Size‐Dependent Phase Stability of a Molecular Nanocrystal: a Proxy for Investigating the Early Stages of Crystallization

Abstract

We make the link between the size-dependent phase stability of a nanocrystal and the phase-transition behavior of emerging crystallites during the earliest stages of crystallization, by using the former as a proxy for the latter. We outline an extension of the classical nucleation theory to describe crystal nucleation and subsequent transformations of competing polymorphic phases that characterize Ostwald's rule of stages. The theoretical framework reveals that the relative stability of the competing phases is a function of cluster size, which in turn varies with time, and therefore explains the complex transformation behavior observed for some systems. We investigated the stability of a nanocrystal of dl-norleucine by means of molecular simulation as a proxy for post-nucleation phase-transformation behavior in emerging crystallites. The simulations reveal that, for nanocrystals, the surface energy of the transition state of a transformation can dominate the barrier to phase change, thus causing metastable phases to be stabilized, not because they are thermodynamically stable, but rather due to kinetic hindering. Therefore, in the context of the earliest stages of crystal growth, not only does phase stability vary as a function of cluster size, and hence time, but thermodynamically feasible transformations are also prone to kinetic hindering.

Polymorphic phase transitions: Macroscopic theory and molecular simulation

“…For molecular crystals, mechanistic insight into martensitic-type transformations has come from simulations of phase transitions in crystals of DL-norleucine [111,[127][128][129][130] and terephthalic acid [131]. The three known forms of DL-norleucine consist of stacked, hydrogen-bonded bilayers, separated by a van der Waals surface.…”

“…The role of the surface in modulating the barriers to phase transition was recognized in simulations carried out on both bulk crystals and nanocrystals of DL-norleucine [128]. In the Phase transformations at the nanoscale are also relevant at earliest stages of crystallization [128,151], where for example a system follows Ostwalds rule of stages [152,153]…”

Do solid-to-solid polymorphic transitions indl-norleucine proceed through nucleation?

“…This continuous behaviour of the crystal properties, suggests the possibility of a transition without a clear nucleation centre which is in accordance with earlier modelling studies on this transition. [17][18][19][20] Furthermore, the recent MD simulations showed partial phase transitions from the b to the a polymorphic form, which result in an intermediate structure. 16 This discussion tries to pin down the mechanism that governs the poorly understood b 4 a transition by means of a further computational and experimental characterisation of the polymorphic forms and the solid-to-solid polymorphic transition.…”

Crystallisation in printed droplets: understanding crystallisation of d-mannitol polymorphs

“…Nonetheless, the rule is empirical and not universally followed; although there are attempts to employ it to explain the dependence of phase stability on the size of crystals. 19,20 In confinement the amount of material is limited and decreases as crystals grow. This suggests that crystallisation in confinement can be either kinetically or thermodynamically controlled.…”