Upturn In Modulus Research Articles

Synthesis, structure, and properties of hybrid organic-inorganic composites based on polysiloxanes. II. Comparisons between poly(methylphenylsiloxane) and poly(dimethylsiloxane), and between titania and silica

The work reported in the preceding article in this series is extended by consideration of polysiloxane–ceramic composites based on atactic poly(methylphenylsiloxane) (PMPS) elastomers instead of poly(dimethylsiloxane). The former is noncrystallizable because of its stereochemically irregular structure, while the latter is crystallizable. In addition, some composites were prepared by the in situ precipitation of titania instead of silica. The resulting materials were characterized using differential scanning calorimetry, equilibrium stress–strain measurements in elongation, small-angle neutron scattering, and transmission electron microscopy. The moduli of the PMPS elastomers were found to increase significantly with increase in amount of either type of filler, with reinforcing upturns at high elongation in the case of the silica. Because the PMPS elastomers were amorphous, it is obvious that strain-induced crystallization is not required for these upturns in modulus. Titania did not give as good reinforcement as did silica, at least in the case of PMPS. Differences in interactions between the polymer and the two fillers are obviously important in this regard, but differences in particle morphology probably also contribute. Specifically, the titania “particles” were significantly larger than the silica particles when observed in TEM, and appeared to be much more porous. The actual domain size as measured by scattering, however, was only approximately 5% larger. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1191–1200, 1998

Torsion Studies of Thermoelasticity and Stress–Strain Isotherms of Unimodal, Bimodal, and Filled Networks of Poly(dimethylsiloxane)

End-linking reactions were used to convert chains of poly(dimethylsiloxane) (PDMS) into (i) unfilled networks having either unimodal or bimodal chain-length distributions, or (ii) filled networks in which either a separately-prepared zeolite had been blended into the polymer prior to end linking, or silica was precipitated into the networks afterwards. The resulting elastomers were studied in torsion, the aspect of particular interest in the case of the unfilled networks being the fraction Me/M of the total couple which is due to changes in conformational energy. The values of Me/M were found to be independent of crosslink density, extent of torsional strain, and extent of any elongation imposed during the torsion. The values for the bimodal networks, however, were much smaller than those for the unimodal ones, presumably because of the non-Gaussian nature of the short chains. None of the unimodal or bimodal unfilled networks showed any upturn in modulus at high torsional deformations similar to the upturns shown by bimodal networks in elongation, biaxial extension, and shear. Neither did the filled networks, but they did show significant increases in modulus in general, thus demonstrating reinforcement at least in this regard.

Monte carlo simulations relevant to the upturns in modulus observed for natural rubber at high elongations

Monte carlo simulations relevant to the upturns in modulus observed for natural rubber at high elongations

Interpenetrating bimodal networks

AbstractSequential interpenetrating networks (IPN's) were obtained from a tetrafunctionally end‐linked network [prepared from hydroxyl‐terminated poly(dimethylsiloxane) (PDMS) chains having a number‐average molecular weight of 21.3 × 103 g mol−1] by swelling it with very short vinyl‐terminated PDMS chains (∼450 g mol−1), which were then themselves tetrafunctionally end linked, Simultaneous IPN's were prepared from a mixture of the same two types of PDMS chains, with different end‐linking agents and catalysts for the two separate reactions. In elongation studies, both types of IPN's showed upturns in modulus which were similar to those shown by the usual bimodal networks, which are prepared from mixtures of chains having identical end groups, and are thus entirely interconnected. The sequential IPN's have values of the high deformation modulus close to those of the interconnected networks, possibly because their lack of connectivity is compensated for by the stretching of the long chains by the short‐chains used to form the second network, Values of the ultimate strength are smaller for the IPN's, thus demonstrating the advantage of direct bonding between the long and short network chains. The simultaneous IPN's, however, have unusually large extensibilities, which makes their energies for rupture comparable to those of the corresponding interconnected bimodal networks.

