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Anal. Chem. 1982, 5 4 , 2284-2289
Properties of the Transition from Normal to Steric Field-Flow Fractionation Marcus N. Myers and J. Calvin Glddlngs” Department of Chemistry, University of Utah, Salt Lake City, Utah 84 112
The relationship among selectlvlty, the separable mass range In fleld-flow fractionatlon (FFF), and the retention volume range, whose ultimate llmlt Is established by the so-called sterlc Inversion, Is discussed. Following this, the properties of normal and sterlc FFF are summarized. The steric foidback is then described and equations are obtalned for both the retentlon ratlo and the particle dlameter at whlch foldback or Inversion occurs. Equatlons are derived relating separatlon range and selectlvlty to condltlons at or near the foldback polnt. By use of the derived equations, plots are generated illustratlng the behavior of FFF systems over the total range of interest, from conditions of no retention to those of the normal FFF regime, the transltlon to steric condltlons, and finally the fully developed condltlons of steric FFF. The plots are applied to both Sedimentation and flow FFF and illustrate particle overlap and separatlon by fleld variations, along wlth shlfts in retention curves and sterlc Inversion points by changes in fleld strength, denslty, and channel thlckness. The plots also show how selectlvlty varles over the entlre range covered by sedimentatlon and flow FFF.
Field-flow fractionation (FFF) shows evidence of being a method of extraordinary versatility (1). Besides its applicability to macromolecules and particles of many different natural and synthetic origins found in both aqueous and nonaqueous media, FFF has shown applicability over an enormous mass range. The experimental range realized to date has a lower extremum of -lo3 molecular weight and an upper extremum of ~ 1 in effective 0 ~ molecular ~ weight, the latter corresponding to a particle of -100 hm diameter. The 1015-foldmass range between these extremes can apparently be utilized in its entirety for separation. However, such a broad range can obviously not be covered continuously in a single experiment sweep. First of all, to maintain high selectivity over even moderate mass ranges requires a large retention volume range in which to elute the separated components (2). High selectivity maintained over, say, a W6-fold mass range would require an elution volume equal to many thousands of column void vo$mes, which cannot be practically realized. Furthermore, increasing particle size does not lead indefinitely to increasing retention because of the onset of steric effects and the ultimate inversion of elution order. The finite retention volume a t which inversion occurs marks an upper retention volume limit beyond which, ideally, particle elution will not occur. However, this limit is typically from lo2to lo3channel void volumes, which provides an enormous retention volume range in which to effect separation. The precise value of the limit depends on experimental conditions, as will be shown later. Various strategies can be used to optimize separations within the large but finite retention volume range available. These strategies involve primarily the manipulation of field strength, in part through field programming, along with choices of flow conditions, carrier liquid, channel dimensions, etc. While the present work will provide background useful
for optimization strategy, we will not deal generally with optimization as such. By contrast, the purpose of this paper is to provide the first general focus on the steric inversion point, trends existing on either side of the inversion, and the corresponding transition in various properties. A number of practical questions will be dealt with, such as the loss in selectivity at the inversion point and the means for shifting the transition from one point to another.
