Application of the integral equation theory of polymers: Distribution function, chemical potential, and mean expansion coefficient

Gan, Hin Hark; Eu, Byung Chan
September 1993
Journal of Chemical Physics;9/1/1993, Vol. 99 Issue 5, p4103
Academic Journal
A recursive integral equation for the intramolecular correlation function of an isolated linear polymer of N bonds is derived from the integral equations presented in the preceding paper. The derivation basically involves limiting the density of the polymer to zero so that polymers do not interact with each other, and thus taking into account the intramolecular part only. The integral equation still has the form of a generalized Percus–Yevick integral equation. The intramolecular correlation function of a polymer of N bonds is recursively generated by means of it from those of polymers of 2, 3,..., (N-1) bonds. The end-to-end distance distribution functions are computed by using the integral equation for various chain lengths, temperatures, and bond lengths in the case of a repulsive soft-sphere potential. Numerical solutions of the recursive integral equation yield universal exponents for the mean square end-to-end distance in two and three dimensions with values which are close to the Flory results: 0.77 and 0.64 vs Flory’s values 0.75 and 0.6 for two and three dimensions, respectively. The intramolecular correlation functions computed can be fitted with displaced Gaussian forms. The N dependence of the internal chemical potential is found to saturate after some value of N depending on the ratio of the bond length to the bead radius.


Related Articles

  • Integral equation theory of polymer blends: Numerical investigation of molecular closure approximations. Yethiraj, Arun; Schweizer, Kenneth S. // Journal of Chemical Physics;6/1/1993, Vol. 98 Issue 11, p9080 

    The thermodynamics of symmetric polymer blends is investigated using the polymer reference interaction site model integral equation theory with the new molecular closures presented in the previous paper. In contrast to the atomic mean spherical approximation reported earlier by Schweizer and...

  • Polymer reference interaction site model theory: New molecular closures for phase separating fluids and alloys. Schweizer, Kenneth S.; Yethiraj, Arun // Journal of Chemical Physics;6/1/1993, Vol. 98 Issue 11, p9053 

    The polymer reference interaction site model integral equation theory when combined with known atomic-like closure approximations is shown to be qualitatively inconsistent with classical mean field predictions for both long wavelength concentration fluctuations and the molecular weight...

  • A Born–Green–Yvon equation for flexible chain-molecule fluids. II. Applications to hard-sphere polymers. Taylor, Mark P.; Lipson, J. E. G. // Journal of Chemical Physics;4/15/1995, Vol. 102 Issue 15, p6272 

    Using the method of Born, Green, and Yvon we have recently derived a coupled set of integral equations for the intermolecular site–site distribution functions which describe the microscopic equilibrium structure of a fluid of flexible chain molecules. Here, we carry out an average over...

  • A self-consistent-field integral equation theory for nonuniform polymer fluids. Woodward, C. E. // Journal of Chemical Physics;9/15/1992, Vol. 97 Issue 6, p4525 

    An integral equation theory is developed for nonuniform polymer fluids. It is based on an exact formulation of the density functional theory for polymers, which is essentially identical in form to the popular self-consistent-field approximations. A nonuniform site–site...

  • Integral equations of the correlation functions for polymeric liquids. Eu, Byung Chan; Gan, Hin Hark // Journal of Chemical Physics;9/1/1993, Vol. 99 Issue 5, p4084 

    The integral equations for intramolecular and intermolecular correlation functions are derived for nonrigid polymeric (polyatomic) liquids by the device of the Kirkwood charging parameters. These integral equations are cast into mean-field-type equations by using the potential elimination...

  • Theory of nonequilibrium effects on the conformation of polymers. Eu, Byung Chan; Gan, Hin Hark // Journal of Chemical Physics;1/1/1995, Vol. 102 Issue 1, p585 

    Two sets of integral equations are presented in this paper for dynamic pair correlation functions for polymeric liquids subjected to shearing. One set of the integral equations is a dynamic and polymeric extension of the Percus–Yevick integral equation for the equilibrium pair correlation...

  • Collapse of a polymer chain: A Born–Green–Yvon integral equation study. Taylor, Mark P.; Lipson, J. E. G. // Journal of Chemical Physics;3/22/1996, Vol. 104 Issue 12, p4835 

    A Born–Green–Yvon (BGY) type integral equation is developed for the intramolecular distribution functions of an isolated flexible polymer chain. The polymer is modeled as a linear array of n identical spherical interaction sites connected by universal joints of bond length σ. In...

  • Conformation of a polymer chain near the solvent critical region. I. The integral equation theory. Vasilevskaya, Valentina V.; Kalatur, Pavel G. // Journal of Chemical Physics;9/22/1998, Vol. 109 Issue 12, p5108 

    Part I. Examines the conformation of polymer chain in monoatomic solvent based on site-site Ornstein-Zernike integral equation in the solvent critical region. Prediction of intrachain attraction between monomeric chains; Induction of conformational changes by strong fluctuating solvent;...

  • Integral equation theory of single-chain polymers: Comparison with simulation data for... Hin Hark Gan; Byung Chan Eu // Journal of Chemical Physics;2/8/1999, Vol. 110 Issue 6, p3235 

    Discusses an integral equation theory of single-chain polymers. Derivation of the single-chain integral equation from the polymer Kirkwood hierarchy for site-site or pair distribution functions; Examination of chain lengths.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics