Polymer Solutions in Good Solvents

From Chapter I we know the properties of dilute (nonoverlapping) coils in a good solvent they are swollen, with a size Rp = N a. At the other end, we know from Chapter II the limit of very concentrated solutions or melts the chains are essentially ideal, with a size Rd = N a, and they interpenetrate each other very strongly. 

What happens in between For a long time, the only interpolation method available was a mean field theory due to Flory and Huggins. However (as realized early by these authors) the mean field idea is not adequate at low and intermediate concentrations. The question remained obscure for a long time. It has now been clarified experimentally (mainly through neutron scattering experiments see Fig. III.l) and theoretically (by certain manipulations as described in Ch q ter X). Fortunately, the final picture is simple and can be explained without referring to abstract theory. 

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Tschoegl, N. W. Influence of hydrodynamic interaction on the viscoelastic behavior of dilute polymer solutions in good solvents. J. Chem. Phys. 40,473-479 (1964). 

Polymer Solutions in Good Solvent Excluded Volume Effect... 

The concentration dependence of the diffusion coefficient is plotted in Fig. 8.9 in the scaling form suggested by Eq. (8.85) for polymer solutions in good solvents. The expected exponent is observed over a limited range of approximately one decade above the overlap concentration 0 and a stronger concentration dependence is seen at higher concentrations, where entanglements become important. 

Since the Tschoegl version of the Zimm theory is applied to polymer solutions in good solvents with reasonable success, the original Zimm... 

This result is interesting because g is a physical quantity which defines the second virial coefficient of a polymer solution in good solvent and for very long chains. In other terms, g defines the second virial coefficient of a solution of Kuhnian chains. For d = 3 (e = 1), the preceding formula gives g = 0.266, a result which, apparently, is not very very precise, because the second term in (12.3.102) is not small with respect to the first one. This question is discussed, in more detail, in Chapter 13. 

Finally, we have considered polymer solutions in good solvents only. For industrial applications, one tends to use more and more water as a solvent. Water soluble polymers have specific properties due to the character of the interactions between monomers in water. Most water soluble polymers, for example, carry ionic charges (they are polyelectrolytes) if the polymers contain hydrophobic groups, they have interesting associating properties. The surface behavior of polyelectrolytes and associating polymers is the subject of intense experimental and theoretical studies [44]. 

However, experiments (25) have indicated that the molecular weight exponent is close to 3.4. From the mc els that have been proposed to improve the reptation approach, it appears that in concentrated polymer solutions in good solvents, the solution viscosity is given as... 

For the purpose of the discussion, polymer solutions in good solvents can be divided into three regions dUute, semidilute, and concentrated (see Fig. 5.1). 

We may thus classify the polymer solutions in good solvent into three regimes ... 

So far, we have considered homogeneous segment density distributions in the brush structures. However, as in semidilute polymer solutions in good solvents, the screening of the excluded volume interaction is expected to produce blob structures. They are also at the basis of the theoretical imderstanding of polymer brushes due to Alexander and de Gennes [52,53[. 

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