Integral equation and thermodynamic perturbation theory for a two-dimensional model of chain-forming fluid

Abstract

In this paper we applied analytical theories for the two dimensional chain-forming fluid. Wertheims thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids were used to study thermodynamical and structural properties of the chain-forming model. The model has polymerizing points at arbitrary position from center of the particles. Calculated analytical results were tested against corresponding results obtained by Monte Carlo computer simulations to check the accuracy of the theories. The theories are accurate for the different positions of patches of the model at all values of the temperature and density studied. The IET's pair correlation functions of the model agree well with computer simulations. Both TPT and IET are in good agreement with the Monte Carlo values of the energy, chemical potential and ratios of free, once and twice bonded particles.

Keywords: Integral equation theory; association; chain forming fluid; thermodynamic perturbation theory.

Figure 1

The molecules of two dimensional chain forming fluid. Particles associate the strongest when arms are collinear and the distance between two particles is equal to r_a.

Figure 2

Pair correlation functions for high temperature T* = 0.3 for different densities and at associative point distance (a) r_a = 1.0 and ρ* = 0.17; (b) r_a = 1.0 and ρ* = 0.626; (c) r_a = 1.43 and ρ* = 0.188; (d) r_a = 1.43 and ρ* = 0.587;. Results from computer simulations are plotted by red solid line and from IET by green dashed line.

Figure 3

Pair correlation functions for low temperature T* = 0.2 for (a) r_a = 1.0 and ρ* = 0.177; (b) r_a = 1.0 and ρ* = 0.759; (c) r_a = 1.43 and ρ* = 0.239; (d) r_a = 1.43 and ρ* = 0.655; legend as for Figure 2. Snapshots of the system for (e) r_a = 1.0 and ρ* = 0.759 and (f) r_a = 1.43 and ρ* = 0.239. Green line connect centers of the particles that form associations.

Figure 4

Pair correlation functions for different distance of patch from center of particle for temperature T* = 0.1 and density ρ* = 0.49. Functions from bottom up (each shifted for 1) are for distances 0.714, 1.0, 1.143, 1.286, 1.429, 1.714 and 2.142.

Figure 5

Density dependence of internal energy for different temperatures and associative point distances from center (a) r_a = 1.0 and T* = 0.2; (b) r_a = 1.0 and T* = 0.3; (c) r_a = 1.43 and T* = 0.2; (d) r_a = 1.43 and T* = 0.3;. Results from computer simulations are plotted by red symbols, from IET by blue dashed line and from TPT by green long dashed line.

Figure 6

Density dependence of ratio of free particles for different temperatures and associative point distances from center for (a) r_a = 1.0 and T* = 0.2; (b) r_a = 1.0 and T* = 0.3; (c) r_a = 1.43 and T* = 0.2; (d) r_a = 1.43 and T* = 0.3. Results from computer simulations are plotted by symbols, from IET by dotted line and from TPT by solid line.

Figure 7

Density dependence of chemical potential for different temperatures and associative point distances from center (a) r_a = 1.0; (b) r_a = 1.43;. Results from computer simulations are plotted by symbols, from TPT by line. Red color is for low temperature T* = 0.2 and green for high temperature T* = 0.3.