spectrometry have been reported for inorganic cosmochemical (22) a n d radiochemical (23, 24) samples and revealed quantitative data in the femtogram range. Spark source mass spectrometry, which allows the simultaneous determination of a variety of metals, has been used for the quantitation of a number of metals including cesium in ashed mammalian blood samples (25). However, the results described above show that FD-MS has the unique feature of allowing the estimation of alkali elements in very small amounts of untreated biological a n d enuironmental samples. Quantitative analyses of lithium, potassium, and rubidium by FD-MS and stable isotope dilution are under way in our laboratory and are expected to enable determinations with similar sensitivity and higher accuracy.
LITERATURE CITED H.-R. Schulten and H. D. Beckey, Org. Mass Spectrom., 6 , 885 (1972). H.-R. Schulten and F. W. Rollgen. Org. Mass Spectrom., 10, 649 (1975). H.-R. Schulten, J . Agric. Food Chem., 24, 743 (1976). H.-R. Schulten and D. Kummler, Fresenius’ 2 . Anal. Chem., 276, 13 (1976). (5) H.-R. Schulten, Methods Biochem. Anal., 24, 313-448 (1977). (6) H.-R. Schulten and H. D. Beckley, Org. Mass Spectrom., 7, 861 (1973). (7) F. W. Rollgen and H.-R. SchuRen, Org. Mass Spectrom., 10, 660 (1975). (8) F. W. Rollgen, U. Giessmann. and H.-R. Schulten, “Advances in Mass Spectrometry”, Vol. VII, N. Daly, Ed., Heyden & Sons, London, 1977, in press, and references cited therein. (9) H. D. Beckey and H.-R. Schulten, Angew. Chem., Int. Ed. Engl., 14, 403 (1975). (10) H.-R. Schulten, Cancer Treat. Rep., 60, 501 (1976). (1) (2) (3) (4)
H.-R. Schulten. W . D. Lehmann, and M. Jarman. in “Quantitative Mass Spectrometry in Life Sciences“, A . P. De Leenheer and R . R. Roncucci, Eds., Elsevier Scientific Publishing Company, Amsterdam, p 187. W. D. Lehmann, H. D. Beckey, and H.-R. Schulten, Anal. Chem., 48, 1572 (1976). W . D. Lehmann, H. D. Beckey. and H.-R. Schulten, Ref. 11. p 177. W. D. Lehmann and H.-R. Schulten, Angew. Chem., Int. Ed. Engl., 16, 184 (1977). W. D. Lehmann and H.-R. Schulten, Horned. Mass Spectrom., in press. H.-R. Schulten and U. Schurath, J . Phys. Chem., 79, 51 (1975). H.-R. Schulten and U. Schurath, Atmos. Environ.. 9 . 1107 (1975). D. A . Segar and J. G. Gonzalez, Anal. Chim. Acta, 58. 7 (1972). K. Govindaraiu. R. Hermann. G. Mevelle. and C. Chourad. At. Absoro. Newsl, 12, j 3 (1973) G E Janauer, F E Smith, and J Mangan, At Absorp Newsl, 6 , 3 11967) k . ~ AV. . Derschau and H. Prugger, Fresenius’ Z . Anal. Chem., 247, 8 (1969). B. M.Gordon, L. Friedman, and G. Edwards, Geochim. Cosmochim. Acta. 12. 170 (1957). B. M. Gordon and L. Friedman, Phys. Rev., 108, 1053 (1957). G. Friedlander, L. Friedman. B. Gordon. and L. Yaffe. Phvs. Rev.. 129. 1809 (1963) D F Ball, M Barber, and P G T Vossen, Biomed Mass Spectrom , 1, 365 (1974)
RECEIVED for review May 27, 1977. Accepted July 19, 1977. Presented in part at the International Symposium on Microchemical Techniques, Davos, Switzerland, May 22-27,1977. This work was supported by the Deutsche Forschungsgemeinschaft, Ministerium fur Wissenschaft and Forschung des Landes Nordrhein-Westfalen and the Fonds der Deutschen Chemischen Industrie.
Plasma Chromatography of Phosphorus Esters J. M. Preston” Defence Research Establishment Ottawa, National Defence Headquarters, Ottawa, Ontario, Canada K 1A 024
F. W.
Karasek and S. H. Kim
Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G 1
Mobility and diffusion coefficients, in air, of 47 ions formed by atmospheric ionic reactions of 16 phosphorus esters and thloesters are reported. Very careful assignment of ions to the peaks of the mobility spectra produced considerable confidence in these assignments. With some compounds, asymmetric peaks indicative of limlted hydration reactions were noted.
