Transient network theories

Tanaka F, Edwards SF. Viscoelastic properties of physically cross-linked networks—transient network theory. Macromolecules 1992 25 1516-1523. 

Jeyaseelan and Giacomin (1995) examine the use of large-amplitude oscillatory-shear (LAOS) rheology of filled polymer melts (HDPE filled with carbon black) and use transient-network theory (which separates filler and polymer entanglement effects) to describe the non-linear flow behaviour. 

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. 

In the experiments, two main types of time-dependent flows have been studied start-up flows and stress relaxation. In the start-up flow experiments, shear flows with constant shear rates and elongational flows with constant elongational rates are started in the system in equilibrium under no external force, and the time-dependent stress build-up in the system is measured. In the stress relaxation experiments, constant deformations are applied to or removed from the system, and the time-dependent relaxation of the stress is measured. In this section, we study these two types within the framework of transient network theory. 

Chapter 9 presents the transient network theory of associating polymer solutions, which is the other one of the two major theories treated in this book. It studies the dynamic and rheological flow properties of structured solutions from a molecular point of view. Thus, linear complex modulus, nonlinear stationary viscosity, start-up flows, and stress relaxation in reversible polymer networks are studied in detail. 

Annable T, Buscall R, Ettelaie R, Whittletone D. The rheology of solutions of associating polymers comparison of experimental behavior with transient network theory. J Rheol 1993 37 695-725. 

Wang, S. Q., Transient network theory for shear-thickening fluids and physically cross-linked systems. Macromolecules, 25, 7003-7010 (1992). 

The transient net work model is an adaptation of the network theory of rubber elasticity. In concentrated polymer solutions and polymer melts, the network junctions are temporary and not permanent as in chemically crosslinked rubber, so that existing junctions can be destroyed to form new junctions. It can predict many of the linear viscoelastic phenomena and to predict shear-thinning behavior, the rates of creation and loss of segments can be considered to be functions of shear rate. 

The procedure used for testing the ideal Donnan theory is applicable to any model that decouples ionic effects from network elasticity and polymer/solvent interactions. Thus we require that nnet depend only on EWF and not C. While this assumption may seem natural, several models which include ionic effects do not make this assumption. For example, the state of ionization of a polymer chain in the gel and the ionic environment may affect the chain s persistence length, which in turn alters the network elasticity [26]. Similarly, a multivalent counterion can alter network elasticity by creating transient crosslinks. 

In fact, transient assembly of H-bonded water files is probably common in enzyme function. In carbonic anhydrase, for example, the rate-limiting step is proton transfer from the active-site Zn2+-OH2 complex to the surface, via a transient, H-bonded water network that conducts H+. Analysis of the relationship between rates and free energies (p K differences) by standard Marcus theory shows that the major contribution to the observed activation barrier is in the work term for assembling the water chain (Ren et al., 1995). 

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