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129Xe NMR as a new tool for studying gas diffusion in liquids: self-diffusion of xenon in water
Volume 195, number
56
CHEMICAL
PHYSICS
LETTERS
31 July 1992
‘29Xe NMR as a new tool for studying gas diffusion in liquids: self-diffusion of xenon in water Hermann
WeingHrtner,
Ralf Haselmeier
and Manfred
Holz
Insiitutjiir Physikalische Chemie und Elektrochemie de-rUniversitiit Karlsruhe, Kaiserstrasse 12, W- 7500 Karlsruhe. Germany Received
8 April 1992; in final form 11 May 1992
We report on a new application of 129Xe NMR for measuring gas diffusion in liquids. Specifically, we present data for the translational diffusion coefficient of xenon in water. The values range from about 1.3 X 10e9 to 3 X 10m9 m* SC’ in the temperature range 5-55°C and are much higher than literature data for xenon diffusivities measured by other techniques. Also, they are roughly of the same order of magnitude as the self-diffusion coefftcient of water ( 1.90X 10m9 versus 2.30X 10e9 m2 s-l), as is also predicted by computer simulation. The activation energy of about 12.8 kJ mol-’ for xenon diffusion is however surprisingly low, if compared with 18.3 kJ mol-’ observed for water in this temperature range. An unexpectedIy strong influence of an added salt on the self-diffusion coefficient of xenon in water is noted.
1. Introduction The physico-chemical quantities associated with the introduction of hydrophobic species in water exhibit a number of uncommon features related to the hydration of these solutes (hydrophobic hydration ) and to their mutual interaction (hydrophobic interaction) [ 11. Since water forms the basis of all biologically important fluids, such hydrophobic effects are of wide interest. We quote for example their relation to globular protein stability, or, the formation of micelles and biological membranes [ 2,3 1. In this context, the solution properties of noble gases like xenon have attracted much interest, as these are considered to represent prototypical hydrophobic solutes [ 1,3]. More generally, xenon may also represent an uncharged, small test particle for studying molecular structures and local dynamics in nonaqueous systems. The explanation of solubilities of inert gases by cavity formation in water has formed a key step for modem concepts underlying the understanding of hydrophobic effects, and subsequently, these aspects have motivated numerous Correspondence to: H. WeingPrtner and M. Holz, Institut fur Physikalische Chemie und Elektrochemie der Universitlt Karlsruhe, Kaiserstrasse 12, W-7500 Karlsruhe, Germany.
596
studies of thermodynamic properties of aqueous solutions of noble gases, and above all, of gas solubilities as a function of temperature and pressure [ 1,4]. Progress in statistical mechanics and computer simulations have contributed to a better understanding of these hydrophobic interactions on a molecular level [ 5-8 1. Here, we report on an experimental study of the self-diffusion of xenon in water using lz9Xe NMR. In the past, NMR spin-echo methods have been mainly applied in self-diffusion studies by ‘H NMR, but a variety of other spin- l/2 or even quadrupolar nuclei can be employed [9-l 11, and we have recently demonstrated [ 9, lo] that the accuracy of such experiments is now comparable with that of conventional tracer experiments at their best. Here, we use lz9Xe NMR for measuring xenon diffusion in water. In contrast to the wealth of thermodynamic data, little is known on gas diffusivities in water, and the available data are contradictory. For example, reported values for the diffusivity of xenon in water at 25°C range from 0.8~ 10e9 to 1.4~ lop9 m2 s-’ [ 12-141. The lack of accurate diffusion data represents a major drawback when trying to understand molecular dynamics in such systems. It is now accepted that in the neighbourhood of hydrophobic solutes the
0009-2614/92/$ 05.00 0 1992 Elsevier Science Publishers
B.V. All rights reserved.
Volume 195, number
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PHYSICS
water structure is more ordered than in the neat liquid. This results in a slowing-down of the rotational and translational motions of water molecules, actually observed in systems containing more complex hydrophobic molecules [ 15,161, and confirmed by computer simulations for model systems consisting of Lennard-Jones solutes [ 5-81. It still is an open question whether this retardation is also reflected by the diffusion of the solute. The above-quoted diffusivities would indeed imply that xenon diffusion is much slower than that of water, but this contrasts with results of computer simulations of LennardJones solutes which have indicated almost equal diffusion rates of solutes and the solvent water [ 7 1.