Phosphorus esters vary tremendously in toxicity. Diethyl methyl phosphonate, for example is essentially innocuous ( I ) while for a substitution product such as parathion the average lethal subcutaneous dose for a 0.5-kg mouse is only 8 mg. The corresponding figure for GB is 0.1 mg (2). Thus phosphorus esters have found wide use as insecticides and are potential weapons of chemical warfare. Their detection in the atmosphere is therefore of considerable interest. Organophosphorus compounds have high proton affinities and thus their detection can be accomplished by ionizing air suspected of containing such compounds, discarding ions of no interest, and recording the resulting current. The ultimate in selectivity is attained by directing the ions into a mass spectrometer with, for example, unit mass resolution u p to the highest masses of interest. Since the ionization process 1746
ANALYTICAL CHEMISTRY, VOL. 49, NO. 12, OCTOBER 1977
has usually been chosen to produce minimal fragmentation, there exist mass numbers which serve as good diagnostics for the organophosphorus compound. For example, one may monitor the mass of the major ion of the mass spectrum of the compound, or may use algorithms which calculate the ratios of the intensities of several ions. Such systems have been used for detection of many atmospheric contaminants (3). For many applications, however, the economic and logistic burden of such a system may be excessive. Interest is therefore growing in developing detectors which exhibit limited selectivity, since these will be adequate in many situations. The prime reason why the requirements for selectivity can be relaxed is that the extremely nucleophilic nature of phosphorus esters reduces the number of interferents capable of garnering an appreciable fraction of the available charge in the atmospheric-pressure ionic reactions. An example of a suitable detector, offering high sensitivity and acceptable selectivity, would be a portable plasma chromatograph ( 4 ) . Actually even simpler instruments which, like the plasma chromatograph, separate ions on the basis of differences in transport coefficients will probably also be acceptable ( 5 ) . Such instruments separate ions according to their mobility coefficients, diffusion coefficients, or both. Actually all such instruments, including the plasma chromatograph operate in low-field conditions; that is, the energy
Table I. Plasma Chromatograph Experimental Conditions Length of drift tube 6.0 cm Applied field 250 Vicm 350 cm'imin of dry nitrogen or air Drift gas 40 cm3/min of dry nitrogen or air Reactant gas Temperature 150 ' C (typical) 7 3 0 Torr (typical) Pressure Gate widths 200 P S Scan time 2 min (typical) an ion acquires from the electric field between collisions does not exceed the thermal energy. In this case the mobility and diffusion coefficients are proportional, and are related by the Einstein equation (6). T h u s measuring either one provides t h e instrument designer with t h e required data. It was for this reason that the present study, measuring t h e mobility coefficients of organophosphorus esters by a laboratory plasma chromatograph, was undertaken.
EXPERIMENTAL The BETA VI plasma chromatograph located at the University of Waterloo was used throughout this study. The operating principle and design of this instrument have been described previously ( 4 ) and will not be repeated here. The experimental conditions are listed in Table I; the compounds studied are listed in Table 11. Insertion of samples was done in several ways. One to three microliters of a solution could be deposited on a platinum wire, and the solvent allowed to evaporate. The wire was then inserted into the heated inlet port. Alternatively, a gas-tight syringe could he used to inject vapor directly. By these means it was possible to select the desired quantity of sample to avoid saturation (which occurs at about 1 Fg) while achieving an ad.. equate signal. The commercial compounds were all of reagent grade, and the other samples were of similar purity. The carrier and drift gases were usually Linde high-purity nitrogen 99.996%. Prior to entry into the plasma chromatograph, both carrier and drift gases were passed through a trap packed with Linde Molecular Sieve 13X. This procedure removes impurities and gives a water concentration estimated at 1-4 ppm. In order to study hydration, though, several compounds were run using, as the carrier gas, air which had been saturated in a water bubbler a t ambient temperature. Finally. several compounds were run using dry air as the drift gas. Figure 1,the mobility spectrum of GB, is presented as a simple example. The mobility coefficient, K , of the ions which produced each peak was calculated from
K = d/rE
(1)
where d is the drift length (6.0 cm), T is the drift time, and E is the electric field. Since the mobility coefficient is inversely proportional to the molecular number density, it is accepted practice to tabulate the
I 3 Reo-res
2
B
Vat
t,
I
-- '
I €
I 4
- T ' ~5
Flgure 1. Typical spectrum, that of GB. The lower trace w a s recorded b e f o r e sample injection and is the spectrum of the reactant ions of dry nitrogen
reduced mobility coefficient, KOwhich is K a t a pressure of 760 Torr and a temperature of 273 K. This is simply
The reduced mobility was calculated for each peak of interest of each spectrum. The reproducibility of plasma-chromatographic drift times has, after considerable experience, been found to be 1 to 1.5%. Uncertainties in applied field, drift-tube length, temperature, or pressure are negligible by comparison. Other quantities such as gas flow rate have little effect on drift time in the conditions used in this study. Thus the values of reduced mobility reported here are precise to better than 2 % .
