Ginzburg-Landau theory of the liquid-solid interface and nucleation for hard spheres

Classical density functional theory, unconstrained crystallization, and polymorphic behavior

While in principle, classical density functional theory (cDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have plagued the study of the crystalline systems using the most sophisticated fundamental measure theory models. In this paper, the reasons for the difficulties are examined and it is proposed that the tensor functionals currently favored are in fact numerically unstable. By reverting to an older, more heuristic model it is shown that all of the technical difficulties are eliminated. Application to a Lennard-Jones fluid results in a demonstration of power of cDFT to describe crystallization in a highly inhomogeneous system. First, we show that droplets attached to a slightly hydrophobic wall crystallize spontaneously upon being quenched. The resulting crystallites are clearly faceted structures and are predominantly HCP structures. In contrast, droplets in a fully periodic calculational cell remain stable to lower temperatures and eventually show the same spontaneous localization of the density into "atoms" but in an amorphous structure having many of the structural characteristics of a glass. A small change of the protocol leads, at the same temperature, to the formation of crystals, this time with the fcc structure typical of bulk Lennard-Jones solids. The fcc crystals have lower free energy than the amorphous structures which in turn are more stable than the liquid droplets. It is demonstrated that as the temperature is raised, the free energy differences between the structures decrease until the solid clusters become less stable than the liquid droplets and spontaneously melt. The presence of energy barriers separating the various structures is therefore clearly demonstrated.

Direct simulations of homogeneous bubble nucleation: Agreement with classical nucleation theory and no local hot spots

We present results from direct, large-scale molecular dynamics simulations of homogeneous bubble (liquid-to-vapor) nucleation. The simulations contain half a billion Lennard-Jones atoms and cover up to 56 million time steps. The unprecedented size of the simulated volumes allows us to resolve the nucleation and growth of many bubbles per run in simple direct micro-canonical simulations while the ambient pressure and temperature remain almost perfectly constant. We find bubble nucleation rates which are lower than in most of the previous, smaller simulations. It is widely believed that classical nucleation theory (CNT) generally underestimates bubble nucleation rates by very large factors. However, our measured rates are within two orders of magnitude of CNT predictions; only at very low temperatures does CNT underestimate the nucleation rate significantly. Introducing a small, positive Tolman length leads to very good agreement at all temperatures, as found in our recent vapor-to-liquid nucleation simulations. The critical bubbles sizes derived with the nucleation theorem agree well with the CNT predictions at all temperatures. Local hot spots reported in the literature are not seen: Regions where a bubble nucleation event will occur are not above the average temperature, and no correlation of temperature fluctuations with subsequent bubble formation is seen.

Bubble nucleation in polymer–CO2 mixtures

We combine density-functional theory with the string method to calculate the minimum free energy path of bubble nucleation in two polymer–CO2 mixture systems, poly(methyl methacrylate) (PMMA)–CO2 and polystyrene (PS)–CO2. Nucleation is initiated by saturating the polymer liquid with high pressure CO2 and subsequently reducing the pressure to ambient condition. Below a critical temperature (Tc), we find that there is a discontinuous drop in the nucleation barrier as a function of increased initial CO2 pressure (P0), as a result of an underlying metastable transition from a CO2-rich-vapor phase to a CO2-rich-liquid phase. The nucleation barrier is generally higher for PS–CO2 than for PMMA–CO2 under the same temperature and pressure conditions, and both higher temperature and higher initial pressure are required to lower the nucleation barrier for PS–CO2 to experimentally relevant ranges. Classical nucleation theory completely fails to capture the structural features of the bubble nucleus and severely underestimates the nucleation barrier.

Irreducible finite-size effects in the surface free energy of NaCl crystals from crystal-nucleation data

In this Letter we report a simulation study in which we compare the solid-liquid interfacial free energy of NaCl at coexistence, gamma_{LS}, with the value that follows from the height of the homogeneous nucleation barrier. The two estimates differ by more than 100%. Smaller discrepancies are found for gamma_{LS} of hard-sphere and of Lennard-Jones particles. We consider a variety of possible causes for this discrepancy and conclude that it is due to a finite-size effect that cannot be corrected for by any simple thermodynamic procedure. By taking into account the finite-size effects of gamma_{LS} obtained in real nucleation experiments, we obtain quantitative agreement between gamma_{LS} estimated in the simulations and derived from the experiments. Our finding suggests that most published solid-liquid surface free energies derived from nucleation experiments will have to be revised.