Nucleation and droplet growth from supersaturated vapor at temperatures below the triple point temperature

Abstract

In 1897 Ostwald formulated his step rule for formation of the most stable crystal state for a system with crystal polymorphism. The rule describes the irreversible way a system converts to the crystal with lowest free energy. But in fact the irreversible way a supercooled gas below the triple point temperature T tr.p. crystallizes via a liquid droplet is an example of Ostwald's step rule.The homogeneous nucleation in the supersaturated gas is not to a crystal, but to a liquid-like critical nucleus. We have for the first time performed constant energy (NVE) Molecular Dynamics (MD) of homogeneous nucleation without the use of a thermostat. The simulations of homogeneous nucleation in a Lennard-Jones system from supersaturated vapor at temperatures below T tr.p. reveals that the nucleation to a liquid-like critical nucleus is initiated by a small cold cluster [S.Toxvaerd, J. Chem. Phys. 143 154705 (2015)]. The release of latent heat at the subsequent droplet growth increases the temperature in the liquid-like droplet, which for not deep supercooling and/or low supersaturation, can exceed T tr.p. . The temperature of the liquid-like droplet increases less for a low supersaturation and remains below T tr.p. , but without a crystallization of the droplet for long times. The dissipation of the latent heat into the surrounding gas is affected by a traditional MD thermostat, with the consequence that droplet growth is different for (NVE) MD and constant temperature (NVT) MD.

Analyzing multistep homogeneous nucleation in vapor-to-solid transitions using molecular dynamics simulations

“…However, it is possible that a thermostat used in the MD simulation influences the crystallization of the particles because, through the thermostat, part of the latent heat released at crystallization is removed from the interior and the surface of the clusters [31]. To avoid unnatural heat transfer with the thermostat, we used NV E (constant energy) ensembles in our MD simulations.…”

“…Although many studies have focused on vapor-to-liquid nucleation by MD simulations [23][24][25][26][27][28][29], few have considered vapor-to-solid nucleation [30,31]. A multistep nucleation for the vapor-to-solid transition was observed in [30], but no detailed analysis of the crystallization process was conducted.…”

Free energy calculations along entropic pathways. II. Droplet nucleation in binary mixtures

“…the chemical potential or pressure. In this case, the supersaturation of the parent vapor phase is simply characterized by a given value of the pressure 35,[48][49][50][51][52][53] (or equivalently of the chemical potential) that departs from the pressure at coexistence. On the other hand, nucleation from a mixture involves a myriad of pathways arising from the larger dimension of the system, with as additional intrinsic variables, the mole fractions for each of the components [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] .…”

Free energy calculations along entropic pathways. I. Homogeneous vapor-liquid nucleation for atomic and molecular systems

“…This is the case, for instance, for vapor-liquid nucleation, a process of great interest for many applications such as for atmospheric nucleation. Possible choices of RCs are e. g. the radius of the incipient droplet or its size (in terms of numbers of atoms within the droplet) 35,[48][49][50][51][52][53] , and the analysis of the underlying pathway is generally made through the determination of the free energy barrier of nucleation and of the critical size of the nucleus beyond which spontaneous growth occurs.…”