Scheutjens-Fleer theory

The experimental thickness measurements may also be compared with theoretical results based on profiles generated by the S.F., Scheutjens Fleer, theory (11). For this calculation we use a value for xs °f 1 (net adsorption free energy), for x of 0.45 (experimental value of the Flory-Huggins parameter) and a polymer solution concentration of 200 ppm. Although the value for xs seems rather arbitrary it has been shown (10) that 6jj is insensitive to this parameter. 

Scheutjens-Fleer theory 5.31, 5.5 square gradient method 5.33 statistics 5.29... 

In this study we present data on two systems, where both these phenomena are reproduced. The difference in solvency of cyclic and linear polymers is also discussed. The results are compared with calculations based on the Scheutjens-Fleer theory [4] and by Monte Carlo simulations [6]. 

Fig. 9.16 Monomer density profile for = 0.1 and various values of N within the SCF approximation. The solid lines are from numerical calculations based on the Scheutjens-Fleer theory. The dotted curve is from eq. (9.30). Note that the ordinate is the potential field V z), which is proportional to the density profile. (From Ref. 157.)...

Structure of Adsorbed Polymer Layers. The Scheutjens—Fleer theory (4, pp. 240-248) predicts a detailed structure of adsorbed poljmaer layers as a function of several parameters. For example, as an adsorbed layer saturates with an increase in the bulk concentration, the fraction of segments in loops increases at the expense segments in trains. Another prediction of the theory is that the... 

Figure 6.19. Volume fraction profile p(z) calculated with the Scheutjens-Fleer (SF) theory. Parameters N 5000, (p = lO . i = 1. 0-5. hexagonal lattice.

Scheutjens-Fleer (SF) Theory. A conceptual model for the effects of NOM on colloidal stability can be developed by using existing theoretical and experimental investigations of polymer and polyelectrolyte adsorption on solid surfaces and of the effects of macromolecules on colloidal stability. The modeling approach begins with the work of Scheutjens and Fleer for uncharged macromolecules, termed here the SF theory (3-5). This approach has been extended to the adsorption of linear flexible strong polyelectrolytes by van der Schee and Lyldema (6), adapted to weak polyelectrolytes (7-9), and applied to particle-particle interactions (8, 10). 

The adsorption processes of polymers at liquid interfaces have been modelled, based on very simple assumptions. More sophisticated models contain a large number of independent system parameters, which are rarely available (Douillard Lefebvre 1990). A quantitative description of polymer adsorption which takes into account peculiarities of the adsorbing molecules has still to be developed. It is not possible yet, to describe the polymer adsorption process on the basis of the theory of Scheutjens Fleer (1979, 1980), which does not apply under dynamic conditions. 

A quantitative analysis of counterion localization in a salt-free solution of star-like PEs is carried out on the basis of an exact numerical solution of the corresponding Poisson-Boltzmann (PB) problem (Sect. 5). Here, the conformational degrees of freedom of the flexible branches are accounted for within the Scheutjens-Fleer self-consistent field (SF-SCF) framework. The latter is used to prove and to quantify the applicability of the concept of colloidal charge renormalization to PE stars, that exemplify soft charged colloidal objects. The predictions of analytical and numerical SCF-PB theories are complemented by results of Monte Carlo (MC) and molecular dynamics (MD) simulations. The available experimental data on solution properties of PE star polymers are discussed in the light of theoretical predictions (Sect. 6). 

Figure 7 Predictions of Scheutjens and Fleer theory for the adsorption of diblock copolymers surface density o versus fraction of anchor segment v. (Reproduced with permission from Ref. 16.)... 

Figure 9 Adsorbed amount versus fraction of anchor segment for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) ABA triblock copolymers adsorbed onto poly(styrene latex). Inset shows the mean-field calculations of surface coverage versus fraction of anchor segment Vx obtained using Scheutjens and Fleer theory. (J. A. Shar, T. Obey, and T. Cosgrove Colloids and Surfaces. In press.)... 

The above discussion on the two components of should lead to a better understanding of physical adsorption. Theoretically, polymer adsorption(so) can be treated by the Scheutjens-Fleer (SF)(si) mean-field theory, the Monte Carlo (MC) method,( 2) or the scaling approach. (83) In Figure 10, two profiles are given for the cases of adsorption (x = 1) and depletion (x = 0) using the SF theory, where x is the Flory-Huggins interaction parameter(84) between a polymer and a solvent with respect to pure components. The polymer coil expands if X < 0.5 and contracts if x These two cases are referred to as good and poor solvents, respectively. From the volume fraction profile c )(z), we can calculate other adsorption parameters, such as F, the adsorbed amount ... 

Very different behavior was found in Ref. 25 near surfaces with preferential attraction for the chain-ends of -C28H5g melts. As shown in Fig. 8.9, longer trains were found to decrease and shorter trains increase in this ease, with a simultaneous increase of long tails and loops. This behavior is well explained by the abundance of chain-ends in the first segmental layer close to the surfaces, which somewhat excludes the other chain units from this region. These characteristics due to sticky chain-ends for -C28Hs8 melt systems are reproduced quite well by Scheutjens-Fleer self-consistent-field lattice theory (see Section 8.2.8). ... 

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