Cycle rank density

As already mentioned, a network is characterized by its cycle rank density 4/Vo-Scanlan and Case have defined an active junction as one joined by at least three paths to the gel network and an active chain as one terminated by active junctions at both its ends. Pearson and Graessley have shown that for a randomly interconnected network whose junctions are of even functionality... 

Reduced force as functions of for Network A. Data for bulk samples (+) and samples swollen with decane (triangles) are given and the polymer volume fractions are indicated with each isotherm. The solid curves were calculated according to theory with parameters given in Table III. The lower dashed line represents the cycle rank density calculated from the chemical constitution of Newtwork A with corrections due to dangling chain ends included. The upperdashed line represents the affine limit for a perfect network obtained with respect to the corrected chemical value of Network A. 

The values were determined using the cycle rank density deduced from elasticity measurements (see text). ... 

Figure 3 is typical of elastomeric networks, showing the decrease of modulus with elongation, as already mentioned in the introduction. Simultaneous increase of cycle rank density and decrease of k are also usual trends in real networks... 

In the Flory-Erman treatment, polymer networks are fully characterized by their "cycle rank", The cycle rank Incorporates the crosslink density and all other structural features of the crosslinked polymer. That is convenient mathematically, but would be synthetically more useful if broken out into conventional structural parameters. For a random network such as is obtained in copolymerizations of vinyl and divinyl monomers, with crosslink functionality of four, the cycle rank density, Vq is [4]... 

In Eq. 4, /V represents the cycle rank (number of independent circuits in the network) density of the swollen network k the Boltzmann... 

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