2. Experimental In probing the structure and dynamics of solutions by xenon NMR, the spin-312 nucleus 13’Xe has been generally used [ 17,181, but very short relaxation times of the order of some milliseconds due to quadrupolar interaction make 13’Xe unsuitable for selfdiffusion measurements. This has directed our interest towards the use of the spin-l /2 nucleus lz9Xe. At a first glance, ‘29Xe NMR appears to be fairly straightforward. The absolute receptivity of 129Xe is comparatively low for self-diffusion measurements by the spin-echo technique, but is still about 32 times that of 13C (the difference results mainly from the higher natural abundance of 26.4% of 129Xe). However, iz9Xe self-diffusion measurements are extremely difficult, owing to low spin densities in solutions and extremely long relaxation times. The mole fraction of xenon in water at 25 “C and atmospheric pressure is of the order of 10m4 [ 41. The spin-lattice relaxation time in degassed samples is not known exactly, but even with undegassed samples it may run up to more than hundred seconds. The self-diffusion coefftcients have been measured by the pulsed field gradient (PFG) technique in the Fourier transform mode [ 111 using a Bruker SXP 4-100 spectrometer in conjunction with an Aspect 2000 computer for signal accumulation and Fourier transformation. General procedures for obtaining highly accurate self-diffusion data with lesscommon nuclei are described elsewhere [ 9, lo]. We discuss here only those aspects which have proved to
LETTERS
31 July 1992
be crucial for overcoming the problems associated with the low signal intensities and long relaxation times in ‘29Xe spin-echo measurements. The measurements were performed in a superconducting Bruker wide-bore magnet (89 mm) at 7.04 T (corresponding to a resonance frequency of 82.98 MHz for ‘29Xe). A special probe head based on the design originally devised by Holz et al. for determining flow velocities by spin-echo experiments [ 19 ] enabled measurements of samples with a volume of about 1.5 cm3. As a major advantage, this probe head enabled direct liquid cooling of the sample, enabling thermostating to within + 0.1 “C. Many commercially available probe heads use gas as a thermostating fluid, which gives poor response in temperature control, so that marked temperature gradients cause disturbing convection in the sample, thus representing an essential source of error. All experiments were performed at elevated gas pressures up to some 5 MPa to obtain a sufficiently high xenon concentration in solution. Accordingly, the measurements were performed in thick-walled glass tubes of 10 mm outer diameter and 6 mm inner diameter. Higher pressures are not of much use, because clathrate formation begins to interfere [ 201, as was also observed in our experiments. For sample preparation xenon was condensed into a glass tube containing a known amount of degassed and frozen water. The xenon pressure was recorded before breaking off the gas flow, freezing the xenon and sealing the tube. After thawing and equilibration at the temperature of interest, the xenon concentration in solution was calculated from the known pressure and temperature dependence of the xenon solubility ]4,201. Major problems arose with the duration of the spinecho experiments when trying to obtain adequate signal-to-noise ratios. The low spin density in conjunction with the comparatively low receptivity imposes long-term averaging, which in view of the very long relaxation times resulted in extremely time-consuming experiments. Therefore, we attempted to enhance relaxation by adding paramagnetic manganese chloride. While this resulted in a drastic shortening of the duration of the experiments, we observed that even MnC12 concentrations of less than lop2 mol dmp3 had a notable effect upon the self-diffusion coefficient of xenon. Therefore, experiments were 597
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carried out at varying MnClz concentrations, followed by extrapolation of the self-diffusion coefftcients to zero salt concentration. The reliability of this procedure was tested at 25°C where the extrapolation value was in agreement with the result obtained with a salt-free sample. Typical conditions of a PFG experiment were: pressure of xenon, 3MPa; sample volume; 1.5 ml; MnCl, concentration, 0.01 mol dm-‘; waiting time per scan, 10 s; number of accumulations, 300; signal-to-noise ratio of the Fourier-transformed spin-echo signal without magnetic field gradient, 15 : 1; reproducibility of self-diffusion coefficients, ? 3%; estimated overall accuracy, + 5% or better. Accurate calibration of the magnetic field gradient, G, causing the spin-echo attenuation, is crucial for obtaining high-quality data. General methods for calibration in PFG experiments with less-common nuclei are described elsewhere [ 101. In our experiments G has been determined from i3C PFG experiments using the data for pure benzene as a calibration standard [lo]. The 13C and ‘29Xe resonance frequencies are close to one another, so that the same probe head could be used for both nuclei, and only its tuning had to be changed. The resulting G value was then used in ‘29Xe experiments for establishing a secondary standard. For this purpose, a sample of xenon dissolved in dodecane at a pressure of 7 MPa was found to be suitable, owing to the fairly high solubility. The resulting self-diffusion coefficient of xenon in dodecane at 25°C of (2.6OkO.05) x 10e9 m* s- ’ was used subsequently for calibration of ‘29Xe PFG experiments. This figure agrees fairly well with a value of 2.29 x 10e9 m* s- ’ at 20°C reported by Pollack and Enyeart [ 2 11.
