Anal. Chem. 1980, 5 2 , 96-101
96
REDUCTION TO PRACTICE-SUMMARY OF METHOD (1)The analytical sample required is a single-crystal silicon wafer approximately (-0.5 mm, +1 mm) 2-mm thick, both surfaces polished and approximately plane-parallel. (2) Tlie spectrometer should be outfitted for mid-IR spectroscopy, and 100 or more scans of 13454 data points (counting only from zero retardation) each at a sample spacing of 2 (spectral range 0-7899 cm-', retardation 0.8516 cm) should be averaged, transformed using 32 768 points, and boxcar apodization, ratioed against an open beam background spectrum, converted to absorbance, and spectral regions integrated as described in the early part of the results. (3) The C and 0 concentrations should be calculated from the (607-602), (626-612), and (1125-1090) integrated absorbances and the integrated absorptivities given for 0.6 cm-l resolution in Table I. The following equations can be used: =
A~626-612)/aSi(626-612)
ppma C = [A(607-602)-
/
( T ~ ~ ~ ( 6 0 7 4 0 2 )Ta'(60i-6021 )I
Each A , ) is the integrated absorbance in the specified wavenumber region. The integrated absorptivities are similarly identified; e.g., a S i ( 6 M 1 2 ) is the integrated absorptivity of silicon in the region 626-612 wavenumbers a t 0.6 cm-' resolution. (4) For convenience, the sequence of calculations has been programmed on the spectrometer computer, and program listings are available from the author. Two programs are used: one (named PSI) correctly sets all spectrometer parameters and acquires and transforms an open-beam background spectrum, and the other (named SIA) measures a silicon sample, performs the transform and calculations, and prints out C and 0 concentrations in ppma. The same open-beam
background spectrum has been used for weeks with accurate results, but acquiring a new background spectrum a t the beginning of each day of use would be a good precaution, especially if the instrument is being used for other purposes.
DISCUSSION The objectives of higher sensitivity and accuracy, easier sample preparation, and automatic operation detailed in the introduction have been met by the analytical method presented here. The feasibility of this analytical method depends on the sensitivity, photometric accuracy, and wavenumber scale stability of a modern laser-referenced interferometric IR spectrometer. Analysis of silicon dopants (B, P, As, etc.) can also be accomplished using this approach. Several additional factors must be considered: (1)cryogenic temperatures are required for observation of some of the analytically important bands; (2) some of the bands of interest are below 400 cm-', necessitating a CsI-Ge or Mylar beamsplitter and a different detector; and (3) the free carrier absoprtion associated with high dopant levels makes the silicon less transparent, necessitating thinner samples. These factors are currently under investigation in this laboratory (6). LITERATURE CITED (1) "Annual Book of ASTM Standards", part 43, p 518, Standard # F-121-76 (1977). (2) Ref. 1, p 523, Standard # F-123-74. (3) Robert John Bell, "Introductory Fourier Transform Spectroscopy", Academic Press, New York, 1972, pp 19-25. (4) A. R. H. Cole, "IUPAC Tables of Wavenumbers for the Calibration of Infrared Spectrometers", Pergamon Press, Oxford, U.K., 1977, p 43. (5) A. S. Zachor and S. M. Aaronson, Appl. Opt., 18, 68 (1979). (6) D. G. Mead and D. W. Vidrine, presented at the FACSS-VI meeting, Philadelphia, Pa., Sept. 20, 1979.
RECEIVED for review May 25, 1979. Accepted July 25, 1979.
Determination of Phosphorus Compounds by Phosphorus-31 Fourier Transform Nuclear Magnetic Resonance Spectrometry David A. Stanislawski and John R. Van Wazer" Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235
A method for the quantitative determination of phosphorus compounds in dilute solution is proposed using ''P Fourier transform nuclear magnetic resonance spectrometry. Fast relaxation of all inorganic and organic phosphorus compounds tested was achieved by use of a soluble organic free-radical (4-amino-2,2,6,6-tetramethylpiperidinooxy). Rapid data accumulation is also facilitated by a 30' pulse angle and proper choice of the parameters involved In data acquisition. Quantitative results (standard deviation less than 3 % ) were achieved in less than 2 h for a four-component aqueous solution of phosphate anions when the total phosphorus concentration was about 200 ppm, with the least concentrated component (orthophosphate) representing 16 % of the total phosphorus. Semiquantitative results were obtained with 17 h of pulsing for a tenfold dilution of this mixture. The method can also be used for the absolute analysis of a mixture by incorporating a mass standard.