THEORY Range and Selectivity. Since the particle mass range subject to continuous fractionation is interrupted by the steric inversion, it is useful for perspective to establish how this range depends on the sterically limited elution volume range. The brief treatment below is valid for all forms of FFF along with exclusion chromatography, hydrodynamic chromatography, etc. The selectivity S has been defined as the absolute value of the ratio of the fractional change in elution volume V , to the corresponding fractional change in particle molecular weight M (2, 3) S = Id log V,/d log MI (1) Depending on elution order, the term between bars can have a positive (normal FFF) or negative (steric FFF, exclusion chromatography) value. It is useful to define the more specific term SA,which can assume either sign S+ = d log V,/d log M (2) Clearly, S = For S , constant eq 2 integrates to
(M,/MJ = (Vr2/VrJ1’’*
(3)
where subscripts “1”and “2” represent the lower and upper extrema, respectively, of molecular weight and the corresponding retention volume values. We note that for a given elution volume range V,,/V,, (or its reciprical, if larger), the molecular weight range M z / M l is inversely related to SA. Thus, for example, a V,,/V,, of lo2 would yield a M 2 / M l of lo2for sedimentation FFF for which S* approaches unity and IO6 for flow FFF for which S , is -1/3. With field programming, of course, the “practical” range of M2/Ml can be greatly extended. The selectivity defined by eq 1 describes the ability of the system to sort out particles on the basis of mass and can be referred to as mass selectivity. If one has a primary focus on particle diameter, or electrical charge density, as the basis of separation, it is possible to use auxiliary definitions, for example, diameter selectivity Sd(or, more loosely, size selectivity) S d = (d log Vr/d log d ( (4)
For particles of fixed shape, where M shown that S d = 3s
a
d3, it can be readily (5)
Normal FFF. In normal (or “Brownian”) FFF, the sample is forced toward the wall of the channel by the imposed field
0003-2700/82/0354-2284$01.25/00 1982 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
to form a layer of unique thickness, which thickness depends upon the interaction of the sample with the field and the opposing diffusion or Brownian motion of the sample away from the wall. These opposing processes result in a steadystate exponential layer distribution of sample near the channel wall c := co exp(-x/l)
Inversm (fold-back ) pOl"1
Normal FFP elurion
0
I 1
I
0
0\ Steric FFF elurion
/
(6)
where co is the wall concentration, x is the distance from the wall ( x = 0 a t the wall), and 1 is essentially the mean layer thickness of the solute. As the solute zones are swept down the channel, those with larger I values penetrate faster moving streamlines and are swept toward the end of the channel a t a higher rate. In the case of an exponential distribution and a parabolic velocity profile confined between infinite parallel plates, the expression for the retention ratio R (void volume Vo/retention volume V,) is found to be R = 6h[coth 1 / 2 1 - 2x1 (7) where X = l/w and w is the thickness of width of the channel. At small values of h (for highly retained1 solutes)
R = 6X
(8) Subtechniques of FFF. A variety of Gelds and gradients may be used to implemlent FFF ( 4 ) . Those utilized in this laboratory have been thermal gradients (thermal FFF), centrifugal or gravitational forces (sedimentation FFF),cross-flow (flow FFF), and electrical fields (electrical FFF). A different expression for X is required in each case since the interaction of the field with the particles operates om a different mechanism. Studies to date in thermal FFF have all been with polymeric species of small size and molecular weight, with operation well below the onset of a significant steric effect; hence we will not elaborate on this method here. Similarly, due to lack of relevant experimental results, we will not discuss electrical FFF, although there is no intrinsic reason to exclude charged particlen large enough to fall in the steric region. In sedimentation FFF, the expression for h becomes (4) 6kT A = (9) a Ap w Gd where k is Boltzmann's constant, T is the temperature, Ap is the density difference between particle and carrier, and G is the gravitational acceleration. Parameter d represents the diameter of spheres; for nonspherical particles d is the diameter of a sphere of equal volume. In the case of flow FFF, in which a cross-flow of carrier is established across the channel to force particles into unique layers, the expression for h is kT A=3aqw Ud where 17 is the viscosity of the carrier and U is the cross-flow velocity. For nonspherical particles d is the Stokes diameter, which is the diameter of a sphere of equal diffusivity. The previous two equations can be written in the form h = &/d" (11) where n is 3 for sedimentation FFF and unity for flow FFF. Using a combination of eq 8, the definition of R as V o /V,, and eq 4,we get a limiting form for size selectivity as a function of n only
Sd = n (12) and, by eq 5 , a similar form of normal (mass) selectivity S = n/3
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(13) The latter expression shows that S for sedimentation FFF
I
O
vo
RETENTON VOLUME, Vr-+
4 -
I
elutmn
I beyond
I this p o m Figure 1. Illustration of increasing particle size sequence in normal FFF and its foldback into an opposite steric FFF sequence. This gives two overlapping particle distributions. No particles should emerge beyond the inversion point.
