Positive Feedback Drives Sharp Swelling of Polymer Brushes near Saturation
Abstract
We resolve the Schr\"oder 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 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.
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