Laboratoire de Physique Théorique
Toulouse - UMR 5152

Abstract

The general frame of this Ph.D. is the study of statistical properties of polymer chains at interfaces. This is a theoretical and fundamental work which aims at linking macroscopic observables (surface tension etc.) to the microscopic organization of chains. The polymer layer (e.g. liquid/solid interface) is described in terms of loops and tails formed by adsorbed polymers. We develop an approach which combines the statistical physics of a loop population of different sizes and scaling laws, suitable to describe polymer coils. Such approach describes analytically adsorbed or grafted polymers layers, in various solvent conditions. This work falls into three sections.

First, a formal link is established between our phenomenological approach and first principles of polymer statistical physics. We argue that this description is a variational theory whose trial probability is the statistical distribution of loop sizes. Hence, this theory is categorized among the two theories usually used to describe polymers at interfaces : the "classical" theory for stretched chains, and "ground state dominance" types of approximations suitable to describe adsorbed layers.

Then, this theory is applied to the issue of the surface tension of different polymer solutions (dilute, semi-dilute and melt). The variations of surface tension with molecular weight, volume fraction in the bulk and temperature are deduced. A comparison is done with experimental measurements of the surface tension, found in the literature. The involved physical phenomena are then reconsidered. In particular, the role of the entropy associated to loop distribution and the tensio-activity of chain ends is enlightened.

Finally, the variational theory is generalized to describe polyelectrolytes at interfaces and the adsorption of polyelectrolytes on an oppositely charged surface is studied. We restrict ourselves to weakly charged and flexible polyelectrolytes without salt. The layer structure is analytically described and the occurence of an external sublayer formed by large loops provides a strong argument for the charge inversion process. In addition, we also were interested in two situations invloving polymer "brushes". The issue of the influence of the concave geometry on the structure and the energy of a brush and the study of mobile polymer connectors. We find that the mechanical and adhesive properties of these polymer junctions strongly depend on the geometry of the connected objects and on polymer characteristics.

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