RESULTS Before tabulating t h e mobilities ineasured in this experiment, it is necessary to discuss the rnethods used t o identify the ion responsible for each experimental peak. Consider the typical spectra in Figure 1. T h e lower trace was recorded before the addition of sample, and thus is produced from the ions found in clean air, the so-called reactant ions. Their identity has recently been confirmed (7). The upper trace (10 X t h e sensitivity) is t h e spectrum of GB in air, thus the additional peaks at 7.64 and 8.03 ms are produced by GB. GB is a typical sample in that its spectrum contains only a few peaks. More often, however, t h e mobility spectrum
Table 11. Compounds Studied Abbreviation GA GB GD VX PAR DIS DIM TH MPAR FEN DMMPA DEBP DCMP DMMP TMPA TEPA
Name Tabun - Ethyl N , A'-dimethylphosphoramidocyanidate Sarin - iso-Propyl methylphosphonof'luoridate Soman - 1, 2, 2-Trimethylpropyl methylphosphonofluoridate Ethyl S-2-diisopropylaminoethyl methylphosphonothiolate Parathion - Diethyl p-nitrophenyl phosphorothionate Disyston - 0,O-Diethyl S-2-ethylthioethylphosphorodithioate Dimethoate - O, O-Dimethyl S-(N-methylcarbamoylmethy1)-phorodithioate Thimet - 0,O-Diethyl S-ethylthiomethyl phosphorodithioate Methyl parathion - Dimethyl 4-nitrophenyl phosphorothionate Fenitrothion - Dimethyl 3-methyl-4-nitrophenyl phosphorothionate Dimethyl morpholinophosphoramidate Diethyl 2-bromoethylphosphonate Diethyl cyanomethylphosphonate Dimethyl methylphosphonate Trimethyl phosphonoacetate Triethyl phosphonoacetate
Source DREO DREO DREO DREO (1)" (1)" (1)"
(1)" (2)"
(3)" (4)*
Aldrich Aldrich Aldrich Aldrich Aldrich
Ltd. Ltd. Ltd. Ltd. Ltd.
a Samples were kindly supplied by: (1)R. Greenhalgh, Agriculture Canada. ( 2 ) H. McLeod, Health and Welfare Canada. ( 3 ) K.M.S. Sundaram, Environment Canada. ( 4 ) P.A. Adie, Defence Research Establishment Suffield. A N A L Y T I C A L CHEMISTRY, VOL. 49, NO. 121, OCTOBER 1977
1747
contains numerous peaks and identifying the particular ion responsible for each one is difficult. Indeed, without a system such as a coupled P C / M S , definite identification is not possible. However, identification which is very probably correct can be based on three factors: (1)It has been well established that the results of chemical ionization mass spectrometry can be applied to plasma chromatography. One general rule is that the quasi-molecular ion M + , MH+ (or (M - H)+ for alkanes) is present in almost all cases. ( 2 ) Reasonable chemistry of the compound, based on achievement of equilibrium in atmospheric pressure reactions, is a strong guide. (3) In all past experience with plasma chromatography a roughly linear relationship between the mobility and the logarithm of the mass of ions of a similar chemical nature has been found (8). On the other hand, two causes of difficulty are: (1)The resolution corresponds to a mass differential of 10 to 20%. Often there are several plausible hypothetical ions in this mass range. ( 2 ) Thermal decomposition on the inlet can obscure results. The procedure, therefore, was to consider the spectra of all the organo- or thiophosphorus esters studied and to devise a consistent identification scheme. The resulting assignments, as listed in Table II1,were used in a least-squares linear regression to find a general mass-mobility relationship for the phosphorus esters. T h e logarithm of the ionic mass, m, was used, and it was found that
KO = 6.212 - 2.004 log ( m )
(3)
T h e final column of Table I11 lists the percentage deviation between the experimental value of KOand the value given by Equation 3. Of the assignments, only two were confirmed by PC/MS, but they appear most reasonable in view of the following: (1)For 15 of the 16 compounds studied the most intense peak was assigned as MH+. (This relationship sometimes did not hold if the reactant ions were completely reacted or long after injection when new peaks due to thermal decomposition on the walls of the instrument were growing.) The 16th compound was GD, which decomposed readily but, even so, the (GD)H+ peak was prominent. (2) T h e correlation coefficient between the logarithms of the ionic masses and the KOvalues is 0.978; 86% of the KO values are within 5% of the values expected for that assignment. (3) Two of the compounds were studied using a PC/MS. For VX, the mass spectral data provided definite identification of the parent peak, (VX)H+,with a mass of 268. A later study of methyl parathion was less conclusive, probably because of sample decomposition, but the (MPAR)H+ peak, mass 264, appeared at the appropriate mobility.
