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Relaxation nuclear magnetic resonance imaging (R-NMRI) of


Polymer 45 (2004) 5611–5618 www.elsevier.com/locate/polymer

Relaxation nuclear magnetic resonance imaging (R-NMRI) of PDMS/PDPS siloxane copolymer desiccation
B.R. Cherry, T.M. Alam*
Department of Organic Materials, Sandia National Laboratories, MS 0888, Albuquerque, NM 87185-0888, USA Received 12 April 2004; received in revised form 24 May 2004; accepted 26 May 2004 Available online 24 June 2004

Abstract Relaxation nuclear magnetic resonance imaging (R-NMRI) was employed to study the effects of desiccation on SiO2-?lled and un?lled polydimethylsiloxane – polydiphenylsiloxane (PDMS/PDPS) copolymers. Uniform NMR spin– spin relaxation time ?T2 ? pro?les were observed across the sample thickness indicating that the drying process is approximately uniform, and that the desiccation of the silicone copolymer is not a H2O diffusion limited process. In a P2O5 desiccation environment, signi?cant reduction of T2 was observed for the SiO2?lled and un?lled copolymer material for desiccation up to 225 days. A very small reduction in T2 was observed for the un?lled copolymer between 225 and 487 days. The increase in relative stiffness with desiccation was found to be higher for the un?lled copolymer. q 2004 Elsevier Ltd. All rights reserved.
Keywords: Siloxanes; Imaging; Desiccation

1. Introduction Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool in the monitoring of polymer aging and the elucidation of aging mechanisms at the molecular level. A wide variety of studies using 1H, 13C, and 17O NMR spectroscopy have been utilized to investigate degradation mechanisms in thermally and oxidatively-aged polymers (see Refs. [1,2] and citations within). Polymer chain mobility and segmental motion is a characteristic that can be related to material properties. NMR spectroscopy probes these polymer motions through measurement of nucleus spin-relaxation data. The spin – spin relaxation time ?T2 ? is one parameter that has been used to characterize the aging effects on various polymer materials [3,4]. Reduction of the T2 relaxation time with aging signi?es a reduction in the polymer chain mobility, such as would be observed during chain cross-linking [5 –9]. Magnetic resonance imaging (MRI) is a non-destructive means of generating spatial pictures of a wide variety of materials [10 – 12]. MRI utilizes magnetic ?eld gradients to impart a spatially dependent resonance frequency on the nuclei probed. Thereby images dependent on the location of
* Corresponding author. Tel.: ? 1-505-844-1225; fax: ?1-505-844-9624. E-mail address: tmalam@sandia.gov (T.M. Alam). 0032-3861/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2004.05.065

nuclei (most commonly 1H) are generated. MRI techniques have been developed to handle the broad resonance lines and short T2 associated with solids, facilitating the study of a variety of materials from polymers to ceramics [3,13 – 26]. Single point imaging (SPI), also known as constant time imaging, developed by Emid and Creyghton [27], is ideally suited to study materials with very short T2 relaxation times. The advantages of NMR spectroscopy and MRI techniques can be coupled to provide valuable insights into the mechanisms and processes of aging. Relaxation nuclear magnetic resonance imaging (R-NMRI) generates an image with various NMR relaxation times measured for each voxel [3,13,21 –25,28– 32]. A voxel is the smallest volume element measured during the experiment. The RNMRI experiments implemented in this study measure the 1 H spin – spin relaxation times ?T2 ? for each voxel of the image. The T2 measurements were carried out using a spin echo approach. To demonstrate the applicability of R-NMRI, the effect of desiccation on the NMR T2 relaxation (and corresponding chain mobility) for a polydimethylsiloxane/polydiphenylsiloxane (PDMS/PDPS) copolymer is presented. Continued desiccation causes a decrease in the average or bulk T2 values over a period of years, indicating the removal of water produces a stiffening of the siloxane material [33 – 36]. In this R-NMRI imaging study the possible

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presence of diffusion-limited processes leading to heterogeneous aging are explored.

