Conditions for quantitative flow FT-1H NMR measurements under repetitive pulse conditios

JOURNAL

OF MAGNETIC

RESONANCE

49, 22-3 1 (1982)

Conditions for Quantitative Flow FT-‘H NMR Measurementsunder Repetitive Pulse Conditions JAMES F. HAW, T. E. GLASS,

AND H. C. DORN

Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Received October 27, 1981; revised March 23, 1982 The problem of quantitation in continuous-flow FT-NMR is treated in detail. The application discussed is continuous-flow liquid chromatography-proton NMR (LC-‘H NMR). Much of the discussion is also applicable to other flow FT-NMR measurements including kinetic studies. A simplified analysis of magnetization under steady-state repetitive pulse conditions including the influence of flow is presented. This analysis illustrates how quantitation errors can arise. A method for calculating molar quantities from integrated LC-‘H NMR spectra is also presented. If signal to noise is adequate, relative quantitation is accurate to +3% under the recommended conditions. INTRODUCTION

The combination of normal-phase liquid chromatography and proton nuclear magnetic resonance is an informative strategy for the analysis of fuel and other samples. In this mode, the NMR spectrometer functions as a HPLC detector. For the last two years, this laboratory has been interested in the development of online continuous-flow LC-‘H NMR (1,2). Other workers have also published reports of the LC-‘H NMR experiment (3, 4). Buddrus et al. (5) recently reported the use of double-precision data accumulation and solvent signal suppression techniques to obtain LC-‘H NMR data with a protonated chromatography solvent. In our previous work, we have noted quantitation errors as severe as f20% in extreme cases. Recently we have been interested in determining the average composition of fuel samples via LC-‘H NMR. Before attempting this work, it was necessary to establish conditions that guarantee quantitative flow NMR measurements under repetitive-pulse steady-state conditions. Furthermore, it was necessary to develop a formalism for calculating molar quantities of each hydrogen type giving rise to signals in the LC-‘H NMR spectra. Quantitative flow NMR measurements are also of importance in kinetic studies. In flow cw-NMR kinetic studies (o-8), the radiofrequency power level must be carefully set to achieve a balance between sensitivity and saturation of slowly relaxing spins. The results of the present study should be applicable to flow FT-NMR kinetic studies as well as the LC-NMR experiment. The most straightforward method for quantitative flow NMR measurements is the inclusion of a reference compound in the same sample. Thus, all sample integrations are relative to the internal reference signal. This minimizes the influence 0022-2364/82/100022-10$02.00/O Copyright 0 1982 by Academic Press. Inc. All rights of reproduction in any form reserved.

22

QUANTITATIVE

FLOW

FT-NMR

MEASUREMENTS

23

of variations in gain within the spectrometer and scaling factors in the computer software which make quantitative comparisons from one spectrum to the next difficult. The amount of reference material must be known for each spectrum. In many cases, it may be preferable to add the quantitation standard directly to the solvent (as is currently done in this laboratory) or to add it via a post column mixing chamber prior to monitoring the NMR spectrum. APPROXIMATE

