Ultrasonic Relaxation Measurements

Ultrasonic absorption measurements have clearly indicated that adenosine 3, 5 -phosphate exists in aqueous or 7M-urea solutions (pH 8.0) as a rapidly equilibrating mixture of syn and anti conformers about the iV-glycosidic bond.  

Tanaka, N. Tanaka, T. Ashida, and M. Kakudo, Acta Cryst., 1976, B32, 155. 

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In a solution where a nonzero volume change between the electronic isomers, HS and LS, is encountered, the position of the spin equilibrium will depend on pressure. The volume change, usually denoted here AF°, may be obtained from the study of the pressure dependence of equilibrium properties such as the magnetic susceptibility or the electronic spectrum. In favorable cases, A F° values may be derived from the amplitude of sound absorption observed in ultrasonic relaxation measurements of a spin equilibrium as will be shown in the... 

In ultrasonic relaxation measurements perturbation of an equilibrium is achieved by passing a sound wave through a solution, resulting in periodic variations in pressure and temperature.40,41 If a system in chemical equilibrium has a non-zero value of AH° or AV° then it can be cyclically perturbed by the sound wave. The system cannot react to a sound wave with a frequency that is faster than the rates of equilibration of the system, and in this case only classical sound absorption due to frictional effects occurs. When the rate for the host-guest equilibration is faster than the frequency of the sound wave the system re-equilibrates during the cyclic variation of the sound wave with the net result of an absorption of energy from the sound wave to supply heat to the reaction (Fig. 4). 

Experimental investigations using fast kinetic methods such as stopped-flow, temperature and pressure jumps, and ultrasonic relaxation measurements have shown that there are two relaxation processes for micellar equilibrium [12-18], characterized by relaxation times ti and T2- The first, ri, is of the order of 10 s (10 to 10 s) and represents the life-time of a surface active molecule in a micelle, i.e. it represents the association and dissociation rate for a single molecule entering and leaving the micelle, which may be represented by Eq. (2.7). 

Ultrasonic relaxation measurements have also been used for the study of stepwise ion association, but in contrast with the DRS method, it detects the ion pairing equilibria rather than the species formed, which must be assumed. NMR and Raman spectroscopy are sensitive only to CIPs and treat SIPs and 2SIPs, with solvent molecules intervening between the partner ions, as if they were free ions. A thorough treatment of the theories relating to ion association of strong electrolytes and the experimental methods used to study it are presented in the review by Marcus and Hefter [29],... 

A fourth contribution to the knowledge of ground state conformations and equilibria was obtained from ultrasonic relaxation measurements on the 2,4-diphenylpentanes in solution (Froelich et al, 1976). 

This report has been written in order to demonstrate the nature of spin-state transitions and to review the studies of dynamical properties of spin transition compounds, both in solution and in the solid state. Spin-state transitions are usually rapid and thus relaxation methods for the microsecond and nanosecond range have been applied. The first application of relaxation techniques to the spin equilibrium of an iron(II) complex involved Raman laser temperature-jump measurements in 1973 [28]. The more accurate ultrasonic relaxation method was first applied in 1978 [29]. These studies dealt exclusively with the spin-state dynamics in solution and were recently reviewed by Beattie [30]. A recent addition to the study of spin-state transitions both in solution and the... 

Here p is the solution density, v the sound velocity, ctp the coefficient of thermal expansion, Cp the specific heat, and F the concentration dependence of the equilibrium, r = [LS] -f- [HS] . The measurement of ultrasonic relaxation thus enables the determination of both the relaxation time x and the... 

The most significant results obtained for complexes of iron(II) are collected in Table 3. The data derive from laser Raman temperature-jump measurements, ultrasonic relaxation, and the application of the photoperturbation technique. Where the results of two or three methods are available, a gratifying agreement is found. The rate constants span the narrow range between 4 x 10 and 2 X 10 s which shows that the spin-state interconversion process for iron(II) complexes is less rapid than for complexes of iron(III) and cobalt(II). 

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... 

Studies on the dynamics of complexation for guests with cyclodextrins have been carried out using ultrasonic relaxation,40 151 168 temperature jump experiments,57 169 183 stopped-flow,170,178,184 197 flash photolysis,57 198 202 NMR,203 205 fluorescence correlation spectroscopy,65 phosphorescence measurements,56,206 and fluorescence methods.45,207 In contrast to the studies with DNA described above, there are only a few examples in which different techniques were employed to study the binding dynamics of the same guest with CDs. This probably reflects that the choice of technique was based on the properties of the guests. The examples below are grouped either by a type of guest or under the description of a technique. 

Ultrasonic relaxation loss, of vitreous silica, 22 429-430 Ultrasonics, for MOCVD, 22 155 Ultrasonic spectroscopy, in particle size measurement, 13 152-153 Ultrasonic techniques, in nondestructive evaluation, 17 421—425 Ultrasonic testing (UT) piping system, 19 486 of plastics, 19 588 Ultrasonic waves, 17 421 Ultrasonic welding, of ethylene— tetrafluoroethylene copolymers,... 

Measurement of an ultrasonic relaxation curve enables evaluation of both the relaxation time, t, and the relaxation amplitude, A. Interpretation of the relaxation time requires knowledge of the equilibrium constant. For a intramolecular isomerization such as a high-spin low-spin equilibrium, the forward and reverse rate constants, kl and respectively, can be evaluated from the relaxation time and the equilibrium constant from Eq. (8) (17). 

Consideration of the thermodynamics of a representative reaction coordinate reveals a number of interesting aspects of the equilibrium (Fig. 5). Because the complex is in spin equilibrium, AG° x 0. Only complexes which fulfill this condition can be studied by the Raman laser temperature-jump or ultrasonic relaxation methods, because these methods require perturbation of an equilibrium with appreciable concentrations of both species present. The photoperturbation technique does not suffer from this limitation and can be used to examine complexes with a larger driving force, i.e., AG° 0. In such cases, however, AG° is difficult to measure and will generally be unknown. 

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. 

Measurement of the relative energies of twist and chair conformations is possible using ultrasonic relaxation techniques which are suitable for observing equilibria in which there is as little as 0.1% of the higher energy conformer. By combining results from this technique with the earUer nmr... 

The experimental techniques used to obtain the properties necessary to derive the kinetic constants of interest from the ultrasonic relaxation times have been previously described in detail [2,3]. Briefly, the degree of micelle ionization (P) and the binding constant (Ka) of an alcohol to mixed micelles were obtained from specific conductivity measurements as a function of surfactant concentration at various fixed alcohol compositions. The binding constant was determined from the slopes of the curves above the cmc, as proposed by Abu-Hamdiyyah et al... 

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... 

Using Eq. (26.1) it is possible to obtain the temperature dependence of the hydrogen jump rate from the experimental data on ultrasonic loss. The Snoek relaxation measurements are especially informative if they are performed at a number of excitation frequencies. It should be noted that the Snoek effect can be observed only for sufficient elastic anisotropy, X -X2, of hydrogen sites. For hydrogen in pure b.c.c. metals, the Snoek effect has not been found [16], in spite of the uniaxial symmetry of tetrahedral sites occupied by hydrogen in these materials. It is believed that the absence of the observable Snoek effect is due to the small value of X1-X2 for hydrogen in the tetrahedral sites of b.c.c. metals. 

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