Equations of state for hard chain molecules

Energy framework approach to the supramolecular reactions: interplay of the secondary bonding interaction in Ph2E2 (E = Se, Te)/p-I-C6F4-I co-crystals

Persistent packing patterns found in pure diorgano-dichalcogenides (Ph₂E₂) and their co-crystals suggest new, energy-based visualization and description of co-crystal formation.

Equations of state for the fully flexible WCA chains in the fluid and solid phases based on Wertheims-TPT2

Based on Wertheim's second order thermodynamic perturbation theory (TPT2), equations of state (EOSs) are presented for the fluid and solid phases of tangent, freely jointed spheres. It is considered that the spheres interact with each other through the Weeks-Chandler-Anderson (WCA) potential. The developed TPT2 EOS is the sum of a monomeric reference term and a perturbation contribution due to bonding. MC NVT simulations are performed to determine the structural properties of the reference system in the reduced temperature range of 0.6 ≤ T* ≤ 4.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. Mathematical functions are fitted to the simulation results of the reference system and employed in the framework of Wertheim's theory to develop TPT2 EOSs for the fluid and solid phases. The extended EOSs are compared to the MC NPT simulation results of the compressibility factor and internal energy of the fully flexible chain systems. Simulations are performed for the WCA chain system for chain lengths of up to 15 at T* = 1.0, 1.5, 2.0, 3.0. Across all the reduced temperatures, the agreement between the results of the TPT2 EOS and MC simulations is remarkable. Overall Average Absolute Relative Percent Deviation at T* = 1.0 for the compressibility factor in the entire chain lengths we covered is 0.51 and 0.77 for the solid and fluid phases, respectively. Similar features are observed in the case of residual internal energy.

A theory for the effect of patch/non-patch attractions on the self-assembly of patchy colloids

In this paper, we develop a thermodynamic perturbation theory to describe the self-assembly of patchy colloids which exhibit both patch-patch attractions as well as patch/non-patch attractions. That is, patches attract other patches as well as the no patch region (we call this region Ψ). In general, the patch-patch and patch-Ψ attractions operate on different energy scales allowing for a competition between different modes of attraction. This competition may result in anomalous thermodynamic properties. As an application, we tune the patch parameters to reproduce the liquid density (suitably scaled) maximum of water. It is then shown that the liquid branch of the colloids phase diagram has liquid densities consistent with both saturated and super-cooled liquid water. Finally, it is shown that the colloids reproduce water's anomalous minimum in isothermal compressibility and negative volume expansivity.

Density functional theory for polymeric systems in 2D

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.

Thermodynamic perturbation theory for fused sphere hard chain fluids using nonadditive interactions

A model is developed for the equation of state of fused chains based on Wertheim thermodynamic perturbation theory and nonadditive size interactions. The model also assumes that the structure (represented by the radial distribution function) of the fused chain fluid is the same as that of the touching hard sphere chain fluid. The model is completely based on spherical additive and nonadditive size interactions. The model has the advantage of offering good agreement with simulation data while at the same time being independent of fitted parameters. The model is most accurate for short chains, small values of Delta (slightly fused spheres) and at intermediate (liquidlike) densities.