Polymers forced vibration methods

Free vibration and forced vibration methods have been employed to determine the respective data. Free vibration was common earlier in polymer blend studies, but forced vibration data is much more common today due to the availability of more sophisticated testing equipment. Free vibration methods include the torsion pendulum, the vibrating reed and the torsional braid analyzer. The torsion pendulum is comprised of an inertial source (disk or rod), which can freely vibrate and is attached to a specimen, which is rigidly fixed at one end. Upon angular deformation of the inertial source and releasing, a damped sinusoidal curve depicts the resultant deformation of the sample [18,19]. Tan S can be calculated from... 

Perhaps the most widely used method for engineering polymers is the direct forced-vibration method. The method has the great advantage that the frequency of the excitation can be changed at will without changing the specimen. Hence it is readily possible to determine the frequency dependence of complex modulus and loss factor over a wide range. 

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... 

Dynamic viscoelastic measurements are useful in studying the structure of polymers, because these mechanical properties are sensitive to glass transition, crystallinity, cross-linking, filling systems (filler or plasticizer), molecular aggregation, and phase separation. To determine dynamic viscoelastic properties, such as storage modulus, loss modulus, and tan, various methods have been proposed, and recently many types of instruments are commercially available. Typical methods to measure the dynamic viscoelasticity are classified into three categories damped free vibration, resonance free vibration, and nonresonance forced vibration. These methods are standardized by the international standard ISO 6721 [3]. 

Dynamic mechanical analysis is quite useful to observe the result of chemical reactions of polymer chains (e.g., transesterification) as evidenced by Figs. 3.12 and 3.13 [26]. The DMA method can be applied isothermally to determine crystallization kinetics (modulus versus time measurements) [13, 27] and reaction rate of thermosetting materials (e.g., epoxy) [28]. For reaction rate determination of liquid systems, the torsional braid analyzer is most appropriate as the braid can be saturated with the prepolymer liquid. A cellulose blotter could be used for the torsion pendulum, and a section of nylon hosiery could be used for forced vibration studies (both supports saturated with liquid prepolymer). 

Normal vibration calculations, if based on a correct structure and correct potential field, would supposedly permit a unique correlation to be made between predicted and observed absorption bands. In most cases this ideal situation is far from being achieved in the study of high polymer spectra. More usually the structure and force field are to some extent unknown, or normal mode calculations are not available, so that other methods must be used in order to establish the origin of bands in the spectrum. Even if complete calculations were available it would be desirable to check their predictions by means other than a comparison of observed and predicted frequency values. One method of doing so is by studying isotopically substituted molecules, and the most useful case is that in which deuterium is substituted for hydrogen. 

The measurement method described in this article is an embodiment of the non-resonance, direct-force-excitation approach that subjects a double-lap shear sample of damping polymer to force from a vibration shaker. In concept this approach can be applied irrespective of whether the material is in a rubbery, glassy, or intermediate state. Each material specimen is small in size and behaves as a damped spring over the entire frequency range. The small specimen size is in contrast with some alternate approaches in which the specimens have sufficiently large dimensions to be wave-bearing. 

The first theoretical estimates of the modulus of elasticity of a polymer was made by Meyer and Lotmar in 1936. They showed that the modulus in the chain direction of a polymer could be calculated from spectroscopic data, using the force constants of the chemical bonds of the chain derived from the vibration frequencies of these bonds in other molecules. They were interested in cellulose and, for the calculation, considered two modes of deformation—bond stretching and bond angle opening. The method has since been extended and improved by Lyons S and Treloar, and the calculations of the latter represent the latest refinement of this type of calculation. The simplicity of the method is very attractive, as can be seen from the following derivation. It should be noted that only the chain atoms are considered, and that interchain forces are neglected. 

In Chapter 9, the vibrational spectra of linear polymers, including a description how one can obtain force constants and vibrational frequencies by calculating the total electronic energy at different bond distances, are discussed first. The theory is supplemented by methods for the treatment of vibrations in disordered polymers, which are very similar to those used in the investigation of the electronic structure in disordered chains (see Chapter 4). In several cases the theoretically computed and experimental vibrational spectra are compared. 

In subsequent studies, the same group was able to alter the NO sensor design and vary the control method by which they position the sensor over the cells. For example, to regulate the tip substrate distance using shear force control, vibration needle-type platinized carbon fiber electrodes modified with a polymer layer containing Ni tetrasnlfonate phthalocyanine tetrasodium salt were used. As... 

In all applications discussed in the following chapters the many-dimensional energy surfaces have been Scanned pointwise as a function of some appropriately chosen set of internal coordinates. Energy values thus obtained have been subjected to polynomial fits in order to find the equilibrium geometry and internal, harmonic force constants. In a few cases (polyyne, hydrogen fluoride, hydrogen cyanide) these force constants have been used for an evaluation of vibrational frequencies and phonon dispersion curves within the framework of the harmonic approximation using standard methods of polymer vibrational spectroscopy (see e.g. refs. l8,19 ). 

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