Anal. Chem. 1990, 62, 217-220 (5) Pirkle, W. H.; Pochapsky, T. C. J. Am. Chem. Soc. 1988, 7986, 708, 5627-28. (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22)
Feibush, B.; Oil-Av, E.; Tamari, T. perkin Tf8nS. 2 1972, 1197-1203. Lochmuller, C. H.; Souter, R. W. J. Chromatogr. 1975, 88, 41-54. Smolkova-Keulemansova, E. J. Chromatogr. 1882, 257, 17-34. Smolkova-Keulemansova, E.; Kralova, H.; Krysl. S.; Feitl, L. J. Chrotn8tOgr. 1982, 247, 3-8. Smolkova-Keulemansova, E.; Feltl, L.; Krysl, S. J. Inclusion Phenom. 1985. 3. 183-196. Koscielskl, T.; Sybllska, D.; Jurczak, J. J. Chromatogr. 1883, 280, 13 1- 134. Konig, W. A.; Lutz, S.; Mischnick-Lubbecke, P.; Brassat, B.; Wenz, G. J. Chromatogr. 1888, 447, 193-197. Khlg, W. A.; Lutz, S.; Wenz, 0.; von der Bey, E. HRC CC,J . High Resolut . Chromatogr Chromatogr Commun 1988, 7 7 , 506. Schurig, V.; Nowotny, H.-P. J. Chromatogr. 1988, 447, 155-163. Armstrong. D. W. PMsburgh Conference Abshect Book; 1989, 001. Daffe, V.; Fastrez, J. J. am. Chem. SOC. 1880. 702, 3601-3607. Croff, A. P.; Bartsch, R. A. Tetrahedron 1983, 39, 1417-1474. Ptha, J.: Ptha, J. J. Ph8rm. Sci. 1985, 74, 987-990. Plha, J.; Rao, C. T.; Lindberg, B.; Seffers, P., submitted for publication in Carbohydr Res. Bouche, J.; Verzele, M. J. Gas Chromatogr. 1888, 8 , 501-505. Hinze. W. L. Sep. Purif. Methods 1981, 70, 159-237. Armstrong, D. W.: DeMond, W. J. chfOm8togf. Sci. 1884, 22, 411-415.
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(23) Armstrong, D. W.; Ward, T. J.; Armstrong, R. D.; Beesley, T. E. Science 1988, 232,1132-1134. (24) Watabe, K.; Charles, R.; GII-Av, E. Angew. Chem. 1989, 707, 195-197. (25) Schurig, V.; Ossig, A.; Link, R. Angew. Chem. 1989, 701, 197-200.
Daniel W. Armstrong* Weiyong Li Department of Chemistry University of Missouri-Rolla Rolla, Missouri 65401
Josef Pitha National Institutes of Health NIA/GRC Baltimore, Maryland 21224 RECEIVED for review July 13,1989. Accepted October 30,1989. Support of this work by the Department of Energy, Office of Basic Sciences (DE FG02 88ER13819) is gratefuly acknowledged.
