Nonideality in Silicone Network Formation via Solvent Swelling and

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Nonideality in Silicone Network Formation via Solvent Swelling and 1 H Double-Quantum NMR April M. Sawvel,*,† Sarah C. Chinn,† Matthew Gee,† Colin K. Loeb,† Amitesh Maiti,† Harris E. Mason,‡ Robert S. Maxwell,† and James P. Lewicki*,† Physical and Life Sciences Directorate, Materials Science Division, and ‡Physical and Life Sciences Directorate, Atmospheric, Earth, and Energy Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States

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†

S Supporting Information *

ABSTRACT: The versatile cross-linking chemistry of poly(dimethylsiloxane) (PDMS)-based materials affords a large research space in which polymers with widely varying elastomeric properties may be synthesized. Parameters such as chain length, cross-link density, cross-link functionality, filler content, and chain chemistry can all be modified to produce materials with specific physical and mechanical properties. Commercial polysiloxane-based, “silicone” elastomers are generally intractable, which makes the precise characterization of their networks problematic. We report here the application of equilibrium solvent uptake analysis and 1H doublequantum nuclear magnetic resonance (1H DQ NMR) spectroscopy to determine the network topology of end-linked PDMS networks with nonideal network topology. Despite their structural complexity, we can quantify both the classical and nonclassical contributions to network structure using 1H DQ NMR which are in reasonable agreement with solvent uptake data. These findings serve as the foundation for future investigations of even more complex commercial silicones using 1H DQ NMR.

■

INTRODUCTION

homonuclear dipolar coupling interactions (RDC or Dres) that persist as a result of incomplete motional averaging due to the topological constraints that exist in polymeric materials. The advantage of the 1H DQ NMR technique is the collection of two different sets of data: the DQ buildup intensity and the decaying reference intensity as a function of DQ evolution time. While the DQ buildup curve contains structural information based solely on the elastically active polymer network chains (distribution of RDCs), the reference decay curve contains information from the coupled network chains as well as signal from uncoupled components of the network such as network defects and dangling chain ends. Careful processing of these independent sets of data makes it possible not only to quantify the intensity of residual dipolar couplings (Dres) but also to determine the distribution of Dres within an inhomogeneous sample along with the relative standard deviation of the distribution (σrel) and the network defect fraction (ωdef).7,8,14,15 When analyzed in both the dry and swollen state, 1H DQ NMR yields a complete description of both the elastic and nonelastic contributions to network microstructure which provides additional insight into the connection between network structure and mechanical properties. Quantification of network defects via the long-time relaxation decay of the reference signal in the swollen state allows for the precise

Polysiloxane (silicone)-based elastomers are widely utilized in several commercial applications,1−3 and understanding their structure−property relationships is key to enabling the design of materials with tailored physical properties as well as improving the understanding of the mechanisms of aging and degradation. While the base chemical reactions that occur during network formation in typical end-linked polysiloxane networks are relatively simple, the overall complexity of the network formation process is increased by the wide range of macromonomer chain lengths, chain chemistries typically utilized, the motional dynamics of the macromonomers, the potential for competing side reactions, and rearrangement processes. This ensemble of chemical and physical complexities present during network formation can lead to significantly nonideal networks when compared to theoretical predictions of network structure based on a knowledge of the starting materials. Understanding and quantifying these nonidealities are key elements to not only understanding the role of network structure on bulk mechanical properties but also understanding how these nonidealities may influence time-dependent phenomena such as material aging in response to a range of environmental stressors. While solvent swelling techniques have long been used to compare theoretical cross-link densities and nonidealities,4,5 1 H DQ NMR has also recently been used extensively to characterize both model silicone networks with ideal structure and commercial formulations with far more complicated network structures.6−13 DQ NMR measures the residual 1H © XXXX American Chemical Society

Received: September 7, 2018 Revised: December 17, 2018

A

DOI: 10.1021/acs.macromol.8b01939 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules Table 1. Results of Prepolymer Characterization by GPC sample

Mn(GPC) (kDa)

σ

Mw(GPC) (kDa)

σ

PDI(GPC) (Mw/Mn)

σ

vPDMS-8 kDa vPDMS-32 kDa vPDMS-124 kDa

8.10 32.3 124

0.40 1.7 1.2

10.0 39.5 157

0.2 1.3 2.6

1.24 1.23 1.27

0.04 0.01 0.01

methyl and Si−H groups in a solution 1H NMR spectrum. Networks were formed with a 2-fold stoichiometric excess of Si−H groups (cross-linker) to terminal vinyl groups on the prepolymers to ensure complete network formation. Complete network formation was verified by observing the absence of residual vinyl groups in a 1H NMR spectrum of cross-linked samples swollen in deuterated toluene (Supporting Information, Figure S1a). Unreacted silane and vinyl groups are expected to be highly mobile in the equilibrium swollen state and, therefore, readily identifiable by 1H solution state NMR. To verify that we were not missing any hidden unreacted species that may be bound within the structural network, we also performed 1H MAS on a sample that showed a small amount of unreacted silane and vinyl groups by 1H solution NMR. 1H MAS NMR (Figure S1b) does not identify any unreacted groups that are not already clearly identified by 1 H solution NMR. By contrast, the solution NMR data reported here more clearly identify unreacted groups as a result of the higher signal sensitivity afforded by the cryoprobe used for these experiments (experimental details below). Neat samples were prepared by weighing the appropriate amount of vinyl-terminated PDMS and cross-linker into a plastic cup and mixing in a high-speed centrifugal mixer (FlackTek, Landrum, SC) at 2500 rpm for 1 min. Polymer residue was scraped from the side of the cup before adding the appropriate volume of catalyst (diluted in 400% v/v toluene) to the cup and mixing for a second time at 2500 rpm for 2 min. The sample was then left on the benchtop to cure at room temperature (23 °C) overnight. Samples made with the largest prepolymer (124 kDa) were degassed prior to room temperature curing to prevent air bubble formation. Cured samples were removed from the plastic cup and postcured at 150 °C for 12 h. Dilute networks were mixed in a similar manner as the neat networks with the addition of 400 wt % (with respect to the mass of polymer used) toluene added to the cup to ensure thorough mixing of all components. Dilute samples were transferred to glass jars and tightly sealed before curing at room temperature (23 °C) until a rigid network had formed, typically 2 days to 1 week. Once network formation was complete, toluene was slowly evaporated from the sample over several days. Finally, the contracted networks were removed from the glass jar, and all traces of residual solvent were removed under vacuum at 40 °C for 12 h. Dried samples were postcured at 150 °C for 12 h. The dilute networks have “Tol” added to the sample name to indicate that these networks were formed in the presence of toluene. Prepolymer molecular weights were determined using gel permeation chromatography (GPC) with HPLC grade 2-butanone (methyl ethyl ketone, MEK) as the mobile phase. Polymer separation was performed using an HPLC from Thermo Fisher Scientific (Waltham, MA), while detection and size determination were achieved using a Dawn Helios II multiangle dynamic light scattering (MALS) detector coupled with an OptiLab T-rEX RI detector, both from Wyatt Technologies (Santa Barbara, CA). Each sample was measured in triplicate. The average values and standard deviations for Mn, Mw, and the polydispersity index (PDI) are reported in Table 1. Mechanical Measurements. Mechanical analysis of the elastomers was conducted using a TA Instruments ARES-LS2 rheometer (New Castle, DE). A dynamic strain sweep was performed from 0.01 to 1% at 23 °C using a cylindrical torsion test geometry. Cylindrical samples were made by mixing the polymer, cross-linker, and catalyst as described above and casting the mixture into a 1 mL plastic syringe to cure at room temperature. Once cured, the plastic syringe was demolded, and the samples were postcured at 150 °C overnight. At least three separate samples were measured for each PDMS chain length. Storage modulus values (G′) are reported from the highest

