Relaxation modulus numerical data

Figure 6. Pressure dependencies of the bulk modulus obtained by the direct numerical differentiation of the in situ volumetric measurements of the glassy B203 under pressure ( relaxed modulus) in the two different runs of compression (solid symbols) and decompression (open symbols). The significant jumps of the effective bulk modulus between the final of compression and onset of decompression for both runs correspond to the jumps between relaxed and almost unrelaxed values. The inset shows pressure dependences of the first coordination number for B from the recent X-ray diffraction data. Both data are from Ref. [129].

So far, the important issue on how to determine MWDs from rheological data has been addressed with limited success, mainly for three reasons. The monodisperse relaxation function F(M,t) must be described precisely in the terminal and plateau regions, one has to provide a correct blending law yielding the polydisperse relaxation modulus G(t) and even if these two obstacles are overcome, specific mathematical procedures are needed in order to solve the ill-posed problem of numerical inversion of integrals. Many different sets of solution parameters are not physically meaningful and appropriate constraints have to be imposed in order to determine an acceptable MWD. 

Having suggested the connections between relaxation descriptors and the data it is now important to realize that here is sufficient information in isochronal scans that, with numerical analysis now readily carried out by computer, detailed parameters that describe relaxation can be determined jointly. Analysis is most conveniently carried out with the aid of a parameterized empirical phenomenological function. The method as implemented by us uses for each relaxation peak a Cole- Cole -like function (4) to represent the complex modulus,... 

Oscillatory shear rheology of EPDM plasticized with resol was used to determine an equilibrium shear modulus Ge), relaxation in compression and strain recovery. Ge was analysed with consideration of crosslink density and permanent entanglements, including evaluation of plasticizer and soluble polymer fraction. Relaxation data were modelled with the empirical Chasset-Thirion equation and it was proposed that longer relaxation times were associated with chains pendant from the network. Relaxation times increased with crosslink density. When the crosslink density was low and pendant chains were longer and more numerous, relaxation times were increased and elastic recovery diminished. ... 

Numerically calculated Cole-Cole plots as shown in Figure 9.2 could be successfully compared to experimental data, and this allows us to calculate the parameter and, hence, the ratio %reakl ep- From measurements at low angular frequencies, it is possible to determine the zero shear viscosity Tio, which usually coincides with the magnitude of the complex viscous resistance. The plateau modulus Gq will be obtained by extrapolation of the Cole-Cole data to the horizontal axis. The terminal relaxation time is then obtained from x = ri(/Go-... 

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