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Anal. Chem. 1985, 57. 1902-1907
were actually mixtures of different colored dyes and many of the dyes were mixtures of the same parent structures varying only in alkyl substitution. The ability of the TLC plates to separate most of the dyes suggests the applicability of on-line LC/MS for the analysis of both the high and low molecular weight dyes. Identification of the dyes in an unknown fuel by HRMS techniques provides an additional piece of analytical information which can be used to distinguish the fuel. The success of the technique is greatly increased by the availability of reference fuels for comparison purposes. Application of the technique is limited by the possible use of identical dye packages in different fuels. The GC/MS data presented for the polar fractions from the three gasolines demonstrated unique and repeatable differences between the fuels. Possible identification problems could occur if different fuels manufactured from similar crude slates and containing the same additive packages are encountered. Again, the use of reference fuels helps but the use of a unique tracer such as the alcohols discussed above greatly increases the certainty of the identification. Registry No. I, 96503-04-7; 11, 85-86-9; 111, 3375-23-3; IV, 2362-57-4;V, 96503-05-8;VII, 2481-94-9; Color IA, 96575-30-3; Color IAR, 96575-31-4;Calcofluor white RWB, 8066-05-5; Calco Rhodamine B Base, 509-34-2; Marker EB, 96575-32-5; 1-octanol, 111-87-5;1-decanol, 112-30-1.
Schoinick, M. E.;Scott, A. C.; Anbar M. “Methods of Identlfying Petroleum in the Marine Environment”; U.S. Department of Commerce, Natlonai Technical Information Service, Report NoCGD-37-77, 1976. Ogata, M.; Miyake, Y. J . Chromafogr. Scl. 1980, 78 ( l l ) , 594-605. Frame, G. M. ConfrolHazard. Mater. Spill., Proc. Nafl. Conf. 1080, 108-184. Chow, T. J.; Snyder, C. 8.; Earl, J. L. IAEA 1075, 791 (4), 95-108. Petrovic. K.; Vltrovic P. J . Chromafogr. 1978, 179, 413-422. Jeites R. J . Chromafogr. Sci. 1074, 12, 599-605. Sieck, L. W. Anal. Chem. 1079, 57 (I), 128-132. Lee, M. D.; Lee, I.C.; Chun, H. D. Hwahak Konghak 1982, 20 (9, 401-41 4. Frank, H. A. J . Forensic Sci. SOC. 1080, 20 (4). 285-292. “Dupont Petroleum Dyes”, Dupont Petroleum Chemlcals Publlcation A-95096, 1973. US. Patent 3 862 120 Issued to R. 8. Orelup, Morton-Norwich Products, Chicago, IL, 1975. U S . Patent 4049393 issued to R. B. Orelup, Morton-Norwlch Products, Chicago, IL, 1977. U.S. Patent 4 009 008 issued to R. B. Orelup, Morton-Norwich Products, Chicago. IL, 1977. Pearce, W. E. Arson Anal. News/. 1977, 1 (3), 1. U.S. Patent 3607074 Issued to R. A. Brown and W. A. Dietz, Esso Research and Englneerlng, Westfield, NJ, 1971. ”Fuels and Fuel Addltlves: Revised Definltlon of Substantially Similar”; Fed. Resist. 1981 46 (July 28) (144, EN-FRL-1821-4) 38582. U.S. Patent 4 141 692 issued to J. L. Keller, Unlon Oil Company of California, Los Angeles CA. 1979. Venkataraman, K., Ed. ”The Analytical Chemistry of Dyes”; Wiley: New York, 1977. White, C. M.; Li, C. Anal. Chem. 1982. 5 4 , 1564-1570. Salnt-Jalm, Y.; Moree-Testa, P. J . Chromafogr. 1980, 798, 188-192. Poiss, P. Hydrocarbon Process. 1973, 61-68.
LITERATURE CITED (1) Albalges, J.; Aibrecht, P. Int. J . fnviron. Anal. Chem. 1970, 6 (2), 17 1-90.
RECEIVEBfor review October 1,1984. Accepted April 11,1985.