determination of the network contribution of dipolar couplings, which are directly proportional to the apparent cross-link density determined by solvent uptake.14,15 While this quantitative DQ NMR technique has been most successfully applied to end-linked PDMS networks specifically formulated to have an idealized structure, application to more complex networks has been hampered by an incomplete understanding of the contributions of nonideality to the DQ results. For example, previous investigations on commercial materials have been limited to establishing correlations between average dipolar coupling values or dipolar coupling distributions to accelerated thermal and irradiative aging as well as mechanical stress.10−12,16−20 While trends relating changes in dipolar coupling distributions as a function of material stress and aging have shed light on some mechanistic details of material degradation, there is still a need to understand these mechanisms further. The application of recently developed quantitative 1H DQ analysis techniques to these complex commercial elastomers would help achieve that goal. Here we report the application of quantitative 1H DQ NMR analysis to a set of simplified silicone networks that were formed under conditions analogous to room temperature cured (RTV) commercial platinum-mediated vinylsilane addition-based formulations.2 This process includes the use of excess cross-linker to drive network formation to completion, exposure to ambient air and moisture during cross-linking, and the implementation of an elevated-temperature postcure. Previous applications of 1H DQ NMR to characterize end-linked PDMS networks were focused on elastomers formulated with a stoichiometric amount of crosslinker and without an elevated temperature postcuring step to yield networks with as close to an ideal structure as possible to validate the development of 1H DQ data processing techniques.8,9,14,15,21−23 While the conditions employed in this study yield nonideal network structures, the resulting structures more closely resemble the complex network topology that exists in commercial materials. The set of samples examined here are used to bridge the gap that exists from the application of quantitative 1H DQ NMR techniques from idealized samples to those that more accurately represent the complexity of silicones that are used in industry. We find that DQ NMR can be used to determine both the classical and nonclassical contributions to the network structure in nonideal networks as well as characterize the defect fraction of the material. This investigation is paramount to ultimately understanding how to use this technique to better understand the aging and degradation mechanisms of commercial silicones.

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EXPERIMENTAL SECTION

Network Preparation and Characterization. Simplified silicone networks were prepared by cross-linking vinyl-terminated terminated PDMS chains of three different lengths. Prepolymers were cross-linked with tetrakis(dimethylsiloxy)silane, a tetrafunctional cross-linker, and a platinum catalyst. All starting materials were purchased form Gelest (Morrisville, PA). The functionality of the cross-linker was determined to be 3.6 by comparing the ratio of B


Article

Macromolecules strain measured (1%) as the average and standard deviation of replicate measurements. It was not possible to make cylindrical samples of the toluene-diluted networks due to the large volume contraction of the samples upon evaporation of the solvent. As a result, mechanical measurements were only performed on the networks made without toluene. Equilibrium Solvent Uptake Experiments. Small, cubic samples were cut from the larger bulk sample and swollen in toluene (molar volume Vs = 106.2 cm3/mol, density ρtol = 0.867 g/cm3) at room temperature (23 °C) for 48 h. Samples were weighed periodically during that time to monitor progress to equilibrium. All samples were weighed before swelling (mi), at swelling equilibrium (msw), and after careful removal of the solvent (mf) using a microbalance (Mettler Toledo, Columbus, OH). Masses taken at equilibrium swelling were performed by removing the sample from the solvent and gently blotting off the excess toluene on the surface of the sample before recording msw. Toluene was slowly removed over 2 days, with the final evaporation step occurring under vacuum at 40 °C for 12 h. Swelling experiments were performed on a minimum of three sections of each sample. Swelling parameters are reported as an average and standard deviation of replicate measurements. The Flory−Rehner model was applied to determine the percent soluble fraction of material extracted from the network (%ωsol), the equilibrium degree of swelling (Q), and the average molecular weight between cross-links (Mc,sw).7,8,14,15,24−26 The percent soluble fraction of each network was calculated by comparing the initial and final masses, as described in eq 1.

%ωsol =

mi − m f × 100% mi

Larmour frequency of 500.13 MHz. Experiments were conducted using a Bruker Prodigy cryoprobe and 5 mm o.d. glass NMR tubes. A 1 H 90° pulse length of 9.5 μs was used with a recycle delay of 15 s. Networked samples were soaked in deuterated toluene (Cambridge Isotope Laboratories, Cambridge, MA) until they reached equilibrium swelling (2−4 days). Swollen samples were placed in an NMR tube with extra deuterated solvent to prevent drying. The tubes were capped, and 1H NMR spectra were obtained within 1 h of sample preparation. Tetramethylsilane (TMS) was used as an external chemical shift reference at 0.00 ppm (Cambridge Isotope Laboratories). 1 H MAS NMR experiments were performed using a Bruker AVANCE III spectrometer operating at a proton Larmour frequency of 399.83 MHz. Experiments were conducted using a Bruker tripleresonance HXY MAS probe with a 90° pulse length of 4.4 μs and a recycle delay of 10 s. Solid samples were packed in 4 mm zirconia rotors spinning at 10 kHz, and TMS was used as a chemical shift reference at 0.00 pm. Solution 29Si NMR experiments were performed on a Bruker Avance III spectrometer operating at a proton Larmour frequency of 500.13 MHz. Experiments were conducted using a Bruker Prodigy cryoprobe tuned to 99.35 MHz with a 90° pulse length of 12.0 μs and a recycle delay of 120 s. The Bruker zgbs pulse sequence was used without 1H decoupling to suppress background signal from the probe and sample tubes.28 Swollen samples were prepared in the same manner as the 1H NMR samples with the addition of 0.75 mM chromium(III) acetylacetonate (Aldrich, St. Louis, MO) as a relaxation agent to reduce the long T1 relaxation time that is often observed with the 29Si nucleus. TMS was used as an external chemical shift reference at 0.00 ppm. Solid-state 29Si MAS NMR experiments were performed on a Bruker AVANCE III spectrometer operating at a proton Larmour frequency of 399.83 MHz. Experiments were conducted using a Bruker triple-resonance HXY MAS probe tuned to 79.43 MHz with a 30° pulse length of 1.45 μs and a recycle delay of 60 s. Solid samples were packed in 4 mm zirconia rotors spinning at 10 kHz, and highpower, inverse gated proton decoupling was employed to reduce line broadening. Kaolinite was used a chemical shift reference at −92 ppm.29 The 1H DQ NMR method allows for the quantification of dipolar coupling interactions between neighboring protons on polymer chains where topological constraints result in incomplete motional averaging of homonuclear (1H−1H) dipolar interactions. The dipolar coupling interactions that persist are termed residual dipolar couplings (RDC or Dres) and are proportional to the dynamic chain order parameter, Sb, and the number of statistical segments between constraints, N.

