1540
Anal. Chem. 1982, 54, 1540-1546 Pretorlus, V.; Smuts, T. W. Anal. Chem. 1966, 38, 274. Ark, R. Proc. R . SOC.London, Ser. A 1959, 252, 538. Giddings, J. C.; Manwaring, W. A.; Myers, M. N. Science 1968, 754, 146. DOUG,F.; Guiochon, G. S e p . Sci. 1970, 5 , 197. Golay, M. J. E. ”Gas Chromatography”; Desty, D. H., Ed., Butterworths: London, 1958; p 36. James, M. R.; Giddings, J. C.; Eyrlng, H. J. Phys. Chem. 1964, 68, 1725. Khan, M. A. “Gas Chromatography . . 1962”; Van Swaay, M., Ed.; Butterworths: London, 1962; p 3. Martin, M.; Blu, G.; Guiochon, G. J . Chromafogr. Sci. 1973, 1 7 , 641. Stewart, 0. H.; Seager, S.L.; Giddings, J. C. Anal. Chem. 1959, 3 7 , 1738. Martin, M.; Guiochon, G. to be submltted for pubilcatlon. Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”; Wiiey: New York, 1960; Chapters 5 and 6. Tlchacek, L. J.; Barkelew, C. H.; Baron, T. AIChE‘!. 1957, 3, 439. Sherwood, T. K.; Plgford, R. L.; Wilke, C. R. Mass Transfer”; McGraw-Hill Kogakusha: Tokyo, 1975; Chapter 4. Page, F.; Corcoran, W. H.; Schllnger, W. G.; Sage, B. H. Ind. Eng. Chem. 1952, 4 4 , 419. Page, F.; Schlinger, W. G.; Breaux, D. K.; Sage, B. H. Ind. Eng. Chem. 1952, 4 4 , 424. Schllnger, W. G.; Berry, V. J.; Mason, J. L.; Sage, B. H. I n d . Eng. Chem. 1953, 45, 662. Opfeli, J. €5.; Sage, B. H. Adv. Chem. Eng. 1956, 7 , 241. Sleicher, C. A. Trans. ASME 1958, 80. 693. Quarmby, A.; Anand, R. K. J. fluid Mech. 1969, 38, 433. Davies, J. T. “Turbulence Phenomena”; Academic Press: New York, 1972; Chapter 2.
(23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39)
Taylor, G. Proc. R. SOC.London, Ser. A 1954, 233, 446. Levensplel, 0. Ind. Eng. Chem. 1958, 5 0 , 343. Hofmann, H. Chem. Eng. Sci. 1961, 74, 193. Bischoff, K. B.; Levenspiei, 0. Chem. Eng. Sci. 1962, 17, 257. Levensplei, 0.; Blschoff, K. B. Adv. Chem. Eng. 1963, 4 , 95. Dymond, J. H.; Smlth, E. B. “The Virial Coefficients of Gases”; Clarendon Press: Oxford, 1969; p 36. Reld, R. C.; Prausnitz, J. M.; Sherwocd, T. K. “The Properties of Gases and Llquids”, 3rd ed.; McGraw-Hili: New York 1977; Chapter 9. Fuiier, E. N.; Schettler, P. D.; Glddings, J. C. Ind. Eng. Chem. 1988, 58, 18. Wiike, C. R.; Chang, P. AIChE J. 1955, 7 , 264. Martln, M.; Eon, C.; Guiochon, G. J. Chromafogr. 1975, 708, 229. Gaspar, G.; Annino, R.;Vidai-Madjar, C.; Gulochon, G. Anal. Chem. 1976, 50, 1512. Glddings, J. C. Anal. Chem. 1984, 3 6 , 1170. Schwartz, R. D.; Brasseaux, D. J.; Mathews, R. G. Anal. Chem. 1986, 38, 303. Vidal-Madjar, C.; Guiochon, G. J. Phys. Chem. 1987. 7 7 , 4031. Schettler, P. D.; Elkelberger, M.; Glddlngs, J. C. Anal. Chem. 1987, 39, 146. Desty, D. H.; Goldup, A.; Luckhurst, G. P.; Swanton, W. T. I n ”Gas chromatography”; Van Swaay, M., Ed.; Butterworths: London, 1962; p 87. Sie, S. T.; Rijnders, G. W. A. Anal. Chim. Acta 1967, 38, 31.
RECEIVED for review February 2,1982. Accepted April 7,1982. Presented at the 13th International Symposium on Chromatography, Cannes, France, June 30-July 4, 1980.