2. Experimental The silica ?lled and un?lled PDMS/PDPS siloxane copolymers were obtained from Honeywell/FM&T (Kansas City, MO) and used without further preparation. The copolymers are comprised of approximately 90.6 wt% dimethyl-siloxane (DMS), 9.0 wt% diphenyl-siloxane (DPS), and 0.4 wt% methyl-vinyl-siloxane (MVS). The silica ?lled copolymer was prepared by milling a mixture of 21.6 wt% fumed silica (Cab-o-Sil M7D, Cabot, Tuscola, IL), 4.0 wt% precipitated silica (HiSil 233, PPG Industries, Pittsburgh, PA), 6.8 wt% ethoxy-endblocked siloxane processing aid (Y1587, Union Carbide, Danbury, CT) with the copolymer. After bin aging for 3 weeks at room temperature, both the ?lled and un?lled siloxane gums were cross-linked with a thermally activated peroxide-curing agent. Typical sample thickness was 2.5 mm. The siloxane copolymer samples were placed in a desiccator containing P4O10 and allowed to dry. At different desiccation times, a portion of the polymer sample (2 mm ? 2 mm ? 2.5 mm) was cut from the center of the pad so that desiccation occurred primarily in one dimension. The cut sample was placed in a standard NMR tube with the desiccationexposed surface aligned perpendicular to the applied imaging gradient ?eld, and analyzed at room temperature. The 1H R-NMRI spectra were collected on a Bruker DRX400 spectrometer using a standard 5 mm broadband probe with a single axis gradient operating at a resonant frequency of 399.9 MHz. To handle the short T2 of solid materials SPI [24,25,27,29 – 31], or constant time imaging techniques were implemented. A maximum gradient strength of 40 G cm21, 8 scan averages, a 345 ms phase encoding time, 48 gradient steps, and a 4 mm ?eld of view resulting in a calculated resolution of 83 mm along the imaging gradient. A repetition time of 4 s was used to avoid saturation effects and ensure a safe duty cycle for the NMR probe. A traditional spin echo ?lter with 31 different echo delays times was placed prior to the SPI sequence to allow measurement of T2 relaxation times for each voxel. A zstorage period of 37 ms was utilized after the spin echo and prior to the SPI sequence as previously described [13]. During the z-storage period, the gradients were switched on and allowed to stabilized, reducing the effects of eddy currents. Phase cycling of the z-storage placed the magnetization along the ^ z-axis to eliminate the effects of T1 relaxation during the storage period [13]. Bulk T2 measurements were collected with the traditional spin echo pulse sequence utilizing an 8.5 ms (p/2) pulse, 4 scans, one dummy scan, and a 1 s recycle delay. The same 31 echo delay periods implemented in the R-NMRI were used for the bulk relaxation experiments. The use of a spin echo based method for T2 measurement was implemented instead

of a Carr – Purcell– Meiboom – Gill (CPMG) [37,38] echo train in order to allow the measurement of very short T2 that could potentially be present in a rigid solid. In addition, the accuracy in ?tting the multi-exponential T2 decay of the PDMS copolymers (see below) was improved through the use of the spin echo ?lter [13]. The one-dimensional (1D) RNMRI images reported in this study represent a projection of a slice along a single axis, essentially providing an average over a 83 mm ? 2.0 mm ? 2.0 mm slice. The motional processes in multi-component siloxanes are complex [5 – 9,15,35,39], such that the segmental motion may not be de?ned by a single correlation time. It is well known that the signal intensity, I?t?; during the spin echo decay for PDMS is described by a double exponential decay [5 –7,9,39]: I?t? ? XA exp?22t=T2A ? ? ?1 2 XA ?exp?22t=T2B ? ?1?

