Polymers wave propagation methods

A comprehensive review of measurement techniques is presented by Capps (167), who also gives data for the complex Young s modulus for a range of polymers. This data includes the rubbery, transition, and glassy regions, and parameters for time-temperature superposition (eq. 45). The measiuement techniques fall broadly into three categories wave propagation methods, resonance methods, and forced-vibration nonresonance methods. The resonance and forced-vibration... 

The different experimental methods for sound wave propagation and for measuring the mechanical response or elastic constants of polymers are summarized below with an attempt to give an idea of the different time scales involved. 

The line-source technique is a transient method capable of very fast measurements. A line source of heat is located at the center of the sample being tested as shown in Fig. 4. The whole is at a constant initial temperature. During the course of the measurement, a known amount of heat is produced by the line source, resulting in a heat wave propagating radially into the sample. The rate of heat propagation is related to the thermal diffusivity of the polymer. The temperature rise of the line somce varies linearly with the logarithm of time. Starting with the Fourier equation, it is possible to develop a relationship which can be used directly to calculate the thermal conductivity of the sample from the slope of the linear portion of the curve ... 

Whorlow (1992) published a book on rheological techniques that inctudes dynamic tests and wave propagation tests. In the appendix, he listed a number of rheologicat inves-tigahon equipment manufacturers. Some of the techniques appiy more to polymers and are not relevant to our discussion. Dynamic vibration tests have been extended to fresh concrete (Teixera et at., 1998). Concord and Tassin (1998) described a method to use rheo-ophcs for the study of thixotropy in synthetic clay suspensions. A rheometer optical analyzer was used on laponite, a synthetic hectorite clay. Laponite was mixed with water and tests were conducted at various intervals for up to 100 days. Rheo-ophcs seems to be... 

It was these studies of the complex dielectric constant as a function of frequency which led to the search for euialogous methods of studying viscoelasticity hy measuring a complex viscosity or elastic modulus. The first success was observation of shear wave propagation in polymer solutions . The only theoretical treatment of wave propagation which could he found as a clue to analysis of the measurements was in a geophysical journal. From the wave propagation the complex shear modulus and its frequency dependence could be derived. 

The experiments show that the value of Young s modulus depends strongly on the method of its measurement. The highest E value is obtained from the propagation of hypersonic waves in polymers lower E values are established in... 

Another method for measuring mechanical properties on the macroscopic scale uses the relation between mechanical properties and the propagation of acoustic waves [89]. The velocity of sound waves and also the damping thereof can be directly deduced from the elastic and viscous properties. For polymers, ultrasound can be used since the damping of the acoustic waves is decreased at high frequencies. However, this method seems not to have been applied to fuel cell-related membrane materials so far. 

Ultrasonic methods have been considered for non-destructive evaluation of compositional changes and mixture uniformity in filled polymers. In principle, it is feasible to determine the size, shape and distribution of filler particles, to detect agglomeration and to assess the extent of filler-matrix interaction, through appropriate application of ultrasonic procedures [48]. The method involves determination of the elastic behaviour of solids by measurement of ultrasonic wave velocity. Propagation of a plane wave in a linear elastic material can be related to its elastic modulus (E) and density (p) according to ... 

For studies of dilute polymer solutions, measurements of high precision are necessary to obtain the small differences between the properties of solutions and solvent. Apparatus for pulse propagation in such solutions at 20 MHz has been described by Miyahara, Wada, and Hassler," and for variable path interferometry by Cerf, and for standing waves by Miyahara. jjj jjjg latter method, the frequency can be varied continuously from 1 to 20 MHz. At lower frequencies (10 to 700 kHz), the free decay of waves in a spherical vessel can be measured. In such measurements, the data are ordinarily left in terms of M (or simply velocity and attenuation, or the acoustic absorption coefficient identified in Chapter 18) with no attempt to convert them to K. ... 

Various sophisticated instrumental methods have been developed to characterize polymer blends and compatibility, including thermal, microscopy, spectroscopy and other processing techniques. Recently, ultrasound has also been applied extensively to the study of polymer blend properties in both solutions and solids. The ultrasonic velocity and attenuation by the interaction of the propagating wave were used to investigate the various physical properties of the polymer blends, including density, compatibility, molecular orientation, and phase inversion. 

As the mechanical properties of the final product often depend on the orientation of the polymer chain, it is very important to characterize the orientation of the polymer chain both quickly and accurately in nondestructive fashion. When Edwards and Thomas [55] used the propagation velocity of an ultrasonic shear wave to detect anisotropic behavior in the mechanical properties of a solid, the results obtained indicated that this method was quite sensitive for semicrystalline polymers but much less effective for amorphous polymers. 

The same method of surface ultrasonic waves can also be used for determining that thickness of the surface layer in which the prt rties differ from the properties within the bulk (IS). The values obtained for polymers of various chemical nature are within 200 and 700 /u, depending on the thidcness of the surface layers of the polymers in heterogeneous filled systems (14). It follows from the theoretically obtained equations that the thidcness of the layer derived from the data on the propagation of surface ultrasonic waves, depends both on the mechanical properties of the bulk and surface layer and on the frequency. The difference in the modulus of elasticity of the bulk and surface layer are associated with the surface tension forces. The frequency-dependence of the thickness is determined by the types of molecular motions involved in the process in accordance with the mechanical models indicated above. 

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