approaches a limiting value of unity and for flow FFF the value 1/3 (3). Steric FFF. Normally, the larger particles interact most strongly with the applied field and form the most highly compressed layers. They are retained longer than smaller particles. However, as the particle diameter becomes appreciable compared with 1, the mechanism of migration undergoes a transition from that of conventional FFF to that of steric FFF. Steric FFF predominates when the particle radius a generally exceeds 1 so that the protrusion of the particle out into the flow stream is determined more by the particle's size than by its Brownian motion. Under these circumstances the movement of the particle down the channel is determined largely by effective particle diameter d (5). The larger particles will be carried in the faster moving streamlines further from the wall and will elute from the system before the smaller particles, a trend just opposite to that observed in normal FFF. It has been shown that a modification of eq 4 for the steric effect gives the following expression for R (6)
R = 6 y ( a - a')
1 - 201 -+ 6h(1 - 2 ~ )coth 2h 1- 2 a (14)
where 01 = a / w = d/2w and y is a dimensionless factor of order unity which allows for certain complications in steric migration. Under normal circumstances h and 01 are small, in which case a greatly simplified expression for R, corresponding to eq 2 but with a sterically controlled term added, can be used
R = 6701 + 6X
(15)
Steric Foldback a n d Maximum Retention. As noted above, retention volume increases with particle diameter until steric effects dominate, at which transition point there is a foldback in elution order, with still larger particles emerging earlier again. This phenomenon is illustrated in Figure 1. Clearly, this situation leads to an upper limit in retention volume beyond which no particles should theoretically emerge (7). This upper limit corresponds to a minimum value of R, termed Ri, which we shall now express in terms of the parameters used above. For this purpose we use the simplified eq 15 because at the inversion of foldback point all relevant terms (i.e., R , a , A) are small and the higher order terms are negligible. The minimum in R is obtained by application of the condition dRldd = 0 to eq 15. An equivalent condition was applied by Martin and Jaulmes assuming y = 1 (7). For our purposes, a and X are written in their d-dependent forms, a = d/2w and X = yO/dn,respectively. The value of y will be assumed independent of d since we presently lack better information. We consequently get the general inversion-point values
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
and Ri = 3(n
+ l)(y/n~)~i(~+~)(2Xo)~i(~+~) (17)
For sedimentation FFF, where n = 3 and the combination of eq 9 and 11 yields Xo = GkT/rApwG
(18)
di = (36kT/ryApG)li4
(19)
Ri = 4ydi/w
(20)
we obtain and Flow FFF is treated by combining eq 10 and 11, yielding Xo = kT/377Uw
(21)
when this and n = 1 are substituted into eq 16 and 17, we get
di = (2kT/3ryqU)'i2
(22)
and Ri
= 6ydi/w
(23)
The possible analytical potential of these equations should be noted. For sedimentationFFF the value of Ri, which should be experimentally observable, is a function of Ap, and hence should yield particle densities or even particle density distributions for complex particulate mixtures. Attempts to observe the steric inversion point, made difficult by the low value of Ri, will be reported in a later communication. Steric Foldback and Separation Range. On the basis of the equations above, we can derive explicit equations for the approximate mass range, M 2 / M l ,which can be handled along a single branch of normal FFF alone or steric FFF alone. We note that the maximum retention volume range, V,,/V,, of eq 3, is given approximately by l/Ri, thus yielding
(M,/Ml)
(l/WS
(24)
where we use S instead of S, because 1/Ri is always >1. Substituting S from eq 13 and Ri from eq 17 gives the approximate range
M 2 / M l N [3(n +
(25)
which, for example, takes the following form for sedimentation FFF
M 2 / M l N ( ~ / 4 y ) ( r y A p G / 3 6 k T ) ~ i ~ (26) We note that these equations understate the practical mass range severalfold because they assume maximum selectivity over the entire range of retention. The reduced selectivity near R = 1 and R = Ri will actually provide a considerable gain in the mass range. Steric Foldback and Selectivity. It is clear that at the steric foldback point, retention volume is constant for small increments in particle diameter, i.e., dV,/dd = 0. Consequently, the selectivities S or S d go to zero, as best seen by examining eq 4 or 5. Actual selectivity curves, to be shown later, can be calculated by combining eq 14,11,4,and 5, along with the definition R = V'/ V, and the appropriate expressions for A,., Selectivity in the vicinity of the steric inversion point can be obtained from the limiting expressions below. If we expand retention ratio R in a Taylor's series around the steric inversion point and discard terms of third order and higher, we get R = Ri
+ B(Ad)2
(27)
where 0 = 1/2(d2R/dd2)i and Ad = d - di. The first-order term
d log R d log X
s = ~d log X d log M
(34)
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13. NOVEMBER 1982 2287
I
10,
I
PARTICLE OUMEIER. d (pm)
Flgure 3. Variation of retention ratio R with din sedimentation FFF wiih parameters w = 0.254 mm. Ap = 0.5 glcms. T = 298 K. y = 0.7, and G = 1000 gravities.
