1990
Anal. Chem. 1983, 55, 1990-1992
tions, which is in turn dictated by the effort to avoid systematic error resulting from a possible change in the sample matrix. The question is then under what conditions is the serious loss of precision a reasonable bargain for the gain in accuracy. The question can be asked also in a more general way: what are the conditions for the DKAM to be preferred to other potentiometric techniques? The sufficient and necessary condition for the DKAM to give valid results is that the modified Nernst equation
E
= E’
+ S log c
does hold during the DKAM measurement. E’ and S must be independent of c but they may change from sample to sample either because the sample matrix causes such changes or because E’ and S are drifting. If E’ and S were not changing from sample to sample, one would use the calibration method. If only E’ changed, the single addition method would be used. There remains one situation when the DKAM could be reasonably used: if S changes from sample to sample (E’ may also change or may remain constant). If the change in S is caused by variations in the sample matrix, we expect from our experience that eq 8 will not hold for such samples, Le., the calibration line of the cell will be nonlinear. This observation limits the range of usefulness of the DKAM to situations when S is drifting with time. This problem can, however, often be overcome by better methods than the DKAM, e.g., frequent redetermination of S or elimination of the drift by a suitable adjustment buffer or by using the analate addition method. If these methods cannot be used for some reason or do not help, only then does the use of the inherently imprecise DKAM seem to be justified. It should also be recognized that the DKAM does not allow for drift that is too fast either, since S has to remain practically constant during one DKAM measurement.
The main limitation in the use of the DKAM was seen to be its error magnifying effect. This may be occasionally counteracted by a rather low uB It has been observed ( 4 , 5 )that the emf differences measured in the course of standard additions (not only double but also single or multiple additions) have a much smaller variance than one would expect on the basis of repeated single readings with a change of corresponding standard solutions. This gain in Q may a t least partly compensate for the error magnifying effect of the DKAM. It should also be noted that if large volume additions are allowed, i.e., they do not cause disturbing matrix effects, then the precision of the DKAM can be considerably improved (1).
In light of the foregoing discussion one might envisage some specific situations when DKAM may prove to be the method of choice; however, in most typical potentiometric applications it appears to be less appealing then other, suitably chosen methods.
LITERATURE CITED HoNai, G.: Pungor, E. Anal. Chlm. Acta 1980, 113, 287. HoNai, G.;Pungor, E. Anal. Chlm. Acta 1980, 113, 295. HoNai, G.;Pungor, E. Anal. Chlm. Acta 1980, 116, 87. Horvai, G. “Critical Study of Potentiornetrlc Measuring Techniques”; Candidate’s Thesis, Budapest, 1979. Efstathiou, C. E.; Hadjiioannou, T. P. Anal. Chem. 1982, 54, 1525. Harbarth, K.; Riedrich, T. “Differentialrechnung fur Funktionen mit mehreren Variablen”; Teubner: Leipzig, 1978. Brand, M. J. D.; Rechnitz, G. A. Anal. Chem. 1970, 42, 1172.
Gyorgy Horvai Erno Pungor* Institute for General and Analytical Chemistry Technical University Budapest, Gell6rt t6r 4,H-1111 Hungary
RECEIVED for review February 14,1983. Accepted July 1,1983.
