Individual Isotopic Species Research Articles

Investigation of the Dynamic Behaviour of H2 and D2 in a Kinetic Quantum Sieving System.

Porous organic cages (POCs) are nanoporous materials composed of discrete molecular units that have uniformly distributed functional pores. The intrinsic porosity of these structures can be tuned accurately at the nanoscale by altering the size of the porous molecules, particularly to an optimal size of 3.6 Å, to harness the kinetic quantum sieving effect. Previous research on POCs for isotope separation has predominantly centered on differences in the quantities of adsorbed isotopes. However, nuclear quantum effects also contribute significantly to the dynamics of the sorption process, offering additional opportunities for separating H2 and D2 at practical operational temperatures. In this study, our investigations into H2 and D2 sorption on POC samples revealed a higher uptake of D2 compared to that of H2 under identical conditions. We employed quasi-elastic neutron scattering to study the diffusion processes of D2 and H2 in the POCs across various temperature and pressure ranges. Additionally, neutron Compton scattering was utilized to measure the values of the nuclear zero-point energy of individual isotopic species in D2 and H2. The results indicate that the diffusion coefficient of D2 is approximately one-sixth that of H2 in the POC due to the nuclear quantum effect. Furthermore, the results reveal that at 77 K, D2 has longer residence times compared to H2 when moving from pore to pore. Consequently, using the kinetic difference of H2 and D2 in a porous POC system enables hydrogen isotope separation using a temperature or pressure swing system at around liquid nitrogen temperatures.

A Hierarchical Algorithm for Calculating the Isotopic Fine Structures of Molecules

This article presents a memory efficient algorithm for accurately calculating the isotopic fine structures of molecules. Treating individual isotopic species of a molecule as different mass states, we introduce the concept of transitions between mass states and represent all mass states of the molecule in a hierarchical structure. We show that there exists a simple relationship between two different mass states at two different levels of the hierarchical structure. This allows us to efficiently and accurately compute both the mass and the abundance of every mass state of a small to medium-sized molecule, whose gross structures include small number of fine structures. A truncated calculation of this algorithm can be applied to calculate a majority of isotopic species (99.99% of cumulative abundance) of a large molecule.

CO2 dynamics in the Amargosa Desert: Fluxes and isotopic speciation in a deep unsaturated zone

Natural unsaturated‐zone gas profiles at the U.S. Geological Survey's Amargosa Desert Research Site, near Beatty, Nevada, reveal the presence of two physically and isotopically distinct CO2 sources, one shallow and one deep. The shallow source derives from seasonally variable autotrophic and heterotrophic respiration in the root zone. Scanning electron micrograph results indicate that at least part of the deep CO2 source is associated with calcite precipitation at the 110‐m‐deep water table. We use a geochemical gas‐diffusion model to explore processes of CO2 production and behavior in the unsaturated zone. The individual isotopic species 12CO2, 13CO2, and 14CO2 are treated as separate chemical components that diffuse and react independently. Steady state model solutions, constrained by the measured δ13C (in CO2), and δ14C (in CO2) profiles, indicate that the shallow CO2 source from root and microbial respiration composes ∼97% of the annual average total CO2 production at this arid site. Despite the small contribution from deep CO2 production amounting to ∼0.1 mol m−2 yr−1, upward diffusion from depth strongly influences the distribution of CO2 and carbon isotopes in the deep unsaturated zone. In addition to diffusion from deep CO2 production, 14C exchange with a sorbed CO2 phase is indicated by the modeled δ14C profiles, confirming previous work. The new model of carbon‐isotopic profiles provides a quantitative approach for evaluating fluxes of carbon under natural conditions in deep unsaturated zones.

