Measured Isotope Effects Research Articles

Isotope effect in niobium self-diffusion

Measurements of the isotope effect in niobium self-diffusion have been made over the temperature range 1900 \ifmmode^\circ\else\textdegree\fi{}C to near the melting point (2468 \ifmmode^\circ\else\textdegree\fi{}C). The measurements were made by simultaneous diffusion of $^{95}\mathrm{Nb}$ and $^{92}\mathrm{Nb}$ isotopes from a thin surface layer and subsequent sectioning. The ratio of $^{92}\mathrm{Nb}$ to $^{95}\mathrm{Nb}$ in each section was determined using a well-type Ge(Li) detector of high efficiency. The low values of the measured isotope effect are similar to other bcc metals (Na, $\ensuremath{\alpha}$- and $\ensuremath{\delta}\ensuremath{-}\mathrm{F}\mathrm{e},\mathrm{C}\mathrm{r}$, and $\ensuremath{\beta}\ensuremath{-}\mathrm{Z}\mathrm{r}$); however, the temperature dependence is different.

5] Measurement of isotope effects by the equilibrium perturbation technique

Publisher Summary This chapter discusses that the classical methods for measuring isotope effects involve direct comparisons of the rates with deuterated and nondeuterated substrates, giving both V/K and V isotope effects and isotope discrimination experiments, for tritium or heavier atom isotope effects that yield only V/K isotope effects. It reviews a new and very sensitive method for measuring isotope effects by equilibrium perturbation. The method requires that the reaction be reversible enough so that an equilibrium can be established, there be a color change or some other monitorable change, such as circular dichroism (CD), optical rotation, fluorescence, electron spin resonance (EPR) during the reaction, and the labeled compound have a high degree of isotope substitution, but be capable of measuring the isotope effects of 1.005, when the colored molecule is involved in the perturbation and about 1.002 when it is not. It is a cheap and rapid method that has proved to be extremely useful for the study of enzymic reactions.

Secondary deuterium isotope effects in solvolysis of 1-aryl-5-methyl-5-hepten-1-yl chlorides. Comparison of .pi. and n participation mechanisms

Three series of deuterated compounds related to 1 were prepared and their solvolysis rates measured. Since the relative contribution of k/sub c/ and k/sub ..delta../ to the observed solvolysis rates of 1 are known and since the isotope effects on the k/sub c/ route can be estimated, it is possible to extract from the data secondary deuterium isotope effects associated with the k/sub ..delta../ process. In all cases, the ..cap alpha..-deuterium isotope effects on k/sub ..delta../ are reduced in magnitude as compared to those in the k/sub c/ process, which is consistent with bridging. ..beta..-deuterium isotope effects on k/sub ..delta../ are essentially nil which can be explained as being due to both conformational restrictions to hyperconjugative electron release from the C-D bonding orbitals caused by bridging and to charge delocalization away from the reaction center. Deuteration of the aliphatic double bond produces inverse isotope effects in all cases where anchimeric assistance is operative. The latter observation clearly demonstrates the direct involvement of the aliphatic double bond in the rate-determining step of the k/sub ..delta../ process. A direct comparison of rates show that 1-aryl-4-methoxy-1-butyl chlorides (3) solvolyze slightly faster than the corresponding chlorides of the series 1. The rate factors are,more » however, too small to confirm the possibility that n and ..pi.. participations proceed by different mechanisms. If the aliphatic methoxyl group is directly involved in the rate-determining step of the k/sub ..delta../ process throughout the series 3, then measured isotope effects reflect transition-state structures with a variable amount of bridging, depending upon the solvent and/or the nature of the aromatic substituent. 3 figures, 1 table.« less

Flavin-dependent substrate photo-oxidation as a chemical model of dehydrogenase action.

As a model of flavin-dependent biological dehydrogenation, flavin-sensitized photodehydrogenation and photodecarboxylation were studied by variation of substrate, flavin, pH and solvent. Evidence for the following rules is given. (1) When the reactive site of a photosubstrate is an alpha-carbon atom of the type CH-CO2-, decarboxylation is preferred over dehydrogenation, whereas the reverse is true for the neutral CH-CO2H. (2) Consequently these reactions do not exhibit a measurable isotope effect with C2H-CO2-, in contrast with the findings by Penzer, Radda, Taylor & Taylor [(1970) Vitam. Horm. (N.Y.) 28, 441--466], which could not be reproduced. When the substate does not contain a carboxylate group, isotope effects occur, in verification of previous reports, e.g. for benzyl alcohol C6H5-C2H20H. (3) The mechanism of flavin-sensitized substrate photodecarboxylation is assumed to consist in a primary carbanion fixation at the flavin nucleus (position 4a, 5 or 8) with concomitant liberation of CO2. This step is followed by rapid fragmentation of the adduct CH-Fl-red., provided that the substrate contains a functional and electron-donating group X, e.g. X = OH, OCH3 or NH2 (but not NH3+ !) in X CH-CO2-. (4) The minimal requirement for flavin-sensitized C-H dehydrogenation is the presence of a hydroxyl group. For example, methanol as substrate and solvent is dehydrogenated at pH sufficiently alkaline for detection of the presence of the active species CH3O-, whereas at more acidic pH substrate dehydrogenation is competing with flavin autophotolysis, which depends on the substituents in the flavin nucleus.

The mutual diffusion study in the systems containing benzene or benzene-d6 at 25 °

The mutual diffusion coefficients of benzene and benzene-d6 were measured at low solute concentrations in each of the following solvents: n-hexane, cyclohexane, dodecane, and hexadecane. The observed mutual diffusion coefficients for the systems containing benzene-d6 were consistently lower than those observed for the corresponding systems containing benzene. The results of this investigation show that a measurable isotope effect exists in liquid diffusion and that the magnitude of the effect depends on the physiochemical properties of the solvents. The magnitude appears to be more closely related to the viscosity of the solvents than to the molecular weights of the solvents.

Effect of heterovalent impurities codiffusing with monovalent tracers in ionic crystals

Tracer-diffusion measurements have been made for $^{45}\mathrm{Ca}$ and $^{22}\mathrm{Na}$ codiffusing into pure NaCl as a function of temperature, initial calcium concentration, and diffusion anneal time. The measured penetration profiles deviate markedly from the Gaussian dependence expected for diffusion from a thin source. The curvature is caused by each divalent Ca ion introducing an extra "extrinsic" vacancy into the diffusion zone in order to maintain charge neutrality. In such cases, the limiting slope has been shown not to be a valid measure of the tracer diffusivity. Computer fits have been generated by a model which corrects for the effect and is found to give excellent agreement with the data except for the most extreme cases. The model can find the initial concentration of the impurity and the diffusivity of the impurity within a factor of 2 from the penetration profile for the monovalent tracer. The effect enters to first order into the measurement of the isotope effect in ionic crystals and can result in major errors in the measured isotope effect for even small deviations from a Gaussian profile. The diffusion coefficients for $^{22}\mathrm{Na}$ diffusing in NaCl over the temperature range of (575-775)\ifmmode^\circ\else\textdegree\fi{}C are given by ${D}_{\mathrm{Na}}=73\mathrm{exp}(\ensuremath{-}2.04\ifmmode\pm\else\textpm\fi{}0.02 \frac{\mathrm{eV}}{\mathrm{kT}})$ ${\mathrm{cm}}^{2}$/sec, and for $^{45}\mathrm{Ca}$, ${D}_{\mathrm{Ca}}=0.23\mathrm{exp}(\ensuremath{-}1.61\ifmmode\pm\else\textpm\fi{}0.03 \frac{\mathrm{eV}}{\mathrm{kT}})$ ${\mathrm{cm}}^{2}$/sec.

Kinetic isotope effects in the reaction of fluorine atoms with molecular hydrogen. II. The F + HD/DH intramolecular isotope effect

The intramolecular kinetic isotope effect in the reaction of fluorine atoms with HD molecules, F+HD→kF+HDHF+D,F+DH→kF+DHDF+H,was measured as function of reaction temperature in the range of 159–413 °K. The measured isotope effect can be expressed as an Arrhenius-type equation: kF+HD/kF+DH = (1.26 ± 0.02) exp[(70 ± 6)/RT]. Experiments were carried out in a fast flow system with direct mass spectrometric analysis of reaction products. The experimental results for kF+HD/kF+DH, as well as results for kF+H2/kF+D2 which were reported in an earlier publication, are compared with calculations based on transition state theory, using empirical and semiempirical models.

Deuterium isotope exchange between carboxylic acids and hydrogen

The catalytic exchange of deuterium between carboxylic acids and hydrogen according to RCOOH(l) + HD(g)⇋RCOOD(l)+H2(g), where R=H or CH3, has been studied with the acids in the pure state at various temperatures, and in solutions of carbon tetrachloride at 25°C. The hydroxyl hydrogen of the acids is about 3–4 times more enriched in deuterium than the hydrogen gas. The measured isotope effects are discussed in terms of molecular force field calculations for formic and acetic acid.

Deuterium isotope effects on proton chemical shifts in benzenes

No experimentally measurable deuterium isotope effect was found in pentadeuterobenzene at low concentration in one polar and three inert solvents. Experimentally significant negative deuterium isotope effects were found in neat pentadeuterated benzene and in three isotopomers of neat nitrobenzene. The negative isotope effects in neat liquids appear to be due primarily to solvent interactions.

Helium Isotope Effect in Solution in Water and Seawater

The isotope effect in the solution of helium in water from 0 degrees to 40 degrees C has been determined by microgasometric measurements of the solubilities of pure helium-3 and helium4. At 0 degrees C helium-3 is less soluble than helium-4 in both distilled water and sea-water by 1.2 percent. The observed fractionation factor is 0.988+/-0.002 at 0 degrees C and appears to decrease with increasing temperature at the rate of 0.0001 per degree Centigrade, although the existence of this trend is of limited statistical certainty. The measured isotope effect is in agreement with the ratio of helium-3 to helium-4 in surface ocean water reported by Clarke, Beg, and Craig.

Isotope Effects as Tools for the Elucidation of Reaction Mechanisms: Predictions from Model Calculations

Model calculations, based on the statistical-mechanical formulation of isotope effects, have been used to predict how analyses of experimentally measured isotope effects may be used to gain information concerning the differences between the reactants and the transition state in a rate process or between the reactants and the products in an equilibrium process. It is shown that while isotope effects cannot be used generally to obtain reliable information about geometry differences, they can be used to determine or set limits on force constant differences and possibly to gain insight into the nature of reaction coordinates. Information of this type can be useful in the elucidation of reaction mechanisms. A method by which isotope effects for large molecular systems may be studied theoretically by working with smaller model molecules is presented.

Reaction of Phenols with Peroxy Radicals

ALTHOUGH it has been known for a long time that phenols inhibit the autoxidation of many organic substances, the exact nature of the inhibition process is still not completely understood1. Most experimental evidence suggests that the reaction involves a straightforward abstraction of the phenolic hydrogen by the substrate peroxy radicals to give a hydroperoxide and a comparatively unreactive phenoxy radical: However, several workers have shown that replacement of the phenolic hydrogen by deuterium has either no effect, or else only a comparatively small effect (∼ 0–60 per cent) on the rate of this reaction1–3. It has therefore been suggested that the rate-determining step involves the prior formation of a complex between the peroxy radical and the phenol followed by a rapid, non-rate determining, hydrogen abstraction1,2. Alternatively, small isotope effects could be secondary effects or could arise in abstraction from the activated complex3. We have now found that the apparent smallness or complete absence of the expected isotope effect is most probably due to the very rapid exchange that occurs between a deuterated phenol dissolved in an organic substrate and traces of moisture or the hydroperoxide products of oxidation. The oxidation of cumene under 760 mm. of oxygen initiated by α,α′-azo-bis-isobutyronitrile (AIBN) was studied in a conventional constant pressure apparatus. The oxidation was partially inhibited by 2,6-di-tert-butyl-4-methylphenol (BMP). In the presence of this inhibitor the initial rate is quite low, but it rises to the rate of the uninhibited reaction as soon as the inhibitor is consumed. This initial rate is proportional to the AIBN concentration and inversely proportional to the BMP concentration, and its reciprocal is proportional to the rate of reaction 1. We have found that exchange can be partially suppressed by using rather high concentration of deuterated BMP and that under these conditions a fairly large isotope effect is observed which increases as the inhibitor concentration is increased. For example, some preliminary experiments at 70° C, with an AIBN concentration of 0.34 mole/1. gave measured isotope effects of 1.6, 1.8 and 2.2 at BMP concentrations of 10−2, 2 × 10−2 and 4 × 10−2 moles/l. respectively. Theoretically, the true isotope effect in the absence of exchange could be obtained by extrapolating to infinite inhibitor concentration. A simpler and, probably, much more accurate procedure is to add an excess of deuterium oxide to the reaction system (∼ 1.0 c.c. D2O to 5 c.c. cumene), thereby maintaining the BMP in its fully deuterated state throughout the early part of the reaction in which the rates are measured. Fig. 1 shows some results obtained in this way at 65° C. with an AIBN concentration of 0.327 mole/l. and a BMP concentration of 10−2 moles/l. In the presence of deuterium oxide the initial rate is ≥4.2 times that obtained with the undeuterated inhibitor, whereas, in the absence of deuterium oxide, this factor was only 2.3. That is, from the average of three determinations, the true deuterium isotope effect for reaction 1 between cumyl peroxy radicals and BMP at 65° C. is ≥4.2 ± 0.5. Our assumption that the major, and possibly only, part played by the deuterium oxide is to maintain the BMP in its fully deuterated state is confirmed by the fact that water has no appreciable effect on the undeuterated inhibitor (see Fig. 1) and that the effects of water and deuterium oxide on the uninhibited oxidation are very small. Experiments of a similar nature using styrene as the substrate gave an isotope effect of about 10.6 at 65° C.

