Rheology elasticity modulus

The effect of oxidative irradiation on mechanical properties on the foams of E-plastomers has been investigated. In this study, stress relaxation and dynamic rheological experiments are used to probe the effects of oxidative irradiation on the stmcture and final properties of these polymeric foams. Experiments conducted on irradiated E-plastomer (octene comonomer) foams of two different densities reveal significantly different behavior. Gamma irradiation of the lighter foam causes stmctural degradation due to chain scission reactions. This is manifested in faster stress-relaxation rates and lower values of elastic modulus and gel fraction in the irradiated samples. The incorporation of O2 into the polymer backbone, verified by IR analysis, conftrms the hypothesis of... 

Dynamic rheological measurements have recently been used to accurately determine the gel point (79). Winter and Chambon (20) have determined that at the gel point, where a macromolecule spans the entire sample size, the elastic modulus (G ) and the viscous modulus (G") both exhibit the same power law dependence with respect to the frequency of oscillation. These expressions for the dynamic moduli at the gel point are as follows ... 

Figure 3. The increase in the incident UV light intensity enhances the cross-linking rate, as indicated by the larger slopes of the elastic modulus (G ) plotted as a function of UV exposure time. The use of either the pulse or continuous modes of irradiation do not affect the rheological properties for the NOA 61 sample. Here, the frequency of oscillation is 10 rad/s and the intensities have units of mW cm 2.

Figure 8. The extent of reaction as a function of UV exposure time, collected from real-time FTIR, along with the elastic modulus (GO as a function of UV exposure time, measured by the in situ rheological technique, shows that an appreciable elastic modulus appears only after high extents of reactions are reached.

We also correlated the elastic modulus (G ) with the extent of reaction by combining data obtained from rheology and FTIR. We found that the elastic modulus did not show an appreciable increase until a short time before the gel point of the sample had been reached. However, in the vicinity of the gel point and beyond, the elastic modulus increased significantly with conversion. Information relating modulus to extent of reaction, which plays a critical role in the application of these systems, can therefore be readily obtained using our approach. 

Now, in rheological terminology, our compressibility JT, is our bulk compliance and the bulk elastic modulus K = 1 /Jr- This is not a surprise of course, as the difference in the heat capacities is the rate of change of the pV term with temperature, and pressure is the bulk stress and the relative volume change, the bulk strain. Immediately we can see the relationship between the thermodynamic and rheological expressions. If, for example, we use the equation of state for a perfect gas, substituting pV = RTinto a = /V(dV/dT)p yields a = R/pV = /Tand so for our perfect gas ... 

Figure 3.25 Storage modulus, elastic modulus, and loss angle for a cone and plate rheological measurement. The data are for a GPPS resin with an MFR of 1.5 dg/min (5 kg, 200°C) measured at 225°C...

The results obtained by the present mechanical measurements are also consistent with the previous experimental results of the dynamic light scattering studies of the collective diffusion coefficient of gels and the rheological studies of the shear modulus of gels. The studies published by different researchers indicate that the concentration dependence of the collective diffusion constant of the polymer networks of gel and that of the elastic modulus are well represented by the following power law relationships [2, 3, 5]... 

Rheologically, the BCC phase behaves as a solid, as expected, i.e. the dynamic elastic modulus is independent of frequency at high frequency in the linear... 

Being a disperse system, the foam exhibits a more complex behaviour when subjected to mechanical loading, compared to that of its constituting phases liquid and gas. Of all rheological parameters the latter are characterised by the viscosity alone. The complete description of the foam system requires knowledge of the constants of elasticity (modulus of... 

For a viscoelastic solid (like an organogel), any rheological description should give a constant finite elastic modulus and infinite viscosity at zero frequency or long times. The situation is somewhat comparable to that of a cross-linked network [2. The equilibrium shear modulus for small deformations is proportional... 

In 1992, Vreeker et al. presented rheological data for aggregated fat networks in the framework of previous fractal theories. These authors indicated that the elastic modulus varied with particle concentration according to a power law, in keeping with the proposed models for the elasticity of colloidal gels. 

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