3. Experimental results Fig. 1 shows the self-diffusion coefficient of xenon in aqueous solutions at 10, 25 and 45 “C as a function of the concentration of added MnCl,. Every data point is the average of at least three measurements. The various symbols indicate measurements at different pressures in the range 0.8 to 5 MPa corresponding to mole fractions of xenon between 6 X 1OM4 and 3.6 x 1O-3. It is seen that within the error limits the data are independent of pressure, and hence of 598
LETTERS
31 July 1992
I
&M 1
2
3
1
3
Fig. I. Self-diffusion coefficients for xenon in water at lo,25 and 45°C as a function of the concentration of added MnCl*. The various symbols indicate measurements at (0) 1 MPa, (0 ) 2 MPa, (0 ) 3 MPa and ( A ) 4 MPa, respectively. M corresponds to conventional molarity units.
the xenon concentration, as is expected within this small concentration range. Further experiments were carried out at temperatures between 5 and 55 “C. The temperature dependence of the xenon diffusivity obtained by extrapolation of results for samples with added MnC12 is shown in fig. 2. An Arrhenius plot yields a straight line with an activation energy of 12.8 + 2 kJ mol-I. The self-diffusion coefficient of water, also shown in fig. 2, exhibits a curvature in the Arrhenius plot over a large temperature range, but corresponds to an effective activation energy of 18.3 kJ mol- ’ in the range of interest [ 221. Data were read off from the smoothed temperature dependence in fig. 2 to obtain values of xenon diffusion coefftcients at rounded temperatures for comparison with literature data [ 12- 141. This comparison is made in table 1.
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Fig. 2. Temperature dependence of the self-diffusion coefficient of xenon in water. The dashed line represents the temperature dependence of the self-diffusion of water [ 221. Table 1 Self-diffusion coefficients of xenon in water, 109D(m2 s-i )
T(“C)
Ref. [ 121
0
10 20 25 50
Ref. [ 131
Ref. [ 141
This work ‘)
1.32
1.17b’ 1.43 1.72 1.90 2.81
0.542 0.41 0.60 2.27
0.827 1.48
a) Smoothed values at rounded temperatures. b, Extrapolated.
4. Discussion The most important aspect is that our data indicate much faster diffusion than reported hitherto #I. It is seen from table 1 that in some cases [ 12,131 discrepancies are even larger than a factor two. Only a data point by Pollack [ 14 ] is comparatively close to #’ Other techniques for probing mutual diffusion are driven by concentration gradient rather than self-diffusion. At trace concentrations of the solute, as present in these gas diffusion studies, the mutual diffusion coefficient becomes equal to the self-diffusion coefficient, so that no distinction between both quantities will be made.
31 July 1992
our results, but is still low. Note that the value obtained by Pollack for xenon in dodecane is consistent with our data. Our activation energy of 12.8 kJ mol-’ contrasts sharply with a value of about 35 kJ mol- ’ quoted in ref. [ 121 and also with a value of about 16 kJ mol- ’ extracted from data in ref. [ 13 1. While the data in ref. [ 121 have been obtained by an indirect technique, and appear to be unreliable, we cannot see obvious sources of inaccuracy in the techniques applied in refs. [ 13,141, respectively. However, in recent years the NMR spin-echo technique has been established as a highly accurate method [ 9- 111, and therefore we regard the present results as the most reliable data obtained hitherto. It is not the purpose of this paper to discuss the implications of our results for the various models and concepts applied in the literature for explaining gas diffusion in liquids. We will mention here only some basic aspects of our data. Needless to say that in the light of our results the conclusions drawn hitherto in the literature deserve reexamination. It is well established that in the neighbourhood of hydrophobic groups the reorientational and translational motions of water molecules are slowed down due to an increase in water structure, presumably due to clathrate-like structures. We are not aware of direct experimental results for water diffusion in the hydration sphere of xenon, but computer experiments on Lennard-Jones solutes in water tell us that the reduction of the diffusion rate in the hydration sphere may be some 20% [ 5-8 1. Then, with a selfdiffusion coefficient of 2.30x low9 m2 s-’ for bulk water at 25 “C [ 221, we obtain a value of about 1.85 x low9 m2 s- ’ for hydration water. The basic question is how this figure compares with the selfdiffusion coefficient of xenon. Our data imply that near 25 ‘C the experimental value for xenon diffusion comes very close indeed to that for hydration water, thus confirming approximately equal diffusion rates of the solute and water, predicted by computer simulations [ 7 1. A further important aspect is related to the observed activation energy. The value of 12.8 kJ mol- ’ is definitely lower than that of 18.3 kJ mol-’ found for pure water. At a first glance, one would tend to assume that the activation energy of water diffusion in the hydration sphere of xenon is even larger than 18.3 kJ mol-‘. If this is true, there is a remarkable 599
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difference between the results for water and xenon, although the values of the self-diffusion coefficients at 25°C are essentially equal. Hence, this equality would not persist at higher temperatures, as is particularly evident from fig. 2. In this context it is worthwhile to note that a still lower activation energy of about 9 kJ mol- ’ has been found for “‘Xe relaxation in aqueous solutions [ 18 1. 13’Xe relaxes by quadrupolar interaction with fluctuating electric field gradients at the nucleus, presumably caused by the rotational and translational motions of water molecules close to xenon [ 6,17,18 1. However, quadrupolar relaxation is a complicated cooperative process, and the activation energy may reflect the behaviour of collective instead of singleparticle motions as well as temperature-dependent static symmetry effects in the hydration shell [ 6 1. An experimental disentanglement of these contributions is difficult, and the low activation energy for the xenon diffusivity may well shed new light on the interpretation of details of the complex quadrupolar relaxation process. This is of particular interest as 13’Xe may represent a probe for molecular dynamics and structures of more complex systems. Finally, as by-products of our study, some further aspects are worthwhile to be mentioned. These are interesting in their own right, and are currently under investigation in this laboratory. One is related to the effect of mass upon diffusion. The self-diffusion coefficient of xenon in water corresponds closely to that reported recently for methane (about 2.0 x 1Oe9 m2 s- ’ extracted from fig. 2 in ref. [ 8 ] ). Both should correspond to Lennard-Jones solutes of almost equal volumes, but their masses differ by a factor of eight. Hence, mass effects upon diffusion appear to be small for such systems. The other is related to the dependence of the xenon diffusivity on the concentration of added MnCl,. The order of magnitude of the latter effect exceeds largely what is expected on the basis of known data for the concentration dependence of transport coefficients in electrolyte solutions [ 23 1. Possible explanations are close solute-solute pairs due to hydrophobic interaction [ 241, or, a specific anion binding phenomenon to nonpolar solutes, which shows up in many other properties of aqueous electrolyte solutions containing non-polar co-solutes [ 25,261. On the macroscopic level, these structures may also be 600
31 July 1992
responsible for the salting-out of gases by electrolytes. In summary, our results demonstrate that NMR spin-echo measurements with less-common nuclei may be successfully employed for obtaining accurate self-diffusion data under conditions where other methods are difficult to apply. They also show the utility of Xe as a small test particle for studying the structure and local dynamics of liquids and solutions. This is particularly interesting for aqueous systems, where xenon acts as a hydrophobic probe. Application to more complex solutions, or even biological systems like membranes or protein suspensions appears to be straightforward (note that in living systems xenon acts as an anaesthetic). Such investigations are particularly promising, when supporting the data evaluation by molecular dynamics simulations [ 6 1. Further experimental investigations of model systems in conjunction with computer simulations, aimed to obtain a more rigorous analysis than given here, are in progress.
Acknowledgement We than Dr. R. Mazitov for valuable advice concerning the sample preparation. Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
References [ I ] F. Franks, in: Water, a comprehensive treatise, Vol. 4, ed. F. Franks (Plenum Press, New York, 1975) p. I. [ 2 ] C. Tanford, The hydrophobic effect: formation of micelles and biological membranes ( Wiley-Interscience, New York, 1973). [3] W. Kauzmann, Advan. Protein Chem. 14 (1959) I.
(41 E. Wilhelm, R. Battino and R.J. Wilcock, Chem. Rev. 77 (1977) 219. [ 51 A. Geiger, A. Rahman and F.H. Stillinger, J. Chem. Phys. 70 (1979) 263. [ 6 ] J. Schnitker and A. Geiger, Z. Physik. Chem. NF 155 ( 1987) 29. [ 7 ] D.C. Rapaport and H.A. Scheraga, J. Phys. Chem. 86 ( 1982) 873. [ 8 ] A. Laaksonen and P. Stilbs, Mol. Phys. 74 ( I99 1) 747. [ 91 B.M. Braun and H. Weingartner, J. Phys. Chem. 92 ( 1988) 1342. [ lo] M. Holz and H. Weingartner, J. Magn. Reson. 92 ( 1991) 115.
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[ 111 P. Stilbs, Progr. NMR Spectry. 19 ( 1987) 1. [ 121 D.L. Wise and G. Houghton, Chem. Eng. Sci. 23 ( 1968) 1211. [ 131 A.J.H. Boerboom and G. Klein, J. Chem. Phys. 50 ( 1969) 1086. [ 141 G. Pollack, Phys. Rev. A 23 (1981) 2660. [ 151 M.D. Zeidler, in: Water, a comprehensive treatise, Vol. 2 (Plenum Press, New York, 1972). [ 161 H.G. Hertz and M.D. Zeidler, Ber. Bunsenges. Physik. Chem. 68 (1964) 821. [ 171 T.R. Stengle, N.V. Reo and K.L. Williamson, J. Phys. Chem. 88 (1984) 3225. [ IS] R.K. Mazitov, H.G. Hertz, V.F. Garanin, K.M. Enikeev, A.V. Il’yasov and V.F. Suchoverchov, Dokl. Akad. Nauk SSSR273 (1983) 131.
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[ 191 M. Holz, Ch. Miiller and A.M. Wachter, J. Magn. Reson. 69 (1986) 108. [20] R.P. Kennan and G.L. Pollack, J. Chem. Phys. 93 (1990) 2724. [ 2 I] G.L. Pollack and J.J. Enyeart, Phys. Rev. 3 1 ( 1985) 980. [22] H. Weing&tner, Z. Physik. Chem. NF 92 (1991) 115. [23] R. Mills and V.V.M. Lobo, Self diffusion in electrolyte solutions; Physical Sciences Data Series No. 36 (Elsevier, Amsterdam, 1989). [24] M. Holz and K.J. Patil, Ber. Bunsenges. Physik. Chem. 95 (1991) 107. [25] H.G. Hertz and M. Holz, J. Phys. Chem. 78 (1974) 1002. [ 261 M. Holz and M. Sorensen, Ber. Bunsenges. Physik. Chem., submitted for publication.
