Abstract
This chapter presents the foundation of the dynamics of unperturbed polymer chains in dilute solution on the basis of dynamic HW chain models within the framework of linear response theory. It is evident that the original (continuous) HW chain is not valid as a dynamic model; the discreteness must be, to some extent, recovered to introduce motional units into the chain. Thus diffusion equations for a time-dependent distribution function for the (constrained) chain are derived so as to be suitable for the treatments of its local and also global (to quasi-global) motions. The eigenvalue problems and time-correlation functions associated with the diffusion operators are then formulated by introducing several unavoidable approximations. Their applications to various dynamical properties are made in the next chapter. It is pertinent and instructive to begin by giving a general consideration of some aspects of polymer dynamics, followed by a brief description of the dynamics of conventional constrained bond chains.
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References
J. G. Kirkwood: Ree. Trav. Chim. 68, 649 (1949); J. Polym. Sci. 12, 1 (1954).
M. Fixman and W. H. Stockmayer: Ann. Rev. Phys. Chem. 21, 407 (1970).
H. Yamakawa: Modern Theory of Polymer Solutions (Harper & Row, New York, 1971).
W. H. Stockmayer: In Molecular Fluids—Fluides Moleculaires, R. Balian and G. Weill, eds. (Gordon & Breach, New York, 1976), p. 107.
M. Doi and S. F. Edwards: The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).
P. E. Rouse, Jr.: J. Chem. Phys. 21, 1272 (1953).
B. H. Zimm: J. Chem. Phys. 24, 269 (1956).
Y. Ikeda: Bull. Kobayashi Inst. Phys. Res. 6, 44 (1956).
J. Erpenbeck and J. G. Kirkwood: J. Chem. Phys. 29, 909 (1958); 38, 1023 (1963).
M. Fixman and J. Kovac: J. Chem. Phys. 61, 4939 (1974).
M. Fixman and G. T. Evans: J. Chem. Phys. 68, 195 (1978).
H. Yamakawa and T. Yoshizaki: J. Chem. Phys. 75, 1016 (1981).
H. Yamakawa: In Molecular Conformation and Dynamics of Macromolecules in Condensed Systems, M. Nagasawa, ed. (Elsevier, Amsterdam, 1988), p. 21.
H. Yamakawa, T. Yoshizaki, and J. Shimada: J. Chem. Phys. 78, 560 (1983).
T. Yoshizaki and H. Yamakawa: J. Chem. Phys. 104, 1120 (1996).
H. Yamakawa and T. Yoshizaki: J. Chem. Phys. 78, 572 (1983).
H. A. Kramers: J. Chem. Phys. 14, 415 (1946).
R. B. Bird, O. Hassager, R. C. Armstrong, and C. F. Curtiss: Dynamics of Polymeric Liquids (John Wiley, New York, 1977), Vol. 2.
C. F. Curtiss, R. B. Bird, and O. Hassager: Adv. Chem. Phys. 35, 31 (1976).
M. Fixman: J. Chem. Phys. 69, 1527 (1978).
H. Yamakawa: Ann. Rev. Phys. Chem. 35, 23 (1984).
M. Doi and K. Okano: Polym. J. 5, 216 (1973).
H. Yamakawa and G. Tanaka: J. Chem. Phys. 63, 4967 (1975).
G. Wilemski: J. Stat. Phys. 14, 153 (1976).
E. Helfand: J. Chem. Phys. 71, 5000 (1979).
E. Helfand, Z. R. Wasserman, and T. A. Weber: Macromolecules 13, 526 (1980).
E. Helfand, Z. R. Wasserman, T. A. Weber, J. Skolnick, and J. H. Runnels: J. Chem. Phys. 75, 4441 (1981).
M. R. Pear and J. H. Weiner: J. Chem. Phys. 71, 212 (1979).
D. Perchak and J. H. Weiner: Macromolecules 14, 785 (1981).
M. Fixman: Proc. Natl. Acad. Sci. USA 71, 3050 (1974).
R. A. Harris and J. E. Hearst: J. Chem. Phys. 44, 2595 (1966).
N. Saito, K. Takahashi, and Y. Yunoki: J. Phys. Soc. Japan 22, 219 (1967).
K. Soda: J. Phys. Soc. Japan 35, 866 (1973); J. Chem. Phys. 95, 9337 (1991).
M. Bixon and R. Zwanzig: J. Chem. Phys. 68, 1896 (1978).
Yu. Ya. Gotlib and Yu. Ye. Svetlov: Polym. Sci. USSR 21, 1682 (1979).
R. G. Winkler, P. Reineker, and L. Harnau: J. Chem. Phys. 101, 8119 (1994).
L. Harnau, R. G. Winkler, and P. Reineker: J. Chem. Phys. 102, 7750 (1995); 104, 6355 (1996).
O. Hassager and R. B. Bird: J. Chem. Phys. 56, 2498 (1972).
A. Messiah: Quantum Mechanics (North-Holland, Amsterdam, 1970), Vol. II.
A. R. Edmonds: Angular Momentum in Quantum Mechanics (Princeton Univ., Princeton, 1974).
A. P. Yutsis, I. B. Levinson, and V. V. Vanagas: The Theory of Angular Momentum (Israel Program for Scientific Translations, Jerusalem, 1962).
H. Mori: Prog. Theor. Phys. (Kyoto) 33, 423 (1965).
R. Zwanzig: J. Chem. Phys. 60, 2717 (1974); In Molecular Fluids—Fluides Moleculaires, R. Balian and G. Weill, eds. (Gordon & Breach, New York, 1976). p. 1.
J. E. Hearst: J. Chem. Phys. 37, 2547 (1962).
T. Yoshizaki, M. Osa, and H. Yamakawa: J. Chem. Phys. 105, 11268 (1996).
T. Yoshizaki and H. Yamakawa: J. Chem. Phys. 84, 4684 (1986).
H. Yamakawa, T. Yoshizaki, and M. Fujii: J. Chem. Phys. 84, 4693 (1986).
H. Yamakawa and T. Yoshizaki: J. Chem. Phys. 91, 7900 (1989).
E. Dubois-Violette and P.-G. de Gennes: Physics 3, 181 (1967).
M. Fixman: Macromolecules 14, 1710 (1981).
A. Z. Akcasu: Macromolecules 15, 1321 (1982).
K. Nagasaka and H. Yamakawa: J. Chem. Phys. 83, 6480 (1985).
M. Fixman: Faraday Discuss. No. 83, 199 (1987); J. Chem. Phys. 89, 2442 (1988).
T. Yoshizaki and H. Yamakawa: J. Chem. Phys. 81, 982 (1984).
J. G. Kirkwood and J. Riseman: J. Chem. Phys. 16, 565 (1948).
H. Murakami, T. Norisuye, and H. Fujita: Macromolecules 13, 345 (1980).
M. T. Record, Jr., C. P. Woodbury, and R. B. Inman: Biopolymers 14, 393 (1975).
J. E. Godfrey and H. Eisenberg: Biophys. Chem. 5, 301 (1976).
B. H. Zimm: Macromolecules 13, 592 (1980).
M. Fixman: J. Chem. Phys. 78, 1588 (1983).
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Yamakawa, E.H. (1997). Chain Dynamics. In: Helical Wormlike Chains in Polymer Solutions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60817-9_9
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DOI: https://doi.org/10.1007/978-3-642-60817-9_9
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