I
PARTICLE DMMETBR, d (Pm)
Flgure 5. Plot of retention ratio R against particle diameter d for eight different field strengths expressed in gravities. Parameters are the same as those in Figure 3 except Ap = 1.0 rather than 0.5 g/cm3.
shifts in R with field strength for the two populations will, in theory, provide particle distributions when fractograms a t different field strengths are acquired. Figure 5 illustrates how retention curves shift with field strength for the previously assumed sedimentation FFF system. These plots have employed a field strength range from lo5 gravities, corresponding to ultracentrifugal conditions, to 0.01 gravities, which can he approached in slowly rotating systems. Parameters other than field strength and density are the same as previously used, i.e., w = 0.254 mm, & = 1.0 g/cm3, and T = 298 K. Figure 5 shows that the minimum R value, R:, decreases with field strength as predicted by eq 20. The Ri range shown in the figure is -55, as expected from eq 20. At the high field strength extreme, Ri 0.001, the steric foldhack would not he expected until approximately 1000 (-1/0.001) void volumes had heen washed through the channel, which is a suhstantially greater elution volume than any so far observed. At the low field strength end, VJ V" reduces to approximately 18, which is well within the range of present observations a t a higher field strength. These curves encourage us to believe that the steric inversion phenomenon can he studied experimentally, especially a t low field strength. Another feature illustrated hy Figure 5 is that the particle diameter corresponding to inversion, di, potentially varies over a wide range, from -0.09 pm to -5 pm, depending on field strength. Again, this range is in accord with the equations, in this case eq 19. Figure 5 also illustrates that higher field strengths, by pushing down Ri and thus increasing the potential elution volume range, is capable of resolving a wider range of particles than low field strengths. This conclusion relates to eq 3, given the larger retention volume range V J V , , of high field strengths. Thus in Figure 5, particles over a diameter range of -20 (massrange -8000) can he resolved on the normal FFF branch a t lo5 gravities, whereas the diameter range is only 6 (mass range 220) a t 0.1 gravities. These values are roughly in accord with eq 26, hut somewhat larger because of the understatement inherent in eq 26. The foregoing results depend on the specific value, 1.0 g/cm3, of the assumed density difference Ap between the particles and the carrier. However, it is important to understand the effects of varying Ap as well as G, since Ap can vary over wide limits. On physical grounds we conclude that the effect of Ap is like the effect of field strength G, since the force on a particle is proportional to both. This is borne out hy the equations, e.g., eq l E and 19, which show that Ap and G always appear together in equivalent roles. Consequently, the family of curves in Figure 5 can he construed as repre-
-
FIELD (gmvllles)
-re 4. Changes in retention ratio R of two dmerent sized particles with changes in field strength. At 1000 gravities me particles elute together, but at most other field strengths they are well resolved. Parameters are the same as those of Figure 3.
One of the negative features of the steric inversion or foldhack is that two particles of different sizes, one undergoing normal FFF migration and the other steric migration, can elute together, displaying no resolution. This point, noted in Figure 1,is more precisely illustrated hy Figure 3, which is a plot of R vs. particle diameter d for a specific sedimentation FFF system (w = 0.254 mm, Ap = 0.5 g/cm3, y = 0.7, T = 298 K) operated a t a field strength of lo00 gravities. For every value of the retention ratio R (except at the point of minimum R and below), there are theoretically two corresponding particle diameters. In other words, the curve is double valued in d. The horizontal arrow shows this for R = 0.0065, at which point particles with d = 0.2 pm and 0.75 pm both elute. Should one encounter nonresolved particles of interest on both sides of the steric inversion, a single step can lead to their resolution: a change in field strength. This is illustrated by Figure 4,which follows the changes in R for the 0.2 pm and 0.75 pm particles noted above as a function of field strength. As the field strength is moved away from lo00 gravities, which is the value for which the two particles emerge together, resolution rapidly increases. For extremely broad continuous particle distributions that span across the steric transition, there will generally he a particle of another size emerging with a given particle no matter what the field strength. However, in some instances the shift in steric inversion point with field strength can he utilized to transfer all particles into a single branch of Figure 3. For overlapping populations, the different magnitude of
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ANALYTICAL CHEMISTRY, VOL.
