Entanglement formation

The combined effects of a divalent Ca counterion and thermal treatment can be seen from studies of PMMA-based ionomers [16]. In thin films of Ca-salts of this ionomer cast from methylene chloride, and having an ion content of only 0.8 mol%, the only observed deformation was a series of long, localized crazes, similar to those seen in the PMMA homopolymer. When the ionomer samples were subject to an additional heat treatment (8 h at 100°C), the induced crazes were shorter in length and shear deformation zones were present. This behavior implies that the heat treatment enhanced the formation of ionic aggregates and increased the entanglement strand density. The deformation pattern attained is rather similar to that of Na salts having an ion content of about 6 mol% hence, substitution of divalent Ca for monovalent Na permits comparable deformation modes, including some shear, to be obtained at much lower ion contents. 

In elongational flow, the entanglement regime was observed at much lower concentrations, even below [r ] c = 0.1 [169], The effect was initially thought to be the result of coil expansion in flow, but was later discarded in favor of the lifetime for entanglement formation, under dynamic conditions of flow. 

Networks obtained by anionic end-linking processes are not necessarily free of defects 106). There are always some dangling chains — which do not contribute to the elasticity of the network — and the formation of loops and of double connections cannot be excluded either. The probability of occurrence, of such defects decreases as the concentration of the reaction medium increases. Conversely, when the concentration is very high the network may contain entrapped entanglements which act as additional crosslinks. It remains that, upon reaction, the linear precursor chains (which are characterized independently) become elastically effective network chains, even though their number may be slightly lower than expected because of the defects. 

This behaviour is thought to be due to the formation of a network structure caused by entanglement of the longchain molecules in solution. Plotting the data of viscosity measurements of pectin solutions of different concentrations reveals the same behaviour, confirming Onogi s observation, with a critical pectin concentration of about 1 % (w/w). 

Through physical interactions such as entanglements, electrostatics, and crystallite formation... 

Entanglement and weak gel formation are characteristic of some oilfield polysaccharides such as guar and starch, but are present only weakly, if at all, in both xanthan and succinoglycan solutions. Solutions of xanthan and succinoglycan are thus able to pass through porous media such as rock, while guar and starch cannot because of their gel-like nature. Hence the different uses of these polymers in the oilfield. 

Since both the temperature dependence of the characteristic ratio and that of the density are known, the prediction of the scaling model for the temperature dependence of the tube diameter can be calculated using Eq. (53) the exponent a = 2.2 is known from the measurement of the -dependence. The solid line in Fig. 30 represents this prediction. The predicted temperature coefficient 0.67 + 0.1 x 10-3 K-1 differs from the measured value of 1.2 + 0.1 x 10-3 K-1. The discrepancy between the two values appears to be beyond the error bounds. Apparently, the scaling model, which covers only geometrical relations, is not in a position to simultaneously describe the dependences of the entanglement distance on the volume fraction or the flexibility. This may suggest that collective dynamic processes could also be responsible for the formation of the localization tube in addition to the purely geometric interactions. 

Many polymers solidify into a semi-crystalline morphology. Their crystallization process, driven by thermodynamic forces, is hindered due to entanglements of the macromolecules, and the crystallization kinetics is restricted by the polymer s molecular diffusion. Therefore, crystalline lamellae and amorphous regions coexist in semi-crystalline polymers. The formation of crystals during the crystallization process results in a decrease of molecular mobility, since the crystalline regions act as crosslinks which connect the molecules into a sample spanning network. 

The models presented in the previous section are of an elementary nature in the sense that they ignore contributions from intermolecular effects (such as entanglements that are permanently trapped on formation of the network). Among the theories that take account of the contribution of entanglements are... 

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