Gaussian core model

Stillinger and Webber [200,201] have studied the phase behavior of the Gaussian core model. In this model the pair potential is given by... 

Clarke has examined the thermodynamic equation of state and the specific heat for a Lennard-Jones liquid cooled through 7 at zero pressure. He found that drops with decreasing temperature near where the selfdiffusion becomes very small. Wendt and Abraham have found that the ratio of the values of the radial distribution function at the first peak and first valley shows behavior on cooling much like that observed for the volume of real glasses (Fig. 6), with a clearly defined 7. Stillinger and Weber have studied a Gaussian core model and find a self-diffusion constant that drops essentially to zero at a finite temperature. They also find that the ratio of the first peak to the first valley in the radial distribution function showed behavior similar to that found by Wendt and Abraham" for Lennard-Jones liquids. However, the first such evidence for a nonequilibrium (i.e. kinetic) nature of the transition in a numerical simulation was obtained by Gordon et al., who observed breakaways in the equation of state and the entropy of a hard-sphere fluid similar to those in real materials. 

Fig. 4.11 Gas-liquid coexistence curves for hard spheres plus interacting polymers in a good solvent (Gaussian core model) from Monte Carlo simulation [52] data for q = 0.67 (te/t) and q = 1.05 (right) versus GFVT predictions (curves). The GFVT critical point is marked by a filled...

One of the simplest models which displays a reentrant crystal/fluid coexistence curve (in both two- and three-dimensions [93, 94]) is a gaussian core model (GCM) [108-111] in which the interaction energy between a pair of particles i and j separated by a distance ry is expressed as... 

The mean field approximation captures some essence of particle interactions (this is what sets it apart from the ideal gas model) but it neglects correlations by its assumption that each particle interacts with an unperturbed equilibrium distribution of particles. The accuracy of the mean field depends on the strength of correlations [9], Among theoretical models for which the mean field is considered exact are hard-spheres in the infinite dimension [10], Another example are particles with the pair interaction U(r) = X u Xr) taken to the limit A 0, and where the function u(r) is bounded and of finite range [11], For experimentally relevant systems A remains finite, and so the corrections to the mean field are always present and real. An example of a system regarded as weakly correlated is the Gaussian core model at room temperature. For this model and these conditions the mean field approximation is a reliable theoretical description [12]. 

Ultrasoft repulsive interactions (without the long-range Coulomb part) have been extensively studied, both for its theoretical aspects and as a description of a soft matter system. Studies reveal two distinct behaviors. Some ultrasoft potentials supports stacked configurations, where two or more particles collapse, even though no true attractive interactions come into play [51, 52]. This behavior leads to a peak in a correlation function around r = 0. To this class of potentials belongs the penetrable sphere model [53]. The Gaussian core model [54], on the other hand, represents the class of soft particles unable to support stacked configurations. 

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