In this paper, the response of single three-dimensional phantom and
self-avoiding polymers to localized step strains are studied for two cases in
the absence of hydrodynamic interactions: (i) polymers tethered at one end with
the strain created at the point of tether, and (ii) free polymers with the
strain created in the middle of the polymer. The polymers are assumed to be in
their equilibrium state before the step strain is created. It is shown that the
strain relaxes as a power-law in time t as t−η. While the strain
relaxes as 1/t for the phantom polymer in both cases; the self-avoiding
polymer relaxes its strain differently in case (i) than in case (ii): as
t−(1+ν)/(1+2ν) and as t−2/(1+2ν) respectively. Here ν is
the Flory exponent for the polymer, with value ≈0.588 in three
dimensions. Using the mode expansion method, exact derivations are provided for
the 1/t strain relaxation behavior for the phantom polymer. However, since
the mode expansion method for self-avoiding polymers is nonlinear, similar
theoretical derivations for the self-avoiding polymer proves difficult to
provide. Only simulation data are therefore presented in support of the
t−(1+ν)/(1+2ν) and the t−2/(1+2ν) behavior. The relevance of
these exponents for the anomalous dynamics of polymers are also discussed.Comment: 10 pages, 1 figure; minor errors corrected, introduction slightly
modified and references expanded; to appear in Phys. Rev.