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

Abstract

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.