Fractionation factor, deuterium

Distillation. Vacuum distUlation (qv) of water, which contains the three molecular species H2O, HDO, and D2O, was the first method used for the large-scale extraction of deuterium (10,58) (Fig. 2). From the equHibrium constant in the Hquid phase it is evident that the distribution of H and D is not statistical. The differences in vapor pressure between H2O and D2O are significant, and a fractionation factor (see Table 7) of 1.05 can be obtained at... 

Distillation of Hquid hydrogen as a method for separating deuterium received early consideration (10,58) because of the excellent fractionation factor that can be attained and the relatively modest power requirements. The cryogenic temperatures, and the requirement that the necessarily large hydrogen feed be extremely pure (traces of air, carbon monoxide, etc, are soHds at Hquid hydrogen temperature) have been deterrents to the use of this process (see... 

Wong, W.W., Cochran, W.J., Klish, W.J., Smith, E.O.B., Lee, L.S. and Klein, P.D. 1988 In vivo isotope-fractionation factors and the measurement of deuterium- and oxygen-18-dilution spaces from plasma, urine, saliva, respiratory water vapor, and carbon dioxide. American Journal of Clinical Nutrition 47 1-6. 

Since the reaction is not reversible, the EIE could not be measured. However, the secondary deuterium EIE could be estimated using the fractionation factors published by Hartshorn and Shiner (1972). This approach predicted that the secondary EIE, (KH/KD)sec, would be equal to 1.115 at 45°C. This corresponds to a (Kh/Kt)kc = 1.170 in the absence of tunnelling. Because the secondary tritium KIE is much larger than the EIE, it seems likely that tunnelling is important in this reaction. 

The secondary deuterium KIEs obtained by converting the secondary tritium KIEs found for the E2 reactions of several different 2-arylethyl substrates into secondary deuterium KIEs with the Swain-Schaad equation (Swain et al., 1958) are in Table 36. As discussed above, one would expect the secondary deuterium isotope effect to reflect the extent to which rehybridization of the /3-carbon from sp3 of the reactant to sp2 in the product has taken place in the transition state. According to this reasoning, the secondary tritium EIE should be a good estimate of the maximum secondary tritium KIE. Because these reactions were not reversible, the EIE could not be measured. However, one can estimate the EIE (the maximum expected secondary KIE) using Hartshorn and Shiner s (1972) fractionation factors. The predicted EIE (Kh/Kd) values were 1.117 at 40°C and 1.113 at 50°C. Seven of the reactions... 

It is instructive to calculate the anharmonic correction to the zero point energy contribution to fractionation factors for isotope exchange equilibria involving hydrogen and deuterium. For example consider the exchange... 

The isotopic abundance of deuterium in the L30+ ion will differ from that in the water with which it is equilibrated. This is expressed in terms of the fractionation factor / which is the ratio of D/H ratios in the lyonium ion and the mixed solvent (water)... 

The value of the fractionation factor for any site will be determined by the shape of the potential well. If it is assumed that the potential well for the hydrogen-bonded proton in (2) is broader, with a lower force constant, than that for the proton in the monocarboxylic acid (Fig. 8), the value of the fractionation factor will be lower for the hydrogen-bonded proton than for the proton in the monocarboxylic acid. It follows that the equilibrium isotope effect on (2) will be less than unity. As a consequence, the isotope-exchange equilibrium will lie towards the left, and the heavier isotope (deuterium in this case) will fractionate into the monocarboxylic acid, where the bond has the larger force constant. 

Similar measurements have given values for the fractionation factor of hydrogen-bonded complexes of the fluoride ion (Emsley et al., 1986c) and the acetate ion (Clark et al., 1988a) in acetic acid solution, [20] and [21]. For the chloride ion in acetic acid, the result (Emsley et al., 1986c) was cp = 1.26, which means that the exchangeable sites in acetic acid molecules in the solvation sphere of the chloride ion are favoured by deuterium compared to the sites in the bulk solvent. 

The values of the fractionation factors in structures [15]-[21] are not strictly comparable since they are defined relative to the fractionation in different solvent standards. However, in aqueous solution, fractionation factors for alcohols and carboxylic acids relative to water are similar and close to unity (Schowen, 1972 Albery, 1975 More O Ferrall, 1975), and it seems clear that the species [15]-[21] involving intermolecular hydrogen bonds with solvent have values of cp consistently below unity. These observations mean that fractionation of deuterium into the solvent rather than the hydrogen-bonded site is preferred, and this is compatible with a broader potential well for the hydrogen-bonded proton than for the protons of the solvents water, alcohol and acetic acid. 

