Multiscale modelling of crystal growth
The growth of crystalline materials is of fundamental importance to both industry and scientists. As an example, to administer a drug orally requires a well-characterised solid, crystalline form of the drug for inclusion in a tablet. Industrial chemists would like to be able to control the size and morphology of the crystals to make the manufacturing process as cheap and efficient as possible. While growth rates and crystal habits can be measured and modelled by macroscale techniques, their prediction is much harder.
The difficulty in predicting crystal-growth behaviour lies in the fact that the growth actually occurs on the molecular level. Molecular-dynamics (MD) simulations can probe such behaviour but they are limited to such small time and size scales (nanoseconds and nanometres) that they are not capable of giving information directly relevant for macroscale growth models. To overcome this limitation we are coupling MD to the kinetic Monte Carlo (kMC) method following the work of Piana et al. (Nature, 2005, 438, 70-73). Instead of simulating individual atoms, kMC considers growth units (molecules) and evolves 2-D or 3-D models of the crystal based on transition probabilities determined using MD simulations. As we simulation only processes relevant to crystal growth, the kMC method can access much longer timescales (micrometres and microseconds) predicting growth rates on a scale relevant for continuum modelling.
Our current work focuses on applying this approach to a model system of Lennard-Jones (LJ) particles. Such a system will permit us to develop a robust method for extracting transition probabilities from the MD simulation. Pictured above is a snapshot of an MD simulation of a slab of solid-like LJ particles (in green) in an FCC lattice, with two (100) faces exposed to a solution of solid- and liquid-like LJ particles (in white), with a total of ~40,000 particles in the periodic simulation cell. Following the dynamic behaviour of the system we can see solid-like particles attach and detach from the FCC lattice over time. The rates at which these processes occur can be then used by the kMC method to study a system much larger than MD method is capable of simulating. Comparison of the kMC results with the MD results, as well as hydrodynamic models, will allow us to assess the coupling of the MD and kMC methods.
We have already studied the interfacial properties of the (110) face of ?-glycine in contact with water using MD simulations. Once we have validated the MD+kMC concept and developed our analysis procedure, we anticipate studying the crystal growth of some organic molecules that are relevant to the food and pharmaceutical industries.
S. Banerjee & H. Briesen, “Molecular dynamics simulations of glycine crystal-solution interface” The Journal of Chemical Physics, 2009, 131, 184705.
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Research funded by:
Dr. rer. nat Ekaterina Elts