(1)

The equilibrium degree of swelling, which is inversely proportional to the volume fraction of polymer in the swollen network (ϕp, Q = 1/ ϕp)7,8 was calculated according to eq 2 and using the density of PDMS (ρPDMS = 0.965 g/cm3) as well as the density of toluene (ρtol) reported above. Q=

mf /ρPDMS + (msw − mi )/ρtol Vsw = Vdry mf /ρPDMS

(2)

The average molecular weight between cross-links (Mc,sw) was calculated according to eq 3, using the volume-fraction-dependent Flory−Huggins interaction parameter (χ = 0.459 + 0.134ϕp + 0.59ϕp2).24−27 The functionality factor ( f) accounts for the functionality of the cross-linker (f = 3.6).7,8 Mc,sw = −

ρPDMS Vsϕp1/3 ln(1 − ϕp) + ϕp + χϕp2

f−2 f

(3)

Sb =

In addition to the metrics described above, we also determined the defect and elastic fractions of the network using 1H DQ NMR data acquired in the swollen state. Under equilibrium swelling conditions, the long-time decay portion of the intensity reference curve (Iref) is solely the result of isotropically mobile components such as dangling chains and loops (assuming the soluble fraction has been removed). Using the method described in detail by Chassé et al.,7,8 the defect fraction (ωdef) was obtained by fitting an exponential decay curve to the slow decay portion of the normalized reference curve (DQ signal subtracted) and extrapolating back to the y-axis. The elastic portion of the network (ωel) is then determined by subtracting the defect fraction from unity (ωel = 1 − ωdef). An example of this is shown in Figure S2. Lastly, the Flory−Rehner equation used to calculate Mc,sw can be corrected to account only for the elastically active fraction of the network, as indicated in eq 4.7,8,14,15 Mc,sw,corr = −

ρPDMS Vsωelϕp1/3 ln(1 − ϕp) + ϕp + χϕp2

f−2 f

Dres 3 r2 = ⟨P2(cos α)⟩ Dstat 5N

(5)

In eq 5, Dstat (8.9 kHz) is dipolar coupling in the absence of motion which is preaveraged by the rotational methyl groups in PDMS, r is the vector describing the deviation of the end-to-end vector, R, from that of the unperturbed melt, Ro (r = R/Ro), and P2(cos α) is the second-order Legendre polynomial describing the time-averaged orientation changes between the dipolar vector and the chain axis. 1 H DQ NMR experiments were performed on a Bruker AVANCE III spectrometer operating at a proton Larmour frequency of 399.83 MHz. Experiments were conducted using a Bruker triple-resonance HXY MAS probe and 4 mm zirconia rotors. All experiments were conducted in the static state, and samples were cut to fill the center coil volume of probe. Samples were soaked in toluene and then redried to remove all soluble fraction of the network prior to 1H DQ NMR analysis. Swollen samples were allowed to expand to equilibrium swelling in deuterated toluene and then cut to fit in the 4 mm rotor while in the swollen state. Extra deuterated toluene was added to the rotor prior to loading the samples and polychlorotrifluoroethylene (PCTFE or Kel-F) caps equipped with an O-ring were used to prevent evaporation of solvent. DQ buildup curves were measured using a pulse sequence (Figure S3) previously described in

(4)

1

NMR Spectroscopy. H solution NMR experiments were performed on a Bruker Avance III spectrometer operating a proton C


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Macromolecules

Table 2. Results of Solvent Uptake Experiments, Defect Fraction (ωdef) Determined from NMR, and the NMR Corrected Mc,swa sample

Q

σ

%ωsol

σ

ωdef NMR

ωel

Mc,sw (kDa)

σ

corrected Mc,sw (kDa)

vPDMS-8 kDa vPDMS-32 kDa vPDMS-124 kDa vPDMS-8 kDa Tol vPDMS-32 kDa Tol vPDMS-124 kDa Tol

2.7 3.9 5.4 3.0 6.5 10.2

0.02 0.01 0.00 0.02 0.23 0.92

1.8 2.8 4.5 2.1 3.2 5.1

0.26 0.05 0.25 0.06 0.24 0.27

0.03 0.06 0.27 0.03 0.06 0.38

0.97 0.94 0.73 0.97 0.94 0.62

2.77 5.88 11.3 3.51 15.8 38.1

0.03 0.04 0.01 0.04 1.11 6.52

2.66 5.51 8.26 3.44 13.8 27.5

a

The standard deviation (σ) is taken from a minimum of three replicate measurements.

detail,20,30,31 which is designed to excite even-quantum coherences. 1 H DQ data were normalized according to previously established methods7,8,14,15,21 where relaxation effects are separated from network structural information with a point-by-point division of the DQ buildup curve by a sum of the DQ intensity (IDQ) and the corrected reference intensity (Iref-defects). The defect fraction or “defects” are determined as described above and illustrated in Figure S3. Because IDQ contains only half of the excited quantum orders (4n + 2), the resulting normalized DQ buildup (InDQ, eq 6) has to reach a plateau value of 0.5. Examples of the IDQ, Iref, and normalized DQ signal intensities are shown in Figure S4. InD =

IDQ IDQ + Iref − exp[− 2τDQ /T2]

