Rod-like Polyelectrolyte Brushes with Mono- and Multivalent Counterions

A model of rod-like polyelectrolyte brushes in the presence of monovalent and multivalent counterions but with no added-salt is studied using Monte Carlo simulation. The average height of the brush, the histogram of rod conformations, and the counterion density profile are obtained for different values of the grafting density of the charge-neutral wall. For a domain of grafting densities, the brush height is found to be relatively insensitive to the density due to a competition between counterion condensation and inter-rod repulsion. In this regime, multivalent counterions collapse the brush in the form of linked clusters. Nematic order emerges at high grafting densities, resulting is an abrupt increase of the brush height. Electrostatic correlation effects of highly charged macro-ions in aqueous solutions have recently attracted much attention [1]. Novel phenomena such as charge inversion and likecharge attraction, which cannot be understood within the Poisson-Boltzmann theory, appear to play a key role in biological processes such as DNA packaging [2] and cell scaffolding dynamics [3]. Such correlations, and their role in determining the overall structural properties of the system, are most pronounced in high density polyelectrolyte solutions where the charge “patterns” that form due to the correlations strongly interact with each other. If the polyelectrolyte is sufficiently stiff in its backbone structure [such as DNA and filamentous actin (F-actin)], a geometric constraint is imposed on the charges in each polyelectrolyte segment to adopt a more or less linear configuration, which makes a solution of such rod-like polyelectrolytes a patterned matrix for the counterions (that is, the ions of opposite charge that are present to neutralize the overall solution). The interplay between these correlations and patterns can lead to novel structural and dynamical properties [4–7], the study of which could be useful in understanding the biological phenomena mentioned above as well as designing functional biomimetic materials. A common realization of such high density assemblies occurs in polyelectrolyte brushes [8], where charged polymers are end-grafted to surfaces. While polyelectrolyte brushes have been mostly studied because of their role in stabilization of colloidal suspensions, understanding their structural properties could help us in a variety of problems in biophysics and -technology. A case in point is filamentous microtubules, i.e. rod-like structures build from tubulin monomers with charged C-terminal amino-acid tails extending from the filament core [9]. The C-terminal tails seem to play key roles in microtubule function, e.g. in connection with binding of microtubule-associated proteins and processivity of the molecular