Square-well Chain Fluids Research Articles

An analytic equation-of-state for mixture of square-well chain fluids of variable well width

An analytic perturbation theory equation of state for a mixture of freely-jointed square-well fluids of variable well width (1≤ λ≤2) is developed. The equation of state is based on second-order Barker and Henderson perturbation theory to calculate the thermodynamic properties of the reference sphere fluid, and on first-order Wertheim thermodynamic perturbation theory to account for the connectivity of spheres to form chains. A real function expression for the radial distribution function of hard spheres and a one-fluid type mixing rule are used to obtain an analytic, closed-form expression, for the Helmohltz free energy of mixtures of square-well spheres. Good results were obtained when this equation of state was used with temperature-independent parameters to correlate vapor–liquid equilibrium data of pure substances and mixtures.

Square-well chain mixture: analytic equation of state and Monte Carlo simulation data

An analytic perturbation theory equation of state developed for mixtures of freely-jointed square-well chain fluids of variable well width is tested against Monte Carlo simulation data. The equation of state is based on second-order Barker and Henderson perturbation theory to calculate the thermodynamic properties of the reference sphere fluid, and on first-order Wertheim thermodynamic perturbation theory to account for the connectivity of spheres to form chains. A real function expression for the radial distribution function of hard spheres and one-fluid type mixing rule are used to obtain an analytic, closed form expression, for the Helmholtz free energy of mixtures of square-well spheres. In order to test the theories, Monte Carlo simulations for binary mixtures of square-well chains were performed to obtain the radial distribution function at the contact point, the compressibility factor, and the configurational internal energy of these mixtures. The proposed equation of state leads to good predictions of compressibility factor of square-well chains and their mixtures when compared with the simulation data.

Application of perturbation theory to a hard-chain reference fluid: an equation of state for square-well chains

An equation of state for square-well chain fluids is developed applying the second-order perturbation theory of Barker and Henderson to a hard-chain reference fluid. The structural information required in the perturbation theory is incorporated using an expression for the radial distribution function of the reference chain fluid proposed by Chiew. The equation of state is simplified by fitting polynomials in density and simple functions of segment number to the original perturbation expressions of first-and second-order. The equation of state is extended to mixtures by applying one-fluid mixing rules and is tested against molecular simulation data of homonuclear chain molecules and mixtures from the literature.

Development of the semi-empirical equation of state for square-well chain fluid based on the Statistical Associating Fluid Theory (SAFT)

A semi-empirical equation of state for the freely jointed square-well chain fluid is developed. This equation of state is based on Wertheim’s thermodynamic perturbation theory (TPT) and the statistical associating fluid theory (SAFT). The compressibility factor and radial distribution function of square-well monomer are obtained from Monte Carlo simulations. These results are correlated using density expansion. In developing the equation of state the exact analytical expressions are adopted for the second and third virial coefficients for the compressibility factor and the first two terms of the radial distribution function, while the higher order coefficients are determined from regression using the simulation data. In the limit of infinite temperature, the present equation of state and the expression for the radial distribution function are represented by the Carnahan-Starling equation of state. This semi-empirical equation of state gives at least comparable accuracy with other empirical equation of state for the square-well monomer fluid. With the new SAFT equation of state from the accurate expressions for the monomer reference and covalent terms, we compare the prediction of the equation of state to the simulation results for the compressibility factor and radial distribution function of the square-well monomer and chain fluids. The predicted compressibility factors for square well chains are found to be in a good agreement with simulation data. The high accuracy of the present equation of state is ascribed to the fact that rigorous simulation results for the reference fluid are used, especially at low temperatures and low densities.

Equation of state for thermodynamic properties of chain fluids near-to and far-from the vapor–liquid critical region

Upon incorporation of contributions from long-wavelength density fluctuations by a renormalization-group theory, a crossover equation of state is developed for describing thermodynamic properties of chain fluids. Outside the critical region, the crossover equation of state reduces to the classical equation; inside the critical region, it gives nonclassical universal critical exponents. The crossover equation of state correctly represents phase equilibria and pVT properties of chain fluids in both regions. Good agreement is obtained upon comparisons with computer simulations for square-well chain fluids. As obtained from experimental vapor–pressure and density data, the square-well segment–segment parameters for n-alkanes from ethane to eicosane are linear functions of molecular weight. Calculated thermodynamic properties agree well with experiment for n-alkanes from methane to hexatriacontane.

