Polymers adsorption theories

We investigate theoretically how the adsorption of the polymer varies with the displacer concentration. A simple analytical expression for the critical displacer concentration is derived, which is found to agree very well with numerical results from recent polymer adsorption theory. One of the applications of this expression is the determination of segmental adsorption energies from experimental desorption conditions and the adsorption energy of the displacer. Illustrative experiments and other applications are briefly discussed. 

An illustrative example is the work of Clark et al, on the conformation of poly(vinyl pyrrolidone) (PVP) adsorbed on silica 0). These authors determined bound fractions from magnetic resonance experiments. In one instance they added acetone to an aqueous solution of PVP in order to achieve theta conditions for this polymer. They expected to observe an increase in the bound fraction on the basis of solvency effects as predicted by all modern polymer adsorption theory (2-6), but found exactly the opposite effect. Their explanation was plausible, namely that acetone, with ability to adsorb strongly on silica due to its carbonyl group, would be able to partially displace the polymer by competing for the available surface sites. 

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. 

Variants of 12.4.33] have also been obtained by others, including Everett who subsumed the difference between z° and in K and, for rod-like molecules parallel to the surface, by Prigogine and Marechal ). Frisch, Simha and Eirich ) derived (2.4.33] for 1 in an embryonic polymer adsorption theory. An equation resembling (2.4.33). 

In Chapter 3, the solution and surface properties of a relatively new class of material, namely, polymeric surfactants, are illustrated in some detail using Flory-Huggins theory and current polymer-adsorption theory. This is followed by a discussion of the phenomenon of steric stabilization of suspended particles and how it is affected by the detailed structure of the stabilizing polymeric species. It concludes with a discussion of the stabilization of emulsions by interfacial and bulk theological effects, and presents closing comments on multiple emulsions. 

Usually, in the polymer adsorption theory, there are three stages adsorption from very dissolved solutions, when the substitution degree of surface is low, and macromolecules are situated at a large distance from each other The transitional stage, in which the distance between macromolecules is not large and their chains partially overlaps the plateau regime, when the macromolecule chains are overlapped, stretched into the solution, and only a small part is bound with the surface. This notion of polymer adsorption makes the theoretical calculations of macromolecule state in the adsorption layer more complicated. 

Scheutjens JMHM, Fleer GJ. Some implications of recent polymer adsorption theory. In Tadros TF, ed. The Effect of Polymers on Dispersion Properties. London Academic Press, 1982 145-168. 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

Our understanding of polymer adsorption has followed in the wake of developments in the theory of adsorption of small molecules and that of polymer solutions. It is useful, at the outset to introduce some of the ideas that have been developed in recent years, particularly with regard to the latter topic. 

There has been a plethora of theories of polymer adsorption in recent years, at least for linear chains adsorbed on regular surfaces these have been adequately reviewed elsewhere (1-4). 

An approximate analysis of polymer adsorption as a set of sequential reactions leads to a simple equation for the adsorption isotherm expressed in terms of three parameters. Comparison of the model with recently published statistical theories reveals remarkable agreement in both the general shape of the isotherms and the predicted effects of molecular weight. The problems of applying such models to experimental data are discussed. 

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). 

The role of the solvent in polymer adsorption has been the subject of much discussion. For example, theories have made predictions about the effect of the polymer/solvent interaction (i.e. Flory Huggins x parameter) on adsorption. For many systems, x parameters had already been tabulated so that a number of adsorption studies focused attention on this parameter. In spite of much effort, available data are ambiguous, sometimes verifying and sometimes contradicting the trends predicted by theory. 

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-... 

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). 

Studies on orthokinetic flocculation (shear flow dominating over Brownian motion) show a more ambiguous picture. Both rate increases (9,10) and decreases (11,12) compared with orthokinetic coagulation have been observed. Gregory (12) treated polymer adsorption as a collision process and used Smoluchowski theory to predict that the adsorption step may become rate limiting in orthokinetic flocculation. Qualitative evidence to this effect was found for flocculation of polystyrene latex, particle diameter 1.68 pm, in laminar tube flow. Furthermore, pretreatment of half of the latex with polymer resulted in collision efficiencies that were more than twice as high as for coagulation. 

In summary, polymeric flocculants generally increase peri-kinetic flocculation rates compared with perikinetic coagulation rates. This is not necessarily true for orthokinetic flocculation, and experimental results in the literature are seemingly in conflict. Collision rate theory predicts that the polymer adsorption step may become rate limiting in orthokinetic flocculation. The present study was designed to elucidate the relationship between polymer adsorption rates and particle flocculation rates under orthokinetic conditions. 

As shown in Fig. 7.7d polymers can destabilize colloids even if they are of equal charge as the colloids. In polymer adsorption (cf. Fig. 4.16) chemical adsorption interaction may outweigh electrostatic repulsion. Coagulation is then achieved by bridging of the polymers attached to the particles. LaMer and coworkers have developed a chemical bridging theory which proposes that the extended segments attached to one of the particles can interact with vacant sites on another colloidal particle. 

J. Klein and G. Rossi Analysis of the Experimental Implications of the Scahng Theory of Polymer Adsorption. Macromolecules 31, 1979 (1998). 

Further, the Gibbs adsorption theory has also been used for systems other than solutions (such as solid-liquid or liquidj-liquid2, adsorption of solute on polymers, etc.). In fact, the Gibbs adsorption theory will be applicable to any system in which adsorption takes place at an interface. 

No quantitative comparison between theory and experiment on polymer adsorption was attempted until the end of the 1970 s. There were two reasons for this delay. First, no acceptable theory had been established. Second, some of the parameters used in most of the published theories could not be directly correlated to experimentally measurable quantities. 

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