where t is the echo spacing, XA and ?1 2 XA ? de?ne the relative fraction of component A and B, and T2A and T2B de?ne the T2 relaxation time for component A and B, respectively. The cross-linked or entangled network species, with the respectively short T2A relaxation comprises a majority of the material. The species with the long T2B spin –spin relaxation time have been assigned to the low molecular weight species separated from the network and dangling chain ends of the network that have a higher mobility [5 –7,9,39]. At short t; the echo decay has mixed Gaussian-exponential behavior indicative of inhomogeneous averaging of the dipolar couplings [39]. The very ?rst part of the decay (which is Gaussian) was ignored during our analysis with the spin echo intensity being ?t to the double exponential de?ned in Eq. (1) (Fig. 1). During the ?tting of the decay in the R-NMRI results, only the fast relaxing component ?XA ? was analyzed. The estimated errors were obtained from the standard deviations of the ?t regressions. Thermal-gravimetric (TG) data was collected using a Netzch STA-449 system. Approximately 30 mg of each sample was used. The samples were placed in an Al2O3 sample cup and allowed to equilibrate with the dry, N2 ?ow gas (approximately 10 min), with N2 ?ow rates were maintained at 100 cc total (60/40 split between balance purge and sample purge). Temperature ramps were started at ambient temperature (, 25 8C) and increased at 10 8C/min until 500 8C was reached. The ?ow from the TG was directed, via a heated transfer line (190 8C), to a Bruker Equinox FTIR equipped with a heated 10 cm gas cell (180 8C). Infrared data was collected during the entire TG ramp, at a rate of approximately one averaged sample every 14 s. Data were collected at 2 cm21 resolution across the range 4000– 700 cm21 using an MCT detector.

3. Results and discussion A 1H NMR spectrum of the PDMS/PDPS copolymer is

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Fig. 1. Representative double exponential ?t of the signal intensity I?t? from spin-echo decay experiments of PDMS/PDPS SiO2-?lled copolymer prior to desiccation. The open circles are the spin echo intensity for the total 1H signal, the solid black line is the ?t based on Eq. (1), the gray dashed-dotted line is the curve for a single exponential decay with constant T2A ; and the dotted line is for a single exponential decay with constant T2B : The inset is the short echo time region expanded to show the small Gaussian behavior.

comprised of two asymmetric resonances at d ? 0 and ? 7 ppm, assigned to the methyl and phenyl protons, respectively. Table 1 lists the T2 relaxation data obtained for the ?lled and un?lled copolymers. For each desiccation time, the bulk T2 relaxation was determined as described by Eq. (1) for the individually integrated methyl and phenyl protons, and for the total integrated spectral intensity (Fig. 1). In agreement with the previous 1H studies of these materials [5 – 7,9,39], the relaxation data is dominated by the cross-linked network species as evident by the large XA

fraction (. 0.92). In the un?lled material, the short relaxation time component fraction ?XA ? increases with desiccation, re?ecting an increase in cross-linking and/or formation of entanglements that reduce chain mobility. In the SiO2-?lled copolymer there is not a signi?cant increase in the fraction of the immobile or short relaxation time component. The 1D R-NMRI images based on T2 relaxation for the SiO2-?lled and un?lled PDMS/PDPS copolymers are shown in Fig. 2 (a) and (b), respectively. The spatial dimension of

Table 1 The 1H spin–spin relaxation ?T2 ? determined from bulk NMR measurements and the R-NMRI experiment for the SiO2-?lled and un?lled PDMS/PDPS copolymers as a function of desiccation time Time PDMS/PDPS Bulk T2 [ms]a T2A Total 0 225 days 487 days SiO2-?lled Un?lled SiO2-?lled Un?lled SiO2-?lled Un?lled 1.90 2.16 1.71 1.40 1.65 1.41 Methyl 1.83 2.08 1.64 1.33 1.58 1.33 Phenyl 2.94 3.22 2.60 2.17 2.43 2.26 T2B Total 15 16 19 29 13 31 Methyl 15 16 20 30 13 32 Phenyl 13 19 8 20 15 28 XA Total 0.95 0.92 0.96 0.96 0.96 0.96 Methyl 0.95 0.92 0.96 0.96 0.95 0.96 Phenyl 0.95 0.90 0.93 0.94 0.94 0.95 1.92 ^ 0.01 2.02 ^ 0.01 1.65 ^ 0.01 1.30 ^ 0.01 1.67 ^ 0.01 1.22 ^ 0.01 T2 R-NMRI (mean) [ms]b

a Error (T2A ^ 0:05 ms; T2B ^ 1 ms) determined from the uncertainty in linear regression. The large error in T2B is primarily due to the small fraction of this component in the copolymer. b Error in images, s?T2 ?; determined from the uncertainty in linear regression ?T2 ^ 0:05 ms?: For 30 T2 measurements present in each R-NMRI image, the p??? ? standard deviation of the mean is given by s?T2 ?= 30:

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Fig. 2. One-dimensional R-NMRI image of spin–spin relaxation ?T2 ? measured across the PDMS/PDPS copolymer for: (a) SiO2-?lled, (b) un?lled materials. The number of days the samples were exposed to desiccation is shown next to each image (0, 225, and 487 days, respectively).

