J. Phys. Chem. 1993,97, 12173-12177
12173
NMR Chemical Shifts of 129XeDissolved in Liquid *Alkanes and Their Mixtures Yoong-Ho L i d and A. D. King, Jr.’ Department of Chemistry, University of Georgia, Athens, Georgia 30602-2556 Received: July 8, 1993; In Final Form: August 23, 1993’
Xenon-1 29 NMR spectra have been measured for solutions containing Xe dissolved in a variety of n-alkanes and their mixtures a t elevated pressures. The resonance frequencies measured for 129Xedissolved in pure n-alkanes are all shifted to higher frequency relative to low-pressure 129Xegas and vary with carbon number in a continuous but nonlinear fashion. Theoretical treatments of solvent-induced chemical shift based on a continuum model of the solvent are found to be inadequate when low molecular weight n-alkanes are involved. However, a simple model, which treats the dominant van der Waals contribution to the chemical shift of the 129Xeresonance as the average of individual pair interactions between X e and the individual methyl and methylene groups present in solution, is shown to accurately account for the chemical shifts observed in both pure n-alkanes and their mixtures. A modification of this simple model, which allows for multiple interactions between 129Xe and the carbon centers of each alkyl chain, is invoked to qualitatively explain the large difference observed between the shielding effects produced by the methyl and methylene groups of the various solvents.
large solvent molecules. However, a recent study performed in this laboratoryI2 suggests that the “cage model” mentioned Naturally occurring xenon contains a large isotopic abundance above,II which considers the chemical shifts to result from X e (26.4%) of the mass 129 isotope, 129Xe, which consists of a spinsolvent pair interactions summed over solvent molecules in the 112 nucleus surrounded by a large (Z= 54) highly polarizable first coordination shell, does, in fact, provide a satisfactory cloud of electrons. This electron cloud is easily distorted by electric explanation for the chemical shifts observed for 129Xedissolved fields generated by permanent and fluctuating electric moments in liquefied gases, i.e. systems in which the Xe atom and solvent arising from the charge distributions centered on neighboring molecules are of comparable size. molecules. As a result, the NMR resonance frequency of 129Xe This paper reports values measured for the chemical shift of is found to be very sensitive to the local environment so that lz9Xe 129Xedissolved in liquids composed of much larger molecules, can be used as a “molecular probe” to examine the internal namely, n-alkanes ranging from n-butane to n-heptadecane and properties of condensed homogeneous phases as well as mitheir mixtures. These data, when combined with the chemical croporous materials such as zeolites. Reference l lists three shifts measured recently for l29Xe dissolved in liquid ethane and excellent review articles that cover early as well as more recent propane,l2 constitute a complete data set for 129Xedissolved in aspects of l29Xe-NMR spectroscopy. n-alkanes, having carbon numbers n,, ranging from n, = 2 to n, The chemical shifts observed for l29Xe dissolved in homogeneous = 17, which can be used to test the various models put forth to liquids are found to vary considerably, one solvent to the n e ~ t . ~ - ~ explain solvent-induced chemical shifts observed with l29Xe as Various models have been invoked to relate the magnitudes of well as other nuclei. these chemical shifts with solvent properties. The approach most frequently followed attempts to correlate solvent-induced chemical Experimental Section shifts with the square of the reaction field strength?,’ using a The NMR spectra reported here were obtained using a JEOL continuum model to describe the solvent. For chemically similar FX-90Q FT N M R spectrometer equipped with a standard 10solvents these treatments reduce to determining how well the mm multinuclear probe operating at 23 f 1 