Yu. Ya. Gotlib2 and V. P. Toshchevikov
Institute of Macromolecular Compounds, Russian Academy of Sciences,
Bol’shoi pr. 31, St. Petersburg, 199004 Russia
Received June 27, 2000;
Revised Manuscript Received September 6, 2000
Abstract—A theory of high-frequency torsional-vibration relaxation processes in a finite fragment of a poly-
mer chain is developed on the basis of the model of elastically coupled rotators. The ends of the polymer chain
are taken to be fixed. The time dependences of the autocorrelation function of the quadrupole order parameter
are calculated. This parameter is manifested in the relaxation properties exhibited by polymers in polarized
luminescence, NMR, mechanical relaxation, dynamic birefringence, etc. The relaxation spectrum of the auto-
correlation function of the order parameter of a chosen rotator depends on the rotator position in a chain and
the relation between the total chain length and the length of the chain rigid segment that determines the torsional
rigidity of the chain. It is shown that, several characteristic decay time laws can be distinguished for the auto-
correlation function of the order parameter of a chosen rotator included in a finite chain. The decay is exponen-
tial at the beginning step of relaxation; next, it follows a stretched exponential law with an exponent of 1/2,
apower-law, and, at larger times, again an exponential with the characteristic time different from that of the
initial exponent. The order parameter autocorrelation function is averaged by the rotator position in a chain, and
the time dependence of the obtained value is calculated. This dependence is determined by the relation between
the chain length and the length of the chain rigid segment.
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