Abstract
We consider the properties of a self-avoiding polymer chain with nearestneighbor contact energyɛ on ad-dimensional hypercubic lattice. General theoretical arguments enable us to prescribe the exact analytic form of then-segment chain partition functionC n ,and unknown coefficients for chains of up to 11 segments are determined using exact enumeration data ind=2–6. This exact form provides the main ingredient to produce a large-n expansion ind −1of the chain free energy through fifth order with the full dependence on the contact energy retained. The ɛ-dependent chain connectivity constant and free energy amplitude are evaluated within thed −1expansion toO(d −5). Our general formulation includes for the first time self-avoiding walks, neighboravoiding walks, theta, and collapsed chains as particular limiting cases.
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References
W. J. C. Orr,Trans. Faraday Soc. 42:12 (1946).
H. Yamakawa,Modern Theory of Polymer Solutions (Harper & Row, New York, 1971); P. J. Flory,Statistical Mechanics of Chain Molecules (Wiley-Interscience, New York, 1969).
P. G. de Gennes,Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, New York, 1979); M. Doi and S. F. Edwards,Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986); K. F. Freed,Renormalization Group Theory of Macromolecules (Wiley, New York, 1987).
M. E. Fisher and B. J. Hiley,J. Chem. Phys. 34:1253 (1961).
D. C. Rapaport,Phys. Lett. A 48:339 (1974);J. Phys. A 9:1521 (1976);10:637 (1977).
T. Ishinabe,J. Phys. A 18:3181 (1985);20:6435 (1987); T. Ishinabe and Y. Chikahisa,J. Chem. Phys. 85:1009 (1986).
V. Privman,J. Phys. A 19:3287 (1986).
J. Mazur and F. L. McCrackin,J. Chem. Phys. 49:648 (1968); F. L. McCrackin, J. Mazur, and C. L. Guttman,Macromolecules 6:859 (1973).
A. Baumgartner,J. Phys. (Paris)43:1407 (1982); see also A. Baumgartner, inApplications of the Monte Carlo Method in Statistical Physics, K. Binder, ed. (Springer-Verlag, Heilderberg, 1987).
K. Kremer, A. Baumgartner, and K. Binder,J. Phys. A 15:2879 (1982); F. Seno and A. L. Stella,J. Phys. (France)49:739 (1988);Europhys. Lett. 7:605 (1989).
H. Meirovitch and H. A. Lim,J. Chem. Phys. 91:2544 (1989);Phys. Rev. A 39:4186 (1989); X.-F. Yuan and A. J. Masters,J. Chem. Phys. 94:6908 (1991).
V. Privman and N. M. Svrakic,Directed Models of Polymers, Interfaces, and Clusters: Scaling and Finite-Size Properties (Springer-Verlag, Berlin, 1989).
K. F. Freed and M. G. Bawendi,J. Phys. Chem. 93:2194 (1989).
J. Dudowicz, K. F. Freed, and W. G. Madden,Macromolecules 23:4803 (1990); J. Dudowicz and K. F. Freed,Macromolecules 24:5076, 5096, 5112 (1991);J. Chem. Phys. 96:1644 (1992).
A. M. Nemirovsky and M. D. Coutinho-Filho,J. Stat. Phys. 53:1139 (1988);Phys. Rev. A 39:3120 (1989).
A. M. Nemirovsky, J. Dudowicz, and K. F. Freed,J. Stat. Phys., in press;Phys. Rev. A, in press.
M. E. Fisher and D. S. Gaunt,Phys. Rev. 133A:224 (1964).
P. R. Gerber and M. E. Fisher,Phys. Rev. B 10:4697 (1974).
D. S. Gaunt, M. F. Sykes, and H. Ruskin,J. Phys. A 9:1899 (1976); D. S. Gaunt and H. Ruskin,J. Phys. A 11:1369 (1978); J. Blease,J. Phys. C 10:925 (1977).
S. G. Whittington, G. M. Torrie, and D. S. Gaunt,J. Phys. A 16:1695 (1983).
D. S. Gaunt, J. E. G. Lipson, J. L. Martin, M. F. Sykes, G. M. Torrie, S. G. Whittington, and M. K. Wilkinson,J. Phys. A 17:211 (1984).
D. S. Gaunt and H. Ruskin,J. Phys. A 11:1369 (1978).
G. A. Baker, Jr., and L. P. Benofy,J. Stat. Phys. 29:699 (1982).
J. Zinn Justin,Phys. Rep. 70:109 (1981).
K. F. Freed,J. Phys. A 18:871 (1985); see also M. Janssens and A. Bellemans,Macromolecules 9:303 (1976).
T. Ishinabe, J. F. Douglas, A. M. Nemirovsky, and K. F. Freed, work in progress.
D. S. Gaunt,J. Phys. A 19:L149 (1986).
T. Hara and G. Slade, submitted for publication.
A. M. Nemirovsky, K. F. Freed, T. Ishinabe, and J. F. Douglas,Phys. Lett. A 162:469 (1992).
A. M. Nemirovsky and K. F. Freed, work in progress.
M. E. Fisher and R. R. P. Singh, inDisorder in Physical Systems, G. Grimmett and D. J. Welsh, eds. (Oxford University Press, Oxford, 1991).
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Nemirovsky, A.M., Freed, K.F., Ishinabe, T. et al. Marriage of exact enumeration and 1/d expansion methods: Lattice model of dilute polymers. J Stat Phys 67, 1083–1108 (1992). https://doi.org/10.1007/BF01049010
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DOI: https://doi.org/10.1007/BF01049010