Isotope Effect in Intermetallic Diffusion

Ten measurements of the isotope effect for diffusion of ${\mathrm{Fe}}^{55}$ and ${\mathrm{Fe}}^{59}$ in pure single crystals of silver and copper have been made over approximately a 300\ifmmode^\circ\else\textdegree\fi{}C temperature interval below the melting point. The measured isotope effect was found to be about $\frac{2}{3}$, significantly less than the value of unity expected from conventional reaction rate theory.It is shown from Vineyard's extension of reaction rate theory that the measured isotope effect is to a good approximation a product of the Bardeen-Herring correlation factor and the fraction of the total translational kinetic energy associated with the diffusing tracer in a tracer-vacancy exchange. It is shown that the ring, interstitialcy, crowdion, and relaxion mechanisms are not responsible for diffusion in the systems studied.The three-frequency theory of correlation for vacancy diffusion in fcc lattices is extended to show that the relative frequency factors are completely specified by a knowledge of the correlation factor and the diffusion coefficients. An expression for the difference in the Arrhenius $Q$ and the activation energy due to the temperature dependence of the correlation factor is derived. This theory is shown to be inconsistent with the observed isotope effect if many-body effects are neglected. It is shown that a "long-range" repulsive interaction between the vacancy and impurity would be necessary if the measured isotope effect is to be explained purely in terms of correlation.

Use of the isotope effect in the study of heterogeneous catalytic reactions

The applicability of the isotope effect on heterogeneous reaction rates as a kinetic tool is discussed. The isotope effect on the exchange reaction rate of ammonia and hydrogen on iron catalyst has been measured using deuterium and tritium as labelling isotope. A general rate equation is derived for this exchange reaction, and it is shown that uder certain conditions information on the reaction mechanism can be obtained from the measured isotope effect.

A multiple exposure x-ray spectrometer

A multiple exposure X-ray spectrometer is described which has been constructed for measuring small changes in lattice spacing of crystals, resulting from various physicochemical operations. The instrument is suitable for both powder and single crystal photographs, and the specimen can be investigated either in vacuo, or in any desired gas. Various experimental errors which arise in determining the position of an X-ray reflexion can be directly evaluated on the spectrometer itself. Its use in measuring isotope effects in crystals is illustrated by typical X-ray spectra comparing CO(NH2)2 with CO(ND2)2 and KH2PO4 with KD2PO4.

