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| - Analytical Approximation to the Scheutjens−Fleer Theory for PolymerAdsorption from Dilute Solution. 1. Trains, Loops, and Tails in Terms ofTwo Parameters: The Proximal and Distal Lengths
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| - Recently an analytical self-consistent mean-field theory was proposed for homopolymeradsorption in the long-chain limit. Here we make direct contact between that formalism and the numericallattice model of Scheutjens and Fleer. The lattice layer closest to the wall is treated in a discrete manner,whereas a continuum description is used further out. This entails a new boundary condition at the wall.Together with the self-consistency condition, this leads to two equations from which the two relevantlength scales (the proximal and distal lengths) follow unambiguously. As a result, analytical solutions inclosed form are obtained for both (mean-field) good solvents (from χ = 0 up to χ ≈ 0.47) and a ϑ solvent(χ = 0.5). For good solvents the agreement between the full lattice calculation and the analytical modelis excellent; for a ϑ solvent the discrepancy can amount to about 10%. The approximations necessary torender the analytical problem tractable are carefully checked against the numerical data.
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