Classical nucleation theory (CNT) is based on the notion of critical nuclei serving as transition states between supersaturated solutions and growing particles. Their excess standard free energy depends on supersaturation, and determines the height of the barrier for phase separation. However, predictions of CNT nucleation rates can deviate from experimental observations by many orders of magnitude. We argue that this is due to oversimplifications within CNT, rendering the critical nucleus essentially a conceptual notion, rather than a truly existing physical entity. Still, given adequate parametrization, CNT is useful for predicting and explaining nucleation phenomena, since it is currently the only quantitative framework at hand. In the recent years, we have been introducing an alternative theory, the so-called pre-nucleation cluster (PNC) pathway. The truly “non-classical” aspect of the PNC pathway is the realization that critical nuclei, as defined within CNT, are not the key to nucleation, but that the transition state relevant for phase separation is based on a change in dynamics of PNCs rather than their size. We provide a summary of CNT and the PNC pathway, thereby highlighting this major difference. The discussion of recent works claiming to provide scientific evidence against the existence of PNCs reveals that such claims are indeed void. Moreover, we illustrate that an erroneous interpretation of the concentration dependence of the free energy has led to a postulated rationalization of the standard free energy of ion pairs and stable ion associates within CNT, which is not sustainable. In fact, stable ion associates are stuck in a free energy trap from the viewpoint of CNT and cannot be considered in a straightforward manner. On the other hand, the notions of the PNC pathway, by dismissing the idea of the CNT-type critical nucleus as a required transition state, overcome this issue. While a quantitative theory of the PNC pathway is eagerly anticipated, the rationalization of experimental observations that are inconsistent with CNT proves its qualitative explanatory power, underpinning great promise towards a better understanding of, for instance, polymorph selection and crystallization control by additives.

中文翻译：

---

关于成核的经典和非经典观点

经典成核理论 (CNT) 基于临界核作为过饱和溶液和生长粒子之间的过渡态的概念。它们的过量标准自由能取决于过饱和度，并决定了相分离势垒的高度。然而，碳纳米管成核率的预测可能与实验观察结果相差许多数量级。我们认为这是由于 CNT 内部的过度简化，使临界核本质上是一个概念概念，而不是真正存在的物理实体。尽管如此，考虑到足够的参数化，CNT 可用于预测和解释成核现象，因为它是目前唯一的定量框架。近年来，我们一直在引入另一种理论，所谓的成核前簇（PNC）途径。PNC 途径的真正“非经典”方面是认识到，在 CNT 中定义的临界核不是成核的关键，但与相分离相关的过渡态基于 PNC 动力学的变化，而不是比他们的大小。我们提供了 CNT 和 PNC 途径的摘要，从而突出了这一主要差异。对最近声称提供科学证据反对 PNC 存在的作品的讨论表明，这种说法确实是无效的。此外，我们说明对自由能浓度依赖性的错误解释导致了 CNT 内离子对和稳定离子缔合体的标准自由能的假设合理化，这是不可持续的。实际上，从 CNT 的角度来看，稳定的离子缔合物被困在自由能陷阱中，不能直接考虑。另一方面，PNC 通路的概念通过驳回将 CNT 型临界核作为所需过渡态的想法，克服了这个问题。虽然热切期待 PNC 途径的定量理论，但与 CNT 不一致的实验观察的合理化证明了它的定性解释能力，为更好地理解，例如，添加剂的多晶型选择和结晶控制提供了巨大的希望。克服这个问题。虽然热切期待 PNC 途径的定量理论，但与 CNT 不一致的实验观察的合理化证明了它的定性解释能力，为更好地理解，例如，添加剂的多晶型选择和结晶控制提供了巨大的希望。克服这个问题。虽然热切期待 PNC 途径的定量理论，但与 CNT 不一致的实验观察的合理化证明了它的定性解释能力，为更好地理解，例如，添加剂的多晶型选择和结晶控制提供了巨大的希望。