For the past 20 years, continuous wave (CW) 31Pnuclear 0003-2700/80/0352-0096$01.OO/O
magnetic resonance (NMR) spectrometry has proved to be an outstanding and generally applicable method (1,2) for the analysis of all kinds of mixtures of phosphorus compounds present as reasonably concentrated solutions or as neat liquids. This method is, of course, nondestructive and the resulting spectra are usually assignable (on the basis of reported data ( 3 , 4 ) )to specific phosphorus compounds without too much trouble. If an assignment is questionable, a drop of the suspected ingredient added to the sample will serve for confirmation, since it is very rare for the resonances of two different compounds to be superimposed. Under optimum conditions, which are readily achieved in the CW mode of NMR operation, the peak areas associated with each component are proportional to the amount of phosphorus in that compound, so that the relative distribution of phosphorus in mixtures may be obtained without the use of separation procedures. The development of the Fourier transform (FT) technique (5)has permitted the extension of 31Pspectrometry to samples containing low concentrations of phosphorus. Although quantitative and semiquantitative assays have been performed C 1979 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
on phosphorus compounds using FT NMR, many of the parameters affecting the FT peak areas (6, 7) were not considered explicitly, so that a general application of these approaches to diverse mixtures of phosphorus compounds would be suspect. The main impact of 31PFT NMR has thus far been in the field of biochemistry (8), where it has been used for semiquantitative and qualitative determinations on biological specimens, including living ones. This work has led to findings that were missed by the array of other analytical methods that had previously been employed. Although FT NMR always allows rapid collection of data, it is necessary to establish the conditions under which the maximum allowable rate of repetitive pulsing can be achieved in order that the limit of detection may be reduced to as low a concentration as possible. In addition, the pertinent parameters must be adjusted so that the peak areas in the NMR spectrum properly represent the relative phosphorus concentrations in the sample. In spite of the widespread utility that a general method for quantitative analysis by 31PFT NMR ought to have, only one reported study has been directed toward the development of such a method. Using Fe(II1) as a relaxation agent (relaxagent), Gurley and Ritchey (9) have reported a set of standard parameters for analyzing mixtures of inorganic phosphates. However, this procedure has limited utility, since the tripolyphosphate anion cannot even be detected at the 20-ppm level, presumably because it is a rather good complexing agent for iron. In this paper, we present another approach which seems to overcome the problem faced by Gurley and Ritchey (9) and which ought to form the basis of a generally applicable 31PFT NMR method for the differential quantitative analysis of phosphorus compounds.
EXPERIMENTAL NMR Spectrometer System. A Varian XL-100-15 multinuclear spectrometer was employed. Field stabilization was provided by an internal 'H lock signal. Fourier transform capabilities were supplied by means of a Transform Technology, Inc. (TTI-100) unit linked directly to the spectrometer. This FT equipment includes a Nicolet 1080 computer, a 100-kHz variable digitizer, and a Diablo magnetic disk unit. The computer is equipped with 20K of memory and has a 20-bit word length. The memory is divided into 4K of permanent memory for program storage and 16K of memory for data storage used in the accumulation of free-induction-decay signals and their subsequent treatment and transformation. The digitizer permits the collection of 6-, 9-, or 12-bit words and thus provides the necessary flexibility to accumulate data over a wide range of sample conditions. The disk unit allows the easy transfer of programs or data between the computer memory and replaceable magnetic disks, which can be used for storage of programs and data. A TTI pulse unit (with peak power output in excess of 1 kW) is used to supply about 600 W to a modified Varian 4415 probe. This assembly provides a 90" pulse for 31Pnuclei of 48-ps duration. The system also allows rapid manual adjustment of the signal phase in transformed spectra. NMR Measurements. All NMR measurements were made using coaxially mounted 5- and 12-mm sample tubes. The lock solvent, typically DzO, was placed in the inner 5-mm tube and the sample occupied the outer tube. This arrangement allows the sample to occupy the larger volume and therefore facilitates the accumulation of usable data, particularly in the case of dilute samples. Spin-lattice relaxation times, T I values, were measured using the standard inversion-recovery method (IO),that is two rf pulses of 180" and 90" separated by a delay time. The data points corresponding to peak amplitudes at each particular delay time were then fitted by the computer to the function S , = S*[l - K exp(-t/TJ], where S , is the signal amplitude at time t after the perturbing pulse and S*is the equilibrium signal amplitude. Pulse imperfections usually result in a value of k slightly less than 2 for the 180" - 7 - 90" pulse sequence. The TI values reported here are not intended to be precise reference values. The reported values merely reflect the relaxation times encountered for actual
