Tests of Theoretical Modulus Values—Statistical Networks

Tests of Theoretical Modulus Values—Statistical Networks 

Alternatively, iVA is the number of mers participating in crosslinks (2 Q minus the number of chain ends (2 N). Tobolsky (162) has criticized the Flory criterion, showing that Eq. (7.9) is incorrect near the gel point. The Flory criterion has been used in most of the network analyses, however, and for purposes of comparison we will carry it along. 

Scanlan has suggested another criterion (282). An effective network junction point is a crosslink in which at least three of the four strands radiating from it lead independently to the network. A crosslink with only two strands anchored to the network simply continues an active strand a crosslink with only one anchored strand is part of a dangling end and can make no elastic contribution at equilibrium. An elastically effective strand is therefore one which joins two effective network junction points. Accordingly, the total number of active strands is simply one half the number of gel-anchored strands radiating from effective junction points  

The two criteria give somewhat different results for the effective strand concentration. Consider, for example, the random addition of C crosslinks to 

A simple calculation of the concentration of active strands, following Langley (255), yields 

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Tests of Theoretical Modulus Values—Statistical Networks... 

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