Speaker
Description
Formation of drops on impurities (condensation cores) is omnipresent in nature and can play a desirable or undesirable role in technology. The transition from vapor state to liquid state starts with the formation of a metastable thin film covering the condensation core, after which the system has to overcome an energy barrier (a critical droplet state) to steadily transform into the liquid state. Both the metastable and critical droplets are small enough to consider the number of molecules in the system as unlimited. However, the widespread approach to studying this microscopic process is molecular modeling within a closed container with a fixed number of molecules. Thus, the question arises, how does the confinement (i.e. limited number of molecules) affect obtained solutions? Besides understanding results of modeling, these effects could be used in practice for stabilizing and preventing nucleation in small containers (see [1–3] for homogeneous nucleation study).
We address this issue firstly on a macroscopic thermodynamic level of description, and then confirm the results within two versions of classical density functional theory: the square-gradient approximation with the Carnahan–Starling equation of state for hard spheres [4] and the random-phase approximation with the fundamental measure theory [5,6].
We consider formation of a droplet around a spherical solid particle immersed in vapor and investigate the number and stability of equilibrium solutions in the canonical ensemble in comparison to the grand canonical ensemble. Depending on the system’s parameters, two modes exist in the canonical ensemble: the first one with an only solution, and the second one with three solutions; the presence of the third solution is due to confinement.
In the case of a small total number of molecules, a solution breaking the spherical symmetry is observed. This sessile droplet, being stable in the canonical ensemble, corresponds to the critical droplet in the grand canonical ensemble. This notion paves the way to obtaining critical solutions as a result of minimization procedure in the canonical ensemble, instead of finding saddle points in the grand canonical ensemble. Thus, in some region of parameters, a transition to the liquid state via a non-spherical critical state is more “cost-effective” in terms of the energy barrier.
References
1. Ø. Wilhelmsen, D. Bedeaux, S. Kjelstrup, D. Reguera, J. Chem. Phys. 140, 024704 (2014).
2. Ø. Wilhelmsen, D. Bedeaux, S. Kjelstrup, D. Reguera, J. Chem. Phys. 141, 071103 (2014).
3. Ø. Wilhelmsen, D. Reguera, J. Chem. Phys. 142, 064703 (2015).
4. R. Evans R., Advances in Physics, 28, 143–200 (1979).
5. R. Roth, R. Evans, A. Lang, G. Kahl, J. Phys.: Condens. Matter 14, 12063–12078 (2002).
6. L. Gosteva, A. Shchekin, Physics of Particles and Nuclei Letters, 20 (5), 1084–1087 (2023).