Resolution Measurement for Ion Mobility Spectrometry Souji Rokushika and Hiroyuki Hatano Department of Chemistry, Faculty of Science, Kyoto University, Kyoto, 606 Japan Michael A. Bairn and Herbert H. Hill, Jr.*
Department of Chemistry, Washington State University, Pullman, Washington 99164-4630
A slngle peak method is used to calculate a resolutlon value equal to the theoretlcai number of peaks that can be separated prlor to (and with the same dimensions as) the peak from wMch the measurements are made. Thls IMS resolution can be calculated by R = t/2W,, where R Is IMS resolution, t Is the Ion drlft time in milliseconds, and W , is the temporal width ol the peak at half helght in mliliseconds. An equation showing the dependence of IMS resolution on varlous Instrumental parameters Is derlved to be R = t / [ W : 4(44.2kTt/qEL)*]”*, where W , is the peak width of the Initial ion plane, k is Boltzmann’s constant, T Is absolute temperature, t Is the drm time of the Ion, 9 Is the charge on the Ion, E Is the dectrk fkid in the Ion drlft region, and L is the length of the ion drm reglon.
Whenever ion mobility spectrometry, also known as plasma chromatography, is discussed as an analytical technique, questions arise concerning its resolution. Just how well can this technique separate one ion from another? How does its resolution compare with that of mass spectrometry? Or, should its separation power be discussed in terms of chromatographic resolution? 0003-2700/85/0357-1902$01.50/0
Unfortunately there is no generally accepted method for determining the resolution of an ion mobility spectrometer. Thus, attempts to answer these practical questions usually revolve around the fundamental ion mobility equation as discussed by Revercomb and Mason ( I )
where K is the ratio of the average velocity of an ion to the electric field intensity and is called the ion mobility constant, q is the charge on the ion, N is the number density of the gas, m is the mass of the solute ion, M is the mass of the drift gas, k is Boltzmann’s constant, T i s the absolute temperature of the drift gas, and Oo is the diffusion collision integral, a measure of the size of the ion of interest. Assuming pressure and temperature are held constant, K is found to be inversely proportional to the product of the square root of the reduced mass of the ion, p = m M / ( m M),and the size of the ion as measured by no
+
For small atomic ions in the same neutral drift gas, mobility, and therefore separation, is controlled by reduced mass ( p ) . 0 1985 Amerlcan Chemical Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 9, AUGUST 1985
For large, molecular ions, however, 1.1 is nearly constant and mobility is controlled by the shape of the ion. For those ions which fall between these two extremes, which includes most of the polyatomic ions for which ion mobility spectra have been reported, separation is a function of both mass and shape. While discussions of ion velocities and mobility constants help to explain basic principles of ion mobility spectrometry, they do not answer practical questions about resolving power. One might attempt to discuss the separation efficiency of ion mobility instruments in chromatographic terms as described by Spangler and Collins (2). Applying Green function techniques to the description of longitudinal diffusion along with standard chromatographic equations for the efficiency of columns, they developed a relation for the height equivalent to a theoretical plate (HETP) within the drift region. Of course HETP is not strictly a resolution measurement but rather a measure of the separating efficiency of a column (or a drift tube). Karasek and Kim introduced the concept of evaluating IMS resolution in terms of the two peak definition commonly used in chromatography (3)
(3) where Atd is the drift time difference between the peak I1 and peak I11 of the three reactant ions commonly observed when @Niis used as the ion source and nitrogen is used as the drift gas. WII and WIII are the respective widths of these peaks. Carrico et al. used this two peak chromatographic definition of resolution to evaluate the use of ceramic-coated electrodes in the reactor and drift regions of an ion mobility spectrometer (4). For a review of this two peak approach to resolution measurement the reader is referred to the recently published book cited in ref 5. IMS resolution has also been defined in terms of mass resolution (2)
R = -M
Ah!i
(4)
where R is the resolution of the spectrometer, M is the mass of the ion, and AM is the mass difference between ions that can be separated with a 10% valley. This approach to IMS resolution served the authors’ purpose of comparing IMS separating power to mass spectrometry but has not been adopted as a convenient method for predicting ion separations. The problem is that it is only appropriate for monatomic ions where mass differences are the primary consideration. Separation in ion mobility spectrometry, however, depends not only on mass but also on size and shape. Isomer separations are often observed in IMS (6-9). If resolution were based solely on mass, then isomer separation would not be possible. The purpose of this paper is to present a practical approach for the determination of IMS resolution that can be used both to compare the separation efficiency of different instruments and to predict the capability of an individual spectrometer to separate ions of interest.
