Weight Fraction Solubles and Crosslink Density

Weight Fraction Solubles and Crosslink Density Till the gel point is reached, all molecules are finite and the weight fraction of solubles, is thus unity. Beyond the gel point more and more molecules enter the network with the consequent decrease of For the homopolymerization of Ay (/ 2), a randomly chosen A/ molecule will be part of the sol if all of its / number of arms lead only to finite chains. Thus, 

An important property of the polymer network is the crosslink density or concentration of effective junction points. An effective junction point can be identified thus. An Af is an effective junction point if three or more of its arms lead out to the infinite network. (Note that if only one arm is infinite, this A/ unit will be just hanging from the network if, on the other hand, two arms are infinite, A/ only forms part of a chain connecting two effective junction points and it itself is not an effective junction point.) 

Let us consider tetrafunctional A4 as an example of A/. The probability that A4 is an effective crosslink of degree 4 is given by 

However, A4 can also be an effective crosslink of degree 3 and the probability that exactly three of the four arms lead out to itifinite network is given (Macosko and Miller, 1976) by f 3 

In general, the probability that an A. unit will be an effective crosslink of degree m is then 

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