Isotope Effect Parameters Research Articles

Diffusion: Isotope Effect and Manning Factor in Liquids

In this paper, the diffusion isotope effect and the Manning factor are investigated by means of Molecular Dynamics simulations in liquid Cu-Ag alloys. The values for the diffusion isotope effect parameter allow for the estimate of the number of atoms that are moving cooperatively in a basic diffusion event as ‘seen’ by a given (tracer) atom. On average, in the considered alloys and considered temperatures, this is limited to between 5 and 15. This is consistent with results of Molecular Dynamics simulations on the average coordination number calculations. This would suggest that, together with a given atom, a majority of the neighbouring atoms are involved in a basic diffusion event. Results for the Manning factor (MD simulation) for Cu-Ag liquid alloys are seemingly in agreement with the direct exchange mechanism where only two atoms are involved in the elementary diffusion event. This is not in apparent agreement with the isotope effect results. It was shown, however, that any ring mechanism, or, more complex, cage mechanism are, in fact, a combination of several simultaneously happening direct exchanges. Any other possible mechanisms for diffusion in liquids is most likely a combination of direct exchanges as well. It can be seen then that the collective nature of all considered mechanisms is very similar and follows the direct exchange signature properties.

The Diffusion Isotope Effect and Diffusion Mechanism in Liquid Cu-Ag and Cu-Ni Alloys

In this paper, the diffusion isotope effect and diffusion mechanism are investigated by means of molecular dynamics simulations in two liquid alloys, Ni-Ag and Ni-Cu. The values for the diffusion isotope effect parameter allow for the estimate of the number of atoms which are moving cooperatively in a basic diffusion event as experienced by a given atomic species. It is shown that the composition dependence ofNDis typically very small. However, the temperature dependence of this parameter is much more pronounced. In addition, it is shown that, on average, in these alloys and temperatures considered,NDis limited to the range: 5<ND<17. This is consistent with results of molecular dynamics simulations on the average coordination number calculations. This would suggest that, together with a given atom, depending on temperature, the neighbouring atoms are all involved in the basic diffusion event.

Alteration of P450 Distal Pocket Solvent Leads to Impaired Proton Delivery and Changes in Heme Geometry

Distal pocket water molecules have been widely implicated in the delivery of protons required in O-O bond heterolysis in the P450 reaction cycle. Targeted dehydration of the cytochrome P450cam (CYP101) distal pocket through mutagenesis of a distal pocket glycine to either valine or threonine results in the alteration of spin state equilibria, and has dramatic consequences on the catalytic rate, coupling efficiency, and kinetic solvent isotope effect parameters, highlighting an important role of the active-site hydration level on P450 catalysis. Cryoradiolysis of the mutant CYP101 oxyferrous complexes further indicates a specific perturbation of proton-transfer events required for the transformation of ferric-peroxo to ferric-hydroperoxo states. Finally, crystallography of the 248Val and 248Thr mutants in both the ferric camphor bound resting state and ferric-cyano adducts shows both the alteration of hydrogen-bonding networks and the alteration of heme geometry parameters. Taken together, these results indicate that the distal pocket microenvironment governs the transformation of reactive heme-oxygen intermediates in P450 cytochromes.

Influence of mass difference on dynamic properties of isotope mixtures

We present the results of molecular dynamics computer simulations of a two-component isotope mixture of Lennard–Jones particles, monodisperse in size but different in masses, at a fixed average density and temperature. We study changes in properties that result from mass heterogeneity, by calculating the diffusion coefficient, velocity autocorrelation function, non-Gaussian and isotope effect parameters, as functions of the degree of mass difference. Our results show that eventhough static properties are not influenced by variation in mass, the dynamic properties are significantly affected and exhibit the presence of “characteristic” values in the mass difference. We also demonstrate that our model gives a simple counter example to a recently proposed universal scaling law for atomic diffusion in condensed matter (Nature 381 (1996) 137).

High-level expression of human liver monoamine oxidase B in Pichia pastoris.

