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45522-AC7
Self-Assembly of Charged Macromolecules: New Simulation Techniques
Electrostatic interactions are important in determining various properties in biological systems as well as in technological applications. Although the basic form of these interactions is well established, the resulting collective phenomena are much less well understood. For example, recently new theoretical explanations have been proposed for the attraction between like-charged spherical colloidal particles in the presence of multivalent counterions. This phenomenon is not predicted by mean-field theories, such as DLVO theory, which instead predict purely repulsive electrostatic interactions between like-charged colloids under all conditions. It is interesting to note that there have not been any experiments that observe like-charged attraction in bulk solution in the presence of multivalent counterions. Quantitative computational verification is lacking as well. Specifically, existing simulation studies are restricted to small colloids, as the size asymmetry between ions and colloids is a limiting factor. Furthermore, all simulation work considers colloid-ion couplings well above the predicted threshold value for effective attractions, making it impossible to verify the onset of such attractions. This is particularly important because the location of this onset may permit to arbitrate between competing theoretical descriptions.
In the first year of this proposal period, we have explored the effect of colloid charge on like-charged attraction using simulations of the primitive model. We have investigated the transition from repulsive to attractive interactions as the colloid charge is increased as well as the change of the induced interactions when the colloid charges are increased well beyond this threshold. To simulate these system we have developed a new algorithm which is able to efficiently simulate charged systems with large size ratios between the constituent particles. Conventional simulation methods are inefficient for systems of particles with large disparities in size. This is because the large particles become trapped by the smaller particles and evolve much more slowly. To overcome this we have extended the geometric cluster algorithm (GCA) to charged systems. The GCA is a rejection-free Monte Carlo method that is able to rapidly decorrelate fluid configurations in the canonical ensemble with periodic boundary conditions. With the GCA, clusters of particles are constructed based on their interaction strength. The particles in a cluster are then moved collectively and nonlocally. Although in principle any pair potential can be used, the long-ranged nature of the Coulomb potential causes the GCA to become very inefficient. The slow decay of the unscreened electrostatic potential results in the inclusion of nearly all particles in each cluster. To reduce the average cluster size, we have developed an approach in which the clusters are constructed based upon only part of the particle interactions. The cluster move is then either accepted or rejected based on the remaining part of the internal energy, which is evaluated in Fourier space, via the standard Metropolis acceptance criterion. Although this cluster method is no longer rejection-free, we have been able to demonstrate that it is still much more efficient than conventional methods for systems with a large size asymmetry.
As a concrete illustration of the capabilities of this new algorithm, we have employed it to determine the minimum required colloid charge for the occurrence of an effective attraction between colloids, as a function of colloid-counterion size ratio. Owing to the efficiency of our new approach, much larger colloid sizes could be investigated than possible previously. The results unambiguously reveal a quadratic dependence of the onset of attraction on the colloid size.
