J. Phys. II France
Volume 4, Numéro 3, March 1994
|Page(s)||533 - 539|
J. Phys. II France 4 (1994) 533-539
"Fluctuating cluster" equations for a polymer to . (Toward exact Flory equation?)Z. Alexandrowicz
Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel and Departamento de Fisica, CCE-UFRN, Campus Universitario, 59072-970 Natal-RN, Brasil.
(Received 8 November 1993, accepted 17 November 1993)
Although Flory's approximation describes very well the radius r of a polymer, it disagrees sharply with an exact expansion (derived from an analogy to n = 0 spins). Here the polymer is described explicitly as a critical cluster of n = 0 spins. While ordinary clusters resemble trees bifurcating into b branches, a cluster of n = 0 spins constitutes a single line, weighted by b phantom bifurcations. Analogous description of the polymer leads to a modified Flory-like equation, which describes r and b, jointly, and to two more equations for r and b in separate. These give very accurate exponents and , correct to . In addition, the approach can be extended to a many polymer system, and to other critical clusters.
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