Relaxation techniques temperature jump

The steady-state and rapid equilibrium kinetics do not give detailed information on the existence of multiple intermediates or on their lifetimes. Such information is provided by fast (or transient) kinetics. The methods can be divided in two categories rapid-mixing techniques (stopped-flow, rapid-scanning stopped-flow, quenched flow) which operate in a millisecond time scale and relaxation techniques (temperature jump, pressure jump) which monitor a transient reaction in a microsecond time scale. Most of the transient kinetic methods rely on spectrophotomet-rically observable substrate changes during the course of enzyme catalysis. 

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. 

Perturbation or relaxation techniques are applied to chemical reaction systems with a well-defined equilibrium. An instantaneous change of one or several state fiinctions causes the system to relax into its new equilibrium [29]. In gas-phase kmetics, the perturbations typically exploit the temperature (r-jump) and pressure (P-jump) dependence of chemical equilibria [6]. The relaxation kinetics are monitored by spectroscopic methods. 

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). 

The first experimental data for a reaction involving proton transfer from a hydrogen-bonded acid to a series of bases which were chosen to give ApK-values each side of ApK=0 are given in Fig. 15 (Hibbert and Awwal, 1976, 1978 Hibbert, 1981). The results were obtained for proton transfer from 4-(3-nitrophenylazo)salicylate ion to a series of tertiary aliphatic amines in aqueous solution, as in (64) with R = 3-nitrophenylazo. Kinetic measurements were made using the temperature-jump technique with spectrophoto-metric detection to follow reactions with half-lives down to 5 x 10"6s. The reciprocal relaxation time (t ), which is the time constant of the exponential... 

The tautomerisation of the N(9)H- and N(7)H-isomers of adenine (93) has been studied in aqueous solution using the temperature-jump technique with Joule heating (Dreyfus et al., 1975). The equilibrium constant K = [N(7)H]/[N(9)H] has a value of 0.28 at 20°C. The reciprocal relaxation time... 

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... 

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. 

Preliminary results (obtained by use of the temperature jump technique) indicate that the reactions are fast (at c = 10 2 relaxation time faster than 50 /usee.) 56> and are of second order. The rate coefficients k are again a function of the donicity, whereas the rate coefficients of the reversed reactions k2 show no relation to the donicity S6 ... 

DR. THOMAS The kinetic parameters of micelles are very well known, having been determined by temperature-jump relaxation methods and various other techniques. There are several kinetic events which can be described. First of all, the fastest event is the exchange of the counter ion (e.g., the sodium counter ion, in sodium lauryl sulfate). These ions exchange... 

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. ... 

Mechanisms for the formation of [W60i9(0H)3] (paratungstate A) have been discussed. The relaxation spectra of aqueous molybdate have been determined by the temperature-jump technique at 25 °C(/i = 1.0 M, pH = 5.5— 6.8, and monomer concentration = 0.01—0.25 M). The results indicate two concentration-dependent relaxation effects, which are sensitive to heptamer, [Mo7 0 24] , and octamer, [Mog026]", formation. ... 

For very rapid reactions such as the ionization of H2O, it is difficult to determine the rate constants using conventional methods. One often-used method is the relaxation method. The system is initially at equilibrium under a given set of conditions. The conditions are then suddenly changed so that the system is no longer at equilibrium. The system then relaxes to a new equilibrium state. The speed of relaxation is measured, usually by spectrophotometry, and the rate constants can be obtained. One technique to change the conditions is to increase temperature suddenly by the rapid discharge from a capacitor. This technique is called temperature-jump technique. 

As better and better methods for following fast reactions with precision were introduced and exploited, characteristic reaction times faster than a second— times measured in milhseconds (ms, 10 s), or microseconds (ps, 10 s), or nanoseconds (ns, 10 s) and then in picoseconds (ps, 10 s)—were measured through stopped-flow techniques (Chance, 1940), flash photolysis (Norrish and Porter, 1949), temperature-jump and related relaxation methods (Eigen, 1954), and then... 

A major advance in the investigation of the intramolecular dynamics of spin equilibria was the development of the Raman laser temperature-jump technique (43). This uses the power of a laser to heat a solution within the time of the laser pulse width. If the relaxation time of the spin equilibrium is longer than this pulse width the dynamics of the equilibrium can be observed spectroscopically. At the time of its development only two lasers had sufficient power to cause an adequate temperature rise, the ruby laser at 694 nm and the neodymium laser at 1060 nm. Neither of these wavelengths is absorbed by solvents. Various methods were used in attempts to absorb the laser power, with partial success for microsecond relaxation times. 

The Raman laser temperature-jump technique has been used in studies of a variety of spin-equilibrium processes. It was used in the first experiment to measure the relaxation time of an octahedral spin-equilibrium complex in solution (14). Its applications include investigations of cobalt(II), iron(II), iron(III), and nickel(II) equilibria. 

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. 

A number of observations indicate interconversion rates for some iron(III) complexes too fast to measure with existing techniques. Relaxation times less than the 30-nsec limit set by the heating rise time of the laser temperature-jump technique were observed for [Fe(benzac2trien)]+, [Fe(Salmeen)2]+, and [Fe(Me2dtc)3] (45, 128). From ultrasonic observations a limit of less than 1 nsec was placed on the relaxation time for the first of these compounds,... 

However, p-jump techniques are not without fault (Takahashi and Alberty, 1969). Most chemical reactions are less sensitive to pressure than to temperature alterations. Thus, a highly sensitive detection method such as conductivity must be employed to measure relaxation times if p-jump is used. Conductometric methods are sensitive on an absolute basis, but it is also fundamental that the solutions under study have adequate buffering and proper ionic strengths. In relaxation techniques, small molar volume changes result, and consequently, even if a low level of an inert electrolyte is present, conductivity changes may be undetectable if pressure perturbations of 5-10 MPa are utilized (Takahashi and Alberty, 1969). 

Robinson, B. H. (1975). The stopped-flow and temperature-jump techniques-principles and recent advances. In Chemical and Biological Applications of Relaxation Spectrometry (E. Wyn-Jones, ed.), pp. 41-48. Reidel Publ., Dordrecht, The Netherlands. 

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... 

The result of Fe +Cl O) 5(NO) is in good agreement with that determined by Kastin et al. (15) using the same experimental technique. For both Fe2+(EDTA)(NO) and Fe2+(NTA)(NO), the relaxation times due to the temperature jump were too fast to be measured. However, an upper limit of 10 /is was established for the relaxation times for both complexes. By use of this value with the equilibrium constants determined for Fe2+(EDTA)(NO) (16) and Fe2+(NTA)(NO) (10), the lower limits of formation rate constants were calculated to be 7 x 10 and 6 x 107 Z/nol -sec at 35 °C, which is in good agreement with that determined by the temperature-jump technique. From the results listed in Table I, we can conclude that the formation rate of Fe2+(EDTA)(NO) is at least 85 times faster than that of Fe2+(H20)5(N0), whereas, the dissociation rate of Fe2+(EDTA)(NO) is about 250 times slower than that of Fe2+(H20)5(N0) at 25 °C. 

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