Three-dimensional kinetic Monte Carlo simulation of crystal growth from solution

Abstract

The growth of urea crystals from water and methanol solutions has been studied with kinetic Monte Carlo simulations. Parameters for the simulations were derived from atomistic molecular dynamics simulations of the growth and dissolution of urea from water and methanol solutions. This approach allows the effect of solvation on the growth and dissolution kinetics to be fully included while extending the size of the simulation to the micrometre length scale and millisecond timescale. r

In Silico Prediction of Growth and Dissolution Rates for Organic Molecular Crystals: A Multiscale Approach

“…Most investigations of crystallization processes using MD consider the distinct faces of the crystal in contact with the solvent [11,12,[14][15][16]33,35,[96][97][98]. However, time scales accessible in regular MD simulation are often not sufficient to resolve dissolution from the perfectly flat interfaces.…”

“…In order to calculate a reliable rate for a transition event, this event should occur at least a few times during the MD simulation [35]. A too small number of events of a certain type would lead to zero or almost zero rates.…”

“…Thus, the definition of a minimal set of distinct states and the estimation of corresponding transition rates are the main challenges for kMC simulations. Many kMC studies consider states on the basis of their nearest-neighbor coordination [33,34] or next-nearest-neighbor coordination [11,35]. Alternatively, the problem of state definition can be solved by identifying the most significant factors defining site reactivity with the help of electronic structure calculations and MD simulations for selected sites on the crystal surface [36].…”

“…Different approaches based on MD [11,20,[33][34][35], accelerated MD [31,37], ab initio MD [38] or even DFT techniques [39] have been reported to determine rate constants, though the last three imply significant computational effort making them less attractive for systems with a high number of potential transitions, as well as for systems consisting of complex molecules with a high internal degree of freedom [40]. Significant steps toward the multiscale modeling of crystallization have been presented in studies conducted by Piana and co-workers [11,33,35], who first combined MD and kMC approaches to investigate the growth of a urea crystal from solution. Their simulations successfully predicted the different crystal morphologies of urea in solutions of methanol and water.…”

“…These steps were completely omitted in our previous studies; however, in Section 2, we give a short survey of the actual state of knowledge and techniques in this field. The third step involves MD simulations to take into account molecular-level processes and to obtain process rate constants for kMC simulations, as was initially proposed by Piana et al [11,33,35]. In comparison to Piana et al, we consider the three-dimensional crystal model in MD simulations, enabling dissolution to be seen on MD time scales even for highly hydrophobic and poorly water-soluble pharmaceutical ingredients.…”