This ratio is related to the density ratio of elastically effective polymer strands of the two networks, νe,2/νe,1, where the inter-network topological entanglement makes dominant contribution to νe,2.
The time-dependent behavior of the network is modelled as detachment of active strands from their junctions and merging of dangling strands with the network.
The viscoelastic behavior of a polymer is modelled as thermally-induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network).
The elastic modulus of the network is found to correlate strongly with the number of elastic strands in the network, except at the highly-crosslinked limit where substantial discrepancy is observed between networks from different precursors.
The model elastomers with controlled lengths of the network strands and known amounts of cross-links and dangling chains are obtained by end-linking the functionally terminated precursor PDMS with known molecular weights using multi-functional cross-linkers.
A remarkably stretchable elastomer with the ultimate strain over 3000% is obtained by optimizing the network topology for high extensibility, i.e., by reducing the amounts of trapped entanglements and the end-to-end distance of the network strands.
For some biological materials, like fibrin protofibril gels or crosslinked F-actin where the polymer persistence length is on the order of the distance between crosslinks, nonlinear elasticity is thought to result from the intrinsically non-linear force-extension relations of the network strands [11].
The model fit parameters provide a description of the network strand length distribution in the tight network and show that the network strand concentration increases and the network strand length decreases when a higher crosslinker concentration was used to prepare the tight network.
Where, ρ the density of rubber, R the gas constant, T the absolute temperature, M e the molecular weight of the network strand [19].
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