(749d) The Role of Interaction Heterogeneity in Colloidal Crystallization

Heterogeneity in a population of particles is generally considered to be a detrimental factor for the self-assembly of ordered structures. While this is well-established for certain types of heterogeneity such as size polydispersity, here we show, using a combination of equilibrium and non-equilibrium simulations, that heterogeneity in the pairwise interaction strength among a collection of particles may in fact be useful for nucleation of crystalline phases. In particular, we consider interaction heterogeneities that may arise, for example, from particle-to-particle variations in the density of DNA oligomer brushes grafted on the surface of micron-scale spherical particles. In this setting, it is now well-known that the multivalent nature of DNA-mediated particle binding introduces constraints for assembly by increasing the temperature dependence of the resultant interparticle potential and consequently narrowing the operating window for high quality crystallization. For a given areal density of DNA strands, this effect becomes particularly pronounced for larger particles and represents a key challenge for DNA-driven assembly of micron-scale particles.

The beneficial impact of population-wide interaction heterogeneity is shown to arise from a synergistic combination of two effects. First, we employ equilibrium umbrella sampling simulations to show that heterogeneity lowers the free energy barrier associated with the nucleation of crystals by the formation of strongly-bound small clusters, even if the overall average binding energy between pairs of particles is held constant. This finding is confirmed by direct, non-equilibrium crystal growth simulations, which demonstrate that crystallization proceeds over a wider range of average interaction energy. On the other hand, these simulations also show that variations in the interaction strength between particles inhibit gelation and polycrystallinity by keeping the number of stable nuclei low, allowing individual nuclei to grow unhindered. In combination, these effects lead to a ‘spreading-out’ of the nucleation process and a concomitant widening of the crystallization window. These results are used to investigate potential avenues for intentionally controlling the nucleation rate in colloidal crystallization experiments.