97
phosphate and organic phosphorus samples intended for assay, in which the dissolved oxygen and trace transition-metal content is unknown. Chemicals. The samples examined by 31PFT NMR included several linear and cyclic sodium salts of the polyphosphates and a variety of organic phosphorus compounds. All chemicals were high-grade commercial products and were used without further purification. A stock solution of the polyphosphates was prepared by accurately weighing portions of the sodium salts and dissolving them in distilled water. This standard solution, 0.659 M in total phosphorus, was then used to prepare samples with lower phosphorus concentrations by diluting a portion of the standard with additional water. A standard sample of organic phosphorus compounds in cyclohexane was also prepared and treated in the same manner. Crystalline vitamin BIZ,obtained from Biochemical Laboratories, Inc.; and the 4-hydroxy-, and the 4-amino-2,2,6,6-tetramethylpiperidinooxy radicals, obtained from Aldrich Chemical Company, Inc., were employed as relaxagents. These materials were weighed directly into the NMR sample tube and a measured portion of the sample was then added. Treatment of Peak Areas. When F T spectra of dilute solutions are plotted without modification, the resulting spectra exhibit almost no signals because they are lost in the plethora of sharp peaks and valleys due to the noise. By employing an exponential weighting function to emphasize the early as compared to the latter portion of the FID, the signals are enhanced relative to the noise. This results because information concerning the signals occurs primarily in the early portion of the FID and information about the noise in the latter portion. This signal enhancement is accomplished by line broadening (proportionate for each signal) but, since the weighting function is set by the operator, the true peak width could be recalculated if needed. Most FT systems also have the capability of averaging overlapping sequences of points in order to smooth the appearance of the spectrum. Finally, data collected in a portion of memory less than the maximum can be given better spectral definition by filling d or portions of the remaining data memory with zeros. We found that by employing only the weighting function and zero-filling (when applicable) we were able to produce spectra that are readily adapted for area measurements. The determination of relative peak areas was made using the cut-and-weigh procedure (2). Although integration could have been employed for concentrated samples, the lciw signal-to-noise ratio common among dilute samples results in poor reproducibility of integral data for such samples. Because deviations can arise from a variety of sources when using the cut-and-weigh method, we sought a method of routine reproduction of peak areas and a clear idea of how much deviation was introduced in each step. The greatest deviation in weighing peaks would be expected to result from the difficulty of choosing a consistent base line and accurately drawing the peaks. We have routinely attempted to select by inspection (using a clear plastic ruler) the midpoint of the noise and draw in the base line. This base line is found to be a t the same level at each of a series of peaks in a well-phased F T spectrum. Practice on one or two well-characterized known mixtures is an invaluable aid in developing consistency in the treatment of the data. In addition, it is helpful to have a set of narrow-through-broad well-shaped peaks from CW spectra in front of you as a guide to proper peak profile when drawing the pattern of an FT peak before reproducing and cutting out. We have found that, for five such independently made drawings, we can reproduce sample peak areas with a mean standard deviation of 1.9%. To determine how much of this deviation is attributable to variations in the thickness of the paper on which the spectrum is reproduced and in the actual cutting out of the spectrum, five reproduced copies of each of four peaks were made. In this case, we found that the peak areas are reproduced with a mean standard deviation of 1.2%. In other words, the shaping of the peaks and choosing of base line introduced somewhat less irreproducibility than did the paper thickness and cutting.
RESULTS AND DISCUSSION Adjustable Parameters. In order to obtain reliable and reproducible peak areas it is important in FT NMR, just as in CW NMR, to adjust the instrumental parameters properly.
