(273e) Clustering Of Counterions On Flexible Polyelectrolytes

Polyelectrolytes consist of repeating ionizable groups which dissociate in water or other polar solvents, making the macromolecules ionized. Natural and synthetic polyelectrolytes are widespread in applications, ranging from detergents and water treatment to proteomics and to signal transduction in cells. While each of these applications is independently unique, all of them share the common feature of utilizing intermolecular interactions in a polyelectrolyte solution which are governed by the effective charge of a macromolecule being lower than the fully ionized value due to coupling of a macromolecule with surrounding counterions. The effect of the counterion screening of an ionized macromolecule is seen as the critical factor for understanding these complex phenomena. The classic Manning theory of counterion condensation constitutes the basis for thermodynamics of dilute polyelectrolyte solutions (Manning, 1963). The condensed counterions are assumed to be distributed uniformly along the molecule, whereas the unbounded ions in the solution are treated by the Debye-Huckel approximation. The remarkable feature of Manning's model is the independence of counterion condensation on the diameters of the counterions and the polyelectrolyte, as well as the universal nature of the effective charge of the polyelectrolyte above the condensation transition.

Manning's concept of counterion condensation was extended by numerous analytical investigations within mean-field and strong-coupling approximations as well as extensive Monte Carlo and molecular dynamics (MD) simulations. While these studies provided a good understanding of the effects of the counterion screening on the thermodynamic properties of polyelectrolytes, little is known about the dynamics of counterion? polyelectrolyte association and spatial and temporal variations of the counterion distribution around its backbone. Besides the fundamental interest in this problem, strong counterion- polyelectrolyte correlations drastically affect local electrostatic interactions that govern phenomena which occur at such time and length scales, like docking of small molecules to biological macromolecules, assembly of polymeric and colloidal materials, polymer-surfactant interactions, and transport in and out of cells.

Here we consider mutual approaching and parting of counterions and a meandering intrinsically flexible polyelectrolyte. In order to address the electrostatic interaction between a flexible polyelectrolyte and the counterions at both large and small length scales, our MD studies were conducted over a broad range of length scales from a few Debye lengths down to the Bjerrum length and to the ionic diameter. Such simulations require details of the charge distribution across the polyelectrolyte at the scale of the ionic diameter and properly addressing the excluded volume effects of ions and neutral solvent molecules as well as their hydrodynamic interactions. In this regard, our simulations employed a model of a flexible polyelectrolyte suspended in a solvent consisting of explicit solvent atoms, with or without added salt. Using MD simulations, we investigate dynamical clustering of such counterions while drifting together with the polyion as the degree of its ionization varies from well below to well above the condensation transition. We observe that strong electrostatic correlations cause counterions coupled with the polyelectrolyte conformation to form clusters within which they are packed with short range orientational order with respect to one another. These clusters randomly grow and shrink in length due to counterions incoming and leaving the polyelectrolyte. The motion of the counterions toward and away from the polyelectrolyte is found to be uncorrelated. Surprisingly, the peculiar trends of counterion dynamical clustering appear to be robust to changes in the degree of the polyelectrolyte ionization as well as to the field driven polyelectrolyte electrophoresis.

Our results show that ?counterion condensation" is a dynamic process in which individual ions enter and leave the vicinity of the polyelectrolyte independently and randomly on a time scale comparable to the diffusion time and that Manning's picture is correct only on the long time average. On the shorter time scale, the amount of charge in the vicinity of the molecule is wildly fluctuating. We analyzed the time fluctuations of the ions by calculating the average time correlation of the net ionic charge within the Bjerrum and the Debye layers. The electrostatic interaction between counterions and a flexible polyelectrolyte at the local level on the fast time scale is found to be closer to the classic Bjerrum model for the formation of dipole-like structures by two oppositely charged ions in simple electrolyte solutions.

Our simulations provide information on the detail arrangement of the condensed counterions along a flexible polyelectrolyte. Next we investigate the motion of the polyelectrolyte and the small ions in a constant DC electric field. From the simulation data, we extract the electrophoretic mobilities of the polyelectrolyte, the counterions and the coions. These results are compared with predictions of theories for the electrophoresis and conductivity of dilute polyelectrolyte solutions.