Institut für Physik, Johannes Gutenberg-Universität, D-55128 Mainz, Staudinger Weg 9, Germany.
Graduate School Materials Science in Mainz, D-55128 Mainz, Staudinger Weg 9, Germany.
Phys Rev E. 2017 Oct;96(4-1):042609. doi: 10.1103/PhysRevE.96.042609. Epub 2017 Oct 25.
Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows us to extract the surface free energy of the nucleus. Neither the knowledge of the (in general nonspherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for colloid-polymer mixtures, which form face-centered cubic colloidal crystals. For a polymer to colloid size ratio of 0.15, the colloid packing fraction in the fluid phase can be varied from melt values to zero by the variation of an effective attractive potential between the colloids. It is found that the approximation of spherical crystal nuclei often underestimates actual nucleation barriers significantly. Nucleation barriers are found to scale as ΔF^{}=(4π/3)^{1/3}γover ¯^{2/3}+const with the nucleus volume V^{}, and the effective surface tension γ[over ¯] that accounts implicitly for the nonspherical shape can be precisely estimated.
呈现并分析了在有限体积中与流体相处于热平衡的晶体核的蒙特卡罗模拟，流体密度范围从稠密熔体到蒸汽。将正则系综中两相间共存的杠杆规则推广到有限体积，通过测量核的体积以及周围流体的压力和化学势，可以提取核的表面自由能。此任务既不需要了解（通常是非球形的）核的形状，也不需要了解角度相关的界面张力。对于胶体-聚合物混合物的 Asakura-Oosawa 模型的变体，该方法的可行性得到了证明，该模型形成面心立方胶体晶体。对于聚合物与胶体的大小比为 0.15，通过胶体之间的有效吸引势的变化，可以将流体相中的胶体堆积分数从熔体值变化到零。结果发现，球形核的近似通常会大大低估实际成核势垒。发现成核势垒的标度为 ΔF^{}=(4π/3)^{1/3}γover ¯^{2/3}+const，其中 V^{}是核的体积，γ[over ¯]是隐含考虑非球形的有效表面张力，可以精确估计。
