Loss modulus Subject

Free- Vibration Methods. Free-vibration instmments subject a specimen to a displacement and allow it to vibrate freely. The oscillations are monitored for frequency and damping characteristics as they disappear. The displacement is repeated again and again as the specimen is heated or cooled. The results are used to calculate storage and loss modulus data. The torsional pendulum and torsional braid analy2er (TBA) are examples of free-vibration instmments. 

Experimentally DMTA is carried out on a small specimen of polymer held in a temperature-controlled chamber. The specimen is subjected to a sinusoidal mechanical loading (stress), which induces a corresponding extension (strain) in the material. The technique of DMTA essentially uses these measurements to evaluate a property known as the complex dynamic modulus, , which is resolved into two component parts, the storage modulus, E and the loss modulus, E . Mathematically these moduli are out of phase by an angle 5, the ratio of these moduli being defined as tan 5, Le. 

Viscoelastic properties of polypeptides in the solid state have been popular subjects of study however, they appear not to have been studied in the l t of liquid crystals so far, except in a few cases 90, 91). The d matnic loss modulus (measured... 

Dynamic mechanical relaxation tests were carried out by use of a Piezotron apparatus. Thin reedlike samples were subject to alternating tension at low applied stress and at a fixed frequency of 3 Hz. From the recorded observations, made as a function of temperature at a controlled rate of 2 °C/min, the storage modulus, E, the loss modulus, E", and the loss tangent, tan 6 = E"/E were determined. 

Fig. 8 Design of an interfacial stress rheometer. Here a magnetized rod is subjected to an oscillatory force generated by the Helmholtz coils. The motion of the rod is detected using a microscope and photodiode array. Differences between the applied force and resulting phase and magnitude of the displacement give information on the viscoelastic properties of the monolayer. Both the storage modulus G and the loss modulus G" can be determined [2,21] (reproduced with permission from the American Chemical Society)...

Another interesting result obtained for solutions of PIB in cyclohexane by Tanaka et al. (2,92) is shown in Fig. 3.4. The reduced storage modulus at infinite dilution is close to the prediction of the Rouse theory while the loss modulus is not. This result indicates the existence of an additional contribution to the intrinsic viscosity at high frequency which might be a frequency-independent high frequency limit [in contrast with the results for PMS (94,99) and for PIB in toluene (2,92)]. We will return to this subject in the following chapter. 

The effect of temperature on the mechanical properties of a liquid can be investigated using a special type of dynamic mechanical analyser called an oscillatory rheometer. In this instrument the sample is contained as a thin film between two parallel plates. One of the plates is fixed while the other rotates back and forth so as to subject the liquid to a shearing motion. It is possible to calculate the shear modulus from the amplitude of the rotation and the resistance of the sample to deformation. Because the test is performed in oscillation, it is possible to separate the shear modulus (G) into storage (G ) and loss modulus (G") by measuring the phase lag between the applied strain and measured stress. Other geometries such as concentric cylinders or cone and plate are often used depending on the viscosity of the sample. 

Rheovibron (dynamic) viscometer is widely used for measurements of dynamic mechanical properties such as loss modulus, storage modulus, and dissipation factor, each as a function of temperature. In this instrument, the test specimen is clamped between strain gauges and subjected to low order of sinusoidal strain at a specified frequency. The value of tan d is directly read and the storage and loss moduli are calculated using sample dimensions and instrument readings. 

Assume an SLS is being subjected to sinusoidal stress cycling with ,=75 GPa, 2=70 GPa and 17 = 14 MPa s. Plot the phase difference, storage modulus and loss modulus as a function of frequency. At what frequency does the maximum energy dissipation occur What is the specific damping capacity of the material at this frequency ... 

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. 

Reinforced vulcanized samples generally present a marked viscoelastic behavior that is usually studied by dynamic viscoelastic measurements. In this experiment, a sample is subjected to periodic sinusoidal shear strain y (at defined frequency (o and temperature T). Its dynamic shear modulus G is complex and can be written as the sum of the storage modulus G, and the loss modulus G". 

NR and SBR blends including carbon black were subjected to large prestrain while storage and loss modulus were measured. The loss modulus was independent of pre-strain except at high carbon black loading of 50% where an increase was found at extension ratio of less than 2. The increase of loss modulus was interpreted as due to elastomer orientation and slip at the polymer-filler interface. Both events are non-linear, with orientation transient crystals formed, while interfadal rupture is an irreversible event for the original structure. 

Dynamic Mechanical Properties n (1) The stress-strain properties of a material when subjected to an applied sinusoidally varying stress or strain. For a perfectly elastic material the strain response is immediate and the stress and strain are in phase. For a viscous fluid, stress and strain are 90° out of phase. (2) The mechanical properties of composites as deformed under periodic forces such as dynamic modulus, loss modulus and mechanical damping or internal friction. (Sepe MP (1998) Dynamic mechanical analysis. Plastics Design Library, Norwich, New York)... 

Rheological studies can provide useful information on the stability and internal microstructure of the multiple emulsions. Some attention was given to this subject in recent years, and the results help clarify certain aspects of stability and release properties of the multiple emulsions (Benichou et al., 2002b). Oscillatory dynamic tests and steady-state analyses, and parameters such as shear or complex modulus (G ), the lag phase between stress and strain (5), the storage modulus (G ), and the loss modulus (G"), provide quantitative characterization of the balance between the viscous and elastic properties of the multiple emulsions. Oscillatory measurements generally indicate that multiple emulsions are predominantly viscous in that the loss modulus... 

Viscosity versus shear rate and shear stress can also be determined at various temperatures with automated cone-plate or parallel plate analyzers, such as supplied by Rheometrics and others. Typically, a sample is subjected to a sinusoidal oscillating strain and the resultant torsional force measured. Strain gauges lead to output of elastic modulus, loss modulus and tan A. These can be obtained over a wide frequency range at a given temperature, or over a broad temperatore range, showing first- and second-order transitions. Typically, the equipment is quite expensive. 

When a gel is subjected to sinusoidal shear oscillation with an angular frequency ca and amplitude yo, the real G and imaginary part G of complex shear modulus, G (G = (G + iG ) - known as storage shear modulus and loss modulus respectively- may be obtained. The storage modulus (G ) is proportional to the elastic energy that is stored in... 

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