Analysis at the Micromolar Level by Cyclic Voltammetry Sir: The main limitation to the effectiveness of voltammetric electroanalysis a t low concentrations arises from the need to distinguish between the faradaic signal and interfering “background currents. The latter are particularly severe when the electrode potential and/or area are changing with time, because the background currents then contain a capacitative component. Accordingly, sensitive electroanalytical techniques generally rely on measurements made on stationary (or very slowly growing) electrodes at constant (or very slightly variable) potential. While such techniques do efficiently separate the nonfaradaic interference from the faradaic signal, they suffer the disadvantage of requiring many separate measurements to construct a voltammogram, so that experiments of long duration are needed for a single analysis. Cyclic voltammetry is a technique that has proved extremely useful in qualitative studies of electrode reactions, but it has rarely been used for quantitative analysis. Chief among the reasons for this is the low signal-to-noiseratio. The capacitative current may exceed the faradaic current at concentrations of lo“ M or less, making accurate quantification impossible in this important concentration range. The faradaic sensitivity increases with the applied sweep rate, but the capacitative “background signal” increases faster. The name “cyclic voltammetry” has been applied to a number of related techniques. Here we mean the imposition of a single isosceles triangular potential wave form on an electrode and the recording of the resultant current as a function of potential. The potential excursion is selected to
start a t a value at which the analyte of interest is not reduced (oxidized), to traverse the region of the reduction (oxidation) wave to a reversal potential in the concentration-polarized range, and then to return to the initial potential. A typical cycle might consist of a ramp that changes the electrode potential to a value more negative by about 15RT/nF followed by a similar positive-going ramp; at a sweep rate of order 100 mV sF1, the entire experiment occupies a few seconds only. The cyclic voltammogram consists of two branches, as illustrated in Figure ICfor a reduction process. One branch, the forward branch I‘,is generated by the negative-going sweep; the backward branch i- arises during the positive-going return sweep. Figure la,b, respectively, shows typical faradaic and nonfaradaic contributions to the branches of the cyclic voltammogram. Whereas Figure l a could be used for chemical analysis, Figure ICis useless for this purpose because it contains a nonfaradaic component of unknown magnitude. In principle, voltammogram l a could be reconstructed from IC by subtracting a replica of curve b, determined from a separate experiment on supporting electrolyte alone. Such experiments are time-consuming and the subtractive correction is not always reliable. In this paper we advocate an alternative, and simpler, method of correcting for background interference: adding the
i” and i branches of cyclic voltammogram ICto produce the single wave-shaped curve shown in Figure Id. Because the
0003-2700/83/0355-1990$01.50/00 1983 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 55, NO. 12, OCTOBER 1983
200
1
1991
1
1 (nA)
f
-1001
I
c
+
1nf
-E(V v s
-200 -0.1
0.0
0. 1
0.2
Ag/AgCl)
0.3
0.4
Flgure 2. Cyclic voltammogram (dots) and branch-addition cyclic voltammogram (solid line) of 11.92 pM K3Fe(C204)3:sweep rate, 50 mV s-'; duration, 22 s.
l = = l +l,f f (C)
50
,,4+;=if+if
E
(d)
0
4 Flgure 1. Cyclic voltammograms illustrating (a) faradaic current i f , (b) nonfaradaic current in,, (c) a typical experimental curve, and (d) the branch-addition concept.
-50 -100-E(V v s
nonfaradaic component l b is approximately symmetrical about the i = 0 axis (it will be exactly so if the nonfaradaic current is purely capacitative), branch addition cancels out the nonfaradaic background. Thus voltammogram I d is virtually identical with the result of branch addition on curve l a , and contains only faradaic information. Moreover, the shape of wave Id lends itself to ready quantification, the height between the anode-going "trough" and the cathodic "crest" being proportional to the analyte concentration. The theory of cyclic voltammetry is sufficiently complicahd
'
that a useful analytical expression for t is available only for the case of a reversible electrode reaction ( I ) , and even in that case the mathematics is far from simple. Nevertheless, nu-
Ag/AgCl)
J
merical methods may be used to determine values of T and t,and hence of T + t,for reversible, quasi-reversible, and irreversible electroreductions. These theoretical studies predict the following: (i) A trough will be found for all but totally irreversible processes (for which an asymptotic base line occurs). (ii) A crest will be exhibited provided that the reversal potential is a t least 5 R T / n F beyond the midwave potential (the potential where + t,has a value equal to the average of its values at the trough and the crest). (iii) The wave height A (the difference between the T + t values at the crest and the trough) is given by -
A = (i
+
- + e
+ i)crest- (i +
= g n A F c ( D_; ;_ y2
(1)
where most symbols have their usual electrochemical significances. Thus the wave height A is proportional to the analyte concentration c and to the square root of the sweep rate u. (iv) The value of the numerical constant g approximates 0.65 for a reversible process and O.68a1l2for an irreversible process. In each case there is a very mild dependence of g on the reversal potential. The value of g for quasi-reversible processes depends on the rate constant k,, as well as on the transfer coefficient a. Interestingly, g is often larger for a quasi-re-
1
0.01 0.1
*
C (rM)
/ 1. 0
10
100
Flgure 4. Logarithmic relationship between wave height A and concentration for Fe(C,04)33- and Zn2+ reductions. The lines have unity slope. Conditions are given in Figures 2 and 3.