54, NO. 13, NOVEMBER 1982
0.m1
awl
0.01
0.1
1
10
PARTICLE DVLMETER. d (pm)
PARTICLB DMMBTBR. d (pm)
Effect of channel thickness won retention C U N ~ Sin sedimentation FFF. Parameters are 0 = I O 3 gravities. Ap = 0.5 glans and T = 298 K. Flgu~e6.
Figure 8. Superposition of retention and selectkiiy curves for sedimentation FFF. Parameters are w = 0.254 mm, Ap = 0.5 glcm'. G = 10' gravities. and T = 298 K. ,_o s,
I ' """'I _______________ ~~
' "' ---------
PhRTlCLE DUMETBR. d 1pm1
, "O 0.m1
0.01
ai
I
IO
PARTICLE DL4MBTER. d (em)
Retention curves for flow FFF at different cross-flow velocities. Parameters are w = 0.254 mm. T = 298 K. and = Flgure 7. P.
senting Ap variations as well as G variations. To allow for Ap we simply transform the number of gravities to the product of gravities and Ap expressed in g/cm3. Figure 6 shows that channel thickness w also has an effect on the retention curves. The figure shows that a given change in w has as large an effect on the steric branch as on the normal FFF branch, as would he predicted hy eq 15 (both a and X are inversely proportional to w). This is in contrast to the effect8 of G and Ap. illustrated in the previous figures, where there is convergence to a common steric curve. We also note the R, is inversely related to w and that di is independent of w,in accordance with eq 20 and 19, respectively. The figure illustrates the fact that channels with the largest w values have the largest separation range. Our analysis suggests that flow FFF would he expected to show the same general features of retention and steric transition as sedimentation FFF. Figure 7 bears this out. This figure is comparable to Figure 5 for sedimentation FFF, showing retention curves a t different field strengths. In the case of flow FFF, the field strength is represented simply hy U, the cross-flow velocity. The parameters we assume are w = 0.254 mm, T = 298 K,and q = lo-*P (approximately valid for water). While the general features of Figures 5 and 7 are the same, distinct differences exist which reflect the different "fields" employed. First of all, the limiting slope of the normal FFF branch (left of the minimum) is unity, which is three times less than that for sedimentation FFF. This increases range
Flgun 8. Selechrfty on a linear scale as a function of particle dmmeter (logarithmic scale)at two field strengths for sedimentation FFF. Parameters are w = 0.254 mm. Ap = 0.5 g/cm3. and T = 298 K.
and reduces selectivity, as noted earlier. Also, Ri and diare clearly more sensitive to changes in field strength than in sedimentation FFF, in agreement with eq 22 and 23. We now return to the subject of selectivity in view of its importance in both the separation and characterization of particles. Figure 8 shows a selectivity plot superimposed on a retention ratio plot for sedimentation FFF. As expected, S approaches unity along the normal FFF branch and onethird along the steric FFF branch of retention. It plunges to zero a t the steric inversion point, reflecting the lack of separation at this point due to the oppositely directed trends of normal and steric FFF. Fortunately, the loss of resolution around this point does not extend over a very large range (see eq 33). Thus any given separation problem hindered by this loss could he carried out by shifting the inversion point by one of the mechanisms mentioned earlier, especially hy changes in field strength. Figure 8 also shows that the selectivity drops to zero for very small particles, for which R approaches unity. This matter was discussed earlier. Clearly the best place to work from a selectivity point of view is in the middle of the normal FFF range where S approaches its maximum value of unity. However, greater separation speed may he realized hy shifting (through changes in field strength) the inversion point somewhat closer to the particle range of interest. The decrease in S will he compensated by the decreased layer thickness, 1, which leads to increased efficiency and speed (8). Figure 9 shows selectivity curves for two different values of field strength in sedimentation field-flow fractionation. The ordinate has been converted from a logarithmic to a linear scale since S varies only from zero to unity. In this way, the considerable superiority of normal sedimentation FFF over
Anal. Chem. 1982, 5 4 , 2289-2291
1 , -
I
0.1
P.4RTICLE DIAMETER, d ( p m )
Flgure 10. Selectivity vs. particle diameter for flow FFF. Parameters P. = 0.254 mm, T = 298 K, and 7 =
are w
steric FFF is clearly illustrated. The figure also shows the greater range over which high selectivity values extend for the higher field strength. Figure 10 shows corresponding linear selectivity plots for flow FFF. Notable is the fact that the limiting selectivity for normal flow FFF is the same as for steric FFF. The wider range over which high selectivity values are maintained relative to sedimentation FFF is apparent.