the relaxation images are perpendicular to the surface directly exposed to the dry desiccation environment, such that the left and right sides of Fig. 2 correlates to the upper/ lower sample surfaces in contact with the desiccating atmosphere. The changes in T2 with desiccation are further shown in Fig. 3, which shows histogram distribution of the T2 values as a function of desiccation time. There is a reduction of the overall T2 value with desiccation for both the SiO2-?lled and un?lled siloxane copolymer through 225 days, with the un?lled material showing the largest change. For the un?lled material, there is a small but continued reduction in the measured T2 value even after 487 days. It should be noted that from previous studies, changes in T2 have been noted for desiccated samples beyond 2 years [40]. A comparison of the mean T2 measured in the R-NMRI experiments and the bulk T2A values (Table 1), indicates that the mean T2 measured by the imaging experiment are the same as those determined from bulk measurements. Accurate determination of the small fraction ?XB ? component with the long T2B values (the low molecular weight and dangling chain ends) during imaging was not possible due to the reduced signal to noise ratios at long spin echo

times of the R-NMRI data, and are not reported. The similar T2 values, in the ?lled and un?lled PDMS/PDPS copolymer before desiccation, shows that the chain and segmental dynamics are similar in these materials. The reduction in T2 (both bulk and imaging) corresponds to a decrease in the local chain mobility [8,41 – 43]. The magnitude of T2 has been shown to be inversely proportional to the reduced 21 effective dipolar coupling, T2 < kV2 l [41 – 43]. With d reduced chain and segmental motions, the averaging of the 1H – 1H dipolar coupling becomes less, leading to an increase in kV2 l: In the SiO2-?lled siloxane, the effects of d desiccation on the observed T2 values are smaller than the un?lled and become negligible after 225 days, demonstrating that the presence of SiO2 helps minimize the effects of drying. Based on the rapid diffusion of water in silicones it has been argued that desiccation should not be a diffusion limited process. Using the reported diffusion coef?cients for PDMS (1.6 – 1.8 ? 1029 m2 s21) only 7– 9 min would be required for H2O to diffuse across the 2.5 mm sample thickness [44,45]. However, the observation of desiccation effects proceeding on the timescale of years argues against a

Fig. 3. Histogram plot of the R-NMRI T2 dispersal (a) SiO2-?lled PDMS/PDPS, (b) un?lled PDMS/PDPS coplymers. The light gray curve (0 d) is for the sample prior to desiccation, the dark gray curve (225 d) was taken after 225 days of desiccation, and the black curve (487 d) is after 487 days of desiccation. Each bin is 20 ms wide.

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simple diffusive process and initially prompted these imaging studies. In addition, images obtained following 6 days of desiccation are identical to the un-desiccated material, revealing that T2 variations occur on a longer time scale. For both materials, a rather uniform T2 pro?le was observed spatially across the sample for each desiccation time. Because the R-NMRI image is a simple onedimensional picture of the material, the T2 measured for each voxel is an average value for each 2D plane perpendicular to the imaging axis (magnetic ?eld), and parallel to the exposed surface. The uniform T2 pro?les imply that the diffusion rate of water is rapid enough that water is transported from the polymer in a uniform manner, without the formation of a chain dynamic gradient within the material, and that the rate of H2O loss from the polymer is signi?cantly slower than the H2O diffusion rate within the polymer. The H2O within the siloxane copolymers is known to arise from several sources: (1) residual or adsorbed water present in the siloxane following production and processing, (2) water produced from the internal condensation of Si – OH present within the siloxane, and (3) water present on the silica-?ller surface. Dihn et al. have shown that the majority of the 1 wt% loss occurring in silica-?lled siloxanes upon desiccation is from the water and Si –OH on the silica ?ller surface [36]. The loss of interfacial water has been shown to increase the long-range hydrogen bonding interactions between the Si – OH on the silica ?ller surface and the oxygen of the polymer backbone [33 –35,43]. Additionally, water lost at the silica surface or from the polymer species will give rise to increased entanglement of the polymer chains, thereby reducing chain mobility (consistent with a reduction in T2 ). Similarly, physical cross-links formed during the internal condensation of SiOH groups also give rise to reduced chain mobility, and corresponding reduction of the observed T2 parameters. In many instances, material performance depends on the heterogeneity of this degradation/aging process at the micron scale. Experimental measurement of this heterogeneity could bene?t computational modeling of the aging process. While the 1D NMR images in Fig. 2 did not reveal classic diffusion limited heterogeneity, more information about the potential heterogeneities in the copolymers may lie in the observed width of the T2 distribution (Fig. 3). Previous MRI studies of polymeric materials have shown a variation in the T2 distribution width with aging or swelling, where the width is a measure of heterogeneity [21 – 23]. Recall, the R-NMRI T2 images in Fig. 2 are not revealing differences in 1H density, but instead are showing the local relaxation parameters of the 1H density in that image slice. The distribution of T2 obtained for both the ?lled and un?lled materials (Fig. 3) shows a very small increased distribution width with desiccation time (compare 0 days to 487 days), but these changes are on the same order as experimental error. Therefore, no de?nitive variation in the T2 distribution widths (corresponding to heterogeneities in