τDQ

ideal network structure. This result indicates that our simplified networks have increased topological constraints and, consequentially, a less ideal network structure than other model networks. It should also be noted that the Mc values corrected to reflect only the elastic portion of the network are lower than those calculated from the uncorrected Flory− Rehner equation. Because the corrected data are assumed to be a more accurate representation of network topology, we will exclusively use the 1H DQ NMR corrected Mc data from this point forward. The soluble fraction for both neat and diluted samples increases with chain length but remains low even in networks made with high molecular weight precursors. Similarly, the soluble fraction is within error for samples prepared with or without solvent. The low soluble fraction indicates that most of the reaction precursors are consumed in network formation, resulting in good network formation across sample types. The formation of a complete network is further evidenced by the absence of any residual vinyl groups in the majority of the networked samples, as detected by 1H solution NMR (Figure S1). The excess amount of cross-linker added to these materials ensures that all of the vinyl groups are consumed during the hydrosilylation reaction.33,34 The increase in soluble fraction at long chain lengths (124 kDa) is likely the result of the high steric hindrance associated with the coordination of vinyl groups at the end of very long PDMS chains with the third and fourth cross-linking positions on our nominally fourfunctional cross-linker. 1H solution NMR (Figure S1) of the 124 kDa sample mixed with toluene (vPDMS-124 kDa Tol) shows a small amount of residual silane (4.9 ppm) and terminal vinyl groups (5.7, 5.9, and 6.2 ppm) that indicate incomplete network formation resulting from steric hindrance. The presence of unreacted starting materials (defects) confirms slightly incomplete network formation for this sample and explains the larger observed soluble fraction at high molecular weight. Consistent with this observation is the higher standard deviation observed for Mc,sw (Table 2) in vPDMS-124 kDa Tol when compared to the other samples studied her. The increased defect fraction and slightly incomplete network formation observed for this sample likely result in a larger deviation of Mc determined from solvent uptake in replicate samples. We also observe an increase in the defect fraction of the material determined by DQ NMR (ωdef, Table 2) with chain length. While the defect fraction is quite low in networks made with lower molecular weight precursors (0.03 and 0.06 for 8 and 32 kDa, respectively), it is much higher in the networks made with the largest prepolymer chain (0.26 neat, 0.38 dilute). The observed increase in defect fraction at the highest chain length supports the idea that steric hindrance plays a role in preventing completion of network formation in samples

(6)

Normalized buildup curves were fit with Tikhonov regularization using a home-built Python program similar to the FTIKREG package.30,32 We employed the kernel function (eq 7) introduced by Chinn et al.12 and described in detail by Chassé et al.23 InDQ (τDQ , Dres) = 0.5(1 − exp{− (0.378DresτDQ )1.5 } cos[0.583DresτDQ ])

(7) The pulse length (τp) was set to 3.4 μs with a recycle delay of 8 s. In this study, 55 time points (τDQ) were used to measure the DQ buildup curve with more time points chosen at earlier τDQ times to increase the reliability of the fit.

■

RESULTS AND DISCUSSION Section 1. Network Nonideality. Solvent uptake experiments were used to determine network structure parameters such as the molecular weight between cross-links (Mc,sw), network cross-link density (1/Mc,sw), and the equilibrium degree of swelling (Q) of the simplified silicone elastomers studied here. Equilibrium solvent swelling has been used extensively to assess the ideality or nonideality of model, endlinked PDMS networks.4,5 Here, we use solvent uptake data not only to determine the degree of network ideality but also to compare the network structure of our materials to those previously studied. Furthermore, we use the network properties determined from swelling data as a standard metric for similar network properties determined from both mechanical and NMR data. The results of solvent uptake experiments along with the defect fraction determined from 1H DQ NMR and both the uncorrected and corrected Mc,sw values are displayed in Table 2. The equilibrium degree of swelling (Q), shown in the first column, increases with increased chain length as well as with the addition of solvent. This result is consistent with a corresponding decrease in cross-link density (increased Mc,sw) for both corrected and uncorrected data. However, comparison of the Q values reported here with those of previously studied end-linked model networks7,8,13−15 reveals that the degree of swelling reported here is lower than would be expected for an D


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Macromolecules

studies where the use of excess cross-linker and an elevatedtemperature postcuring step resulted in nonideal network structure due to an increased concentration of physical crosslinks (trapped entanglements) within the network as well as additional chemical cross-links that result from condensation of the excess cross-linker.34,35 We used 29Si MAS and 29Si solution NMR to look for direct spectroscopic evidence of silicon Q4 groups that would arise not only from hydrosilylation but also from condensation of the cross-linker. However, our results (Figure S5) show only a large peak at −23.2 ppm (MAS and solution) for all networked samples as well as a small peak at 9.1 ppm for lower molecular weight samples (solution only, Figure 5b). The peak at −23.2 ppm is consistent with previous chemical shift assignment to dioxygen bonded silicon atoms (Dn) with 2-fold functionality that occur within the PDMS network backbone.36 The small peak at 9.1 ppm is consistent with mono-oxygen bonded silicon atoms with a CH2 (MCH2) substitution that results from the β-addition reaction at the PDMS chain ends.33,36 The βaddition peak is small due to the low concentration of PDMS chain ends as a result of the high molecular weight precursors used in this study and was only observable with the use of a solution-state cryoprobe with enhanced signal sensitivity compared to room temperature probes. Unfortunately, the background signal from the solutions probe (−80 to −120 ppm) obscured any possible Qn species that may exist in this region. Given the use of a 4-functional cross-linker [tetrakis(dimethylsiloxy)silane] that contains Si−O−Si moieties at its center, we would expect to observe MCH2, Dn, and Q4 peaks that result not only from the hydrosilylation reaction but also from the cross-linker condensation reaction.33,34,36 However, previous 1H−29Si CP-MAS studies on model PDMS networks demonstrated that Qn species resulting from hydrosilylation were not observable in networks made with precursor molecular weights (Mn) above 1.8 kDa due to the low concentration of chain ends.36 In light of this information, it is not surprising that we do not observe any Qn species in our 29 Si MAS data given that the molecular weight of the PDMS precursors used here far exceed the molecular weight threshold for detection. While we do expect additional Q4 species to be present as a result of cross-linker condensation, the concentration of these groups is also not likely high enough to be detected with 29Si MAS NMR. Although we do not directly observe the additional chemical cross-links in our networks that result from the use of excess cross-linker and an elevated temperature postcuring step using silicon NMR, this phenomenon has been documented elsewhere.34,35 The increase in both physical and chemical cross-links that likely result from condensed cross-linker within the network explains why the difference in both the defect fractions and soluble fractions of these networks (Table 2) are so similar when mixed in the neat and diluted states. The addition of solvent does reduce the contribution of trapped entanglements to network elasticity, but network formation is still driven largely to completion as a result of the reaction and processing conditions. The nonideal network structure observed in the samples studied here supports the notion that reaction stoichiometry and postcuring thermal treatment have a significant influence on the resulting network structure of silicone elastomers. This observation and the forthcoming comparison of these results to both mechanical and 1H DQ NMR data represent a critical step toward linking the extensive insights gained from the

made with larger molecular weight precursors. This phenomenon is exaggerated in the presence of solvent, as evidenced by the significantly larger defect fraction (0.38) and the residual starting materials (1H NMR, Figure S1) observed in vPDMS124 kDa Tol. The time to network formation was dramatically increased from several hours to several days or weeks when networks were formed in the diluted state. While the presence of solvent improves mixing of the starting materials, it increases the physical separation between vinyl end groups and the cross-linker after the network has begun to form and reactants have more restricted motion. The restricted motion imposed by chemical and physical cross-links that form during hydrosilylation reduce the incidence of interaction between chain-terminating vinyl groups and chemical cross-linking sites as the reaction proceeds. Previous studies have clearly documented a decrease in the rate of the hydrosilylation reaction as an increasing number of reactive groups are consumed.33,34 Solvent molecules trapped within the network as it forms exaggerate this effect and yield not only a longer gelation time but also a higher defect fraction in the resulting networked material. The degree of network nonideality is further evaluated by comparing network cross-link densities determined from solvent uptake data to the theoretical cross-link densities determined from GPC data in Figure 1. In a truly ideal

