Polymers elastic waves

The mechanical properties of polymers are controlled by the elastic parameters the three moduli and the Poisson ratio these four parameters are theoretically interrelated. If two of them are known, the other two can be calculated. The moduli are also related to the different sound velocities. Since the latter are again correlated with additive molar functions (the molar elastic wave velocity functions, to be treated in Chap. 14), the elastic part of the mechanical properties can be estimated or predicted by means of the additive group contribution technique. 

The usual polymers do not conduct electricity. Consequently, heat cannot be transferred by electrons in these polymers. Heat must be mostly transported by elastic waves (phonons in the corpuscular picture). The distance at which the intensity has decreased to ie is known as the free path length. This free path length is comparatively independent of temperature for glasses, amorphous polymers, and liquids and is about 0.7 nm. From this., it can be concluded that the weak decrease in thermal conductivity observed for amorphous polymers below the glass-transition temperature is essentially due to a decrease in the heat capacity with temperature (see Figures 10-26 and 10-4). 

Measurements of the velocity and attenuation of elastic waves at ultrasonic frequencies are important, especially for oriented polymers and composites. Compact solid specimens with dimensions of the order of 10 mm are required. 

Nakamura, Y. andOtani, T. (1993)Smdy of surface elastic wave induced on backing material and diffracted field of a piezoelectric polymer film hydrophone, J. Acoust. Soc. Am., 94,1191 9. 

Acoustic emission has recently been shown to be a promising technique for evidence of deltydration phenomena in Nafion-like membrane (Legros et al. 2009). Upon mechanical sohdtationthe membrane polymer can generate transient elastic waves, called acoustic emission. The waves, caused by stmctural change in the polymeric materials undergoing dehydration, can be converted to electrical signals by piezoelectric sensors. 

The sets of equations are solved by the assumption of periodic waves and, by expansion in powers of the wave number, a relation is found for the limiting case of long waves so that the elements of the dynamical matrix elastic constants of the continuum. It is also possible to derive the Raman frequencies from the lattice dynamics analysis but this does not seem to have been done for polymer crystals, though they have been derived for example, for NaCl and for diamond. 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

Continuing to use PVAc as the canonical example of a stable and easily reproducible polymer monolayer, we show how the two quantities, the static elasticity es from 77-A the isotherm, and the corresponding ej deduced from the SLS experiment, compare and contrast with each other for the time being, we defer to later the SLS results. This is shown in Fig. 12. Agreement between the two is remarkable up to respective maximum points. The observed deviation at higher 77 is not expected since the monolayer state is no longer maintained, hence the static elastic responses in macroscopic scales are not likely to be the same as the dynamic response to spontaneous capillary waves. 

In this section we will describe how a proper accounting for film dynamics, based on a model of the thin-film/acoustic-wave interactions, can be used to quantitatively evaluate the shear modulus values as a function of temperature. As described in Section 3.1, an equivalent-circuit model can be used to relate the measured TSM electrical characteristics to the elastic properties, density, and thickness of a polymer film coating the device. Consequently, measurements made with polymer-coated TSM devices can be used to extract the shear elastic properties of the film. 

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