Structure of sticky-hard-sphere random aggregates: The viewpoint of contact coordination and tetrahedra

Abstract

We study more than 10^{4} random aggregates of 10^{6} monodisperse sticky hard spheres each, generated by various static algorithms. Their packing fraction varies from 0.370 up to 0.593. These aggregates are shown to be based on two types of disordered structures: random regular polytetrahedra and random aggregates, the former giving rise to δ peaks on pair distribution functions. Distortion of structural (Delaunay) tetrahedra is studied by two parameters, which show some similarities and some differences in terms of overall tendencies. Isotropy of aggregates is characterized by the nematic order parameter. The overall structure is then studied by distinguishing spheres in function of their contact coordination number (CCN). Distributions of average CCN around spheres of a given CCN value show trends that depend on packing fraction and building algorithms. The radial dependence of the average CCN turns out to be dependent upon the CCN of the central sphere and shows discontinuities that resemble those of the pair distribution function. Moreover, it is shown that structural details appear when the CCN is used as pseudochemical parameter, such as various angular distribution of bond angles, partial pair distribution functions, Ashcroft-Langreth and Bhatia-Thornton partial structure factors. These allow distinguishing aggregates with the same values of packing fraction or average tetrahedral distortion or even similar global pair distribution function, indicative of the great interest of paying attention to contact coordination numbers to study more precisely the structure of random aggregates.

Colloidal and Sedimentation Behavior of Kaolinite Suspension in Presence of Non-Ionic Polyacrylamide (PAM)

“…To explain the FB algorithm very briefly, it is a method that creates irregular tight packing from a random distribution of points. This technique is also known as the “neighbor separation algorithm” (NS) [ 69 , 70 ]. The key advantage of this method is that the diameters of the spheres can change from one step to the next depending on how the ensemble is currently arranged.…”

General theory of charge regulation within the Poisson-Boltzmann framework: Study of a sticky-charged wall model

“…The first implementation of a sticky potential is generally credited to Baxter who studied thermodynamic properties of sticky hard-spheres [1]. The adhesive interactions between spheres can give rise to clusters [6] and, as clusters grow and combine, eventually lead to phase transition. Since then, the sticky hard-sphere model has been explored by numerous groups, and today, it is considered as a good representation of colloidal gels [7][8][9].…”

“…Fig. (6) plots the surface density of adsorbed polarizable and non-polarizable counterions. As expected, based on the results in Fig.…”

Structural diversity of random aggregates of identical spheres

“…The main differences between these two kinds of aggregates that simulation reveals is a strong difference in coordination number, as it appears possibly independent of packing fraction for aggregates formed by aggregation and strongly dependent upon this parameter for aggregates formed by dynamics methods. Moreover, the maximum packing fraction that can be reached in random aggregates formed by aggregation is about 0.60 [18,29], whereas it reaches 0.64 for aggregates formed by dynamic reorganization [30] which is sometimes considered to be the maximum value that can be attained for fully random aggregates [23,30]. 1 However, geometrical properties of random aggregates are difficult to analyze in the absence of periodic properties that allow defining a primary cell typical of the structure, as is the case for ordered structures.…”

“…Hence, there is some strong interest in being able to compare more precisely the geometrical differences between random aggregates formed either dynamically or by aggregation in a systematic fashion, across a large range of packing fraction. In a previous work, we addressed aggregates formed by GA algorithms [21,29], using various characterization tools. The packing fraction of the aggregates built in these studies ranged from 0.370 up to 0.593, which is roughly the maximum packing fraction that can be reached by GA algorithms as going beyond involves long-range reorganizations [29,38].…”