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‘29Xe NMR as a new tool for studying gas diffusion in liquids: self-diffusion of xenon in water Hermann
WeingHrtner,
Ralf Haselmeier
and Manfred
Holz
Insiitutjiir Physikalische Chemie und Elektrochemie de-rUniversitiit Karlsruhe, Kaiserstrasse 12, W- 7500 Karlsruhe. Germany Received
8 April 1992; in final form 11 May 1992
We report on a new application of 129Xe NMR for measuring gas diffusion in liquids. Specifically, we present data for the translational diffusion coefficient of xenon in water. The values range from about 1.3 X 10e9 to 3 X 10m9 m* SC’ in the temperature range 5-55°C and are much higher than literature data for xenon diffusivities measured by other techniques. Also, they are roughly of the same order of magnitude as the self-diffusion coefftcient of water ( 1.90X 10m9 versus 2.30X 10e9 m2 s-l), as is also predicted by computer simulation. The activation energy of about 12.8 kJ mol-’ for xenon diffusion is however surprisingly low, if compared with 18.3 kJ mol-’ observed for water in this temperature range. An unexpectedIy strong influence of an added salt on the self-diffusion coefficient of xenon in water is noted.
1. Introduction The physico-chemical quantities associated with the introduction of hydrophobic species in water exhibit a number of uncommon features related to the hydration of these solutes (hydrophobic hydration ) and to their mutual interaction (hydrophobic interaction) [ 11. Since water forms the basis of all biologically important fluids, such hydrophobic effects are of wide interest. We quote for example their relation to globular protein stability, or, the formation of micelles and biological membranes [ 2,3 1. In this context, the solution properties of noble gases like xenon have attracted much interest, as these are considered to represent prototypical hydrophobic solutes [ 1,3]. More generally, xenon may also represent an uncharged, small test particle for studying molecular structures and local dynamics in nonaqueous systems. The explanation of solubilities of inert gases by cavity formation in water has formed a key step for modem concepts underlying the understanding of hydrophobic effects, and subsequently, these aspects have motivated numerous Correspondence to: H. WeingPrtner and M. Holz, Institut fur Physikalische Chemie und Elektrochemie der Universitlt Karlsruhe, Kaiserstrasse 12, W-7500 Karlsruhe, Germany.
596
studies of thermodynamic properties of aqueous solutions of noble gases, and above all, of gas solubilities as a function of temperature and pressure [ 1,4]. Progress in statistical mechanics and computer simulations have contributed to a better understanding of these hydrophobic interactions on a molecular level [ 5-8 1. Here, we report on an experimental study of the self-diffusion of xenon in water using lz9Xe NMR. In the past, NMR spin-echo methods have been mainly applied in self-diffusion studies by ‘H NMR, but a variety of other spin- l/2 or even quadrupolar nuclei can be employed [9-l 11, and we have recently demonstrated [ 9, lo] that the accuracy of such experiments is now comparable with that of conventional tracer experiments at their best. Here, we use lz9Xe NMR for measuring xenon diffusion in water. In contrast to the wealth of thermodynamic data, little is known on gas diffusivities in water, and the available data are contradictory. For example, reported values for the diffusivity of xenon in water at 25°C range from 0.8~ 10e9 to 1.4~ lop9 m2 s-’ [ 12-141. The lack of accurate diffusion data represents a major drawback when trying to understand molecular dynamics in such systems. It is now accepted that in the neighbourhood of hydrophobic solutes the
0009-2614/92/$ 05.00 0 1992 Elsevier Science Publishers
B.V. All rights reserved.
Volume 195, number
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PHYSICS
water structure is more ordered than in the neat liquid. This results in a slowing-down of the rotational and translational motions of water molecules, actually observed in systems containing more complex hydrophobic molecules [ 15,161, and confirmed by computer simulations for model systems consisting of Lennard-Jones solutes [ 5-81. It still is an open question whether this retardation is also reflected by the diffusion of the solute. The above-quoted diffusivities would indeed imply that xenon diffusion is much slower than that of water, but this contrasts with results of computer simulations of LennardJones solutes which have indicated almost equal diffusion rates of solutes and the solvent water [ 7 1.
