Anal. Chem. 1902, 54,324-326
ACKNOWLEDGMENT The authors wish to acknowledge H. J. Wieck for helpful discussions leading to this work. LITERATURE CITED
Y
15uA
Bradley, A.; Fales, J. CHEMTECH 1971, April, 232. Bradley, A., CHEMTECH 1973, August, 507. Evans, J.; Kuwana, T. Anal. Chem. 1977, 49, 1632. Evans, J.; Kuwana, T. Anal. Chem. 1979, 51, 358. Oyama, N.; Brown, A. P.; Anson, F. C. J. Nectroanal. Chem. 1978,
I
112
1’0
I
0’6
0’0 V
v5
0’4
87, 435. Nowak, R.; Schultz, F.; Umafia, M.; AbruRa, H.; Murray, R. J. Electroanal. Chem. 1978, 94, 219, Nowak, R.; Schultz, F.; UmaRa, M.; Lam, R.; Murray, R. Anal. Chem. 1980, 52, 315. Watklns, B.; Behllng, J.; Kariv, E.; Miller, L. J . Am. Chem. SOC.1975, 97, 3549. Lennox, J.; Murray, R. J. Nectroanal. Chem. 1977, 78, 395. Sheehan, J.; Hess, G. J. Am. Chem. SOC. 1955, 77, 1067. Evans, J.; Kuwana, T.; Henne, M.: Rover. G. J. Nectroanal. Chem. 1977, 80, 409. Line, W.; Kwong, A.; Weethall, H. Blochim. Biophys. Acta 1971, 242,
I
0’2
0’0
SCE
Figure 1. Cycllc voltammograms of (A) unmodified carbon paste electrode in 0.1 M KCI supportlng electrolyte, (B) unmodified carbon paste electrode in 0.1 M KCI supportlng electrolyte containing 0.1 m M o-tolidine, and (c) carbon paste that has o-tolldine attached In a solution Containing only 0.1 M KCI supporting electrolyte. The scan rate was 50 m V / s in each case.
50 cycles between 0.0 and 1.0 V vs. SCE. The surface concentration of o-tolidine was calculated to mol/cm2 by integrating the area under the peaks be 3 X in curve C. This concentration is larger than the maximum value calculated from the titration and surface area analyses. The most likely reason for this is that the geometrical surface area of the electrode, which was used in the calculation, is smaller than the actual area due to surface roughness of the carbon paste.
CONCLUSION The determination of surface acidic groups by back-titration is a useful method of characterizing carbonaceous materials, which would probably give better results on substrates with higher surface areas. In fact, the surface area of graphite seems to be about the lower limit for this type of analysis. The acrylic acid polymer film seems to be a viable alternative to present attachment schemes in the construction of chemically modified electrodes. The advantages of this procedure are that the reactions used are relatively simple, electrodes constructed using this technique are stable, a large surface concentration can be obtained, and reaction schemes requiring either aqueous or nonaqueous environments can be used. Also, the modified electrodes have a long shelf life (room temperature in a capped vial); samples prepared 6 months earlier were electrochemically indistinguishable from freshly prepared samples.
194
Hilneman. W. R.; Wieck, H. J.; Yacynych, A. M. Anal. Chem. 1980, 52, 345.
Domask, W.; Kobe, K. Anal. Chem. 1952, 24, 989. Belcher, R.; Wllson, C. “New Methods of Analytical Chemistry”, 2nd Ed. Relnhold New York, 1964; p 71. Dautartas, M.; Evans, J.; Kuwana, T. Anal. Chem. 1979, 51, 104. Olson, C.; Adams, R. Anal. Chlm. Acta 1960, 22, 582. Oyama, N.; Anson, F. J. Nectrochem. SOC. 1980, 127, 247. Boehm, H.; Diehl, E.; Heck, W.; Sappok, R. Angew Chem. 1984, 3 , 669.
Kamln, R.; Wilson. G. Anal. Chem. 1980, 52, 1198. Stullk, J.; MaJer, V.; Vesely, J. J. Electroanal. Chem. Interfaclal Nectrochem. 1973, 113.
Wleck, H. J.; Iannlello, R. M.; Osborn, J. A,; Yacynych, A. M., submltted for publication In Anal. Chim. Acta.
‘
Present address: Department of chemistry, Universlty of Massachusetts, Amherst, MA 01003.
