Montero de Hijes P, Vega C
Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
J Chem Phys. 2022 Jan 7;156(1):014505. doi: 10.1063/5.0072175.
We determine, for hard spheres, the Helmholtz free energy of a liquid that contains a solid cluster as a function of the size of the solid cluster by means of the formalism of the thermodynamics of curved interfaces. This is done at the constant total number of particles, volume, and temperature. We show that under certain conditions, one may have several local minima in the free energy profile, one for the homogeneous liquid and others for the spherical, cylindrical, and planar solid clusters surrounded by liquid. The variation of the interfacial free energy with the radius of the solid cluster and the distance between equimolar and tension surfaces are inputs from simulation results of nucleation studies. This is possible because stable solid clusters in the canonical ensemble become critical in the isothermal-isobaric ensemble. At each local minimum, we find no difference in chemical potential between the phases. At local maxima, we also find equal chemical potential, albeit in this case the nucleus is unstable. Moreover, the theory allows us to describe the stable solid clusters found in simulations. Therefore, we can use it for any combination of the total number of particles, volume, and global density as long as a minimum in the Helmholtz free energy occurs. We also study under which conditions the absolute minimum in the free energy corresponds to a homogeneous liquid or to a heterogeneous system having either spherical, cylindrical, or planar geometry. This work shows that the thermodynamics of curved interfaces at equilibrium can be used to describe nucleation.
我们借助弯曲界面热力学形式，确定了硬球体系中含有固体团簇的液体的亥姆霍兹自由能，它是固体团簇尺寸的函数。这是在粒子总数、体积和温度恒定的条件下进行的。我们表明，在某些条件下，自由能分布可能存在多个局部极小值，一个对应均匀液体，其他对应被液体包围的球形、圆柱形和平面形固体团簇。界面自由能随固体团簇半径以及等摩尔面与张力面之间距离的变化，是成核研究模拟结果的输入数据。这是可行的，因为正则系综中的稳定固体团簇在等温等压系综中会变得临界。在每个局部极小值处，我们发现各相之间的化学势没有差异。在局部极大值处，我们也发现化学势相等，尽管在这种情况下核是不稳定的。此外，该理论使我们能够描述模拟中发现的稳定固体团簇。因此，只要亥姆霍兹自由能出现极小值，我们就可以将其用于粒子总数、体积和整体密度的任何组合。我们还研究了在哪些条件下自由能的绝对极小值对应均匀液体或具有球形、圆柱形或平面几何形状的非均匀体系。这项工作表明，平衡态下弯曲界面的热力学可用于描述成核过程。