Generalized Flory equations of state for copolymers modeled as square-well chain fluids

The Generalized Flory–Dimer (GFD) equation of state has been extended to fluids containing copolymers modeled as heteronuclear chains of freely-jointed tangent spheres that interact via a site–site square-well potential. Compressibility factors are obtained for block, alternating and random copolymer fluids. The GFD theory for square-well copolymers requires expressions for the insertion factors of SW monomers in SW monomer mixtures, SW dimers in SW dimer mixtures, and SW heteronuclear dumbbells in SW heteronuclear dumbbell fluids. These insertion factors are obtained using recently-derived perturbation-theory-based equations of state. The effects of variations in composition, segment size ratios, and well-depth ratios on the compressibility factor are studied. The predictions of the Generalized Flory–Dimer theory are compared to compressibility factors obtained from discontinuous canonical molecular dynamics simulation. The Generalized Flory–Dimer theory accurately predicts the compressibility factors of square-well copolymer fluids for a variety of cases including those in which the size ratio and well-depth ratio of the two components are different.

A completely analytic equation of state for the square-well chain fluid of variable well width

A completely analytic perturbation theory equation of state for the freely-jointed square-well chain fluid of variable well width (1 ≤ λ ≤ 2) is developed and tested against Monte Carlo simulation data. The equation of state is based on second-order Barker and Henderson perturbation theory to calculate the thermodynamic properties of the reference monomer fluid, and on first-order Wertheim thermodynamic perturbation theory to account for the connectivity of monomers to form chains. By using a recently developed real function expression for the radial distribution function of hard spheres in perturbation theory, we obtain analytic, closed form expressions for the Helmholtz free energy and the radial distribution function of square-well monomers of any well width. This information is used as the reference fluid in the perturbation theory of Wertheim to obtain an analytic equation of state, without adjustable parameters, that leads to good predictions of the compressibility factors and residual internal energies for 4-mer, 8-mer and 16-mer square-well fluids when compared with the simulation results. Further, very good results are obtained when this equation of state with temperature-independent parameters is used to correlate the vapor pressures and critical points of the linear alkanes from methane to n-decane.

Equation of state for the square-well chain fluid based on the dimer version of Wertheim's perturbation theory

An equation of state for the freely jointed square-well chain fluid developed using Wertheim's thermodynamic perturbation theory and incorporating structural information on the square-well dimer fluid (TPT-D) is tested against the results of the Monte Carlo (MC) simulations. The performance of Wertheim's first order thermodynamic perturbation theory (TPT1) and the TPT-D theory are evaluated using MC simulation results for the square-well monomers and square-well dimers to avoid introducing errors due to approximations in evaluating the thermodynamic properties of the reference fluids. The dimer version of Wertheim's thermodynamic perturbation theory (TPT-D) increases the accuracy of the predicted value of compressibility factor of chain fluids in all ranges of density and temperature studied. To obtain the thermodynamic properties needed, NVT MC simulations were performed for the bulk phase of the square-well monomer, and for dimer, 4-mer, 8-mer and 16-mer square-well chain fluids. These MC simulation res...

Generalized Flory equations of state for square-well chains

The hard chain Dickman–Hall generalized Flory (GF) and Honnell–Hall generalized Flory-dimer (GF-D) equations of state are extended to square-well chain fluids. The molecules are modeled as a pearl necklace of freely jointed spheres that interact via site–site square-well intermolecular potentials. Equations of state for square-well monomers and square-well dimers (required in the GF-D theory) are obtained from integral equations with a mean spherical approximation (MSA) closure. The theories are compared to Monte Carlo simulation data for the pressure of square-well 4-mers, 8-mers, and 16-mers. The GF-D theory is in excellent agreement with the simulation data; the GF theory overestimates the pressure in all cases. A closed-form equation of state for square-well chains is obtained by employing equations of state for square-well monomers and for square-well dimers using second order perturbation theory. The resulting equation is very accurate when compared to simulations, but not as accurate as when the monomer and dimer equations of state are obtained via the MSA. The effect of intramolecular attractions on the compressibility factor is investigated via Monte Carlo simulation and the GF-D theory. It is found that, for the chain lengths studied, intramolecular attractions have a very small effect on the pressure of the system.