Nucleation in a Potts lattice gas model of crystallization from solution

Abstract

Nucleation from solution is important in many pharmaceutical crystallization, biomineralization, material synthesis, and self-assembly processes. Simulation methodology has progressed rapidly for studies of nucleation in pure component and implicit solvent systems; however little progress has been made in the simulation of explicit solvent systems. The impasse stems from the inability of rare events simulation methodology to be combined with simulation techniques which maintain a constant chemical potential driving force (supersaturation) for nucleation. We present a Potts lattice gas (PLG) to aid in the development of new simulation strategies for nucleation from solution. The PLG captures common crystallization phase diagram features such as a eutectic point and solute/solvent melting points. Simulations of the PLG below the bulk solute melting temperature reveal a competition between amorphous and crystalline nuclei. As the temperature is increased toward the bulk melting temperature, the nucleation pathway changes from a one step crystalline nucleation pathway to a two step pathway, where an amorphous nucleus forms and then crystallizes. We explain these results in terms of classical nucleation theory with different size-dependant chemical potentials for the amorphous and crystalline nucleation pathways. The two step pathway may be particularly important when crystallization is favored only at postcritical sizes.

Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

“…However, most real components, from proteins to ions [17] to the wide variety of recently synthesized nanoparticles [8,9], interact via anisotropic or "patchy" attractions. Simulation work [18][19][20][21][22] reveals assembly pathways of such components to be in general richer than those of their isotropic counterparts. Experimental realization of such systems is growing.…”

Reaction coordinates, one-dimensional Smoluchowski equations, and a test for dynamical self-consistency

“…For example, in crystal nucleation from a supersaturated solution there is currently no proper way to control the supersaturation along a transition path without disrupting the dynamics for solute insertions or solvent-solute swaps. 56 In other cases, for example, in methane hydrate nucleation, 57 the transition paths are prohibitively long for transition path sampling simulations. Therefore, it would be useful to identify optimal reaction coordinates using only short time dynamics, and not fulllength transition paths.…”

Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways

“…16,27 We study a three component system of anisotropic particles on a cubic lattice, where each particle i is characterised by species s i ∈ {1, 2, 3} and orientation q i ∈ {1, . .…”

“…[12][13][14] However, the expense of detailed atomistic models and the low solubility of CaCO 3 prohibit modelling of the entire multi-stage process. More quantitative studies of multi-stage processes [15][16][17] are possible using simple lattice models. In common with biomineral nucleation, these show existence of amorphous precursors to the assembly of anisotropic particles.…”

“…Lattice models remain a useful tool in nucleation theory, yielding insights into nonclassical phenomena, [15][16][17] multistep pathways, 18,19 heterogeneous nucleation, 20,21 and limitations of calculation methodology. 22,23 In the following contribution, we present a lattice model of nucleation from solution, where the solute may form disordered, ordered, or semi-ordered solids.…”