Calculation of individual isotope equilibrium constants for geochemical reactions1

Theory is derived from the work of Urey (Urey H. C. [1947] The thermodynamic properties of isotopic substances. J. Chem. Soc. 562–581) to calculate equilibrium constants commonly used in geochemical equilibrium and reaction-transport models for reactions of individual isotopic species. Urey showed that equilibrium constants of isotope exchange reactions for molecules that contain two or more atoms of the same element in equivalent positions are related to isotope fractionation factors by α = (Kex)1/n, where n is the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example 13C16O18O and 1H2H18O. The equilibrium constants of the isotope exchange reactions can be expressed as ratios of individual isotope equilibrium constants for geochemical reactions. Knowledge of the equilibrium constant for the dominant isotopic species can then be used to calculate the individual isotope equilibrium constants. Individual isotope equilibrium constants are calculated for the reaction CO2g = CO2aq for all species that can be formed from 12C, 13C, 16O, and 18O; for the reaction between 12C18O2aq and 1H218Ol; and among the various 1H, 2H, 16O, and 18O species of H2O. This is a subset of a larger number of equilibrium constants calculated elsewhere (Thorstenson D. C. and Parkhurst D. L. [2002] Calculation of individual isotope equilibrium constants for implementation in geochemical models. Water-Resources Investigation Report 02-4172. U.S. Geological Survey). Activity coefficients, activity-concentration conventions for the isotopic variants of H2O in the solvent 1H2 16Ol, and salt effects on isotope fractionation have been included in the derivations. The effects of nonideality are small because of the chemical similarity of different isotopic species of the same molecule or ion. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation factors. The derivations can be extended to calculation of individual isotope equilibrium constants for ion pairs and equilibrium constants for isotopic species of other chemical elements. The individual isotope approach calculates the same phase isotopic compositions as existing methods, but also provides concentrations of individual species, which are needed in calculations of mass-dependent effects in transport processes. The equilibrium constants derived in this paper are used to calculate the example of gas-water equilibrium for CO2 in an acidic aqueous solution.

Calculation of individual isotope equilibrium constants for geochemical reactions

Theory is derived from the work of Urey (Urey H. C. [1947] The thermodynamic properties of isotopic substances. J. Chem. Soc. 562–581) to calculate equilibrium constants commonly used in geochemical equilibrium and reaction-transport models for reactions of individual isotopic species. Urey showed that equilibrium constants of isotope exchange reactions for molecules that contain two or more atoms of the same element in equivalent positions are related to isotope fractionation factors by α = (K ex) 1/n, where n is the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example 13C 16O 18O and 1H 2H 18O. The equilibrium constants of the isotope exchange reactions can be expressed as ratios of individual isotope equilibrium constants for geochemical reactions. Knowledge of the equilibrium constant for the dominant isotopic species can then be used to calculate the individual isotope equilibrium constants. Individual isotope equilibrium constants are calculated for the reaction CO 2g = CO 2aq for all species that can be formed from 12C, 13C, 16O, and 18O; for the reaction between 12C 18O 2aq and 1H 2 18O l; and among the various 1H, 2H, 16O, and 18O species of H 2O. This is a subset of a larger number of equilibrium constants calculated elsewhere (Thorstenson D. C. and Parkhurst D. L. [2002] Calculation of individual isotope equilibrium constants for implementation in geochemical models. Water-Resources Investigation Report 02-4172. U.S. Geological Survey). Activity coefficients, activity-concentration conventions for the isotopic variants of H 2O in the solvent 1H 2 16O l, and salt effects on isotope fractionation have been included in the derivations. The effects of nonideality are small because of the chemical similarity of different isotopic species of the same molecule or ion. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation factors. The derivations can be extended to calculation of individual isotope equilibrium constants for ion pairs and equilibrium constants for isotopic species of other chemical elements. The individual isotope approach calculates the same phase isotopic compositions as existing methods, but also provides concentrations of individual species, which are needed in calculations of mass-dependent effects in transport processes. The equilibrium constants derived in this paper are used to calculate the example of gas-water equilibrium for CO 2 in an acidic aqueous solution.