The high-level heterologous expression, purification, and characterization of the mitochondrial outer membrane enzyme human liver monoamine oxidase B (MAO B) using the methylotrophic yeast Pichia pastoris expression system are described. A 2-L culture of P. pastoris expresses approximately 1700 U of MAO B activity, with the recombinant enzyme associated tightly with the membrane fraction of the cell lysate. By a modification of the published procedure for purification of bovine liver MAO B [Salach, J. I. (1979) Arch. Biochem. Biophys. 192, 128-137], recombinant human liver MAO B is purified in a 34% yield ( approximately 200 mg from 2 L of cell culture). The isolated enzyme exhibits an M(r) of approximately 60, 000 on SDS-PAGE and 59,474 from electrospray mass spectrometry measurements, which is in good agreement with the mass predicted from the gene sequence and inclusion of the covalent FAD. One mole of covalent FAD per mole of MAO B is present in the purified enzyme and is bound by an 8alpha-S-cysteinyl(397) linkage, as identified by electrospray mass spectrometry of the isolated tryptic/chymotryptic flavin peptide. Recombinant human liver MAO B and bovine liver MAO B are shown to be acetylated at the seryl residues at their respective amino termini. The benzylamine oxidase activity of recombinant MAO B ranges from 3.0 to 3.4 U/mg and steady-state kinetic parameters for this enzyme preparation compare well with those published for the bovine liver enzyme: k(cat) = 600 min(-1), K(m)(benzylamine) = 0.50 mM, and K(m)(O(2)) = 0.33 mM. Kinetic isotope effect parameters using [alpha,alpha-(2)H(2)]benzylamine are also similar to those found for the bovine enzyme. Recombinant MAO B exhibits a (D)k(cat) = 4.7, a (D)[k(cat)/K(m)(benzylamine)] = 4.5, and a (D)[k(cat)/K(m)(O(2))] = 1.0. In contrast to bovine liver MAO B, no evidence was found for the presence of any anionic flavin radical either by UV-vis or by EPR spectroscopy in the resting form of the enzyme. These data demonstrate the successful heterologous expression of a functional, membrane-bound MAO B, which will permit a number of mutagenesis studies as structural and mechanistic probes not previously possible.

Tracer diffusion and mechanism of non-Arrhenius diffusion behavior of Zr and Nb in body-centered cubic Zr–Nb alloys

Tracer diffusion of Zr95 and Nb95 has been measured in a set of β-Zr-Nb alloys (Zr-5.5 at. % Nb, Zr-16.3 at. % Nb, and Zr-28.1 at. % Nb) in a wide temperature range from 1035 to 1871 K. All experimental concentration profiles revealed a Gaussian-like behavior over two to three decades in logarithm of concentrations. Experimental data were analyzed in terms of the Manning’s random alloy model and the partial correlation factors were calculated as functions of temperature. The partial correlation factors vary smoothly over the whole temperature range, whereas the diffusivity shows a pronounced curvature of the Arrhenius plots. A correlation was found between the degree of deviation from the Arrhenius behavior of the diffusion coefficients of both components and the lattice dynamics features of the measured phonon dispersions in their dependence on the Nb content in these alloys. The temperature dependence of the isotope effect parameter E of Zr diffusion was measured in the Zr-5.5 at.% Nb alloy. E essentially increases with temperature and the energy transfer factor ΔK deduced for the alloy was found to be somewhat larger than the corresponding values for pure β-Zr, especially at low temperatures. The whole set of experimental data leads to the conclusion that only one diffusion mechanism—the vacancy mechanism—is operating in the whole investigated temperature range.

Coupling strength and isotope effect for the ionic plasmon mechanism for the s-wave condensate in high- Tc cuprates

We have proposed that the ionic plasmon be accepted as the boson that mediates the Cooper pairing in the s-wave condensate in p-type cuprates. We show here that the coupling strength λ ≈ 10 and the isotope effect parameter α ≈ 0 for the superconducting CuO 2 layer can be explained by plausibility arguments in a straightforward manner by considering the diffuse scattering of the ionic plasmons by the native defects.

