Surface scaling analysis of hydrogels: From multiaffine to self-affine scaling

TL;DR

This study demonstrates that smoothing multiaffine hydrogel surfaces induces a transition to self-affine scaling, aligning simulations with experimental AFM observations of gel surface structures.

Contribution

It reveals how smoothing transforms multiaffine surfaces into self-affine ones, bridging simulation results with experimental AFM data.

Findings

Smoothing causes a transition from multiaffine to self-affine scaling.

Both simulated and experimental surfaces exhibit non-trivial small-scale scaling.

A crossover to scale-independent behavior occurs at larger scales.

Abstract

We show that smoothing of multiaffine surfaces that are generated by simulating a crosslinked polymer gel by a frustrated, triangular network of springs of random equilibrium lengths [G.M. Buend{\'\i}a, S.J. Mitchell, P.A. Rikvold, Phys. Rev. E 66 (2002) 046119] changes the scaling behavior of the surfaces such that they become self-affine. The self-affine behavior is consistent with recent atomic force microscopy (AFM) studies of the surface structure of crosslinked polymer gels into which voids are introduced through templating by surfactant micelles [M. Chakrapani, S.J. Mitchell, D.H. Van Winkle, P.A. Rikvold, J. Colloid Interface Sci., in press]. The smoothing process mimics the effect of the AFM tip that tends to flatten the soft gel surfaces. Both the experimental and the simulated surfaces have a non-trivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales.