Viscoelastic Model Correlation

Based on the results of the characterization studies, the viscoelastic residual moments of the cross-ply specimens were predicted by the viscoelastic analysis using Equation 8.39 together with the curvature-moment relations in Equation 8.50 for the intermittent cure specimens. 

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A related issue is that the modulus is a viscoelastic property, as evidenced by the temperature/strain-rate dependence, and that for most poljnners (at least those without a large beta transition near the alpha transition) time-temperature superposition of, for example, the shear relaxation modulus is valid (80). Further, G Sell and McKenna (81) have shown that the 5neld stress vs strain rate also seems to obey time-temperature superposition. Hence there is a correlation between the viscoelastic properties and the yield response of pol5uners, though one that is not generally stated explicitly. We note that some of the models mentioned previously, such as those of Caruthers group (41,42), Tervoort and co-workers (40), and Knauss and Emri (35), are (nonlinear) viscoelastic models that have yield arising due to the nonlinear response induced by the material clock (see Viscoelasticity). 

Note that the term y in Eqs. 2-15 and 2-16 has a different significance than that in Eq. 2-14. In the first equation it is based on a concept of relaxation and in the others on the basis of creep. In the literature, these terms are respectively referred to as a relaxation time and a retardation time, leading for infinite elements in the deformation models to complex quantities known as relaxation and retardation functions. One of the principal accomplishments of viscoelastic theory is the correlation of these quantities analytically so that creep deformation can be predicted from relaxation data and relaxation data from creep deformation data. 

As shovra previously (fig.l), the con )lex influence of the metal ions even on viscoelastic properties of the gels might be sufficiently demonstrated by considering the border lines of each defined field only (fig.2-4). The squares of the adjusted correlation coefficirats lay between 0.9778 and 0.9965 for G and between 0.9951 and 0.9996 for G /G . The resulting sinple models only contained parameters significant at levels with a < 0.15, describing direct influences of each of the three cations in one set and interactions between two cations. 

The correlation between rheology and thermodynamics is likely to prove a fruitful area for investigation in the future. Very little is as yet known about the detailed mechanisms of non-linear viscoelastic flows, such as those involved in large-amplitude oscillatory shear. Mesoscopic modelling will no doubt throw light on the role of defects in such flows. This is likely to involve both analytical models, and mesoscopic simulation techniques such as Lattice... 

Due to the clear correlation between molecular properties which can be calculated by computational methods and the physical properties of the nematic phase, the dielectric anisotropy (Ae) and the birefringence (An) can be predicted with reasonable accuracy by molecular modeling [28]. On the other hand, the viscoelastic terms and Kj, K2, are currently not really predictable, even if some recent results based on neural networks [3b], Monte Carlo simulations [29] and molecular mechanics approaches [30] give rise to some careful optimism (Figures 4.8 and 4.9). 

Time dependency also enters into the consideration of the rheological response of any viscoelastic system. In the steady-state testing of such materials as molten polymers, the selected time scale should be sufficiently long for the system to reach equilibrium. Frequently, the required period, t > 10" sec, is comparable to that in thixotropic experiments. More direct distinctions between these two types of flow are the usual lack of elastic effects and larger strain values at equilibrium observed for the thixotropic materials (see Table 7.4). There is a correlation between these two phenomena, and theories of viscoelasticity based on thixotropic models have been formulated by Leonov [1972, 1994]. Inherent to the concept of thixotropy is the yield stress. 

Since the viscoelastic and creep properties of polymeric materials are often correlated with their glass-transition temperatures (Tg) [40], we considered that DSC would be a useful technique to investigate commercial maxillofacial materials. In our pioneering study [41], the effects of pigments on the DSC plots were studied for a heat-polymerized maxillofacial silicone (MDX 4-4515, Dow Coming, Midland, MI, USA), which served as a model material. 

In Chapter 3, we used the Rouse model for a polymer chain to study the diffusion motion and the time-correlation function of the end-to-end vector. The Rouse model was first developed to describe polymer viscoelastic behavior in a dilute solution. In spite of its original intention, the theory successfully interprets the viscoelastic behavior of the entanglement-free poljuner melt or blend-solution system. The Rouse theory, developed on the Gaussian chain model, effectively simplifies the complexity associated with the large number of intra-molecular degrees of freedom and describes the slow dynamic viscoelastic behavior — slower than the motion of a single Rouse segment. 

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