Self-consistent field theory adsorption isotherms

Such adsorption isotherms may be predicted using numerical self-consistent field theory. This involves a relatively straightforward extension of the ap-... 

Figure 6.18. Interfacial tension between polystyrene and poly(vinyl pyridine) in the presence of styrene-2-vinyl pyridine block copolymer, as calculated by self-consistent field theory for the system whose interfacial excess is shown in figure 6.17. The value of the Flory-Huggins interaction parameter Xps-pvp was taken as 0.11, which provides a good fit to the adsorption isotherm below the CMC. After Shull et al. (1990).

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.

The development of adsorption theory provides the explanation of the macromolecule behavior in the adsorption layer and provides the basis of arguments on the experimental results. A few theoretical models, describing the adsorbed macromolecule, are widely used now. Self-consistent field theory or mean field approach is used to calculate the respective distribution of trains, loops, and tails of flexible macromolecule in the adsorption layer [22-26]. It allows one to find the segment density distribution in the adsorption layer and to calculate the adsorption isotherms and average thickness of the adsorption layer. Scaling theory [27-29] is used to explain the influence of the macromolecule concentration in the adsorption layer on the segment density profile and its thickness. Renormalization group theory [30-33] is used to describe the excluded volume effects in polymer chains terminally attached to the surface. The Monte Carlo method has been used for the calculation of the density profile in the adsorption layer [33-35]. 

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