Anharmonic phonons and the anomalous isotope effect in La2-xSrxCuO4.

A model for the variation of an interionic potential near the orthorhombic to low-temperature-tetragonal structural phase transition in La-Sr-Cu-O can explain variations both above and below 0.5 in the superconducting isotope-effect parameter \ensuremath{\alpha}. In particular, we posit a quadrupolar potential in which the four outer wells deepen as the phase transition is approached. This model can reproduce the experimentally observed variations in both ${\mathit{T}}_{\mathit{c}}$ and \ensuremath{\alpha}.

Anharmonic phonons and the isotope effect in superconductivity.

Anharmonic interionic potentials are examined in an Einstein model to study the unusual isotope-effect exponents for the high-${\mathit{T}}_{\mathit{c}}$ oxides. The mass dependences of the electron-phonon coupling constant \ensuremath{\lambda} and the average phonon frequency \ensuremath{\surd}〈${\mathrm{\ensuremath{\omega}}}^{2}$〉 are computed from weighted sums over the oscillator levels. The isotope-effect exponent is depressed below 1/2 by either a double-well potential or a potential with positive quadratic and quartic parts. Numerical solutions of Schr\"odinger's equation for double-well potentials produce \ensuremath{\lambda}'s in the range 1.5--4 for a material with a vanishing isotope-effect parameter \ensuremath{\alpha}. However, low phonon frequencies limit ${\mathit{T}}_{\mathit{c}}$ to roughly 15 K. A negative quartic perturbation to a harmonic well can increase \ensuremath{\alpha} above 1/2. In the extreme-strong-coupling limit, \ensuremath{\alpha} is 1/2, regardless of anharmonicity.

Limitations on electronic mechanisms for high temperature superconducting oxides

The effects of electronic mechanisms for electron pairing in high temperature superconducting oxides on both the transition temperature T c and the isotope effect parameter α are considered. It is shown that for the higher T c oxides, measured values of T c and α together with estimates of the phonon contributions are not consistent with high-frequency electronic mechanisms. Limitations of the theory and some constraints on low-frequency electronic mechanisms are also discussed.

Isotope effect and hole superconductivity

We consider a hole superconductor described by a Hamiltonian proposed by Hirsch. For a discussion of the isotope effect within this model the influence of lattice vibrations on the hopping interaction is proposed. Both a harmonic interaction as well as an anharmonic approximation are used to calculate the superconducting critical temperature and the isotope effect parameter α in the weak coupling limit. While the harmonic hole-lattice coupling describes the usual isotope effect, increasing anharmonicity of the hole-lattice coupling decreases the isotope effect leading to a situation known in the high-temperature superconducting oxides.

Vanadium self-diffusion in pure vanadium and in dilute vanadium-iron and vanadium-tantalum alloys

Abstract Measurements of vanadium self-diffusion have been made over the temperature range 1050–1874°C. The solute enhancement factor b for vanadium self-diffusion has also been measured in dilute vanadium-iron and vanadium-tantalum alloys. These results, together with the authors' previously published results on iron impurity diffusion in vanadium, are analysed using the vacancy models of Le Claire (1970) and Jones and Le Claire (1972) to calculate the isotope effect parameters fi , which are then compared with the measured values of fiδK of Coleman. Wert and Peart (1968). Our results confirm the existence of three regimes: (1) free single vacancy migration between 1200 and 1550°C, (2) divacancy contribution at higher temperatures and (3) acceleration of diffusion due to other defects such as dislocations, subgrain boundaries and/or vacancy-interstitial impurity pairs at low temperatures.

