Dispersion sound absorption

To answer the above question new results have been obtained by the study of very fast protolytic reactions in aqueous solution. These were carried out during the last few years by means of relaxation methods (sound absorption, dispersion of the dissociation field effect, temperature jump method) (for a survey cf. [3]). The neutralization reaction HgO+ -j- OH- - (Ha0)8 is the most characteristic example. It was possible to determine the rate constant of this reaction by measuring the time dependence of the dissociation field effect of very pure water of specific conductivity of 6 7 10-8 (at 25°C). 

The variation with frequency of the sound absorption coefficient, p, which rises to a maximum in the centre of the dispersion zone, is given by... 

ULTRASONIC ABSORPTION An Introduction to the Theory of Sound Absorption and Dispersion in Gases, Liquids and Solids, A.B. Bhatia. Standard reference in the field provides a clear, systematically organized introductory review of fundamental concepts for advanced graduate students, research workers. Numerous diagrams. Bibliography. 440pp. 5)4 x 8)4. 64917-2 Pa. 8.95... 

The quantity t differs from r = tvS, the isobaric, adiabatic relaxation time, by the factor r /r = (C — Cvlb)/C . Both the sound-velocity dispersion and excess sound absorption a can be written in terms of r ... 

K. Herzfeld, in Dispersion and Absorption of Sound by Molecular Processes, edited by D. Sette, Academic, New York, 1963, p. 272 ff. 

In contrast to the relatively limited number of experimental approaches utilized to determine electron collisional information for C02 laser species, many different types of experiments have been employed in the determination of heavy particle rates as a function of temperature, for temperatures slightly below room temperature up to several thousand degrees. At room temperature, measurements have been obtained using sound absorption and/or dispersion as well as impact-tube and spectrophone techniques. High temperature rate data have been obtained primarily from shock tube experiments in which electron beam, infrared emission, schlieren, and interferometric diagnostic techniques are employed. For example, as many as 36 separate experiments have been conducted to determine the relaxation rate of the C02 bending mode in pure C02 [59]. The reader is referred to the review by Taylor and Bitterman [59] of heavy-particle processes of importance to laser applications for a detailed description and interpretation of available experimental and theoretical data. 

This result shows that the phase velocity of the disturbance is a = afo/ia cos (p) and that the disturbance attenuates as x increases with a characteristic decay length given by / = ayo/(cua sin (p). The consequent dependence of the phase velocity on the frequency [see equations (115) and (116)] represents sound dispersion, and the attenuation illustrates sound absorption. Various specific results follow directly from equations (114)-(116). As CD 0, a (i o attenuation) as cd oo, a ayo... 

Stationary relaxation methods include sound absorption und dlNpcrRlon and dielectric dispersion. A sound wave is used to perturb thc system (hat causes temperature and pressure alterations on an oscillating electric field. Then, chemical relaxation is measured by determining adsorbed energy (acoustical absorption or dielectric loss), or a phase lag that is dependent on the frequency of a forcing function (Bernasconi, 1986 Sparks, 1989). In this chapter, only transient relaxation methods will be discussed. 

Techniques for measuring the complex sound speeds and moduli of polymers are described in the section on test methods. The data shows that the real and imaginary components of the elastic moduli are frequency dependent. The frequency dependence is strongest for materials with high values of the loss factor r. Materials with frequency-dependent elastic moduli are called dispersive, and measurements and theory show that sound absorption mechanisms lead to dispersion. The real and imaginary part of an elastic modulus are related by the Kramers-Kronig relations, which are presented in the next section. 

Detailed studies show that the relaxation time T ib can be calculated from the frequency v found from the inflection point in the dispersion curve, or from the maximum of sound absorption ([192]). For molecules simulated by harmonic oscillators, Tyib is expressed via (Pi,o) by Eq. (8.45). Then, one can ultimately find the transition probability (Pio) or a related quantity Z ib = l/Pi,o which is the number of collisions needed for the deactivation of the first vibrational energy level. 

The consistency of these various methods may be evaluated from the results listed in Table I of data obtained with polystyrene in solvents of low viscosity by the sound absorption (SA) and NMR relaxation methods, for poly(p-chloro-styrene) by dielectric dispersion (DD), for polystyrene labelled with nitroxyl by the ESR method and for a styrene copolymer with a small concentration of 9-p-vinylphenyl-lO-phenylanthracene residues by depolarization of fluorescence (DF). It may be seen that sound absorption and dielectric dispersion yield similar transition frequencies in the range of 12-35 MHz at 10-25 C,... 

Thus, any deviation from first-order kinetics will indicate that the azobenzene residues in the system under study isomerize at different rates. Such a dispersion of the rate constant for hindered rotation was postulated by other investigators. Cochran et al reached this conclusion on the basis of the molecular weight dependence of the relaxation times observed with polystyrene by sound absorption studies. Valeur and MonnerieS subjected a solution of polystyrene with anthracene residues incorporated into the chain backbone to a nanosecond light flash and found that the time-dependence of the anthracene fluorescence deviated from a simple exponential decay this was ascribed to differences in the local conformational mobility of the chain. 

The comparison of spectral line shapes computed on the basis of the ab initio dipole surface of He-Ar with absorption measurements has demonstrated the soundness of the data. The agreement indicates that exchange effects due to intra-atomic correlation and higher-order dispersion terms contribute significantly to the induced dipole. However,... 

For gases which deviate significantly from ideality, one may either derive a dispersion formula for a given equation of state, or else correct the observed sound velocity or absorption to ideality before fitting data to equations (79), (81), (82), or (83). 

The stress-strain relations for viscoelastic materials are reviewed. The simplest case of intrinsic absorption in polymers is a molecular relaxation mechanism with a single relaxation time. However, the relaxation mechanisms which lead to absorption of sound are usually more complicated, and are characterized by a distribution of relaxation times. Under causal linear response conditions the attenuation and dispersion of sound in a... 

Some detectors employ the optothermal effect the absorbed modulated infrared radiation heats the sample and its environment, thus producing sound waves which are recorded with a microphone. They can be combined with scanning spectrometers and interferometers. A Golay cell (Golay, 1949) measures the optothermal pressure change by a light beam which is deflected by a reflecting membrane. The first infrared process spectrometer, the URAS, alieady employed the absorption bands of a detector gas to specifically analyze the concentration of this particular gas in a sample. This is a non-dispersive spectrometer already mentioned in Sec. 1. 

Strictly connected with these ideas are experiments on the absorption and dispersion of sound waves in melanins (370). A resonance absorption was found at 1 MHz, and a rather sophisticated theoretical interpretation allowed correlation of the shear spectrum with the presence of partially ordered structures. Particularly interesting is the observation that hydrated melanins and melanosomes are exceptionally black materials with respect to ultrasound absorption. 

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