A system of patchy colloidal particles interacting with a solute that can associate multiple times in any direction is a useful model for patchy colloidal mixtures. Despite the simplicity of the interaction, predicting the thermodynamics of such systems remains a challenge because of the presence of multi-body correlations. Earlier Marshall and Chapman1
developed a perturbation theory to describe the thermodynamics of this system. Input to the theory is a multi-body cluster partition function for the reference fluid of hard-sphere solvent molecules in a defined inner-shell (or coordination volume) of the hard-sphere solute. The multi-body contribution to these partition functions are approximated with those of isolated clusters and the bulk solvent effect is obtained by superposition of pair correlation function and a three body correction. This TPT2 based approach cannot describe multi-body effects at high densities. In this work we emphasize the importance of packing effects in the reference system in determining the multi-body effects in associating mixtures. To incorporate correct multi-body cluster integrals for dense reference systems2,3
, we obtain distribution information from hard sphere simulations. We show that a partition function with accurate cluster integrals for dense reference systems better captures the distribution of solvent around the solute up to high system densities. Using this updated reference, we find that theory better describes both the bonding state and the excess chemical potential of the colloid in the physical system. Results for different association strengths and concentrations will be shown. Also, extension to different associating geometries and asymmetric mixtures of these colloids will be shown.
We establish that the complex multi-body effects in the associating mixtures of different association geometries can be accurately determined if correct reference information is used. The present approach opens avenues to model a range of systems as a mixture of patchy and spherically symmetric colloids, with completely patchy and completely spherical being the extremes. Such a system is very helpful in studying self-assembly of patchy colloids, properties of supramolecular star molecules, and also in determining ion-solvent, ion-ion interactions in electrolyte systems. This work provides an excellent theory for studies ranging from phase equilibria to study of new structures for complex systems with isotropic and anisotropic interactions.
1. Marshall, B. D. & Chapman, W. G. Thermodynamic perturbation theory for self assembling mixtures of multi-patch colloids and colloids with spherically symmetric attractions. Soft Matter 9, 11346–11356 (2013).
2. Reiss, H., Frisch, H. L. & Lebowitz, J. L. Statistical Mechanics of Rigid Spheres. J. Chem. Phys. 31, 369–380 (1959).
3. Torquato, S. & Stell, G. Microstructure of two‐phase random media. I. The n‐point probability functions. J. Chem. Phys. 77, 2071–2077 (1982).