Abstract
In a previous publication, we reported a new cell model for the equation of state of polymer melts. The equation contains external degrees of freedom explicitly as a function of molecular weight of repeating unit. In this paper, we apply the theory to 20 polymer melts and a blend melt. The linear lengths of the coarse-grained particle (CGP) of several polymers coincide with those obtained by scattering experiments. In addition, we estimated the characteristic quantity T* of the equation of state per repeating unit using van der Waals constants and the critical temperature of the repeating unit or monomer. The values, T*, agreed with those from our result per repeating unit. This result suggests the quantitative validity of our theory. We strongly suggest that our theory must be related to the conformer model by Matsuoka and the helical wormlike chain model by Yamakawa, because T* must be dependent on the chemical structure and stiffness of the polymers.
Similar content being viewed by others
Log in or create a free account to read this content
Gain free access to this article, as well as selected content from this journal and more on nature.com
or
References
M. Murakami, J. Chem. Phys., 120, 6751 (2004).
J. E. Lennard-Jones, F. R. S. and A. F. Devonshire, Proc. R. Soc. London, Ser. A, 163, 53 (1937).
J. E. Lennard-Jones, F. R. S. and A. F. Devonshire, Proc. R. Soc. London, Ser. A, 165, 1 (1938).
T. L. Hill, “Introduction to Statistical Thermodynamics,” Addison-Wesley, Reading, MA, 1962.
K. Fujisawa, T. Siomi, F. Hamada, and A. Nakajima, Polym. J., 13, 993 (1981).
S. Onogi, “Rheology for Chemist,” Kagaku Dojin, Kyoto, 1982.
A. J. Kovacs, Adv. Polym. Sci., 3, 394 (1964).
I. C. Sanchez and R. H. Lacombe, Macromolecules, 11, 1145 (1978).
I. Prigogine, “The Molecular Theory of Solutions,” North-Holland, Amsterdam, 1957.
P. J. Flory, R. A. Orvoll, and A. Vrij, J. Am. Chem. Soc., 86, 3507 (1964).
H. Eyring and J. O. Hirschfelder, J. Phys. Chem., 41, 249 (1937).
S. Glasstone, K. J. Laidler, and H. Eyring, “The Theory of Rate Processes,” McGraw-Hill, New York, N.Y., 1941.
D. Patterson, Macromolecules, 2, 672 (1969).
D. W. Van Krevelen and P. J. Hoftyzer, “Properties of Polymers,” Elsevier, Amsterdam, 1976.
R. C. Reid, J. M. Prausnitz, and B. E. Poling, “The Properties of Gases and Liquids,” McGraw-Hill, New York, N.Y., 1987.
“Handbook of Chemistry,” The Chemical Society of Japan, Maruzen, Tokyo, 1993.
T. R. McCalla, “Introduction to Numerical Methods and Fortran Programming,” John Wiley & Sons, New York, N.Y., 1967.
P. Zoller and D. Walsh, “Standard Pressure–Volume–Temperature Data for Polymers,” Technomic Publishing, Lancaster, PA, 1995.
A. Quach, P. S. Wilson, and R. Simha, J. Macromol. Sci. Phys., 9, 533 (1974).
P. A. Rodgers, J. Appl. Polym. Sci., 48, 1061 (1993).
M. Misawa, T. Kanaya, and T. Fukunaga, J. Chem. Phys., 94, 8413 (1991).
G. R. Mitchell, B. Rosi-Schwartz, and D. J. Ward, in “Self Order and Form in Polymeric Materials,” A. Keller, M. Warner, and A. H. Windle, Ed., Chapman & Hall, London, U.K., 1995, p 95.
A. Bjørnhaug, Ø. Ellefsen, and B. A. Tønnesen, J. Polym. Sci., 12, 621 (1954).
P. G. de Gennes, “Scaling Concepts in Polymer Physics,” Cornell University Press, Ithaca, N.Y., 1979.
S. Matsuoka, “Relaxation Phenomena in Polymers,” Hanser, New York, N.Y., 1992.
P. J. Flory, “Statistical Mechanics of Chain Molecules,” John Wiley & Sons, New York, N.Y., 1969.
H. Yamakawa, “Helical Wormlike Chains in Polymer Solution,” Springer, Berlin, 1997.
Rights and permissions
About this article
Cite this article
Murakami, M. Application of a New Cell Model for the Equation of State to 20 Polymer Melts and a Blend Melt. Polym J 37, 363–367 (2005). https://doi.org/10.1295/polymj.37.363
Published:
Issue date:
DOI: https://doi.org/10.1295/polymj.37.363