Vanadium self-diffusion in pure vanadium and in dilute vanadium-iron and vanadium-tantalum alloys

Abstract Measurements of vanadium self-diffusion have been made over the temperature range 1050–1874°C. The solute enhancement factor b for vanadium self-diffusion has also been measured in dilute vanadium-iron and vanadium-tantalum alloys. These results, together with the authors' previously published results on iron impurity diffusion in vanadium, are analysed using the vacancy models of Le Claire (1970) and Jones and Le Claire (1972) to calculate the isotope effect parameters fi , which are then compared with the measured values of fiδK of Coleman. Wert and Peart (1968). Our results confirm the existence of three regimes: (1) free single vacancy migration between 1200 and 1550°C, (2) divacancy contribution at higher temperatures and (3) acceleration of diffusion due to other defects such as dislocations, subgrain boundaries and/or vacancy-interstitial impurity pairs at low temperatures.

Observations on the geometry of hydrogen transfer in [1,5] sigmatropic rearrangements

The present investigation was undertaken with the objective of identifying a (1,5) sigmatropic rearrangement occurring in a cyclic system which is not capable of such distention of the ..pi.. framework. The case for study was the rearrangement of the 9aH-quinolizine to the 4H-quinolizine. The temperature dependence of the isotope effect was again applied as the criterion of TS/sup + +/ geometry in H transfer. It has frequently been demonstrated, though not directly derivable (at present) from conventional transition-state theory of the isotope effect, that a bent TS/sup + +/, i.e., one involving H transfer at an acute angle, can be correlated with a temperature-independent k/sub H//k/sub D/. That is to say, the finding of isotope effect parameters of (..delta..E/sub a/)/sup H//sub D/ approx. = 0 and A/sub H//A/sub D/>>1.2 has been empirically shown to be most congruent with a bent TS/sup + +/.

Isotope effect for diffusion of tin inβ−titanium-titanium

The isotope effect for diffusion of $^{113}\mathrm{Sn}$ and $^{121}\mathrm{Sn}^{m}$ in Ti has been measured at five temperatures in the bcc $\ensuremath{\beta}$ phase. Separation of the Sn isotopes was effected by $\ensuremath{\beta}$ spectroscopy on electroplated sources. The effect is small and highly temperature dependent, varying from 0.18 \ifmmode\pm\else\textpm\fi{} 0.03 at 972\ifmmode^\circ\else\textdegree\fi{}C to 0.37 \ifmmode\pm\else\textpm\fi{} 0.03 at 1525\ifmmode^\circ\else\textdegree\fi{}C. When corrected for the mass difference between the Sn tracers used and the Ti solvent, the magnitude of the effect seems to be consistent with a relaxed vacancy mechanism as observed in "normal" bcc metals. Between 1000 and 1200\ifmmode^\circ\else\textdegree\fi{}C the isotope-effect parameter increases quite rapidly. The temperature variation seems to be inconsistent with the hypothesis that two competing mechanisms of bulk diffusion operate over the bcc temperature range. The data do seem to be consistent with three possible alternative mechanisms for diffusion: enhancement by dislocation networks which anneal out at higher temperatures, enhancement due to the presence of $\ensuremath{\omega}$ embryos at low temperatures, and diffusion by highly relaxed vacancies with a large coefficient of thermal expansion and specific heat of formation.

Correlation Factors and Isotope Effect for Self‐Diffusion by Mono‐ and Divacancies in H.C.P. Crystals

AbstractThe tensor components of the Bardeen‐Herring correlation factor for a divacancy mechanism of self‐diffusion in an h.c.p. crystal are calculated and compared with Mullen's results on the monovacancy mechanism. The relationship between the correlation factors and the isotope effect parameters is discussed, in the monovacancy case making use of the work of Batra. For monovacancy diffusion parallel to the c‐direction the correlation factor provides an upper limit for the isotope effect parameter, whereas for diffusion perpendicular to the c‐axis the isotope effect parameter can be slightly larger than the correlation factor. For the divacancy case it is demonstrated analytically that the correlation factor parallel to the c‐axis provides an upper limit for the isotope effect parameter in this direction. Numerical calculations show that the upper limit of the isotope effect parameter perpendicular to the c‐axis exceeds the correlation factor at most by a few per cent.

