Relaxation ultrasonic

The ultrasonic relaxation loss may involve a thermally activated stmctural relaxation associated with a shifting of bridging oxygen atoms between two equihbrium positions (169). The velocity, O, of ultrasonic waves in an infinite medium is given by the following equation, where M is the appropriate elastic modulus, and density, d, is 2.20 g/cm. ... 

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... 

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... 

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). 

Fe(acac2trien)]N03. For the iron(III) complex of the hexadentate Schiff-base ligand acac2trien, the barrier heights have been determined from ultrasonic relaxation [94] as AG[h = 6-28 kcalmoD = 2196 cm and AGJil = 5.85 kcalmol= 2046 cm The difference of zero-point energies has been obtained from equilibrium studies as AG° = 0.43 kcal mol =... 

The observation of a single set of resonances in the NMR spectra of [Fe(HB(pz)3)2], spectra that are clearly obtained for a mixture of the high-spin and low-spin forms of the complex, indicates that the equilibrium between the two states is rapid on the NMR time scale [27]. Subsequent solution studies by Beattie et al. [52, 53] using both a laser temperature-jump technique and an ultrasonic relaxation technique have established that the spin-state lifetime for [Fe(HB(pz)3)2] is 3.2xl0 8 s. These studies also established... 

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). 

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. 

Another approach that has been used to extract rate constants from ultrasonic relaxation data involves using independently determined equilibrium constants to determine concentrations of each species at equilibrium163 or, for special cases where molecule-specific electrodes exist, direct determination of equilibrium concentrations.167,168... 

Table 11 Equilibrium constants and association and dissociation rate constants for alcohol/ CD complexes determined by ultrasonic relaxation at 25°C...

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,... 

Pulse ultrasonic relaxation method, 32 18 Pump-and-probe techniques, 46 137 Purification, of actinide metals, see Actinide, metals, purification XjPj Purified protein, 36 94 Purple acid phosphatases, 40 371, 376, 43 362, 395-398, 44 243-245 biological function, 43 395 homology, 43 397... 

Resonator ultrasonic relaxation method, 32 18 Respiratory chains, 45 351-354 aerobic growth, 45 354-357 anaerobic growth, 45 357-359 autotrophic growth, 45 359-362 complexes, proteins, 38 240-241 membrane-bound Fe—S enzymes, 38 302-303... 

The pressure dependence of the NMR spectrum of a nickel(II) complex which undergoes a coordination-spin equilibrium has been used to obtain the volume difference between the planar and octahedral isomers (118). In this case both the temperature and pressure dependence of the NMR spectra were analyzed simultaneously to yield five parameters, AH0, AS0, A V°, and the chemical shifts of the two isomers. Subsequent determinations from the electronic spectra and ultrasonics relaxation are in good agreement with the NMR result (13). 

The volume difference can be found without the use of high-pressure techniques in favorable cases from the amplitude of the sound absorption observed in ultrasonic relaxation of the spin equilibrium. This method will be described below in Section III,C. 

Methods E, electronic spectra G, Gouy N, NMR U, ultrasonic relaxation. 

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). 

The dynamics of an octahedral spin equilibrium in solution was first reported in 1973 for an iron(II) complex with the Raman laser temperature-jump technique (14). A relaxation time of 32 10 nsec was observed. Subsequently, further studies have been reported with the use of this technique, with ultrasonic relaxation, and with photoperturbation. Selected results are presented in Table III. 

Methods T, Raman laser temperature-jump U, ultrasonic relaxation P, photoperturbation. 

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. 

The spin-equilibrium dynamics of iron(III) complexes in solution have been examined with the techniques of Raman laser temperature-jump, ultrasonic relaxation, and photoperturbation. The complexes investigated, the relaxation times observed, and one of the derived rate constants are presented in Table IV. Many of the relaxation times are quite short, and some of the original temperature-jump results (45) were found to be inconsistent with more accurate ultrasonic experiments (20) and later photoperturbation experiments (102). It has not been possible to repeat some of these laser temperature-jump observations. Instead, the expected absorbance changes and isosbestic points were found to occur within the heating rise time of the laser pulse, consistent with the ultrasonic and photoperturbation experiments (20). Consequently, none of the original Raman laser temperature-jump results is included in Table IV. 

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