Non-Affine Deformations at a Concentration Transition in Cross-Linked Elastomers in the Light of the 3D XY Spin Glass Model

Abstract

X-ray and mechanical spectroscopy on liquid-crystalline elastomers give evidence of rubber elasticity, which depends upon the crosslink concentration. After applied macroscopic deformations, mesoscale non-affine deformations in these systems might lead to long relaxation times. Basing on the example of the crosslink-dependent smectic A − nematic (SmA−N) transition in polysiloxanes, we propose to use the three-dimensional Villain spin glass model and reduce it to the lattice version of the three-dimensionalXYspin-glass model. By using the Monte Carlo loop algorithm in this model, we found a percolation threshold depending on the crosslink concentration.