Abstract
We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick-type integral equation for a velocity-averaged version of Hill's energetic criterion.
Highlights
The concepts of clustering and percolation have been widely used in order to explain several phenomena in very diverse areas including Physics, Chemistry, Biology, Geology, Sociology and Economics
The main peak in the cluster correlation functions is higher for the VA criterion than for the Hill’s criterion (HE) criterion
We can see here that the VA criterion identifies a larger amount of clusters than the HE criterion up to a certain size—which depends on the density
Summary
The concepts of clustering and percolation have been widely used in order to explain several phenomena in very diverse areas including Physics, Chemistry, Biology, Geology, Sociology and Economics. With reference to chemical–physics, phenomena such as nucleation,[1] hydrogen bonding,[2] insulator–conductor, sol–gel and glass transitions[3,4,5,6,7,8,9] as well as bridging in granular materials[10] are currently studied from this point of view. In all these cases, the system under study can be thought of as a collection of individuals (atoms, molecules, grains, etc.) that, with generality, we call particles. The concept of connectivity between the particles plays an important role
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