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44861-AC7
Counterion Condensation and Collapse of Polyelectrolyte Chains in a Poor Solvent: Computer Simulations and Theoretical Study

Andrey V. Dobrynin, University of Connecticut

We have developed a necklace model of polyelectrolyte chain in which the necklace structure appears as a result of the counterion condensation on the polyelectrolyte backbone. This necklace structure optimizes the correlation-induced attraction of the condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges. The new feature of this necklace globule is that it can be formed even in good solvent conditions for the polymer backbone. Using the scaling analysis we have calculated the diagram of state of polyelectrolyte chain as a function of the solvent quality for the polymer backbone and value of the Bjerrum length. To test the predictions of a scaling model, we have performed molecular dynamics simulations of polyelectrolyte chains with the degrees of polymerizations N=124-304 and fraction of charged monomers f=1/3 in good, theta and poor solvent conditions for the polymer backbone. We have identified the range of parameters in which the necklace globule is formed due to correlation-induced attractive interactions in the good solvent conditions for the polymer backbone. The results of the molecular dynamics simulations are in a qualitative agreement with the predictions of a scaling model.

We performed molecular dynamics simulations of dilute and semidilute polyelectrolyte solutions without hydrodynamic interactions to study Rouse dynamics of polyelectrolytes. Polyelectrolyte solutions are modeled by an ensemble of bead-spring chains of charged Lennard-Jones particles with explicit counterions. The simulations were performed for partially and fully charged polymers with the number of monomers N=25-373. We show that the simulations of the Rouse dynamics give qualitatively similar results to the experimentally observed dynamics of polyelectrolyte solutions. Our simulations showed that the chain relaxation time depends nonmonotonically on polymer concentration. In dilute solutions this relaxation time exhibits very strong dependence on the chain degree of polymerization, tau~N^3. The chain relaxation time decreases with increasing polymer concentration of dilute solutions. This decrease in the chain relaxation time is due to chain contraction induced by counterion condensation. In the semidilute solution regime the chain relaxation time decreases with polymer concentration as c^(-1/2). In this concentration range the chain relaxation time follows the usual Rouse scaling dependence on the chain degree of polymerization, tau~N^2. At high polymer concentrations the chain relaxation time begins to increase with increasing polymer concentration. The crossover polymer concentration to the new scaling regime does not depend on the chain degree of polymerization indicating that the increase in the chain relaxation time is due to the increase of the effective monomeric friction coefficient. The analysis of the spectrum and of the relaxation times of Rouse modes confirms the existence of the single correlation length, which describes both static and dynamic properties of semidilute solutions.

Using molecular dynamics simulations in combination with scaling analysis we have studied the effects of the solvent quality and the strength of the electrostatic interactions on the conformation of spherical polyelectrolyte brushes in salt-free solutions. The spherical polyelectrolyte brush could be in a star-like spherical conformation, a “star of bundles” conformation in which polyelectrolyte chains self-assemble into clusters of pinned cylindrical micelles, a micelle-like conformation with a dense core and charged corona or could form a thin polymeric layer uniformly covering the particle surface. These different brush conformations appear as a result of the fine interplay between electrostatic and monomer-monomer interactions. The brush thickness depends nonmonotonically on the value of the Bjerrum length. This dependence of the brush thickness is due to counterion condensation inside the brush volume. We have also established that bundle formation in poor solvent condition for the polymer backbone can also occur in a planar polyelectrolyte brush. In this case the grafted polyelectrolyte chains form hemispherical aggregates at low polymer grafting densities, cylindrical aggregates at an intermediate range of the grafting densities and vertically oriented ribbon-like aggregates at high grafting densities.

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