2. Experimental In probing the structure and dynamics of solutions by xenon NMR, the spin-312 nucleus 13’Xe has been generally used [ 17,181, but very short relaxation times of the order of some milliseconds due to quadrupolar interaction make 13’Xe unsuitable for selfdiffusion measurements. This has directed our interest towards the use of the spin-l /2 nucleus lz9Xe. At a first glance, ‘29Xe NMR appears to be fairly straightforward. The absolute receptivity of 129Xe is comparatively low for self-diffusion measurements by the spin-echo technique, but is still about 32 times that of 13C (the difference results mainly from the higher natural abundance of 26.4% of 129Xe). However, iz9Xe self-diffusion measurements are extremely difficult, owing to low spin densities in solutions and extremely long relaxation times. The mole fraction of xenon in water at 25 “C and atmospheric pressure is of the order of 10m4 [ 41. The spin-lattice relaxation time in degassed samples is not known exactly, but even with undegassed samples it may run up to more than hundred seconds. The self-diffusion coefftcients have been measured by the pulsed field gradient (PFG) technique in the Fourier transform mode [ 111 using a Bruker SXP 4-100 spectrometer in conjunction with an Aspect 2000 computer for signal accumulation and Fourier transformation. General procedures for obtaining highly accurate self-diffusion data with lesscommon nuclei are described elsewhere [ 9, lo]. We discuss here only those aspects which have proved to
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31 July 1992
be crucial for overcoming the problems associated with the low signal intensities and long relaxation times in ‘29Xe spin-echo measurements. The measurements were performed in a superconducting Bruker wide-bore magnet (89 mm) at 7.04 T (corresponding to a resonance frequency of 82.98 MHz for ‘29Xe). A special probe head based on the design originally devised by Holz et al. for determining flow velocities by spin-echo experiments [ 19 ] enabled measurements of samples with a volume of about 1.5 cm3. As a major advantage, this probe head enabled direct liquid cooling of the sample, enabling thermostating to within + 0.1 “C. Many commercially available probe heads use gas as a thermostating fluid, which gives poor response in temperature control, so that marked temperature gradients cause disturbing convection in the sample, thus representing an essential source of error. All experiments were performed at elevated gas pressures up to some 5 MPa to obtain a sufficiently high xenon concentration in solution. Accordingly, the measurements were performed in thick-walled glass tubes of 10 mm outer diameter and 6 mm inner diameter. Higher pressures are not of much use, because clathrate formation begins to interfere [ 201, as was also observed in our experiments. For sample preparation xenon was condensed into a glass tube containing a known amount of degassed and frozen water. The xenon pressure was recorded before breaking off the gas flow, freezing the xenon and sealing the tube. After thawing and equilibration at the temperature of interest, the xenon concentration in solution was calculated from the known pressure and temperature dependence of the xenon solubility ]4,201. Major problems arose with the duration of the spinecho experiments when trying to obtain adequate signal-to-noise ratios. The low spin density in conjunction with the comparatively low receptivity imposes long-term averaging, which in view of the very long relaxation times resulted in extremely time-consuming experiments. Therefore, we attempted to enhance relaxation by adding paramagnetic manganese chloride. While this resulted in a drastic shortening of the duration of the experiments, we observed that even MnC12 concentrations of less than lop2 mol dmp3 had a notable effect upon the self-diffusion coefficient of xenon. Therefore, experiments were 597
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carried out at varying MnClz concentrations, followed by extrapolation of the self-diffusion coefftcients to zero salt concentration. The reliability of this procedure was tested at 25°C where the extrapolation value was in agreement with the result obtained with a salt-free sample. Typical conditions of a PFG experiment were: pressure of xenon, 3MPa; sample volume; 1.5 ml; MnCl, concentration, 0.01 mol dm-‘; waiting time per scan, 10 s; number of accumulations, 300; signal-to-noise ratio of the Fourier-transformed spin-echo signal without magnetic field gradient, 15 : 1; reproducibility of self-diffusion coefficients, ? 3%; estimated overall accuracy, + 5% or better. Accurate calibration of the magnetic field gradient, G, causing the spin-echo attenuation, is crucial for obtaining high-quality data. General methods for calibration in PFG experiments with less-common nuclei are described elsewhere [ 101. In our experiments G has been determined from i3C PFG experiments using the data for pure benzene as a calibration standard [lo]. The 13C and ‘29Xe resonance frequencies are close to one another, so that the same probe head could be used for both nuclei, and only its tuning had to be changed. The resulting G value was then used in ‘29Xe experiments for establishing a secondary standard. For this purpose, a sample of xenon dissolved in dodecane at a pressure of 7 MPa was found to be suitable, owing to the fairly high solubility. The resulting self-diffusion coefficient of xenon in dodecane at 25°C of (2.6OkO.05) x 10e9 m* s- ’ was used subsequently for calibration of ‘29Xe PFG experiments. This figure agrees fairly well with a value of 2.29 x 10e9 m* s- ’ at 20°C reported by Pollack and Enyeart [ 2 11.
3. Experimental results Fig. 1 shows the self-diffusion coefficient of xenon in aqueous solutions at 10, 25 and 45 “C as a function of the concentration of added MnCl,. Every data point is the average of at least three measurements. The various symbols indicate measurements at different pressures in the range 0.8 to 5 MPa corresponding to mole fractions of xenon between 6 X 1OM4 and 3.6 x 1O-3. It is seen that within the error limits the data are independent of pressure, and hence of 598
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I
&M 1
2
3
1
3
Fig. I. Self-diffusion coefficients for xenon in water at lo,25 and 45°C as a function of the concentration of added MnCl*. The various symbols indicate measurements at (0) 1 MPa, (0 ) 2 MPa, (0 ) 3 MPa and ( A ) 4 MPa, respectively. M corresponds to conventional molarity units.
