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Stress–Strain Relation for Polymer Networks Near the Isotropic–Nematic Transition

Walasek. Janusz
Radosław Jedynak
Organization: Kazimierz Pulaski University of Technology and Humanities
Journal / Anthology

Macromolecular Theory and Simulations
Year: 2013
Volume: 22
Issue: 7
Page range: 385–393

A network of polymer chains, which is undergoing an external deformation, is considered. Each of the network chains is linear and consists of segments interacting by nematic potential orienting interactions between segments within a chain and segments of other chains. Interactions are considered in calculations within the limit of theMaier and Saupemolecular mean-fieldmodel. Chains of the network are connected at junctions with arbitrary functionality; this is the number of chains issuing from a junction. This parameter is included in calculations. The network free energy is calculated. Then, formulas for the work of the system elongation and the stress-strain relation are obtained. This is done for the network, which is elongated uniaxially and in an arbitrary direction to the nematic axis. Parameters used in these formulas are as follows: the network junction functionality, the system thermodynamic temperature, the strength of interactions between segments and the average orientation of the segments within the network. Calculations are performed for the limit of long chains. In the isotropic phase, the elongation work is given by the neo-Hookean constitutive equation and is an invariant of orientation of the elongation axis. In the nematic phase, that work depends strongly on the relative orientation of the system elongation and the nematic field direction. A formula for the stress of the elongated network is obtained. This formula is described by the following parameters: the network topological structure, the relative orientation of the elongation direction and the nematic field, and the intensity of the nematic molecular mean field.