Model study for large deformation of physical polymeric gels

Abstract

A model for large deformation of polymer gels with physical cross-linking is developed and shown to be in good agreement with experimental stress-strain curves which show strain hardening in intermediate strains followed by strain softening in large deformations near the yield strain. The model takes into account the coil-helix transition equilibrium and allows for the distribution of the end-to-end distance. The gel is considered to be formed by long flexible chains and crystalline zones acting as junctions of the chains. The number of segments contained in a flexible chain is variable due to the equilibrium between the two regions. As the end-to-end distance increases due to the deformation, more and more segments are reeled out from the junction zone. Finally, one end of the chain is librated from the junction and the chain becomes dangling. The appearance of dangling chains causes the strain softening because they cease to contribute to the elasticity. From the parameter dependence of the stress-strain relations, it was found that the yield behavior depends strongly on the distribution of end-to-end distance. The yield strain is approximately given by the ratio of the upper limit of the number of segments and the average end-to-end distance. The standard deviation of the end-to-end distance affects significantly the width of the peak in the stress-strain curve, thus determining the degree of strain softening.