Abstract

Void-size distributions have been calculated for the shifted-force Lennard-Jones fluid over substantial temperature and density ranges, both for the liquid-state configurations themselves, as well as for their inherent structures (local potential energy minima). The latter distribution is far more structured than the former, displaying fcc-like short-range order, and a large-void tail due to system-spanning cavities. Either void distribution can serve as the basis for constraints that retain the liquid in metastable states of superheating or stretching by eliminating configurations that contain voids beyond an adjustable cutoff size. While acceptable cutoff sizes differ substantially in the two versions, ranges of choices have been identified yielding metastable equations of state that agree between the two approaches. Our results suggest that the structure-magnifying character of configuration mapping to inherent structures may be a useful theoretical and computational tool to identify the low-temperature mechanisms through which liquids and glasses lose their mechanical strength.

Conclusions

The inherent structure formalism is a useful way of describing molecular dynamics in liquids. The properties of the liquid phase are determined by the sampling of various local potential energy minima (mechanically stable particle packings) and anharmonic thermal vibrations about these minima. Inherent structures also provide a means by which unwanted configurations can be removed from the partition function (imposition of a constraint). Here, we have studied one such constraint: the inherent-structure void-constrained ensemble. In this constrained ensemble, limits are placed on the maximum size of voids allowed to form in the inherent structures of the superheated liquid. The equation of state of the stable and superheated shifted-force Lennard-Jones liquid is extremely sensitive to the severity of the constraint. However, as long as the corresponding inherent structures contain voids in excess of five average interparticle separations, the resulting equation of state is consistent with simulation results in the void-constrained ensemble, in which voids greater than 1.5 times the average interparticle separation are not allowed to form within the instantaneous unquenched liquid. Therefore, the sampling of potential energy basins that have inherent structures containing voids greater than 5 average interparticle separations is important in determining the equilibrium properties of liquids near the triple point.

The distribution of voids within inherent structures was analyzed to determine whether there is an objective criterion to determine when the system is overconstrained. For the void-constrained ensemble, where voids are prevented from forming within the unquenched liquid, the pressure is independent of the constraint if the void distribution has a well-developed large-void tail. The void-size distribution must include a second inflection point, sampling the infrequently visited yet important large cavities, in order for the liquid to be "naturally" constrained. Within the inherent-structure void-constrained ensemble, there is no corresponding geometric criterion to determine if the liquid is overconstrained. For all severities of constraint studied, the slowly decaying large-void tail is always present; the second inflection point, a prerequisite for the development of the large-void tail, occurs at void sizes well below that of the maximum-allowed void diameter (even for the most severely constrained system).

Even at the triple-point density, the presence of large voids (in excess of five average interparticle separations) within the liquid’s inherent structures is necessary for the properties of the liquid to attain their true equilibrium values. We therefore analyzed the statistical geometry of voids in inherent structures for stable and superheated liquids at densities between the critical and triple points. The distribution of voids within inherent structures of both the stable and metastable liquids are identical; a thermodynamically stable liquid, even at its triple-point density, samples local potential-energy minima that contain very large cavities. We found that these large cavities are connected, spanning the length of the simulation cell. Hence, strictly from an energetic viewpoint, even a thermodynamically stable liquid is unstable with respect to boiling. This result has potential significance in the study of the fracture of liquids and amorphous solids at low temperatures. In order to investigate this connection, a useful starting point is to study the temperature and tension-dependent correspondence between inherent structure cavities and voids in the unquenched fluid.

The inherent structures of liquids above the triple-point temperature and below their triple-point density are separated into two distinct regions: a compact region, containing all the particles at a density higher than the mean system density, and the void region (a single, particle-free cavity, percolating throughout the system). The compact region is responsible for the bimodal distribution of voids at small void sizes, caused by the formation of distorted tetrahedra (first peak) and octahedra (second peak), found undistorted in the fcc crystal. The void region accounts for the broad shoulder in the distribution, at intermediate void sizes, and the slowly decaying large-void tail. The void-size distribution is a function of the system density and the range of the intermolecular potential. The first peak of the distribution is invariant with changes in the density and the range of the potential; the second peak and large-void tail are sensitive to changes in these variables.

The present work offers insight into the dual role of attractive forces in determining the properties of liquids and amorphous materials. Attractive forces are responsible for the cohesive strength of liquids. Yet, paradoxically, attractions are also (and solely) responsible for the existence of large voids in configurations corresponding to potential-energy minima. Clearly, mapping the range of temperature and tensions where attraction is stabilizing or destabilizing is important.

More generally, this study points to the importance of understanding and investigating the intimate relation between metastability and constraints. Simulations are the natural method for studying the effects of constraints microscopically and hence should become a basic tool in the fundamental investigation of metastability. We believe that much can be learned about the liquid state of matter under both stable and metastable conditions from this type of investigation.

[S1063-651X(97)03805-1]
PACS number(s): 61.20.Gy, 64.60.My, 64.70.Fx, 05.70.-a