Storage modulus 662 Subject

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. 

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. 

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". 

Joseph et had also prepared the oil palm microfibril-reinforced NR composites by conventional mechanical blending. The used microfibrils were separated from the oil palm fibres by using the steam explosion method, and were subsequently subjected to treatments such as mercerization, benzoylation, and silane treatment. They found that the storage modulus value of untreated and treated microfibril-reinforced NR composites was higher than that of macrofibre-reinforced composites. The Tg values of microfibril-reinforced composites were slightly higher than that of macrofibre-reinforced composites. The treated microfibril-reinforced NR composites displayed better adhesion between fibre and NR matrix. 

Thermal stability properties are measured by two complementary methods, i.e. tensile-type measurements at elevated temperatures using a hot-air environmental chamber and also the Dynamic Mechanical Thermal Analyzer (DMTA) method. In the DMT A test a small rectangular strip (40 mm X 10 mm x 2 mm) is subjected to constant cyclic deformation over a changing temperature range and the storage modulus ( ) recorded and used to relate change of stiffness with temperature. 

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). 

A discussion of this subject is presented below. The additional oMitribution GX is said to arise from permanently trapped (inter-chain) entanglements in the network. Linear polymers of high molecular wd t exhibit a storage modulus G (constant over a wide range of frequencies This plateau modulus... 

Unked membrane. Furthermore, the storage modulus after cross-linking is not decreased after 300 °C but it reaches a plateau and this behavior is characteristic of cross-linked networks. The cross-linked membranes were subjected to treatment with the Fenton s reagent in order to evaluate their oxidative stability. In all cases they preserved their mechanical properties showing thus the high oxidative stability of the cross-linked structures. 

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