Langevin-Rondelez model

The experimental literature on electrophoresis in polymer solutions invokes theoretical models, including the Langevin-Rondelez treatment(8), the Ogston model(9), and reptation-type models(4). The Langevin and Rondelez form treated in the last chapter is modified for electrophoresis by replacing 5 with /x and omitting the 7o/ 7 term, leading to... 

This theory has been partially confirmed by sedimentation experiment (Langevin and Rondelez, 1978). The value of the slope so far found was —0.50 0.10. We now have some evidence to believe that in the semidilute range of polymer solution the solvent is forced through in orderly fashion around the blob of radius C but still cannot penetrate the interior of the blob. Note that this theory is reminiscent of the pearl necklace model and the hydrodynamic equivalent sphere. 

Here v, y v = —v S, and y = —y 8 are scaling exponents, notation being chosen for consistency with the remainder of the book, and a is a scaling prefactor. In Langevin and Rondelez s particular theoretical model, v = 3/4 and y = 0. They attempted to confirm y = 0 experimentally. 

The same drag coefficient determines s and Dp, leading to Dp/Dpo s/sq, implying that Eq. 9.18 should also govern probe diffusion. Indeed, Bu and Russo(22) show that their measurements agree with Eq. 9.18. As seen above, in probe polymer systems Dp/Dpo depends strongly on M, with a M. This dependence is inconsistent with the physical model invoked by Langevin and Rondelez in their ansatz for their equation. However, the diffusion coefficients of solvent molecules and other very small probes do appear to be independent of M, so Eq. 9.18 may have a limited domain of validity. 

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