23 research outputs found
Dimer percolation and jamming on simple cubic lattice
We consider site percolation of dimers (``neadles'') on simple cubic lattice.
The percolation threshold is estimated as . The jamming threshold is estimated as .Comment: 3 pages, 4 figures, submitted to EPJ
Agrégation, percolation et séparation de phase d'une assembée de sphères dures browniennes adhésives. Approche par Simulation hors réseau.
The complex fluids form a class of materials exhibiting a large originality in their static and dynamic properties which results from the chemical structure of the constituting elementary particles and their spatial organization in particular on mesoscopic scales.These systems often involve phenomena of aggregation, gelation and/or phase separation due to the interactions between their constituents.The objective of this thesis is to understand and model the formation of these structures and their way of filling the space by monitoring these processes by computer simulations. These simulations are based on off-lattice hard spheres models which can mimic for example an assembly of spherical micelles in attractive or repulsive interactions.Les fluides et systèmes complexes constituent une classe de "matériaux" au sens large dont l'originalité des propriétés statiques et dynamiques résulte à la fois de la structure chimique des particules élémentaires qui les constituent et de leur organisation dans l'espace en particulier aux échelles mésoscopiques. Ces systèmes sont souvent le lieu de phénomènes d'agrégation, de gélification et/ou de séparation de phase dus aux interactions entre les entités constituantes. Les structures complexes ainsi formées peuvent s'étendre sur des échelles allant du nanomètre au macroscopique et sont parfois transitoires ou réversibles ce qui génère l'apparition de propriétés rhéologiques remarquables.Si les systèmes présentent une grande diversité au niveau des interactions responsables des structures et au niveau de leur énergie (polymères associatifs, systèmes hétérogènes nanophasés, mélanges de colloïdes et de polymères, gels chimiques et physiques, biopolymères), au-delà des spécificités propres à chaque système nous sommes particulièrement intéressés par la recherche de lois de comportements "universelles" résultant de l'organisation spatiale des structures.L'objectif de cette thèse est de comprendre la formation de ces structures et leur façon de remplir l'espace par modélisation des processus à l'aide de la simulation numérique. Le modèle numérique est base sur un système de sphères dures hors réseau qui modélise par exemple un ensemble de micelles sphériques en interaction (attraction, répulsion).La première étape consiste à distribuer les sphères dures dans une boite cubique puis à les animer d'un mouvement brownien afin d'aboutir à un système parfaitement bien équilibré. L'introduction de paramètres décrivant la portée et l'intensité des forces attractives entre les sphères permet une étude "statique" de la transition sol-gel.Les phénomènes d'agrégation irréversible limitée par la diffusion (DLCA) conduisent à des structures fractales qui sont modélisées par l'intermédiaire d'une probabilité de collage entre amas égale à 1 (deux amas qui se rencontrent se collent toujours de façon irréversible). Les résultats obtenus, temps de gel, dimension fractale sont analysés et comparés avec d'autres modèles, notamment sur réseau. La modélisation hors réseau permet une étude à toutes les échelles spatiales (y compris locales).Une autre partie de ce travail a porté sur l'étude des phénomènes d'agrégation réversible. La ligne de percolation de notre modèle est comparée à celle obtenue dans l'approximation de Percus-Yevick avec les relations de fermeture de Ornstein-Zernike. La séparation de phase est clairement observée dans une certaine gamme d'interaction (distance et force) et comparée par l'intermédiaire du paramètre d'adhésivité (tau^-1) aux résultats expérimentaux et théoriques
Influence of the Brownian step size in off-lattice Monte Carlo simulations of irreversible particle aggregation
Depletion from a hard wall induced by aggregation and gelation
Diffusion-limited cluster aggregation and gelation of hard spheres is simulated using off-lattice Monte Carlo simulations. A comparison is made of the wall-particle correlation function with the particle-particle correlation function over a range of volume fractions, both for the initial system of randomly distributed spheres and for the final gel state. For randomly distributed spheres the correlation functions are compared with theoretical results using the Ornstein-Zernike equation and the Percus-Yevick closure. At high volume fractions (φ > 40%) gelation has little influence on the correlation function, but for φ < 10% it is a universal function of the distance normalized by correlation length (ξ) of the bulk. The width of the depletion layer is about 0.5ξ. The concentration increases as a power law from the wall up to r ≈ ξ, where it reaches a weak maximum before decreasing to the bulk value
Influence of the Brownian step size in off-lattice Monte Carlo simulations of irreversible particle aggregation
The influence of the Brownian step size in off-lattice Monte Carlo simulations of the aggregation and gelation of spheres is studied. It is found that the kinetics are strongly influenced if the step size is larger than the mean smallest distance between the sphere surfaces. The structure of the clusters and the gels is influenced, but only over length scales smaller than the step size. Using large step sizes leads to a narrower size distribution of the clusters. Implications of the present results are discussed for simulations reported in the literature in which the Brownian step size was chosen equal to the sphere diameter
3d Monte Carlo simulation of site-bond continuum percolation of spheres
We present off-lattice Monte Carlo simulations of
site-bond percolation of semi-penetrable spheres or, equivalently,
of hard spheres with a finite bond range. We will show that the
crucial parameter is the effective volume fraction (),
i.e. the volume that is occupied or within the bond range of at
least one particle. For the equivalent system of semi-penetrable
spheres is the porosity. The bond percolation threshold
() can be described in terms of by a simple
analytical expression:
, with
independent of the bond range and a
constant that decreases with increasing bond range
Monte Carlo simulation of particle aggregation and gelation: II. Pair correlation function and structure factor
Diffusion-limited cluster aggregation and gelation are studied using lattice and off-lattice Monte Carlo simulations. The pair correlation function g(r) and the structure factor S(q) of the particle gels were investigated as a function of the volume fraction (0.5\mbox{--}49\%) and time. At volume fractions below , the gel structure is fractal on small length scales with . g(r) shows a weak minimum at the correlation length (), before reaching the average concentration at large length scales. The cut-off function of g(r) varies during the aggregation process, but at a given , where is the gel time, it is a universal function of . At high volume fractions, the structure is dominated by excluded-volume interactions, while at low volume fractions, it is determined by the connectivity
Monte Carlo simulation of particle aggregation and gelation: I. Growth, structure and size distribution of the clusters
Lattice and off-lattice Monte Carlo simulations of diffusion-limited cluster aggregation and gelation were done over a broad range of concentrations. The large-scale structure and the size distribution of the clusters are characterized by a crossover at a characteristic size (). For , they are the same as obtained in a dilute DLCA process and for they are the same as obtained in a static percolation process. is determined by the overlap of the clusters and decreases with increasing particle concentration. The growth rate of large clusters is a universal function of time reduced by the gel time. The large-scale structural and temporal properties are the same for lattice and off-lattice simulations. The average degree of connectivity per particle in the gels formed in off-lattice simulations is independent of the concentration, but its distribution depends on the concentration