(520d) Modeling a Mixture of Two-Site Associative Fluids with Small Bond Angle: A Two-Density Formalism Approach
Predicting the thermodynamic properties and self-assembly of patchy colloids and of hydrogen bonding molecules (e.g., hydrogen fluoride and water) continues to be a challenge of statistical mechanics based theories. The most commonly applied approach is Wertheim’s perturbation theory and its extensions for associating particles. Wertheim reorganized statistical mechanics into a form where each bonding state of a molecule is represented by a separate density. If each association bond can be treated independently, this approach allows for the development of a very general equation of state for associating molecules (SAFT) with any number of association sites. However, when including steric effects within clusters this multi–density approach can become clumsy. An alternative is to treat associating molecules with multiple bonding sites in Wertheim’s two–density formalism for one site associating fluids where molecules are either bonded or unbonded with no site level information in the definition of the densities. This allows for a simpler more transparent derivation for many associating systems. Here we apply the two density approach to the case of a mixture of patchy colloids with small bond angles such that steric effects cannot be ignored. The effect of steric hindrance and also ring formation is included, and the equation of state derived for this system is bond angle dependent. In our work, the bond angle refers to the angle separating the vectors connecting the centers of the two associating sites. To verify the theory predictions, new monte carlo (MC) simulations have been performed. The theory predictions for distribution of associated chain and ring structures as a function of bond angle are in an excellent agreement with MC simulation.