The barrier to ice nucleation in monatomic water

Abstract

Crystallization from a supercooled liquid initially proceeds via the formation of a small solid embryo (nucleus), which requires surmounting an activation barrier. This phenomenon is most easily studied by numerical simulation, using specialized biased-sampling techniques to overcome the limitations imposed by the rarity of nucleation events. Here, I focus on the barrier to homogeneous ice nucleation in supercooled water, as represented by the monatomic-water model, which in the bulk exhibits a complex interplay between different ice structures. I consider various protocols to identify solidlike particles on a computer, which perform well enough for the Lennard-Jones model, and compare their respective impact on the shape and height of the nucleation barrier. It turns out that the effect is stronger on the nucleus size than on the barrier height. As a by-product of the analysis, I determine the structure of the nucleation cluster, finding that the relative amount of ice phases in the cluster heavily depends on the method used for classifying solidlike particles. Moreover, the phase which is most favored during the earlier stages of crystallization may happen, depending on the nucleation coordinate adopted, to be different from the stable polymorph. Therefore, the quality of a reaction coordinate cannot be assessed simply on the basis of the barrier height obtained. I explain how this outcome is possible and why it just points out the shortcoming of collective variables appropriate to simple fluids in providing a robust method of particle classification for monatomic water.

Classical nucleation theory predicts the shape of the nucleus in homogeneous solidification

“…The R lm values that we determine by performing these integrals can be inserted into the summations in Eqn. (9) and these summations can, in turn, be inserted into Eqn. (7) to get an expression for g(θ, φ)/γ in terms of spherical harmonics.…”

“…g(θ, φ)/γ, however, is just a finite valued function of the polar angles. As such, it too can be expanded in spherical harmonics using a similar expression to (9). As shown in the Appendix, when one substitutes the expansions for g/γ and r/r in the linearized Eqn.…”

“…As shown in Eqn. (9) we can represent the shape r(θ, φ) by using an expansion in the spherical harmonics with coefficients given by Eqn. (10).…”

“…Furthermore, because these functions are linear combinations of the spherical harmonics it is straightforward to extract the final coefficients that appear in Eqn. (9) from the coefficients of the basis functions in Eqn. (14).…”

“…This approach thus takes account of material-specific information and generates atomistic insight. When this method is applied, however, a vast amount of information including all atomic coordinates is typically generated, and sophisticated data a) Electronic mail: bc509@cam.ac.uk analysis methods are therefore required to interpret the results [7][8][9] .…”