DISCUSSION Assignment of Ions As mentioned earlier, the mobility spectrum produced by a plasma chromatograph can contain several peaks, even for a pure sample. Since the resolution by mass is only about 1070, some ambiguity in ion identification results. Ideally, identification of the ionic species responsible for each peak should be done by coupling the plasma chromatograph to a mass spectrometer. I t is often true, however, particularly if many related compounds (not of low molecular weight) are studied, that mass identification is not essential. Usable ion identifications could usually be made by use of previous mass-mobility relationships, and by various experimental devices such as adding additional water, nitric oxide, or other compound to increase the concentration of particular reactant ions and thus that of all ions in the 1748
ANALYTICAL
CHEMISTRY,
VOL. 49, NO. 12, OCTOBER 1977
Table 111. Ion Mobilities Deviation Compound DMMP
KOa
2.066 1.406
GB GA
DEBP DCMP
GD
TMPA
DMMPA
1.95b 1.84 1.71 1.8Z6 1.73 1.63 1.6gb 1.15b 1.82 1.5B6 1.48 1.39 1.13 2.06 1.92b 1.76 1.65 1.92 1.6gb 1.54 1.26 1.15 1.77 1.576 1.14 1.07
Ion identity MH' M , H' MH' M(H, 0)" M(H2-O),H+ MHM(H20)" M(H,O)?H' (M - Br)H(M - Br), H' MH' - CN MHM(H,O)H+ MNO' M, H' MH+- C(CH,), MH' - C(CH; ); M H + - CH, MH' MH' - CH, 0 MH* MNO M , H' M: H'
of K O C
-4%
-8% -10%
-13%
+ 4%
+
-
CH, OCH, T
5% 6%
MH' - CH, 0 MH' -3% hl, H' - CH, OCH, M, H' - 4% TEPA 1.45b -4% MH' A 14% 1.23 M, H' - C, H i OC2H; 4 7% 0.97 M , HDIM 1.47b MH+ TH 1.37b MH' MPAR 1.80 NO, C, H5OH+ 1.36b hlH' 1.31 M(H20)" VX MH' -4% 1.30b 2.09 DIS (S(CH,),SCH,CH,)H+ 1.34b MH' FEN 1.80 NO, C, H. OH1.72 NO: ck HI (CH, )OH+ MH' - CH, 0 1.40 1.31b MH' M(H,O)H+ 1.26 N02C,HjOH+ PAR 1.78 1.27b MH+ 1.22 M(H, 0)" a K Ois in units of cm2 s - ' , with an error of 2%. Multiply K Ovalues by 0.02354 to obtain D , in cm2/s. Highest intensity peak. Difference between K Oand the value given by Equation 3 (phosphorus-containing ions only). Values < 2% suppressed.
