Theories of Polymer Adsorption

Theories of Polymer Adsorption B.l Isolated Polymer Chains 

It is well known that a free flexible polymer chain in bulk solution behaves as a random coil. When such a polymer chain is adsorbed on a surface, there occurs a change in its conformation. Some portions of the polymer chain get in direct contact with the surface 

Two main approaches have been developed to treat the problem of polymer adsorption  

1) The random walk approach, which is based on Flory s treatment of the polymer chain in solution in this case the surface was considered as a reflecting barrier. 

2) The statistical mechanical approach, in which the polymer configuration is treated as being composed of three types of stracture - trains, loops, and tails - with each having a different energy state. 

The random walk approach is based on the random-walk concept, which was originally apphed to the problem of diffusion and later adopted by Flory [3] to deduce the conformations of macromolecules in solution. The earliest analysis was by Simha et al. [4], who neglected volume effects and treated the polymer as a random walk. Basically, the solution was represented by a three-dimensional lattice. 

According to the SF theory, the boimd fraction p and the direct surface coverage 

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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). 

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 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-... 

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

Most of the early theories of polymer adsorption were not concerned with the interaction between adsorbed polymers so that they have little relevance for a comparison with experimental results. In actuality, the adsorbed mass per unit area is very large even when adsorption of polymers occurs from a very dilute solution. In this section, some typical theories allowing for the interaction between adsorbed polymers are reviewed. 

Many studies have revealed that the adsorption behavior of macromolecules is very specific for individual polymer-solvent-substrate systems. Hence, the formulation of a general theory of polymer adsorption might be extremely difficult. Nevertheless, we believe that more experimental studies with well characterized polymers and surfaces are imperative of this difficulty to be overcome. 

The theory of polymer adsorption and configuration is still not fully developed because the difficulties encountered in designing experiments are immense. A technique is required to measure the configuration of a polymer molecule at the interface and thus obtain concentration also. 

Meredith JC, Johnston KP. Theory of polymer adsorption and colloid stabilization in supercritical fluids. 2. Copolymer and end-grafted stabilizers. Macromolecules 1998 31, 5518-5528. 

Similar considerations are important in theories of polymer adsorption, although here the relative magnitudes of surface-solvent and surface—segment interaction energies have to be taken into account. 

Surveying the literature, it appears that the interfacial behavior of proteins is a controversial subject. The main reason is that many studies have been performed under insufficiently defined conditions and/or that conclusions have been drawn on the basis of too scanty experimental evidence. Furthermore, the theoretical description of adsorbed layers of simple, flexible polymers is still in its infancy (5,6). As the structure of proteins is much more complex than that of those simple polymers, theories of polymer adsorption need to be greatly extended to become applicable to proteins. Clearly, our current knowledge of protein adsorption mechanisms and of the structure of the adsorbed layer is far from complete. 

The whole discussion of polymer adsorption so far makes the fundamental assumption that the layer is at thermodynamic equilibrium. The relaxation times measured experimentally for polymer adsorption are very long and this equilibrium hypothesis is in many cases not satisfied [29]. The most striking example is the study of desorption if an adsorbed polymer layer is placed in contact with pure solvent, even after very long times (days) only a small fraction of the chains desorb (roughly 10%) polymer adsorption is thus mostly irreversible. A kinetic theory of polymer adsorption would thus be necessary. A few attempts have been made in this direction but the existing models remain rather rough [30,31]. 

Although Xs is referred to as an energy parameter and Ua are adsorption energies it is clear that they are actually viewed as enthalpies by the original authors of the self-consistent field theory of polymer adsorption. This needs to be appreciated in reading the literature since great confusion can arise otherwise. 

The simplest theories of polymer adsorption are mean-field theories. In fact, it is possible simply to apply the square gradient theory of surface segregation developed in section 5.1 to polymer solutions by setting the degree of polymerisation of one of the components to unity. An analogous theory was developed by de Gennes (1981) and applied to adsorption from theta solvents (under which circumstances mean-field theory can be expected to be reasonably accurate) by Klein and Pincus (1982). 

The above picture of depletion flocculation is, of course, very schematic and simple-minded, but it should serve to illustrate the concepts involved. A more detailed discussion would involve the introduction of complex theories of polymer adsorption and solution phenomena that are beyond the scope of this book. 

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... 

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... 

Many uses of polymers are concerned with the properties of polymers at interfaces. Chapter 2 presents a summary of theories of polymer adsorption and discusses the properties and state of polymers at interfaces and methods for determining the details of their structure, conformations, and so on. The basic theory of colloid-interaction forces in terms of DL VO theory is presented, together with a discussion of the different basic stabilization mechanisms of colloids. 

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] ... 

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