Oxygen-17-induced proton relaxation rates for alcohols and alcohol solutions

Article

Oxygen-17-induced Proton Relaxation Rates for Alcohols and Alcohol Solutions

Thomas C. Farrar ^a , Mark A. Wendt ^a , and M.D. Zeidler ^b

^a

Department of Chemistry, University of Wisconsin, 1101 University Avenue, Madison, 53706 WI, USA

^b Institut für Physikalische Chemie der RWTH, Templergraben 59, D-52056 Aachen, Germany

O uso de amostras de álcoois enriquecidas com ¹⁷O, para medir o tempo de correlação do vetor internuclear OH funciona bem quando o próton da hidroxila sofre uma troca rápida. Para álcoois tais como metanol e etanol, a taxa de troca da hidroxila para amostras puras é relativamente lenta, mesmo à temperatura ambiente, podendo resultar em erros sistemáticos significativos se efeitos de troca lenta não forem considerados. Para trocas lentas do próton da hidroxila, ¹⁷OH, o sinal é uma função relativamente complexa da razão de troca química do próton da hidroxila, do acoplamento de spin OH (cerca de 80 Hz para álcoois e água) e do tempo de relaxação para o oxigênio. A largura de linha do OH pode tornar-se tão grande, devido à relaxação escalar com o núcleo de oxigênio, que o sinal torna-se muito difícil de detectar. Para etanol puro enriquecido com ¹⁷O, à temperatura ambiente, o tempo de relaxação do oxigênio é de aproximadamente 3,0 ms e a largura de linha do próton da hidroxila é maior do que 1000 Hz.

The use of ¹⁷O enriched samples of alcohols to measure the correlation time of the OH internuclear vector works well when the hydroxyl proton exchanges rapidly. For alcohols such as methanol and ethanol the hydroxyl exchange rate for neat samples is relatively slow even at room temperature and significant systematic errors result if slow exchange effects are not considered. For slow exchange the hydroxyl proton, ¹⁷OH, signal is a relatively complex function of the chemical exchange rate of the hydroxyl proton, the OH spin coupling (about 80 Hz for alcohols and water) and the relaxation time for the oxygen. The OH linewidth can become so large due to scalar relaxation with the rapidly relaxing oxygen nucleus that the signal becomes very difficult to detect. For neat ¹⁷O enriched ethanol at room temperature the oxygen relaxation time is about 3.0 ms and the hydroxyl proton linewidth is over 1000 Hz.

Keywords: oxygen-17, proton, relaxation time, NMR line width, exchange rate, quadrupole coupling

Introduction

A number of recent investigations have reported molecular correlation times for water, simple alcohols and binary solutions of alcohols that are based on the measurement of proton spin lattice relaxation times of oxygen-17 enriched samples^1-5. For protonated samples the spin-lattice relaxation rate, R₁, for protons interacting with other protons is given by the dipolar relaxation equation:

The various parameters have the standard meaning. This equation is not very useful for studying the dynamics of the hydroxyl proton because a significant part of the relaxation arises from intermolecular interactions for which neither the internuclear distance r_HH or the correlation time, t_c, are well defined. For this reason relaxation time experiments have been carried out for the deuterium nucleus. Deuterium relaxation time experiments are attractive since the deuterium quadrupole coupling constant, c_D, is typically ten times greater than dipolar coupling; consequently, intermolecular interactions can be ignored. For a spin-1 nucleus such as ²H the relaxation rate, R₁ is given by:

where c_Dis the deuterium quadrupole coupling constant (qcc) in units of Hz, t_c^Dis the molecular correlation time in seconds, and w₀is the Larmor frequency. For deuterium nuclei the asymmetry parameter, h, typically has a value of 0.1 or less and the h²/3 term can be justifiably neglected. Until recently it was assumed that c_Dwas either close to the solid state value (which can be measured accurately via solid state NMR) or was mid-way between the gas phase value (measured via microwave spectroscopy) and the solid state value. Since gas phase c_Dvalues for -OD deuteriums are about 300 kHz and the solid state values are about 190 kHz, there was considerable uncertainty in molecular correlation times obtained from deuterium relaxation time measurements.

