JOURNAL OF NON-CRYSTALLINE SOLIDS, vol.353, pp.4143-4156, 2007 (Journal Indexed in SCI)
Clear evidence of the existence of fractional kinetics containing the complex power-law exponents were obtained by conductivity measurements of polymerization reaction of polyvinylpyrrolidone (PVP) performed inside a dielectric cell. We established the relationship between the Fourier image R(j omega) of the complex memory function K(t) and the time-dependent mean square displacement (r(2)(t). This relationship helps to understand the origin of the different power-law exponents appearing in the real part of complex conductivity Re[sigma(omega)] and find a physial/geometrical meaning of the power-law exponents that can form the complex-conjugated values. The complex-conjugated values of the power-law exponents leading to oscillating behavior of conductivity follows from the fractional kinetics suggested by one of the authors (R.R.N.). The relationships [R(j omega) double left right arrow Re[sigma(omega)] double left right arrow < r(2)(t)>] are becoming very efficient in classification of different types of collective motions belonging to light and heavy carriers involved in the relaxation/transfer process. The conductivity data obtained for Re[sigma(omega)] during the whole polymerization process of the PVP at different temperatures (80, 90, 100 degrees C) are very well described by the fitting function that follows from the suggested theory. Original fitting procedure based on the application of the eigen-coordinates (ECs) method helps to provide a reliable fitting procedure in two stages and use the well-developed and statistically stable linear least square method (LLSM) for obtaining the correct values of the fitting parameters that describe the behavior of Rc[sigma(omega, T-r)] in the available frequency range for the current time of the chemical reaction T, measured during the whole process of polymerization. The suggested theory gives a unique possibility to classify the basic types of motions that take place during the whole polymerization process. (c) 2007 Published by Elsevier B.V.