Stretch-collapse transition of polyelectrolyte brushes in a poor solvent

von Goeler, F.; Muthukumar, M.
December 1996
Journal of Chemical Physics;12/22/1996, Vol. 105 Issue 24, p11335
Academic Journal
This paper describes the behavior of charged, polymer brushes in electrolyte solutions of varying solvent quality. The brush height, d, dependence on the chain length, L (=Nl, where l is the Kuhn length), the grafting density s, and solvent conditions is determined. We consider a monomer-monomer potential consisting of three components: (1) a long-ranged, screened Coulombic component of strength νsline;/l (l is the Kuhn length) and range κ[SUP-1]; (2) a short-ranged, two-body component of strength &wsline;l; and (3) a short-ranged, three-body component of strength νsline;l(3). In particular, we examine the transition from a stretched state to a collapsed state in a poor solvent (&wsline;<0) as the solvent quality is decreased. Using dimensional analysis, Monte Carlo methods, and a variational technique, a first order transition is observed as predicted by the scaling arguments of Ross et al. and Borisov et al. for high charge/grafting densities. Using a variational procedure, we derive an analytical expression for the brush size and determine, quantitatively, the critical conditions for a first order transition in terms of key dimensionless variables, νN[SUP&frac52;]), κlN[SUP½], wN[SUP&frac32;], and uN[SUP2] (where v= 2π&ssgma;l[SUP2]νsline;, w = σl[SUP2]&wsline;, and u = σ[SUP2]l[SUP4]νsline;).


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