Quantitative Characterization of Network Structures

Since no Maxwell Demon is at hand to officiate in these unions, each pair of units participating in the formation of a cross-linkage will be selected at random it is required merely that the partners be in suitable proximity at the instant of formation of the linkage. From a chemical point of view, cross-linkages are scattered throughout the bulk of the 

The two quantities p and pt are satisfactory for the quantitative description of any random network structure. Alternative quantities sometimes are used to advantage, however. Instead of pt, one may prefer to specify the number N of primary molecules 

Any real network must contain terminal chains bound at one end to a cross-linkage and terminated at the other by the end ( free end O of a primary molecule. One of these is indicated by chain AB in Fig. 92, a. Terminal chains, unlike the internal chains discussed above, are subject to no permanent restraint by deformation their configurations may be temporarily altered during the deformation process, but rearrangements proceeding from the unattached chain end will in time re- 

The total number of chains, both internal and terminal, is v+Nj as is evident from Fig. 91,b. For every primary molecule there will be two terminal chains, i.e., a total of 2N. The number of internal chains must therefore be v — N. Hence a fraction of the chains given by 

Under all ordinary circumstances the average lengths of terminal chains and of internal chains will be the same, or nearly so hence represents the weight fraction of the structure which is active in deformation. For certain applications, as for example to crystallization induced by stretching, 8a is an appropriate measure of the effective portion of the 

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