The isolated repulsive chain

Colloid stabilization with amphiphilic polymers [2,114,115] requires the formation of a thick polymer layer around each particle in order to create a repulsive steric force that overcomes the van der Waals attraction. This is usually done by adsorbing on the colloidal particle a polymer solution in a good solvent, which builds up on the surface a fluffy layer with a thickness of the order of the radius of gyration of isolated polymer chains, in general of the order of a few hundred angstroms. 

Thus, to calculate the swelling of an isolated chain and the osmotic pressure of a set of chains in the vicinity of the Flory point, a determination of the partition functions 3 (E, — H S) and 3 N x S) by dimensional renormalization is sufficient. The calculations will be performed to first orders in x and y for a space dimension d = 3 — e (0 < s < 1), and we note that the purely repulsive terms have been already calculated in Chapter 10. The partition functions will be represented by series in terms of x and y. Finally, in order to study the behaviour of long polymers, we shall treat these series by using the direct renormalization method. 

The structure and the behaviour of polymer chains in solutions have, since the 1930s, been the object of intensive experimental work. The main effort has been carried out on the isolated chain in good solvent, and the swelling caused by repulsive interaction between monomers. The effect had already been predicted by Kuhn, in an article published in 1934, describing the spatial occupancy of chains (Raumerfullung). The swelling of a rubber (cross-linked chains) in a solvent can be observed directly with the naked eye. In the case of linear chains, the observation of all aspects of this effect has, however, required the use of instrumentation which has grown heavier, year by year. 

The repulsive interaction screens concentration correlations. The screening factor for two points placed at a distance r, is equal to exp( — r/ e). Therefore, the screening effect is weak when r < e. In this case, the structure function H q) is dominated by the contribution of the form function H(q) and, in the q interval under consideration, it has the same behaviour as the form function H q) of the isolated chain. Now, for qX 1 and C - 0, we have seen that... 

It is apparent that the experimentally measured repulsion extends much further out from the surface than would be expected for isolated chains. The theoretical curve presented in Fig. 12.2 ignores the elastic repulsion that must... 

Theories of elastic steric stabilization Dolan and Edwards (1974) have calculated the elastic free energy of repulsion for isolated polymer chains attached terminally to parallel flat plates. It was shown in Section 11.4.1.1. that probability distribution function for a random flight chain obeys the diffusion equation... 

Flory (1969) has argued that the occupied-volume exclusion (repulsion) for an isolated chain is exactly balanced in the bulk state by the external (repulsive) environment of similar chains, and that the exclusion factor can therefore be ignored in the solid state. Direct observation of single-chain dimensions in the bulk state by inelastic neutron scattering gives values fully consistent with unperturbed chain dimensions obtained for dilute solutions in theta solvents (Cotton et al., 1972), although intramolecular effects may distort the local randomness of chain conformation. 

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