In this work we develop a new theory to model self assembling mixtures of single patch colloids and colloids with spherically symmetric attractions. In the development of the theory we restrict the interactions such that there are short ranged attractions between patchy and spherically symmetric colloids, but patchy colloids do not attract patchy colloids and spherically symmetric colloids do not attract spherically symmetric colloids. This results in the temperature, density, and composition dependent reversible self assembly of the mixture into colloidal star molecules. This type of mixture has been recently synthesized by grafting of complimentary single stranded DNA [L. Feng, R. Dreyfus, R. Sha, N. C. Seeman, and P. M. Chaikin, Adv. Mater. 25(20), 2779-2783 (2013)]. As a quantitative test of the theory, we perform new monte carlo simulations to study the self assembly of these mixtures; theory and simulation are found to be in excellent agreement.

We develop a comprehensive approach to model associating fluids with small bond angles using Wertheim's perturbation theory. We show theoretically and through Monte Carlo simulations that as bond angle is varied various modes of association become dominant. The theory is shown to be in excellent agreement with Monte Carlo simulation for the prediction of the internal energy, pressure, and fractions in rings and chains, double bonded over the full range of bond angles.

We apply Wertheim's theory to develop an equation of state for one site patchy colloids where the patch can bond multiple times. We allow for the possibility of ring formation without the introduction of empirical parameters and show that for moderate patch coverage the infinite series of chain graphs is well represented by the first two terms. The theory is found to be in excellent agreement with new NVT and NPT Monte Carlo simulations. The approach described here can easily be converted to the form of a density functional theory to describe inhomogeneous patchy colloid systems.

It has been extensively demonstrated through first principles quantum mechanics calculations that water exhibits strong hydrogen bond cooperativity. Equations of state developed from statistical mechanics typically assume pairwise additivity, meaning they cannot account for these 3-body and higher cooperative effects. In this paper, we extend a second order thermodynamic perturbation theory to correct for hydrogen bond cooperativity in 4 site water. We demonstrate that the theory predicts hydrogen bonding structure consistent spectroscopy, neutron diffraction, and molecular simulation data. Finally, we implement the approach into a general equation of state for water.

In the framework of Wertheim's theory, we develop the first classical density functional theory for patchy colloids where the patch can bond more than once. To test the theory we perform new Monte Carlo simulations for the model system of patchy colloids in a planar slit pore. The theory is shown to be in excellent agreement with simulation for the density profiles and bonding fractions. It is also shown that the theory obeys the wall contact rule by accurately predicting bulk pressures from the wall contact density.