Semi-dilute and Concentrated Solutions

Working in very dilute solution the dimensional changes with temperature of the polystyrene coil in a poor solvent, cyclohexane, have been studied. Two domains are recognized one (the 0-region) where R is independent of the reduced temperature t [t = (T— 0)/O] in the second the coil collapses and R t -i/ in accordance with predicted behaviour. This system has been studied further in the region of the lower critical solution temperature (LCST), that is near the solvent critical point. The temperature range was 70— 220 °C and in this r on Edwards equation is modified to  

Conformational studies of block copolymers have also been very rewarding. The system PS-PMMA diblock copolymer has been studied, by deuteriating the styrene segment, and using SANS and light scattering techniques in toluene. The radii of gyration of PSD homopolymer (M = 88 000) measured by both methods and that of PMMA block (M = 203 000) in the diblock copolymer 

Richards, A. Maconnachie, and G. Allen, report to the European Polymer Symposium, Strasbourg, May 1978. 

Studies of polyelectrolytes, using DjO as solvent to enhance the contrast between polymer and solvent, have been carried out using carboxymethyl cellulose (CMQ and poly(methacrylic acid) (PHA). Values of the radius of gyration have been determined as a function of the degree of polymerization (N), the degree of neutralization of the carboxylic acid groups (a,), and the poly-electrolyte concentration (C). In the case of PMA in which N = 15 it was found that 

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In that way, the thermodynamic approach with the use of conformational term of chemical potential of macromolecules permitted to obtain the expressions for osmotic pressure of semi-diluted and concentrated solutions in more general form than proposed ones in the methods of self-consistent field and scaling. It was shown, that only the osmotic pressure of semi-diluted solutions does not depend on free energy of the macromolecules conformation whereas the contribution of the last one into the osmotic pressure of semi-diluted and concentrated solutions is prelevant. 

That fact the scaling method and presented thermodynamic approach from seeming opposite positions lead to practically the same result in the form (8) and (35) can be named as mysterious incident if it were not two circumstances. First is exactly free energy of the conformation makes the main contribution into the osmotic pressure of the semi-diluted and concentrated solutions. The second is the peculiarity of the point c = c. ... 

This result is appHcable to semi-dilute and concentrated solutions [21], and is also useful to check many simulations that do not include HI. For non-draining chains, introducing Gaussian statistics in Eq. (35), and transforming the summations over a large number of units in Eq. (34) into integrals, the translational friction coefficient can finally be written as [ 15]... 

Dynamic scattering can also provide information about relaxation modes of polymers at higher values of the wavevector q ( 7 >1). Equation (8.164) can be generalized to higher wavevectors and to semi-dilute and concentrated solutions by noticing that the decay of the... 

The aim of the theories developed for polymer solutions has been to explain experimental observations such as deviations from Raoult s law and the molecular weight dependence of solubility at any given temperature. Indeed, it is necessary to account for the phase diagram for polymer solutions in general. The more recent theories deal with semi-dilute and concentrated solutions. No single theory currently explains ail the experimental observations for polymer solutions. Some of the more significant are [8-16] ... 

It is also necessary to account for the influence of temperature on the interaction between various aggregates. Its diminishing facilitates the transit of aggregates to the adsorbent surface and as a result in some cases the aggregative adsorption increases with temperature. There are many factors influencing adsorption from semi-dilute and concentrated solutions, which may be explained now only on the qualitative level. 

In a good solvent, c whereas in a theta solvent, c It is often more convenient to use the polymer volume fraction, 0, rather than concentration, because then for a polymer in the absence of solvent, 0 = 1. Using 0, two concentration regimes can be distinguished from the dilute regime. If the coils are overlapped, i.e. 0 > 0, where 0 is the overlap volume fraction, but there is still not much polymer in solution, 0 < 1, then the solution is said to be semi-dilute. However, if 0 > 0 and 0 1, the solution is concentrated. Polymer chains in dilute, semi-dilute and concentrated solutions are sketched in Fig. 2.13. 

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