Relaxation chain entanglements

The solidity of gel electrolytes results from chain entanglements. At high temperatures they flow like liquids, but on cooling they show a small increase in the shear modulus at temperatures well above T. This is the liquid-to-rubber transition. The values of shear modulus and viscosity for rubbery solids are considerably lower than those for glass forming liquids at an equivalent structural relaxation time. The local or microscopic viscosity relaxation time of the rubbery material, which is reflected in the 7], obeys a VTF equation with a pre-exponential factor equivalent to that for small-molecule liquids. Above the liquid-to-rubber transition, the VTF equation is also obeyed but the pre-exponential term for viscosity is much larger than is typical for small-molecule liquids and is dependent on the polymer molecular weight. 

A new stress-relaxation two-network method is used for a more direct measurement of the equilibrium elastic contribution of chain entangling in highly cross-linked 1,2-polybutadiene. The new method shows clearly, without the need of any theory, that the equilibrium contribution is equal to the non-equilibrium stress-relaxation modulus of the uncross-linked polymer immediately prior to cross-linking. The new method also directly confirms six of the eight assumptions required for the original two-network method. 

Analogous results have been found for stress relaxation. In fibers, orientation increases the stress relaxation modulus compared to the unoriented polymer (69,247,248,250). Orientation also appears in some cases to decrease the rate, as well as the absolute value, at which the stress relaxes, especially at long times. However, in other cases, the stress relaxes more rapidly in the direction parallel to the chain orientation despite the increase in modulus (247.248,250). It appears that orientation can in some cases increase the ease with which one chain can slip by another. This could result from elimination of some chain entanglements or from more than normal free volume due to the quench-cooling of oriented polymers. 

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. 

Even if completely homogeneous and disordered in the relaxed state, a real network differs from the ideal network, defined in Chapter I. Three types of network defects are commonly considered to be present in polymer networks unreacted functionalities, closed loops, and permanent chain entanglements. Within each group there are several possibilities dependent on the arrangement of chains the effect of defects on the elastic properties of the network is thus by no means simple, as has been stressed e.g. by Case (28). Several possible arrangements are shown in Fig. 1, where only nearest neighbour defect structures have been drawn. 

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... 

Here three constants appear Go is the equilibrium modulus of elasticity 0p is the characteristic relaxation time, and AG is the relaxation part of elastic modulus. There are six measured quantities (components of the dynamic modulus for three frequencies) for any curing time. It is essential that the relaxation characteristics are related to actual physical mechanisms the Go value reflects the existence of a three-dimensional network of permanent (chemical) bonds 0p and AG are related to the relaxation process due to the segmental flexibility of the polymer chains. According to the model, in-termolecular interactions are modelled by assuming the existence of a network of temporary bonds, which are sometimes interpreted as physical (or geometrical) long-chain entanglements. 

In more recent years extensive work by Cohen-Addad [92-95] and Brereton [96-98] has lead to a more comprehensive understanding of the effect of chain entanglements on the decay of transverse relaxation in the NMR experiment. In their scale-invariant model, the polymer chain is considered to consist of a series of sub-units, the smallest of which... 

The bis-urea thin filaments can be very long in non-polar solvents such as 1,3,5-trimethylbenzene. Consequently, these solutions show a high viscosity r]/r]Q = 8 at a concentration C = 0.04 molL and at T = 20 °C) and a high concentration dependence of the viscosity (ri/rio C ) [43]. As in the case of UPy based supramolecular polymers, the value of this exponent is in agreement with Cates s model for reversibly breakable polymers [26,27]. However, the solutions are not viscoelastic, even at concentrations well above the overlap concentration [43]. Consequently, the relaxation of entanglements, probably by chain scission, must be fast (r < 0.01 s). 

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