OC. A center-band chemical shifts of the various nuclei of interest correlate with the frequency of 24 784 000.0 Hz was employed for all measurements. Bayliss-McRae function, g(n)?,* or its square? where g(n) (n2 Pulse widths of 65 ps (-goo) and a 4-s repetition time were used - 1)/(2n2 l), with n denoting the index of refraction of the in the data collection. A high-pressure sapphire NMR tubesolvent. This approach has been used to interpret the solventvalve assembly, described in ref 12, was used in these studies. induced chemical shifts of 129Xefor systems in which the solvents Each Xe-hydrocarbon solution was prepared directly in the are grouped according to a given class, i.e. homologous series sapphire tube. In the caseof n-butane, gaseous Xe was introduced such as n - a l k a n e ~ ~or, ~1,-alkanok4 ~ However, the continuum first, followed by thecondensation of n-butaneunder tank pressure model treats the solvent as a continuous dielectric and as such at -0 OC, following themethodoutlined in ref 12. The procedure offers little insight as to the specific nature of the intermolecular was reversed in the cases of the other n-alkanes, all of which are interactions that give rise to these chemical shifts. liquids at room temperature. Here the sapphire N M R tubeWith the exception of a recent paper in which 129Xechemical valve assembly was first loaded with the hydrocarbon liquid, and shifts are compared with van der Waals interaction energies the Xe gas was then introduced at approximately 40 psig. With calculated according to the PISA mode1,lOalternative approaches the exception of n-heptadecane, literature values are available which invoke specific Xesolvent pair interactions, such as the for the solubility of Xe in the alkane solvents used here,” allowing “cage model” by Rummens,” have found little use in explaining one to calculate that the mole fraction concentration of Xe does the large chemical shifts observed for 129Xe dissolved in such not exceed X,, = 0.1 for the solutions employed in these solvents, presumably because of difficulties encountered in experiments. Duplicate measurements involving Xe dissolved in accounting for pair interactions between monatomic Xe and the a given liquid hydrocarbon indicate that l29Xe chemical shifts are measured to a precision of fO.l ppm in these experiments. t Current address: Cheil Foods & Chemicals, Inc., Ichungun, Majangmyun, Research grade xenon gas (quoted purity 99.995%), purchased Kyungkido, South Korea. from Cryogenic Rare Gas Co., was used for all measurements. *Abstract published in Advance ACS Abstracts, November 1, 1993.
Introduction
+
0022-3654/93/2097-12 173%04.00/0 0 1993 American Chemical Society
12174
Lim and King
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
TABLE I: Measured Values of Chemical Shift 6(-u) and the Values of d b and -uw for *BXe Dissolved in All Liquid RA~nes index of refraction
6(-u)
-uw
-Ub
6(-u)/-u,
(PpmP (PpmP
compound no (25 "C)* (ppm)'j 93.8 1.24lC ethane' 126.7 1.29oE propane' 146.6 1.329 n-butane 155.2 1.355 n-pentane 161.5 1.372 n- hexane 167.2 1.385 n-heptane 171.0 1.395 n-octane 173.0 1.403 n-nonane 176.9 1.410 n-decane 177.3 1.415 n-undecane 177.9 n-dcdecane 1.420 180.8 1.423 n-tridecane 182.0 1.427 n-tetradecane 183.0 1.430 n-pentadecane 184.2 1.433 n-hexadecane 1.435 185.2 n-heptadecane
(ppm)*
*0°
-uw
(PP~)'
~
0.635 0.938 1.160 1.137 1.184 1.211 1.237 1.260 1.280 1.301 1.302 1.317 1.332 1.338 1.341 1.345'
93.1 125.7 145.4 154.1 160.3 166.0 169.8 171.7 175.6 176.0 176.6 179.5 180.7 181.7 182.8 183.3
140 ~
Y
154.1 160.9 168/167 166.0 171/170 169.9 173.0 175.4
1
0 I
156/155
100
c
I o
80 I
179.4
I
0
I
1
1
5
10
15
182.4 1861185
184.5
Data from ref 12. Unless otherwise noted, data from ref 16.e Data from ref 18. Average experimental error fO.l ppm. Estimated uncertainty f 0.001 ppm. /Calculated using a magnetic susceptibility estimated by the ABIS method; ref 19.g Estimated uncertainty f 0.1 ppm. Data from ref 2. T = 23.5 "C. ' Data from ref 3. T = 25 "C.