In 1982 Leyte and coworkers⁴ used oxygen-17 enriched samples of water to obtain correlation times. The proton chemical exchange rate in water is known to be rapid⁹. If a water sample is enriched with oxygen-17 and the proton exchange is rapid, the relaxation rate R₁ (total) for all protons in the sample will be given by:

where X is the mole fraction of H₂¹⁷O, R₁(total) is the observed relaxation rate, R₁(H) is the relaxation rate arising from both intermolecular and intramolecular proton-proton interactions (see Eq. 1 above), and R₁^H(¹⁷O) is the proton relaxation arising from the dipolar interaction with the oxygen-17. In the extreme narrowing region (wt_c << 1) and R₁^H(¹⁷O) is given by:

where S is the spin of the oxygen-17 (S = 5/2), and t_c^OHis the correlation time for the OH internuclear vector. If the OH bond distance is known accurately, then the correlation time can be readily obtained from Eq. 4 above. In practice, several samples are normally used with differing amounts of O-17 enrichment and R₁(total) is plotted as a function of X; the slope of this plot is R₁^H(¹⁷O) The parameter t_c^OHin Eq. 4 is the correlation time for the OH (or OD) internuclear vector. Since the OD internuclear vector is coincident (or nearly so within a degree or two) with the principal axis of the deuterium quadrupole coupling tensor, t_c^OH in Eq. 4 and t_c^Din Eq. 2 must be equal. Given the value for t_c^Dand the value for the spin-lattice relaxation time for the OD deuteron, one may now calculate the value of c_D.

This was a clever and innovative idea and with it Leyte and his co-workers were able to obtain the temperature dependence of c_Din water. This same methodology has been used more recently in an effort to obtain information about the temperature and concentration dependence of c_Din simple alcohols^1,2 and in water/DMSO (DMSO = dimethylsulfoxide) mixtures^6,7. Some of the results of the alcohol work have been very puzzling. For example, the work on methanol¹ and ethanol² indicated that c_Dfor the OD deuteron increased with decreasing temperature and the value near the melting point was higher than that for gas phase samples. This work with O-17 enriched alcohol made the important assumption that the hydroxyl proton exchange rate was fast and consequently all hydroxyl protons felt the presence of the oxygen-17. We report data below which indicate that this assumption is only valid for methanol and ethanol in a limited number of special circumstances.

Results and Discussion

For binary mixtures of methanol in various solvents, the lifetime of the OH bond varies as a function of solvent, temperature and concentration; the lower the temperature or concentration, the longer the lifetime. Fig. 1b shows the room temperature proton spectrum of a binary mixture of 1.0 mole percent methanol with 99 mole percent benzene-d₆ (there is a 1 percent proton impurity in the deuterated benzene) and a trace of tetramethylsilane (TMS). The spectrum in Fig. 1b shows TMS (singlet), OH (quartet), CH₃ (doublet) and benzene-d₆ impurity (singlet) at chemical shift values of approximately 0.0, 0.5, 3.0 and 7.0 ppm, respectively. At room temperature, the J-coupling for the OH and methyl resonances are well resolved up to a concentration of about 2.0 mole percent methanol in benzene. For methanol in dimethyl sulfoxide the fine structure is well resolved up to concentrations of about 15.0 mole percent methanol⁸.

The ¹⁷O enriched hydroxyl proton spectra of methanol and ethanol can be rather complex. For neat ¹⁶O methanol at room temperature, the proton NMR spectrum consists of two singlets, as shown in Fig. 1a. This is clear indication that the hydroxyl proton exchange is rapid compared to the spin-spin coupling constant, J, between the methyl protons and the hydroxyl proton. However, this spectrum is a sensitive function of temperature and concentration. The spectrum in Fig. 2 was taken at -20 °C and clearly shows the spin coupling; the hydroxyl proton is now a quartet and the methyl proton resonance is a doublet. The J-coupling is about 6 Hz so the exchange rate must be slow compared to 1/J. For J = 6 Hz, this indicates an OH bond lifetime that is substantially longer than 200 milliseconds. As the temperature decreases the exchange becomes still slower. If one has a mixed sample of H₃C¹⁷OH and H₃C¹⁶OH and the exchange is slow one will observe, at temperatures of -20 °C and lower, the doublet and quartet for the H₃C¹⁶OH molecule. The H₃C¹⁷OH proton spectrum will be quite different. Since ¹⁷O has a spin of 5/2, it will split the OH proton into six lines and each of these lines will, of course, be further split into quartets by the J-coupling with the methyl protons.

