Shear loss modulus, polymers

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. 

Table 2. Influence of Asphalt Type and Polymer Type on SHRP Stiffness Parameter, Shear Loss Modulus and Dynamic Viscosity of Neat and Rubber Modified Paving Grade Asphalt Cements.

Figure 3. Plots of shear loss modulus, G", versus reduced frequency neat, polymer and rubber modified paving grade AC10-3 binders. Reference material Novaphalt AC10.

The Rheometric Scientific RDA II dynamic analy2er is designed for characteri2ation of polymer melts and soHds in the form of rectangular bars. It makes computer-controUed measurements of dynamic shear viscosity, elastic modulus, loss modulus, tan 5, and linear thermal expansion coefficient over a temperature range of ambient to 600°C (—150°C optional) at frequencies 10 -500 rad/s. It is particularly useful for the characteri2ation of materials that experience considerable changes in properties because of thermal transitions or chemical reactions. 

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). 

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... 

The development of a maximum in tan 5 or ihe loss modulus at the glass-to-rubber transition is explained as follows. At temperatures below Tg the polymer behaves elastically, and there is little or no flow to convert the applied energy into internal work in the material. Now It, the energy dissipated as heat per unit volume of material per unit time because of flow in shear deformation, is... 

Oscillatory shear data for two nearly monodisperse linear polymers with M/Me = 40, reduced by their terminal loss modulus maximum. Triangles are the storage modulus G and circles are the loss modulus G". Filled symbols are for polybutadiene with... 

Figure 9.15. Loss modulus of glass beads filled polyamide-6 vs. shear frequency. [Adapted, by permission, from Ou Y-C, Yu Z-Z, Polym. Int., 37, No.2, 1995,113-7.]...

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).

Through use of classical network theories of macromolecules, G has been shown to be proportional to crosslink density by G = nKT -i- Gen, where n is the nnmber density of crosslinkers, K is the Boltzmann s constant, T is the absolnte temperature, and Gen is the contribution to the modulus because of polymer chain entanglement (Knoll and Prud Homme, 1987). The loss modulus (G") gives information abont the viscous properties of the fluid. The stress response for a viscous Newtonian fluid would be 90 degrees out-of-phase with the displacement but in-phase with the shear rate. So, for an elastic material, all the information is in the storage modulus, G, and for a viscous material, aU the information is in the loss modulus, G". Refer to Eigure 6.2, the dynamic viscosities p and iT are defined as... 

Aqueous viscoelastic surfactant solutions for hair and skin care are disclosed in U.S. Patent 5,965,502. Rheology conditions are specified for optimum flow behavior, in terms of the shear modulus as a function of temperature and pH. A representative graph of the storage and loss modulus as a function of angular frequency is presented in the patent and this is shown in Figure 4.8. Cited compositions contain anionic, betainic, and nonionic surfactants, electrolytes, and a water-soluble polymer. A nonionic gel personal cleanser is specified in U.S. Patent... 

These differences are shown in the following examples where measurements of the dynamic moduli, G and G" are used to monitor the structure of gel networks. Measurements are performed by imposing an oscillatory shear field on the material and measuring the oscillatory stress response. The stress is decomposed into a component in phase with the displacement (which defines the storage modulus G ) and a component 90 out of phase (which defines the loss modulus G"). The value of G indicates the elastic and network structure in the system (15, 17, 18) and can be interpreted by using polymer kinetic theories. 

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