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Козлов, Г. В.; Шустов, Г. Б.; Заиков, Г. Е.

doi:10.1023/a:1016119527174

Cited by 2 publications

(3 citation statements)

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“…Cantor's set is considered in one‐dimensional Euclidean space ( d = 1), and so its fractal dimension is d f < 1 by virtue of the fractal definition. For fractal objects in Euclidean spaces with higher dimensions ( d > 1) like ν, one should accept d f or7, 8 where d is the dimension of the Euclidean space in which the fractal is considered.…”

Section: Theorymentioning

confidence: 99%

“…Within the framework of this formalism, a capacity for the precise description of nonlinear phenomena, such as spatial correlations,4 can be represented. In the past, fractional derivation has also been successfully applied to the description of the properties of polymers 5–8. In this article, this approach is used for the calculation of the average end‐to‐end distance (〈 h

_{italics}^{2}

〉 1/2 ) of a polymeric chain of polycarbonate (PC) in two different solvents.…”

Section: Introductionmentioning

confidence: 99%

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Application of the fractional derivative theory to the estimation of the end‐to‐end distance of polycarbonate chains

Козлов

Долбин

Shogenov

et al. 2004

J of Applied Polymer Sci

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This study has led to two main conclusions. First, fractional derivation can be used to calculate the average end-to-end distance of a polymeric chain as precisely as other existing computational techniques. Second, knowledge of the changes in the molecular characteristics of a polymeric chain is needed for the correct calculation of the indicated parameters. In other words, one should take into consideration the dynamics when the structure of a macromolecular coil is varied.

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Section: Theorymentioning

confidence: 99%

_{italics}^{2}

〉 1/2 ) of a polymeric chain of polycarbonate (PC) in two different solvents.…”

Section: Introductionmentioning

confidence: 99%

Application of the fractional derivative theory to the estimation of the end‐to‐end distance of polycarbonate chains

Козлов

Долбин

Shogenov

et al. 2004

J of Applied Polymer Sci

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“…This approach has been successfully used for the description of autodecelerated N o2 (t) curves. 9 The second approach is by using fractional integration and derivation. 3,4,10 -12 Within the framework of this formalism, one may call it a success if it allows sequentially complicated nonlinear phenomena such as memory affects and spatial correlations.…”

Section: Introductionmentioning

confidence: 99%

A theoretical description of the oxidation kinetics of polymer melt in fractal mediums

Козлов

Долбин

Заиков

2006

J of Applied Polymer Sci

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It is shown that the fractal approach using fractional integration and derivation gives an adequate description of decelerated curves in relation to consumed oxygen-and time. A clear physical interpretation of the fractal exponent as a fractional part of the fractal dimension of a macromolecular coil is obtained. It also indicates that classical equation is a particularly limiting case of the fractal relationship applicable to Euclidean mediums. The initial oxygen amount is represented as a constant in basic fractal relationship, which is also a function of the macromolecular coil structure.

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Cited by 2 publications

References 1 publication

Application of the fractional derivative theory to the estimation of the end‐to‐end distance of polycarbonate chains

Application of the fractional derivative theory to the estimation of the end‐to‐end distance of polycarbonate chains

A theoretical description of the oxidation kinetics of polymer melt in fractal mediums

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