Dynamical shear modulus

Polymer Dynamic shear modulus (frequency > 1 Hz) S/MPa Quasi-static Young s modulus (frequency 0.01 Hz) E/MPa Ratio 3S/E... 

A torsional pendulum (Figure 5.80) is often used to determine dynamic properties. The lower end of the specimen is clamped rigidly and the upper clamp is attached to the inertia arm. By moving the masses of the inertia arm, the rotational momentum of inertia can be adjusted so as to obtain the required frequency of rotational oscillation. The dynamic shear modulus, G, can be measured in this manner. A related device is the dynamic mechanical analyzer (DMA), which is commonly used to evaluate the dynamic mechanical properties of polymers at temperatures down to cryogenic temperatures. 

Figure 11. Schematic diagram of a torsion pendulum for measuring dynamic shear modulus and damping. A typical damped oscillation curve is illustrated at the bottom of the figure (25)...

Thus in the mesoscopic approximation or, in other words, in the mean-field approximation, the dynamic shear modulus of the melt or the concentrated solution of the polymer (strongly entangled systems) is represented by a function of a small number of parameters... 

In some cases, network structure is modified by aminolysis reactions25. An example is the polymer formed from diglycidylic ester of o-phthalic acid and diaminodiphenilmethane. Aminolysis makes the chain between crosslinks shorter and influences the properties of the polymer (dynamic shear modulus in a rubbery... 

In the same way also the dynamic shear modulus may be found... 

Figure 5. Dynamic shear modulus-temperature behavior (torsion pendulum, 1 Hz) of 50% w/w HS copolyurethanes based on diisocyanates FDI-a (F) and MDI (M). Soft segment glass transition and hard-segment melting are in the temperature regions indicated, respectively, by and Tm.

In the initial selection of an acoustic absorbing material for an underwater application, the first considerations are often the density, and the complex dynamic shear modulus. These quantities can be measured in the laboratory,requiring only small sample sizes and hence are useful as a guide to material development. 

Figure 19.1 Dynamic shear modulus (1 cycles/s) of aPS and sPS as a function of temperature...

Figure 19.13 Dynamic shear modulus (cycles/s) of sPS, rubber modified with a mixture of 15 % Kraton G 1651 and 20 % S//BA particles produced in microsuspension...

Figure 20.7 Real part of the dynamic shear modulus G plotted against temperature for (1) sPS, (2) HDPE and (3) SEBS. Reprinted from Ref. 33 by permission of Wiley-VCH...

Figure 20.8 (a) Real part of the dynamic shear modulus G plotted against temperature for sPS/HDPE/SEBS at different compositions (wt%) (1) 0 90 10 (2) 18 72 10 (3) 36 54 10 (4) 54 36 10 (5) 72 18 10 (6) 90 0 10. (b) Real part of the dynamic shear modulus G measured at -140 °C for sPS/HDPE (solid symbols) and sPS/ HDPE/SEBS (open symbols) plotted against sPS/HDPE weight ratio. Reprinted from Ref. 33 by permission of Wiley-VCH... 

One instmment capable of measuring the dynamic shear modulus is a dynamic mechanical analyzer (DMA). A DMA measures the viscoelastic properties of a material by measuring the mechanical response that is deformed under periodic stress. Operation of a DMA tool offered by TA Instruments is as follows The sample is clamped between the ends of two parallel arms, which are mounted on low-force flexure pivots, allowing motion only in the horizontal plane. The distance between the two arms is adjustable by means of a precision mechanical slide to accommodate a wide range of sample lengths (from < 1 mm up to 65 mm). An electromagnetic motor attached to one arm drives the arm/sample to a strain (amplitude) selected by the operator. As the arm/sample system is displaced, the sample undergoes a flexural deformation [as depicted schemati-... 

Figure 4.17 Dynamic shear modulus vs. measurement frequency for an...

FIGURE 17.19 Changes occurring when keeping a 4.5% solution of a whey protein isolate (in 0.4 M NaCl) at 68.5°C for various times t (h). Shown are fraction of the protein undenatured (crei), gel permeability (7 /1015 m2), and dynamic shear modulus (<7/Pa). (From results by M. Verheul, S. P. F. M. Roefs. Food Hydrocolloids 12 (1998) 17.)... 

Torsional Pendulum Analysis (TPA). A freely oscillating torsional pendulum (7) operating at ca. 1 Hz was used for the determination of dynamic shear modulus of all cured samples as a function of temperature. The procedure recommended in ASTM-D-2236-70 was followed. 

Figure 4 shows the TPA results for the bisphenol-A and the bisphenol-S linked polymers cured at 280°C for six days. Both the dynamic shear modulus and the mechanical loss factor are given as a function of temperature from -150°C to about +300°C. During a TPA run, a temperature scan covering the complete glass-to-rubber transition could not be achieved because the sample softened as the glass transition temperature, Tg, was approached. 

Figure 2-13. The response of a sample to a sinusoidal shear strain y(t) is a sinusoidal shear stress a t) that leads the strain by a phase angle 8. Arrows show the physical meaning of the stresses

Smith, J. R., Smith, T. L., and Tschoegl, N. W. (1970). Rheological properties of wheat flour doughs. III. Dynamic shear modulus and its dependence on amplitude, frequency and dough composition. Rheol. Acta 9, 239-252. 

We would like to thank our colleagues at the Rdim and Haas Company for their helpful suggestions and providing technical sources for the manuscript, and particularly Mr Marc Adler, Dr Ronald Novak and Dr Bany Snyder. We also thank Dr Richard Ketz for the dynamic shear modulus results and Dr Cbao-jrai Chung for the particle electiophcxesis results. 

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