Dynamics of polymer chains trapped in a slit

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Abstract
We investigate the dynamics of polymer solutions confined in ultra-thin slits (20-200 Å), including both excluded volume effects and hydrodynamic interactions through a scaling analysis. 1) In the dilute regime, for chain extension R larger than the slit thickness d, the overall translational diffusion coefficient Dt is predicted to scale like [FORMULA] which is much larger than the value expected from the Debye-Bueche approximation [FORMULA] (where RF2 is the chain size measured in the slit plane). For the internal modes, we find a structure of the Rouse type at wavelength larger than d. This is due to screening of hydrodynamic interactions, an intrinsic feature of slit systems. The eigenmode frequency scales like Δωq = Td1/3 q10/3/η s 2) In the « 2d » semi-dilute regime characterized by a monomer-monomer correlation length ξ2 larger than d, we find modes reminiscent of a gel for qξ2 < 1 (with a relaxation rate [FORMULA] )and internal mode structure of a confined chain for qξ > 1. The self-diffusion coefficient of a chain is predicted to scale like Ds ~ N -2 c-2 d-1/3. 3) At higher concentration, we reach the « 3d » semi-dilute regime (ξ < d) and we recover the dynamics of the bulk polymer solution (Ds ~ N-2 c-1.75)