chain dynamics) was observed in the R-NMRI of these materials. The question of whether the smaller variations in the T2 times at longer desiccation times represent real changes in the materials, reveal heterogeneities, or are within experimental error also needs to be discussed. In Table 1, it can be seen that the values for the bulk T2 and mean R-NMRI T2 measurements, as well as trends are slightly different. From an experimental point of view, the bulk T2 measurements are expected to be more precise due to large sample volume detected, higher signal to noise, and a less complicated pulse sequence. On the other hand, the bulk T2 measurement is an average T2 value over the entire sample volume (2 mm ? 2 mm ? 2.5 mm), while the R-NMRI is the average of 30 separate T2 measurements (2 mm ? 2 mm ? 83 mm). It has been suggested that the differences between the bulk and the average R-NMRI data, as well as the differences between the 256 and 487 day data of the copolymers may be due to heterogeneities in the polymer, or experimental error. The T2 distribution from the 30 different R-NMRI slices (Fig. 3) gives a measure of the error and any heterogeneity over a 2.5 mm length scale. Larger heterogeneities (. 10 mm) are not expected to be present within these materials. These distributions (Fig. 3(a)) clearly show that there are no signi?cant differences between the 225 and 487 day T2 values in the SiO2-?lled material (within experimental data). In contrast, the distributions in Fig. 3(b), reveal that for the un?lled material there is a small distinct change between 225 and 487 days of desiccation. This type of distribution analysis reveals the weakness of relying on a single T2 value (bulk or average) to address small T2 changes occurring within the material. The estimated error given in Table 1 for the mean R-NMRI T2 values was determined from the standard deviation of mean (SDOM) for the 30 measured T2 values for each T2 -map (Fig. 2). Histograms obtained from 2D and 3D images are expected to produce a improved measure of changes in distributions. A further comparison between the ?lled and un?lled PDMS/PDPS copolymers is shown in Fig. 4. The relative stiffness, de?ned as:
21 D?T2 ? ?

T2 ?t?21 T2 ?0?21

?2?

for the two materials is plotted as a function of desiccation time ?t?: The relative stiffness, measured by Maxwell et al. [35,43] for a SiO2-?lled PDMS/PDPS copolymer, is plotted for comparison and is consistent with the present results. The increased effect on the relative stiffness during desiccation of the un?lled copolymer is apparent. In previous studies of desiccation effects on PDMS/PDPS copolymers, Maxwell and co-workers concluded that the increased stiffness in silica ?lled copolymer is a result of water removal from the surface of the silica ?ller. When this water was removed, the interaction strength (hydrogen bonding) between the silica ?ller and the polymer chain