Mechanistic Interpretations and Simulations of Induced Peaks in Liquid Chromatography John J. Stranahan and Stanley
N. Demlng”
DepaHment of Chemistry, University of Houston, Houston, Texas 77004
A general model that does not depend upon a specific retention mechanism Is proposed to explain the appearance of anomalous peaks In liquid chromatography. The model Is then applled to reversed-phase Ion-Interaction (ion-pair) chromatography to account for induced peaks observed In real systems.
“Ghost peaks” ( I ) , “vacancy peaks” (2-5), split peaks (3, 6-8), and other types of induced peaks (6) often appear in liquid chromatograms when a multicomponent eluent is used or when the sample is dissolved in a solution different from the mobile p h e . Induced peaks have been observed in steric exclusion chromatography (1, 9, l o ) , in normal phase chromatography ( 4 , 5 ) ,and in reversed-phase liquid chromatography with both isocratic elution (11-13) and gradient elution (14). Reasons given for the occurrence of induced peaks include solvent displacement (1, 12), preferential solvation (1,9, IO),ion interaction on the stationary phase ( I I ) , solvent demixing (14),preferential evaporation of a component of the sample ( l ) slow , or incomplete mixing of the sample solvent (7),local changes in mobile phase moderator concentrations caused by injection of the sample (4), solvophobic interactions in the mobile phase (12),competing distribution processes (13), and the presence of impurities (6). The intent of this paper is to present a unifying approach to the explanation of many of these seemingly diverse phenomena.
THEORY The basis of the present work is the assumption that not only is the distribution of the sample affected by the composition of the mobile and stationary phases, but the distributions of the mobile phase components are also affected by t h e local presence of t h e sample (11). By a simple redefinition of the “sample”, the work can be extended to cover the interactions of eluent components with each other. Figure 1 is a schematic representation of the phases in a liquid chromatographic system. The large shaded region (L) represents the bulk liquid (mobile) phase; in this work, it is assumed that the bulk liquid phase contains more than one component. It is also assumed that each component J of the bulk liquid phase and each component I of the sample is adsorbed onto the stationary phase according to a steady-state equilibrium distribution quotient, Qjor Qi (15). The smaller shaded region (A) below the bulk liquid phase represents this adsorbed (stationary) phase. The black region in Figure 1 indicates the location of an injected sample (I) that will be distributed between the stationary and mobile phases. The injection end of the column is on the left; the sample and the mobile phase move from left to right with time. Figure 2 is a schematic representation of one of the effects a sample can have on the distribution of one of the eluent components. In the diagram, an upward deviation from the top of the L region represents an increased concentration (or excess) of the component of interest above its steady-state equilibrium value; a downward deviation from the top of L indicates a decreased concentration (or deficiency) of the
0003-2700/82/0354-1540$01.25/00 1982 American Chemlcal Society
ANALYTICAL CHEMISTRY, VOL. 54. NO. 9, AUGUST 1982
Li
....................................... ..................... : : : .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ...............
ti
tIm). The upper two chromatogram show 20-pL injections of 5 mM sodium octanesulfonate, which under these conditions elutes slower than EIPA. The middle chromatogram is a UV trace and shows a large deficiency in EIPA eluting at 3.4 min followed by an excess of EIPA at 5.0 min. Similar chromatograms have been reported previously (11, 13, 17,18). The upper chromatogram in Figure 8 is a CAP trace and shows a negative peak at 3.4 min which has the same explanation as the negative peak at 3.4 min in the UV trace just below. The negative peak at 5.0 min on the CAP trace corresponds to the elution of octanesulfonate whose response is downward on the CAP trace; however, the octanesulfonate coelutes with an excess of EIPA which diminishes the magnitude of this negative peak. Thus, Figure 8 shows the same elution proflie as the right side of Figure 3 for a sample that elutes slower than the IIR. Note that in each of Figures 6-8, an IIR deficiency peak elutes first, followed by an IIR excess peak. Simulation of IIR Induced Peaks. If it is assumed that the major interaction of a charged solute with an oppositely charged IIR occurs in the adsorbed phase (11,19),then it can be shown (20) that Qi
= exp(80i + PI,xja?