If the proton-proton coupling is well resolved, indicating very slow exchange, the ¹⁷OH spin coupling will also be well resolved; the OH coupling in water and simple alcohols is about 80 Hz. In a 5.0 mole percent binary mixture of ethanol and chloroform, the natural abundance ¹⁷O-NMR spectrum is a well resolved doublet with a splitting of 80.0 ±1.0 Hz. The width of the doublet lines is 75.0 Hz. Although for neat ethanol, the ¹⁷O spectrum is an unresolved doublet, the line widths can be deduced from oxygen spin lattice relaxation time measurements and the ¹⁷O linewidth; the result is a spin coupling of about 80 Hz and linewidths of about 120 Hz. The oxygen T₁ value is about 3.0 ms. The broader proton lines in the neat liquid are due to the significantly shorter ¹⁷O relaxation time.

Under conditions of slow chemical exchange there will be separate hydroxyl proton resonance lines for the H₃C¹⁷OH and H₃C¹⁶OH molecules. The ¹⁷OH proton spectrum will be a sextet of quartets and will span a region of about 500 Hz. The proton lines will be rather broad because they are spin-coupled to O-17 which has a relaxation time at room temperature of about 3.0 ms. If two nuclei, for example I and S, are spin-coupled and nucleus S has a lifetime that is short compared to 1/(2pJ), where 2pJ is the coupling constant in units of seconds, then the local magnetic field, 2pJS(t)/g_I, produced at nucleus I by nucleus S fluctuates with a correlation time t_s= T₁(S). In this event, only the average value of the J-coupling is seen and nucleus I does not exhibit the expected multiplet, but a singlet whose line width is a function of the strength of the J-coupling and the lifetime of the S nucleus. The lifetime of a nucleus I in a given spin-state can be shortened either by chemical exchange or by being coupled to a second nucleus, S, which has a short spin-state lifetime. For the hydroxyl proton ¹⁷OH spectrum, I = H and S = ¹⁷O, the linewidths, Dn_1/2, of the proton lines are related to the proton spin-spin relaxation rate, R₂. In particular, Dn_1/2 = 1/(pT₂) = R₂/p, where R₂ is given by the well-known scalar coupling relation¹⁰

where S is the spin of the oxygen (S = 5/2), t_Sis the lifetime of the ¹⁷O (t_S= T₁(¹⁷O)), J is the ¹⁷OH spin coupling constant (about 80 Hz) and w_Hand w_Sare the NMR resonance frequencies (in units of s^-1) of the proton and oxygen, respectively. Since T₁(¹⁷O) is about 3.0 ms at room temperature, (w_H- w_S)²t_S² < 1 and Eq. 5 becomes

For J @ 80 Hz, and t_S= T₁(¹⁷O) = 0.003 s, we have R₂^H @ 4,000 s^-1 and the proton line width Dn_1/2@ 1000 Hz. The final proton spectrum, then, is a set of six unresolved lines each with a width of about 1000 Hz and a separation of about 80 Hz; the ¹⁷OH proton will be so broad that it will disappear into the noise level of the spectrum. Since the total integrated line intensity is spread over such a wide range, the signal will be very difficult, if not impossible, to observe. The fact that T₁ for the OH proton is relatively long while T₂ is quite short exacerbates the problem of observing the OH resonance line. Figure 3 shows a simulated room temperature spectrum of an 80/20 mixture of H₃C¹⁷OH/H₃C¹⁶OH, using a value of 80.0 Hz for the OH spin coupling constant, and hydroxyl proton line widths of 30Hz and 0.5 Hz for the CH₃¹⁷OH and CH₃¹⁶OH, respectively. As can be seen, even for this mild line broadening (the actual line broadening is a factor or 30 greater at room temperature) the signal from the oxygen-17 enriched hydroxyl protons is almost lost in the noise. For the greater line widths occuring in a typical sample, the oxygen-17 enriched hydroxyl proton signal is completely lost in the noise.

As the temperature of the sample decreases the dipolar contributions to the proton T₁ and T₂ will increase and both relaxation times will become shorter in the usual Arrhenius fashion. The proton exchange rate will also decrease, that is, the lifetime of the OH bond will increase. Decreasing temperature will also lead to a substantial decrease in the ⁷O relaxation times. For example, the T₁ minimum (w₀t_c @ 1) in ¹⁷O enriched ethanol occurs at a temperature of about -120 °C. At this temperature T₁(¹⁷O @ 5 x 10^-5 s) and the proton scalar relaxation contribution here is about R₂^H@ 36 s^-1 and Dn_1/2@ 10 Hz. The oxygen relaxation rate is now so fast and the lifetimes of the oxygen spin states are so short that the oxygen nuclei have effectively decoupled themselves from the protons. Near the T₁ minimum the proton lines for all -OH protons will still be broad, but a significant part of the broadening arises from the dipolar relaxation which is most efficient at the T₁ minimum.