Figure 1. Theoretical cross-link density (1/Mn) versus cross-link densities determined from solvent uptake (1/Mc,sw) in both neat and diluted samples.

network where chemical cross-links formed at the terminal vinyl groups on prepolymer chains are the only contributor to the elasticity of the network, the molecular weight between cross-links from solvent uptake would be roughly equal to length of the prepolymers determined from GPC (Mn). However, additional chemical or physical cross-links formed during sample processing would reduce Mc,sw and, therefore lead to higher than predicted cross-link density expected from the length of the prepolymers. The large difference in measured cross-link density from theoretical indicates a significant contribution of physical constraints, such as trapped entanglements, to network elasticity. The decrease in overall cross-link density observed for diluted samples suggests that the addition of solvent during the gelation process improves mixing of the reactants and reduces the formation of trapped entanglements during curing. However, the diluted networks still display nonideal network behavior in the form of a much higher overall cross-link density determined from solvent uptake than would be anticipated from GPC data. This discrepancy is consistent with previous E


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Macromolecules

Figure 2. Measured and calculated storage modulus (G′) of neat networks plotted as a function of prepolymer chain length (a) and comparison of cross-link density determined from G′ (1/Mc,Mech) with cross-link density (1/Mc,sw) determined from solvent uptake (b).

Figure 3. (a) Distribution of 1H−1H dipolar couplings (Dres) in neat samples from 1H DQ NMR experiments performed in the dry state. (b) Relative distribution widths (σrel) for all samples analyzed in the dry state.

cross-link density (1/Mc,sw) (Figure 2b) clearly shows a discrepancy of ∼20% between the two. Quan et al.35 demonstrated that PDMS networks formed with a siliane:vinyl ratio at or above 1.7 in combination with an elevatedtemperature postcure had nonideal structure and a higher observed shear modulus (G′) than those that did not undergo a postcuring step. It was hypothesized that the additional chemical cross-links generated from cross-linker condensation were much more elastically active than cross-links formed during the gelation phase. This may explain why the G′ values calculated from solvent uptake data in this study do not have an exact agreement with measured G′ values. However, we must also consider the possibility that the low strain regime used in our experiments was not enough to completely disentangle the network. Section 3. 1H Double Quantum NMR. The dipolar coupling distribution curves generated from 1H DQ experiments performed on neat samples in the dry state are shown in Figure 3a along with the relative distribution widths of both neat and diluted samples in Figure 3b. Relative distribution widths are calculated by dividing the standard deviation of the distribution curve by the average value of the distribution curve (σrel = σ/Dres,avg). While the width of the measured dipolar coupling distribution curves narrows with increasing chain length, the relative distribution widths are the same across all samples. Chassé et al.14,15 reported relative distribution widths of ∼0.3 for end-linked polymers mixed without solvent present, similar to the neat samples reported here. They also reported a σrel value of ∼0.13 for end-linked network samples cured in the presence of ∼400 wt % toluene. However, we observe a relative distribution width of 0.3 for both the dilute and the neat networks. The increase in relative distribution

study of ideal, model networks to the more complex network topology that is typically observed in commercial silicones. Section 2. Mechanical Testing. The measured storage modulus for networks prepared without solvent (neat) are shown in Figure 2a along with the calculated storage modulus based on both solvent uptake and GPC data. Theoretical storage modulus values taken from swelling and GPC data were calculated based on the relationship between Mc and G′ that is derived from phantom network theory (eq 8).26

(1 − )ρ G′ = 2 f

PDMS

Mc

RT (8)

The storage modulus decreases with increased chain length for both measured and theoretical values. The increase in elasticity with prepolymer chain length agrees with increased Q values and decreased cross-link density observed in solvent uptake measurements. However, the storage modulus values reported here are higher than those of other model networks prepared without excess cross-linker and an elevated-temperature postcure.13,37,38 The higher observed moduli are consistent with the hypothesis that the cross-linker stoichiometry and processing conditions lead to networks with a higher overall concentration of physical and chemical cross-links. Measured storage modulus values are also higher than those calculated from both GPC and swelling data. While the storage modulus calculated from GPC data is expected to be much lower than the measured values based on the nonideal network behavior observed in solvent uptake studies, the values calculated from solvent uptake data should be in closer agreement. A direct comparison of the cross-link density determined from mechanical data (1/Mc,Mech) with swelling F


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Macromolecules width for the diluted samples indicates an increase in network heterogeneity, despite improved mixing. This increase further confirms that cross-linker stoichiometry and postcuring conditions play a critical role in determining the resulting network structure. The relative distribution widths of swollen state data (Figure S6) are also 0.3 for both neat and dilute networks. Previous investigations report σrel values of 0.8 for swollen, end-linked networks, regardless of the amount of solvent present during cross-linking.14,15 By comparison, the samples studied here show a decreased distribution of chain lengths between topological constraints in the swollen state. The decreased relative distribution observed can also be attributed to the increased concentration of fixed junctions in our networks. The shortest end-linked network reported by Chassé et al.14,15 was 5 kDa and had an equilibrium swelling volume (Q) of ∼7 when mixed with 400 wt % toluene and ∼3.5 when mixed with only 20 wt % toluene. In this study, the shortest chain network reported is 8 kDa. This molecular weight corresponds to equilibrium Q values of 2.7 in neat samples (0 wt % toluene) and 3.0 in dilute samples (400 wt % toluene). The decreased Q values reported here for networks made with slightly longer chains confirms that the networks examined in this study have significantly more topological constraints present than those previously reported in the literature. Networks with an increased concentration of fixed junctions and lower equilibrium swelling volume (given similar prepolymer chain lengths) would be expected to have a decreased spatial distribution of cross-links, even in the swollen state. The RDC distribution curves from 1H DQ data collected in both the dry and the swollen state were further analyzed to determine the fixed network contribution along with entanglement contributions to dipolar couplings.14,15 The average dipolar coupling value (Dres,avg) taken from integration of the dry RDC distribution curve has been shown to represent both residual dipolar couplings that arise from the fixed portion of the network as well those that arise from swellable entanglements in model PDMS networks. Including both contributions consistently leads to an overestimation of crosslink density determined by NMR when compared to solvent uptake data for silicone elastomers.7,8,21 However, it has recently been demonstrated that network contributions (Dres,n) to the dipolar coupling distribution can be determined from analysis of 1H DQ NMR data taken in the swollen state.14,15 In this approach, the contribution of fixed topological constraints (physical and chemical cross-links) within a given network is determined according to eq 9: Dres, n =

Figure 4. Cross-link density determined from average dipolar coupling values (1/Mc,avg) and determined from network dipolar coupling (1/Mc,n) values plotted as a function of cross-link density determined from defect corrected solvent uptake data in both neat and diluted samples. Dotted lines represent linear fits to the data. The slope of these fits are labeled in the corresponding marker color.