Effect of a Difference of the Column Saturation Capacities for the Two Components of a Mixture on the Relative Intensities of the Displacement and Tag-Along Effects in Nonlinear Chromatography Sir: The displacement and tag-along effects have been predicted by computations based on the use of the semiideal model of nonlinear chromatography (1). They are often observed in preparative applications of liquid chromatography, when the column is overloaded, and have been reported in many recent contributions (2-4). These effects are due to the fact that the velocity associated to a certain concentration of one of the components (5)depends also on the concentration of the other components locally present (6). The intensity of the displacement and the tag-along effects controls the shape of the profiles of the individual component bands of a mixture when these bands are not completely resolved. It is important to note that the displacement effect also controls the profile of an elution band after it has been separated from the bands of the compounds eluted after it. The profile of this band may never recover from the consequences of its interaction with the later eluted bands (6, 7). It is therefore important to understand what are the parameters which determine the intensity of these two effects and their relative intensity. The intensities of the displacement and of the tag-along effects depend essentially on the sample size, the composition of the feed and the parameters of the competitive equilibrium isotherm of the components involved. Most work carried out so far has been mainly concerned with the relative composition of the feed (1-4). The analytical solution of the ideal model has been derived in the case of a binary mixture, when the two components have competitive Langmuir equilibrium isotherms (6). This solution shows that the factor which controls the intensities of the displacement and the tag-along effects is not the mere relative composition of the feed or ratio of the concentrations of the two components (Co,2/Co,1)but is rather the ratio of the individual loading factors for the two components (Lf,Z/Lf,l= q s , l ~ O , P / q a , z ~ O , 1where , L,l and Lf,, are the individual loading factors of the two components, qs,land qs,2their column saturation capacities, and Co,land C0,, their concentrations in the feed). The loading factor of the column for a given compound is the ratio of the actual amount injected 0003-2700/90/0362-02 17$02.50/0
with the sample to the column saturation capacity for this compound (Lf,i= Ni/(l - c)SLqs,i,where Ni is the amount injected, in moles, qs,i is the column packing saturation capacity in mol/mL, t is the column packing porosity, and S and L are the column cross-section area and length, in cm2 and cm, respectively).
INTENSITY OF THE DISPLACEMENT EFFECT The intensity of the displacement effect can be measured by the ratio of the concentrations of the first eluted component in the front (CIN) and the rear (CIM) sides of the second shock. If the second component does not displace the first one, there is no rear shock for the first component band. If the second component displaces strongly the first one, there will be an important rear shock for the first band. The ratio of the concentrations of the first component on both sides of the shock is given by eq 54 of ref 6
-C1,A'-
-1+-
C1,M
b2 4 r 1
In eq 1, bl and b2 are the second coefficients of the binary Langmuir isotherms of the two components and CY = a2/al, the ratio of their f i s t coefficients,is also the analytical relative retention. rl in eq 1 is the root of eq 22 of ref 6, which is in almost all cases nearly identical with Co,l/Co,z. The competitive Langmuir isotherms are written a:C: 6
qi = 1
,
+ blCl + bzC2
where i = 1, 2. With a Langmuir isotherm, the column saturation capacity, qs,i,is equal to the ratio ai/ bi. Introducing into eq 1 the value of rl = Co,l/Co,zand the relationships between the coefficients of the competitive Langmuir isotherm, a , and the column saturation capacities, we obtain
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Since the intensity of the displacement effect is measured by the amplitude ratio of the concentrations of the first component on both sides of the rear concentration shock of the first component band, it will depend essentially on the ratio of the individual loading factors for the two components. If the loading factor for the second component is small or negligible with respect to the loading factor of the f i t component, the displacement effect will be small or insignificant. On the other hand, if the loading factor of the second component is larger than that of the first component, the displacement effect will be important. Since the theory discussed here is an application of the ideal model, it is not surprising to see that a significant displacement effect can be observed a t low loading factors for both components if the ratio of the loading factor of the second component to that of the first one is large. With the ideal model, the asymptotic band profile a t low sample sizes is a rectangular triangle (8). We see from eq 3 that if the two components of a binary mixture have the same column saturation capacity, the intensity of the displacement effect is controlled by the relative composition of the feed. However, if the column saturation capacities are different for both components, the ratio of these two capacities will modify the effect of the relative composition of the feed. If the column saturation capacity of the first component is lower than that of the second one (i.e., in this case the two single component isotherms diverge rapidly, the one with the stronger slope a t the origin having the higher asymptote), the ratio of the loading factors (Lf,,/L,,)will be smaller than the ratio of the component concentrations in the feed and the intensity of the displacement effect will appear to be reduced. Conversely, if the column saturation capacity of the first component is larger than that of the second one, the ratio of the loading factors will be higher than the ratio of their concentrations in the feed. The displacement effect will be more intense than anticipated on the basis of the feed composition. In this latter case, the single compound isotherms of the pure components are expected to intersect. There is nothing particular in this fact, as the two isotherms are not really drawn in the same qi, Ci plane. These isotherms are plots of the amounts of one component sorbed in the stationary phase at equilibrium versus its concentration in the mobile phase. The two plots are merely superimposed on the same graph, leaving the intersection point with no more physical meaning than a mirage. The properties of the competitive Langmuir isotherms in such a case have been discussed (9). It should be pointed out, however, that the competitive Langmuir isotherm model rarely accounts better than fairly for the actual competitive isotherms when the column saturation capacity of the first component is lower than or close to that of the second component. It tends to do quite poorly when the column saturation capacity of the first component is larger than that of the second one.