STEADY-STATE

ANALYSIS

One of the fundamental problems in acquiring quantitatively accurate NMR spectra arises from variable spin-lattice relaxation times in the sample. When sensitivity is not a severe limitation, it is usually sufficient to wait four or five times the longest T, in the sample between each radiofrequency pulse. Long pulse delays are a luxury that cannot be afforded when sensitivity is limited. Thus, it is common (especially in 13C NMR) to use a pulse repetition rate that is comparable to or shorter than typical T, values. With the typical conditions under which the repetitive pulse FT experiment is performed, the signal will reach a steady-state value after several pulses. In their classic paper on FT-NMR, Ernst and Anderson (9) solved the Bloch equations for the steady-state components of the magnetization. The existence of a steady state was further explored by Freeman and Hill (10). The observable magnetization immediately after the pulse (M,,(+,J is a complicated function of T, and other factors. If the various spins in the sample have different spin-lattice relaxation times, quantitation errors will arise if pulse repetition is faster than complete relaxation for any of the spins. In the following analysis, a single spin exactly on resonance is considered. Specifying “on-resonance” fixes the phase of the observable magnetization so that it is aligned with they ’ axis in the rotating frame of reference. This stipulation greatly simplifies the analysis developed by Ernst and Anderson without compromising its accuracy for the purpose of this discussion. Under this condition, the observable magnetization immediately after the pulse is given by (1 - E,) sin cr _ --M,c+o, (1 - El cos a) + E:(cos (Y- E,) ; MJ E, and E2 symbolize the exponentials e-T’T1 and e-T’Tz, respectively, where T is the pulse repetition rate, and u is the flip angle (a = YH~T). It should be noted that the signal intensity can be a function of the frequency offset from the transmitter under two conditions. If transmitter pulse power is limited, signals far off resonance will be attenuated. This is rarely a problem for ‘H NMR on modern instruments where the condition yH, 9 AF is usually easily achieved. Second, if T is less than the observed spin-spin relaxation time, severe periodic intensity distortions can result. Practically, T is always at least as long as T; to avoid excessive line broadening. The quantity Ez in Eq. [ l] should be replaced by E: to take into account magnetic field inhomogeneity. Spin-echo effects can arise in an inhomogeneous magnetic field under multiple-pulse conditions (I 1, 12). Ethos produce undesirable intensity distortions (I 3) and should be suppressed by homospoil pulse sequences

24

HAW, GLASS, AND DORN

RESIDENCE

TIME

W

FIG. 1. T,(obbr)as a function of residence time.

or other methods. If E: is identical for all spins in the sample (corresponding to each signal having the same linewidth), then the intensity of each signal in the transformed spectrum is proportional to MXYC+oj/M,,. This is generally the case in flow NMR, where linewidths are usually controlled by magnet homogeneity and residence time. Evaluation of Mfi+,,,/A4,, as a function of T, T,, T:, and (Y will permit one to gain insight into the problem of quantitation under steady-state repetitive pulse conditions. It should be noted that the simplified analysis above is strictly true only in the absence of strong homonuclear spin-spin coupling. The classical Bloch equations tend to break down in coupled spin system (14). The density matrix method (25, 16) must be used for a rigorous treatment. The simplified analysis above is sufficient for the purpose of this study. The inclusion of effects due to flow will now be made. Since one of the first flow NMR experiments (Z7), the effect of flow has been described as if it were a relaxation mechanism. Effective relaxation times are calculated which include the effect of the average residence time (7) within the cell volume 1 -=-1 +I, 121

T 1(stat)

T ICobs)

7

-= Both residence time and pulse duration are commonly symbolized by 7; these are as a function of 7 for four spins with T, different quantities. Figure 1 shows T,cobsj = 2 set, Tl = 4 set, T, = 8 set, and T, = 16 set, respectively. It should be noted that the effect of short T values is to level the effective (or observed) spin-lattice relaxation times. This suggests that quantitation in flow NMR may be more readily achieved by using a smaller cell volume or a higher flow rate. Equation [l] can now be recast in terms of EICobs)and E :(&):

MY(+w _ -_ MO

(1 - El(obsJsin a (1 - Ems)

COS a)

This equation is useful in estimating

+

(E,*(,b,,)‘(Cos

quantitation

[41 a

-

E,(obs))

’

errors which can result in flow

QUANTITATIVE

FLOW

FT-NMR

MEASUREMENTS

25

NMR. The use of E 3 assumes that no significant refocusing of magnetization is occurring. Equations [2] and [ 31 imply that flow in an exponential process with time constant 7. A recent theoretical study by workers in this laboratory shows that although treating flow as an exponential process is physically unrealistic for cylindrical flow cells, exponential flow and the more realistic laminar flow are nearly indistinguishable by the repetitive pulse steady-state analysis. Spin-lattice relaxation times could also be partially equalized by the addition of a paramagnetic relaxation reagent to the flow stream. In terms of the LC-‘H NMR experiment, this would be most easily achieved by adding a second flow stream to the analytical flow stream via a low dead volume post-column mixing chamber. With regard to flow NMR kinetic measurements, the rate of reaction and the product distribution must be independent of the relaxation reagent used. To a limited extent, not degassing the solvent is beneficial. Dissolved oxygen is effective in reducing relaxation times. Reference Response Factor The most useful quantitation standard found to date for LC-‘H NMR is hexamethyldisiloxane (HMDS). This material is also a useful chemical shift reference (0.07 ppm relative to TMS). Having selected a reference material, one must then decide how to add it. The most simple method is to add it to the LC solvent directly. Two problems with this approach will be pointed out later. One could also add the reference material post-column via a mixing chamber. The flow rate reproducibility specifications of many LC pumps are adequate for producing a constant concentration of reference material in the mixed stream. Careful flow rate measurements must be made if the exact number of moles of the reference material observed during a time interval is to be known with a high degree of accuracy. Finally, a coaxial flow cell with the reference material in the outer, nonflowing region could be constructed. Coaxial cells are commonly used in conventional NMR quantitative measurements. The response of a coaxial standard would require calibration because of uncertainties in the relative volumes of the two regions and rf inhomogeneities. Bulk magnetic susceptibility differences could also contribute to lineshape problems with this approach. This laboratory has elected the simplest method, adding the reference material to the solvent directly. To relate the number of moles of protons giving rise to any signal in a particular LC-‘H NMR file, it is necessary to relate the integrated signal to the integrated reference signal. It is assumed that there is adequate digitization along the frequency domain axis. Since the reference is present in the flow stream at a fixed concentration, the total accumulated reference signal is a function of the volume over which the LC-‘H NMR file is collected. To relate integrated signal intensity to a molar response, the reference response factor is defined. This factor is a function of volume [51 The superscript x designates the volume element or file that the reference response

26

I

HAW, GLASS, AND DORN

I

I

,

I

I

I

I

I

I

I

I

I

,

I,,

,

,

,

,

,

,

,

,

FIG. 2. Lineshape obtained for chloroform in the flow probe (nonflowing, 16K points, ~-KHZ bandwidths). At 1 ml/min, the line is broadened by approximately 20% due to residence time. The frequency axis is 1 Hz per division.

factor is calculated for. The quantity nref is the number of protons in the reference compound and is 18 for HMDS. The quantity M,, is the molar concentration of reference material in the flow stream; Href designates the integrated reference signal. To calculate the number of moles of protons giving rise to any resolved signal in a given LC-‘H NMR file, it is necessary to multiply the integrated signal value by the reference response factor for that file. This formalism should also be useful in flow FT-NMR kinetic studies. EXPERIMENTAL

The chromatographic hardware consisted of a Waters Associates M-45 pump, a Valco injection value equipped with a homemade injection loop of approximately 120 ~1 volume, and a Laboratory Data Control refractive index detector. A variety of liquid-chromatography columns have been used in quantitative LC-‘H NMR analyses. These include Whatman Magnum-9 PAC columns (250 X 9 mm i.d. and 500 X 9 mm i.d.) and a glass Merck Silica Gel Size A (240 X 10 mm i.d.) column. For fuel analyses the solvent composition was 97.5% Freon 113 (Miller-Stephenson Chemical Comp.) 2.5% chloroform-d(99.8%d, Aldrich). This solvent also contained 0.00300M HMDS. The solvent was not degassed. Most hydrocarbon hydrogens have proton T, times of 4 to 6 set in this solvent. The small amount of chloroformd is not necessary for many of the samples studied in this laboratory but appears to promote a more constant column activity level, presumably because it contains a small amount of D20 as a stabilizer. A Jeol FX-200 nuclear magnetic resonance spectrometer equipped with an Oxford 4.7-T superconducting solenoid magnet (54-mm bore) was used to obtain ‘H spectra at 199.50 MHz. A floppy disk system was used for data storage and each

QUANTITATIVE

FLOW

FT-NMR

27

MEASUREMENTS

II 1 ; 1 5 r, PULSE FIG. 3. Normalized integral ratio ml/min (X) and 1.0 ml/min (0).

