Theory of Monolayers of Non-Gaussian Polymer Chains grafted onto a Surface Part 1.-General.pdf

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Theory of Monolayers of Non-Gaussian Polymer Chains grafted onto a Surface Part 1.-General.pdf

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Theory of Monolayers of Non-Gaussian Polymer Chains grafted onto a Surface Part 1.-General

J. CHEM. SOC. FARADAY TRANS., 1994, 90(6), 889-893 889 Theory of Monolayers of Non-Gaussian Polymer Chains grafted onto a Surface Part 1 .-General Theory Victor M. Amoskov and Victor A. Pryamitsyn Institute of the Problems of the Mechanical Engineering, 61 Bolshoy pr. , V.O., 199178 St.-Petersburg, Russia A theory describing layers of polymer chains grafted to a flat surface (polymer brush) is developed. We consider a brush of chains with arbitrary extensibility and, within the framework of molecular field theory, we suggest a general scheme for calculating the selfconsistent pseudo-potential, which determines the structure of the brush. This potential appears to be defined only by the mechanism of extensibility and is independent of the interactions between chains in the brush. A model potential for freely jointed chains (FJC) was calculated and used for describing an FJC polymer brush in good solvent conditions. We found good agreement between our results and the numerical calculations of Skvortsov eta/ . The properties of polymers adsorbed at solid/liquid or liquid/ liquid interfaces are important in areas such as tribology and biophysics. One type of adsorption is grafting or end adsorption, in which polymer chains are attached by one end to a surface. This may be achieved in several ways, for example, by constructing a block-copolymer in which one block is strongly adsorbed onto the surface. Similar struc- tures appear in the superstructures of block-copolymers. The resulting structure is usually called a brush. The theory of brushes has been developed by many authors. I- Initially, polymer brushes were analysed using the scaling method by Alexander, De Gennes2 and Birshtein and Z h ~ l i n a . ~ The general result of these theories was that the polymer chains in the brush are strongly stretched. To explain this result, let us consider a system consisting of long polymer chains grafted, by one end, to a flat surface. The number