Junction topological neighbor

Classical molecular theories of rubber elasticity (7, 8) lead to an elastic equation of state which predicts the reduced stress to be constant over the entire range of uniaxial deformation. To explain this deviation between the classical theories and reality. Flory (9) and Ronca and Allegra (10) have separately proposed a new model based on the hypothesis that in a real network, the fluctuations of a junction about its mean position may may be significantly impeded by interactions with chains emanating from spatially, but not topologically, neighboring junctions. Thus, the junctions in a real network are more constrained than those in a phantom network. The elastic force is taken to be the sum of two contributions (9) ... 

If the polymers under consideration are regarded as model networks in which/ chains connect a given junction point with/nearest topological neighbor junction points, one can assume a certain ordering in the network structure [134]. If now the junction is placed into a cell of a crystalline... 

The possibility of chain rearrangement so that topological neighboring junctions move in concert to resist chain deformation is implicit in the structure of the theory. Both minor and major chain rearrangements can be expected depending on the extent of chain entanglement. 

Within the domain defined crudely by the locations of these closest topological neighbors (four in number in a tetra-functional network) as many as fifty or more other junctions may reside. The situation is depicted in Fig. 3. The paths (not shown) that connect spatial neighbors, indicated by X in Ihe figure, to the central junction may include many chains we shall be content to let these connections remain obscure. It suffices to observe that elastomeric networks are copiously interpenetrated structures, as these considerations clearly show. They bear little resemblance to a lattice-or even to a disordered lattice - often Invoked Incorrectly as a suitable analog. 

Fig. 4. (A) A central tetrafunctional junction surrounded by four other topologically neighboring junctions and a number of spatially neighboring junctions. (B) Schematic drawing of a slip link, with its possible motions along the network chains specified by the distances a, and its locking into position as a cross-link.

Figure 1.15 Schematic presentation of a dry model network. The sphere has a radius equal to the end-to-end distance of a chain. The filled and the open circles represent the topological and the spatial neighbors of the central junction, respectively. The dark line represents the shortest path from the central junction to its nearest spatial neighbor. (Reprinted from [129] with kind permission of Marcel Dekker, inc.)...

---