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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture.

B U Felderhof1

  • 1Institut für Theorie der Statistischen Physik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany.

The Journal of Chemical Physics
|August 24, 2017
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Summary
This summary is machine-generated.

This study generalizes Einstein's relation for Brownian particles to binary fluid mixtures, yielding a new mutual diffusion coefficient expression. The derived relation aligns with existing theories under specific conditions, validating its applicability.

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Area of Science:

  • Statistical Mechanics
  • Physical Chemistry
  • Fluid Dynamics

Background:

  • Brownian motion and Einstein's relation are fundamental in diffusion studies.
  • Existing theories for mutual diffusion in mixtures have limitations or differing results.

Purpose of the Study:

  • To derive a generalized Einstein relation for the mutual diffusion coefficient of binary fluid mixtures.
  • To compare this new relation with existing models from irreversible thermodynamics and Brownian suspension theories.

Main Methods:

  • Utilizing Einstein's method for deriving the relation between diffusion and friction coefficients.
  • Applying this method to a binary fluid mixture.
  • Comparing derived expressions with those from de Groot and Mazur, and Batchelor.

Main Results:

  • A generalized Einstein relation for the mutual diffusion coefficient was derived.
  • The derived relation shows agreement with de Groot and Mazur for nearly incompressible solutions and to first order in solute density.
  • Consistency was found with the generalized Smoluchowski equation for Brownian suspensions.

Conclusions:

  • The generalized Einstein relation provides a unified approach to diffusion in fluid mixtures.
  • The study reconciles differing theoretical results in irreversible thermodynamics and Brownian motion.