-
spectrum associated with that reactant. It became clear that if consistent assignments throughout a series of chemically similar compounds produced a linear relationship between mobility and the logarithm of the ionic mass, then the assignments merited considerable confidence. In the next few paragraphs the assignments for each of the compounds studied will be discussed. Samples were run using either dry nitrogen (1-4 ppm water) or moist air (3% water - 100% humidity at 25 "C) as carrier gas, that is, the gas which contributes the reactant ions. In both cases (Ref. 7 and recent work by FWK and SHK), the reactant ions are (H,O),NH,+, (H,O),NO+, and (H,O),H+, where n is zero or a small integer, the value changing with humidity. In this experiment using moist air, the proton ion is about 79% (H,O),H+, 12% (H20)3H+,8% (HZO)jH+ and 1% heavier ions. For dry nitrogen the equilibrium distribution is about 88% (H20),H+and 12% (H20)3H+. Thus most of the protons are four times hydrated in the first case, twice in the latter.
REDUCED MOBILITY (cm* v - ' s - ' )
Figure 2. Main peak of parathion, recorded 4 min after 0.15 kg were injected into dry nitrogen as drift and carrier gas
Hydration. Carroll et al. (7)recently threw a welcome light on plasma chromatography by pointing out that an ion and its hydrated forms, M(H20),H+,n = 0, 1, 2..., will appear as a single peak in mobility spectra if the forward and reverse rates of the ionic hydration reactions are sufficiently fast that numerous reactions occur during a drift time. Since these rates are not known for phosphorus esters, one might expect a single peak (rapid reactions), separate peaks (one or both reactions slow), or an intermediate case. This presupposes that the equilibrium constants are such that significant hydration will occur a t the humidity and temperature used. Figure 2 is the structure of the main peak of parathion as recorded in this experiment, with the smaller peak of lower mobility adjacent to it. Now Spangler (9) showed that plasma chromatographic peaks are well described by a Gaussian shape, and so two Gaussians, matched to the experimental peaks in height and center line and with half-width corresponding to the high-mobility side (no reaction-broadening) of the main peak, were summed and incorporated into the figure. Clearly the two experimental peaks are not due to two unrelated ions, for then the sum of the two Gaussians would adequately describe their shape. We conclude that the peaks are associated by a reaction, and that the reaction is not fast enough to unify the peaks nor slow enough to completely separate them. The Gaussian approximation can be seen to overestimate the unbroadened wing, implying that the observed difference is conservative. There is also a suggestion of broadening due to a second reaction. Since this reaction is surely hydration, we conclude that the two peaks are (PAR)H+and (PAR)(H20)H+.Similar peak shapes were noted with DCMP, MPAR, and F E N , so similar assignments were made. On chemical grounds one would expect GA and GB to be more hydrophilic, thus the rate of the dehydration reaction to be slower, thus the peaks to be separated. Furthermore, higher hydrates would be expected. Peaks consistent with this analysis were identified in both cases. A full understanding of this question of hydration reactions as they affect plasma chromatography is of considerable interest. The information required is not just PC/MS analysis, a t particular conditions of humidity, temperature, and pressure, but also the values of the rate and equilibrium constants of the chain of hydration reactions. We hope to undertake this work in the future. Dimerization. Two types of association between sample molecules were observed, dimerization to form M2H+,and condensation reactions involving the loss of a good leaving group to form ions such as M2H+ - CH30CH3. Loss of methoxy groups from the parent ion was also observed. Anomalies. T h e group of ions exhibiting the largest variation from the mass-mobility relationship of the class (Table 111) are ( D C M P ) H + , ( D C M P ) ( H 2 0 ) H + , a n d (DCMP)NO+ (barely detectable except under the conditions described below). The identification of these ions was almost