George H. Heider, Jr. Mark B. Gelbert’ Alexander M. Yacynych’ Department of Chemistry Rutgers, The State University of New Jersey New Brunswick, New Jersey 08903 RECEIVED for review February 2,1981. Resubmitted October 16,1981. Accepted November 19,1981. A.M.Y. thanks the Rutgers Research Council, Biomedical Research Support Grants, the National Institutes of Health (Grant No. GM 28125-Ol),the National Science Foundation (Grant No. CHE 8022237) for research support, and Rutgers University for a summer fellowship. G.H.H. acknowledges the Rutgers B.A./Ph.D. program for summer fellowships. M.B.G. thanks the Rutgers undergraduate summer fellowship program for support during the course of this work.
Series Difference Detection for Reduction of Interferences in Chromatography Sir: The quantitation of components in complex mixtures by chromatography is frequently limited by the presence of interferences. The problem is particularly acute when the mixtures are of biological or environmental origin, and elaborate clean-up and/or derivitization methods are often required for these analyses. In this paper we described a simple and general technique for minimizing the effect of interferences which are present as broad bands. The technique (1) applies to a variety of chromatographic systems, and we will illustrate it through a HPLC-UV application. Consider the chromatogram shown in Figure l a which was obtained with the usual chromatographic ar-
rangement outlined in Figure 2a, where the output is the difference signal between detectors 1and 2, respectively, which are in parallel. The precision to which the peak of interest can be quantitated is directly dependent upon the precision to which its base line can be estimated, and in the present case it is unlikely to be very high. However, if the parallel arrangement is modified such that the eluant from detector 1flows into detector 2 via a cell (the series arrangement) as shown in Figure 2b, then the chromatogram in Figure l a appears as that in Figure lb, where the interference is considerably reduced. The method may be readily understood in terms of Figure
0003-2700/82/0354-0324$0 1.2510 0 1982 American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 54, NO. 2, FEBRUARY 1982
pending on the volume ( u ) of the cell. These latter peaks arise from offset difference signals, with the degree of offset depending on the value of %”. If the volume of the band is “b”, then Figure 3b-d corresponds to situations where u > b, u = b, and u < b, respectively. In Figure 3b, base line conditions are reached between the positive and negative peaks, since the sample is completely held in the cell after elution from the first detector. In Figure 3c, the leading edge of the band enters the second detector while the lagging edge leaves the first, and the positive peak leads smoothly to the negative peak. In Figure 3d, the volume of the band exceeds that of the cell, and the leading edge of the band resides in the second detector while the lagging edge is still held in the first. This leads to partial cancellation of the signals, and the peak intensity is reduced. If the peak in Figure 3a follows normal distribution, then peaks 3b-d are governed by eq 1where S,
(b) PEAK OF INTEREST
INTERFERENCE
PEAK OF INTEREST
INTERFERENCE
I,. o
m VOLUME l m l l
?
325
VOLUME l m l l
u, x represent signal intensity, the standard deviation, and the elution volume, respectively, and p1and p2 correspond to the mean of the normal and inverted peaks, respectively. The maxima and minima of the signals in Figure 3b-d are given by eq 2 from which it is clear that the difference between p1
2
Figure 1. Chromatograms of 2,4,5-trichiorophenoi in an interfering
H H
matrix obtained with (a) the parallel arrangement and (b) the serles arrangement. (a1
-I I
~
SAMPLE INTRODUCTION
DETECTOR 1
COLUMN
I
L
DETECTOR2
-
-;=;q 3LUMN
DETECTOR 1
DETECTOR 2
Flgure 2. Schematics of arrangement.
(a)the parallel arrangement and (b) the series
3. The peak in Figure 3a obtained with the parallel arrangement is transformed to the peaks in Figure 3b-d defa1
and p2, Le., “u” controls the position of the peak and the trough. For example, if u = 0.5 mL, p1 = 5.0 mL, and pz = 6.0 mL, the peak and trough occur at 4.9 and 6.1 mL, respectively. If p2 is changed to 5.5 mL, the positions of the peak and trough are shifted to 4.7 and 5.8 mL, respectively. The position of the maximum which defines the retention volume in conventional chromatography is therefore inapplicable in difference detection. The corresponding value which defines the retention characteristics of the component in question at a given value of “u” is represented by the position at which the signal returns to base line after tracing the first peak. This point equals (pl w2)/2. By analogy with conventional analysis, the difference signal may be quantified either by the peak-to-trough height or by the s u m of the areas of the positive and negative peaks. In the absence of interferences, the precision obtained by the series difference method will be similar to that obtained by conventional analysis. However, if interferences of the type shown in Figure l a are present, the precision will be greater with the series difference technique since the base line does not have to be assigned if the peak-to-trough height method is used. Alternatively, if area measurements are conducted, the slope of the base line is necessarily much smaller in the series difference technique,
+
fbl
Figure 3. Chromatograms obtained with (a) the parallel arrangement and (b)-(d) various series arrangements.