Dipolar coupling values are plotted directly against cross-link density to highlight the expected correlation of dipolar couplings to segmental orientation (eq 5). Both Dres,avg and Dres,n increase with cross-link density, reflecting the decrease in segmental motion of the network that arises from increased topological constraints. We also observe that Dres,avg is higher than Dres,n in all samples which illustrates the contribution of both entanglements and fixed junctions to Dres,avg. The difference between the two values (ΔDres = Dres,avg − Dres,n) is expected to represent nonclassical elasticity contributions to the network, such as the contribution of swellable entanglements to the dipolar coupling distribution. Here, we note that the magnitude of ΔDres is dependent on the sample preparation method (neat or diluted), which is in agreement with the observations of Chassé et al.14,15 Lastly, comparison of Dres,n (solid black circles and solid blue triangles; Figure 4) with the apparent cross-link density determined from solvent uptake shows direct proportionality of the network dipolar coupling value to cross-link density in both the neat and diluted samples. A linear fit to the Dres,n values plotted in Figure 4 gives a slope of 1.1 and 1.2 for neat and diluted samples, respectively. The linear fits also yield near zero y-intercept values (0.01 for neat and 0.03 for diluted), which confirms that the network dipolar coupling values calculated here are an accurate representation of the apparent cross-link density of the network. Previous comparisons of Dres with cross-link density attributed nonzero intercepts to entanglement contribution and near-zero intercepts as direct correlation.14,15 The near-zero intercepts observed here appear to indicate a good correlation between Dres,n and apparent cross-link density, despite a slope above 1 for both sample sets. It should be noted, however, that the previous work this study is based on was performed with two different χ parameters used to determine 1/Mc,sw in this comparison. Chassé et al. initially used the χ parameter published by Horkay et al.27 (χ = 0.459 + 0.134ϕp + 0.59ϕp2) but later followed with a correction that used the χ parameter published by Kuwahara et al.39 (χ = 0.445 + 0.297ϕp) based on an improved correlation Mc,sw with Mc,NMR data as well as theoretical calculations. We have examined the correlation of Dres,n with 1/Mc,sw using the

Dres(Q ) Q 2/3

(9)

where Dres(Q) is the average dipolar coupling value determined in swollen samples and Q2/3 is the equilibrium swelling volume determined from solvent uptake experiments raised to the 2/3 power. This relationship was derived from a power-law fit to the average dipolar coupling values measured in a series of partially swollen model PDMS networked samples as a function of the swelling volume and holds true for affinely deformed networks in the second stage of swelling (above Q′ or at full equilibrium swelling). Average and network dipolar coupling values for both the neat and diluted sample sets are plotted in Figure 4 as a function of cross-link density determined from solvent uptake. G


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Macromolecules updated χ parameter in Figure S7. The slope of a linear fit to the data using the Kuwahara χ parameter is 0.7 for the neat samples with a y-intercept of 0.06. Likewise, the slope of a linear fit to the diluted samples using the Kuwahara χ parameter is 0.9 with a y-intercept of 0.04. It appears that the Horkay χ parameter leads to an overestimation of cross-link density by Dres,n when compared to solvent uptake, while the Kuwahara χ parameter leads to an underestimation of crosslink density by Dres,n compared to solvent uptake for these samples. However, the fits using either χ parameter result in near-zero y-intercepts. Chassé et al.14,15 observed a quantitative linear correlation for Dres,n with apparent cross-link density regardless of the χ parameter used (m = 1.04 for Horkay and m = 1.01 for Kuwahara) and virtually no intercept for both. However, Chassé and co-workers also point out that the ϕp dependence of χ is an ad-hoc adjustment that is used to overcome the limitations of the Flory−Rehner model40 and that the choice of χ parameter is somewhat subjective.8,14,15,23 While the data reported by Chassé et al.14,15 showed a better correlation of Dres,n with the cross-link density determined from solvent uptake (regardless of the χ parameter used), the samples studied here have a more complex network topology than those previously studied due to the use of excess crosslinker, an elevated-temperature postcure, and the very large molecular weight of PDMS precursors used. The observation of a near-linear correlation between Dres,n and the cross-link density for the nonideal networks studied here demonstrates that this technique can be applied to silicone elastomers that more closely represent the complex cross-linking chemistry present in commercial materials. We also recognize that the sample population in this study is limited and are in the process of completing a follow-up investigation that includes a larger sample set of monomodal and bimodal PDMS networks with nonideal network structure. While chain entanglements are expected to be the primary contribution to ΔDres, it has also been hypothesized that effects such as cross-link junction fluctuations constrained by neighboring chains and defects trapped within the network could also contribute to ΔDres. To further examine this phenomenon, we plot the ΔDres values measured for both the neat and diluted samples sets as a function of precursor chain length in Figure 5. The values of ΔDres are higher in diluted networks, which likely represents the increased contribution of swellable entanglements to the elasticity of these networks

compared to those prepared without solvent. This result is consistent with the decrease in the trapped entanglement contribution that we observe in solvent uptake data (Table 2 and Figure 1) when networks are formed in the presence of toluene. The samples studied here are expected to have a high degree of entanglement contribution to the elasticity of the network given that the shortest chain precursor studied (8 kDa) is near the entanglement molecular weight (Me) of PDMS (∼10 kDa),41 and the larger samples (32 and 124 kDa) are made with precursors that are well above Me. We also observe that the shortest chain samples in both the neat and dilute cases have the highest ΔDres values. While this may appear to contradict the idea that entanglement contributions should increase with precursor molecular weight, it should also be noted that short chain networks were observed to have more physical cross-links (trapped entanglements) compared to those made with the longer chain prepolymers according to our solvent uptake data. The excess cross-linker added and the elevated-temperature postcure employed in this study are likely to have increased the hydrosilylation reaction rate,34 thereby immobilizing interpenetrating network chains with the rapid formation of chemical cross-links. This immobilization effect would be especially pronounced in the shortest chain sample which is expected to have the fastest reaction rate among the samples studied here due to the high concentration of reactive chain ends. It is possible that the increased concentration of physical and chemical cross-links in the short chain networks would reduce the ability of cross-link junctions to fluctuate around their mean position, which could further contribute to ΔDres.14,15 Furthermore, we observe a slight increase in ΔDres in the diluted network made with the 124 kDa prepolymer compared to the diluted network made with the 32 kDa prepolymer. This small increase in ΔDres could be attributed to the large increase in defect fraction that was determined to be present in this sample. Defects resulting from incomplete chemical cross-linking of a large chain prepolymer would likely be long dangling chains or large loops that could easily be constrained by neighboring chemically or physically crosslinked chains and therefore become a nonclassical contribution to network elasticity. The complex network topology that results from preparing these simplified elastomers in a manner similar to commercial materials (excess cross-linker and an elevated-temperature postcure) is not only reflected in the swelling and mechanical data but also reflected in structural parameters quantified by NMR (ωdef, Dres,avg, σrel, Dres,n, and ΔDres). Although follow-up studies are planned to verify the correlation of Dres,n with 1/Mc,sw in nonideal PDMS networks formed with varying length precursor chains, this preliminary work validates the application of 1H DQ NMR to quantify the network microstructure of silicone elastomer formulations as a function of preparation synthesis method, with base network structures that share some of the polymer network complexities in commercial, filled silicone rubbers.

