Long-time self-diffusion of rigid rods at low concentrations: A variational approach

Jan K.G. Dhont, Willem J. Briels, Michel P.B. van Bruggen

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Abstract

No theoretical predictions exist for the concentration dependence of long-time self-diffusion coefficients of rod-shaped Brownian particles with a finite aspect ratio. The reason for this is that the relevant Smoluchowski equation is extremely complicated and cannot be solved explicitly, even on the two-particle level. We present an alternative approach where the Smoluchowski equation is solved in approximation by a variational method. The variational principle is applied to calculate the dependence of the long-time translational self-diffusion coefficient of spherocylinders with hard-core interaction to leading order in concentration, with the neglect of hydrodynamic interactions, up to aspect ratios of 30. The first order in concentration coefficient α is found to depend on the aspect ratio p as α = 2 + 10/32(p − 1) + 1/53(p − 1)2.
Original languageUndefined
Pages (from-to)3809-3816
Number of pages8
JournalMacromolecules
Volume32
Issue number11
DOIs
Publication statusPublished - 1999

Keywords

  • METIS-106338
  • IR-60868

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