Fundamental parameters of the network topology

Let be the number of cross-link junctions of the type (i,k) in the network. The number of junctions of multiplicity k is 

The upper limit depends on whether there is an end group or not. 

Converting this to the number of chains, the number of elastically effective chains can be found by 

The number 2k - i is the number of paths that are not connected to the network matrix. The sum on i starts from 2 because i = 1 indicates that the branch point is the end branch point that has already been counted. The end groups do not contribute to elasticity of the network because they are free from external stress, but they contribute to the viscosity and the relaxation time of the network due to friction with the solvent molecules. 

2 Structure parameters of multiply cross-linked gels 

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