Poly-liquid behaviors of self-associating fluids and mesoscopic aggregation in liquid solutions

Abstract: In conflict with standard notions of thermodynamics, mesoscopically-sized inclusions (``clusters'') of a solute-rich liquid have been observed in equilibrated solutions of proteins and other molecules. According to a complexation scenario proposed earlier, a steady-state ensemble of finite-sized droplets of a metastable solute-rich liquid can emerge in a solution, if the solute molecules can form transient complexes with each other and/or solute. Here we solve for the thermodynamics of an explicit model of a self-associating fluid in which particles can form transient dimers. We determine ranges of parameters where two distinct dense liquid phases, dimer-rich and monomer-rich respectively, can co-exist with each other and the solute-poor phase. We find that within a certain range of the dimer's binding strength, thermodynamic conditions for mesoscopic clusters to emerge are indeed satisfied. The location and size, respectively, of the corresponding region on the phase diagram are consistent with observation. We predict that the clusters are comprised of a metastable monomer-rich dense liquid, while the bulk solution itself contains substantial amounts of the dimer and exhibits large, pre-critical density fluctuations. Surprisingly, we find that the dense phase commonly observed during the macroscopic liquid-liquid separation should be dimer-rich, another testable prediction. The present findings provide further evidence for the complexation scenario and suggest new experimental ways to test it.