Abstract
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.
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Abbreviations
- A:
-
Helmholtz free energy of the reference fluid
- Aassoc :
-
associating Helmholtz free energy
- Achain :
-
chain Helmholtz free energy
- Aideal :
-
Helmholtz free energy of ideal state
- A monoR :
-
Helmholtz free energy of the reference fluid
- B2, B3 :
-
second and third virial coefficients for the compressibility factor
- fa,b :
-
mayer function
- gM(σ):
-
reference fluid pair correlation function
- k:
-
Boltzmann’s constant
- m:
-
number of segments in a chain
- N:
-
number of monomers
- T, T*:
-
temperature, reduced temperature
- s:
-
number of associating sites
- Xa :
-
fraction of monomers
- YM(σ):
-
cavity correlation function evaluated at the bond length s
- ZM :
-
reference fluid compressibility factor
- ρ, ρ*:
-
total number density of monomer segments, reduced density
- ψa,b :
-
the association potential
- assoc:
-
association
- ideal:
-
ideal gas
- chain:
-
chain term
- M:
-
monomer
- *:
-
reduced units
- a, b:
-
associating sites
References
Allen, M. P. and Tildesley, D. J., “Computer Simulation of Liquids,” Clarendon Press, Oxford (1977).
Barker, J. A. and Henderson, D., “Perturbation Theory and Equation of State for Fluids: The Square-well Potential,”J. Chem. Phys.,47, 2856 (1967).
Banaszak, M., Cheiw, Y. C. and Radosz, M., “Thermodynamic Perturbation Theory: Sticky Chains and Square-well Chains,”Phys. Rev. E,48, 3760 (1993).
Carnahan, N. F. and Starling, K. E., “Equation of State for Nonattracting Rigid Spheres,”J. Chem. Phys.,51, 635 (1969).
Chang, J. and Sandler, S. I., “An Equation of State for the Hardsphere Chain Fluid: Theory and Monte Carlo Simulation,”Chem. Eng. Sci.,49, 2777 (1994).
Chang, J. and Sandler, S. I., “The Wertheim Integral Equation Theory with the Ideal Chain Approximation and a Dimer Equation of State: Generalization to Mixtures of Hard-sphere Chain Fluids,”J. Chem. Phys.,103, 3196 (1995).
Chapman, W. G., “Prediction of the Thermodynamic Properties of Associating Lennard-Jones Fluids: Theory and Simulation,”J. Chem. Phys.,93, 4299 (1990).
Dickman, R. and Hall, C. K., “Equation of State for Chain Molecules: Continuous-space Analogy of Flory Theory,”J. Chem. Phys.,85, 4108 (1986).
Dickman, R. and Hall, C. K., “High Density Monte Carlo Simulations of Chain Molecules: Bulk Equation of State and Density Profile Near Walls,”J. Chem. Phys.,89, 3168 (1998).
Ghonasgi, D. and Chapman, W. G., “A New Equation of State for Hard Chain Molecules,”J. Chem. Phys.,100, 6633 (1994).
Honnell, K. G., Hall, C. K. and Dickman, R., “On the Pressure Equation for Chain Molecules,”J. Chem. Phys.,87, 664 (1987).
Honnell, K. G. and Hall, C. K., “A New Equation of State for Athermal Chains,”J. Chem. Phys.,90, 1841 (1989).
Tavares, F.W., Chang, J. and Sandler, S. I., “Equation of State for the Square-well Chain Fluid Based on the Dimer Version of Wertheim’s Perturbation Theory,”Molecular Phys.,86, 1451 (1995).
Wertheim, M. S., “Fluids with Highly Directional Attractive Forces. I. Statistical Thermodynamics,”J. Stat. Phys.,35, 19 (1984a).
Wertheim, M. S., “Fluids with Highly Directional Attractive Forces. II. Thermodynamic Perturbation Theory and Integral Equations,”J. Stat. Phys.,35, 35 (1984b).
Wertheim, M. S., “Fluids with Highly Directional Attractive Forces. III. Multiple Attraction Forces,”J. Stat. Phys.,42, 459 (1986a).
Wertheim, M. S., “Fluids with Highly Directional Attractive Forces. IV. Equilibrium Polymerization,”J. Stat. Phys.,42, 477 (1986b).
Yethiraj, A. and Hall, C. K., “Generalized Flory Equations of State for Square-well Chains,”J. Chem. Phys.,95, 8494 (1991).
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Yeom, M.S., Chang, J. & Kim, H. Development of the semi-empirical equation of state for square-well chain fluid based on the Statistical Associating Fluid Theory (SAFT). Korean J. Chem. Eng. 17, 52–57 (2000). https://doi.org/10.1007/BF02789253
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DOI: https://doi.org/10.1007/BF02789253