝑓(𝛼)]
vs. conversion (panel b). Only the low temperature peaks (< 500 K) from TPD spectra of 30 ppm
moisture re-exposed samples were used for the fitting.
S2. Iterative regression analysis
S2.1 Vacuum heat-treated samples
Fig. S3: Peak deconvolution of TPD signals at 𝛽= 0.002 K/s from vacuum heat-treated
samples of M9897 using the iterative regression analysis. Second order reaction was assumed for
all the peaks.
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Fig. S4: Peak deconvolution of TPD signals at 𝛽= 0.025 K/s from vacuum heat-treated
samples of M9897 using the iterative regression analysis. Second order reaction was assumed for
all the peaks.
Fig. S5: Peak deconvolution of TPD signals at 𝛽= 0.05 K/s from vacuum heat-treated samples
of M9897 using the iterative regression analysis. Second order reaction was assumed for all the
peaks.
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Table S2: Average activation energy 𝐸𝑎 (kJ/mol) and average ln(𝜐) from the iterative
regression analysis of vacuum heat-treated samples. Second order reaction (𝑛 = 2) was assumed
for all the peaks.
Peaks
Average 𝐸𝑎 (kJ/mol)
Average ln(𝜐)
Average Area (%)
Peak I
132.6
21.2
37.7
Peak II
161.7
24.1
33.0
Peak III
201.3
28.8
15.4
Peak IV
238.5
30.9
13.9
S2.2 samples re-exposed to 30 ppm of moisture
Fig. S6: Peak deconvolution of TPD signals at 𝛽= 0.0018 K/s from 30 ppm moisture reexposed M9787 samples using the iterative regression analysis. First order reaction was assumed
for the first two peaks and second order reaction was assumed for the remaining peaks.
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Fig. S7: Peak deconvolution of TPD signals at 𝛽= 0.0075 K/s from 30 ppm moisture reexposed M9787 samples using the iterative regression analysis. First order reaction was assumed
for the first two peaks and second order reaction was assumed for the remaining peaks.
Fig. S8: Peak deconvolution of TPD signals at 𝛽= 0.025 K/s from 30 ppm moisture re-exposed
M9787 samples using the iterative regression analysis. First order reaction was assumed for the
first two peaks and second order reaction was assumed for the remaining peaks.
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Table S3: average activation energy 𝐸𝑎 (kJ/mol) and average ln(𝜐) from the iterative
regression analysis of 30 ppm moisture re-exposed M9787 samples. First order reaction (𝑛 = 1)
was assumed for the first two peaks and second order reaction (𝑛 = 2) was assumed for the
remaining peaks.
Peaks
Average 𝐸𝑎 (kJ/mol)
Average ln(𝜐)
Average Area (%)
Peak I
54.2
10.9
5.4
Peak II
67.9
12.8
1.8
Peak III
131.3
20.5
45.7
Peak IV
176.5
26.4
34.4
Peak V
216.6
31.2
12.6
S2.3 As-received samples
Figs. S9 and S10 show the results of iterative regression analysis of the TPD experiment
signals from M9787 at the heating rates of 0.025 and 0.125 K/s, respectively.
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Fig. S9: Peak deconvolution of TPD signals at 𝛽= 0.025 K/s from as-received samples of M9897
using iterative regression analysis. First order reaction (𝑛 = 1) was assumed for the first two
peaks and second order reaction (𝑛 = 2) was assumed for the remaining peaks. Inset bar plots
show the activation energies (left) and pre-exponential factors (right) for each of the peaks
considered for the fitting.
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Fig. S10: Peak deconvolution of TPD signals at 𝛽= 0.125 K/s from as-received samples of
M9897 using the iterative regression analysis. First order reaction was assumed for the first two
peaks and second order reaction was assumed for the remaining peaks. Inset bar plots show
activation energies (left) and pre-exponential factors (right) for each of the peaks considered for
fitting.
S3. DFT calculations
Optimized structural parameters from the DFT calculations are given in the Table S4. The
DFT computed parameters are in good agreement with the available parameters in the literature.
