Modulus entanglements

A careful inspection of Tables 4 and 5 shows that changes, even limited, in the details of SAPA chemical structure may affect noticeably their fracture behavior. Although it has been carried out [1], a systematic study of their effects falls out of the scope of this article, because too many parameters are concerned. They include yield stress, p relaxation characteristics, tensile modulus, entanglement density, Mw / ratio, and also, in the high temperature range, the gap (Ta-T) between Ta and the test temperature T. Instead, emphasis will just be put here on two features whose explanation is quite simple. 

Figure 9.1. Schemalic illuslralion of dependence of Ihe modulus of a polymer on a variety of factors. A is an amorphous polymer of moderate molecular weight whereas B is of such a high molecular weight that entanglements inhibit flow. Similar effects are shown in C and D, where the polymer is respectively lightly and highly cross-linked. In E and F the polymer is capable of crystallisation, F being more highly crystalline than E...

Langley, N.R. and Polmanteer, K.E., Relation of elastic modulus to crosslink and entanglement concentrations in rubber networks. J. Polym. Sci. Polym. Phys. Ed., 12(6), 1023-1034 (1974). 

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. 

Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

So far, the existence of a well-defined entanglement length in dense polymer systems has been inferred indirectly from macroscopic experiments like measurements of the plateau modulus. However, its direct microscopic observation remained impossible. The difficulty in directly evaluating the entanglement... 

Equation (29) shows that the modulus is proportional to the cycle rank , and that no other structural parameters contribute to the modulus. The number of entanglements trapped in the network structure does not change the cycle rank. Possible contributions of these trapped entanglements to the modulus therefore cannot originate from the topology of the phantom network. 

According to the arguments based on the constrained-junction model, the term Gch should equate to the phantom network modulus onto which contributions from entanglements are added. 

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