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Journal ArticleDOI

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

TL;DR: In this article, the authors investigated the scaling analysis of adaption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions.
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 $|\phi|^4$ 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 $|\phi|^4$ 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.
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Journal ArticleDOI
TL;DR: The gyration tensor and related shape descriptors are calculated to present the shape characteristics of highly structured conformations for the polymer-attractive sphere model system.
Abstract: In a recent computational study, we found highly structured conformations for the polymer-attractive sphere model system. Those conformations are of highly ordered spherical shape or form two-dimensional planar, compact to extended, random coil structures. The observed conformations range from desorbed to partially or even completely adsorbed. In order to present their shape characteristics, here we calculate the gyration tensor and related shape descriptors.

97 citations

Journal ArticleDOI
TL;DR: Evidence is provided that adsorbed polymer layers are very sensitive to saturation effects, which start to influence the semidilute surface scaling even much below the saturation threshold.
Abstract: We consider end-grafted chains at an adsorbing surface under good solvent conditions using Monte Carlo simulations and scaling arguments. Grafting of chains allows us to fix the surface concentration and to study a wide range of surface concentrations from the undersaturated state of the surface up to the brushlike regime. The average extension of single chains in the direction parallel and perpendicular to the surface is analyzed using scaling arguments for the two-dimensional semidilute surface state according to Bouchaud and Daoud [J. Phys. (Paris) 48, 1991 (1987)]. We find good agreement with the scaling predictions for the scaling in the direction parallel to the surface and for surface concentrations much below the saturation concentration (dense packing of adsorption blobs). Increasing the grafting density we study the saturation effects and the oversaturation of the adsorption layer. In order to account for the effect of excluded volume on the adsorption free energy we introduce a new scaling vari...

16 citations

Journal ArticleDOI
TL;DR: The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with excluded volume interaction (EVI) than for ideal chains because the EVI effectively reduces the depletion effect near the walls.
Abstract: The massive field theory approach in fixed space dimensions $dl4$ is applied to investigate a dilute solution of long-flexible polymer chains in a good solvent between two parallel repulsive walls, two inert walls, and for the mixed case of one inert and one repulsive wall. The well-known correspondence between the field theoretical ${\ensuremath{\phi}}^{4}$ $O(n)$-vector model in the limit $n\ensuremath{\rightarrow}0$ and the behavior of long-flexible polymer chains in a good solvent is used to calculate the depletion interaction potential and the depletion force up to one-loop order. In order to make the theory UV finite in renormalization-group sense in $3\ensuremath{\le}dl4$ dimensions we performed the standard mass renormalization and additional surface-enhancement constants renormalization. Besides, our investigations include modification of renormalization scheme for the case of two inert walls. The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with excluded volume interaction (EVI) than for ideal chains because the EVI effectively reduces the depletion effect near the walls. Our results are in qualitative agreement with previous theoretical investigations, experimental results, and with the results of Monte Carlo simulations.

13 citations

Journal ArticleDOI
TL;DR: The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order.
Abstract: Taking into account the well known correspondence between the field theoretical ϕ(4) O(n)-vector model in the limit n → 0 and the behavior of long flexible polymer chains in a good solvent, the universal density-force relation is analyzed and the corresponding universal amplitude ratio B(real) is obtained using the massive field theory approach in fixed space dimensions d < 4. The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order. Besides, the monomer density profiles for the dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations.

11 citations

Journal ArticleDOI
TL;DR: In this article, the universal density-force relation is analyzed and the correspondent universal amplitude ratio $B_{real}$ is obtained using the massive field theory approach in fixed space dimensions d=3 up to one-loop order.
Abstract: The universal density-force relation is analyzed and the correspondent universal amplitude ratio $B_{real}$ is obtained using the massive field theory approach in fixed space dimensions d=3 up to one-loop order. The layer monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall are obtained. Besides, taking into account the Derjaguin approximation the layer monomer density profiles for dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The last mentioned situation is analyzed for both cases when wall and particle are repulsive and for the mixed case of repulsive wall and inert particle. The obtained results are in good agreement with previous theoretical results and with the results of Monte Carlo simulations.

10 citations