versible process than for either a reversible or an irreversible process. The branch-addition concept has been studied experimentally on solutions of K3Fe(C204)3 in 0.10 M K2C204/0.01 M H2C204and ZnS04 in 0.10 M K2S04at a static mercury drop electrode of area 4.182 X lo4 m2. The first system is known to behave reversibly (2) and the second, quasi-reversibly (3). Typical cyclic voltammograms are shown in Figures 2 and 3, respectively. The current data, acquired digitally at 80-ms intervals, appear as dots on these diagrams. Smoothing, interpolation, and addition of the two branches of the cyclic voltammograms produced the solid lines. These lines exhibit the wave shape as predicted by theory. Notice that the quasi-reversible wave of Figure 3 is considerably more peaked,
1992
Anal. Chem. 1983, 55, 1992-1994
corresponding t o a larger g value. Figure 4 establishes the proportionality of the wave height A to the analyte concentration as predicted in eq 1. Evidently, branch-addition cyclic voltammetry is useful for rapid and accurate analysis in the micromolar range and lower. This technique expands the usage of cyclic voltammetry to include quantitative as well as mechanistic analysis. A more complete account of the theoretical and experimental aspects of branch-addition cyclic voltammetry will be published later. Registry No. Fe(Cz04)33-,15321-61-6;Zn2+,23713-49-7.
LITERATURE CITED (1) Myland, J. C.; Oldham, K. 8. J . Electroanal. Chern., in press. (2) Bond, A. M. "Modern Polarographlc Methods in Analytical Chemistry"; Marcel Dekker: New York and Basel, 1980;pp 16, 19. (3) Bond, A. M. "Modern Polarographic Methods In Analytlcal Chemlstry"; Marcel Dekker: New York and Basel, 1980,p 100.
Keith B. Oldham* Cynthia G. Zoski Department of Chemistry Trent University Peterborough, Ontario K9J 7B8, Canada
RECEIVED for review May 11, 1983. Accepted June 22,1983.
Laser Fluorometric Detection for Thin-Layer Chromatography Sir: Improvements in liquid chromatography columns and equipment over the past decade have greatly increased the separating power of that technique and have resulted in the use of the descriptive term high-performance liquid chromatography (HPLC). Similarly, the term high-performance thin-layer chromatography (HPTLC) has been adopted as a result of recent technological advances, which have increased the separating power of thin-layer chromatography (I). Despite the exceptional separating efficiencies attained with HPTLC, the peak capacity of the technique is generally low relative to HPLC. However, the static nature of developed thin-layer plates facilitates the use of multidimensional detection, which can minimize the limitation of low peak capacity. Thus research into new modes of selective detection is perhaps even more important in the development of HPTLC than it has been in HPLC. Components separated by thin-layer chromatography are generally detected photometrically, using either absorbance or fluorometric modes of operation (2). Lasers have been employed in the fluorometric detection of aflatoxins separated by thin-layer chromatography ( 3 , 4 ) . Beam collimation and high power are unique spectral characteristics of the laser, which can be particularly beneficial for fluorometric detection in thin-layer chromatography. Separated component spot diameters in HPTLC can be as small as 1 mm (5). I t is not possible to focus conventional light sources to these dimensions without prohibitive losses in power; however, the collimated beams of lasers can be easily focused to beam diameters less than 100 pm. The high powers available with lasers can result in significant signal increases in fluorometric detection. Moreover, high laser power makes it possible to utilize certain nonlinear excited fluorescence processes in thin-layer chromatography detection. Two-photon excited fluorescence (TPEF) and sequentially excited fluorescence (SEF) are two nonlinear excited fluorescence techniques which have been utilized in liquid chromatography detection (6, 7). The T P E F process involves the simultaneous absorption of two photons in order to produce a resonant transition in a molecule. Fluorescence is monitored from the lowest excited singlet state of the molecule. The SEF process involves sequential resonant excitation, with fluorescence being monitored from a highly excited state. The principal analytical advantage of these two-photon excitation processes is that they are governed by different selection rules than conventional (one-photon) excitation (81, and this can provide an added dimension for spectral selectivity in fluorometric detection.
