Percolation in binary and ternary mixtures of patchy colloids

Abstract

We investigate percolation in binary and ternary mixtures of patchy colloidal particles theoretically and using Monte Carlo simulations. Each particle has three identical patches, with distinct species having different types of patch. Theoretically we assume tree-like clusters and calculate the bonding probabilities using Wertheim's first-order perturbation theory for association. For ternary mixtures we find up to eight fundamentally different percolated states. The states differ in terms of the species and pairs of species that have percolated. The strongest gel is a trigel or tricontinuous gel, in which each of the three species has percolated. The weakest gel is a mixed gel in which all of the particles have percolated, but none of the species percolates by itself. The competition between entropy of mixing and internal energy of bonding determines the stability of each state. Theoretical and simulation results are in very good agreement. The only significant difference is the temperature at the percolation threshold, which is overestimated by the theory due to the absence of closed loops in the theoretical description.

The role of sample height in the stacking diagram of colloidal mixtures under gravity

“…[31]. Theory and Monte Carlo simulations for the bulk phase behaviour are in semi-quantitative agreement with each other [32,33].…”

“…One of these indicates whether the full mixture percolates, and the other two The other four states are equilibrium percolated gels: (i) a mixed gel (M) in which the mixture percolates but none of the species percolates independently, (ii) a bicontinuous gel or bigel (B) in which the mixture and both species percolate, (iii) two gels (G i , i = 1, 2) in which the mixture and the species i percolate. See [33,34] for further details about the bulk behaviour.…”

Superadiabatic demixing in nonequilibrium colloids

“…the left hand side of Eq. (7). Here, the internal force density field arises from the interparticle interaction potential u(r N ) and is defined via the average…”

“…In equilibrium, mixing entropy can overcome strong energetic repulsion that arises due to internal interactions between the constituent particles. It is a driving mechanism, if not an antagonist, for a wide range of structuring and self-assembly phenomena [1][2][3][4][5][6][7][8][9][10][11][12] . The systems and phenomena where mixing entropy plays a crucial role cover a broad range, ranging from the fundaments of liquid state theory to specific applications.…”

“…For the liquid crystal physics displayed by anisotropic particles, mixing entropy plays a role for the isotropic-nematic-nematic phase separation for bidisperse rod-like particles 5 , and for rod-plate mixtures, where biaxiality competes with demixing 6 . Mixing entropy is relevant for percolation in binary and ternary mixtures of patchy colloids 7 , and for selectivity in spatially inhomogeneous binary fluid mixtures 8 .…”