| Issue |
J. Phys. II France
Volume 4, Number 3, March 1994
|
|
|---|---|---|
| Page(s) | 533 - 539 | |
| DOI | https://doi.org/10.1051/jp2:1994143 | |
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)
Abstract
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.
© Les Editions de Physique 1994