The excitation process in TPEF and the emission process in SEF are very inefficient relative to the corresponding processes in conventional fluorescence ( 4 9 ) . Nevertheless, the low optical background levels for the techniques, a result of the large blue-shift between excitation and emission wavelengths, and the high powers available with pulsed lasers, can result in reasonably sensitive detection. Fluorescence signal levels for these techniques are quadratically dependent on laser power and inversely dependent on the cross sectional area of the focused laser beam a t the sample.
EXPERIMENTAL SECTION Apparatus. Separated components were detected by using the apparatus shown in Figure 1. Excitation for each of the fluorometric modes of detection was provided by a N2-pumped dye laser (National Research Group, Madison, WI, Model NRG-0.5-5-150/B Nz laser and Model NRG-DL-0.03 dye laser) tuned to 488 nm using Coumarin 481 dye. The average output power of the laser was 8 mW (peak power approximately 25 kW) when operated at 60 Hz. The laser radiation was initially passed through a Corning GG-455 sharp cutoff filter, which removed interfering N2laser radiation from the emission region. The laser radiation was then focused onto the thin-layer plate at an angle of 45' with a 200-mm focal length lens. The thin-layer plate was scanned in front of the focused laser beam at approximately 6 mm/min, using a modified syringe pump (Harvard Apparatus Co., Inc., Dover, MA, Model 600-900). Fluorescence emission was collected normal to the thin-layer plate with a f / l , 25 mm focal length, quartz lens. A combination of three Corning 7-54 band-pass filters and a 2-cm saturated CuS04cell was used to isolate the TPEF and SEF emission. This filter combination has a fwhm band-pass of approximately 50 nm centered at 360 nm with a peak percent transmission of 20%. For the detection of conventional fluorescence, the 7-54 band-pass filters and CuS04cell were removed and the emission was passed through a Corion OG 570 sharp cutoff filter and a monochromator (Instruments SA, Inc., Metuchen, NJ, Model H 20). The monochromator was operated at 585 nm with a 6-nm band-pass. The isolated emissions for the TPEF and SEF techniques were detected with a RCA 1P28 photomultiplier tube (PMT) operated at 850 V and mounted in a dry ice cooled housing. For the detection of the isolated conventional fluorescence emission, the PMT voltage was reduced to 650 V and the PMT was not cooled. The photocurrents were measured with a quantum photometer (Pacific Precision Instruments, Concord, CA, Model 126) operated in a nanoampere measuring mode. A 10-stime constant was used to filter the photometer output before recording on a strip chart recorder. A thin-layer plate spotted with a concentrated solution of 2-(l,l'-biphenyl)-4-yl-5-phenyl-1,3,4-oxadi~ole (PBD) was placed in position and used to provide a fluorescence signal while the
0003-2700/83/0355-1992$01.50/063 1983 American Chemical Soclety
