Cross-linking patterns and their images in swollen and deformed gels

TL;DR

This paper demonstrates how cross-link density patterns in polymer gels can be visualized through swelling, revealing their structure and deformation behavior, with distinctions between gel and solid elasticity.

Contribution

It introduces a method to visualize cross-link patterns in gels via swelling and analyzes their deformation responses, highlighting fundamental differences from solid elasticity.

Findings

Isotropic deformations magnify original patterns in gels.

Anisotropic deformations distort the pattern images.

Different responses to stretching are due to fundamental elasticity differences.

Abstract

Using the theory of elasticity of polymer gels we show that large-scale cross-link density patterns written into the structure of the network in the melt state, can be revealed upon swelling by monitoring the monomer density patterns. We find that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotropic deformations distort the image (both types of deformation yield affinely stretched images in $\theta$ solvents). We show that in ordinary solids with spatially inhomogeneous profile of the shear modulus, isotropic stretching leads to distorted density image of this profile under isotropic deformation. Using simple physical arguments we demonstrate that the different response to isotropic stretching stems from fundamental differences between the theory of elasticity of solids and that of gels. Possible tests of our predictions and some potential applications are discussed.