Segment density profile adsorption

FIG. 14 Segment density profile for adsorption from a good solvent. (From Ref. 50.)... 

The theory of polymer adsorption is complicated for most situations, because in general the free energy of adsorption is determined by contributions from each layer i where the segment density is different from that in the bulk solution. However, at the critical point the situation is much simpler since the segment density profile is essentially flat. Only the layer immedia-... 

Fig. 3.36 Segment density profiles from a Monte Carlo computer simulation of adsorption of a BAB triblock at a planar interface, where the hydrophobic B block is preferentially adsorbed (Balazs and Lewandowski 1990). Profiles are plotted for different A segment-surface interaction parameters, AS, with Xas = 0 and a chain length - 30 units.

Figure 3.33. Segment density profiles for the terminally anchored surfactant molecules corresponding to the system of fig. 3.32a. Adsorption energy parameter = 4.8...

To characterize the structure of adsorption layer, it is very important to know the profile of density of segment distribution. In many works, the ultimate goal was to predict the concentration profile,( )(z), in the interfacial region as a function of the distance z from the interface. For many years, att ts were made to derive the structure of polymer layers from some theory. In this case, each chain is submitted to an average potential which is a combination of... 

The statistical thermodynamics of block copolymer adsorption was considered elsewhere.Many theories attempt to characterize adsorption by smface density, block segment distribution profile, and the thickness of adsorbed layer. As a rule, an adsorbed diblock copolymer has one block adsorbed on the surface in a rather flat conformation, whereas the other block, having a lower surface activity, forms dangling tails. Because of their freely dangling blocks, adsorbed diblock copolymers are often interpenetrated. The adsorption of block copolymers leads to the segregation of blocks in the adsorption layer. It was found that both kinetic and equilibrium features of the block copolymer adsorption are intimately related to the phase behavior of the block copolymer solution. In particular, a very strong increase in the adsorbed amount is observed when the system approaches the phase boundary. As a consequence, a partial phase separation phenomenon may proceed in the surface zone. 

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]. 

In the simplest case, the segment density profile of the adsorption layer can be described by well-known equations [18] ... 

All theoretical models take into accoimt the energy of interaction of monomer links of the macromolecule with the solvent and surface. They allow one to obtain the segment density profile in the adsorption layer by minimizing of free energy of this system. 

The typical segment density profile of the AB block copolymer is shown in Fig. 7. The adsorbed segments of A form a relatively compact layer near the surface. The soluble B blocks stretch into the solution and form the brushes [38]. The thickness of adsorption layer depends on the polymerization degree of the chain of the B block copolymer. 

Figure 13 demonstrates the segment density profile of sodium poly(styrene sulfonate) adsorbed on polystyrene latex in NaCl solution [48]. The segment density profiles of Na poly(styrene sulfonate) do not practically depend on the surface charge. The shape of curve depends on the NaCl concentration. An increase of salt concenliation leads to an increase of the thickness of the adsorption layer, as predicted by theory. 

In order to discuss a number of important quantities we consider the interfacial profile for the case of positive adsorption. Such a profile is sketched in fig. 5.6. It represents the polymer concentration dz) as a function of the distance z from the interface. The quantity c(z) is related to the volume fraction concentration profile of segments belonging to free molecules, having no contact with the surface. The excess adsorbed amount r (the amount of... 

The problem is to relate v (z) to the surface potential - v (0) or the surface charge density a° = a(O)) and the volume fraction profiles of the components. Early versions t-2) of a polyelectrolyte adsorption model neglected the volume of the small Ions and solved (numerically) the Poisson-Boltzmann equation 13.5.6). A more sophisticated, yet simpler, approach was proposed by Bflhmer et al. who accounted for the Ion volume by adopting a multilayer Stem model, see fig. 5.17. This Is a straightforward extension of the monolayer Stern model discussed in sec. 3.6c. The charges of the ions and the segments are assumed to be located on planes in the centres of the lattice layers. The lattice is thus con-... 

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