Non-affine displacements in flexible polymer networks

TL;DR

This study investigates the validity of the affine deformation assumption in flexible polymer networks by measuring bead displacements in polyacrylamide gels under shear, revealing non-affinity influenced by network inhomogeneities.

Contribution

It provides experimental quantification of non-affine displacements in polymer gels and links these deviations to structural inhomogeneities and current theoretical models.

Findings

Non-affinity increases with polymer density and cross-linking.

Structural inhomogeneities are likely due to heterogeneous gelation kinetics.

Macroscopic elasticity aligns with standard flexible polymer network models.

Abstract

The validity of the affine assumption in model flexible polymer networks is explored. To this end, the displacements of fluorescent tracer beads embedded in polyacrylamide gels are quantified by confocal microscopy under shear deformation, and the deviations of these displacements from affine responses are recorded. Non-affinity within the gels is quantified as a function of polymer chain density and cross-link concentration. Observations are in qualitative agreement with current theories of polymer network non-affinity. The measured degree of non-affinity in the polyacrylamide gels suggests the presence of structural inhomogeneities which likely result from heterogeneous reaction kinetics during gel preparation. In addition, the macroscopic elasticity of the polyacrylamide gels is confirmed to behave in accordance with standard models of flexible polymer network elasticity.