Skip to main content
Log in

Rigorous and simplified lattice-hole equations of state for calculating specific volumes of common pure polymers

  • Published:
Korean Journal of Chemical Engineering Aims and scope Submit manuscript

Abstract

Specific volumes of common pure polymers such as low- and high-density poly(ethylene), poly(n-butyl methacrylate), poly(styrene), and poly(o-methylstyrene) were calculated by the NLF and the MF-NLF equations of state, which were developed from nonrandom lattice-hole theory. Both models contain only two molecular parameters for a pure r-mer. The NLF model is based on the rigorous approximation of lattice-hole theory and thus it is somewhat complicated in practice. The MF-NLF model is based on the two-fluid approximation of the same lattice-hole theory and thus is relatively more semi-empirical than the NLF, while preserving comparable accuracy. In this work the models were comparatively applied to the calculation of the specific volumes of pure polymers, and the results obtainedto date were presented with emphasis on the practical utility of the models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Beret, S. and Prausnitz, J. M., “A Generalized van der Waals Equation for Polymers and Other Fluids”,Macromolecules,8, 878 (1975).

    Article  CAS  Google Scholar 

  • Flory, P. J., “Statistical Thermodynamics of Liquid Mixtures”,J. Am. Chem. Soc,87, 1833 (1965).

    Article  CAS  Google Scholar 

  • Guggenheim, E. A., “Mixtures”, Clarendon Press, Oxford, 1952.

    Google Scholar 

  • Hellwege, V. K.-H., Knappe, W. and Lehmann, P., “Die Isotherms Kompressibilitaet einiger amorphoer und teilkristalliner Hochpolymerer im Temperaturbereich von 20-250°C und bei Drucken bis zu 2000 kp/cm2”,Kolloid Seitschrift und Zeitschrift fiter Polymere,183, 110 (1961).

    Article  Google Scholar 

  • Kumar, S. K., Suter, U. W. and Reid, R. C., “A Statistical Mechanics-Based Lattice Model Equation of State “,Ind. Eng. Chem. Res.,26, 2532 (1987).

    Article  CAS  Google Scholar 

  • Lee, C. S. and Yoo, K. P., “Lattice Hole-based Equations of State and Their Applications to Complex Fluids”, Proc. Int. Symp. on Molec. Therm, and Molec. Simulation, January 12-15, Hosei University, Tokyo, Japan, 53 (1997).

    Google Scholar 

  • Nies, E. and Stroeks, A., “A Modified Hole Theory of Polymeric Fluids. 1. Equation of State of Pure Components”,Macromolecules,23, 4088 (1991).

    Article  Google Scholar 

  • Okada, M. and Nose, T., “Quasichemical Treatment of Hole Theory of r-Mers. I. Pure Liquids”,Polymer J.,13, 399 (1981).

    Article  CAS  Google Scholar 

  • Olabisi, O. and Simha, R., “Pressure-Volume-Temperature Studies of Amorphous and Crystallizable Polymers. I. Experimental”,Macromolecules,8, 206 (1975).

    Article  CAS  Google Scholar 

  • Panayiotou, C. and Vera, J. H., “Statistical Thermodynamics of r-Mer Fluids and Their Mixtures”,Polymer J.,14, 681 (1982).

    Article  CAS  Google Scholar 

  • Press, W. H., Teukolsky, S.A, Vetterling, W.T. and Flannery, B.P., “Numerical Recipes in Fortran-The Art of Scientific Computing”, 2nd ed., Ch. 9, Cambridge University Press, 1992.

  • Prigogine, L, Bellemans, A. and Mathot, V., “The Molecular Theory of Solutions”, North-Holland Publishing Co., Amsterdam, 1957.

    Google Scholar 

  • Quach, A and Simha, R., “Pressure-Volume-Temperature Properities and Transitions of Amorphous Polymers; Polystyrene and Poly(orthomethylstyrene)”,J. of Applied Physics,42(12), 4592 (1971).

    Article  CAS  Google Scholar 

  • Rodgers, P. A, “Pressure-Volume-Temperature Relationships for Polymeric Liquids: A Review of Equations of State and Their Characteristics Parameters for 56 Polymers”,J. of Applied Polym. Sci.,48, 1061 (1993).

    Article  CAS  Google Scholar 

  • Sanchez, I. C. and Lacombe, R. H., “An Elementary Equation of State for Polymer Liquids”,Polym. Letters Edition,15, 71 (1977).

    Article  CAS  Google Scholar 

  • Sanchez, I. C. and Lacombe, R. H., “Statistical Thermodynamics of Polymer Solutions”,Macromolecules,11(6), 1145 (1978).

    Article  CAS  Google Scholar 

  • Simha, R. and Somcynsky, T., “On the Statistical Thermodynamics of Spherical and Chain Molecular Fluids”,Macromolecules,2, 341 (1969).

    Article  Google Scholar 

  • Smirnova, N. A. and Victorov, A. I., “Thermodynamic Properties of Pure Fluids and Solutions from the Hole Group Contribution Model”,Fluid Phase Equilibria,34, 235 (1987).

    Article  CAS  Google Scholar 

  • Yoo, K.-P., Kim, H. Y. and Lee, C. S., “Unified Equation of State Based on the Lattice Fluid Theory for Phase Equilibria of Complex Mixtures. Part I. Molecular Thermodynamic Framework”,Korean J. Chem. Eng.,12(3), 277 (1995a).

    Article  CAS  Google Scholar 

  • Yoo, K.-P., Kim, H. Y. and Lee, C. S., “Unified Equation of State Based on the Lattice Fluid Theory for Phase Equilibria of Complex Mixtures. Part H. Application to Complex Mixture”,Korean J. Chem Eng.,12(3), 289 (1995b).

    Article  CAS  Google Scholar 

  • Yoo, K.-P., Shin, M. S., Yoo, S. J., You, S. S. and Lee, C. S., “A New Equation of State Based on Nonrandom TwoFluid Lattice Theory for Complex Mixtures”,Fluid Phase Equilibria,111, 175 (1995c).

    Article  CAS  Google Scholar 

  • You, S. S., Yoo, K.-P. and Lee, C. S., “Modeling of Supercritical Fluid Phase Equilibria Using a New Nonrandom Lattice Fluid Theory”,J. Supercritical Fluids,6, 69 (1993).

    Article  CAS  Google Scholar 

  • You, S. S., Yoo, K.-P. and Lee, C. S., “An Approximate Nonrandom Lattice Theory of Fluids. General Derivation and Application to Pure Fluids”,Fluid Phase Equilibria,93, 193 (1994a).

    Article  CAS  Google Scholar 

  • You, S.S., Yoo, K.-P. and Lee, C.S., “An Approximate Nonrandom Lattice Theory of Fluids. Mixtures”,Fluid Phase Equilibria,93, 215 (1994b).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ki-Pung Yoo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shin, H.Y., Yoo, KP., Lee, C.S. et al. Rigorous and simplified lattice-hole equations of state for calculating specific volumes of common pure polymers. Korean J. Chem. Eng. 15, 15–19 (1998). https://doi.org/10.1007/BF02705300

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02705300

Key words

Navigation