INTENSITY OF THE TAG-ALONG EFFECT The intensity of the tag-along effect is measured by the length of the concentration plateau of the second component left behind by the first component. This plateau results from the fact that the velocity associated to a certain concentration of the second component is a decreasing function of the local concentration of the first component (because of the competition for access to retention sites). The limit of this velocity for a zero concentration of the first component is larger than the velocity associated to the same concentration of the pure second component (6). This creates a discontinuity in the concentration dependence of the velocity associated to a certain concentration of the second component, hence the origin of the concentration plateau on the rear part of the second component band profile.
The length of the concentration plateau of the second component is given by eq 49 of ref 6
Y(Y - 1)
At =
~
CY2
(tR,0,2 -
(4)
where to is the dead time, tR,0,2 is the limit retention time of the second component at very low sample size (tR,0,2 = (1 + Fa&,), and y is a function of the isotherm coefficients (7 = (&r1 + b2)/(b1r1 + bz). In the simplifying assumption that rl is practically equal to the concentration ratio, Co,l/Co,z,eq 4 becomes 1+-
at =
\"
+
a]
or
which is equivalent to L,Z
1 + 7
Equation 7 shows f i t that the intensity of the tag-along effect depends essentially on the ratio of the loading factors and is proportional to the difference between the limit column capacity factors at very low sample size. When the loading factor for the first component is much smaller that the loading fador for the second component, the intensity of the tag-along effect is low and proportional to the ratio L , , / L , , (eq 6). We have seen that, under these conditions, the displacement effect is intense. On the contrary, when the loading factor for the second component is much smaller than the loading factor for the first one, the ratio L,,/L,, in eq 7 is small, the intensity of the tag-along effect is high, and it is essentially given by the difference ( k b2 - k b,,). In the intermediate cases, the intensity of the tag-along effect is given by eq 7 . For a given feed composition and sample size, an increase in the column saturation capacity of the second component results in a decrease of the ratio of the loading factors, hence an increase of the intensity of the tag-along effect. As a conclusion, a variation in the loading factor ratio and, accordingly, a variation in the ratio of column saturation capacities at constant feed composition and sample size have opposite influences on the displacement and the tag-along effects. This is illustrated by the three chromatograms in Figure 1, showing the individual band profiles of the components of a binary mixture with a 1:3 relative composition of the feed and a constant sample size. The column saturation capacity for the second component is successively lower than (Figure la), equal to (Figure lb), and higher (Figure IC)than the column saturation capacity for the first component. Obviously, the intensity of the displacement effect decreases and the intensity of the tag-along effect increases with decreasing ratio of the loading factors (Lf,2/Lf,l)at constant feed composition and sample size, from Figure l a to Figure IC.
ANALYTICAL CHEMISTRY, VOL. 62, NO. 2, JANUAR)
15, 1990
219
^ ^
,/
Flgure 2. Dimensionless plots of the individual elution band profiles for a binary mixture, plots of blC1 and b z C zversus ( t - to)/(tR,o,zt o ) for both components. Conditions as in Figure 1, except that in all three cases L f , l = 5 % and the feed composition is adjusted so that Lf,z/Lf,l= 3.0. The figure shows the elution profiles obtained for the two compounds under the following three sets of conditions: Condition 1, qs,l = 5, qS,* = 1 0 relative composition of feed, 1:6; condition 2, qs,l = 7.5, qs,2= 7.5, relative cornposition of feed, 1:3; condition 3, qS,, = 10, q8,2 = 5, relative composition of feed, 2:3. For both components, the three elution profiles cannot be distinguished.