the xenon concentration, as is expected within this small concentration range. Further experiments were carried out at temperatures between 5 and 55 “C. The temperature dependence of the xenon diffusivity obtained by extrapolation of results for samples with added MnC12 is shown in fig. 2. An Arrhenius plot yields a straight line with an activation energy of 12.8 + 2 kJ mol-I. The self-diffusion coefficient of water, also shown in fig. 2, exhibits a curvature in the Arrhenius plot over a large temperature range, but corresponds to an effective activation energy of 18.3 kJ mol- ’ in the range of interest [ 221. Data were read off from the smoothed temperature dependence in fig. 2 to obtain values of xenon diffusion coefftcients at rounded temperatures for comparison with literature data [ 12- 141. This comparison is made in table 1.
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Fig. 2. Temperature dependence of the self-diffusion coefficient of xenon in water. The dashed line represents the temperature dependence of the self-diffusion of water [ 221. Table 1 Self-diffusion coefficients of xenon in water, 109D(m2 s-i )
T(“C)
Ref. [ 121
0
10 20 25 50
Ref. [ 131
Ref. [ 141
This work ‘)
1.32
1.17b’ 1.43 1.72 1.90 2.81
0.542 0.41 0.60 2.27
0.827 1.48
a) Smoothed values at rounded temperatures. b, Extrapolated.
4. Discussion The most important aspect is that our data indicate much faster diffusion than reported hitherto #I. It is seen from table 1 that in some cases [ 12,131 discrepancies are even larger than a factor two. Only a data point by Pollack [ 14 ] is comparatively close to #’ Other techniques for probing mutual diffusion are driven by concentration gradient rather than self-diffusion. At trace concentrations of the solute, as present in these gas diffusion studies, the mutual diffusion coefficient becomes equal to the self-diffusion coefficient, so that no distinction between both quantities will be made.
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our results, but is still low. Note that the value obtained by Pollack for xenon in dodecane is consistent with our data. Our activation energy of 12.8 kJ mol-’ contrasts sharply with a value of about 35 kJ mol- ’ quoted in ref. [ 121 and also with a value of about 16 kJ mol- ’ extracted from data in ref. [ 13 1. While the data in ref. [ 121 have been obtained by an indirect technique, and appear to be unreliable, we cannot see obvious sources of inaccuracy in the techniques applied in refs. [ 13,141, respectively. However, in recent years the NMR spin-echo technique has been established as a highly accurate method [ 9- 111, and therefore we regard the present results as the most reliable data obtained hitherto. It is not the purpose of this paper to discuss the implications of our results for the various models and concepts applied in the literature for explaining gas diffusion in liquids. We will mention here only some basic aspects of our data. Needless to say that in the light of our results the conclusions drawn hitherto in the literature deserve reexamination. It is well established that in the neighbourhood of hydrophobic groups the reorientational and translational motions of water molecules are slowed down due to an increase in water structure, presumably due to clathrate-like structures. We are not aware of direct experimental results for water diffusion in the hydration sphere of xenon, but computer experiments on Lennard-Jones solutes in water tell us that the reduction of the diffusion rate in the hydration sphere may be some 20% [ 5-8 1. Then, with a selfdiffusion coefficient of 2.30x low9 m2 s-’ for bulk water at 25 “C [ 221, we obtain a value of about 1.85 x low9 m2 s- ’ for hydration water. The basic question is how this figure compares with the selfdiffusion coefficient of xenon. Our data imply that near 25 ‘C the experimental value for xenon diffusion comes very close indeed to that for hydration water, thus confirming approximately equal diffusion rates of the solute and water, predicted by computer simulations [ 7 1. A further important aspect is related to the observed activation energy. The value of 12.8 kJ mol- ’ is definitely lower than that of 18.3 kJ mol-’ found for pure water. At a first glance, one would tend to assume that the activation energy of water diffusion in the hydration sphere of xenon is even larger than 18.3 kJ mol-‘. If this is true, there is a remarkable 599
