1962
Anal. Chem. 1984, 56, 1962-1967
ACKNOWLEDGMENT The author wishes to thank J. C. Van Loon for his helpful suggestions. Registry No. Au, 7440-57-5;Pd, 7440-05-3; Pt, 7440-06-4; Fe, 7439-89-6; Pb, 7439-92-1. LITERATURE CITED (1) Beamish, F. E.; Van Loon, J. C. "Analysis of Noble Metals"; Academic Press: New York, 1977; Chapter 7.
(2) Johnson, E. L. Am. Lab. (Falrfleld, Conn.) 1982, 13, 98. (3) Gjerde, D. T.; Fritz, J. S. J. Chromatogr. 1980, 788, 391-399. (4) Tsuda, T.; Nom, T.; Genkichi, N. J. Chromatogr. 1982, 242, 33 1-336. (5) Seymour, M. D.;Fritz, J. S. Anal. Chem. 1973, 4 5 , 1394-1399. (6) Wetzel, R. A.; Anderson, C. L.; Schleicher, H.; Crook, G. D. Anal. Chem. 1979, 57, 1532-1535. (7) Smith, R. M.; Marteli, A. E. "Crltical Stability Constants"; Plenum Press: New York, 1976; Vol. 4.
RECEIVED for review January 30,1984. Accepted May 7,1984.
Use of Resonant Two-Photon Ionization with Supersonic Beam Mass Spectrometry in the Discrimination of Cresol Isomers Roger Tembreull and David M. Lubman*
Department of Chemistry, The University of Michigan, Ann Arbor, Michigan 48109
The supersonic molecular beam technique is used to produce ultracold molecules in a light carrier for ultraviolet (UV) spectroscopy. A UV spectrum which is broad at room temperature is thus transformed into a spectrum which exhibits sharp vibronic features under supersonic beam conditions. Resonant two-photon ionization (RPPI) is then used to study the intermediate-state absorption spectrum by monitoring the total ion yield of the two-photon process. I n particular we have studied the RPPI spectra of the ortho, meta, and para isomers of cresol in an attempt to develop a sensitive means of detecting and discriminating these compounds by monitoring the parent ion in a time of flight mass spectrometer. No fragmentation is observed at the laser power levels used in these experiments. I n addttion, the spectra of the cresols are studied as a function of the carrier gas used in the molecular jet in order to determine the conditions for maximizing rotational and vibrational cooling. The possibility of dlrect air sampling at 1 atm is investigated and an estimate of the real discrimination and sensitivity limits of the technique are discussed.
The supersonic molecular beam method is a powerful technique for preparing ultracold molecules for spectroscopy (1-15). The visible-ultraviolet absorption spectrum of most aromatic hydrocarbons at room temperature is a structureless contour composed of a large number of populated vibrational and rotational states. Thus, UV-VIS spectroscopy at room temperature in the gas phase is often not a useful technique with regard to selectivity in analysis. However, using a supersonic adiabatic expansion of a small percentage of a large polyatomic molecule in a light carrier gas such as He or Ar allows a rapid relaxation of the internal degrees of freedom through two-body collisions. The result is that the internal energy of the molecules is converted into the translational energy of the carrier gas and only low rotational and vibrational energy levels are populated in the ground-state molecules. Consequently, a UV-VIS spectrum which is broad at room temperature is transformed into a spectrum which exhibits sharp, discrete structure under supersonic beam conditions. Thus, arises the possibility of using this unique 0003-2700/84/0356-1962$0 1.5010
spectral fingerprint as a means of identifying molecules (2, 10-14). The great selectivity potentially available using the supersonic beam can be combined with the excellent sensitivity of multiphoton ionization spectroscopy to provide a very powerful technique for chemical analysis. This senstivity is a result of the high efficiency of ionization which may be typically several percent of the molecules in the laser ionization region (4,17-21). This sensitivity is further enhanced by the use of a supersonic beam. Since the population of the internal degrees of freedom is reduced to the lowest states, these states can be much more efficiently pumped in an electronic transition. Further, MPI enables one to obtain soft ionization with high efficiency at modest laser energies (4, 16-29). The unique property of multiphoton ionization compared to other methods of ionization used in mass spectrometry is the wavelength selectivity possible with this technique (4,5, 17,20,21,25,27). The process used in this study is resonant two-photon ionization where one photon excites a molecule to an intermediate electronic state and a second photon pumps the molecule above its ionization potential (IP) resulting in ionization. A molecule will ionize only if the total energy of the two photons absorbed exceeds the P of the molecule. The ionization spectrum that results reflects the one-photon absorption cross section of the intermediate state since the second photon rapidly pumps the intermediate state into a structureless continuum of states where the cross section does not vary