Field theoretical analysis of adsorption of polymer chains at surfaces: Critical exponents and Scaling

Abstract

The process of adsorption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions is investigated. The performed scaling analysis is based on formal analogy between the polymer adsorption problem and the equivalent problem of critical phenomena in the semi-infinite $|\varphi {|}^4$ n-vector model (in the limit $n\to 0$) with a planar boundary. The whole set of surface critical exponents characterizing the process of adsorption of long-flexible polymer chains at the surface is obtained. The polymer linear dimensions parallel and perpendicular to the surface and the corresponding partition functions as well as the behavior of monomer density profiles and the fraction of adsorbed monomers at the surface and in the interior are studied on the basis of renormalization group field theoretical approach directly in d=3 dimensions up to two-loop order for the semi-infinite $|\varphi {|}^4$ n-vector model. The obtained field- theoretical results at fixed dimensions d=3 are in good agreement with recent Monte Carlo calculations. Besides, we have performed the scaling analysis of center-adsorbed star polymer chains with $f$ arms of the same length and we have obtained the set of critical exponents for such system at fixed d=3 dimensions up to two-loop order.

arXiv comment22 pages, 12 figures, 4 tables

References in corpus (7)

• Massive Field-Theory Approach to Surface Critical Behavior in Three-Dimensional Systems
• The Adsorption and Collapse Transitions in a Linear Polymer Chain near an Attractive Wall
• Critical Adsorption in Systems with Weak Surface Field: The Renormalization-Group Approach
• Surface critical behavior of random systems at the ordinary transition
• Surface critical behavior of random systems at the special transition
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• Influence of long-range correlated quenched disorder on the adsorption of long flexible polymer chains on a wall

Cited by in corpus (4)

• Polymer chains in confined geometries: Massive field theory approach
• Universal amplitude in density-force relations for polymer chains in confined geometries: Massive field theory approach
• Polymer adsorption on a fractal substrate: numerical study
• Influence of long-range correlated surface and near the surface disorder on the process of adsorption of long-flexible polymer chains