Scheutjens-Fleer theory, polymer adsorption isotherms

Recent polymer adsorption theories, such as those of Roe (3) and of Scheutjens and Fleer (h) allow the calculation of displacement isotherms, so that we could study the dependency of these isotherms on various parameters by numerical methods. However, all the essential features of displacement can also be demonstrated by means of a simple analytical expression for the critical point, which can be derived in a straightforward way. 

In this paper we present results for a series of PEO fractions physically adsorbed on per-deutero polystyrene latex (PSL) in the plateau region of the adsorption isotherm. Hydro-dynamic and adsorption measurements have also been made on this system. Using a porous layer theory developed recently by Cohen Stuart (10) we have calculated the hydrodynamic thickness of these adsorbed polymers directly from the experimental density profiles. The results are then compared with model calculations based on density profiles obtained from the Scheutjens and Fleer (SF) layer model of polymer adsorption (11). 

J. M. H. M. Scheutjens and G. J. Fleer (1979) Statistical-theory of the adsorption of interacting chain molecules. 1. Partition-function, segment density distribution, and adsorption-isotherms. J. Phys. Chem. 83, pp. 1619-1635 ibid. (1980) Statistical-theory of the adsorption of interacting chain molecules. 2. Train, loop, and tail size distribution. 84, pp. 178-190 ibid. (1985) Interaction between 2 adsorbed polymer layers. Macromolecules 18, pp. 1882-1900... 

Figure 1. Theoretically calculated adsorption isotherm for a polymer of 100 segments adsorbing from a theta solvent (x=0.5). The isotherm was obtained from the self-consistent field theory of Scheutjens and Fleer. Two arrows indicate the values of the concentration difference Cb-Cs between bulk and surface zone one for adsorption (high cb ) and one for desorption (cb =0). The length of the arrows is a measure of the rate of the corresponding processes.

Other lattice polymer efforts have been based on the self-consistent fleld theory of Scheutjens and Fleer (150,151). This approach differs from previously posed statistical theories for chain molecules in that the partition function is expressed in terms of the distribution of chain conformations rather than the distribution of segment densities. The equilibrium distribution of chain (ie model protein) conformations is thus calculable. Quantities predicted using this approach include the force between parallel plates coated with protein (152,153), the adsorption isotherm (154,155), and the segmental density distribution (154-157). 

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