significantly as a function of wavelength. Thus, RBPI serves as a means of observing absorption spectra of excited states through excitation or ionization spectroscopy. The advantage over absorption methods is the great sensitivity available through production and detection of ions. In addition, the ability to produce ions allows us to use RBPI spectroscopy as a means of achieving real-time spectral selection of a compound prior to mass analysis in a mass spectrometer. Thus, the possibility exists for three-dimensional mass spectrometry where the three axes are ionization signal intensity, wavelength, and mass selection (14, 25). Limited spectral discrimination has been used to distinguish between such isomeric pairs as azulene and naphthalene (13, anthracene and phenanthrene (20)) ortho, meta, and para isomers of xylene (28)) and cresol and toluidine (29-30)a t room temperature. This is possible because the electronic or 0 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 11, SEPTEMBER 1984
vibrational structure of the particular isomers at room temperature is sufficiently different. However, orders of magnitude in selectivity can be achieved by using the supersonic beam technique to produce spectra with sharp vibrational structure which can be used to uniquely and unambiguously identify each isomeric compound. In this paper we apply laser photoionization with the supersonic beam technique in order to distinguish the isomers of cresol in a mass spectrometer. The ortho, meta, and para isomers are difficult to distinguish in electron beam ionization mass spectrometry since they have the same mass and very similar fragmentation patterns. It is shown that cooled isomeric molecules in supersonic beams have significantly different ionization spectra that permit easy and unique identification of these compounds. We have studied the cooling attainable using different carrier gases and estimated the sensitivity and degree of discrimination possible. In addition, using pulsed molecular beam techniques we have demonstrated the ability to directly sample and detect low concentrations of cresol from the atmosphere. EXPERIMENTAL SECTION The supersonic beam-time of flight mass spectrometer unit used in these experiments is similar to that of our previous work (14). This device is constructed using a pulsed valve which produces a molecular beam crossing the ionization region at right angles to the TOFMS. The laser beam then enters along the axis perpendicular to both and ionizes the molecular beam inside the acceleratingregion of the mass spectrometer. The vacuum system consists of a stainless steel chamber pumped by a 6-in. diffusion pump. A liquid nitrogen cooled baffle is used to obtain a background pressure of 4 0 “ torr. The supersonic beam source is a Quanta-Ray PSV-1 pulsed nozzle. This source provides gas pulses of -55 ps full width at half-maximum (fwhm)at “choked flow”, Le., when the maximum flow rate through the orifice has been achieved under the given conditions (31).The present experiments were performed at a 10-Hzrepetition rate which correspondsto that of the laser system. The typical reservoir pressure was 1atm although experiments using pressures up to 7 atm were performed. Various carrier gases were used including helium, argon, nitrogen, air, P-10 (10% methane/Ar mixture), carbon dioxide, methane, and ethane. With 1atm of back pressure, an aperture diameter of 0.05 cm, and Ar as the carrier gas, the average chamber pressure was -1.5-2.0 X torr. This number may vary from 8 X lo4 to 3 X torr depending on the carrier gas used. The nozzle to excitation region distance was fixed at 9.25 cm, which places the molecular beam well within ita “free-flow”region for the carrier gases under study (32). The isomers of cresol were seeded into the carrier gas at their room temperature vapor pressures by flowing a slow continuous stream of carrier gas over the sample and into the orifice region. This method assures a constant, steady concentration of the sample in the carrier gas. The concentration is determined by measuring the sample weight loss at a given carrier gas flow over a time interval of several hours. The concentration in Ar is found to be -12 ppm for p-cresol, -12 ppm for rn-cresol,and -20 ppm for o-cresol at room temperature. In order to obtain accurate low concentrations of cresol in carrier gas the diffusion tube method was used (33). The valve was heated to 80 OC in order to minimize sample sticking to the walls. It may operate at up to 150 OC although the pulse shape and performance changes as the temperature is increased over the operating temperature used. However, when changing samples the valve was baked above 120 O C and a clean flow of nitrogen continuously purged the valve. After baking, only trace impurities from previous experiments could be detected. The ions produced by laser photoionization were detected with a TOFMS modified aa in our earlier work for use with a supersonic beam (4, 14). In this particular study a Galileo Channeltron electronmultiplier Model 4816 with a cone-shapedface was used. This considerably lowers the attainable resolution compared to a flat detector since the ions follow different length paths to the cone. However, the TOF device was just used to monitor the parent ion of cresol, and discrimination by mass selectivity was
