Adsorption, polymer scaling theory

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]. 

De Gennes24,54) investigated the adsorption of a flexible polymer on a flat surface from good solvents using the scaling theory. Three different regimes, i.e. dilute, semidilute, and plateau regions, were considered. 

The theoretical description of excluded volume effects on the adsorption from good solvents is still unsatisfactory. The scaling theory for polymer adsorption has not yet been subject to experimental tests. 

The basic ideas of the scaling theory for homogeneous polymer solutions have also been used to set up a framework for a theoiy describing the adsorption of polymers from good solvents. The aim Is to derive power laws for q> z), valid in certain regimes in most cases numerical coefficients are ignored. So far, the model has only been formulated for weak adsorption, l.e., small x - We shall treat some more details of this model in the following subsection (5.4c). 

In order to estimate the first contribution from the elastic adsorption, a C gel picture is used, in which the gel is a collection of adjacent blobs of radius that has a characteristic relaxation time Ti / >coop, where Dcoop r/bnrji is the cooperative diffusion constant of the gel, T is temperature and t] is the viscosity of the solvent [80]. Each blob is associated with a partial polymer chain (the polymer chain between two next-neighboring cross-linking points). The scaling theory relates this molecular structure of the gel with its elastic modulus E by the equation [80]. 

De Gennes PG (1976) Scaling theory of polymer adsorption. J Phys 37 1445-1452 De Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, Ithaca De Gennes PG (1981) Polymer solutions near an interface. 1. Adsorptirai and depletion layers. Macromoleeules 14 1637-1644... 

De Gennes PG (1983) Scaling theory of polymer adsorption proximal expontmt. J Phys Lett 44 L241-L246... 

Polymer adsorption may result in bridging attraction or steric repulsion between two particles. The scaling theory of polymer adsorption that accounts for the interactiOTi between the polymer and the surface and for variation of polymer concentration near the surface [53, 54] was used for derivation of the interaction potential between two spherical colloidal particles coated by polymer [55-57] ... 

The scaling theory has also been modified to show the eonformation of the maeromolecule of star polymers in adsorption layer [52,53]. 

An investigation of the kinetics of adsorption of polystyrene onto gold plate from cyclohexane solution (0 solvent) showed [59] that the experimental result does not agree with the scaling theory approximated to the 0 solvent. The permeability of a partially formed adsorbed layer depends on the history of its formation. The kinetics are much slower than if it is governed by end-in raptation and is insensitive to the molecular weight of polymer. 

Scaling theory of polymer adsorption proximal exponent", (with P. Pincus) J. Phvs. Lett.. 44, L-241 (1983). 

This chapter is concerned with the application of liquid state methods to the behavior of polymers at surfaces. The focus is on computer simulation and liquid state theories for the structure of continuous-space or off-lattice models of polymers near surfaces. The first computer simulations of off-lattice models of polymers at surfaces appeared in the late 1980s, and the first theory was reported in 1991. Since then there have been many theoretical and simulation studies on a number of polymer models using a variety of techniques. This chapter does not address or discuss the considerable body of literature on the adsorption of a single chain to a surface, the scaling behavior of polymers confined to narrow spaces, or self-consistent field theories and simulations of lattice models of polymers. The interested reader is instead guided to review articles [9-11] and books [12-15] that cover these topics. 

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