The Estimation of Statistical Parameters Determining the Relaxation Times of Nematic Elastomers: A Three-Chain Network Model

Abstract

A simplified “three-chain” network model formed from freely jointed polymer chains consisting of Gaussian elements with fixed mean-square lengths is proposed for describing local dynamic properties of nematic elastomers. The boundaries of a polymer network are supposed to be fixed when sample volume and shape do not change with ordering. Relaxation times characterising intrachain motions in both isotropic and ordered states are determined by two factors. The first (“dynamic”) factor is related to the friction of chain elements and the second one (“statistical” factor) is determined by statistical mean–square fluctuations of segment projections on the three axes of rectangular frame of reference. The “statistical” factor of relaxation times is calculated here as a function of the order parameter and the parameter characterising the degree of network crosslinking. Statistical factor obtained in the framework of a network model consisting of Gaussian subchains is compared with that calculated here by using freely-jointed-rods chain model. Good agreement is shown between statistical factors obtained in the framework of the two chain models considered. This result confirms the validity of describing the dynamics of real rod-like mesogenic groups in nematic elastomers in terms of a simplified chain model consisting of Gaussian segments with fixed average lengths which do not change with ordering. The influence of “dynamic” factor on the relaxation spectrum of a nematic elastomer is discussed qualitatively.