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resulting from the silica ?ller reducing or hindering the production of new entanglements and/or cross-links of the polymer chains, or that the rate of water loss from SiO2?lled materials is reduced. Water sorption of silica-?lled PDMS is a factor of ?ve higher than the un?lled material [45], suggesting a stronger af?nity of water at the SiO2siloxane surface. For the un?lled siloxane the larger observed changes in relative stiffness suggest that desiccation favors the production of entanglements and/or crosslinks within this material. A ?nal question, how do these variations in T2 relate to changes in the physical properties of the material? In similar PDMS/PDPS copolymers, T2 has been related to the equilibrium storage modulus ?G0 ? [7,8]:
21 Fig. 4. Relative change in the stiffness, D?T2 ?; of the copolymers with desiccation as measured by the relative change in the inverse spin–spin 21 21 relaxation ?T2 ?; see Eq. (2). The ?lled symbols depict the D?T2 ? values for the silica ?lled copolymers while the open symbols are for the un?lled PDMS/PDPS copolymer. The circles represent the bulk T2 measurements and the triangles are for the mean R-NMRI measured T2 values. The ?lled squares are the relative stiffness measured for similar silica-?lled copolymers and are shown for comparison [35]. Lines are meant as guides for the eye.

1=T2 < C?G0 ?2

?3?

increases causing the segmental motion of the polymer chains to be reduced [33 – 35,43]. For the un?lled siloxane material, this interaction with the SiO2 ?ller is not a possibility and requires an additional explanation to explain the large increase in relative stiffness upon desiccation (Fig. 4). It has been argued that the difference in the relative stiffness between the un?lled and ?lled siloxane copolymers is due to non-equivalent water content in the samples, with SiO2-?lled copolymers containing more water. Dihn et al. utilized a mass spectroscopy detected temperature-programmed desorption technique to quantify the water content and concluded that the additional water present in the ?lled materials is present on the SiO2 ?ller surface [36]. To address this question for the present siloxane materials thermal-gravimetric infrared (TG-IR) data for the PDMS/ PDPS copolymers were obtained. The weight loss as a function of temperature is shown in Fig. 5. These TG-IR results show that the SiO2-?lled materials indeed contain more water (0.2 –0.4 wt%) than the un?lled siloxanes, even though a portion of the weight loss in the un?lled copolymer was due to volatilization of alkanes. The TG-IR data also reveals that decomposition of the PDMS/PDPS copolymer occurs at temperatures above 350 8C, at which point the siloxanes volatilized. Even though there is a difference in the total water content in the SiO2-?lled and un?lled copolymers, the similarity in T2 values prior to desiccation shows that the chain dynamics are similar, and do not correlate with the overall water content. The changes in T2 (relative stiffness) may be related to the different water loss during desiccation, with decreased change in relative stiffness for the SiO2-?lled material

where C is proportionality constant (material dependant). More recent reports have presented a linear relationship [43]. The proportionality constant C in Eq. (3) has not been explicitly determined for the copolymer studied; however, the general quadratic relationship between T2 and the storage modulus is expected to hold. Based on the data reported by Maxwell et al. [8] C was approximately 21 MPa22 s21 for a RTV-5370 PDMS/PDPS copolymer. If we assume a similar proportionality constant for the PDMS/PDPS copolymer, the estimated total change in equilibrium storage modulus ?DG0 ? with desiccation is 8 and 29% for the ?lled and un?lled materials, respectively. These types of relationships allow the effective imaging of physical properties such as modulus to be carried out.

4. Conclusion R-NMRI provided insights into the desiccation process occurring within PDMS/PDPS copolymers. Reduction of the spin – spin relaxation times ?T2 ? with desiccation is uniform (, 100 mm scale) across the sample thickness, indicating the hardening of the copolymer is not H2O diffusion limited within the material. The silica ?lled material appeared to be stabilized from further desiccation effects past 225 days while a continued small reduction in T2 was observed for the un?lled copolymer through 487 days of desiccation. The relative stiffness for both the ?lled and un?lled PDMS/PDPS copolymers increased with desiccation, consistent with previous studies [35,43]. However, the relative stiffness of the un?lled materials was more strongly affected. The af?nity of water to the SiO2-siloxane interface is proposed as the reason for the differences between the desiccation behavior in the SiO2-?lled and un?lled PDMS/ PDPS copolymer material.

Acknowledgements The authors would like to acknowledge Dr M.K. Alam

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Fig. 5. The percent weight loss for the SiO2-?lled (solid line) and un?lled (dashed line) PDMS/PDPS copolymer, respectively as a function of temperature determined from TG-IR. At low temperatures (below 350 8C), H2O is the dominant volatile species in the SiO2-?lled material, in the un?lled material organic alkanes are also out-gassed.

for the TG-IR data collection and analysis. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. This work is supported under the Sandia Research Foundation program.

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