Polymer Brushes: Scaling, Compression Forces, Interbrush Penetration, and Solvent Size Effects

Abstract

This work discusses the results of a self-consistent-field calculation of conformational and thermodynamic properties of polymers end-grafted to a surface in athermal solvents. Three primary issues are addressed. First, we address the question raised recently by Carignano and Szleifer as to whether the second virial treatment of previous numerical and analytical self-consistent-field theories provides an adequate description of polymer brushes. We show that, for grafted chains that are sufficiently long, there exists a broad range of grafting densities where the lateral pressure and the brush thickness both scale as predicted by the second virial treatment. For shorter chains (of 100 monomers or less), no distinct scaling regime is observed. A related effect due to finite chain lengths is the interpenetration of brushes upon compression and its importance to compression forces. We find that, even for quite large chains (of up to 1000 monomers), there is significant interbrush penetration at high compression. However, the force profiles are relatively insensitive to penetration at such high compressions. Instead, finite chain lengths affect the interaction forces most prominently at the onset of the interactions. Next, we address the crossover from wet brushes to dry brushes as the molecular weight of the solvent increases. This crossover is driven purely by entropic effects and is interpreted on the basis of the conformation of the polymeric solvent molecules in the vicinity of the brush. It is found that the state of the brush is determined by two crossover scaling variables, the ratio of the degree of polymerization of the free and grafted chains, N_f/N_g and N_fσ^2, where σ is the grafting density. Finally, we investigate brush configurations and interactions in mixed solvents. It is observed that, for polymer brushes in a solution of mixed free polymers and monomers, there are three distinct regimes in the interactions between two brushes. Upon the onset of the interaction, the brushes attract one another as the solvent is transferred from an unfavorable proximity to the brush to the infinite reservoir. Then, there is a very rapidly increasing repulsive force as the brushes begin to overlap and the remainder of the free polymer is removed from the system. Once all of the polymeric component has been squeezed out of the brushes, the compression becomes indistinguishable from the compression of brushes in a monomeric solvent.