Unentangled network

Experimental estimates of p and // usually must rely on a model for the crosslinking chemistry, making quantitative tests of the phantom model difficult. Network defects preclude the use of Eqs (7.31) and (7.41), written in terms of the molar mass of a network strand M. Indeed, since Ms is not known for real networks and the affine and phantom models predict the same classical form of the stress-elongation curve [Eqs (7.32) and (7.33)] there is no practical means of determining which (if either) model is correct for small deformations of unentangled networks. For these reasons, we henceforth describe the modulus of all classical models as a network of strands with apparent molar mass M ... 

The results in this section were all derived for unentangled networks. The Edwards tube model for entangled networks gives identical results with N replaced by N, the number of Kuhn monomers in an entanglement strand in the preparation state, because both entanglement strands and network strands are assumed to deform affinely in the Edwards tube model. If the Edwards tube model were correct, the universal relations [Eqs (7.91) and (7.92)] would still apply for entangled networks, since they are independent of N. However, the non-affine tube models predict that entangled networks will swell considerably more than the Edwards tube model predicts. 

The total pair-wise entanglement contribution is simply the sum of dS for strand pairs with all possible sets of internal coordinates. In a network of N strands there will be N(N — l)/2 such pairs. However, classification is only significant for pairs that are relatively close. Pairs separated by more than a few radii of gyration will belong to unentangled class exclusively. This assures that the total entropy change will be proportional only to N. 

Another amazing property of polymer networks is their ability to change volume manyfold when exposed to an appropriate solvent. When a network polymer is swollen in a solvent it is called a gel. In this section, the swelling of unentangled gels is treated. At the level of the Edwards tube... 

Stukalin EB, Cai LH, Kumar NA, Leibler L, Rubinstein M (2013) Self-healing of unentangled polymer networks with reversible bonds. Macromolecules 46(18) 7525-7541... 

A new concept has been recently introduced to dilute a loose network of polymer chains not with a solvent (water) but with multiple short covalently attached unentangled side chains. In such a case, they could never evaporate and would provide a permanent non-leachable diluent that would reduce the moduli to a value of ca 1 kPa, forming anew class of stable supersoft elastomers [229,230]. 

Elastomer is a general term used for cross-linked polymeric materials such as rubber with elastic properties described above. However, elastomers are not purely elastic materials and they exhibit damping, that is, fractional energy loss per cycle in, say, an oscillatory experiment. The energy loss is due primarily to stress relaxation (viscous dissipation) of inelastic pendant chains and unentangled loops in the network. In the case of a prescribed stress sinusoidal deformation, the applied stress is expressed as... 

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