TIME
Flgure B. Simulated chromatogramsshowing the results of injecting 5 units of a charged sample component I into a mobile phase containing 2 unks/tube of an oppositely charged component ?1 (IIR): (soli line) IIR; (dotted line) sample. Model parameters for eq 4 and 5: PS = -1.75, 81, = 1.6, = 0.20, Po, = -1.4, P I , 1.6, @jil = 0.22.
teraction chromatography. After a discrete transfer, the distribution quotients of I and J (Qi and Qj) are approximated from eq 4 and 5 using the current, bulk liquid phase concentrations of I and J (til and cjl). The two phases are then “equilibrated”. New equilibrium concentrations of I and J in the bulk liquid phase are then obtained from the previously calculated distribution quotients Qi
(2)
where Qi is the distribution quotient of the charged solute I, Bo, is a parameter that includes several constant terms, &, is a parameter that is a measure of the interaction between adsorbed I and the IIR, and xja is the mole fraction of IIR (eluent component J) in the adsorbed phase. The mole fraction of IIR in the adsorbed phase can be related to the concentration of IIR in the bulk liquid phase by a Langmuir adsorption isotherm (16)
(3) where cjl is the bulk liquid phase concentration of IIR at adsorption equilibrium in mol/L, and /3g is a constant in mol/L (Pjl = 55.5 exp[AGo/RT], where AGO is the Gibbs free energy of adsorption at infinite dilution, R is the gas constant, and T is the temperature in K). Although the Langmuir adsorption isotherm is strictly valid only under ideal surfactant behavior, it has been found to adequately describe the adsorption of many surfadants in real systems (16). Substituting eq 3 in eq 2 gives (20)
8i = exdP0, + Pli[cjl/(cjl + Pj1)121
=I
P
(4)
A quantitative refinement i s now made to the basic ioninteraction model of Bidlingmeyer et al. (11): not only does the IIR cause a change in the distribution quotient of the solute (see eq 2) but the solute also causes a local change in the distribution quotient of the IIR. Therefore, the distribution quotient of either a charged solute or a charged IIR can be described by a mathematical function involving the concentration of the other charged component. Thus, the distribution quotient for the IIR can be written as eq 4 with i’s and j’s interchanged:
Equations 4 and 5 can be incorporated into the computer simulation algorithm to simulate induced peaks in ion-in-
= Cia/Cil
(6)
and
and from the mass balance equations
ni = nia + nil
(8)
+ nj1
(9)
and
nj = nja
where ni and nj are the total numbers of moles of I and J, respectively, and nia,nil, nja,and njl are the numbers of moles of componentsI and J in the adsorbed and bulk liquid phases. Equations 4 and 5 are then used to recalculate Qi and Qj from which improved concentration estimates are made. The process is iterated until constant equilibrium values are obtained. After equilibration, the next transfer is performed and the iterative process is repeated. Figure 9 was obtained by simulating the injection of a rapidly eluting charged solute into a mobile phase containing an oppositely charged IIR. The solid line represents the concentration of IIR as it elutes from the column; a deficiency in IIR elutes first, followed later by an excess of IIR. The dotted line represents the concentration of sample; the sample coelutes with the deficiency in IIR. This is the same elution profile shown on the left side of Figure 3 and in the real experiments in Figure 6 for a sample that elutes more rapidly than the IIR. The solid line in Figure 9 predicts a higher IIR base line between the deficiency and the excess of IIR; this slightly raised base line is evident between 2.8 and 3.3 min in the real chromatogram in the middle of Figure 6. Figure 10 is a simulation of an injection of a charged sample that elutes a t about the same rate as an oppositely charged IIR. The solid line (IIR) shows the elution of a large deficiency of IIR followed immediately by the elution of a large excess of IIR. The dotted line (sample) shows the leading portion of the sample coeluting with the large deficiency in IIR, and
ANALYTICAL CHEMISTRY, VOL. 54, NO. 9, AUGUST 1982 * 1545
C
Figure I O . Simulated chromatograms: pol= -2.9, conditions are as In Figur189.
!
I
2
3
TIME CRINUTEI)
TIME
PI = 0.23.
Other
Flgure 12. Chromatograms resulting from the injection of 20 pL of 0.1 M sodium octanesulfonate a specified number of seconds after injection of 10 pL of 2 mM aniline. Mobile phase: methanol-water (35:85), 1 mM HCI, no added IIR in rhe eluent. Downward spike on each chromatogram indicates Injection of sodium octanesulfonate.
