Temporary network

The pattern can be obtained from the polymer temperature or concentration variations in addition to the change of G°N. The relaxation function may be too complicated a mathematical expression ever to be calculated, nonetheless, it obeys a property of invariance which allows the superposition of all normalised relaxation curves to one another by adjusting a suitable factor to the time scale of each curve. The time shift factor is found to obey the equation 

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Rubber-like models take entanglements as local stress points acting as temporary cross finks. De Cloizeaux [66] has proposed such a model, where he considers infinite chains with spatially fixed entanglement points at intermediate times. Under the condition of fixed entanglements, which are distributed according to a Poisson distribution, the chains perform Rouse motion. This rubber-like model is closest to the idea of a temporary network. The resulting dynamic structure factor has the form ... 

The plateau region appears when the molecular weight exceeds Mc [(Mc)soln. for solutions], and is taken to be a direct indication of chain entanglement. Indeed the presence of a plateau may be a more reliable criterion than r 0 vs M behavior, especially in solutions of moderate concentration where viscosity may exhibit quite complex concentration and molecular weight behavior. It is postulated that when M greatly exceeds Mc, a temporary network structure exists due to rope-like interlooping of the chains. Rubber-like response to rapid deformations is obtained because the strands between coupling points can adjust rapidly, while considerably more time is required for entire molecules to slip around one another s contours and allow flow or the completion of stress relaxation. 

The combined viscosity and diffusion measurements on concentrated systems by Bueche et al. (33), were described in Section 2. The results suggest that viscosity behavior above Mc can be explained simply in terms of an enhanced Stokes friction for the molecules. Bueche (7, 224) suggested that since polymer molecules in concentrated systems are looped through the coils of neighboring molecules, relative motion must be resisted by the need for these loops to slip around one another. Each molecule is assumed to participate in an average of E such temporary couples, creating (for E > 1) a temporary network... 

Generally, T2 relaxation times are very sensitive to slower relative translational motions of the polymer chains and can provide information on intramolecular couplings, such as chemical crosslinks and chain entanglements. Numerous studies on both permanent and temporary networks are presented in a series of papers by Charlesby and co-workers 74,86 94). In the case of extracted polymer networks, T2s relaxation is observed in the crosslinked (gel) fraction, while T2 relaxation occurs in the soluble fraction of the irradiated polymer86 . It is shown that the fraction of more mobile protons, (1-f). has the same general trend with increasing... 

An entangled polymer, with a characteristic Me value, can be considered as a temporary network with polymer strands of molar mass Me. The maximum extension ratio, Anet> that can be achieved is ... 

There must be a procedure for granting controlled temporary network access for personnel ((Part 11.10(d)). 

The function F(t — t ) is related, as with the temporary network model of Green and Tobolsky (48) discussed earlier, to the survival probability of a tube segment for a time interval (f — t ) of the strain history (58,59). Finally, this Doi-Edwards model (Eq. 3.4-5) is for monodispersed polymers, and is capable of moderate predictive success in the non linear viscoelastic range. However, it is not capable of predicting strain hardening in elongational flows (Figs. 3.6 and 3.7). 

Miiller-Plathe F (2002) Coarse-graining in polymer simulation From the atomistic to the mesoscopic scale and back. J Chem Phys Phys Chem 3 754—769 Muller R, Picot C, Zang YH, Froelich D (1990) Polymer chain conformation in the melt during steady elongational flow as measured by SANS. Temporary network model. Macromolecules 23(9) 2577—2582... 

Schieber JD, Neergaard J, Gupta S (2003) A full-chain temporary network model with sliplinks, chain-length fluctuations, chain connectivity and chain stretching. J Rheol 47(l) 213-233... 

The principle of the NMR approach to semi-local properties of polymeric melts is considered in Section 2 it is shown how the existence of a temporary network structure is detected from the relaxation of the transverse magnetisation of protons attached to chains. The observation of segmental motions from the longitudinal relaxation of proton magnetisation is described in Section 3 it is also shown how local motions in concentrated polymeric solutions can be probed from the diffusion process of small molecules. Section 4 is devoted to the analysis of the effect of entanglement relaxation on NMR properties. 

In this Section, the attention is focused on properties of the tramsverse relaxation of protons attached to polymer molecules it is sensitive to the presence of temporary network structures in molten polymers. Any high polymer melt is picttjred as an ensemble of chain segments with temporarily fixed ends. 

NMR investigations into properties of the temporary network structure formed in polybutaiene were made by varying both the modulus of temporary elasticity and the polymer concentration ( >. 

The presence of a temporary network structure manifests itself through the first factor in the right hand side of Eq. 17. It comes from the h (t) component of the relaxation function. The second factor results from fast non-isotropic motions of monomeric imits which give rise to the (t r(t) function defined in equations (6) and (9). It must be noticed that the reference temperature Ti = Tg(,xi,2) +50 which appears in NMR properties, is close to the reference temperature Tj introduced from viscoelastic measiurements [11]. The second factor reflects a free volume effect it depends necessarily on an expansion coefficient which is about equal to 10-3K. 

Integral temporary network models and molecular theories. 

Both these models find their basis in network theories. The stress, as a response to flow, is assiimed to find its origin in the existence of a temporary network of junctions that may be destroyed by both time and strain effects. Though the physics of time effects might be complex, it is supposed to be correctly described by a generalized Maxwell model. This enables the recovery of a representative discrete time spectrum which can be easily calculated from experiments in linear viscoelasticity. 

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