Positive Feedback Drives Sharp Swelling of Polymer Brushes near Saturation

TL;DR

This paper demonstrates that polymer brushes exhibit a sharp swelling transition near saturation due to positive feedback mechanisms, challenging standard models and providing a predictive theoretical framework.

Contribution

It introduces an extended mean-field theory incorporating a concentration-dependent interaction parameter to explain the sharp swelling behavior.

Findings

Swelling sharply increases above 98% RH, matching liquid state.

The theory quantitatively predicts the wetting crossover behavior.

Experimental results resolve the Schröder paradox for PNiPAAm brushes.

Abstract

We resolve the Schr\"{o}der paradox for PNiPAAm brushes, showing experimentally that swelling at 100\% relative humidity (RH) matches the liquid state. This occurs via a sharp increase in swelling above 98\%~RH, a behavior standard models fail to explain. Our extended mean-field theory explains this via a positive feedback between swelling and solvent quality, driven by a concentration-dependent $\chi$ parameter. The swelling isotherm quantitatively predicts the dynamic wetting crossover: the advancing contact angle at high velocities drops sharply as ambient humidity surpasses the 98\%~RH threshold.