## Abstract

For the first time we achieved incontestable evidence that the real process of dielectric relaxation during the polymerization reaction of polyvinylpyrrolidone (PVP) is described in terms of the fractional kinetic equations containing complex-power-law exponents. The possibility of the existence of the fractional kinetics containing non-integer complex-power-law exponents follows from the general theory of dielectric relaxation that has been suggested recently by one of the authors (R.R.N). Based on the physical/geometrical meaning of the fractional integral with complex exponents there is a possibility to develop a general theory of dielectric relaxation based on the self-similar (fractal) character of the reduced (averaged) microprocesses that take place in the mesoscale region. This theory contains some essential predictions related to existence of the non-integer power-law kinetics and the results of this paper can be considered as the first confirmation of existence of the kinetic phenomena that are described by fractional derivatives with complex-power-law exponents. We want to stress here that with the help of a new complex fitting function for the complex permittivity it becomes possible to describe the whole process for real and imaginary parts simultaneously throughout the admissible frequency range (30 Hz-13 MHz). The fitting parameters obtained for the complex permittivity function for three temperatures (70, 90 and 110 °C) confirm in general the picture of reaction that was known qualitatively before. They also reveal some new features, which improve the interpretation of the whole polymerization process. We hope that these first results obtained in the paper will serve as a good stimulus for other researches to find the traces of the existence of new fractional kinetics in other relaxation processes unrelated to the dielectric relaxation. These results should lead to the reconsideration and generalization of irreversibility and kinetic phenomena that can take place for many linear non-equilibrium systems.

Original language | English |
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Pages (from-to) | 418-434 |

Number of pages | 17 |

Journal | Physica B: Condensed Matter |

Volume | 388 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 15 Jan 2007 |

### Funding

One of us R.R.N. wants to express his deep thankfulness for the receiving of the financial support in the frame of the Grant TUBITAK and Prof. A. Erzan for the possibility to visit Istanbul Technical University and work with his Turkish colleagues. Two of us (R.R.N. and A.A.A.) want to express also their deep acknowledgments to the Russian Ministry of Science and Higher Education, which sponsored this project in the frame of the grant: “Russian Scientific Potential of the Leading Higher Schools. Number of Grant: 2.1.1.4012”.

Funders | Funder number |
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Russian Ministry of Science and Higher Education | |

Russian Scientific Potential of the Leading Higher Schools | 2.1.1.4012 |

TUBITAK |

## Keywords

- Dielectric relaxation
- Fractional kinetics with complex-power-law exponents
- Polymerization reactions