Recent Studies of Rubberlike Elasticity

Forming elastomeric networks by end linking functionally-terminated polymer chains has the advantage of minimizing imperfections in the network structure, with associated improvements in ultimate properties. These improvements are found to be particularly marked when mixtures of very short and relatively long chains are end linked, thus giving bimodal networks. Such (unfilled) networks show very large increases in reduced stress or modulus at high elongations and, since such a toughening effect is of interest with regard to both fundamental questions and potential applications, a variety of experiments were carried out to elucidate its origin. These experiments included stress-strain isotherms over a wide range in temperature and degree of swelling, stress-temperature coefficients, and birefringence-temperature coefficients. All of the experimental results indicate the origin of the upturns in modulus to be intramolecular, specifically non-Gaussian effects arising from the very limited extensibility of the short chains present in the networks. This limited extensibility and its effects on elastomeric properties were investigated using a theory of rubberlike elasticity based on network distribution functions generated from rotational isomeric state models for the specific chains of interest. Polymers studied to date by this theoretical approach are poly(dimethylsiloxane), (amorphous) polyethylene, polymeric sulfur, and polymeric selenium.

A non-Gaussian theory of rubberlike elasticity based on rotational isomeric state simulations of network chain configurations. III. Networks prepared from the extraordinarily flexible chains of polymeric sulfur and polymeric selenium

Distribution functions for the end-to-end separation of polymeric sulfur [-S-] and selenium [-Se-] are obtained from Monte Carlo simulations which take into account the chains’ geometric characteristics and conformational preferences. Comparisons with the corresponding information on polyethylene [-CH2-] demonstrate the remarkable equilibrium flexibility or compactness of these two molecules. Use of the S and Se distribution functions in the three-chain model for rubberlike elasticity in the affine limit gives elastomeric properties very close to those of simple Gaussian networks, even though their distribution functions appear to be significantly non-Gaussian. Specifically, unlike the case of polyethylene, even very short S and Se chains show only slight upturns in modulus at high elongations; this is consistent with their unusually high flexibility.

The use of model polyisobutylene networks to study strain-induced crystallization

Model elastomeric networks were prepared by trifunctionally end linking hydroxyl-terminated chains of polyisobutylene having number-average molecular weights in the range 10−3Mn = 2.4 – 10.7 g mol−1. Their stress-strain isotherms in elongation at 25°C in the unswollen state showed significant increases or upturns in modulus at high elongations, due to strain-induced crystallization. Increase in degree of cross-linking (decrease in Mn) was found to decrease the elongation required to initiate crystallization and the maximum extensibility, but to increase the magnitude of the upturn in modulus.

A non-Gaussian theory of rubberlike elasticity based on rotational isomeric state simulations of network chain configurations. I. Polyethylene and polydimethylsiloxane short-chain unimodal networks

The present theoretical approach to rubberlike elasticity is novel in that it utilizes the wealth of information which rotational isomeric state theory provides on the spatial configurations of chain molecules. Specifically, Monte Carlo calculations based on the rotational isomeric state approximation are used to simulate spatial configurations, and thus distribution functions for the end-to-end separation r of the chains. Results are presented for polyethylene (PE) [CH−2] and polydimethylsiloxane (PDMS) [Si(CH3)2–O–] chains most of which are quite short, in order to elucidate non-Gaussian effects due to limited chain extensibility. Large values of r were found to be more prevalent in PDMS than in PE, primarily because of the unusually large Si–O–Si bond angle in the PDMS chain, which increases its spatial extension. The use of these distribution functions in place of the Gaussian function for network chains gives upturns in modulus at high elongations, because of the rapidly diminishing number of configurations consistent with the required large values of r, and thus, correspondingly large decreases in the entropy of the network chains. Networks of PDMS should have values of the non-Gaussian increases in modulus significantly different from those for (amorphous) PE networks having the same number of skeletal bonds and stretched to the same relative length.