98
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
The rf pulse units, filters, and analog-to-digital converter (ADC) needed for the F T experiment introduce a number of parameters not found in the CW experiment. These parameters and their effects on the FT experiment are considered below. In the typical F T NMR experiment, spins which normally have their magnetization aligned along the direction (z axis) of the field, Ho, of the magnet are caused to precess toward the y axis by applying short, intense bursts of rf power producing another magnetic field directed along the x axis. These pulses are followed by a period of time in which the spins are allowed to return to their equilibrium magnetization in the field of the magnet. In order to obtain quantitatively useful data, we must be sure that a true representation of the spectrum is obtained. Accurate spectra result if several conditions are met: (1)the magnitude of the rf pulse should be large compared to the chemical-shift range, W, so that all the spins within this range precess at the same angle about the applied field; (2) the duration of the pulse, t,, should be short compared to the relaxation times, T , and T 2 ,of the nuclei; and (3) the pulse-repetition interval should be long compared to the relaxation times to provide sufficient time for the spins to return to their equilibrium magnetization. In interpreting FT NMR spectra exhibiting several resonances, it is important to know that an accurate measurement of the 90°-pulse duration, T ~ makes , it possible to optimize the conditions of an experiment (11). The magnetic field actually experienced by a spin depends on the field position at which the pulse is set, with a spin resonating further away from the pulse not being tipped as effectively toward the y axis as is a closer lying spin. However, if the angle between the effective rf field direction and the transverse plane of the rotating coordinate system is kept below 30°, the maximum variation in observed peak area due to this cause may be maintained under 5% by adjusting the delay between pulses to a t least 3 times the longest relaxation time, T1. The maximum chemical-shift range which can be covered and still meet these conditions is given by Avrnru = tan 3O0/4rw = 1.44 X 1 0 5 / ~ 9where 0 T~~ is given in microseconds. When the angle, 8, through which the magnetization is rotated toward the y axis is shortened (this is accomplished by decreasing the duration of the rf pulse) the information content of the spectrum is unaltered (12). It is important to realize, however, that the signal amplitude and the time necessary to restore the magnetization to equilibrium are affected differently. Quantitatively the signal amplitude is decreased by a factor of (1- sin e), while the magnetization in the z direction is decreased only by (1 - cos B ) . These relationships mean that the decrease in signal amplitude is less than the accompanying gain in time needed for relaxation of the magnetization to equilibrium. For example, the signal intensity corresponding to a 30' pulse decreases to a value 0.50 that of a 90° pulse, while the time required for relaxation is only 0.13 that of the 90° pulse. Therefore, we can pulse 7.5 times more rapidly a t 30' than at 90' for a net improvement in signal-to-noise over the same time period of 1.37. Employing the ADC to record a free-induction decay (FID) signal demands that various restrictions be imposed on the collection of data points. Because the use of the computer in FT NMR has been treated extensively elsewhere (13),only a brief mention of these limitations is necessary here. Because a sine wave must be sampled at least twice per cycle in order to be characterized, there must be a limiting time between successive samplings of a decay signal equal to 1 / ( 2 X spectral width). When this time is multiplied by the total number of data points to be stored in the computer memory, the acquisition time is obtained, and its reciprocal equals the point-to-point resolution of the resulting spectrum. Thus, a
choice of any two of these variables (spectral width, acquisition time, number of data points, and resolution) determines the other two. As a practical example, in order to obtain a 2000-Hz spectrum (50 ppm for 31Pa t a field of 23 487 G) with a 1-Hz resolution, we can only collect 4096 data points at a pulse repetition rate of one per second. As longer time-averaging becomes necessary for weaker samples, the ADC imposes an additional constraint. This constraint is a function of three parameters: (1)the signalto-noise ratio corresponding to a single scan, a value that is related to the sample concentration; (2) the fixed word length, LO,of the computer, and (3) the adjustable word length, d , of the analog-to-digital converter, a quantity often called the "ADC Resolution". In the case of very weak signals, where long-term averaging is important to develop an acceptable signal-to-noise ratio (S/N) in the frequency spectrum, we find that it is often necessary to use ADC word lengths smaller than the maximum available for a particular computer system. As an example, consider the case of using a computer with a 20-bit word to resolve a sample containing two signals having single-scan S / N ratios of 0.1 and 0.01. It takes 160000 scans to get a final S / N ratio of 4 for the weaker signal. In the case in which this signal would just about fill a 9-bit ADC word, we would find that the stronger signal would overflow computer memory after about 21 000 scans. In order to accommodate both signals it would then be necessary to use a 6-bit ADC resolution. Although many state-of-the-art NMR spectrometers