Polymer damping behavior

Dynamic mechanical experiments yield both the elastic modulus of the material and its mechanical damping, or energy dissipation, characteristics. These properties can be determined as a function of frequency (time) and temperature. Application of the time-temperature equivalence principle [1-3] yields master curves like those in Fig. 23.2. The five regions described in the curve are typical of polymer viscoelastic behavior. 

The damping behavior of polymers can be altered to optimize either the temperature span covered or the damping effectiveness for particular temperatures. The area under the loss modulus temperature curve tends to be constant for some polymer combination, which has been expressed by the empirical "temperature band width law" of Oberst (2) ... 

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. ... 

These equations are often used in terms of complex variables such as the complex dynamic modulus, E = E + E", where E is called the storage modulus and is related to the amount of energy stored by the viscoelastic sample. E" is termed the loss modulus, which is a measure of the energy dissipated because of the internal friction of the polymer chains, commonly as heat due to the sinusoidal stress or strain applied to the material. The ratio between E lE" is called tan 5 and is a measure of the damping of the material. The Maxwell mechanical model provides a useful representation of the expected behavior of a polymer however, because of the large distribution of molecular weights in the polymer chains, it is necessary to combine several Maxwell elements in parallel to obtain a representation that better approximates the true polymer viscoelastic behavior. Thus, the combination of Maxwell elements in parallel at a fixed strain will produce a time-dependent stress that is the sum of all the elements ... 

Liquids, on the other hand, flow if snbjected to a stress they do not store the energy bnt dissipate it almost entirely as heat and thns possess high damping ehar-acteristics. Viseoelastie polymers exhibit both elastic and damping behavior. Hence, if a sinusoidal stress is apphed to a linear viscoelastic matmal, the resnlting strain will also be sinusoidal, but wiU be out of phase when there is energy dissipation or damping in the polymer. 

Several authors used the continuum mechanics for modeling conventional polymer composites as well as PNC. Ren and Krishnamoorti [2003] used a K-BKZ integral constitutive model to predict the steady-state shear behavior of a series of intercalated nanocomposites containing an organo-MMT and a disordered styrene-isoprene diblock copolymer. The model predicts the low-y shear stress properties calculated from the experimental linear stress relaxation and the relaxation-based damping behavior. However, as it does not take into account the effect of clay platelet orientation, it is unable to predict the shear stress behavior at intermediate y and the normal stress behavior at all y and clay contents. 

Based on damping theory (Kim and Sperling 1997 Sophiea et al. 1994a), the damping behavior of a polymer can be evaluated from its dynamic mechanical behavior by expressing it as the area under the tan 8 versus temperature curve (Keskkula et al. 1971) or the area under the linear loss modulus versus temperature... 

L. H. Sperling, T. W. Chiu, and D. A. Thomas, Glass-Transition Behavior of Latex-Interpenetrating Polymer Networks Based on Methacrylic-Acrylic Pairs, J. Appl. Polym. Sci. 17(8), 2443 (1973). Polyacrylate/polymethacrylate latex IPNs. Glass transition and damping behavior. 

DMA is a very powerful method capable of providing information on the thermal mechanical behavior of polymer composites as well as viscoelastic polymer materials and the blends due to the temperature dependence of the storage modulus, loss modulus, and tan S. The glass transition behavior, which is sensitive to molecular mobihty, material stiffness, and damping behavior of a polymeric material, can be studied using DMA. 

As shown in Chapter 10, molecular dynamics in polymers is characterized by localised and cooperative motions that are responsible for the existence of different relaxations (a, (3, y). These, in turn, are responsible for energy dissipation, mechanical damping, mechanical transitions and, more generally, of what is called a viscoelastic behavior - intermediary between an elastic solid and a viscous liquid (Ferry, 1961 McCrum et al., 1967). 

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