certainly confirmed by injecting a few !millilitersof nitric oxide into the carrier gas during the residence time of DCMP in the plasma chromatograph. In the subsequent spectrum, the peak a t KO= 1.39 cm2 V-l s-l was a t least ten times its previous size, largely a t the expense of the peak a t K O= 1.48 cm2 V-' s-'. Thus these peaks were identified as being caused by (DCMP)NO+ and ( D C M P ) ( H 2 0 ) H C ,respectively. T h e identification of the parent peak followed. (It is far more intense than the other two). However, one should again note that definite identification is possible only with a coupled mass spectrometer. If each of these ions carried one water of hydration, for example, they would each fit the mass-mobility relationship well. The matter of these anomalous mobilities was examined further by means of the experiments with DEBP. DCMP and D E B P are very similar, differing only in the substituent on the methyl group (CN for DCMP, CHzBr for DEBP). T h e highest-mobility ions are formed by the loss of CN and Br, respectively, and so the resulting ions are similar, differing, in fact, only in one CH2 group. As might be expected, the mobility coefficients of these two ions are closely related; KO for the lighter ion is 98% of the value from Equation 3 and the more bulky ion is 3% slower. T h e similarities end here, however, since DCMP does not usually lose CN (the intensity of (DCMP)H+- C N is small), while Br appears to be a good leaving group. Ready loss of bromine, even to the extent that the parent peak (DEBP)H+ is no longer found, was expected from studies of brominated alkanes (10). Indeed, it seems clear that the KO= 1.15 cm2 V-I s-l peak (of D E B P is (DEBP Br)2H+rather than (DEBP)H+because the peak caused by (DEBP)H+- Br is found only when the intensity of the former is low. Thus these peaks cannot be caused by an equilibrium of a parent ion and a parent minus a substituent, but rather by a dimer-monomer reaction. Since this establishes that the only monomer present in significant quantity is (DEBP)H+ - Br, the dimer must be (DEBP - Br)2Hf. T h u s from this study we conclude that the parent and "simple-" addition ions of DCMP have anomalous mobilities. Since DCMP is similar to DMPA and TEPA, the anomalously low mobility can be attributed only to the cyanide group. The fact that GA, the only other cyanide-containing compound studied, shows no anomaly is presumably due to the different chemical environment of the cyanide group in this molecule. P a r a t h i o n Series. The parathion series, PAR, MPAR, and F E N , gave rise to interesting spectra which provided some convincing evidence for the ion identifications postulated herein. For each insecticide the ma,jor ion was MH+, in agreement with the chemical ionization mass spectrometery data of Ref. 11. None of the phosphorus-containing ions of this series exhibit any anomalous mobilities (Table 111) and, in fact, (FEN)H+ and (MPAR)(H,O)H+, whose masses differ by four, were found to have the same mobility. In each spectrum a peak a t KO= 1.79 f 0.01 cm2 V-' s-l was found. This is precisely the previously reported (12) mobility of the ion of p-nitrophenol which can be formed from each of these insecticides by rupture of the oxygen-phosphorus bond. In the case of fenitrothion, loss of CH2 is required to form this ion and, in fact, both (FEN)H+- CH2 and NO2C6H4(CH3)OH+ (i.e., p-nitrophenol ion plus CHJ were observed. This discussion (see also later) accounts in a most reasonable manner for all the product ions produced by these three insecticides. Drift Gas. The experiments discussed here were performed using dry nitrogen as the drift gas, that is, the gas in the drift space. When air was used instead, only small differences would be expected (8)and, in fact, no difference in mobilities was observed. C o m p a r i s o n w i t h P r e v i o u s W o r k . Moye (13) recently published work on the plasma chromatography of pesticides, A N A L Y T I C A L CHEMISTRY, VOL. 49, NO. 12, OCTOBER 1 9 7 7
1749
including organophosphorus pesticides. He obtained vastly different spectra for parathion and methyl parathion which, he felt, reduced the value of plasma chromatography as an analytical tool. We also studied these compounds, and fenitrothion, and found very reasonable relationships between the mobilities and masses of ions of this series (Table 111). When the data necessary to calculate the KOvalues for the two parathions are extracted from Moye's paper, it is found that his paper and this one agree precisely that the reduced mobility of the major peak of parathion (which we identify as (PAR)H+) is KO = 1.27 cm2 V-' s For methyl parathion, however, there is disagreement. We find K O= 1.36 cm2 V 1 s for the main peak (MPAR)H+,and an insignificantly small peak a t KO= 1.18 cm2 V-' s-'; Moye reported the latter as the mobility of the major peak. A likely explanation lies in the method of sample introduction. Throughout this work, and during Moye's work on parathion, the solvent was allowed to evaporate from the wire before insertion. However his methyl parathion spectrum was obtained using the insecticide in hexane solution; his mobility of 1.18cmLV s l corresponds (Equation 3) to an ionic mass of about 338 which could easily be (MPAR)(C6H1,)H+(mass 350). Thus the variations which Moye found and ascribed to unknown effects were probably due to interactions with solvent. Diffusion Coefficients. As mentioned earlier, the plasma chromatograph operates in the low-field domain. The mobility and diffusion coefficients are therefore related by (6)
cussed above, although electrostatic repulsion could also contribute. These factors were not rigorously considered by Spangler.