eliminate hand setting of the ADC word length by putting it under computer control, it is important to realize that an incorrect choice of the word length in the older systems can lead to overflow of computer memory which would lead to incorrect relative peak areas. Relaxation Times and Relaxagents. The longitudinal relaxation times, T1 values, and the wide range of these encountered for the 31Pnucleus (14, 15) present the greatest obstacle to obtaining analytically useful NMR spectra of solutions with low phosphorus content. Typical relaxation times for phosphorus cover a range of 1 to 25 s. T o obtain analytically useful data, we have seen that we must allow 3 times the value of the longest TI between successive pulses for an accuracy of *5%. In an unfavorable case, e.g., P[OCH(CH,),], with T1 = 18.5 s, this totals almost a full minute of delay between successive pulses. Because data acquisition typically requires only a few seconds, most of this time is completely wasted. Clearly then, it would be advantageous to be able to reduce relaxation times for all the phosphorus nuclei to approximately one third of the actual time needed for data acquisition, say 1-2 s. The most commonly employed method of reducing T , values is to add a small amount of a paramagnetic material to the sample. By this means, a very rapid relaxation mechanism is incorporated into the overall relaxation process. Typically, organometallic derivatives of iron, chromium, or other transition metals are employed as relaxagents (16). However, since phosphorus compounds are often good complexing agents, differences between them as ligands can lead to quite different relaxation effects for the various phosphorus resonances in a mixture. In addition, relaxation of a strong complex may often be severe enough to result in excessive line broadening that negates analytical application. In order to eliminate these problems encountered when using typical transition-metal relaxagents, we investigated the activities of a new group of paramagnetic relaxagents-the organic free radicals, as well as a transition-metal species encased in a shell-like ligand structure. The effects of these novel relaxagents on the TI values of a mixture of sodium phosphates are shown in Table I. Although both of the free radicals and the vitamin BI2function as relaxagents, several
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
Table I. Comparison of the Effects of Several Novel Relaxagents on the Observed T I Values of a Mixture of Sodium Phosphates with Individual Components Present at the 0.1 M Level
Table 111. Effect of 4-Amino-2,2,6,6-tetramethylpiperidinooxy Radical on the Observed T,Values of Concentrated and Dilute Mixtures of Organic Phosphorus Compounds T , value ( s )
T , values ( s ) for a sample containing
0.01 M 4-hy- 0.01 M 0.003 M droxy 4-amino re- vitamin radi- no radlaxagent BIZ cala icalb
compound Na,HPO, (ortho) Na,P,O, (PYro) Na,P,O, (trimeta) Na4P4012
( tetrameta)
7.51
4.14
1.96
1.36
4.98
1.52
1.25
1.44
22.48
19.39
2.64
2.76
19.66
16.11
3.10
2.86
a The 4-hydroxy derivative of the 2,2,6,6-tetramethylpiperidinooxy radical. The 4-amino derivative of the 2,2,6,6-tetramethylpiperidinooxy radical.
Table 11. Effect of 4-Amino-2,2,6,6-tetramethylpiperidinooxy Radical o n the Observed T , Values of Concentrated and Dilute Mixtures of Inorganic Polyphosphates T , ( s ) at various concentrations of added free radical 0.000
component
molar concn of P
Na,HPO, Na,P,O, Na,P,O, Na,P,O,,
0.10 0.20 0.13 0.20
7.5 5.0 22.5 19.7
2.0 1.6
1.1 0.8
1.8
1.0 1.0
Na,HPO, Na,P,O, Na,P,O, Na,P,O,,
0.010
12.8 0.5 21.9 19.7
4.8 0.9 3.9 3.9
0.020 0.013 0.020
M
0.025 0.047 0.069 M M M
1.9
2.3
0.9 0.7 0.8 0.8
1.7
1.5 0.8 1.0
1.8
1.1
1.1
distinctions are readily noted. It appears that even the large protective shell provided by the organic ligands in vitamin Blz is not sufficient t o prevent selective complexation. The pyrophosphate seems to be relaxed by the vitamin Blz much more than are the other phosphates in the mixture, perhaps by substituting for the cyanide ligand of the vitamin. Indeed, if the concentration of the relaxagent is increased relative to the concentration of phosphates, the pyrophosphate resonance is appreciably broadened, so that the analytical utility of this relaxagent is poor. T h e relaxing actions of the organic free radicals are seen to be fairly comparable. All Tl values are appreciably lowered; and the range of T1 values is reduced to 1.85 and 1.50 s for the hydroxy and amino radicals, respectively, as compared to a range of 17.5 s for the sample containing no added relaxagent. Because the amino derivative showed a slightly more compact range of T1values, it was chosen for further examination. In Table 11, we compare the results of increasing the free-radical concentration in a mixture of sodium phosphates a t two different dilutions. In both cases, the T1values are lowered most substantially for the sample containing the largest concentration of the radical. Additionally, even though two of the components without relaxagent exhibit substantial differences in relaxation time a t the two concentrations, the radical concentration of 0.07 M (about 12.5 mg/mL) seems to be quite effective in holding all T1 values within a fairly narrow range around 1 s.
99
component
0.07 M free radical
molar concn no free of P radical
(C,H9 ),P (C,H,),P (C,H,O),PO
0.6 0.6 0.6
(C,H, ) 3p (C, H. .P ( C;H;O) ,PO
0.006 0.006 0.006
7.34 12.57 15.87
0.58 0.58 0.63 0.64 0.70 0.7 1
-__
Table IV. Determination by ,'P CW NMR of the Composition of a Mixture of Inorganic Phosphates, 0.659M in Total Phosphorus percentage composition component
1
run no. 2 3 4
___
5
av.