(m-xylene

INTERVAL isI

aCH,/total

dodecane

protons)

vs pulse

interval

for 0.5

diskette had sufficient data storage capacity for 58 (1024 point) LC-‘H NMR files. Additional details of the LC-‘H NMR experiment may be found in Ref. (1). Several changes in the flow cell design were employed to promote quantitative results. A 3-mm-o.d., 2-mm-i.d. tube was used as the active volume in all cases. The volume of the active region with this cell is approximately 40 ~1 as opposed to 120 ~1 for the design in Ref. (1). In one configuration, a glass spiral of approximately 350 ~1 volume is in-line below the active volume. This is used to ensure that full equilibrium magnetization is achieved prior to observation. In this configuration, the HPLC column is external to the magnet. In another configuration, a glass LC column is mounted in the NMR probe. No equilibration spiral is needed in this configuration since full magnetization is achieved while the chromatographic separation is occurring. Supercon systems are well suited to flow NMR experiments since sufficient room is available in the probe for equilibration volumes and mixing chambers. Available space in most electromagnet system probes is so limited that compromises must be made in flow probe design. RESULTS

AND

DISCUSSION

One advantage of the smaller flow cell used in these studies is superior lineshape. Figure 2 shows a typical lineshape for chloroform obtained after careful homo-

28

HAW,

GLASS, TABLE

REPRODUCIBILITY

No. of pulses 150 300 450 600

OF LC-‘H

AND

DORN

1 NMR

QUANTITATION

Volume (ml)

K(Vm) (X10’)

Integral m-xylene (YCH, Integral HMDS

mM aCH3 protons

6.99 13.98 20.97 27.96

0.3883 0.7765 1.165 1.553

0.7850 0.3935 0.2716 0.1909

0.3048 0.3055 0.3164 0.2965

geneity adjustment. Not only is the linewidth (1.0 Hz) superior to that obtained with a larger flow cell, but more importantly, the base of the signal is narrower than obtained with previous flow cells. The linewidth at the height of the 13C satellite peaks is 39 Hz. These values compare favorably with the typical lo-mm spinning lineshape on our instrument (0.3, 15 Hz). This is important for quantitative analysis. If a small signal is adjacent to an intense signal with a broad base, accurate integration of the small signal will be very difficult. The smaller flow cells permit the various regions of the spectrum to be integrated with improved reliability. A low-volume flow cell is also desirable from a chromatographic viewpoint since the active volume ultimately controls the maximum obtainable chromatographic resolution. To illustrate the effect of variable spin-lattice relaxation times on quantitation accuracy and to show in part the influence of flow rate, the following experiment was performed. A solution of known concentrations of dodecane and m-xylene in Freon 113 was prepared. The solution was pumped through the flow probe. A chromatographic column was not used. Spectra were collected using a variety of pulse intervals for flow rates of 0.5 and 1.0 ml/min. In all cases 90” pulses were used. In each spectrum, the total signal from dodecane (methyl plus methylene) was integrated. The a-methyl signal from m-xylene was also integrated. The ratio of these quantities, normalized with the known concentration ratio, gives a measure of quantitative accuracy. These data are presented in Figure 3. For both flow rates, the ratio is very low for short repetition rates reflecting the longer T, of the (Ymethyl protons. For the I-ml/min data, quantitation (*2%) is obtained at a pulse interval of approximately 2.3 sec. If this represents a near complete flushing of the active volume from one pulse to the next, an active volume of 38 ~1 is implied. This agrees very well with the volume estimated (40 ~1) from coil height and cell internal diameter. At 0.5 ml/min, spin-lattice relaxation is able to compete effectively with the residence time in producing Tltobs). Quantitation (+2%) is achieved at a pulse interval of approximately 3.4 set suggesting a cell volume of 28 ~1. A low value is obtained since T is only partly responsible for observed relaxation at this flow rate. For routine quantitative LC-‘H NMR, a 3 to 3.5-set pulse interval is used at a flow rate of 1 ml/min. A 4.5 to 5-set pulse interval is used for 0.5 ml/ min. In all cases 90” pulses are used. To determine the utility of the reference response factor formalism, the following experiment was performed. A solution of m-xylene in isooctane was prepared for