71 -
TIME
Figure 11. Slmulated chromatograms: pol= -4.5, pw= 0.24. Other conditions are as in Flgure 9. the trailing portion coeluting with the excess of IIR. This is the same elution profile shown in the middle of Figure 3 and in the real experiments in Figure 7 for a sample that elutes at the same rate as the IIR. Figure 11 shows the results of a simulated injection of a charged solute that elutes more slowly than an oppositely charged IIR. The dotted line (sample) shows the sample coeluting with the excess of IIR. The solid line predicts a higher IIR base line between the deficiency and the excess of IIR; this slightly raised base line is evident between 4.0 and 4.7 min in the real chromatogram in Figure 8. Thus, Figure 10 shows the same elution profile as the right side of Figure 3 and the real chromatograms in Figure 8 for a sample that elutes slower than the IIR. Pulsed Injections af Oppositely Charged IIR. Figure 12 shows a set of real chromatograms obtained with a methanol-water (35:65) mobile phase, 1mM in HCl, with no added IIR in the eluent. The UV responses are shown for 10-pL injections of 2 mM aniline dissolved in the eluent, each followed by a later (post) injection of 20 p L of 0.1 M sodium octanesulfonate dissolved in the eluent. The sodium octanesulfonate is transparent to the UV detector. The times of the postinjections, in ijeconds after the injection of aniline, are shown on the chro~natograms. In the upper chromatogram, the more rapidly eluting sodium octanesulfonate was injected 29 s after the aniline and has just begun to overtake the aniline as it elutes from the column. As a result, the aniline is split into a large peak at 2.2 min and a small peak at 2.5 min. The larger peak corresponds to aniline that has not yet been overtaken by the octanesulfonate; the riimaller peak a t later retention time
T tNE
Figure 13. Simulated chromatograms showing the results of injecting 2 unlts of a charged component I followed by a postinjection of 100 units of an oppositely charged component J. Delay time (number of transfers) is indicated at the beginning of each chromatogram. Detector response is proportional to the concentration of component I only. Model parameters for eq 4 and 5: Po, = -1.4, p,, = 1.3, PI,= 0.22, 0 0 , = -2.8, 01, = 1.3, pi1 = 0.17. corresponds to aniline that has been overtaken and retarded by the octanesulfonate. The chromatograms in Figure 12 show an increase in the magnitude of the peak at longer retention time and a decrease in the magnitude of the peak at shorter retention time as the injection delay time is shortened; this occurs because a larger portion of the aniline is overtaken and retarded by the octanesulfonateas the delay time is shortened. Peak splitting of this type has been observed previously in a separation technique in which the IIR is injected onto the column in pulses rather than dissolved in the eluent (8). The chromatographic simulation algorithm and the ioninteraction model described in the previous section were used to generate the chromatograms shown in Figure 13. These chromatograms are simulations of peak splitting caused by the injection of a charged sample followed by the injection of an oppositely charged IIR. The simulated chromatograms are plots of the concentration of aniline as a function of tube number (time). The delay of the postinjection of IIR is indicated at the beginning of each chromatogram and corresponds to the number of transfers performed by the CSA before injection of IIR. Figure 13 shows that as postinjection delay time is decreased, there is an increase in the magnitude of the peak eluting at later retention time and a decrease in the magnitude of the earlier eluting peak. This behavior is
Anal. Chem. 1082, 54, 1546-1551
ACKNOWLEDGMENT We thank B. A. Bidlingmeyer,B. Sachok, and W. P. Price, Jr., for helpful discussions. LITERATURE CITED
TINE
Flgure 14. Simulated chromatograms showlng details of the second chromatogram from the top In Flgure 13: (solid line) component I; (dotted line) component J.
the same as that exhibited in the real chromatograms in Figure 12. Figure 14 shows a composite chromatogram of the concentrations of aniline and IIR for the simulation in Figure 13 with a 20 tube delay. The tall dotted peak in Figure 14 corresponds to the elution of IIR, and the two smaller peaks on either side correspond to a split aniline peak. The early eluting portion of aniline has not been overtaken by the IIR, while the later eluting portion of the aniline sample has been strongly retarded by the IIR. This type of splitting occurs only when the sample and IIR coelute. Thus, it can be avoided if conditions are adjusted so that the postinjected component is completely eluted from the column before the sample components of interest elute (8).