Na-HPO, 15.6 15.9 15.4 16.8 15.4 ll5.8 (k0.6) Na,P,O, 32.5 31.3 31.7 29.2 30.5 3'1.0 (+1.3) Na,P,09 20.4 20.1 19.8 20.5 20.6 20.3 (+0.3) Na,P,O,, 31.5 32.7 33.1 33.5 33.5 32.9 (kO.8)
actua1 value 15.8 31.8 20.5 31.9
Table V. A General Set of Parameters for Differential Analysis by 31PFT NMR parameter
value
spectral width no. of data points acquisition time resolution no. of pulses pulse angle delay between pulses (=acq. time) amount of free radical
2000 Hz 8192 2.096 s 0.49 Hz 3000 30" 2.096 12.5 me/mL
Unlike the transition-metal relaxagents, which we have seen form phosphate complexes, the organic free radicals do not give evidence of significant chemical interaction with the phosphates, as would be expected. In addition, we see that the organic free radicals are sufficiently soluble in aqueous mixtures to produce T1 values around 1 s. By using a 30'pulse angle, pulsing may be as rapid as once every second without destroying the analytical utility of the NMR measurements for all of the components present in the mixture. The organic free radicals are also seen to be effective in reducing the relaxation times of organic-phosphorus compounds. Table I11 demonstrates the effect of the 4-aminopiperidinooxy radical (0.07 M) on the T1 values of several organic phosphorus species in cyclohexane. Although considerably more of the radical could be dissolved in organic solvents, we find that this amount is again sufficient to reduce all TI values to a small range around 1 s. Differential Analysis. As previously mentioned, CW 31P NMR is a generally useful method for performing differential analysis of mixtures of phosphorus compounds and was therefore used to determine the percent contribution of various sodium phosphate components in a standard sample, 0.659 M in total phosphorus. In Table IV the analytical results are presented for each of five different determinations; and the
100
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
Table VI. Determination by 'lP FT NMR of the Composition of a Mixture of Inorganic Phosphorus, 6.59 mM in Total Phosphorus, Using the Parameters of Table V -_____run no.
percentage composition
-_
component
1
2
3
4
5
Na,HPO, Na,P,O, Na,P,O, Na,P,O,,
14.3 34.7 19.8 31.2
15.8 36.4 19.2 28.7
14.9 33.2 21.3 30.6
13.6 35.8 18.9 31.8
17.1 33.7 20.1
* Determination A
._.-___.___I_____.__-
a v.
15.3 ( + 1.6) 34.8 (i1.4) 20.0 ( * 1.0) 30.0 ( t 1 . 7 )
27.5
Aa
actual value
12.4 32.6 21.6 33.5
15.8 31.8 20.5 31.9
was run using 4K of data storage and a 1-s acquisition time with no delay between pulses.
averages of these (with the standard deviation in parentheses) are compared to the composition of the sample as determined from the weights of the individual components used to prepare the mixture. The agreement is quite good, with the mean standard deviation being 0.8% of the total phosphorus. A tenfold dilution of the standard, however, is sufficient to prevent the successful application of single-pass CW 31P NMR for differential analysis. I t is a t and below this level, 0.05 M, that the FT procedure becomes the NMR method of choice. Combining our knowledge of the effectiveness of the organic free-radical relaxagent with our understanding of the requirements which must be met to obtain analytically useful FT spectra, we put together a generally useful set of experimental conditions for performing differential analysis of mixtures of phosphorus compounds (Table V). These parameters can be modified to meet the needs of resolution or time in particular cases. The application of the above set of parameters to a dilute sample (6.59 mM in total P) of the phosphate standard yielded the results shown in Table VI. As in the case of the CW measurements, five individual spectra were recorded and standard deviations for this set of data are shown in parentheses. Although the results are not quite as good as those observed for CW spectra, the mean standard deviation of 2.09% of the total phosphorus for this set of data certainly makes it acceptable as an analytically accurate technique. The largest deviations are observed for the most concentrated components and therefore seem to be associated with errors in the choice of a consistent base line. Each of the above determinations resulted from 1.7 h of collection time. Reducing the acquisition time to 1 s by using only 4K of data storage produces the results shown in the last column of Table VI. These results represent 1 h of data collection and can be seen to lie within or very close to the 2a limits corresponding to the longer collection time. We find in this case, however, that the largest deviation from the actual values occurs with the weakest signal, a finding which may result from the decreased resolution inherent in shorter acquisition time. The data presented in Table VI correspond to a mixture containing about 200 ppm total phosphorus, with individual components as low as 32 ppm. The convenience of being able to detect phosphorus near the 1-ppm level for the least concentrated substitutent led us to examine a further dilution. The results obtained for a sample with 20 ppm total phosphorus, having only 3 ppm Na2HP04are as follows: Na2PH04, 14.3%; Na4Pz07,39.8%; Na3P309, 17.4%; and Na4P4OI2, 28.5%. These data were collected using a 1-s repetition over a 17-h period. The larger deviations from the actual values observed here, as compared to the previous cases, are undoubtedly attributable to the decrease in the S / N ratio. Nonetheless, these results give a good semiquantitative estimate. Absolute Analysis. The method described above can readily be converted to an absolute method simply by adding a mass standard to the inner tube along with the free-radical
Table VII. Absolute Jetermination b y "P FT NMR of the Composition of a Mixture of Inorganic Phosphates Using the Parameters in Table V concentration, ppm composition Na,P,O,
run no.
