Ultrasonic relaxation technique

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... 

Relaxation times become important when studying the approach to equilibrium either directly or as a result of a small perturbation from equilibrium. They also emerge directly from ultrasonic relaxation techniques for studying single and multiple equilibria (Section 2.6). However, they only apply to first order or pseudo- first order processes (Section 3.15). 

It appears interesting to note that quite recently Zana224 also claimed to have observed (with DAP in cyclohexane applying an ultrasonic relaxation technique) a decrease of the average relaxation frequency with increasing DAP concentration. 

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... 

Ultrasonic relaxation techniques have been used to estimate the energy barrier to syn-anti conformational interconversion in cytidine 2, 3 -mono-phosphate, in the presence and absence of ethidium bromide. Raman spectroscopic measurements on a number of dinucleoside monophosphate crystals of precisely known sugar-phosphate structure have been compared with those of B- and A-form DNA, to give information on the comparative rigidity of the backbone in the nucleic acids. The same technique, applied to poly(dA-dT) and poly[d(A-T)] at different temperatures, suggests that some of the furanose... 

The advantage of the ultrasonic-relaxation technique is its capacity to give data for strongly biased systems, which are less amenable to study by, for example, nmr or vibrational spectroscopy. Thus AH fE Z) and AH° E - Z) for ethyl acetate were determined as 4.2 and —4.5 kcal mol respectively (Bailey and North, 1968). 

Polyatomic anions (free and associated with cations in solution), can b used as probes, through their vibrational spectra, to identify the species present in solution and determine their relative concentrations (1). Ultrasonic relaxation techniques provide information about the kinetics of the formation of the same... 

The use of ultrasonic absorption techniques has decreased in recent years because the experiments are time consuming. The advent of the laser T-jump, which covers a large part of the range of relaxation times explored by ultrasonic relaxation techniques, has also contributed to this situation. The apparatuses still in use are now fully automated and computer-driven, and the time required for data acquisition has been greatly reduced. 

Expressions for the amplitudes of the fast and slow relaxation processes characterizing micellar solutions have been derived for the ultrasonic relaxation techniques for the fast exchange process and for jump techniques (T-jump, p-jump, SF) for the two relaxation processes. - In an effort to save space, these expressions are not given here. Nevertheless, it is recalled that the analysis of the amplitudes of the relaxation signals can be useful in several respects (see Chapter 2, Section II.C). For instance, if the relaxation process responsible for the observed relaxation signal is identified, the analysis of the relaxation amplitudes can provide the values of thermodynamic quantities characterizing the process. For micellar solutions, the amplitude of the xdtrasonic relaxation yields... 

Chemical relaxation methods such as SF, TJ, PJ, concennation jump, and ultrasonic relaxation techniques have been used to study the kinetics of the rate of micellar solubilization. The residence time of a micelle at a given aggregation number is of the order of 0.2 to 10 (tsec, whereas the mean lifetime of a... 

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... 

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). 

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,... 

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... 

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. 

Relaxation techniques based on ultrasonics have been widely used to obtain rate constants for fast reactions. In this method a system at equilibrium is perturbed by the passage of a sound wave, which induces pressure and temperature variations. Ah... 

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. 

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. 

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. 

The kinetics and dynamics of crvptate formation (75-80) have been studied by various relaxation techniques (70-75) (for example, using temperature-jump and ultrasonic methods) and stopped-flow spectrophotometry (82), as well as by variable-temperature multinuclear NMR methods (59, 61, 62). The dynamics of cryptate formation are best interpreted in terms of a simple complexation-decomplexation exchange mechanism, and some representative data have been listed in Table III (16). The high stability of cryptate complexes (see Section III,D) may be directly related to their slow rates of decomplexation. Indeed the stability sequence of cryptates follows the trend in rates of decomplexation, and the enhanced stability of the dipositive cryptates may be related to their slowness of decomplexation when compared to the alkali metal complexes (80). The rate of decomplexation of Li" from [2.2.1] in pyridine was found to be 104 times faster than from [2.1.1], because of the looser fit of Li in [2.2.1] and the greater flexibility of this cryptand (81). At low pH, cation dissociation apparently... 

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