The Apollo SWC Experiment: Results, Conclusions, Consequences

The Apollo Solar Wind Composition (SWC) experiment was designed to measure elemental and isotopic abundances of the light noble gases in the solar wind, and to investigate time variations in the solar-wind composition. The experiment was deployed on the first five Apollo lunar landing missions. The crews exposed a foil at each of the five landing sites, and solar wind particles were collected for time periods ranging from 77 minutes in July 1969 (Apollo 11) to 45:05 hours in April 1972 (Apollo 16). The foils were returned to Earth, where the collected noble gas particles were analysed in ultra-high vacuum mass spectrometer systems. We briefly describe here the flight hardware, and the technical tests and calibrations. The experimental results were published in various scientific journals, PhD theses and NASA science reports, some of them not readily accessible after three decades. In this paper, therefore, the results obtained by the five experiments on the fluxes of the isotopes of He, Ne and Ar are summarized and discussed, so that averages and variations in solar wind composition can be more easily compared with more recent data, particularly those to be obtained by the Genesis mission. The helium flux determined for the five exposure periods varied by a factor of four, with a time-weighted average of 1.2 × 107 cm−2 s−1. Although the composition varied much less than the He-flux, definite variations were found for the 4He/3He and He/Ne ratios. The weighted average solar wind abundance ratios obtained were 4He/3He = 2350 ± 120, 4He/20Ne = 570 ± 70, 20Ne/22Ne = 13.7 ± 0.3, 22Ne/21Ne = 30 ± 3, 20Ne/36Ar = 49 ± 7 and 36Ar/38Ar =5.4 ± 0.3 (errors correspond to the 2σ level). We also measured the flow directions of individual isotopic species. We found that the lunar environment did not significantly affect the solar wind composition measured at the lunar surface, and we conclude that the SWC results are representative of the solar wind prevailing in interplanetary space at the time of the five foil exposures. Finally, we discuss, from today's perspective, some of the implications and conclusions that can be drawn from the SWC results, concerning the Sun and its history, the solar system, the galaxy and the universe.

Adsorption in gas mass spectrometry II. Effects on the measurement of isotope amount ratios

Gas adsorption in the mass spectrometer inlet system (equipped with molecular leak) causes a deviation from linearity of the measured lnR i 1 data versus time, which affects the extrapolation to time t = 0 required to obtain the isotope amount ratios of a sample. The model first presented in (R. Gonfiantini, S. Valkiers, P.D.P. Taylor, P. De Bièvre, Adsorption in gas mass spectrometry. I. Effects on the measurement of individual isotopic species, Int. J. Mass Spectrom. Ion Proc. (1997) in press) is further developed in order to show the effects of adsorption on the data obtained in long measurements of SiF 4 samples and improve the extrapolation InR i/1 values to t = 0. The model enables to estimate the isotope fractionation factors for the processes of gas effusion through the molecular leak, and for adsorption and desorption on the inlet system walls. The fractionation factors obtained for gas effusion and adsorption are close to the expected value of ( M 1/ M i ) 1/2, where M 1 and M i are the molar masses of the isotopic species considered. The isotope fractionation factor for desorption, which can be evaluated only indirectly from the data fitting, indicates that the heavy isotopes are preferentially retained in the adsorbate. Model extrapolation of data obtained during the first 10 hours of measurement gives values of R i/1 0 which are slightly but significantly smaller than those given by linear extrapolation of the first two hour data. The difference is, in relative terms, −(1.88 ± 0.23) × 10 −4 for the 29Si/ 28Si ratio and −(3.25 ± 0.47) × 10 −4 for the 30Si/ 28Si ratio. The resulting molar mass for silicon is (1.0 ± 0.1) × 10 −6 parts lower than that obtained with the isotope amount ratios of the linear extrapolation. This effect is not negligible but it cancels by using synthetic isotope mixtures for the measurement calibration. The model does not match the data after 15 h of measurement. This may imply that more than one adsorption mode occurs. Effects related to molecule fragmentation and the space charge distribution in the ion source are discussed.

