Dynamic shear storage modulus

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).

The dynamic shear storage modulus (G1) and loss modulus (G") were measured from -150° to 50°C using the forced torsion fixture on a Rheometric Mechanical Spectrometer (RMS). When the storage modulus dropped below 10 Pa. this fixture became insensitive. For moduli less than 10 Pa, the parallel plate fixture with serrated disks was used. The parallel plate fixture was used to extend the dynamic mechanical measurements to high temperatures. Degradation above about 250°C dictated this temperature as an upper limit for RMS measurements. Further discussion of equations and use of these fixtures are given elsewhere (2,8). 

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). 

The distribution of relaxation time and that of retardation time are quantitatively related. Also, the result from any linear viscoelastic experiment is quantitatively related to distribution of relaxation or retardation time. Therefore, from the result of one type of linear viscoelastic measurement, the data of any other type of measurement can be calculated, provided the data are available for a wide range of time scales. For example, dynamic shear storage modulus, G (a>) and dynamic shear loss modulus, G"(co), may be calculated from relaxation modulus, G(t). The method of calculation is described in textbooks [6] and outside of scope of this book. The importance here is to recognise that the distribution of the relaxation time is related to every data of linear viscoelasticity. 

The evolution of the dynamic viscosity rp (co, x) or of the dynamic shear complex modulus G (co.x) as a function of conversion, x, can be followed by dynamic mechanical measurements using oscillatory shear deformation between two parallel plates at constant angular frequency, co = 2irf (f = frequency in Hz). In addition, the frequency sweep at certain time intervals during a slow reaction (x constant) allows determination of the frequency dependence of elastic quantities at the particular conversion. During such experiments, storage G (co), and loss G"(co) shear moduli and their ratio, the loss factor tan8(co), are obtained ... 

Pakalapati et al [115] investigated some carbon/thermoplastic laminates. The materials were pultruded and they consisted of 50 v/o unidirectional continuous polyacrylonitrile-based carbon fibres in DuPont J-2 aromatic polyamide-based thermoplastic matrix. They were subjected to anodic and cathodic currents in sea water. Dynamic mechanical analysis was carried out in situ to measure the shear storage modulus (G ) and shear loss modulus (G") of 1.27mm diameter rod shaped samples, subjected to small amplitude torsional oscillations. The moduli were constant with time in air. 

Figure 11.8 Dynamic mechanical analysis, plot of shear storage modulus G with respect to shear loss modulus G" for CEBC 66.32.40 as obtained from frequency sweeps at various temperatures above and below the order-disorder transition (240 O 235 230 A 225 O 220...

It turns out that stress relaxation following a simple shear deformation is seldom employed experimentally. A more common technique is to measure the steady state response to small sinusoidal deformations as a function of angular frequency to. The dynamic storage modulus G (to) and loss modulus G"(to) in small sinusoidal deformations are related to G(t) ... 

Other types of linear viscoelastic experiments may be used. Dynamic shear compliance measurements provide the storage and loss compliances J (co) and J"(co). An equation analogous to Eq.(3.12) is available for determining the initial modulus from J"(co) ... 

The bulk rheological properties of the PFPEs, including the melt viscosity (p), storage modulus (G ), and loss modulus (G"), were measured at several different temperatures via steady shear and dynamic oscillation tests. Note that we denoted p as melt viscosity and r as solution viscosity. An excellent description of the rheology is available in Ferry [99]. 

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. 

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