For the case of moderately rapid chemical exchange and very little ¹⁷O enrichment the proton linewidths are still largely determined by scalar relaxation with the oxygen. In an early elegant paper by Meiboom⁹ the pH dependence of the proton chemical exchange in water, it is clearly shown that even for ¹⁷O at natural abundance levels (0.037%), the proton T₂ value is determined by the scalar relaxation due to the small amount of oxygen-17 present. The amount of broadening is, of course, rather small because the concentration of oxygen-17 is quite small.

This same phenomenon of proton line broadening due to coupling to a quadrupolar nucleus is often seen. Protons that are spin-coupled to nitrogen-14 have linewidths that are typically several hundred Hertz wide. The narrower -NH proton linewidths are to be expected. Although directly bonded NH and OH spin coupling constants are comparable, the nitrogen relaxation times are much longer. The result is that the proton line broadening is typically less severe.

Summary

Hydroxyl proton spin-spin relaxation times, R₂^H and, consequently, the ¹⁷OH proton linewidths are related to three different processes: dipolar relaxation, chemical exchange broadening and scalar relaxation via O-17 spin coupling. At high temperatures or in acidified samples the chemical exchange of the hydroxyl protons is fast in alcohols and in water, therefore the spin coupling will be suppressed and a relatively narrow resonance line will be seen. In this situation, ¹⁷O enrichment studies should provide reliable information about the OH intramolecular correlation time. For pure samples in which the OH exchange is slow, scalar relaxation caused by J-coupling with rapidly relaxing O-17 nucleus can cause the hydroxyl ¹⁷OH line to disappear into the noise and the only hydroxyl proton signal observed in a mixture of R¹⁷OH and R¹⁶OH will be that from the R¹⁶OH molecules. Failure to recognize this situation will lead to significant systematic errors in relaxation time experiments. In light of these complications, we have measured the correlation times in methanol using a newly developed method¹¹. The results of the new experiments show the expected behavior for the temperature and concentration dependence of c_Dfor the OD deuteron in neat methanol¹² and in binary mixtures of methanol and carbon tetrachloride¹¹.

Acknowledgment

We thank the National Science Foundation, grant number CHE-9500735 for the support of this research. We thank T.D. Ferris for the O-17 spectral data.

References

1.Ludwig, R.; Zeidler, M.D. Mol. Phys. 1994, 82, 213.

2.Ludwig, R.; Gill, D.S.; Zeidler, M.D. Z. Naturrforsch. 1990, 46a, 89.

3.van der Maarel, J.R.C.; Lankhorst, D.; de Bleijser, J.; Leyte, J.C. Chem. Phys. Lett. 1985, 122, 541.

4.Lankhorst, D.; Schriever, J.; Leyte, J.C. Ber. Bunsenges. Phys. Chem. 1982, 86, 215.

5.van der Maarel, J.R.C.; Lankhorst, D.; de Bleijser, J.; Leyte, J.C. J. Phys. Chem. 1986, 90, 1470.

6.Gordalla, B. C.; Zeidler, M.D. Mol. Phys. 1986, 59, 817.

7.Ludwig, R.; Zeidler, M.D.; Farrar, T.C. Z. Naturforsch. 1994, 49a, 1131.

8.Wendt, M.A.; Meiler, J.; Weinhold, F.; Farrar, T.C. Molec. Phys. 1998, 93, 145.

9.Meiboom, S. J. Chem. Phys. 1961, 34, 375; see also Meiboom, S.; Luz, Z.; Gill, D. J. chem. Phys. 1957, 27, 1411.

10.Farrar, T.C. An Introduction to Pulse NMR Spectroscopy, 3rd edition; The Farragut Press; Madison, 1998.

11.Wendt, M.A.; Farrar, T.C. Molec. Phys. 1999, 95, 1077.

12.Wendt, M.A.; Zeidler, M.D.; Farrar, T.C. in press Molec. Phys.

Received: March 29, 1999

Publication Dates

• Publication in this collection
  21 June 2001
• Date of issue
  Aug 1999

History

• Received
  29 Mar 1999