__.____
1
2
3
4
-
actu
5
a1
35.9 35.2 38.3 31.1 33.4 34.8
31.5
(i2.7)
Na,P,O,,
42.9 45.7 45.9 44.3 46.3 45.0 .-_____-~___---
41.8
(t 1.4)
relaxagent and the lock solvent. We have employed KHZPO4, a primary standard, to determine the phosphorus composition of a mixture containing Na3P0309and Na4P4OI2(Table VII) using the parameters given in Table V. The concentration of a particular component is given by the equation: concn of component = concn of s t d X peak area of component
5.5
X peak area
of std
where the 5.5 factor accounts for the difference in volume between the samples in the 5- and 12-mm tubes. While the standard deviations (given in parentheses) are quite acceptable, the method produces concentrations higher than the actual values. Two possible sources for this discrepancy are: (1)a difference in sample detection within the spacial region occupied by the 5-mm as compared to that occupied by the 12-mm tube; (2) deviations in the tube diameters leading to a slightly different volume factor than that given above. Discussion. The foregoing results clearly establish 31PFT NMR as a useful means of differential or absolute analysis of dilute mixtures of phosphorus compounds. Although the F T technique introduces several parameters not important to CW NMR, their effect on the spectrum is understood and they can be adjusted to provide analytically accurate results. The F'T method permits accurate distinctions between phosphorus components a t the 200-ppm level of total phosphorus in a reasonable period of time (about 2 h) for spectrum accumulation. Further reductions in the sample concentration require longer accumulation times and/or lead to loss in the sensitivity and accuracy of the technique, even a t the 20-ppm level. Since many phosphorus compounds are good complexing agents for transition metals, even rather small amounts of magnetically active transition-metal species may lead to differential relaxation with apparent signal disappearance due to excessive broadening (16). Therefore we tentatively recommend that samples, such as ore extracts, which are high in metal content should have the metal removed before NMR analysis. Relaxagents based on organic free radicals offer much promise in 31PNMR and are worthy of further investigation as alternatives to the commonly used transition metals.
Anal. Chem. 1980, 52, 101-104
LITERATURE CITED
101
(8) C. T. Burt, T. Glonek, and M. Barany, Science. 195, 145-49 (1977). (9) T. W. Gurley and W. M. Ritchey, Anal. Chem., 47, 1444-46 (1975). (IO) D. Canet, G. C. Levy, and I. R . Peat, J . Magn. Reson.. 18, 199-204
(1) J. R. Van Wazer, "Determination of Organic Structures by Physical Methods", F. C. Nachod and J. J. Zuckerman, Eds., Academic Press, New York, 1971, p 323. (2) J. R. Van Wazer and T. Glonek, "Analytical Chemistry of Phosphorus Compounds", M. Halmann. Ed., Wiley, New York, 1972, p 151. (3) M. M. Crutchfield, C. H. Dungan, J. H. Letcher, V. Mark, and J. R. Van Wazer, "31PNuclear Magnetic Resonance", Interscience Division of John Wiley, New York, 1967. (4) G. Marvel, "Annual Reports on NMR Spectroscopy", E. F. Mooney, Ed., Academic Press, New York, 1973, p 1. (5) T. C. Farrar and E. D. Becker, "Pulse and Fourier Transform NMR", Academic Press, New York, 1974. (6) F. Kasler, "Quantitative Analysis by NMR Spectroscopy", Academic Press, New York. 1973. (7) D. E. Leyden and R. H. Cos, "Analytical Applications of NMR", Interscience Division of John Wiley, New York, 1977.
