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Silberberg's hypothesis: polymer melts close to surfaces and in thin films

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According to Silberberg's hypothesis ^[1] the chain conformations of polymer melts close to hard and structureless surfaces should be conceived as random walks simply reflected at the film surfaces, i.e., the parallel chain extensions would remain unperturbed. See the left panel of the figure. The Silberberg hypothesis is the basis for the boundary conditions commonly used in the mean-field description of polymer solutions.^[2]

This hypothesis has been put to a test by Monte Carlo simulation of the bond-fluctuation model of polymer melts confined between two smooth walls ^[3]. Confirming the analytical predictions by A.N. Semenov and A. Johner ^[4] the chain size parallel to the walls is found to diverge logarithmically:

R_x²/N = b² + log(N) / h.

Hence, the directions parallel and perpendicular to the walls are coupled.

Systematic deviations are also found from the plateau expected in the Kratky^[2] representation, q²F(q), of the single chain form factor F(q) (evaluated parallel to the walls). Our results are in good qualitative agreement with the non-monotonous behavior predicted by theory. This effect might give rise to an erroneous estimation of the chain extension from scattering experiments. For large h the deviations are linear with the wave vector q, but are very weak. In contrast, for thin films very strong corrections are found (albeit logarithmic in q) suggesting a possible experimental verification of our results.

Related publications

1. A. J. Silberberg, Colloid Interface Sci. 90, 86 (1982).

2. Polymer Physics
   M. Rubinstein, R. H. Colby, Oxford University Press, Oxford (2003).

3. A. Cavallo, M. Mueller, J.P. Wittmer, A. Johner, K. Binder
   Single chain structure in thin polymer films:
   Corrections to Flory's and Silberberg's hypotheses
   J.Phys.: Condens. Matter, 17 (25 May 2005) 1697-1709; cond-mat/0412373.

4. A. N. Semenov, A. Johner
   Theoretical notes on dense polymers in two dimensions
   Eur. Phys. J. E 12, 469 (2003).