1963
not critical since the isomers of cresol have the same molecular ion mass. The signal from the output of the TOF is signal averaged by an in-house-constructed boxcar integrator (Evans, Assoc., Berkeley, CA) with the gate placed on the molecular ion species at MW = 108 so that this peak is monitored as a function of wavelength, A LeCroy WlOOB amplifier was used to amplify the signal by 1OOX. Before passing through the ionization region of the TOF device, the laser beam was collimated to -2 mm with a positive-negative (30/10 focal length ratio) lens telescope system. The light beam was attenuated with several Corning 7-54 filters so that the energy remained below 0.10 mJ. Above this energy level space charge broadening and spectral saturation may occur. Th length of the beam in the interaction region is -2.5 cm so that a cylinder -0.1 cm3 is swept out of the beam. The laser source is a Quanta-Ray DCR-1A Nd:YAG pumpeddye laser. In order to produce tunable UV light, the output from the dye laser was frequency doubled in a phase-matched KD*P crystal. This was performed for the various dyes by using the Quanta-Ray WEX-1 wavelength extension device which can produce scannable UV radiation over the frequency-doubled range of each dye. The dye laser wavelength was scanned with a stepping-motor controlled by a Quanta-Ray CDM-1 control display module. RESULTS AND DISCUSSION The essence of this technique is demonstrated in Figure 1, which shows the ionization spectra for 0-,m-, and p-cresol in a supersonic expansion of Ar as a function of wavelength. These spectra were taken by scanning the frequency-doubled dyes R590 and R575 over their tuning range while the parent ion peak was monitored with the gate of our boxcar integrator. The dye curves were not corrected for laser energy although the power is reasonably constant over the central portion of the spectra. The beauty of this experiment lies in the fact that the spectra for these isomers have very distinctive and sharp features in a supersonic jet which allow unambiguous identification of these compounds. Further, the resonant two-photon ionization technique allows production of ions for identification by mass spectrometry. The spectra in Figure 1 are actually three-dimensional plots where only the ionization signal vs. wavelength axes are shown and the mass axis monitoring the parent ion is orthogonal to the other two axes and extending out of the paper. Fluorescence measurements often have the capability of providing the same spectroscopic information as R2PI (2,10-13); however, fluorescence measurements cannot provide identification by mass discrimination. The truly important feature of R2PI for study of cresol and several related compounds is that these molecules have low quantum yields in fluorescence because of rapid radiationless processes (34). However, efficient and sensitive ionization of these molecules is readily achieved. In examining Figure l a we see that p-cresol ionizes with several sharp features (-0.4 A), where the band at 282.97 nm appears to be the origin of the AI B1 transition. Beyond this wavelength to the red, no other bands are observed for p-cresol at least until 284.5 nm. In this region, essentially no ionization is observed for m- and o-cresol since in both cases the spectra is shifted to the blue of the para isomer. In Figure l b vibronic structure appears for all three isomers which is clearly different for each compound. Note that p-cresol exhibits fewer transitions over a given wavelength region from the origin than does the ortho or meta isomer because of its higher degree of symmetry. An important question for useful analysis is the repeatability of the spectral information. In particular, the key variable is the ability to reproducibly measure the peak of the origin band for p-cresol as an example. The calibration of our dye laser appears to be good to at least *0.002 nm. The range of our measurements is f0.015 nm over 100 trials, and the precision of these measurements has been found to be 0.004 nm, although we have reported our wavelength information
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WAVELENGTH (nm) Figure 1. Resonant twephoton ionization (R2PI)spectra of the isomers of cresol expanded in a supersonic let of argon in the region (a)284.5-277.5 nm and (b) 278.5-272.5 nm. The spectrum was performed by monitoring the parent ion at MW = 108 in a time of flight mass spectrometer. The reservoir pressure was 1 atm argon and the laser energy per pulse was -0.1 mJ. The vertical axis is ionization signal in arbitrary units.
