Ultrasonic absorption

The methods so far discussed involve a single discrete perturbation of the chemical system with direct observation of the attendant relaxation. An oscillating perturbation of a chemical equilibrium can also lead to a hysteresis in the equilibrium shift of the system. This effect can lead to the determination of a relaxation time. The process will obviously be more complex than with discrete perturbations, and there will be problems in the monitoring. 

Sound waves provide a periodic oscillation of pressure and temperature. In water, the pressure perturbation is most important in non-aqueous solution, the temperature effect is paramount. If cu (= 2 nf, where/is the sound frequency in cps) is very much larger than t (t, relaxation time of the chemical system), then the chemical system will have no opportunity to respond to the very high frequency of the sound waves, and will remain sensibly unaffected. 

A number of techniques are necessary to cover the five decades in frequency from lO to 10 Hz corresponding to relaxation times of 10 to 10 s. A wide frequency range can be spanned with only two or three methods, requiring only a few ml of sample and relatively straightforward equipment. In the 10-100 kHz range considerable volumes of sample are still required (although the material is recoverable ). 

Ultrasonic absorption played a major historical role in an understanding of the mechanisms of metal complex formation. It has also been used to study stereochemical change in metal 

One of the parameters which can be measured directly is a, the attenuation con-stant a may be divided into several parts, the actual number depending on the number (n) of discrete chemical relaxation phenomena in the system under consideration. Thus, 

Another term which is sometimes used is the chemical absorption cross-section, Q, defined as 

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Ultrasonic absorption is used in the investigation of fast reactions in solution. If a system is at equilibrium and the equilibrium is disturbed in a very short time (of the order of 10"seconds) then it takes a finite time for the system to recover its equilibrium condition. This is called a relaxation process. When a system in solution is caused to relax using ultrasonics, the relaxation lime of the equilibrium can be related to the attenuation of the sound wave. Relaxation times of 10" to 10 seconds have been measured using this method and the rates of formation of many mono-, di-and tripositive metal complexes with a range of anions have been determined. 

Ultrasonic absorption is a so-called stationary method in which a periodic forcing function is used. The forcing function in this case is a sound wave of known frequency. Such a wave propagating through a medium creates a periodically varying pressure difference. (It may also produce a periodic temperature difference.) Now suppose that the system contains a chemical equilibrium that can respond to pressure differences [as a consequence of Eq. (4-28)]. If the sound wave frequency is much lower than I/t, the characteristic frequency of the chemical relaxation (t is the... 

Figure 4-2. The phase lag between concentration and pressure in ultrasonic absorption. The cyclic pressure changes are produced by the sound wave. The cyclic concentration changes are a response to the pressure changes.

The several experimental methods allow a wide range of relaxation times to be studied. T-Jump is capable of measurements over the time range 1 to 10 s P-jump, 10 to 5 X 10" s electric field jump, 10 to 10 s and ultrasonic absorption, 10 to 10 " s. The detection method in the jump techniques depends upon the systems being studied, with spectrophotometry, fluorimetry, and conductimetry being widely used. 

This value agrees well with the rest found in [191] but not with point (4), which was shown to be ZR = 3.1 in ultrasonic experiment [216], No such discrepancy was found for pure nitrogen. Therefore it may be attributed to the low sensitivity of ultrasonic absorption measurements when nitrogen is present at small concentration in a gas mixture. 

Bulk viscosity, rj, is evaluated from the ultrasonic absorption coefficient a and shear viscosity ri by "... 

Fig. 4. Schematic diagram of experimental arrangement for pulsed ultrasonic absorption measurements. According to Ref. [29]...

It has been stated above that the difference of partial molar volumes of the LS and HS isomers AK° can be obtained from the relaxation amplitude A of ultrasonic absorption. An independent method for the determination of AE° is based on the pressure dependence of the equilibrium constant. The pressure derivative of being determined by ... 

In solution, [Co(terpy)2]2+ is also in a high-spin/low-spin equilibrium. Ultrasonic absorption measurements determined the spin equilibrium relaxation time in both water and MeOH solution to be less than 2 ns.249 Electron-donating functional groups such as methoxyl appended to the terpy ring result in a shift towards the high-spin form of the complex,250 as does replacement of one pyridyl ring with a pyrazole.251... 

Wyn-Jones, E., The Use of Ultrasonic Absorption and Vibrational Spectroscopy to Determine the Energies Associated with Conformational Changes, 5, 205. 

