POLYELECTROLYTE BRUSH DENSITY PROFILES

A study of the density profile of polyelectrolyte brushes in electrolyte solutions is presented. We consider a monomer-monomer potential with two components: (1) a short-ranged excluded volume component with strength (w) over bar l(3) (l is the Kuhn length) and (2) a screened Coulombic long-ranged component with strength (v) over bar/l and range kappa(-1). We examine the dependence of brush height, d, with polyelectrolyte chain length L (=lN), grafting density, sigma, and kappa. The dimensionless variables are wN(3/2), vN(5/2), and kappa lN1/2, where v = 2 pi sigma (v) over bar l(2), and w = (w) over bar sigma l(2). Dimensional analysis, computational enumeration, and a variational procedure are used to obtain the characteristics of the density profile. Four regimes of electrostatic interaction are identified: (1) a weak interaction regime in which d similar to L(nu) with an effective nu between 1/2 and 3/5 depending on wN(3/2); (2), intermediate regime for intermediate values of vN(5/2) where the scaling d similar to vN(3) is possible if kappa lN(1/2) is, small; (3) a regime where both kappa lN(1/2) and vN(5/2) large where the electrostatic interaction is essentially short-ranged due to screening and d similar to (w + (2v/kappa(2)l(2))(1/3)lN; and (4) a fully stretched (saturation) regime where d approximate to lN due to finite extensibility of the chains. The various crossover behaviors between these asymptotic regions are also obtained with quantitative details.