QUANTITATIVE

FLOW FT-NMR

MEASUREMENTS

29

PULSES

FIG. 4. Integral ratio HMDS/m-xylene

(Y-CH~ vs number of pulses (fixed pulse interval).

injection on a Whatman Magnum 9-PAC column (9 X 500 mm). The m-xylene peak had a width of approximately 2 ml under these semipreparative conditions. Four separate injections were made. In each case the number of scans was increased by 150 over the previous run. All of the m-xylene eluted in a period defined by the first 100 scans so each file contained a signal from the same quantity of m-xylene. Each successive file was taken over an increasingly larger volume element, so the total quantity of HMDS detected by the experiment was increased from one run to the next. The resulting data for this experiment are in Table 1. If the reference response factor can be used for purposes of quantitation, then the same amount of material should be calculated from each run. Table 1 shows that this is in fact the case. This experiment also includes error from injection irreproducibility. Clearly, the precision of the total experiment is excellent. The data in Table 1 are plotted in Fig. 4 to illustrate the linear dependence of the integral ratio (HMDS/ m-xylene c&H,) versus the number of pulses. At this point several potential sources of error need to be mentioned. If the quantitation material is added directly to the solvent and analytical scale chromatography is used, early eluting peaks may be so concentrated that a significant amount of the solvent is displaced. This will make the reference response factor erroneously high. To estimate the extent of displacement on Whatman Magnum9 columns, 120 ~1 of a neat alkane was injected and the concentration of alkane at the peak maximum was calculated via the reference response factor. The concentration was only 5% under these worst-case conditions. Alkanes are only very weakly retained on normal phase columns and hence give sharp peaks. If solvent displacement is a problem, adding the reference material post-column will be advantageous. For the more interesting (and latter eluting) aromatic compounds, the extent of displacement is insignificant. Care must also be taken in preparing the LC solvent. Many nonaqueous solvents have substantial coefficients of thermal expansion. If the temperature in the magnet bore is not identical to the temperature

30

HAW, GLASS, AND DORN TABLE ACCURACY OF LC-‘H

NMR RELATIVE QUANTITATION Ethyl benzene

Known relative molar concentrations Measured relative molar concentrations Percentage error

2

m-Xylene

(DATA

RELATIVE

Tetralin

TO WI-XYLENE)