Several other nmr procedures have been used for the determination of fractionation factors. These have advantages in some systems. Instead of determining the effect of the concentration of an exchanging site on the averaged chemical shift, the effect on the averaged relaxation rate of water protons can be used in a very similar way (Silverman, 1981 Kassebaum and Silverman, 1989), For example, addition of the enzyme Co(ii)-carbonic anhydrase to an aqueous solution increases the observed value of XjT because the proton-relaxation rate is the average of that for the bulk solvent (cfl. 0.3 s ) and that for water bound to the cobalt ca. 6x 10 s ). The average is different in an H2O/D2O mixture if the bulk solvent and the Cobound solvent have different deuterium contents, and it has been used to determine a value for the fractionation factor of Co-bound water molecules in the enzyme. 

A ratio defining the isotopic distribution of two isotopes equilibrated between two different chemical species. If X, followed by a subscript, represents the mole fraction of an isotope (denoted by that same subscript), then the fractionation factor, often symbolized by , with respect to chemical species A and B is (Xi/X2)a/(-X i/-X 2)b- Fractionation factors can also refer to different sites, A and B, within the same chemical species. As an example, the deuterium solvent fractionation factor, used in studying solvent isotope effects, is = (AD/A"H)soiute/(- o/... 

Fig. 10 Changes in the hydrogen bond between Zn OH and Ser48 during hydride transfer to NAD in the liver alcohol reaction.40 The values are deuterium fractionation factors.

The NMR determinations of the site-specific hydrogen isotope ratios at natural deuterium abundance permitted one to assess primary and secondary thermodynamic fractionation factors in exchange reactions avoiding the synthesis of selectively labelled reagents and their degradations691. 

Values of fractionation factors for a-deuterium isotope effects... 

We see from these results that the fractionation factors for the symmetrical transition states reflect the values for the reactant (and product). However, whereas the reactant fractionation factors span a range of 11% (from 0.97 to 1.08) the transition state factors are more widely dispersed covering a range of 18% (from 0.94 to 1.12). These results will be discussed further, but first we have to consider an argument advanced by Shiner (197 Id) in which the a-deuterium isotope effect is used to measure tjY. 

Fig. 20 Values of the fractionation factors + and 0KY are known but the deduction of transition state structure from the a-deuterium isotope effect requires a further assumption. We...

Similarly the argument from the er-deuterium isotope effect depends on the value one assumes for the fractionation factor for the transition state at r = 1. The simple geometric mean shown in Fig. 20 can only be a plausible guess. Again, for the Hammett relations, one has to make assumptions about the values of p for the transition state at r = 1 (Fig. 23). Furthermore there are also assumptions in separating the kinetic and thermodynamic contributions. 

Equation (35) allows an evaluation of the fractionation factor for the hydroxide ion on the assumption that the autoprotolysis is adequately described by the simplest equation (i.e. 33). The resultant value is 0-42. This figure does not agree too well with the results of a careful direct study of the fractionation of deuterium between dissolved hydroxide ions and water (Heinzinger and Weston, 1964b), (048 at 13-5°C). 

The fractionation factor < LA correspondingly refers to the deuterium distribution between the acid and methanol (< LA = (D/H)LA/(D/H)Me0L). From the expression for the limit ->-l, we obtain... 

Presumably less nucleophilically assisted solvolyses could show higher a-deuterium isotope effects, and there is a linear relationship between the magnitude of nucleophilic solvent assistance (Table 2) and the a-deuterium isotope effect for solvolyses of 2-propyl sulpho-nates (Fig. 7). Another measure of nucleophilic assistance is the ratio k2 (OH )/, where k2 is the second-order rate constant for nucleophilic attack by OH and kx is the first-order rate constant for reaction with the solvent water, and a linear correlation was obtained by plotting the ratio versus the experimentally observed isotope effects for methyl and trideuteriomethyl sulphonates, chlorides, bromides and iodides (Hartman and Robertson, 1960). Using fractionation factors the latter correlation may also be explained by a leaving group effect on initial state vibrational frequencies (Hartshorn and Shiner, 1972), but there seems to be no sound evidence to support the view that Sn2 reactions must give a-deuterium isotope effects of 1-06 or less. 

The emichment of tritium is usuaUy determined by the tritium separation (fractionation) factor during electrolysis, and by measuring the initial and final amounts of water. However, many workers have reported that the value of the separation factor of tritium depends on the electrode material, the type of electrolytic emiclunent ceU, the current density, the mode by which water is fed into the electrolytic cell, and the temperature of the electrolytic cell. In 1991, a rehable method was proposed for estimating tritium concentrations in water, based on a rehable correlation between the water electrolytic emiclunent of deuterium and tritium. The constancy of the ratio, k, during the electrolysis, k = a(fi — — 1), was... 

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