here some limitations in our results which stem from uncertainties in the steric branch of FFF. While steric effects are described by fairly simple theoretical equations, such as the first term on the right of both eq 14 and 15, factor y conceals some fairly complicated hydrodynamic phenomena which are not fully quantified (9). For example, y has been observed to increase with flow velocity, which means that the right hand side of the foregoing curves would all shift slightly with velocity. There is probably a slight size dependence to y as well. Furthermore, the magnitude of y is not known for various kinds of nonspherical particles. Despite the above limitations, we believe that the above model provides a simple and effective treatment of FFF over a very broad range. We expect the variations in y to be quite small relative to the enormous range of the other parameters covered. Therefore the model and the subsequent results are expected to provide a useful treatment of FFF, not only adequate for most present applications but also an effective guide for future refinements.
LITERATURE CITED Giddlngs, J. C. Anal. Chem. 1981, 5 3 , 1170. Giddlngs, J. C.; Yoon, Y. H.; Myers, M. N. Anal. Chem. 1975, 47, 126. Giddings, J. C. Pure Appl. Chem. 1979, 51, 1459. Giddings, J. C.; Myers, M. N.; Caldwell, K. D.;Fisher, S. R. "Methods of Biochemical Analysis": D. Giick, D., Ed.; Wiley: New York, 1960; p 79. Giddings, J. C.; Myers, M. N. S e p . Sci. Technol. 1978, 13, 637. Glddings, J. C. S e p . Sci. Technol. 1978, 13, 241. Martin, M.; Jauimes, A. Sep. Sci. Techno/. 1981, 16, 691. Glddings, J. C. S e p . Sci. 1973, 8 , 567. Caidweil, K. D.;Nguyen, T. T.; Myers, M. N.: Giddings, J. C. Sep. Scl. Technol. 1979, 14, 935.
CONCLUSIONS The foregoing equations and plots provide fundamental information on the steric inversion and trends extant on either side of the inversion point. The study should serve as a useful background source for experimentalists and others dealing with conditions near those of the steric transition. This work is clearly required as one of the important bases for any complete optimization studies in FFF. The results of this paper are expected to be fairly accurate over the range dominated by normal FFF. However, we note
2289
RECEIVED for review July 6,1982. Accepted August 9, 1982. This material is based upon work supported by the National Science Foundation under Grant No. CHE 79-19879.
Discrimination of Isomers of Xylene by Resonance Enhanced Two-Photon Ionization David M. Lubman* and Me1 N. Kronick Quanta-Ray, h e . , 1.250 Charleston Road, Mountain View, California 94043
Resonant two-photon lonlratlon Is shown to be a sensitive technlque capable of dlscriminatlng isomers of xylene in air at atmospheric pressure. I n addltlon, this technlque can be combined with an lon-mobility spectrometer (IMS) In whlch the abillty to monlitor xylene at a concentration on the order of several parts per billion can be demonstrated. The Isomers of xylene cannot be dlscrlmlnated on the basis of their spectroscopy at the normal elevated temperature of an IMS. However, It Is shown that by proper selectlon of the temperature the characterlstic lonlration spectra of the isomers may be observed.
Multiphoton ionization (MPI) has been shown to be valuable as a sensitive and selective means of detection for chemical analysis. High sensitivity is achieved through ef-
ficient ionization (1-4) and the ability to detect ions with high efficiency. Spectral selectivity is provided by the use of a tunable dye laser (5-13). If the laser source is tuned to an allowed n-photon transition in a MPI process, ionization is greatly enhanced. This is referred to as REMPI, i.e., resonance enhanced multiphoton ionization. In the case of REMPI, ionization occurs via a real intermediate state. Since the density of states above the lowest energy state populated is usually quite high, subsequent absorptions are resonant or nearly resonant. In resonant two-photon ionization (R2PI) the first photon is absorbed by a real state while the second photon ionizes the molecule. The spectrum that results reflects the one-photon absorption spectrum of that real state and can often be used to identify a molecule uniquely. Resonant two-photon ionization has been demonstrated as a technique capable of monitoring polyaromatic molecules at atmospheric pressure in real time (2,14). Other methods such
0003-2700/82/0354-2289$01.25/00 1982 American Chemical Society