Adsorption in gas mass spectrometry. I. Effects on the measurement of individual isotopic species

The adsorption-desorption process of gas molecules on the walls of the mass spectrometer inlet system was studied in order to assess quantitatively its influence on measurement results. The effects on individual isotopic species in SiF 4 measurements required for the re-determination of the Avogadro constant are discussed in this paper, while the effects on isotope amount ratio determinations will be discussed in a companion paper. A model based on the Langmuir adsorption isotherm is developed, which fits well the experimental observations and provides the means to investigate adsorption and desorption kinetics in the inlet system. A parameter called the ‘apparent leak-rate coefficient’ is introduced; this represents the relative variation with time of any isotopic species in the inlet system. All the adsorption parameters appearing in the balance equations are derived from the apparent leak-rate coefficient. Application of the model to long mass-spectrometric measurements of SiF 4 yields a rate constant of 6.5 × 10 −5 s −1 for SiF 4 effusion through the molecular leak of the inlet system. Adsorption and desorption rate-constants are equal to 20–25% of the leak rate-constant, and the adsorption sites are about two orders of magnitude lower than the number of Ni and Cu atoms present on the inlet system walls.

Measuring the ratio of aqueous diffusion coefficients between 6Li +Cl − and 7Li +Cr − by osmometry

Osmotic equilibrium is a singular occurrence in the evolution of an osmotic cell because at this event the net solution flux is zero such that −J w · V ̄ w = J s · V ̄ s . At this juncture, the diffusion coefficient of the solute through the membrane (ω) equals the solute flux ( J s ) divided by the osmotic pressure (ΔΠ). Because the solute permeability coefficient (ω) is related to the Fickian diffusion coefficient ( D) through the gas constant, temperature, and the membrane's thickness and tortuosity, the ratio of ω values for individual isotopic species equals the ratio of D values for the same isotopic components. A 0.9450 molal LiCl solution was placed within sealed dialysis tubing and osmoted against a kilogram of deionized water at 22°C. Osmotic equilibrium occurred at 164 ± 10 min. The ratio of ω6Li +Cl − ω7Li +Cl − was measured to be 1.011 ± 0.003—a value close to the square root of the mass ratio between 7LiCl and 6LiCl (= 1.012) as calculated by Graham's Law. The measured diffusion coefficient ratio was used to predict the degree of hyperfiltration-induced fractionation of Li isotopes as a function of membrane ideality. When a membrane's σ exceeds 0.95 (as is likely for low-porosity shales) the 6Li 7Li ratio on the high-pressure side of the membrane can theoretically vary by more than 0.0017.

Self‐consistent numerical model for analyzing thermal layering of liquid mixtures of hydrogen isotopes inside a spherical inertial confinement fusion target

A self‐consistent numerical model has been developed to describe the thermally induced behavior of a liquid layer of hydrogen isotopes inside a spherical inertial confinement fusion (ICF) target and to calculate the far‐field temperature gradient which will sustain a uniform liquid layer. This method is much faster than the trial‐and‐error method previously employed. The governing equations are the equations of continuity, momentum, energy, mass diffusion–convection, and conservation of the individual isotopic species. Ordinary and thermal diffusion equations for the diffusion of fluxes of the species are included. These coupled equations are solved by a finite‐difference method using upwind schemes, variable mesh, and rigorous boundary conditions. The solution methodology unique to the present problem is discussed in detail. In particular, the significance of the surface tension gradient driven flows (also called as Marangoni flows) in forming uniform liquid layers inside ICF targets is demonstrated. Usi...

Thermally induced behavior of liquid mixtures of hydrogen isotopes inside a spherical inertial confinement fusion target

A theory is presented which is intended to explain thermally induced formation of uniform liquid layers of ternary mixtures of hydrogen isotopes inside a spherical inertial confinement fusion (ICF) target. The governing equations are the equations of stream function, modified vorticity, and energy, and the equations of conservation of the individual isotopic species. The equations for the diffusion fluxes of the species include both ordinary and thermal diffusions. These coupled equations are solved by a finite-difference method using upwind schemes and variable mesh. The results demonstrate the influence of the concentration- and temperature-induced surface tension gradients in creating the uniform liquid fuel layer inside an ICF target. Comparison of the present theory with the experimental data is made for targets filled, respectively, with D2 and mixtures of H2 and D2, producing good agreement in both cases.

