Positive Feedback Drives Sharp Swelling of Polymer Brushes near Saturation

Abstract

We resolve the Schröder 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 $χ$ 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.

Figures (3)

• Figure 1: Typical experimental procedure for measuring the swelling isotherm at high RHs. The plot shows the measured brush thickness (blue line), the RH (orange line, right axis), and the applied dry N$_2$ flow rate (green line, right axis) as a function of time, where a 100% flow rate corresponds to 0,5L/min. The experiment begins with a nearly saturated brush; modulating the N$_2$ flow rate induces deswelling and subsequent reswelling. The blue dashed line indicates the measured brush thickness in bulk liquid. The vertical black dotted line marks the onset of condensation, determined by the point where unphysical behavior appears in the optical model fit (see main text).
• Figure 2: Swelling behavior for different humidities at different temperatures above and below the lower critical solution temperature. The inset compares swelling in the vapor phase to swelling in the liquid phase.
• Figure 3: Experimental data, theoretical models, and the link to dynamic wetting. (a) The sharp swelling threshold is directly mirrored in the dynamic wetting, causing the advancing contact angle at high velocities to drop sharply only as ambient RH surpasses 98%. The solid curves are fits using the adaptive wetting model Butt2018. (b) The experimental swelling isotherm at 12 $^\circ$C (blue dots) exhibits a sharp increase above 98% RH, a behavior not captured by the standard mean-field theory with any constant $\chi$ (e.g., black dashed line for $\chi=0.3$). (c) Our extended mean-field model explains this behavior via a positive feedback loop, revealed by the decrease in the derived classical interaction parameter, $\chi_\mathrm{class}$, with increasing solvent fraction $\varphi$. Large circles mark the state at 100% RH for each temperature.