Dynamic mechanical storage modulus, polymers

Rheological measurements under oscillating conditions yield the dynamic mechanical properties of polymers, i.e. the storage modulus, G, the loss modulus, G , and a mechanical damping or internal friction, tan 5. In studies of the response of a material to vibrational forces, stress, strain, frequency and temperature are the key variables. When a material is subjected to cyclical stress under conditions analogous to those encountered in the intended applications, the data reflect both... 

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. 

The physical properties of the acid- and ion-containing polymers are quite interesting. The storage moduli vs. temperature behavior (Figure 8) was determined by dynamic mechanical thermal analysis (DMTA) for the PS-PIBMA diblock precursor, the polystyrene diblock ionomer and the poly(styrene)-b-poly(isobutyl methacrylate-co-methacrylic acid) diblock. The last two samples were obtained by the KC>2 hydrolysis approach. It is important to note that these three curves are offset for clarity, i.e. the modulus of the precursor is not necessarily higher than the ionomer. In particular, one should note the same Tg of the polystyrene block before and after ionomer formation, and the extension of the rubbery plateau past 200°C. In contrast, flow occurred in... 

Dynamic mechanical testers apply a small sinusoidal stress or strain to a small sample of the polymer to be examined and measure resonant frequency and damping versus temperature and forced frequency. Instrument software computes dynamic storage modulus (G ), dynamic loss modulus (G") and tan delta or damping factor. Measurements over a wide range of frequency and temperature provide a fingerprint of the polymer with sensitivity highly superior to DSC. 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

Most of the physical properties of the polymer (heat capacity, expansion coefficient, storage modulus, gas permeability, refractive index, etc.) undergo a discontinuous variation at the glass transition. The most frequently used methods to determine Tg are differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical thermal analysis (DMTA). But several other techniques may be also employed, such as the measurement of the complex dielectric permittivity as a function of temperature. The shape of variation of corresponding properties is shown in Fig. 4.1. 

Above the -relaxation process, the 2,4-TDI/PTMO polymer displayed a short rubbery plateau at a storage modulus of about 5 MPa while 2,6-TDI/PTMO was capable of crystallization, as evidenced by the ac-loss process. This difference in dynamic mechanical properties demonstrates the effect of a symmetric diisocyanate structure upon soft-segment properties. As previously discussed, single urethane links can sometimes be incorporated into the soft-segment phase. The introduction of only one of these diisocyanate molecules between two long PTMO chains inhibits crystallization if the diisocyanate is asymmetric. In the case of a symmetric diisocyanate, soft-segment crystallization above Tg can readily occur. The crystals formed were found to melt about 30°C below the reported melting point for PTMO homopolymer, 37°-43°C (19), possibly because of disruption of the crystal structure by the bulky diisocyanate units. 

The dynamic mechanical property data for Groups 1,2,and 3 materials were obtained from a Polymer Laboratory Model 983 Dynamic Mechanical Thermal Analyzer (DMTA), and include log tan S (loss factor), log E (storage modulus), and log E (loss modulus). Frequency was held constant at 10 Hz for all samples. The superposed results are shown for each group in Figures 2-10. 

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... 

Using a computerized data reduction scheme that incorporates a generalized WLF equation, dynamic mechanical data for two different polymers were correlated on master curves. The data then were related to the vibration damping behavior of each material over a broad range of frequencies and temperatures. The master curves are represented on a novel reduced temperature nomograph which presents the storage modulus and loss tangent plots simultaneously as functions of frequency and temperature. ... 

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