Crystal nuclei in melts: a Monte Carlo simulation of a model for attractive colloids

Abstract

As a model for a suspension of hard-sphere-like colloidal particles where small non-adsorbing dissolved polymers create a depletion attraction, we introduce an effective colloid–colloid potential closely related to the Asakura–Oosawa model, but that does not have any discontinuities. In simulations, this model straightforwardly allows the calculation of the pressure from the virial formula, and the phase transition in the bulk from the liquid to crystalline solid can be accurately located from a study where a stable coexistence of a crystalline slab with a surrounding liquid phase occurs. For this model, crystalline nuclei surrounded by fluid are studied both by identifying the crystal–fluid interface on the particle level (using suitable bond orientational order parameters to distinguish the phases) and by ‘thermodynamic’ means, i.e. the latter method amounts to compute the enhancement of chemical potential and pressure relative to their coexistence values. We show that the chemical potential can be obtained from simulating thick films, where one wall with a rather long-range repulsion is present, since near this wall, the Widom particle insertion method works, exploiting the fact that the chemical potential in the system is homogeneous. Finally, the surface excess free energy of the nucleus is obtained, for a wide range of nuclei volumes. From this method, it is established that classical nucleation theory works, showing that for the present model, the anisotropy of the interface excess free energy of crystals and their resulting non-spherical shape has only a very small effect on the barrier.

Keywords:

• nucleation
• crystal-melt interface
• colloid-polymer mixtures
• finite size effects
• phase coexistence

Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under grant No's SFB-TR6/A5 and VI237/4-3. We thank the Hochleistungsrechenzentrum Stuttgart (HLRS) and the Zentrum für Datenverarbeitung Mainz for generous grants of computing time at the HERMIT and MOGON supercomputers.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Deutsche Forschungsgemeinschaft (DFG): [Grant Number SFB-TR6/A5], [Grant Number VI237/4-3]; Hochleistungsrechenzentrum Stuttgart (HLRS); Zentrum für Datenverarbeitung Mainz; Graduate School of Excellence Materials Science in Mainz.