Wavefronts and Rays as Characteristics and Asymptotics, by A. Solved Problems in Classical Mechanics: Analytical and Numerical Solutions with Comments, by O. Stochastic Control and Mathematical Modeling: Applications in Economics, by H. Superlattice to Nanoelectronics, by Raphael Tsu pp.

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## the mesoscopic theory of polymer dynamics springer series in chemical physics

Physics Encounters Consciousness, 2nd edn. Advances in Nanotechnology and the Environment, edited by Juyoung Kim pp. Principles and Applications, edited by Di Wei pp. Optics of Nanomaterials, by Vladimir I. Electricity and Magnetism, 2nd ed. Lasers in the Preservation of Cultural Heritage: Principles and Applications, by C. The Mesoscopic Theory of Polymer Dynamics, 2nd edn. Random Processes on Graphs and Lattices, by G.

Fast Car Physics, by Chuck Edmondson pp. The mechanism for movement of the chain through these restrictions is called reptation.

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- The Mesoscopic Theory of Polymer Dynamics (Springer Series in Chemical Physics).
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In the blob model, [13] the polymer chain is made up of Kuhn lengths of individual length. The chain is assumed to form blobs between each entanglement, containing Kuhn length segments in each. The mathematics of random walks can show that the average end-to-end distance of a section of a polymer chain, made up of Kuhn lengths is. Therefore if there are total Kuhn lengths, and blobs on a particular chain:.

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The total end-to-end length of the restricted chain is then:. This is the average length a polymer molecule must diffuse to escape from its particular tube, and so the characteristic time for this to happen can be calculated using diffusive equations. A classical derivation gives the reptation time:.

The linear macromolecules reptate if the length of macromolecule is bigger than ten times.

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There is no reptation motion for polymers with , so that the point is a point of dynamic phase transition. Due to the reptation motion the coefficient of self-diffusion and conformational relaxation times of macromolecules depend on the length of macromolecule as and , correspondingly.

The dynamics of shorter chains or of long chains at short times is usually described by the Rouse model. Reptation Not to be confused with reputation. Reptation—motion of long linear, entangled macromolecules amorphous polymers. The blob model, explaining the entanglement of long polymer chains.

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The tube model, explaining the basically one-dimensional mobility of long polymer chains. Dynamics of Entangled Polymers. Pierre-Gilles de Gennes Symposium.

## Vladimir N. Pokrovski

Retrieved 6 April American Institute of Physics. The Journal of Chemical Physics. Brownian motion in the equilibrium state". Journal of the Chemical Society, Faraday Transactions 2.

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