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Frequency dispersion of sound propagation in Rouse polymer melts via generalized dynamic random phase approximation

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Abstract.

An extended generalization of the dynamic random phase approximation (DRPA) for L-component polymer systems is presented. Unlike the original version of the DRPA, which relates the \(\left({L\times L} \right)\) matrices of the collective density-density time correlation functions and the corresponding susceptibilities of concentrated polymer systems to those of the tracer macromolecules and so-called broken-links system (BLS), our generalized DRPA solves this problem for the \(\left({5\times L} \right)\times \left({5\times L} \right)\) matrices of the coupled susceptibilities and time correlation functions of the component number, kinetic energy and flux densities. The presented technique is used to study propagation of sound and dynamic form-factor in disentangled (Rouse) monodisperse homopolymer melt. The calculated ultrasonic velocity and absorption coefficient reveal substantial frequency dispersion. The relaxation time \(\tau \) is proportional to the degree of polymerization N, which is N times less than the Rouse time and evidences strong dynamic screening because of interchain interaction. We discuss also some peculiarities of the Brillouin scattering in polymer melts. Besides, a new convenient expression for the dynamic structure function of the single Rouse chain in \(\left({{\vec {q}},p} \right)\) representation is found.

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Authors and Affiliations

  1. Physics Department, Moscow State University, 119992, Leninskie Gory, Moscow, Russia

    I. Ya Erukhimovich

  2. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky prospect 29, 119991, Moscow, Russia

    Ya V. Kudryavtsev

Authors
  1. I. Ya Erukhimovich
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  2. Ya V. Kudryavtsev
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Correspondence to I. Ya Erukhimovich.

Additional information

Received: 30 April 2003, Published online: 3 September 2003

PACS:

43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions - 47.10. + g Fluid dynamics: General theory - 83.80.Sg Polymer melts

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Erukhimovich, I.Y., Kudryavtsev, Y.V. Frequency dispersion of sound propagation in Rouse polymer melts via generalized dynamic random phase approximation. Eur. Phys. J. E 11, 349–365 (2003). https://doi.org/10.1140/epje/i2003-10022-x

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