DEFINITIONS Since ion mobility spectrometry cannot be completely characterized as either mass spectrometryor chromatography, it is not surprising that a working definition of IMS resolution does not fit neatly into one of these two categories. The definition proposed in this paper is that IMS resolution (R) is equal to the ratio of the length that the ion pulse travels (L)to the width (W? of the ion plane after traversing distance L
R = L/W‘
(5)
To convert this spatial definition of resolution into a more
1903
practical, temporal definition, both terms are simply divided by the average drift velocity of the ion pulse (Vd)
where t is the drift time of the ion pulse and W is the temporal width (Le., the time that it takes an ion cloud to move through the terminal perpendicular plane of the drift region) of the ion peak. h u m i n g that this ion cloud is Gaussian in shape, its width is defined as 4.7 times the standard deviation (u). This definition of peak width is not to be confused with that used in chromatography where peak width is defined as 4u. Unlike the chromatographicpeak width which must be measured at 13.4% of the peak height, IMS peak width occurs at 6.25% of the peak height and is conveniently equal to two times the peak width at half height. Thus, IMS resolution can be determined from an ion mobility spectrum by the relation
R = t/2wh
(7)
where w h is the temporal width of the ion pulse measured at half of the height of the ion peak. The width of an ion peak in mobility spectrometry can be attributed to four band broadening mechanisms: the initial pulse width, diffusion broadening, mutual charge repulsion broadening, and ion/ molecule reaction broadening (1). For reasons that will be discussed later, only the effects of the initial pulse and diffusional broadening are considered here. If the initial width of the ion pulse is Gaussian in shape (an assumption which is not accurate but which is viable for the first approximation approach taken in this paper), the final peak width can be expressed as a function of both the initial width and the contribution of diffusion during the ion migration process
w2 =
woz+ w,z
(8)
The initial ion pulse width (Wo) is taken to be twice the time that the entrance gate is open. This value is an estimate of the initial ion pulse width based on the assumption that the actual pulse is wider than the gate open time due to gate leakage, capacitance, and response time. Currently, investigations are under way to establish more clearly the actual pulse width and its contribution to band broadening. An expression for the diffusion broadened peak width (wd) can be derived from the normal distribution of the diffusion process
= (2Dt)1/2 (9) where u’ is the spatial standard deviation of the diffusion process, D is the diffusion coefficient, and t is the time that diffusion occurs and is equivalent to the drift time. Through the Nernst-Einstein relation the diffusion coefficient can be expressed in terms of the mobility constant ( K ) u’
D = k4T ,
(10)
where k is Boltzmann’s constant, Tis the absolute temperature, and q is the ionic charge. Since the mobility constant is simply the ratio of the ion velocity to the electric field, eq 9 can be converted into an expression for the spatial diffusional broadening of the peak width (W,’)
This relation can be converted to an expression for the temporal diffusion broadened width (wd) by dividing by the ion velocity (vd = L/t)
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 9, AUGUST 1985
44.212T ' I z t
Table I. Data for Primary Positive Reactant Ion at Various Electrical Field Gradients
wd=(EL)
Combining eq 6,8,and 12, the IMS resolution equation can be written as
,
potential, V
electric field, V/cm
drift time, ms
500 1000 1500 2000 2500
37.7 71.4 107 143 179 214
54.78 27.36 18.36 13.78 10.99 9.22
3000
If conditions are such that Table 11. Drift Times of Methyl Esters
w,
