Collapse observed by light scattering

Perzynski et al.2 measured (by light scattering) the (mean) square J g( P) of the radius of gyration of polystyrene chains of molecular mass Mw = 1.26 x 106 (S = 2092 nm2) for various temperatures T( TF) and for various volume fractions in the range 10 5 q 10-4. The radii are extrapolated at zero concentration for a given temperature T, we write 

In principle, these results should be compared with the mean square radius of gyration of the same chains (of equivalent area S) measured at the temperature T aoF(S) (see Chapter 14, Section 6.9.6). However, as was seen in Section 3.1, it is in practice difficult to determine T ooF(S). This is why, with Perzynski, we define the experimental gyration swelling approximately, by choosing a reference temperature Tt (35 °C) which is arbitrary but close to TF (34 °C) 

The vaues of XG obtained in the experiment for various temperatures inferior or equal to 35 °C are given in Table 16.7. We note that when the temperature decreases from 35 °C to 28 °C, the radius of gyration decreases by a factor 0.87. 

let us consider a collapsed chain filling completely the volume of a sphere of radius R0. We can admit that the end points are located at random in the sphere whose centre is assumed to coincide with the origin. Consequently, we have 

Let us return to the theoretical expressions of the (end-to-end) swelling. We denote by X the swelling which is calculated with the help of eqn (14.3.7) 

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