CONCLUSION The low-field mobility coefficients of 47 different ions formed by atmospheric-pressure ionic reactions of phosphorus esters have been measured. These ions are parent ions, hydrates, partial or full dimers, or decomposition products of the phosphorus esters. The excellent linear correlation between mobility and mass of these ions means that the mobility of similar ions can, with confidence, be determined from the regression fit of the data presented here. One must note, however, that only two of these ions were definitely identified, by use of a PC/MS instrument. While mobility spectra can be identified in the manner used here, and thus give useful data, exact identity of the ions is not assured. The Einstein equation was used t o calculate the diffusion coefficients from the experimental low-field mobility coefficients.
ACKNOWLEDGMENT We acknowledge comments on hydration reactions by Martin J . Cohen.
LITERATURE CITED R . D. O'Brien. "Toxic Phosphorus Esters", Academic Press, New York and London, 1960, pp 83-89 "The ProSlem of Chemical and Biological Warfare", Vol 2, Almqvist and Wiksell. Stockholm. 1973. DD 55-58. J A. Buckley, J. B. French,'and N. M. Reid, Can. Aeronaut. Space J . , 20. 231-233 (1974). F. W. Karasek, Anal Chem.. 46, 710A-717A (1974). C. S. Harden and T. C. Imenson. "Detection and Identification of Trace Quantities of Orqanic Vapors in the AtmosDhere bv Ion Cluster Mass Spectrometry a i d the Ionization Detector System".Edgewood Arsenal Technical Report (1973). E W. McDaniel and E.A. Mason, "The Mobility and Diffusion of Ions in Gases". John Wilev and Sons. New York. N.Y.. 1973. D. I. Carroll, I. Dzidic, R. N. Stillwell. and E. C. Hornina, Anal. Chem., 47, 1956-1959 (1975) H E Revercomb and E A Mason, Anal Chem 47, 970-983 (1975) G E SDanaler and C I Collins Anal Chem 47 403-407 11975) F W Karaskk. 0 S Tatone and D W Dennev J Chromatoar 07 137-145 (1973) R. L. Holmstead and J. E. Casida. J , Assoc. Off. Anal. Chem., 47, 1050-1055 (1976). F. W. Karasek, S. H. Kim, and H. H. Hill Jr., Anal. Chem., 48, 1133-1137 (19761. H A. Moye, J Chromatogr S o , 13. 285-290 (1975)
kT D=-K
e
which is the Einstein equation. Here D is the diffusion coefficient, e the electronic charge, T the temperature, and k Boltzmann's constant. This relationship is exact, and thus diffusion coefficients can be calculated to the same accuracy as the mobility coefficients were measured. We have not listed these values, but note that k T / e = 23.54 mV for T = 0 "C. I t is of interest to compare the resulting diffusion coefficients with those calculated by measuring peak widths. Spangler (9) derived an equation between the peak width at half height, the diffusion coefficient, and the duration of the gate pulse, but it was found that the diffusion coefficients calculated in this manner were uniformly about five times too high, i.e., the experimental peaks were five times wider than predicted. This additional broadening was probably due primarily t o reactions continuing in the drift space, as dis-
-
RECEIVED for review April 26, 1977. Accepted July 19, 1977.
Peak Broadening Factors in Thermal Field-Flow Fractionation LaRell K. Smith, Marcus N. Myers, and J. Calvin Giddings" Department of Chemistry, University of Utah, Salt Lake City. Utah 84 112
Previous observations of plate-height effects in field-flow fractionation (FFF) are briefly noted. The theory of plate height in FFF is reviewed and expanded. Contributing terms are divided into ideal and nonideal categories, the latter resulting mainly from relaxation, polydispersity, and multipath effects. A method for distinguishing these terms from one another is presented. When applied to data from a standard column, it shows behavior approaching ideality, dominated by the nonequilibrium plate height term. Cases in which the channel surface was roughened and distorted exhibited nonideal behavior, establishing the critical role of surface finish. 1750
A N A L Y T I C A L CHEMISTRY, VOL. 49, NO. 12, OCTOBER 1977
The retention of peaks in field-flow fractionation has been found to occur much as predicted by theory (1-8). The dependence (or lack of it) on channel dimensions, particle size or molecular weight of solute, field strength, flow velocity, and other variables is well understood. Peak width, by contrast, has not generally yielded results in accord with theory ( I , 5, 8). Peaks have, in most cases, been broader than predicted, and this divergence has increased with the approach to the conditions of high resolution that we theoretically may expect of FFF. This work represents an attempt to study and isolate the