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CONCLUSIONS We have demonstrated here that reaction conditions commonly used in the preparation of commercial silicone materials such as changes in reactant stoichiometry, exposure to ambient water and oxygen, and the use of postcuring methods have a significant and quantifiable influence on the resulting network topology. The resulting networks have nonideal behavior and an increased level of structural complexity than the idealized model networks that have been

Figure 5. Comparison of the nonclassical contributions to elasticity determined from NMR (ΔDres) in both neat and diluted samples. H


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Macromolecules

United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes. IM release number LLNL-JRNL-757701.

previously been synthesized to establish basic structure− function relationships in polysiloxanes.4,5,9,21,36,42−44 Specifically, the presence of excess cross-linker combined with the implementation of an elevated-temperature postcure yields networks with a significantly higher than expected cross-link density as measured by solvent uptake and dynamic mechanical analysis due to additional physical cross-links that arise from these conditions. The 1H DQ NMR method has been successfully applied to accurately quantify both the classical and the nonclassical contributions to network elasticity, despite their nonideal behavior. The results obtained here can serve as the foundation for further investigations of more complex silicones, which contain diverse cross-linking chemistries, heterogeneous filler phases, multimodal chain lengths, and the addition of various functional groups to the PDMS backbone. We anticipate that this method may also be applied to monitor the mechanisms of in-situ aging and degradation of commercial silicones that are subject to environmental stressors including long-term compressive strain and thermal cycling during their service lifetimes.

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(1) Fearon, F. W. G.; Zeigler, J. M. Silicon Based Polymer Science: A Comprehensive Resource. In Advances in Chemistry; ACS: Washington, DC, 1990; Vol. 224. (2) Clarson, S. J.; Semlyen, J. A. Siloxane Polymers; Prentice Hall: Englewood Cliffs, NJ, 1993. (3) Brook, M. A. Silicon in Organic, Organometallic, and Polymer Chemistry; Wiley: New York, 2000. (4) Mark, J. E.; Sullivan, J. L. Model Networks of End-Linked Polydimethylsiloxane Chains. I. Comparisons Between Experimental and Theoretical Values of the Elastic Modulus and the Equilibrium Degree of Swelling. J. Chem. Phys. 1977, 66, 1006−1011. (5) Queslel, J. P.; Mark, J. E. Swelling Equilibrium Studies of Elastomeric Network Structures. In Analysis/Reactions/Morphology. Advances in Polymer Science; 1985; Vol. 71, pp 230−247. (6) Schlögl, S.; Trutschel, M.-L.; Chassé, W.; Riess, G.; Saalwächter, K. Entanglement Effects in Elastomers: Macroscopic vs Microscopic Properties. Macromolecules 2014, 47, 2759−2773. (7) Chassé, W.; Lang, M.; Sommer, J.-U.; Saalwächter, K. CrossLink Density Estimation of PDMS Networks with Precise Consideration of Networks Defects. Macromolecules 2012, 45, 899− 912. (8) Chassé, W.; Lang, M.; Sommer, J.-U.; Saalwächter, K. Correction to Cross-Link Density Estimation of PDMS Networks with Precise Consideration of Networks Defects. Macromolecules 2015, 48, 1267− 1268. (9) Saalwächter, K.; Chassé, W.; Sommer, J.-U. Structure and Swelling of Polymer Networks: Insights From NMR. Soft Matter 2013, 9, 6587−6593. (10) Maxwell, R. S.; Chinn, S. C.; Alviso, C. T.; Harvey, C. A.; Giuliani, J. R.; Wilson, T. S.; Cohenour, R. Quantification of Radiation Induced Crosslinking in a Commercial, Toughened Silicone Rubber, TR55 by 1H MQ-NMR. Polym. Degrad. Stab. 2009, 94, 456− 464. (11) Maxwell, R. S.; Chinn, S. C.; Solyom, D.; Cohenour, R. Radiation-Induced Cross-Linking in a Silica-Filled Silicone Elastomer as Investigated by Multiple Quantum 1H NMR. Macromolecules 2005, 38, 7026−7032. (12) Chinn, S. C.; Alviso, C. T.; Berman, E. S. F.; Harvey, C. A.; Maxwell, R. S.; Wilson, T. S.; Cohenour, R.; Saalwächter, K.; Chassé, W. MQ NMR and SPME Analysis of Nonlinearity in the Degradation of a Filled Silicone Elastomer. J. Phys. Chem. B 2010, 114, 9729− 9736. (13) Mayer, B. P.; Lewicki, J. P.; Weisgraber, T. H.; Small, W.; Chinn, S. C.; Maxwell, R. S. Linking Network Microstructure to Macroscopic Properties of Siloxane Elastomers Using Combined Nuclear Magnetic Resonance and Mesoscale Computational Modeling. Macromolecules 2011, 44, 8106−8115.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01939. Figure S1: 1H NMR of swollen networks; Figure S2: example plot of the long-time decay signal (Iref − IDQ) in a swollen sample used for ωdef,NMR determination; Figure S3: 1H MQ pulse sequence used in this study; Figure S4: example of the experimental DQ intensity (IDQ) and the reference intensity (Iref) collected on a swollen networked sample plotted with the normalized DQ signal intensity (InDQ); Figure S5: (a) 29Si MAS of neat and diluted samples; (b) 29Si solution NMR of neat and diluted samples; Figure S6: relative distribution widths for swollen 1H DQ NMR data; Figure S7: network residual dipolar coupling values (Dres,n) plotted against cross-link density determined with different χ parameters (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*(A.S.) E-mail [email protected]. *(J.L.) E-mail [email protected]. ORCID

April M. Sawvel: 0000-0002-8810-807X Harris E. Mason: 0000-0002-1840-0550 James P. Lewicki: 0000-0002-2467-702X Present Address

M.G.: California State University Chico, 400 West First Street, Chico, CA 95929. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. This document was prepared as an account of work sponsored by an agency of the United States government. Neither the I


