Abstract
We study a three-species analogue of the Potts lattice gas model of nucleation from solution in a regime where partially disordered solute is a viable thermodynamic phase. Using a multicanonical sampling protocol, we compute phase diagrams for the system, from which we determine a parameter regime where the partially disordered phase is metastable almost everywhere in the temperature-fugacity plane. The resulting model shows non-trivial nucleation and growth behaviour, which we examine via multidimensional free energy calculations. We consider the applicability of the model in capturing the multi-stage nucleation mechanisms of polymorphic biominerals (e.g., CaCO3). We then quantitatively explore the kinetics of nucleation in our model using the increasingly popular "seeding" method. We compare the resulting free energy barrier heights to those obtained via explicit free energy calculations over a wide range of temperatures and fugacities, carefully considering the propagation of statistical error. We find that the ability of the "seeding" method to reproduce accurate free energy barriers is dependent on the degree of supersaturation, and severely limited by the use of a nucleation driving force Δμ computed for bulk phases. We discuss possible reasons for this in terms of underlying kinetic assumptions, and those of classical nucleation theory.
Highlights
Predicting the rate at which crystalline material precipitates from a supersaturated solution remains a significant challenge to atomistic and molecular simulation due to a large disparity between the physical time scales of the process and the time scales which are accessible to computational models.1–3 To date, very few studies have computed quantitative absolute nucleation rates from such simulations.4A challenging example where nucleation kinetics remain well beyond the reach of atomistic simulation is biomineralisation
Our implementation of the method relies on constructing functions ηN1(N1) and ηE(E), which, when used as bias energies in our Metropolis acceptance criteria, allow our Monte Carlo (MC) scheme to sample uniformly in N1 and E, where N1 is the total number of solvent particles in the system
We have shown that the heights of the barriers to nucleation of the metastable phases in relation to that of the stable crystal vary with temperature, leading to a parameter regime where the free energy barriers to nucleation of all three phases are equal
Summary
Predicting the rate at which crystalline material precipitates from a supersaturated solution remains a significant challenge to atomistic and molecular simulation due to a large disparity between the physical time scales of the process and the time scales which are accessible to computational models. To date, very few studies have computed quantitative absolute nucleation rates from such simulations.. We find that the barriers to solid state transformation between the three solute phases, once nucleated, are too low to allow our model to capture the dissolution and regrowth pathway to crystallisation. Where f ss′ = exp[ β(μs′ − μs) is the ratio of fugacities of species s′ and s, β = (kBT)−1 is the inverse temperature of the system, and ∆E is the change in energy of the lattice configuration due to the proposed move. We study the phase behaviour of the system as a function of temperature kBT and fugacity ratio f in the parameter regime where μ2 = μ3 with the following interaction strengths:. A solvent rich state for low values of f
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
