A theory of percolation in liquids

DeSimone, Tony; Demoulini, Sophia; Stratt, Richard M.

doi:10.1063/1.451615

Cited by 109 publications

(62 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, and rather surprisingly, it has been shown by means of Monte Carlo simulations that the second-virial approximation is reasonably accurate for spherical particles too, provided that the hopping distance is small relative to the particle size. 29 It is not clear why this is so but presumably this is caused by mutual cancellation of higher-order virials. It is reasonable to presume that this is also the case for platelike particles.…”

Section: Discussionmentioning

confidence: 99%

“…spheres the second-virial approximation would not be suitable either, but it turns out not to be very inaccurate if λ D, 29 possibly because of mutual cancellation of higher-order virials.…”

Section: Appendix A: Second-virial Approximationmentioning

confidence: 99%

“…The concept of the connectedness criterion is corroborated by the experimental observation that in practice the nanotubes in conducting networks do not actually touch each other; 5 our model is therefore a generalization of the so-called cherry-pit model that has earlier been used for spherical particles. 23,29 The next step is to computef + , for which it is convenient to make use of Straley's oblique coordinate system. 30 This means instead of Cartesian coordinates r we shift to one that has two axes along the orientations u and u of two test rods and the third one along the shortest line connecting them,…”

Section: Application To Carbon Nanotubesmentioning

confidence: 99%

See 2 more Smart Citations

Connectivity percolation of polydisperse anisotropic nanofillers

Otten¹,

Schoot²

2011

The Journal of Chemical Physics

127

168

View full text Add to dashboard Cite

We present a generalized connectedness percolation theory reduced to a compact form for a large class of anisotropic particle mixtures with variable degrees of connectivity. Even though allowing for an infinite number of components, we derive a compact yet exact expression for the mean cluster size of connected particles. We apply our theory to rodlike particles taken as a model for carbon nanotubes and find that the percolation threshold is sensitive to polydispersity in length, diameter, and the level of connectivity, which may explain large variations in the experimental values for the electrical percolation threshold in carbon-nanotube composites. The calculated connectedness percolation threshold depends only on a few moments of the full distribution function. If the distribution function factorizes, then the percolation threshold is raised by the presence of thicker rods, whereas it is lowered by any length polydispersity relative to the one with the same average length and diameter. We show that for a given average length, a length distribution that is strongly skewed to shorter lengths produces the lowest threshold relative to the equivalent monodisperse one. However, if the lengths and diameters of the particles are linearly correlated, polydispersity raises the percolation threshold and more so for a more skewed distribution toward smaller lengths. The effect of connectivity polydispersity is studied by considering nonadditive mixtures of conductive and insulating particles, and we present tentative predictions for the percolation threshold of graphene sheets modeled as perfectly rigid, disklike particles.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Appendix A: Second-virial Approximationmentioning

confidence: 99%

Section: Application To Carbon Nanotubesmentioning

confidence: 99%

See 1 more Smart Citation

Connectivity percolation of polydisperse anisotropic nanofillers

Otten¹,

Schoot²

2011

The Journal of Chemical Physics

127

168

View full text Add to dashboard Cite

show abstract

“…It is worth mentioning that most of the theoretical studies 19,20,21,22 on connectivity and percolation in continuum systems based on Coniglio's type equations were focused in the rather simple Stillinger's connectivity criterion. 23 This criterion states that two particles are bonded if they are separated by a distance shorter than a given connectivity distance d. In this case, d is an ad hoc parameter, which must be chosen on physical grounds.…”

Section: Introductionmentioning

confidence: 99%

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

Pugnaloni

Zarragoicoechea

Vericat

2006

The Journal of Chemical Physics

View full text Add to dashboard 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.

show abstract

“…To describe the features of the vibrational spectra of disordered media, the ideas of fractal geometry and the theory of percolation are applied effectively [10]. According to the percolation model [11], water structure at room temperature can be represented as an infinite percolation cluster containing smaller clusters, small groups of molecules, and individual molecules in its cavities.…”

Section: Introductionmentioning

confidence: 99%

Long-Term Structural Modification of Water under Microwave Irradiation: Low-Frequency Raman Spectroscopic Measurements

Yakunov

Biliy

Naumenko

2017

Advances in Optical Technologies

View full text Add to dashboard Cite

Raman scattering has been used to study the influence of 2.45 GHz microwave on the structure of water. It has been shown that treatment of the distilled water samples by electromagnetic field leads to long-term changes in the vibrational density of states. It was established that the retention time of structural changes of the water samples depends on the sample volume. The experimental results have been interpreted on the basis of the percolation model. It has been suggested that the change in the chemical composition of the water treated by microwaves can lead to a change in the structure of the percolation cluster formed by the network of hydrogen bonds. The time of the equilibrium structure recovery of the percolation cluster after termination of the microwaves depends on the cluster size and is much slower than the recovery in the chemical composition of water.

show abstract

A theory of percolation in liquids

Cited by 109 publications

References 39 publications

Connectivity percolation of polydisperse anisotropic nanofillers

Connectivity percolation of polydisperse anisotropic nanofillers

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

Long-Term Structural Modification of Water under Microwave Irradiation: Low-Frequency Raman Spectroscopic Measurements

Contact Info

Product

Resources

About