End-anchored polymers in good solvents from the single chain limit to high anchoring densities
An increasing number of applications utilize grafted polymer layers to alter the interfacial properties of solid substrates, motivating refinement in our theoretical understanding of such layers. To assess existing theoretical models of them, we have investigated end-anchored polymer layers over a wide range of grafting densities, σ, ranging from a single chain to high anchoring density limits, chain lengths ranging over two orders of magnitude, for very good and marginally good solvent conditions. We compare Monte Carlo and molecular dynamics simulations, numerical self-consistent field calculations, and experimental measurements of the average layer thickness, h, with renormalization group theory, the Alexander–de Gennes mushroom theory, and the classical brush theory. Our simulations clearly indicate that appreciable inter-chain interactions exist at all simulated areal anchoring densities so that there is no mushroom regime in which the layer thickness is independent of σ. Moreover, we find that there is no high coverage regime in which h follows the predicted scaling, h ∼ Nσ1/3, for classical polymer brushes either. Given that no completely adequate analytic theory seems to exist that spans wide ranges of N and σ, we applied scaling arguments for h as a function of a suitably defined reduced anchoring density, defined in terms of the solution radius of gyration of the polymer chains and N. We find that such a scaling approach enables a smooth, unified description of h in very good solvents over the full range of anchoring density and chain lengths, although this type of data reduction does not apply to marginal solvent quality conditions.