An exponential approximation for continuum percolation in dipolar hard-sphere fluids

Self Cite

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by T.L. 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 like integral equation for a velocity-averaged version of Hill's energetic criterion.

Section: Introductionmentioning

confidence: 99%

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

Pugnaloni

Zarragoicoechea

Vericat

2006

Self Cite

“…These equations, as well as computer simulations, have been applied together with Stillinger criterion to study clustering and percolation in several continuum systems. They include: the ideal gas [15][16][17][18] ; simple hard spheres 19,20 ; hard spheres with (sticky) adhesion 15,21 ; hard spheres with square wells 22,23 ; hard spheres with Yukawa tails 24 ; charged hard spheres 25 ; Lennard-Jones fluids 26 and dipolar hard spheres [27][28][29] .…”

Section: Introductionmentioning

confidence: 99%

“…hard spheres with Yukawa tails 24 ; charged hard spheres 25 ; Lennard-Jones fluids 26 and dipolar hard spheres [27][28][29] .…”

mentioning

confidence: 99%

New criteria for cluster identification in continuum systems

Pugnaloni

Vericat

2002

Self Cite

Two new criteria, that involve the microscopic dynamics of the system, are proposed for the identification of clusters in continuum systems. The first one considers a residence time in the definition of the bond between pairs of particles, whereas the second one uses a life time in the definition of an aggregate. Because of the qualitative features of the clusters yielded by the criteria we call them chemical and physical clusters, respectively. Molecular dynamics results for a Lennard-Jones system and general connectivity theories are presented.Comment: 31 pages, 11 figures, The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at http://ojps.aip.org/jcpo

“…1,2 These theoretical methods have been employed by various workers to examine clustering and percolation behavior of a number of particulate systems including randomly centered spheres, 3 permeable spheres, 4 adhesive spheres, 4 concentric-shell spheres, 5 adhesive charged spheres, 6 and dipolar hard-spheres. 7 The basis of the integral equation approach is the concept of physical clusters. 8 In this approach, the Boltzmann factor e (12)ϵexp͓Ϫu (12)/kT͔ is separated into the connected e ϩ (12) and blocking e* (12) parts so that e (12) ϭe ϩ (12)ϩe* (12), where u(r) represents the potential of interaction between particles.…”

Section: Introductionmentioning

confidence: 99%

Connectedness-in-probability and continuum percolation of adhesive hard spheres: Integral equation theory

Chiew

1999

Integral equation theory was employed to study continuum percolation and clustering of adhesive hard spheres based on a ''connectedness-in-probability'' criterion. This differs from earlier studies in that an ''all-or-nothing'' direct connectivity criterion was used. The connectivity probability may be regarded as a ''hopping probability'' that describes excitation that passes from one particle to another in complex fluids and dispersions. The connectivity Ornstein-Zernike integral equation was solved for analytically in the Percus-Yevick approximation. Percolation transitions and mean size of particle clusters were obtained as a function of connectivity probability, stickiness parameter, and particle density. It was shown that the pair-connectedness function follows a delay-differential equation which yields analytical expressions in the Percus-Yevick theory.