In silico Prediction of Absolute Rates of Crystal Growth from Solution

Predicting rates of crystal growth from solution in silico remains extremely challenging, but presents a lucrative engineering opportunity to more efficiently design crystals for pharmaceutical, catalytic, and other purposes. Mechanistic crystal growth models [1-3] capture key thermodynamic and kinetic phenomena, and they have successfully predicted steady-state crystal shapes. [4,5] These models can facilitate in silico crystal growth rate predictions if rates of attachment to and detachment from kink sites are known; kinks are favorable surface sites for attachment of growth units (atoms, molecules, etc.). Complex computational techniques are currently the only approach to calculate these rates. Moreover, these methods are necessary to gain mechanistic insight to aid future development of a model to predict attachment/detachment rates.

In this work, we demonstrate that in silico predictions of absolute crystal growth rates can yield favorable agreement with experimentally measured growth rates. We examine a proof-of-concept system – NaCl in water – which provides valuable insights that will aid future investigations of organic molecules and organic salts. We compute the rates of Na⁺ and Cl^- attachment and detachment at kink sites and also elucidate the mechanistic role of water molecules during these events. [6] These rates are implemented in the mechanistic spiral growth model [7,8] to make in silico NaCl crystal growth rate predictions, which are in approximate agreement with experimental measurements. [9-11] These results promote the investigation of additional systems and, ultimately, the development of a model to predict attachment and detachment rates. It will be interesting to explore the role of rotational degrees of freedom and functional groups during kink attachment/detachment of organic molecules.

[1] J. Li, C.J. Tilbury, S.H. Kim, M.F. Doherty, Prog. Mater. Sci. 2016, 82, 1-38.

[2] M.A. Lovette, A.R. Browning, D.W. Griffin, J.P. Sizemore, R.C. Snyder, M.F. Doherty, Ind. Eng. Chem. Res. 2008, 47, 9812-9833.

[3] P. Dandekar, Z.B. Kuvadia, M.F. Doherty, Annu. Rev. Mater. Res. 2013, 43, 359-386.

[4] S.H. Kim, P. Dandekar, M.A. Lovette, M.F. Doherty, Cryst. Growth Des. 2014, 14, 2460-2467.

[5] C.J. Tilbury, D.A. Green, W.J. Marshall, M.F. Doherty, Cryst. Growth Des. 2016, 16, 2590-2604.

[6] M.N. Joswiak, M.F. Doherty, B. Peters, in prep.

[7] W.K. Burton, N. Cabrera, F.C. Frank, Phil. Trans. R. Soc. Lond. A 1951, 243, 299-358.

[8] R. Snyder, M.F. Doherty, P. Roy. Soc. A-Math. Phy. 2009, 465, 1145-1171.

[9] H. Offerman, G. von Brachel, A. Al-Sabbagh, F. Farelo, Cryst. Res. Technol. 1995, 30, 651-658.

[10] S.B. Zhang, J.J. Yuan, H.A. Mohameed, J. Ulrich, Cryst. Res. Technol. 1996, 31, 19-25.

[11] S. Al-Jibbouri, J. Ulrich, J. Cryst. Growth 2002, 234, 237-246.