(1975). (11) D. E Jones and H. Sternlicht, J . Magn. Reson., 6 , 167-87 (1972). (12) J. W. Cooper, "Topics in Carbon-I3 NMR Spectroscopy", Vol. 2, G. C. Levy, Ed., Interscience Division of John Wiley, New York, 1976, p 392, (13) R. R. Ernst and W. A. Anderson. Rev. Sci. Instrum., 37, 93-102 (1966). (14) S. W. Dale and M. E. Hobbs, J . P h y s . Chem., 75, 3537-46 (1971). (15) W. E. Morgan and J. R. Van Wazer, J . Am. Chem. Soc.. 97, 6347-52 (1975). (16) T. W. Gurley and W. M. Ritchey, Anal. Chem., 48, 1137-40 (1976).
RECEIVED for review May 2, 1979. Accepted October 25, 1979. We thank the Institute Mondial dii Phosphate, Paris, France, for financial support and interest in this work.
Dual Beam Fiber Optic Time-of-Flight Spectrometer W. B. Whitten" and H. H. Ross Analytical Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830
persion to wavelength dispersion. For a hypothetical fiber with a fused silica core, transit time dispersion with wavelength has been calculated to range from 0.07 ns nm-' km a t 900 nm to 1.1ns nm-' km-' a t 400 nm ( 1 ) . Modal dispersion can be estimated from the fiber bandwidth; for example, a bandwidth of 1 GHz km-' would correspond to a Gaussian full width a t half maximum of 0.4 ns km Fiber attenuation can be a problem a t the shorter wavelengths. While attenuations of less than 5 dB km-' are not unusual in the near infrared, the attenuation a t 400 nm might be as much as 50 dB km-'. As noted in our earlier study ( I ) , transmitted intensity can be increased substantially with only a small decrease in spectral resolution if the fiber is shortened because the transmission decreases exponentially while resolution increases linearly with fiber length. Time-correlated single photon counting techniques were used for our prototype spectrometers in both this and the previous study. The light pulses are generated by a weak spark source and attenuated so that a t most a single photon is detected per flash. The detected photons will have a wavelength distribution identical to the spectrum which would be measured by the detector under qteady, high intensity conditions. The arrival time relative to the flash can be determined with subnanosecond precision with commercially available instrumentation. After a large number of flashes, the transit time distribution of the detected photons is obtained. This distribution can then be related to the wavelength distribution if the dispersive properties of the fiber are known. Our earlier spectrometer ( I ) was based on an 1100-m fiber in a single beam configuration. That is, sample absorbance was measured by alternately placing a sample and blank in the light path. This procedure is subject to several sources of error, the most important of which is probably variation of the spectral output of the source during the time of the measurement. In the present investigation, a dual beam spectrometer has been constructed with the original fiber divided into two unequal lengths. Photons passing through the two fibers arrive at the detector at somewhat different times so that the sample and blank spectra can be measured concurrently. Recause all measurements are in the time do-
A dual beam spectrometer has been constructed whlch uses the variation in light velocity with wavelength In an optical fiber to provide spectral dispersion in the time domain. Two fibers of different lengths constitute the sample and reference channels which are time-delay multiplexed and monitored by a single photomuitlpller. Thne-correlated single photon counting techniques provide the necessary timing accuracy for satisfactory spectral resolution.
'.
It has recently been shown that a fiber optic waveguide can serve as the dispersing medium in a time-of-flight optical spectrometer ( I ) . Characteristic features of time domain spectrometers include inherent time resolution, mechanical rigidity, and single detector operation. In this paper, we show how the combination of time delay with fiber length and wavelength dispersion can be used for dual beam operation of a fiber optic time-of-flight spectrometer. Orofino and Unterleitner (2) suggested that optical fibers be used for spectrometry in the time domain. The group velocity, ug, of a light pulse in a dispersive medium is given by
vg = c / n (1
X dn +; c)
In this expression, c is the velocity of light in vacuum and n, the index of refraction, is a function of wavelength, A. For a graded index, multimode fiber (31, all rays of a given wavelength will have about the same transit time, T , as a ray passing along the center of the fiber of length L T
= L/U,
(2)
Franks et al. ( 4 , 5 )studied the pulse broadening due to modal dispersion and wavelength (material) dispersion in a commercial graded index fiber and found that sufficient spectral resolution could be obtained to calculate the attenuation vs. wavelength of the fiber. The spectral resolution which can be obtained from a fiber optic spectrometer will be limited by the ratio of modal dis0003-2700/80~0352-0101$01 .OO/O
c
1979 American Chemical Society