loading factors. According to eq 40 of ref 6, the retention time of the front shock of the second component is given by tf,2
= t, + t o +
(tR,0,2 -
Qs.PC0.1
1+-
QSJC02
1+-
to)
x
( [( -
1+- Qs,2CO,1 )Lf,2]1'z)'
(8)
~QS,lC0,2
QS,PCO,l
At constant value of the loading factor for the second component, L,, when the ratio of the column saturation capacities, qs2/q41, decreases, the retention time of the second component
increases and the degree of band overlapping decreases. A similar result can be derived from eq 70 of ref. 6, which states that exact separation between the two bands (ideal "touching bands") is achieved for a sample size equal to ( . -1\2
1+%,lCO,2
Figure 1. Individual elution band profiles for a binary mixture: calculated chromatograms for a 25 cm long column: column efficiency, 5000 theoretical plates; phase ratio, F = 0.25; mobile phase linear velocity, 0.125 cm/s; relative retention, a = 1.20; ko,i = 6.0; relative feed composition, 1:3; sample size, 0.083 mmol of the first component and 0.249mmol of the second component; (a) qs.l = 10, q8,2= 5; L f , l = 1 % , Lf,z = 6 % , L f , 2 / L f , l = 6.0; (b) q8,1 = 7.5, q s , 2 = 7.5, L f , i = 1.33%, Lf,z = 4 % , Lf,z/Lf,T = 3 . 0 (C) 98.1= 5, Qs,z = 10, Lf.1 = 2 % , Lf,z = 3 % , Lf,Z/Lf,i= 1.5.
While the relative intensity of the displacement and/or tag-along effects depends on the loading factor ratio, the degree of band overlay depends on the absolute value of the
According to eq 9, when the ratio qs,2/qs,l decreases (either qs,2decreases or qs,l increases, or both), Lf,2,T increases and we observe a better separation at constant loading factor. On the other hand, however, at constant sample size the loading factor is inversely proportional to the column saturation capacity. The ratios of the column saturation capacities are 0.5, 1, and 2 for parts a, b, and c of Figure 1, respectively. According to the previous discussion and if the loading factor for the second component remained constant, the separation should become worse from Figure l a to Figure l b and to Figure IC. However, since the sample size is kept constant and the column saturation capacity for the second component is increased from Figure l a (5 mmol/mL) to Figure l b (7.5 mmol/mL) and Figure IC(10 mmol/mL), the loading factor for the second component decreases from Figure l a to Figure ICand the actual separation improves in the same order.
220
Anal. Chem. 1990, 62, 220-224
DIMENSIONLESS PLOT OF A TWO-COMPONENT BAND SYSTEM In a previous publication, we have shown that dimensionless profiles can be obtained for the solutions of the ideal model of chromatography for a single component. At constant column efficiency, the elution bands observed for different sample sizes and different compounds can be scaled by plotting a dimensionless concentration, bC, versus a dimensionless time, (t - tO)/(tR,O - to). The scaling factor in this case is the loading factor. A similar result can be obtained for the elution bands of the components of a binary mixture, but some restricting conditions must be satisfied. The column efficiency must remain constant. In addition, the loading factors of both components and their limit relative retention, a , must also remain constant, which is a serious limitation to the interest of that kind of reduced plots. Figure 2 shows that, when the conditions just stated are met, identical reduced plots are obtained for the elution bands of the components of a binary mixture when the column saturation capacity and the feed composition are varied while keeping constant the two loading factors. LITERATURE CITED (1) Guiochon, G.; Ghodbane, S. J . Phys. Chem. 1988, 92, 3682. (2) Perry, J., Communication, VIth International Symposium on Preparative Chromatography, Washington. DC, May 1989.
