Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systems

Abstract

Computer simulations are employed to obtain subcritical isotherms of small finite sized systems inside the coexistence region. For all temperatures considered, ranging from the triple point up to the critical point, the isotherms gradually developed a sequence of sharp discontinuities as the system size increased from approximately 8 to approximately 21 molecular diameters. For the smallest system sizes, and more so close to the critical point, the isotherms appeared smooth, resembling the continuous van der Waals loop obtained from extrapolation of an analytic equation of state outside the coexistence region. As the system size was increased, isotherms in the chemical potential-density plane developed first two, then four, and finally six discontinuities. Visual inspection of selected snapshots revealed that the observed discontinuities are related to structural transitions between droplets (on the vapor side) and bubbles (on the liquid side) of spherical, cylindrical, and tetragonal shapes. A capillary drop model was developed to qualitatively rationalize these observations. Analytic results were obtained and found to be in full agreement with the computer simulation results. The analysis shows that the shape of the subcritical isotherms is dictated by a single characteristic volume (or length scale), which depends on the surface tension, compressibility, and coexistence densities. For small reduced system volumes, the model predicts that a homogeneous fluid is stable across the whole coexistence region, thus explaining the continuous van der Waals isotherms observed in the simulations. When the liquid and vapor free energies are described by means of an accurate mean-field equation of state and surface tensions from simulation are employed, the capillary model is found to describe the simulated isotherms accurately, especially for large systems (i.e., larger than about 15 molecular diameters) at low temperature (lower than about 0.85 times the critical temperature). This implies that the Laplace pressure differences can be predicted for drops as small as five molecular diameters, and as few as about 500 molecules. The theoretical study also shows that the extrema or apparent spinodal points of the finite size loops are more closely related to (finite system size) bubble and dew points than to classical spinodals. Our results are of relevance to phase transitions in nanopores and show that first order corrections to nucleation energies in finite closed systems are power laws of the inverse volume.

Microcanonical Approach to the Simulation of First-Order Phase Transitions

“…Decreasing e, the droplet grows to the point that, for periodic boundary conditions, it reduces its surface energy by becoming a strip [12], see Fig. 2 (in D = 3, the droplet becomes a cylinder, then a slab [13]). At lower e the strip becomes a droplet of disordered phase.…”

Finite size effects in neutron star and nuclear matter simulations

“…The same is true for any system of particles interacting through Lennard-Jones-like potentials (i.e., short-ranged, attractive and with a hard core). Moreover, re-sults from [12] suggest that at sufficiently low but finite temperatures (namely, sub-critical), this results shoud approximately describe the behavior of the liquid phase in coexistence.…”

“…In those calculations we only considered the three traditional simple shapes: sphere, rod and slab. While those three shapes almost exhaust the possible results from simulations of large enough Lennard-Jones and NM systems [9,10,12] in cubic cells, it's not clear that these three shapes constitute a representative set of the possible results in other geometries.…”

“…In [12], the authors show both analitically and numerically that at the liquid-vapor coexistence region of a Lennard-Jones fluid, the liquid phase is shaped in a very distinct way for a given density and temperature. They assume a cubic cell under Periodic Boundary Conditions (PBC) and show that if that cell is large enough, the shapes of these pseudo-pasta are limited to one spherical drop, one cilindrical rod, one slab, one cilindrical hole or one spherical hole in the simulation cell (in order of increasing number density).…”

“…At least not for every observable. In [9,11,12], for example, grand canonical montecarlo simulations are performed for a Lennard-Jones fluid at densities that correspond to phase coexistence in the (mean field) Van der Waals approximation. The liquid phase in these simulations appears ordered in non-homogeneous structures eerily reminiscent to those observed in systems with competitive interactions.…”