I 20
"C
Figure 1. Van der Waals shielding constants, -uw,for IZ9Xedissolved in n-alkanes shown plotted as a function of the carbon number, 4, of the
solvents.
a
The liquid hydrocarbons were purchased from a variety of suppliers. Each samplewas checked for purity by GC and distilled if necessary, with the result that a minimum purity of 99.0 mol % was maintained for each liquid n-alkane employed here. (A complete list of suppliers and purities may be found in ref 14.) The n-butane was CP grade (quoted purity 99.0%), purchased from Matheson.
using volume magnetic susceptibilitiesderived from liquid density datal6and molar magnetic ~usceptibilities'~ found in the literature. The resulting values are listed in column 4 of Table I. The van der Waals contributions to solvent-induced chemical shift are deshielding in nature, so that it is convenient to record such effects as the negative of the van der Waals shieldingconstant ('OW).
StephenZohas shown that the van der Waals contribution to the solvent-induced chemical shift is proportional - to the mean square electric field at the nucleus of interest, p,which arises from the fluctuations of electrons located on neighboring solvent molecules:
Results and Discussion The resonance frequencies, Y , measured for IZ9Xedissolved in the various n-alkanes are reported in column 3 of Table I as chemical shifts, 6(-u),using the resonance frequency of an isolated IZ9Xeatom, YO = 24 774 801 Hz,as a reference:I4 6(-u)
= (5) x lo6 YO
Thischoice for uois appropriate for this work because the chemical shift defined according to this convention can be equated to the negative of the shielding constant, u, which represents the sum of all environmental effects on the shielding of the xenon nucleus. Solvent effects on the shielding constants of nuclei are generally explained within the theoretical framework developed by Buckingham and co-workers, which considers the overall shielding constant, u, to be a sum of four terms:I5
= ub + u,
+ ow+ UE
(2) Here Ub represents the contribution to u caused by the bulk magnetic susceptibility of the solvent, a, arises from anisotropies of the molecular susceptibilities of the solvent molecules, UE represents changes in the shielding constant due to the effects of permanent electric moments of the solvent molecules, and uw accounts for the decrease in shielding of the xenon nucleus caused by van der Waals interactions between the xenon atom and the solvent molecules. The ua and U E terms are expected to be vanishingly small for these solvents and can be set equal to 0 without introducing any appreciable error. In situations where the sample is contained in a cylindrical sample tube oriented perpendicular to the magnetic field, such as is the case with the JEOL FX-90 Q used here, Ob is related to the volume magnetic susceptibility of the solvent, XV, byI5 d
(3) Values for b b have been calculated for each of the n-alkane solvents
(4) The constant, B, in eq 4 is quite large for IZ9Xe,whose nucleus is surrounded by a large, highly polarizable electron cloud. As a consequence, values of -uwfor IZ9Xeare large and very sensitive to variations in-solvent properties which alter the mean square electric field, $. The van der Waals shielding constants listed in column 5 of Table I are shown plotted as a function of carbon number, %, in Figure 1. Here one sees that -uwincreases with carbon number in a decidedlynonlinear manner and appears to approach a limiting value of approximately 190 ppm at large values of n,. This insensitivity of -a, to at large carbon numbers indicates that the - mean square field at the nucleus of a dissolved xenon atom, $, does not change significantly with increasing chain length among the larger members of the n-alkane series. As noted earlier, various authors have attempted to explain the variation observed for -uwamong chemically similar nonpolar solvents in terms of a continuum model which treats the solvent as a continuous dielectri~.~.~ Basically, these authors equate 9 of eq 4 to the square of the reaction field within the solvent, which, depending upon the derivation, leads one to expect that the van der Waals term -uwshould be proportional to g(n) = (n2 - 1)/(2nZ 1)6 or ( g ( t ~ )=) ~[(n2- 1)/(2n2 + 1)12,7 where n represents the solvent index of refraction. The second of these approaches has frequently been used to interpret gas-liquid chemical shifts observed with IZ9Xedissolved in hydrocarbon ~olvents,2.~~~ where it is found that the van der Waals shielding constant for IZ9Xeis linear in
+
-uw = a
+ 8( -)n Z - l
2n2 + 1
where a! and /3 are constants. However, the n-alkanes used in these studies were ordinary liquids having carbon numbers ranging
NMR Chemical Shifts of l29Xe
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12175
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