Network, transient

The severity of the transient conditions can be established on the basis of past experience or data collected from similar installations. However, for large and more critical installations, such as a generating station or a large switchyard, it is advisable to carry out transient network analysis (TNA) or electromagnetic transient programme analysis (EMTP) with the aid of computers. For more details refer Gibbs et al. (1989) in Chapter 17. Where this is not necessary, the system may be analysed... 

Pietralla M, Kilian H-G (eds) (1987) Permanent and transient networks. Prog Colloid Polym Sci vol 75... 

When the monomer concentration exceeds c [see Eq. (112) and Fig. 38], the different polymer molecules are no longer separated but interpenetrate each other forming a transient network of lifetime xg. At constant temperature this network structure is characterized by a concentration-dependent correlation length (c), which may be considered as the mean mesh size of the pseudo gel. 

A semi-dilute solution has an entangled aspect similar to a network. An individual chain can be envisioned as constituted by a series of blobs of size equal to the transient network mesh size [16], which obviously decreases with increasing concentration. For c=c , is similar to the chain mean size. For c c, however, the mesh size is independent on the chain length. In a good solvent, according to Eqs. (5) and (6), these conditions are satisfied by ... 

For r>R(., the mesh size of the transient network should be equal to the blob size at distance R,., i.e.. 

D = D° exp(-ac ), where D is the diffusion, D represents the zero-concentration limit, c is the concentration, a and v are parameters, fits the data from a wide variety of probes and matrix polymers ( ). Several theoretical justifications for this behavior have been presented (97-1011. but it is not possible to tell yet which, if any, is uniquely correct. The treatments range from simple physical considerations (98) to treatments of hydrodynsumical interaction of probe and matrix (97,991. Other more complex and general treatments (1001 do not explicitly arrive at the stretched exponential form, but do closely fit the available data. Much more work needs to be done on probe diffusion in such transient networks. Beyond enhancing the arsenal of gel characterization, the problem is quite fundamental to a number of other important processes. 

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

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

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. 

A pseudo solid-like behavior of the T2 relaxation is also observed in i) high Mn fractionated linear polydimethylsiloxanes (PDMS), ii) crosslinked PDMS networks, with a single FID and the line shape follows the Weibull function (p = 1.5)88> and iii) in uncrosslinked c/.s-polyisoprenes with Mn > 30000, when the presence of entanglements produces a transient network structure. Irradiation crosslinking of polyisoprenes having smaller Mn leads to a similar effect91 . The non-Lorentzian free-induction decay can be a consequence of a) anisotropic molecular motion or b) residual dipolar interactions in the viscoelastic state. 

Surfactant solutions with rod-like micelles can have notable viscosities up to six times higher than the water viscosity [37]. This can be explained by the presence of entangled rodlike micelles (often also called worm-like micelles or thread-like micelles) which arrange themselves in a supramolecular transient network [38-41 ]. Such solutions often have elastic properties but they do not show a yield stress. This means that even high viscous solutions flow under the influence of very small shear stress. In this situation they show a zero shear viscosity which is given by ... 

In dilute solutions of polymers the chains are hydrodynamically isolated from each other and the solutions behave as a liquid. When the concentration of the polymer in the solution is increased the polymer chains become entangled, forming a transient network of obstacles. This entanglement takes place above... 

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. 

If we now Increase the concentration beyond the colls Interpenetrate more and more and the concentration fluctuations. In the dilute regime taking place over distances of order a. become smaller. A simple picture of the semldllute solution is that of a transient network with an average mesh size between Interchain crossings the quantity Is called the correlation length (see also sec. I.7.7c). A mesh volume of size 5 (also called a "blob" contains N. 

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. 

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. 

Odenwald, M., Eicke, H.-F. and Meier, W. (1995) Transient networks by ABA triblock copolymers and microemulsions A rheological study. Macromolecules, 28, 5069-5074. 

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