Shear storage modulus, polymers

Fig. 11. Effect of dielectric constant of dispersed particle on the ER effect in a polymer gel. The increment in shear storage modulus induced by an ac electric field of 0.4 kV/mm is plotted as a function of the real part of the dielectric constant of the particle...

Figure 1. Dynamic shear storage modulus and loss tangent as a function of temperature for PS-0.02MAA-Na plasticized to varying degrees by diethylbenzene (DEB) curves 1, "5 2, 80 3, 84 4, 88 5, 92 6, 100 wt % polymer(adapted from ref. 25).

Figure 13. Shear storage modulus of the combined LC polymer specified in Scheme 4 as a function of the extent of cross-linking [11].

Samples of H-H and H-T PS were also subjected to the measurements of the dynamic shear complex viscosity and dynamic shear moduli at 160° and 190°C (53). At lower shear stress the behavior of the H-T is essentially Newtonian. The departure from the Newtonian behavior occurs above 10 dyn/cm. On the other hand, the behavior of the H-H PS is non-Newtonian even at 160°C. and at low shear stresses of 10 dyn/cm. The melt viscosity of H-H PS decreases more rapidly with stress as does the melt viscosity of the H-T polymer. As temperature and stress is increased, the rheological behavior of the two polymers are the same (as can be seen at 190°C.). The dynamic shear storage modulus reveals also a small but significant difference in the rheological behavior of H-T and H-H PS as the G with u for the H-H PS is smaller than for the H-T polymer. Results from the melt rheology studies also indicate as does solution behavior that the polymer chain in H-H PS is stiffer than is H-T PS (53). 

C. D. Han and M. S. Jhon, Correlation of the first normal stress difference with shear stress and of the storage modulus with loss modulus for homopolymers, J. Appl. Polym. Sci. 32(3), 3809— 3840 (1986). 

This section examines the dynamic behavior and the electrical response of a TSM resonator coated with a viscoelastic film. The elastic properties of viscoelastic materials must be described by a complex modulus. For example, the shear modulus is represented by G = G + yG", where G is the storage modulus and G" the loss modulus. Polymers are viscoelastic materials that are important for sensor applications. As described in Chapter S, polymer films are commmily aj lied as sorbent layers in gas- and liquid-sensing applications. Thus, it is important to understand how polymer-coated TSM resonators respond. 

When the stress is decomposed into two components the ratio of the in-phase stress to the strain amplitude (j/a, maximum strain) is called the storage modulus. This quantity is labeled G (co) in a shear deformation experiment. The ratio of the out-of-phase stress to the strain amplitude is the loss modulus G"(co). Alternatively, if the strain vector is resolved into its components, the ratio of the in-phase strain to the stress amplitude t is the storage compliance J (m), and the ratio of ihe out-of-phase strain to the stress amplitude is the loss compliance J"(wi). G (co) and J ((x>) are associated with the periodic storage and complete release of energy in the sinusoidal deformation process. Tlie loss parameters G" w) and y"(to) on the other hand reflect the nonrecoverable use of applied mechanical energy to cause flow in the specimen. At a specified frequency and temperature, the dynamic response of a polymer can be summarized by any one of the following pairs of parameters G (x>) and G" (x>), J (vd) and or Ta/yb (the absolute modulus G ) and... 

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