Dissociative impurity diffusion by 1-D interstitial migration

The implications of 1-D interstitial migration for dissociative impurity diffusion are discussed. It is pointed out that, in contrast to the case of 3-D migration, with 1-D interstitial migration long-range impurity diffusion cannot take place without vacancy motion. Further it is shown that, in the direction of interstitial migration, a value of isotope effect parameter E of E approximately=0 may be expected. This is in contrast to the correlation factor f for which, under the same conditions, a value of f>0 would be expected.

Theory of tracer-diffusion in the wurtzite-structure with applications to hexagonal ice

A theory for the tracer self-diffusion by a vacancy mechanism in the wurtzitelattice is developed into which the effects of Bardeen-Herring correlation are included in a rigorous way. The isotope effect parameter is calculated for the limiting case in which the jump process may be treated as the jump of an individual particle and by means of classical statistics.

Diffusivity and Isotope-Effect Measurements in Equiatomic Fe-Co

Several radioactive isotopes of Fe and Co were simultaneously diffused into an equiatomic FeCo alloy which exhibits fcc, bcc, and CsCl-type ordered phases with decreasing temperature. Penetration profiles were obtained by standard lathe sectioning and a grinding-sectioning technique described in this paper. From In D-versus-$\frac{1}{T}$ plots, activation energies of 68.5 and 55 kcal and frequency factors of 1.26 and 0.25 ${\mathrm{cm}}^{2}$/sec were obtained for diffusion of ${\mathrm{Fe}}^{59}$ in the fcc and bcc phases, respectively. From similar plots, activation energies of 69.4 and 60.0 kcal and frequency factors of 1.33 and 2.00 ${\mathrm{cm}}^{2}$/sec were obtained for diffusion of ${\mathrm{Co}}^{57}$ in the fcc and bcc phases of the FeCo alloy. The average isotope-effect parameters were 0.66 in the fcc phase and 0.52 in the bcc phase. Manning's theory for concentrated alloys was used to calculate correlation factors for the FeCo alloy. From these calculated values and experimentally measured isotope-effect parameters, $\ensuremath{\Delta}K$ was determined to be slightly larger in the fcc and bcc phases of the FeCo alloy than has been reported in pure Fe. The observed decrease in the isotope-effect parameter with increasing degree of order during the bcc-to-CsCl-type ordering transformation is explained in terms of an increase in atom-jump correlation with the onset of long-range order.

Isotope Effect for Diffusion of Iron in Vanadium

The diffusion coefficients of iron, using ${\mathrm{Fe}}^{59}$ as the radioactive tracer, and the isotope-effect parameter, using ${\mathrm{Fe}}^{55}$ and ${\mathrm{Fe}}^{59}$ as tracers, have been measured in vanadium over a temperature range of more than 800\ifmmode^\circ\else\textdegree\fi{}C by standard sectioning and counting techniques. The diffusion of ${\mathrm{Fe}}^{59}$ in vanadium exhibits the anomalous behavior of having not one but two straight lines in a plot of $\mathrm{ln}D$ versus $\frac{1}{T}$, with a change of slope occurring near 1350\ifmmode^\circ\else\textdegree\fi{}C. The data have been analyzed into the sum of two exponentials: $D=2280$ $\mathrm{exp}(\ensuremath{-}\frac{101500}{\mathrm{RT}})$ at high temperatures, and $D=0.0936$ $\mathrm{exp}(\ensuremath{-}\frac{67600}{\mathrm{RT}})$ at low temperatures. The values of the isotope-effect parameter for the ${\mathrm{Fe}}^{59}$ and ${\mathrm{Fe}}^{55}$ isotopes are approximately constant near 0.7 at low temperatures, but decrease rapidly with increasing temperature above 1350\ifmmode^\circ\else\textdegree\fi{}C. The measurements are interpreted to indicate that two mechanisms of diffusion operate in vanadium. The mechanism predominant at low temperatures is identified as motion of a single vacancy; that at high temperatures is probably motion of divacancies.