(1) Berek, D.; Bleha, T.; PevnB, Z. J . Chromatogr. Sci. 1978, 14, 560-563. (2) Rellley, Charles N.; Hlldebrand, Gary P.; Ashley, J. W. Anal. Chem. 1982, 34, 1198-1213. (3) Scott, R. P. W.; Scott, C. G.; Kucera, P. Anal. Chem. 1972, 4 4 , 100-1 04. (4) Slais, K.; Krejci, M. J . Chromatogr. 1974, 9 1 , 161-166. (5) Hendrlx, D. L.; Lee, R. E., Jr.; Baust, J. G. J. Chromatogr. 1981, 210. 45-53. (6) Keller, Roy A.; Glddings, J. Calvin J . Chromatogr. 1980, 3 , 205-220. (7) Tseng, Paul K.; Rogers, L. B. J . Chromatogr. Sci. 1978, 16, 436-438. (8) Stranahan, John J.; Deming, Stanley N.; Sachok, Bohdan J. Chromatwf. 1980, 202, 233-237. (9) Campos, A.; Borque, L.; Flgueruelo, J. E. J . Chromatogr. 1977, 740, 219-227. (10) Katlme, I.; Campos, A,; Rlvera, J. M. T. Eur. Polym. J . 1979, 75, 291-293. (11) Bldllngmeyer, 8. A.; Demlng, S. N.; Price, W. P., Jr.; Sachok, B.; Petrusek, M. J . Chromatogr. 1979, 186, 419-434. (12) McCormlck, R. M.; Karger, B. L. J . Chromatogr. 1980, 199, 259-273. (13) Denkert, M.; Hackzell, L.; Schlll, 0.;Sjijgren, E. J . Chromatogr. 1981, 218, 31-43. (14) Parrls, N. A. “Instrumental Liquid Chromatography”; Elsevler: Amsterdam, 1976; Chapter 12. . Ramette, Richard W. “Chemical Equlllbrium and Analysis”; AddisonWesley: Readlng, MA, 1981; Chapter 4. Rosen. Milton, J. “Surfactants and Interfacial Phenomena”; Wiley: New York, 1978; Chapter 2. Parrls, N. J. Liq. Chromatogr. 1980, 3 , 1743-1751. Su, S. Y.; Jurgenson, A,; Boiton, D.;Winefordner, J. D. Anal. Lett. 1981, 74, 1-6. Knox, J. H.; Hartwick, R. A. J . Chromatogr. 1981, 204, 3-21. Stranahan. John J.; Deming, Stanley N., unpublished work, Unlverslty of Houston, 1981.
RECE~VED for review March 10,1982. Accepted April 12,1982. This work was supported in part by a grant from Chevron Research Company.
Plasma Chromatography with Laser-Produced Ions David M. Lubman* and Me1 N. Kronlck Quanta-Ray, Inc., 1250 Charleston Road, Mountain Vlew, California 94043
Laser multiphoton lonlzation (MPI) is used to produce ions In an ion moblllty spectrometer. The Ions created are then separated by gaseous electrophoresis, Le., according to their moblllty In a drtft gas under the Influence of an applied electric field. The MPI process allows direct lonlzatlon of organic compounds with production of only one peak whlch is elther the molecular Ion or MH’. The problem of multiple peaks occurrlng due to the Ion-molecule process In plasma chromatography Is thus slgniflcantiy reduced. This technlque can provlde great sensitivity, Le., at least down to 1 ppb In the case of benzene. I n addltion, the laser wavelength can provlde an additional means of dlscrlmlnation of molecules In an Ion moblllty spectrometer.
We introduce a unique method for producing ions for plasma chromatography (PC). This technique involves using laser multiphoton ionization to ionize molecules directly under atmospheric conditions in a commercial ion mobility spectrometer. 0003-2700/82/0354-1546$01.25/0
There are many reviews of the theory of plasma chromatography (1-15). In conventional plasma chromatography, ions are initially produced in a carrier gas by a 63Ni@-decay source. These ions initiate a sequence of ion-molecule reactions that eventually yield a few molecular ions which then undergo ion-molecule reactions with the trace compound to form the ions measured in a drift tube. In the drift region the ions are moved through a column of gas by an electric field and separated according to their mobilities. Nitrogen is usually used as the drift gas to prevent further ion-molecule reactions. Eventually the ions diffuse to a detector where either positive or negative ions are detected. The output of the detector is in the form of current as a function of time. An ion mobility spectrum is thus obtained which fingerprints molecules in a manner similar to gas chromatography. Since the drift time of the ions is in the millisecond regime, the separation and detection can be performed in real time. In addition, N2 can serve as a universal column thus alleviating the problem of column choice inherent in gas chromatography. The initial creation of ions through the use of the ionmolecule reaction technique often produces data difficult to 0 1982 American Chemlcal Society