Effect of isotope shifts in the blue–green band spectrum of the lead dimer

The absorption spectrum of gaseous Pb2 has been investigated in the blue – green spectral region. Owing to the overlap between the six dominating isotopic Pb2 molecules formed by natural lead – in combination with the very dense structure of the [Formula: see text] transition – it is impossible to rotationally resolve the Doppler limited spectrum. Still, regions of rotational structure were resolved. These were explained by interference effects between the absorption spectra of the individual isotopic species. The regions of resolved rotational structure form a pattern similar to a moiré pattern. The information gained is used together with laser induced fluorescence data in a reanalysis of the F and X states. The following main molecular constants for the 208Pb2 molecule have been derived (cm−1):[Formula: see text]

Preparation of stable isotope-incorporated peptide internal standards for field desorption mass spectrometry quantification of peptides in biologic tissue.

Stable isotopes have been incorporated into two opioid pentapeptides, leucine enkephalin and methionine enkephalin, using chemical- and enzymatic-catalyzed reactions. Oxygen-18 from H218O was the stable isotope incorporated. High-performance liquid chromatography separated the chemical reaction mixture into three fractions: hydrolyzed peptide fraction, 18O-incorporated enkephalin, and 18O-incorporated enkephalin ester. Analysis of individual isotopic species (18O2, 18O16O, 16O2) in the latter two fractions was done with field desorption mass spectrometry. Porcine esterase II was used to hydrolyse enkephalin esters and recover stable isotope. Up to 90% 18O2 was incorporated. Yields of 18O2 species for the overall procedure were for leucine enkephalin, 56%, and for methionine enkephalin, 38%. This scheme represents the first fast and facile preparation of a stable isotope-incorporated peptide internal standard for use in measuring peptides in biologic extracts and is readily extended to any peptide with a free carboxyl group. Fast atom bombardment-collision activated dissociation-linked field (B/E) scan mass spectrometry unambiguously locates the two 18O atoms in the carboxyl group of the peptide and not in a peptide amide bond or tyrosine side chain. The two 18O-labeled peptide internal standards were used to measure, in a structurally unambiguous fashion, endogenous leucine enkephalin and methionine enkephalin in thalamus tissue at the ppb level. A microcomputer was used for data acquisition and reduction.

Vibration rotation spectra and x, y-type Coriolis interaction of chlorogermane

The vibration rotation spectra of chlorogermane were measured and the three fundamental perpendicular bands were analyzed. The successive Q branches in ν 4 band are resolved into the individual isotopic species of germanium. The effect of the x, y-type Coriolis interaction between ν 2 and ν 5 bands is discussed with the aid of simulated spectra.

Separation Factors in Multicomponent Mixtures of Isotopes

The discussion is restricted to vapor-liquld equllibria; for the case of general isotoplc exchange equllibria, equllibrium constants must be used instead of vapor pressures. The single-stage separation factor for the distribution of the isotoplc species 1 and k between the gas and liquid phase is, for a given temperature, alpha (i/k) = P/sup o/(i)/P/sup o/(k). In the jcomponent system, all separation factors, except j-1, can be derived according to alpha (i/k) = alpha (l/k)/ alpha (l/i). An equation is derived that gives the dependence of the effective separation factor on the individual separation factors as defined by the concentration of the individual isotopic species in the mixture. Discussion is also given on the rule of the geometric mean, and systems in which it holds or does not hold are examined. (P.C.H.)

New Prospects in Isotope Separation

THE identification of the heavy hydrogen isotope and its separation gave considerable impetus to the search for methods of bulk separation of the isotopes of other elements. Previous to this time, the experimental man of science had been content to demonstrate that displacements of normal isotope ratios could be secured by one or other method. Aston and Harkins had shown that these ratios could be changed by diffusion processes in the cases of neon and chlorine. Bron-sted and Hevesy changed slightly the atomic weight of mercury by distillation methods. It was the separation of the hydrogen isotopes and the demonstration of their extraordinary utility in many problems of chemical, physical and biological interest that re-awakened the interest in more complete separations of other isotopic elements. The simultaneous advances in the study of the nucleus, by bombardment with swift-moving primary particles, enhanced the desire for individual isotopic species of the elements, at the same time that it provided an alternative tool for research in the form of artificially produced radioactive elements.