Determination of z and b from gyration swelling

Theory gives us the end-to-end swelling 0(z) = R2/°R2 but the measured quantity is the Z average of the gyration swelling 

For reasons of simplicity, we shall neglect polydispersion effects and write 

It is still necessary to determine the curve XG(z) in order to associate a value of z with each experimental value of 3 G. For this, we shall write 

Note that, in this formula, the end-to-end swelling X0(z), the variation of which is strong, is well-known, whereas N(z), which is less well-known, does not vary much. We shall use the approximate expression (13.1.58) 

Inserting these values as ordinates in Fig. 15.7, we get values of z, which are found in Table 15.2. In this table we also find values of average areas Sw, calculated with the help of relation (15.2.12) from molecular masses Mw. The value of the interaction b is deduced from the formula 

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