[dI
328
Anal. Chem. 1982, 5 4 , 326-328
and the base line is therefore much easier to establish. A potential drawback of the difference method is that peak broadening may occur in the cell, and thus a trade off situation exists where interferences are reduced at the expense of peak broadening. The extent of broadening will depend upon the volume of the cell and may be quite small in practice as in the example illustrated in Figure 1. Optimization of the cell for the analysis at hand is straightforward and may be achieved by setting the cell volume at or slightly below the bandwidth of the peak in question. In the example shown in Figure 1, the cell consisted of a length of tubing whose volume was about 0.7 of the bandwidth. In summary, the cell introduces an additional parameter in chromatography and can be used in any situation where the output is represented by the difference signal between the two detectors. Liquid chromatography, UV, fluorescence,
conductometric,polarographic, and refractive index detection systems (2) among others may be readily modified to the configuration shown in Figure 2b. LITERATURE CITED (1) U S . Patent Pending. (2) Snyder, L. R.; Klrkland, J. J. “Introduction to Modern Liquid Chromatography”; Wiley: New York, 1974.
Sujit Banerjee* Edward J. Pack, Jr. Life and Environmental Sciences Division Syracuse Research Corporation Merrill Lane Syracuse, New York 132104080 RECEIVED for review June 11,1981. Resubmitted September 17, 1981. Accepted October 30, 1981.
Effect of Liquid-Phase Diffusion Resistance on Retention Time in Gas-Liquid Chromatography Sir: When gas chromatography is used to measure the retention time, it is generally assumed that the retention time of an infinitesimally small sample will correspond to the true thermodynamic value; however, Lichtenthaler et al. (1)observed that the retention time decreases with increasing flow rate, and Braun and Guillet (2) observed that the retention time decreases as the thickness of the liquid layer increases. Previous models do not account for these phenomena. They arise from the diffusional resistance in the liquid phase which reduces the effective adsorption capacity. In this study, we propose a model that assumes a nonuniform concentration for the liquid phase in order to include the liquid-phase diffusional resistance. Also the model assumes that the gas-phase concentration is a function only of the column length. This assumption may not be true when the gas flow velocity varies with the radial coordinate, but it is approximately correct when the diffusional resistance in the liquid is more significant than that in the gas phase.
THE MATHEMATICAL MODEL A capillary column is used to approximate and simplify the concentration distributions in the gas and liquid phases. We assume the column length is L, the inner diameter is R, and the liquid-layer thickness on the column wall is H. The gas-phase concentration is a function of axial coordinate z only. The concentration in the liquid phase depends both on the axial coordinate z and the radial distance r. The differential equations governing the gas-phase concentration 4 and the liquid-phase concentration 4’ are
a$)’
- (2,R + H,t) = 0
(4)
ar dJ’(z,R,t)= @(z,R,t)
(5)
Here M is the mass of the sample injected and K is the partition coefficient. The initial condition, eq 3, is an impulse at t = 0; the boundary condition, eq 4, is an impermeable wall at the solid interface; and the boundary condition, eq 5, assumes equilibrium at the gas-liquid surface. The solution of the diffusion equation in a finite liquid layer, subject to a concentration change d(z,R,t) at the surface, with the initial condition f‘ = 0, is (3) 4’(z,r,t) = Kjt+(z,R,t)$F(r,t a - A) dX (6) 0
where F(r,t) is the response to the step change on the surface. The step-response concentration of the one-dimensional diffusion, eq 2, subject to eq 4 is ( 4 ) 4 F(r,t) = 1- - C7r n=02n 1 (2n 1) r ( r - R ) - (2n f 4 y t
+
+
H The functions 4 and 4’ must satisfy conservation of mass
M = 2a
l:ARr4(z,r,t) dr dz
+
Note that we have approximated r by R in the integrand of the second term because H is small compared to R. We use eq 6 and 7 to eliminate 4 in the second term in eq 8; thus, eq 8 becomes where u is the flow velocity of the carrier gas and D,and D1 are the diffusivities of the sample in the gas and liquid phases, respectively. The approximation for the right-hand member of eq 2 follows from the assumption that the thickness of the liquid is small compared to the radius of the column. The initial and boundary conditions are
M = 2 ~ 1 ~ L ~ r 4 ( z , dz r , tdr) -m
(3) 0003-2700/82/0354-0328$01.25/0
+
dX dr dz (9) 0 1982 American Chemical Society