(3) Newburger, J.; Guiochon, G., Communication, VIth International Sym-
posium on Preparative Chromatography, Washington, DC, May 1989. (4) Cox, G. B.; Eble,: Snyder, L. R., Communication, 13th International Symposium on Column Liquid Chromatography, Stockholm, Sweden, June 1989. (5) Lin, B.; Golshan-Shirazi,S.;Ma, 2 . ; Guiochon, G. Anal. Chem. 1988, 60, 2647. (6) Golshan-Shirazi, S.; Guiochon, G. J . Phys. Chem. 1989. 93, 4143. (7) Golshan-Shirazi, S.; Guiochon, G. J . Chromatogr., in press. (8) Golshan-Shirazi, S.; Guiochon, G. J . Phys. Chem., in press. (9) Huang, J. X.; Guiochon, G. J . Colloid Interface Sci 1989, 128, 577.
’
Author to whom correspondence should be addressed, at the University of Tennessee.
Sadroddin Golshan-Shirazi Georges Guiochon*J Department of Chemistry University of Tennessee Knoxville, Tennessee 37996-1600 and Division of Analytical Chemistry Building 4500-S, M.S. 120 Oak Ridge National Laboratory Oak Ridge, Tennessee 37831-6120 RECEIVED for review August 22, 1989. Accepted October 26, 1989. This work has been supported in part by Grant CHE8901382 of the National Science Foundation and by the cooperative agreement between the University of Tennessee and the Oak Ridge National Laboratory.
TECHNICAL NOTES Anion-Exchange Separation of Carbohydrates with Pulsed Amperometric Detection Using a pH-Selective Reference Electrode William R. Lacourse,* David A. Mead, Jr.,l and Dennis C. Johnson Department of Chemistry, Iowa State University, Ames, Iowa 50011 INTRODUCTION The activity of noble metal electrodes (i.e., Au and Pt) is observed to decrease for the anodic, amperometric detection of virtually all electroactive, aliphatic, compounds at constant (dc) applied potentials. This loss of activity is commonly attributed to “fouling” of electrode surfaces by adsorbed organic reactants and/or reaction products, as well as the formation of surface oxides a t large, positive, values of applied potential (I, 2). Pulsed amperometric detection (PAD) is based on multistep potential waveforms, applied a t a frequency of ca. 1Hz, which incorporate amperometric detection with alternated anodic and cathodic polarizations to clean and reactivate the electrode surface. In the detection of the -CH,OH functionalities of alcohols and carbohydrates, adsorbed carbonaceous species (e.g., free radicals) are oxidatively desorbed by an electrocatalytic process simultaneously with the anodic formation of surface oxide following a positive potential step applied after the brief detection period. The inherent activity of the “clean” electrode surface is then regenerated by a subsequent negative potential step which causes the cathodic dissolution of the oxide film prior to the next detection step in the waveform. This on-line, intermittent, pulsed cleaning and reactivation of the electrode is sufficient to maintain a uniform and reproducible electrode activity. Present address: Commonwealth Edison, Maywood, IL 60153.
A disadvantage of PAD is observed for detection processes which occur a t potential values for which surface oxide is formed simultaneously with the desired detection process. The result is a large base-line signal in liquid chromatographic applications of PAD. Furthermore, the base line is commonly observed to drift because of the gradual increase in the true electrode area caused by surface reconstruction under the repeated conditions of the oxide on/off cycles in the PAD waveform. Also, the base-line signal is very sensitive to changes in solution pH because of the inherent pH dependency of the oxide formation reaction. Integrated pulsed amperometric detection (IPAD), previously known as potential sweep-pulsed coulometric detection (PS-PCD) (3),was developed to minimize the base line found for PAD in detection processes occurring with simultaneous oxide formation. IPAD incorporates a rapid, cyclic potential sweep within the detection period of the multistep waveform. The cyclic sweep, which commences in a positive direction from a potential value at which the electrode is virtually free of oxide, proceeds through the potential region of the desired anodic response for the analyte and then returns to a potential at which all oxide formed during the postive scan is cathodically dissolved. The electrode current is integrated during the cyclic sweep and, accordingly, the anodic charge accumulated for oxide formation on the positive scan is compensated automatically by the cathodic charge for subsequent dissolution of the oxide on the negative scan (3). Hence, P A D
0003-2700/90/0362-0220$02.50/0 0 1990 American Chemical Society