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Macromolecules (14) Chassé, W.; Schlö g l, S.; Riess, G.; Saalwä c hter, K. Inhomogeneities and Local Chain Stretching in Partially Swollen Networks. Soft Matter 2013, 9, 6943−6954. (15) Chassé, W.; Schlögl, S.; Riess, G.; Saalwächter, K. Correction: Inhomogeneities and Local Chain Stretching in Partially Swollen Networks. Soft Matter 2015, 11, 4337−4338. (16) Maxwell, R. S.; Cohenour, R.; Sung, W.; Solyom, D.; Patel, M. The Effects of γ-Radiation on the Thermal, Mechanical, and Segmental Dynamics of a Silica Filled, Room Temperature Vulcanized Polysiloxane Rubber. Polym. Degrad. Stab. 2003, 80, 443−450. (17) Chinn, S.; DeTeresa, S.; Sawvel, A.; Shields, A.; Balazs, B.; Maxwell, R. S. Chemical Origins of Permanent Set in a Peroxide Cured Filled Silicone Elastomer − Tensile and 1H NMR Analysis. Polym. Degrad. Stab. 2006, 91, 555−564. (18) Patel, M.; Chinn, S.; Maxwell, R. S.; Wilson, T. S.; Birdsell, S. A. Compression Set in Gas-Blown Condensation-Cured Polysiloxane Elastomers. Polym. Degrad. Stab. 2010, 95, 2499−2507. (19) Gjersing, E.; Chinn, S.; Giuliani, J. R.; Herberg, J.; Maxwell, R. S.; Eastwood, E.; Bowen, D.; Stephens, T. Investigation of Network Heterogeneities in Filled, Trimodal, Highly Functional PDMS Networks by 1H Multiple Quantum NMR. Macromolecules 2007, 40, 4953−4962. (20) Giuliani, J. R.; Gjersing, E. L.; Chinn, S. C.; Jones, T. V.; Wilson, T. S.; Alviso, C. T.; Herberg, J. L.; Pearson, M. A.; Maxwell, R. S. Thermal Degradation in a Trimodal Poly(Dimethylsiloxane) Network Studied by 1H Multiple Quantum NMR. J. Phys. Chem. B 2007, 111, 12977−12984. (21) Saalwächter, K. Proton Multiple-Quantum NMR for the Study of Chain Dynamics and Structural Constraints in Polymeric Soft Materials. Prog. Nucl. Magn. Reson. Spectrosc. 2007, 51, 1−35. (22) Saalwächter, K. Detection of Heterogeneities in Dry and Swollen Polymer Networks by Proton Low-Field NMR Spectroscopy. J. Am. Chem. Soc. 2003, 125, 14684−14685. (23) Chassé, W.; Valentín, J. L.; Genesky, G. D.; Cohen, C.; Saalwächter, K. Precise Dipolar Coupling Constant Distribution Analysis in Proton Multiple-Quantum NMR of Elastomers. J. Chem. Phys. 2011, 134, 044907−044910. (24) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (25) Flory, P. J.; Rehner, J., Jr. Statistical Mechanics of Cross-Linked Polymer Networks II. Swelling. J. Chem. Phys. 1943, 11, 521−526. (26) Boyd, R. H.; Phillips, P. J. The Science of Polymer Molecules; Cambridge University Press: Cambridge, UK, 1993. (27) Horkay, F.; Hecht, A. M.; Geissler, E. Thermodynamic Interaction Parameters in Polymer Solutions and Gels. J. Polym. Sci., Part B: Polym. Phys. 1995, 33, 1641−1646. (28) Cory, D. G.; Ritchey, W. M. Suppression of Signals from the Probe in Bloch Decay Spectra. J. Magn. Reson. 1988, 80, 128−132. (29) Mackenzie, K.; Smith, M. E. Multinuclear Solid-State NMR of Inorganic Materials; Elsevier: Oxford, 2002. (30) Saalwächter, K.; Ziegler, P.; Spyckerelle, O.; Haidar, B.; Vidal, A.; Sommer, J.-U. 1 H Multiple-Quantum Nuclear Magnetic Resonance Investigations of Molecular Order Distributions in Poly(Dimethylsiloxane) Networks: Evidence for a Linear Mixing Law in Bimodal Systems. J. Chem. Phys. 2003, 119, 3468−3482. (31) Saalwächter, K. 1H Multiple-Quantum Nuclear Magnetic Resonance Investigations of Molecular Order in Polymer Networks. II. Intensity Decay and Restricted Slow Dynamics. J. Chem. Phys. 2004, 120, 454−464. (32) Weese, J. A. Reliable and Fast Method for the Solution of Fredholm Integral Equations of the First Kind Based on Tikhonov Regularization. Comput. Phys. Commun. 1992, 69, 99−11. (33) Kovermann, M.; Saalwächter, K.; Chassé, W. Real-Time Observation of Polymer Network Formation by Liquid- and SolidState NMR Revealing Multistage Reaction Kinetics. J. Phys. Chem. B 2012, 116, 7566−7574. (34) Esteves, A. C. C.; Brokken-Zijp, J.; Laven, J.; Huinink, H. P.; Reuvers, N. J. W.; Van, M. P.; de With, G. Influence of Cross-Linker

Concentration on the Cross-Linking of PDMS and the Network Structures Formed. Polymer 2009, 50, 3955−3966. (35) Quan, X. Properties of Post-Cured Siloxane Networks. Polym. Eng. Sci. 1989, 29, 1419−1425. (36) Beshah, K.; Mark, J. E.; Ackerman, J. L.; Himstedt, A. Characterization of PDMS Model Junctions and Networks by Solution and Solid-State Silicon-29 NMR Spectroscopy. J. Polym. Sci., Part B: Polym. Phys. 1986, 24, 1207−1225. (37) Yoo, S. H.; Cohen, C.; Hui, C.-Y. Mechanical and Swelling Properties of PDMS Interpenetrating Polymer Networks. Polymer 2006, 47, 6226−6235. (38) Yoo, S. H.; Yee, L.; Cohen, C. Effect of Network Structure on the Stress-Strain Behaviour of Endlinked PDMS Elastomers. Polymer 2010, 51, 1608−1613. (39) Kuwahara, N.; Okazawa, T.; Kaneko, M. Osmotic Pressure of Moderately Concentrated Polydimethylsiloxane Solutions. J. Polym. Sci., Part C: Polym. Symp. 1968, 23, 543−553. (40) Chassé, W.; Saalwächter, K.; Sommer, J.-U. Thermodynamics of Swollen Networks as Reflected in Segmental Orientation Correlations. Macromolecules 2012, 45, 5513−5523. (41) Mark, J. E. Physical Properties of Polymers Handbook; Springer: New York, 2007. (42) Clarson, S. J.; Galiatsatos, V.; Mark, J. E. An Investigation of the Properties of Non-Gaussian Poly(Dimethylsiloxane) Model Networks in the Swollen State. Macromolecules 1990, 23, 1504−1507. (43) Mark, J. E. Bimodal Networks and Networks Reinforced by the In Situ Precipitation of Silica. Br. Polym. J. 1985, 17, 144−148. (44) Pan, S. J.; Mark, J. E. Reinforcement of Polydimethylsiloxane Precipitation of Silica: A New Method for Preparation of Filled Elastomers. Makromol. Chem., Rapid Commun. 1982, 3, 681−985.

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Nonideality in Silicone Network Formation via Solvent Swelling and

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