Ultrasonic absorption relaxation

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

Figure 2.1 Shape of the perturbation (in full line) used in chemical relaxation methods and response of the system (dashed line) (A) step perturbation as in T-jump (B) rectangular perturbation as in shock-tube (0 = duration of tiie perturbation) (C) harmonic perturbation as in ultrasonic absorption relaxation.

Studies have been performed using the ultrasonic absorption relaxation for the study of the surfactant exchange. Mixtures of sodium nonylsulfate with sodium hexyl- and pentylsulfates showed more than one relaxation process, However, the experimental conditions did not permit a determination of the... 

Most of these investigations were performed using chemical relaxation methods, ultrasonic absorption relaxation for the exchange process and T-jump, p-jump, or stopped-fiow for the micelle formation/breakdown. More recently, NMR methods have started to be used for the same purpose. 

Two main relaxation processes were evidenced by Michels et al. i in a study of solutions of the block copol5miers L64 and PF80 (see characteristics in Table 4.1). The ultrasonic absorption relaxation method revealed for L64 solutions a main relaxation process with a relaxation time in the 0.1 to 1 xs range. Faster processes of much smaller amplitude were detected and attributed to conformational changes or hydra-... 

Finally, we will only mention the ultrasonic absorption relaxation method which is, in fact, several different experimental techniques that permit the determination of relaxation times in the range 10 to 5 X 10 sec. Several of the dissociation field effect results in Table II have been confirmed by this method, and much new data on ligand substitution of alkali metal complexes have also been acquired by ultrasonic techniques (Eigen, 1963). Eigen and Tamm (1962) have thoroughly reviewed the role these techniques have played in revealing the mechanism of fast consecutive substitution reactions in metal complexes. 

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... 

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. 

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... 

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,... 

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). 

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. ... 

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. 

Fig. 3. Ultrasonic absorption curve for a single relaxation process.

Fig. 4. Ultrasonic absorption data for an intramolecular spin-equilibrium relaxation.

The rate of spin-orbit relaxation of NO (AT2/ ) has been measured using ultrasonic absorption by Bauer et al. 6, and is included in Table 11. 

Ultrasonic relaxation spectroscopy (URS) is nothing but a special treatment of data from ultrasonic absorption measurements. Micelle dynamics involves characteristic relaxation processes, namely micelle-monomer exchange and micelle formation-breakdown. Ultrasonics can provide information about the kinetics of the latter, the fast relaxation process also, theoretical expressions for the relaxation time and relaxation strength such as those derived by Teubner [76] provide self-consistent estimates of both. 

Chemical relaxation methods are widely used to study the kinetics of fast chemical reactions in solution. In particular, ultrasonic absorption techniques have been used to investigate fast exchange processes with relaxation times in the range 0.3 xs to 0.3 ns. The longer end of this time range has become accessible in recent years through the use of cylindrical resonator methods [1] which have lowered the frequency range covered by fictional pulse echo methods. 

Figure 1 shows the results of the ultrasonic absorption measurements. The data is expressed as log(a// ) vs. log/, where/ represents the measurement frequency and or, the absorption coefficient Solid lines in Fig. 1 represent the curve fitted to the single relaxation... 

Previous investigations of helix-coil transition kinetics, which used a variety of fast relaxation methods (electric field jump, ultrasonic absorption, dielectric relaxation and temperature jump), encountered many difficulties (12). The systems studied were long homopolymers (>200 residues) that often had hydrolyzable side chains. Controversial results have been reported, depending on the experimental technique employed, because unwanted side chain reactions or molecular reorientation were often difficult to distinguish from the helix-coil conformational change. However, as observed here, a maximum in the relaxation times was detected for these experiments ranging from 15 ps to 20 ns and was attributed to the helix-coil transition. 

---