Networks with temporal junctions

Typical examples are networks in aqueous solutions of polymers with short hydrophobic chains attached at both chain ends (telechelic polymers), such as hydrophobic poly(ethylene oxide), hydrophobic ethoxylated urethane (called HEUR) [1-5], hydrophobic poly(A -isopropylacrylamide) [6,7], poly(propylene oxide)-poly(ethylene oxide)-poly(propylene oxide) triblock copolymers [8-10], etc. These networks are analogous to the polymer networks whose elastic properties are studied in Chapter 4. They differ, however, in the important point that the network junctions can break and recombine. We extend the theoretical framework of rubber elasticity to suit for the study of polymer networks with temporal cross-link junctions. 

The firs t systematic study of the reversible networks was the transient network theory developed by Green and Tobolsky [ 11 ], in which stress relaxation in rubber-Uke polymer networks was treated by the kinetic theory of rubber elasticity suitably extended so as to allow the creation and annihilation of junctions during the network deformation. 

Another stream of the study of temporal networks concerns a model network whose history involves cross-links added at a certain stage, a part of which is subsequently removed so as not to be present in the final stage of deformation (called an addition-subtraction network). On the basis of such model composite networks, Flory [14] calculated the stress relaxation, and found that it obeys slow dynamics including a logarithmic dependence of the stress, which is closer to power law rather than exponential. 

Flory s intuitive argument was later confirmed by Fricker [15] with minor modification by a replica calculation. Owing to the rather arbitrary assumption about chain creation and annihilation, the addition-subtraction network model is difficult to apply to real physical gels. 

In this chapter, we focus on thetelechelic polymers, and construct a molecular rheology that contains only the molecular parameters whose origin can easily be identified [16-19]. 

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