Adsorption 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 (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. 

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.)... 

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 ... 

The earlier models (2-5) dealt primarily with the conformation of a single molecule at an interface and apply at very low adsorption densities. More recent treatments (6-10) take into account polymer-polymer and polymer-solvent interactions and have led to the emergence of a fairly consistent picture of the adsorption process. For details of the statistical theories of polymer adsorption, the reader is referred to publications by Lipatov (11), Tadros (12) and Fleer and Scheutjens (13). 

It is of considerable interest to compare the present model with the predictions of the statistical theories. In particular, the results will be compared with the theories of Scheutjens and Fleer (9,10,13). These authors have pointed out that their results are in general agreement with other published models. Comparison of the adsorption isotherms shown in Figure 1 with those given by Scheutjens and Fleer (see, for example, Figure 5 of Reference 13) shows excellent qualitative agreement. In each case, the isotherms consist of three regions as described above. 

Figure 2. Comparison of adsorption isotherms based on the present model (solid lines) with the statistical theory of Scheutjens and Fleer (symbols). The following values of the parameters were used...

Recent polymer adsorption theories, such as those of Roe (3) and of Scheutjens and Fleer (h) allow the calculation of displacement isotherms, so that we could study the dependency of these isotherms on various parameters by numerical methods. However, all the essential features of displacement can also be demonstrated by means of a simple analytical expression for the critical point, which can be derived in a straightforward way. 

In this paper we present results for a series of PEO fractions physically adsorbed on per-deutero polystyrene latex (PSL) in the plateau region of the adsorption isotherm. Hydro-dynamic and adsorption measurements have also been made on this system. Using a porous layer theory developed recently by Cohen Stuart (10) we have calculated the hydrodynamic thickness of these adsorbed polymers directly from the experimental density profiles. The results are then compared with model calculations based on density profiles obtained from the Scheutjens and Fleer (SF) layer model of polymer adsorption (11). 

In modern statistical theories (see Scheutjens and Fleer, 1980, and Fleer and Lyklema, 1983) it is found that there does exist a certain critical adsorption free energy, customarily called xs, above which the moleculq adsorbs strongly and below which it does not adsorb. Typical values of xs, (crit) range from 0.2 - 0.4 kT. 

Scheutjens, J. M. H. M., and G. J. Fleer (1980), "Statistical Theory of the Adsorption of Interacting Chain Molecules. 2. Train, Loop, and Tail Size Distribution", J. Phys. Chem. 84/2, 178-90. 

J. M. H. M. Scheutjens and G. J. Fleer (1979) Statistical-theory of the adsorption of interacting chain molecules. 1. Partition-function, segment density distribution, and adsorption-isotherms. J. Phys. Chem. 83, pp. 1619-1635 ibid. (1980) Statistical-theory of the adsorption of interacting chain molecules. 2. Train, loop, and tail size distribution. 84, pp. 178-190 ibid. (1985) Interaction between 2 adsorbed polymer layers. Macromolecules 18, pp. 1882-1900... 

Scheutjens JMHM, Fleer GJ. Statistical theory of the adsorption of interacting chain molecules. I. Partition function, segment density distribution and adsorption isotherms. J Phys Chem 1979 83 1619-1635. 

Scheutjens and Fleer (1982) have developed a theory for depletion stabilization and depletion flocculation based upon their statistical thermodynamic approach to polymer adsorption and steric stabilization. This theory is cast in terms of the most primitive model for a polymer molecule, the random flight chain. This weakens the theory in so far as providing quaintitative predictions at the fundamental level for real systems is concerned. The theory does, however, offer qualitative results over a wide range of conditions, being especially powerful in establishing the various trends involved. 

Figure 1. Theoretically calculated adsorption isotherm for a polymer of 100 segments adsorbing from a theta solvent (x=0.5). The isotherm was obtained from the self-consistent field theory of Scheutjens and Fleer. Two arrows indicate the values of the concentration difference Cb-Cs between bulk and surface zone one for adsorption (high cb ) and one for desorption (cb =0). The length of the arrows is a measure of the rate of the corresponding processes.

Molecular-based theories are useful for developing rational stabilizer design criteria and investigating the correlation with bulk phase behavior for stabilizers in supercritical fluids. Molecular theories of polymer adsorption, such as the lattice self-consistent field (SCF) theory of Scheutjens and Fleer[69], allow chain structure, adsorption energy, solubility, length, and concentration to be varied independently. Simulation, while more computationally intensive, offers the additional advantages of... 

Other lattice polymer efforts have been based on the self-consistent fleld theory of Scheutjens and Fleer (150,151). This approach differs from previously posed statistical theories for chain molecules in that the partition function is expressed in terms of the distribution of chain conformations rather than the distribution of segment densities. The equilibrium distribution of chain (ie model protein) conformations is thus calculable. Quantities predicted using this approach include the force between parallel plates coated with protein (152,153), the adsorption isotherm (154,155), and the segmental density distribution (154-157). 

Another to emerge from Scheutjens and Fleer s theory [28] is the difference in shape between experimental and theoretical adsorption isotherms in the low concentration region. Experimental isotherms are usually rounded, whereas those pre-... 

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