The Polyelectrolyte Brush: Poor Solvent
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THE POLYELECTROLYTE BRUSH: POOR SOLVENT
RICHARD S. ROSS* AND PHIL PINCUS*t *Department of Physics, University of California, Santa Barbara, CA 93106 tMaterials Department, University of California, Santa Barbara, CA 93106
ABSTRACT We investigate the end grafted polyelectrolyte brush in the poor solvent regime of the corresponding neutral polymer system. Using Poisson-Boltzmann theory for the electrostatics and Flory-Huggins-mean-field theory for the excluded volume and Van-der-Waals-like monomer interactions, we find the existence of a first order phase transition to a collapsed state for moderate to highly charged polyelectrolytes in the poor solvent regime. Irreversibilities in the disjoining pressure between planar grafted surfaces are predicted. For polyelectrolytes grafted to spherical and cylindrical surfaces with small radii of curvature, the phase transition is predicted to become second order in the infinite molecular weight limit. A phase diagram for the entire poor solvent regime is given. INTRODUCTION Electrically charged polymers, polyelectrolytes, generally have organic backbones which are insoluble in polar solvents 1 ,2 . Their solubility is induced by disocciation and hydration energies associated with the polar groups. Previous studies of end grafted polyelectrolytes in the overlapping brush regime have focused on the dominance of the electrostatic energy in determining brush structure and compressibility 3 ,4,5 . It is the purpose of this article to explicitely consider the effects of solvent quality on the global properties of polyelectrolyte brushes. We will show that within the mean field approximations for both the electronic and polymeric componenets, a first order phase transition in which the brush collapses may be induced by modification of the solvent quality. This collapse transition is quite analagous to that observed by Tanaka and coworkers 6 ,7 in polyelectrolyte gels. An extension of the calculation is made to the case of a curved grafting surface, both cylindrical and spherical with small radii of curvature relative to the layer thickness. We find that the collapse transition is then very weakly first order, turning second order in the infinite molecular weight limit, corresponding to star polyelectrolytes in two and three dimensions. PLANAR POLYELECTROLYTE BRUSH In this section we describe an extension of a calculation by Pincus 5 for the equilibrium conformation of a planar polyelectrolyte brush, wherein we now include the effects of monomer interactions through Flory-Huggins mean field terms. The brush geometry is shown in Fig. 1. We assume an Alexander-deGennes step function monomer density profile8 ,9 , in which polymers with degree of polymerization N are irreversibly end-grafted to a planar surface with a mean distance between grafting sites d < Rg so that the chains strongly overlap (brush regime). All chains are stretched uniformly away from the grafting plane, their free ends lying at the extent of the brush L. The monomer concentration for neutral polymers in good solv
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