Transient network model

Jongschaap RJJ, Wientjes RHW, Duits MHG, MeUema J. A generalized transient network model for associative polymer networks. Mactomolecules 2001 34 1031-1038. 

Kamphuis, H., and Jongschapp, R.J.J. (1985). The rheological behaviour of suspension of fat particles in oil interpreted in terms of a transient-network model. Coll. Polymer Set. 263, 1008-1024. 

At this stage, we can see easily that our present model is a special case of the two-state transient network model in which chains take either A-state or B-state. The conversion between them... 

Fig. 9.12 (a) Stress overshoot of the transient network model under shear flow. The total number of active... 

Fig. 9.17 Nonlinear stress relaxation of the transient network model with a quadratic chain dissociation rate under a constant shear deformation for y = 0.5. The decay rate is fixed as (a) /3q = 0 and (b) /3q = 1. The total number Ve of active chains and the number Vg of chains that remain active from the initial state are shown on a logarithmic scale. These are normalized by the stationary value of Ve. The shear stress hxy, the first normal stress difference N, and the second normal stress difference N2 are shown in the unit of Ve B T. (Reprinted with permission from Ref. [19].)...

Another group of m( els is based on the notion of a transient network, introducing a finite lifetime for crosslinks into the classical rubber elasticity. This contains some excellent physical points. However, the dependence of Tt on the molecular mass is not attacked and remains unexplained in this picture. Thus, we do not describe the transient network models. 

Transient Network Models for Viscoelastic Properties in the Terminal Zone... 

Lele AK, Mashelkar R A. Energetically crosslinked transient network (ECTN) model implications in transient shear and elongation flows. J Non-Newtonian Eluid Mech 1998 75 99-115. 

Although the current permeability model properly reflects many of the important features of foam displacement, the authors acknowledge its limitations in several respects. First, the open pore, constricted tube, network model is an oversimplification of true 3-D porous structures. Even though communication was allowed between adjacent pore channels, the dissipation associated with transverse motions was not considered. Further, the actual local displacement events are highly transient with the bubble trains moving in channels considerably more complex than those used here. Also, the foam texture has been taken as fixed the important effects of gas and liquid rates, displacement history, pore structure, and foam stability on in situ foam texture were not considered. Finally, the use of the permeability model for quantitative predictions would require the apriori specification of fc, the fraction of Da channels containing flowing foam, which at present is not possible. Obviously, such limitations and factors must be addressed in future studies if a more complete description of foam flow and displacement is to be realized. 

FUali, M., Ouazzani, M.J., Michel, E., Aznar, R., Porte, G. and AppeU, J. (2001) Robust phase behavior of model transient networks. /. Phys. Chem. B, 105, 10528-10535. 

Of these four methods, only the population-balance method and network, or percolation, models arise from first principles. Network models that allow replication of pore-level mechanisms have the decided disadvantage of requiring large amounts of computation time and providing results on a prohibitively small grid. It seems unlikely that network or percolation models can be useful in transient displacements that demand tracking of saturation, surfactant concentration, and foam on laboratory scales, let alone field scales. 

We interpret the flare effect as a cooperative extension of molecules over the volume seen as birefringent. This cooperative extension would arise if the chains were behaving as if connected, that is, like a transient network. The fact that this connectedness arises only beyond a given concentration signifies that a cooperative effect is involved, implicit in the network model just described. The fact that it appears only at a critical strain rate, e , however, introduces a new important factor the time dependence of the connectedness. Namely, the connectedness can exist only over a very short time (t J defined by... 

Letwimolnun et al. [2007] used two models to explain the transient and steady-state shear behavior of PP nanocomposites. The first model was a simplified version of the stmcture network model proposed by Yziquel et al. [1999] describing the nonlinear behavior of concentrated suspensions composed of interactive particles. The flow properties were assumed to be controlled by the simultaneous breakdown and buildup of suspension microstructure. In this approach, the stress was described by a modified upper-convected Jeffery s model with a modulus and viscosity that are functions of the suspension structure. The Yziquel et al. model might be written ... 

Maestro et al. (2004) [9] studied the R effect on the formation and disruption of the transient network formed by worm-hke micelles, using C12EO4 as the cosurfactant Oscillatory results at low and intermediate frequencies were fitted to the Maxwell model, as had been done in other pubUcations [9j. The obtained parameters Go and Tm are presented in Eigure 12.8 vs. ratio R. It can be observed that when R is increased. Go continuously grows, nearly reaching a plateau. On the other hand, Tm quickly increases up to the R for which the viscosity maximum is found, and then decreases up to phase separation. Kunieda s group found the same tendencies for other worm-hke micellar systems, like the water-polyoxyethylene cholesteryl ether Ch(EO) -Ci2(EO) systems [lOj. Eigure 12.9 shows some until... 

Feldman KE, Kade MJ, Meijer EW, Hawker CJ, Kramer EJ (2009) Model transient networks from strongly hydrogen-bonded polymers. Macromolecules 42(22) 9072-9081... 

This chapter is devoted to the molecular rheology of transient networks made up of associating polymers in which the network junctions break and recombine. After an introduction to theoretical description of the model networks, the linear response of the network to oscillatory deformations is studied in detail. The analysis is then developed to the nonlinear regime. Stationary nonhnear viscosity, and first and second normal stresses, are calculated and compared with the experiments. The criterion for thickening and thinning of the flows is presented in terms of the molecular parameters. Transient flows such as nonhnear relaxation, start-up flow, etc., are studied within the same theoretical framework. Macroscopic properties such as strain hardening and stress overshoot are related to the tension-elongation curve of the constituent network polymers. 

We have successfully carried out the first phase of extending our original kinetic network model for calculating steady-state properties (3,4) to apply to transient experiments involving step changes in shear rate. The model is seen to possess the ability to describe these stress transients. In addition, a number of new rheological tests have been proposed as potential means to... 

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