As observed in a recent special issue on the topic (see P. G. Debenedetti et al. J. Chem. Phys. 160, 100401; 2024), Gibbs' paper also offered the thermodynamic basis for the first thinking about nucleation — the basic process by which a new and more stable crystalline phase of a substance forms from a bulk liquid, for example ice forming in super-cooled water. The most widely employed theory based on Gibbs' perspective is the classical theory of nucleation. It provides a simple framework to predict the nucleation rate, that is, the number of nucleation events per unit volume per unit time. This theory makes a range of simplifying assumptions, for example, that nuclei of the new phase start out as small spherical samples, even though other geometries are possible. It also assumes that small samples have physical properties much like bulk materials, which is rarely the case.

Nevertheless, this theory has been in use for nearly a century, even though it remains challenging to test because of the profound difficulties of doing accurate experiments. To begin with, the nucleation rate for most atomic or molecular liquids at low temperatures is generally very short — on the nanosecond to picosecond scale for the pure droplet with a 1 mm diameter typically used in experiments. Any observation therefore demands extremely fast measurements of tiny metastable samples.

正如最近关于该主题的特刊中所观察到的那样（参见 PG Debenedetti 等人J. Chem. Phys. 160 , 100401; 2024），吉布斯的论文还为首次思考成核作用提供了热力学基础——成核作用的基本过程。物质的新的、更稳定的结晶相由大量液体形成，例如在过冷水中形成冰。基于吉布斯观点的最广泛应用的理论是经典成核理论。它提供了一个简单的框架来预测成核率，即单位时间内每单位体积的成核事件数。该理论做出了一系列简化假设，例如，新相的核最初是小的球形样本，尽管其他几何形状也是可能的。它还假设小样品的物理特性与散装材料非常相似，但这种情况很少发生。

尽管如此，这一理论已经使用了近一个世纪，尽管由于进行精确实验的巨大困难而对其进行测试仍然具有挑战性。首先，大多数原子或分子液体在低温下的成核速率通常非常短——对于实验中通常使用的直径为 1 毫米的纯液滴来说，成核速率为纳秒到皮秒。因此，任何观察都需要对微小的亚稳态样品进行极快速的测量。