Equilibrium clusters in suspensions of colloids interacting via potentials with a local minimum

Abstract

In simple colloidal suspensions, clusters are various multimers that result from colloid self-association and exist in equilibrium with monomers.There are two types of potentials that are known to produce clusters: a) potentials that result from the competition between short-range attraction and long-range repulsion and are characterized by a global minimum and a repulsive tail and b) purely repulsive potentials which have a soft shoulder. Using computer simulations, we demonstrate in this work that potentials with a local minimum and a repulsive tail, not belonging to either of the known types, are also capable of generating clusters. A detailed comparative analysis shows that the new type of cluster-forming potential serves as a bridge between the other two. The new clusters are expanded in shape and their assembly is driven by entropy, like in the purely repulsive systems but only at low density. At high density, clusters are collapsed and stabilized by energy, in common with the systems with competing attractive and repulsive interactions.

Clusters of lysozyme in aqueous solutions

“…It is easy to see that this cluster is built from two small pentamers joined together. This model of cluster organization was reported by us earlier 45 . Its key feature -the large-cluster exponent of 0.5, that corresponds to the ideal-chain statistics and implies no excluded volume interactions, can be explained by the ability of clusters to "pass through" each other via the exchange of particles mechanism.…”

“…At some density, it becomes beneficial for the particles to cross over the barrier into the local minimum instead of continuing moving uphill on the potential energy surface, see Figure 4(b), bottom row. At that point, the assembly of clusters becomes driven by the potential energy, as observed earlier 45 , while the shrinking of the average distance stops, since it leads to a higher potential energy compared to that offered by the clustering route. It follows from this analysis that the concentration at which assembly of clusters changes its mechanism should be equal to , the density at which the shifting in stops.…”

“…Consequently, the formation of clusters necessarily costs potential energy. In the analysis of a potential with a local minimum similar to that studied here 45 Second, the particles with undergo a uniform compression as they try to minimize the potential energy. This results in the shift of the average distance to the left, see Figure 4(b), middle row, just as for the model without the local minimum.…”

Attraction between Like-Charged Macroions Mediated by Specific Counterion Configurations

“…The free energy ΔF(r CC ), where r CC is the distance between the centers of the colloids, was decomposed into entropic and internal energy contributions in temperature-dependent studies. 91 Three different temperatures, 290, 300, and 310 K, were considered to test how ΔF(r CC ) varies with T. Results were averaged over four independent trajectories to obtain convergence. The resultant PMFs were fitted to the linear expression of free energy ΔF(r CC ) = ΔU(r CC ) − TΔS(r CC ), treating ΔU(r CC ) and ΔS(r CC ) as adjustable parameters.…”

Probabilistic inverse design for self-assembling materials

“…The short-ranged attractive, long-ranged repulsive (SALR) isotropic pair interaction type is frequently used in simulation studies of equilibrium cluster fluids-of broad interest due to both their interesting microstructures and the potential implications of clusters for bulk material properties, such as viscosity. [47][48][49][50][51][52][53] This class of pair potentials is believed to provide a reasonable description of charge-stabilized colloids with short-range (e.g., osmotic depletion or hydrophobic) attractions. Typical ranges for the attractive interaction are 1-10% of the particle diameter.…”