Clustered fluid states and cluster percolated states formed by competing interactions are found to exist exclusively within the two phase region of the state diagram for an appropriately selected reference attractive fluid.

The fluid phase behavior of colloidal suspensions with short-range attractive interactions is studied by means of Monte Carlo computer simulations and two theoretical approximations, namely, the discrete perturbation theory and the so-called self-consistent Ornstein-Zernike approximation. The suspensions are modeled as hard-core attractive Yukawa (HCAY) and Asakura-Oosawa (AO) fluids. A detailed comparison of the liquid-vapor phase diagrams obtained through different routes is presented. We confirm Noro-Frenkel's extended law of scaling according to which the properties of a short-ranged fluid at a given temperature and density are independent of the detailed form of the interaction, but just depend on the value of the second virial coefficient. By mapping the HCAY and AO fluids onto an equivalent square-well fluid of appropriate range at the critical point we show that the critical temperature as a function of the effective range is independent of the interaction potential, i.e., all curves fall in a master curve. Our findings are corroborated with recent experimental data for lysozyme proteins.

The so-called extended law of corresponding states, as proposed by Noro and Frenkel [J. Chem. Phys. 113, 2941 (2000)], involves a mapping of the phase behaviors of systems with short-range attractive interactions. While it has already extensively been applied to various model potentials, here we test its applicability to protein solutions with their complex interactions. We successfully map their experimentally determined metastable gas–liquid binodals, as available in the literature, to the binodals of short-range square-well fluids, as determined by previous as well as new Monte Carlo simulations. This is achieved by representing the binodals as a function of the temperature scaled with the critical temperature (or as a function of the reduced second virial coefficient) and the concentration scaled by the cube of an effective particle diameter, where the scalings take into account the attractive and repulsive contributions to the interaction potential, respectively. The scaled binodals of the protein solutions coincide with simulation data of the adhesive hard-sphere fluid. Furthermore, once the repulsive contributions are taken into account by the effective particle diameter, the temperature dependence of the reduced second virial coefficients follows a master curve that corresponds to a linear temperature dependence of the depth of the square-well potential. We moreover demonstrate that, based on this approach and cloud-point measurements only, second virial coefficients can be estimated, which we show to agree with values determined by light scattering or by Derjaguin-Landau-Verwey-Overbeek (DLVO)-based calculations.

One major goal in condensed matter is identifying the physical mechanisms that lead to arrested states of matter, especially gels and glasses. The complex nature and microscopic details of each particular system are relevant. However, from both scientific and technological viewpoints, a general, consistent and unified definition is of paramount importance. Through Monte Carlo computer simulations of states identified in experiments, we demonstrate that dynamical arrest in adhesive hard-sphere dispersions is the result of rigidity percolation with coordination number $$\langle${}{n}_{b}$\rangle${}$ equal to $2.4$. This corresponds to an established mechanism leading to mechanical transitions in network-forming materials [Phys. Rev. Lett. 54, 2107 (1985)]. Our findings connect the concept of critical gel formation in colloidal suspensions with short-range attractive interactions to the universal concept of rigidity percolation. Furthermore, the bond, angular, and local distributions along the gelation line are explicitly studied in order to determine the topology of the structure at the critical gel state.

Percolation in suspensions driven only by short-ranged attractions has been studied for a long-time due to its imminent relation with equilibrium and non-equilibrium processes, such as gelation and glass transition. Recently, the effects of an additional long-range repulsion have received attention as the competition between both contributions of the potential features are shown to be important to understand the phase behavior of many charged colloidal systems, such as proteins in aqueous solutions. Due to the inherent importance of the percolation in determining the structure of a fluid and its pertinent relation with dynamical arrest, here, we use Monte Carlo computer simulations to systematically study the influence of the repulsion on the percolation. The formation and geometry of clusters when a system percolates are investigated. Our results indicate that the addition of the long-ranged repulsion increases the average cluster size, resulting in the shift of the percolation threshold to lower volume fractions. We also show that the structure of small clusters is mostly affected by the attraction, while the morphology of intermediate and large size clusters is determined by the energetic balance between attraction and repulsion.

Cluster morphology of spherical particles interacting with a short-range attraction has been extensively studied due to its relevance to many applications, such as the large-scale structure in amorphous materials, phase separation, protein aggregation, and organelle formation in cells. Although it was widely accepted that the range of the attraction solely controls the fractal dimension of clusters, recent experimental results challenged this concept by also showing the importance of the strength of attraction. Using Monte Carlo simulations, we conclusively demonstrate that it is possible to reduce the dependence of the cluster morphology to a single variable, namely, the reduced second virial coefficient, $B_2^{*}$, linking the local properties of colloidal systems to the extended law of corresponding states. Furthermore, the cluster size distribution exhibits two well-defined regimes: one identified for small clusters, whose fractal dimension, $d_f$, does not depend on the details of the attraction, i.e., small clusters have the same $d_f$, and another related to large clusters, whose morphology depends exclusively on $B_2^{*}$, i.e., $d_f$ of large aggregates follows a master curve, which is only a function of $B_2^{*}$. This physical scenario is confirmed with the reanalysis of experimental results on colloidal-polymer mixtures.