On the Formation of Equilibrium Gels via a Macroscopic Bond Limitation
  Restricting the number of attractive physical "bonds" that can form between particles in a fluid suppresses the usual demixing phase transition to very low particle concentrations, allowing for the formation of open, percolated, and homogeneous states, aptly called equilibrium or "empty" gels. Most demonstrations of this concept have directly limited the microscopic particle valence via anisotropic (patchy) attractions; however, an alternative macroscopic valence limitation would be desirable for greater experimental tunability and responsiveness. One possibility, explored in this paper, is to employ primary particles with attractions mediated via a secondary species of linking particles. In such a system, the linker-to-primary particle ratio serves as a macroscopic control parameter for the average microscopic valence. We show that the phase behavior of such a system predicted by Wertheim's first order perturbation theory is consistent with equilibrium gel formation: the primary particle concentrations corresponding to the two-phase demixing transition are significantly suppressed at both low and high linker-to-primary particle ratios. Extensive molecular dynamics simulations validate these theoretical predictions but also reveal the presence of loops of bonded particles, which are neglected in the theory. Such loops cause densification and inhibit percolation, and hence the range of viable empty gel state conditions is somewhat reduced relative to the Wertheim theory predictions. 
Beth A. Lindquist and Ryan B. Jadrich and Delia J. Milliron and Thomas   M. Truskett
cond-mat.soft