Polymer systems applying nonlinear dynamics

Material functions must however be considered with respect to the mode of deformation and whether the applied strain is constant or not in time. Two simple modes of deformation can be considered simple shear and uniaxial extension. When the applied strain (or strain rate) is constant, then one considers steady material functions, e.g. q(y,T) or ri (e,T), respectively the shear and extensional viscosity functions. When the strain (purposely) varies with time, the only material functions that can realistically be considered from an experimental point of view are the so-called dynamic functions, e.g. G ((D,y,T) and ri (a), y,T) or E (o),y,T) and qg(o),y, T) where the complex modulus G (and its associated complex viscosity T] ) specifically refers to shear deformation, whilst E and stand for tensile deformation. It is worth noting here that shear and tensile dynamic deformations can be applied to solid systems with currently available instruments, whUst in the case of molten or fluid systems, only shear dynamic deformation can practically be experimented. There are indeed experimental and instrumental contingencies that severely limit the study of polymer materials in the conditions of nonlinear viscoelasticity, relevant to processing. 

The empirical rule of Cox-Merz describes similarities between the steady state shear viscosity as a function of shear rate and the dynamic viscosity as a function of angular velocity. The rule states that at equal values of frequency and shear rate the steady state values of the dynamic viscosity closely approach the steady state shear viscosity. As pointed out by Booij[Booij] etal the Cox-Merz rule is not applicable to strongly nonlinear melts. Utracki[Utracki] also discnssed the Cox-Merz rule and showed that it does not apply to immiseible polymer blends and filled polymer systems. Therefore, it is not surprising that the plots in Figure 4 do not coincide. More important that attempting to invoke the Cox-Merz rule is the fact that capillary date are needed to make viscosity... 

Although the Zwanzig and Mori techniques are closely related and, from a purely formal point of view, completely equivalent, the elegant properties of the Mori theory such as the generalized fluctuation-dissipation theorem imply the physical system under study to be linear, whereas this is not necessary in the Zwanzig approach. This is the main reason we shall be able to face nonlinear problems within the context of a Fokker-Planck approach (see also the discussion of the next section). An illuminating approach of this kind can be found in a paper by Zwanzig and Bixon, which has also to be considered an earlier example of the continued fraction technique iq>plied to a non-Hermitian case. This method has also been fruitfully applied to the field of polymer dynamics. 

We Initiate here the microscopic description of PDA within the ir-electron framework of Parlser-Parr-Pople (PPP) theory. Quite aside from the crystallinity and Interesting nonlinear optical properties of PDAs, we are convinced that related it-electron descriptions should apply to PA, PDA, and other conjugated polymers. Furthermore, the nature of the low-lying excited states of polymers Is a prerequisite for understanding their relaxation and dynamics. In sharp contrast to ir-electron models, a more realistic treatment of triple bonds leads to Important and previously overlooked Coulomb correlations. We focus below on the novel aspects of excitations In ene-yne systems. 

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