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Table S4: DFT computed and experimental parameters for 𝛼-quartz bulk.
Parameters
This Work
Experiment1
Computational 2-3
a(Å)
5.03
4.913
5.04, 5.052
c(Å)
5.51
5.405
5.52, 5.547
∠(𝑆𝑖 − 𝑂 − 𝑆𝑖)(°)
144.2
143.7
147.4,147.9
r(Si-O) (Å)
Type equation here.(
162.6
161.4
163.3, 162.5-162.8
Type equation here.)
The adsorption energy, 𝐸𝑎𝑑𝑠 of an atom or a molecule on the slab is defined as.
𝐸𝑎𝑑𝑠 = −(𝐸𝑠𝑙𝑎𝑏+𝑎𝑑𝑠𝑜𝑟𝑏𝑎𝑡𝑒 − 𝐸𝑠𝑙𝑎𝑏 − 𝐸𝑎𝑑𝑠𝑜𝑟𝑏𝑎𝑡𝑒 )
(S1)
where 𝐸𝑠𝑙𝑎𝑏+𝑎𝑑𝑠𝑜𝑟𝑏𝑎𝑡𝑒 , 𝐸𝑠𝑙𝑎𝑏 , and 𝐸𝑎𝑑𝑠𝑜𝑟𝑏𝑎𝑡𝑒 represent the energy of the slab with the
atom/molecule, energy of the clean slab, and the energy of an isolated atom/molecule,
respectively. The 𝐸𝑎𝑑𝑠 values are positive numbers, where the increase in positive number
indicates the strong binding to the surface. In the case of H2O adsorption on the hydroxylated
surface, the adsorption energy is computed using:
𝐸𝑎𝑑𝑠 = 𝑁
1
𝐻2𝑂
[𝐸𝑠𝑙𝑎𝑏+𝐻2 𝑂 − 𝐸𝑠𝑙𝑎𝑏 − 𝑁𝐻2 𝑂 𝐸𝐻2 𝑂 ]
(S2)
where 𝐸𝑠𝑙𝑎𝑏+𝐻2 𝑂 , 𝐸𝑠𝑙𝑎𝑏 , 𝐸𝐻2 𝑂 represent the hydrated slab, hydroxylated slab, and the energy of
water molecule, respectively.
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For each minimum energy path (MEP) from the CI-NEB,4 we calculated the activation energy
barrier, 𝐸𝑎𝑐𝑡 as:
(S3)
𝐸𝑎𝑐𝑡 = 𝐸𝑇𝑆 − 𝐸𝐼𝑆
where 𝐸𝑇𝑆 and 𝐸𝐼𝑆
represent the energy of the transition state, and energy of initial state
(reactants) respectively.
Surface energy of the (101) 𝛼-SiO2 slab was calculated as.
1
𝐸𝑠𝑢𝑟𝑓 = 2𝐴 [𝐸𝑠𝑙𝑎𝑏 − 𝑁𝑏𝑢𝑙𝑘 𝐸𝑏𝑢𝑙𝑘 ]
(S4)
where 𝐴, 𝐸𝑠𝑙𝑎𝑏 , 𝑁𝑏𝑢𝑙𝑘 , and 𝐸𝑏𝑢𝑙𝑘 represent the slab surface area, energy of the slab, energy of the
bulk crystal, and the number of bulk units in the slab, respectively.
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L. Levien, C. T. Prewitt, D. J. Weidner, Am. Mineral 65, 920 (1980).
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A. V. Bandura, J. D. Kubicki, J. O. Sofo, J. Phys. Chem. C 115, 5756 (2011).
3.
T. P. M. Goumans, A. Wander, W. A. Brown, C. R. A. Catlow, Phys. Chem. Chem. Phys.
9, 2146 (2007).
4.
G. Henkelman, B. P. Uberuaga, H. Jonsson, J. Chem. Phys. 113, 9901 (2000).
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