Naphthalene

1.054

1.ooo

1.039

1.039

1.074 f1.9%

1.000

1.059 +1.9%

0.9743 -6.2%

at which the solution was prepared, the accuracy of the molar concentration will be lost. Relative amounts of various eluents may still be determined without any loss in accuracy. The accuracy and reproducibility of pump performance is critical. The flow rate of our pump was measured over an extended period of time and found to be 0.96 ml/min at a setting of 1.0 ml/min. Flow rates can vary slightly from solvent to solvent even if the pump has a compressibility correction circuit. Flow rate reproducibility specifications of HPLC pumps are generally good (typically 0.3%). Flow rates can vary widely if check valves or seals are beginning to fail. Periodic pump inspection is recommended. Pump pulsation should be suppressed as this can cause lineshape distortions. A final potential source of error is spectral background. One obvious source of this is solvent background. If this is small, a correction may be applied. Although the methods described by Buddrus et al. (5) make acquisition of LC-‘H NMR data possible in protonated solvents, in the solvent region quantitative utility is precluded. Solvent bands, solvent 13C satellites, and the residual solvent signal due to incomplete saturation are still significant. It is doubtful that the WEFT sequence (18) will be of much use in LC-‘H NMR. If the delay period is significant relative to the residence time, incomplete cancelation of the solvent signal will occur. The WEFT sequence can also introduce severe quantitation errors. This is especially true if one or more of the spins in the sample have T, values close to that of the solvent. Background contributions from the probe and flow cell itself are also possible. The flow cell and receiver coil should be rinsed with chloroform-d before final probe assembly. Finally, dry air should be blown through the flow probe (at a low rate) during data acquisition. Several simple model mixtures were run under quantitative conditions to further establish the accuracy of the method. Table 2 shows relative compositional data for four aromatic compounds present in a simulated fuel sample. The flow rate was 0.5 ml/min and a pulse interval of 5 set was used. These data are typical. The error in determining naphthalene resulted from significant chromatographic tailing. The latter LC-‘H NMR files for this compound had very poor signal to noise. Relative composition is easily determined to +3% if the signal to noise is not a limiting factor. Compounds which are unresolved (chromatographically) may still be determined if distinct resonances are resolved on the chemical shift axis.

QUANTITATIVE

FLOW

FT-NMR

31

MEASUREMENTS

ACKNOWLEDGMENTS We gratefully acknowledge financial support for this work (Washington, D.C.), the U.S. Air Force (Wright-Patterson Department of Energy.

provided by the Naval Research Laboratory Air Force Base, Dayton, OH), and the U.S.

REFERENCES 1. 2. 3. 4. 5. 6.

J. J. E. J. J. C.

F. HAW, T. E. GLASS, AND H. C. DORN, Anal. Chem. 53, 2327 (1981). F. HAW, T. E. GLASS, AND H. C. DORN, Anal. Gem. 53, 2332 (1981). BAYER, K. ALBERT, M. NIEDER, E. GROM, AND T. KELLER, J. Chromatogr. BUDDRUS AND H. HERZOG, Org. Mugn. Reson. 13, 153 (1980). BUDDRUS, H. HERZOG, AND J. W. COOPER, J. Magn. Resort 42,453 (1981). A. FYFE, M. COCIVERRA, S. W. H. DAMJI, T. A. HOSTETTER, D. SPROAT,

186, 497 (1979).

AND

J. Magn. Reson. 23, 377 (1976). 7. 8. 9. 10. II. 12.

13. 14. 15. 16. 17. 18.

C. C. R. R. E. R. R. G. S. P. P. S.

A. FYFE, S. W. H. DAMJI, AND A. KOLL., J. Am. Chem. Sot. 101,951 (1979). A. FYFE, S. W. H. DAMJI, AND A. KOLL., J. Am. Gem. Sot. 101,956 (1979). R. ERNST AND W. A. ANDERSON, Rev. Sci. Instrum. 37,93 (1966). FREEMAN AND H. D. W. HILL, J. Chem. Phys. 54, 3367 (1971). L. HAHN, Phys. Rev. 80, 580 (1950). FREEMAN AND H. D. W. HILL, J. Magn. Reson. 4, 366 (1971). KAISER, E. BARTHOLDI, AND R. R. ERNST, J. Chem. Phys. 60, 2966 (1974). BODENHAUSEN AND R. FREEMAN, J. Magn. Reson. 36, 221 (1979). SCHABLIN, A. HOHENER, AND R. R. ERNST, J. Magn. Reson. 13, 196 (1974). MEAKIN AND J. P. JESSON, J. Magn. Reson. 13, 354 (1974). M. DENIS, G. J. BENE, AND R. C. EXTERMAN, Arch. Sci. 5, 32 (1952). L. PAI-T AND B. D. SYKES, J. Chem. Phys. 56, 382 (1972).

J. O’BRIEN,