Mass Ratio of the Lithium Isotopes from the Spectrum ofLi2

Wave-number data.---The blue-green absorption bands of lithium have been photographed in the second order of a 21-foot grating. In the main, ${\mathrm{Li}}^{7}$${\mathrm{Li}}^{7}$, system the 2,0, 1,0, 0,0, 0,1 and 0,2 bands and in the isotopic, ${\mathrm{Li}}^{6}$${\mathrm{Li}}^{7}$, system the 1,0, 0,0, 0,1 bands and a somewhat incomplete 0,2 band have been measured and analyzed. Wave numbers of the lines of all these bands are tabulated. An unsuccessful attempt was made to identify ${\mathrm{Li}}^{6}$${\mathrm{Li}}^{6}$ band lines.Vibrational constants.---Values of $\ensuremath{\Delta}{G}_{v}$ are calculated by least squares and from them are deduced the vibrational constants of the main and isotopic systems. The constants are given by the following equations: $\ensuremath{\Delta}{{G}_{v}}^{\ensuremath{'}\ensuremath{'}}=351.374\ensuremath{-}5.181 ({v}^{\ensuremath{'}\ensuremath{'}}+\frac{1}{2})$, $\ensuremath{\Delta}{{G}_{v}}^{\ensuremath{'}}=270.941\ensuremath{-}6.266 ({v}^{\ensuremath{'}}+\frac{1}{2})$, $\ensuremath{\Delta}{{{G}_{v}}^{\ensuremath{'}\ensuremath{'}}}^{i}=365.923\ensuremath{-}5.619 ({v}^{\ensuremath{'}\ensuremath{'}}+\frac{1}{2})$, $\ensuremath{\Delta}{{{G}_{v}}^{\ensuremath{'}}}^{i}=282.081\ensuremath{-}6.791 ({v}^{\ensuremath{'}}+\frac{1}{2})$. The isotopic mass coefficient $\ensuremath{\rho}={(\frac{\ensuremath{\mu}}{{\ensuremath{\mu}}^{i}})}^{\frac{1}{2}}=\frac{{{\ensuremath{\omega}}_{e}}^{i}}{{\ensuremath{\omega}}_{e}}$ was calculated for the lower and upper states. The resulting values are, from the $^{1}\ensuremath{\Sigma}$ state, $\ensuremath{\rho}=1.04141\ifmmode\pm\else\textpm\fi{}0.00008$ (considered the most trustworthy figure) and from the $^{1}\ensuremath{\Pi}$ state, $\ensuremath{\rho}=1.0411\ifmmode\pm\else\textpm\fi{}0.0002$. These results are shown to correspond to a higher isotopic mass ratio ${\mathrm{Li}}^{7}$/${\mathrm{Li}}^{6}$ than that indicated by the massspectrograph results of Costa. By employing the $Q$ branch of the 0,2 isotope band, $\ensuremath{\Delta}{{{G}_{1\frac{1}{2}}}^{\ensuremath{'}\ensuremath{'}}}^{i}$ was found and the relation $\frac{{{x}_{e}}^{i}}{{x}_{e}}=\ensuremath{\rho}$ was verified to within the probable error.Rotational and electronic constants.---From rotational term differences, values of ${B}_{v}$ were computed for the main and isotopic systems by least squares. The calculated constants are: ${{B}_{v}}^{\ensuremath{'}\ensuremath{'}}=0.6721\ensuremath{-}0.00708 ({v}^{\ensuremath{'}\ensuremath{'}}+\frac{1}{2})$, ${{B}_{v}}^{\ensuremath{'}}=0.5577\ensuremath{-}0.00888 ({v}^{\ensuremath{'}}+\frac{1}{2})$, ${{{B}_{v}}^{\ensuremath{'}\ensuremath{'}}}^{i}=0.7302\ensuremath{-}0.00830 ({v}^{\ensuremath{'}\ensuremath{'}}+\frac{1}{2})$, ${{{B}_{v}}^{\ensuremath{'}}}^{i}=0.6046\ensuremath{-}0.00922 ({v}^{\ensuremath{'}}+\frac{1}{2})$. From the relation $\frac{{{B}_{e}}^{i}}{{B}_{e}}={\ensuremath{\rho}}^{2}$ are obtained values of $\ensuremath{\rho}$ which agree to within their probable error (one part in 1500) with the more accurate results obtained from the vibrational constants. The $\ensuremath{\Lambda}$-doubling for the two lowest vibrational levels of the $^{1}\ensuremath{\Pi}$ state was investigated and found sensibly equal for the main and isotopic band systems. The origins of the two band systems were computed to be ${\ensuremath{\nu}}_{e}=20436.25\ifmmode\pm\else\textpm\fi{}0.02$ and ${{\ensuremath{\nu}}_{e}}^{i}=20436.29\ifmmode\pm\else\textpm\fi{}0.04$, indicating no measurable electronic isotope effect.