Measurement of the exponent

The exponent v characterizes the swelling of a long polymer chain in very dilute solutions. In theory, it could be measured in several ways. However, can we trust results obtained by the simplest technique which consists in measuring the intrinsic viscosity These measurements produce values for the exponent v which are always lower than those obtained by light scattering measurements of the radius of gyration. It was necessary to explain this discrepancy in order to make a proper comparison between experimental and theoretical values of the exponent v. 

In fact, as shown by Weill and des Cloizeaux,13 measurements related to dynamics should be avoided. Indeed, we pointed out in Chapter 13, Section 1.4.3, that the lengths which take part in the determination of dynamical physical quantities, include not only the mean square end-to-end distance or the radius of gyration of polymers, but also the hydrodynamic radius. Now, it is easy to show that the hydrodynamic radius reaches its asymptotic behaviour 

Better experimental values of the exponent v are obtained from measurements of the radius of gyration of polymers and of the second virial coefficient, in dilute solutions. Indeed, when the number of links increases, these quantities reach the asymptotic regime much more rapidly. However, the realization of a true asymptotic state for these quantities remains the main difficulty to overcome. Some progress has recently been made thanks to the elaboration of samples of high molecular mass Mw = 5 x 107. 

The previous study of the intermediate regime shows that the boundary between this regime and the asymptotic regime occurs at about z = 35, which, in the most favourable cases, implies a molecular mass M = 6 x 107. It seems therefore that static observation (radiation scattering) allows us a rather close approach to the asymptotic regime. 

1 Methods for the static measurement of the exponent v When we increase the equivalent Brownian areas of a chain or of a sequence of a chain, the corresponding mean square radius of gyration increases asymptotically as sv. There are several methods of proving this power law by static measurements. 

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Let us consider further simple technique of determination of fractal dimension -D of macromolecular coil in diluted polymer solution, within the framework of which the Eq. (11) was obtained. The determination of value is the first stage of macromolecular coils study within the framework of fractal analysis (see chapter 1) and the similar estimations are performed by measurement of the exponents in Mark-Kuhn-Hou-wink t5q)e equations, linking intrinsic viscosity [r ] (the Eq. (1)), translational diffrisivity or rate sedimentation coefficient with pol5mers molecular weight MM [3] ... 

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