The Partitioning of Components between Sol and Gel

If the degree of cross-linking p is small (and the primary chain length therefore great), 0 =tf s, giving 

The probability that a primary molecule composed of y units possesses i cross-linked units is 

The relative abundances of cross-linkages and of various primary species in the sol and in the gel fractions may be obtained by extension of this procedure. Since 4 l equals the fraction of the cross-linkages (or of the cross-linked units) occurring in the sol fraction, we can write 

Similarly, the fraction p of the units in the gel which are cross-linked is 

The number and weight average values of y in the sol fraction are, respectively,  

---