Despite considerable process in predicting the structure and stability of crystalline solids, we are yet to fully understand the ways in which nucleation kinetics can be controlled to affect the precipitation of metastable polymorphs. Calculating the rates at which competing structures nucleate from solution is immensely challenging due both the time and lengthscale limitations of molecular simulation.
A variety of methods are available for circumventing such issues. These include parameterisation of classical nucleation theory (CNT) rate expressions based on molecular dynamics (MD) simulations seeded with crystalline seeds [1], calculations based on explicitly computed free energy barriers, and various path sampling approaches [2]. Many of these depend (to varying extent) on the assumption that dynamics of a nucleus size metric are well-approximated by a one-dimensional Smoluchowski equation - i.e. they are diffusive. When comparing to experiment, the effect of this and other kinetic approximations are often dwarfed by both statistical uncertainty and inaccuracy of the molecular force field.
In this work [3], we study a simple lattice model of nucleation from solution exhibiting multiple solid phases in order to probe the inherent limitations to the accuracy of these methods. The simplicity of this model allows us to calculate phase diagrams and nucleation free-energy barriers to a high degree of precision. We compare the latter to estimates produced via seeding simulations and find significant supersaturation-dependent discrepancies in the barrier height, up to a factor of two in the worst-case scenario, leading to a dramatic error in nucleation rate. Calculations of the rate using correct free energy barriers are found to be in broad agreement with partial-path transition interface sampling (PPTIS) calculations [4], but both deviate from unbiased estimates of the rate in the regime accessible to brute force computation of the mean first passage time (MFTP). Disagreement between these methods can still reach multiple orders of magnitude. We present possible explanations for this behaviour in terms of a breakdown of the diffusion approximation, and discuss the extent to which calculated nucleation rates can be considered predictive.
[1] N. E. R. Zimmermann, B Vorselaars, D. Quigley, B. Peters, Journal of the American Chemical Society 137 (41), 13352–13361 (2015)
[2] T. S. van Erp and P. G. Bolhuis, Journal of Computational Physics 205, 157–181 (2005)
[3] Y. Lifanov, B. Vorselaars and D. Quigley, Journal of Chemical Physics 145, 211912 (2016)
[4] D. Moroni and P. G. Bolhuis, Journal of Chemical Physics 120, 4055 (2004)
Advances in molecular simulation , Interfacial and confined phenomena , Non-equilibrium thermodynamics
