General aspect of the structure function

The polymer in the experiment19 reported in Fig. 15.21 is polystyrene of molecular mass A/w = 7.5 x 106, at a concentration p — 11.38 g/I in benzene. In the limit of zero concentration, the radius of gyration measured by scattering has the value (see Table 15.1, p. 724) 

Let us now consider the neutron scattering experiment,20 the results of which are shown in Fig. 15.22. The corresponding samples are made of polystyrene of molecular mass Mw = 5x 105. The mass-concentrations are 

In the limit of zero concentration, the radius of gyration has the value (see Table 15.1) 

The range of reciprocal space explored here with neutrons, is really in the asymptotic domain qRa 1 the reason for this is that the wave vector ka is large with respect to 1 /Ra. This is the domain in which we are going to study the structure function, and in the semi-dilute regime, the latter is written as 

Note the screening effect in Fig. 15.22 when the solute concentration increases, the structure function drops at q = 0 and the curvature of J(x) decreases (in absolute value) besides, for large values of q, l q) oc p2 H(q) increases with p, which simply reflects the increase of substance. The drop of f(0) oc p21/(8) and the decrease of the curvature in J( k) are related to a change of the analytical properties of H q), considered as a function of q. When p increases, the poles of H(q) in the complex plane of q move away towards oo along the imaginary axis. 

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A simple analysis of eq 17 shows the general aspects of the structure-function relations expected to control /3. This demonstration is simplistic in its lack of explicit bridge orbital structure, but it demonstrates the compromises needed to optimize Consider... 

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