(272d) A Monte Carlo Analysis of Crystallization Free Energy Barriers in Colloidal Systems with DNA-Mediated Interactions

Colloidal systems provide excellent opportunities for in-depth studies of crystallization with both experimental and computational approaches. In atomic systems, nucleation rates are extremely rapid and it is usually very difficult to observe dynamically the process of crystallization, whereas micron-sized hard spheres aggregate on timescales that are many orders of magnitude longer and can be followed using simple optical microscopy.

A long-standing aim of colloidal crystallization research has been the fabrication of novel or useful crystal structures that may have applications as templates for photonic band-gap structures. Several types of interaction systems have been used to control crystallization, ranging from simple hard spheres to electrostatic interactions to tunable short-range attraction wells. The latter has been realized experimentally using single-stranded DNA grafted on polystyrene micron-sized particles [1]. It was demonstrated that fully reversible crystallization at reasonable nucleation rates was possible within a narrow temperature window and DNA density. More recently, attempts at crystallization in binary ?A-B? systems in which A attracts B but A-A and B-B repel have demonstrated much longer aggregation times and more difficult crystallization.

A key feature of the DNA system is that it is tunable ? the DNA strands can be mounted on spacers of variable lengths and stiffness, the DNA density can be modified, and binding strength can be changed. Moreover, it is possible to measure the effective pair potential between microspheres [2], which can be used as input to molecular simulations. The aim of this work is to investigate, using Monte Carlo simulations, the effects of the DNA-mediated interaction potential on the nucleation barrier in both single-component and binary systems. A computational framework recently proposed by Auer and Frenkel [3] is applied in which the crystallization free energy barrier is computed using a combination of Umbrella Sampling [4] and Parallel Tempering [5]. The approach applies a bias potential to favor the nucleation of crystallites of varying sizes in each parallel tempering window, which are then used to sample the crystallization probability across the entire crystallite size window of interest. The simulations first are applied to experimentally measured potentials for single-component systems and then extended to study the influence of the A-B interaction physics in binary systems.

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