Structure and dynamics of polymer brushes near the Θ point: A Monte Carlo simulation

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Abstract
Grafted polymer layers under variable solvent conditions are studied by Monte Carlo simulations using the bond fluctuation model. Structural information such as monomer density profiles, brush thickness, mean-square displacement of monomers, and positions of the monomers along the chain are obtained for temperatures above, at, and below the Θ point. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. At the Θ point, more extensive simulations are performed to investigate the structural and dynamical properties. While the brush thickness at the Θ point agrees very well with the scaling and self-consistent field predictions, the latter deviate from our results for the monomer density profile and the distribution function of the free chain ends. It is not clear whether these deviations result from our chains being too short or from a basic inadequacy of the theory. For the dynamics at the Θ point, both the relaxation of the chain configurations and the mean-square time displacement of the chains are studied. The relaxation time τ for a polymer brush of chain length N and surface coverage σ are found to behave as τ∼N3σb with an apparent exponent b≂1.6. For poor solvent conditions below the Θ point, we find that the layer (with randomly fixed grafting sites) develops considerable lateral inhomogenity in its density, which has not been predicted by previous theories.