On the Structure and Pressure of Tethered Polymer Layers in Good Solvent

Abstract

The structural and thermodynamic properties of tethered polymer chains in the good solvent regime are studied using the single-chain mean-field theory. The mushroom to brush transition is found to be broad. For surface coverages below the brush regime, i.e., mushroom regime and crossover region, the relevant length scale of the layers is found to be the bulk radius of gyration of the chains, R g , while in the brush regime the relevant length scale is the distance between tethering points as assumed in the analytical approaches. The onset of the brush regime corresponds to the beginning of the overlap between the chains as measured by the distance-dependent lateral radius of gyration of the chains. The predictions of the theory for the height of the polymer layer and the lateral pressures as a function of the surface coverage are compared with recent experimental observations of Kent and co-workers. Excellent agreement is found for the height of the brush for all surface coverages. The experimental lateral pressures multiplied by the square of the bulk radius of gyration are found to be a universal function of the reduced surface coverage, * =πR g 2 . The predictions of the theory are in good agreement with the experimental measurements up to values of the reduced surface coverages * ∼8. For higher reduced surface coverages the theoretical results deviate from the scaling found experimentally. This deviation is consistent with the fact that these surface coverages correspond to the brush regime. The theoretical lateral pressure is found to be better described as a universal function of * ∼8 from low to relatively high surface coverages. From the analysis of the average conformational properties of the chains, it is argued that the behavior of the measured lateral pressures at high reduced surface coverages may be due to nonequilibrium effects. From the comparisons between the theory and the experiments it is found that most of the measurements correspond to the crossover region between the mushroom and the brush regimes. This explains the scaling found for most experimental properties