The ultrasonic absorption spectrum for a series of inorganic salts with /i-CD showed one relaxation process.166 No absorption was observed for solutions only containing /i-CD. The equilibrium constants determined from competitive binding isotherms were relatively low (2-30 M-1). The relaxation frequency (/, ) was related to the observed relaxation rate constant, which is equal to the sum of the association and dissociation processes. The association rate constants for all salts with the exception of perchlorate were similar and this result was interpreted to mean that... 

The presence of hydrogen bonding in water is shown by its anomalous thermophysical properties and has been confirmed by more recent methods of investigating its structure such as NMR, neutron scattering, dielectric relaxation, ultrasonic absorption,... 

II. Ultrasonic Absorption — Relaxation Phenomena Involving T and P Changes Molecular conformations, solute-solvent interactions, chemical reactions... 

Several methods are successfully applicable in this field, e.g. dielectric relaxation methods 164>, IR investigations in the near, fundamental, and far IR regions 165>, RAMAN spectroscopy 166>, NMR spectroscopy 32-34-16 ), and ultrasonic absorption i 8-i70). 

Conformational Changes, Determination of Associated Energy by Ultrasonic Absorption and Vibrational Spectroscopy (Wyn-Jones ani Pethrick) 5 205... 

The separation of the two stages is easier to discern when the rates of the two processes are so different, but it can also be seen in the ultrasonic spectra of metal-sulfate systems (Sec. 3.4.4). Ultrasonic absorption peaks can be attributed to formation of outer-sphere complexes (at higher frequency, shorter t) and collapse of outer-sphere to inner-sphere complexes (at lower frequency). In addition to uv spectral and ultrasonic detection, polarimetry and nmr methods have also been used to monitor and measure the strength of the interaction. There are difficulties in assessing the value of ATq, the outer-sphere formation constant. The assemblage that registers as an ion pair by conductivity measurements may show a blank spectroscopically. The value of Aq at T" K may be estimated using theoretically deduced expres-... 

Conventional, flow, temperature-jump, ultrasonic absorption, electric-field jump and nmr line broadening have all been used to measure the rates. UV-vis spectrophotometry and conductivity are the monitoring methods of choice. A variety of solvents have been used. The focus has been often on the dissociation since the dissociation rate constant appears in general to be the main controller of the overall stability. 

Apart from the temperature-jump technique, other relaxation methods that have been used are those of ultrasonic absorption" " and electric-field pulse. Another technique that has been used for some of the more slowly included guest molecules is that of stopped-flow. ... 

Hersey and Robinson also foundthat many guest species that show kinetic behavior apparently explicable in terms of a single-step binding, give a discrepancy between the values of the equilibrium constant determined kinetically and those determined from equilibrium studies. It was found that the equilibrium constant, deterrmned spectrophotometrically, was usually greater than the ratio of the forward and backward rate-constants, determined kinetically. They therefore suggested that this discrepancy could be adequately explained if the two-step mechanism just described was used to interpret the results. A similar proposal has also been made by Hall and coworkers, who observed a large discrepancy between AV° values for the inclusion of 1-butanol and 1-pentanol by alpha cyclodextrin, calculated from equilibrium-density measurements and kinetic, ultrasonic-absorption data. 

Gordon Atkinson I think there is, at least in principle, a way to examine a system for distribution of very similar paths. This is by relaxation technique, particularly ultrasonic absorption. A distribution of similar, though not identical paths, implies a distribution of relaxation times centered at a certain frequency. But there is a subtle experimental problem involved in distinguishing between a single relaxation time and a rather closely spaced distribution of relaxation times. 

In collaboration with the laboratory of virology of the Institute of Molecular and Cellular Biology of Strasbourg, our laboratory studied the ultrasonic absorption of the BMV (Brom mosaic virus) capside and of the dissociated system. The capside is made of 180 proteins it can easily be dissociated into 90 dimers. 

Some time ago we measured the dielectric dispersion of a plant virus particle and found a critical frequency in the kHz region, therefore in a region that may well correspond to the eventual maximum of your ultrasonic absorption. We were able to describe the mechanism leading to this dispersion in terms of the rotation of the complete virus particle and of the motion of associated (or bound) counterions on the elongated surface of the particle. 

I wonder if one of these mechanisms can be related to the one responsible for the strong ultrasonic absorption you observe with the capside. 

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