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difference between the results for water and xenon, although the values of the self-diffusion coefficients at 25°C are essentially equal. Hence, this equality would not persist at higher temperatures, as is particularly evident from fig. 2. In this context it is worthwhile to note that a still lower activation energy of about 9 kJ mol- ’ has been found for “‘Xe relaxation in aqueous solutions [ 18 1. 13’Xe relaxes by quadrupolar interaction with fluctuating electric field gradients at the nucleus, presumably caused by the rotational and translational motions of water molecules close to xenon [ 6,17,18 1. However, quadrupolar relaxation is a complicated cooperative process, and the activation energy may reflect the behaviour of collective instead of singleparticle motions as well as temperature-dependent static symmetry effects in the hydration shell [ 6 1. An experimental disentanglement of these contributions is difficult, and the low activation energy for the xenon diffusivity may well shed new light on the interpretation of details of the complex quadrupolar relaxation process. This is of particular interest as 13’Xe may represent a probe for molecular dynamics and structures of more complex systems. Finally, as by-products of our study, some further aspects are worthwhile to be mentioned. These are interesting in their own right, and are currently under investigation in this laboratory. One is related to the effect of mass upon diffusion. The self-diffusion coefficient of xenon in water corresponds closely to that reported recently for methane (about 2.0 x 1Oe9 m2 s- ’ extracted from fig. 2 in ref. [ 8 ] ). Both should correspond to Lennard-Jones solutes of almost equal volumes, but their masses differ by a factor of eight. Hence, mass effects upon diffusion appear to be small for such systems. The other is related to the dependence of the xenon diffusivity on the concentration of added MnCl,. The order of magnitude of the latter effect exceeds largely what is expected on the basis of known data for the concentration dependence of transport coefficients in electrolyte solutions [ 23 1. Possible explanations are close solute-solute pairs due to hydrophobic interaction [ 241, or, a specific anion binding phenomenon to nonpolar solutes, which shows up in many other properties of aqueous electrolyte solutions containing non-polar co-solutes [ 25,261. On the macroscopic level, these structures may also be 600
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responsible for the salting-out of gases by electrolytes. In summary, our results demonstrate that NMR spin-echo measurements with less-common nuclei may be successfully employed for obtaining accurate self-diffusion data under conditions where other methods are difficult to apply. They also show the utility of Xe as a small test particle for studying the structure and local dynamics of liquids and solutions. This is particularly interesting for aqueous systems, where xenon acts as a hydrophobic probe. Application to more complex solutions, or even biological systems like membranes or protein suspensions appears to be straightforward (note that in living systems xenon acts as an anaesthetic). Such investigations are particularly promising, when supporting the data evaluation by molecular dynamics simulations [ 6 1. Further experimental investigations of model systems in conjunction with computer simulations, aimed to obtain a more rigorous analysis than given here, are in progress.
Acknowledgement We than Dr. R. Mazitov for valuable advice concerning the sample preparation. Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
References [ I ] F. Franks, in: Water, a comprehensive treatise, Vol. 4, ed. F. Franks (Plenum Press, New York, 1975) p. I. [ 2 ] C. Tanford, The hydrophobic effect: formation of micelles and biological membranes ( Wiley-Interscience, New York, 1973). [3] W. Kauzmann, Advan. Protein Chem. 14 (1959) I.
(41 E. Wilhelm, R. Battino and R.J. Wilcock, Chem. Rev. 77 (1977) 219. [ 51 A. Geiger, A. Rahman and F.H. Stillinger, J. Chem. Phys. 70 (1979) 263. [ 6 ] J. Schnitker and A. Geiger, Z. Physik. Chem. NF 155 ( 1987) 29. [ 7 ] D.C. Rapaport and H.A. Scheraga, J. Phys. Chem. 86 ( 1982) 873. [ 8 ] A. Laaksonen and P. Stilbs, Mol. Phys. 74 ( I99 1) 747. [ 91 B.M. Braun and H. Weingartner, J. Phys. Chem. 92 ( 1988) 1342. [ lo] M. Holz and H. Weingartner, J. Magn. Reson. 92 ( 1991) 115.
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[ 111 P. Stilbs, Progr. NMR Spectry. 19 ( 1987) 1. [ 121 D.L. Wise and G. Houghton, Chem. Eng. Sci. 23 ( 1968) 1211. [ 131 A.J.H. Boerboom and G. Klein, J. Chem. Phys. 50 ( 1969) 1086. [ 141 G. Pollack, Phys. Rev. A 23 (1981) 2660. [ 151 M.D. Zeidler, in: Water, a comprehensive treatise, Vol. 2 (Plenum Press, New York, 1972). [ 161 H.G. Hertz and M.D. Zeidler, Ber. Bunsenges. Physik. Chem. 68 (1964) 821. [ 171 T.R. Stengle, N.V. Reo and K.L. Williamson, J. Phys. Chem. 88 (1984) 3225. [ IS] R.K. Mazitov, H.G. Hertz, V.F. Garanin, K.M. Enikeev, A.V. Il’yasov and V.F. Suchoverchov, Dokl. Akad. Nauk SSSR273 (1983) 131.
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[ 191 M. Holz, Ch. Miiller and A.M. Wachter, J. Magn. Reson. 69 (1986) 108. [20] R.P. Kennan and G.L. Pollack, J. Chem. Phys. 93 (1990) 2724. [ 2 I] G.L. Pollack and J.J. Enyeart, Phys. Rev. 3 1 ( 1985) 980. [22] H. Weing&tner, Z. Physik. Chem. NF 92 (1991) 115. [23] R. Mills and V.V.M. Lobo, Self diffusion in electrolyte solutions; Physical Sciences Data Series No. 36 (Elsevier, Amsterdam, 1989). [24] M. Holz and K.J. Patil, Ber. Bunsenges. Physik. Chem. 95 (1991) 107. [25] H.G. Hertz and M. Holz, J. Phys. Chem. 78 (1974) 1002. [ 261 M. Holz and M. Sorensen, Ber. Bunsenges. Physik. Chem., submitted for publication.
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