to the nearest 0.01 nm. Thus, this technique represents a unique means of identifying molecules according to their spectral peaks. Of course, one must accurately calibrate the laser from one system to another before analysis; however, this can be done either by using a high-resolution spectrophotometer or by using a test compound whose spectrum is accurately documented. A second important variable is the peak width (fwhm). This will ultimately affect the attainable resolution between isomers in this experiment. For a particular carrier gas, the width of the peak may vary by as much as fO.O1 nm over many different spectra This is true provided other factors such as space charge broadening do not significantly affect the peak width. Since the peak width is typically 0.04 nm, it may vary by as much as 25%. However, the measurement of the accuracy must be in relation of the peak broadening to the loss of spectral resolution compared to the peak of the second component to which the comparison is being made. For example, in discriminatingthe p-cresol peak at 282.97 nm from the rn-cresol peak at 277.87 nm, we find a maximum loss of resolution of 0.2%. The relative error in this measurement is small because of the narrow peak widths and the large separation of the peaks of interest. The ability to measure the distance in wavelength between these peaks is also excellent with a precision of better than 0.008 nm if desired.
It should be noted that the maximum laser energy was 0.10 mJ for all the ionization spectra in this paper. This is of importance in practical analysis because as the power of the laser is increased the mass spectrometer ion peak initially undergoes space charge broadening which causes loss of ions from the acceleration region. As the power is further raised the wavelength spectrum becomes saturated so that the sharp peaks become broad and unresolvable and the structure disappears at high laser intensities. This may be due to a combination of power broadening and/or a nonresonant background ionization that becomes significant as the power becomes higher. At these energy levels the height of the sharp spectral feature may be limited by space charge effects. In addition, as the power further increases fragmentation occurs and the parent ion peak decreases at resonance while the off-resonant background increases. This occurs since the absorption off-resonance is not as strong as on-resonance so that fragmentation does not occur in the former case at comparable laser energy levels. On resonance, fragment ions are formed at higher laser power at the expense of the intensity of the parent ion. In order to maximize the cooling achieved we studied the effect of several different carrier gases on the spectrum of p-cresol. We expected from the work of McClelland et al. (37) to obtain the best rotational cooling and therefore sharpest
ANALYTICAL CHEMISTRY, VOL. 56, NO. 11, SEPTEMBER 1984
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:a)
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N2
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Figure 2. RPPI spectra of p-cresoi by using varlous carrier gases including (a)helium, (b) argon, (c) nitrogen, and (d) alr at 1 atm reservoir pressure. The spectra were performed by monitorlng the parent ion of p-cresol in a TOFMS. The vertical axis is Ionization signal in arbitrary units.
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Figure 3. RPPI spectrum of a mlxture of cresol isomers in laboratory alr at 1 atm reservoir pressure. The vertical axis is ionization signal In arbitrary units. vibronic structure from Ar. However, the vibrational degrees of freedom are in very poor equilibrium with the translational and rotational modes because of the large differences in energy so that the cooling attained is incomplete and low-intensity bands due to hot-band population appear to be present. It was hoped, therefore, that by using diatomic and polyatomic carrier gases vibrational cooling would be enhanced. In Figure 2 are shown spectra taken for p-cresol for various carrier gases including He, Ar,Nz,and air. In addition we also investigated other carrier gases such as COz,P-10, methane, and ethane. The amount of extra vibrational cooling which should remove any lines caused by hot-band population that can be attained by using diatomic or polyatomic carrier gases is not important compared to the broadening of the vibronic structure in relation to that observed for Ar carrier since the degree of rotational cooling is decreased by these polyatomic carrier gases. Although Ar provides relatively the cleanest spectrum,
real atmospheric sampling requires the use of 1atm of air as the reservoir gas. Figure 2 shows the spectrum of p-cresol under these conditions where the results are found to be very similar to that of pure nitrogen. This spectrum is a result of using room air by opening the reservoir to atmospheric pressure. The ability to directly sample air from the atmosphere is made possible by using pulsed sources where, in our case, the beam is effectively on for 55 ps at 10 Hz or 550 ps per second; thus reducing the required pumping by a factor of 1/2000 compared to a continuous flow. An important question is whether actual discriminationcan be achieved between the isomers of cresol. Figure 3 is a spectrum taken of a mixture of the three cresol isomers with 1atm of room air as the carrier gas. The three isomers were placed in separate containers in the reservoir so that the liquids would not mix. The concentration is therefore the room vapor pressure of each isomer divided by 1atm of air
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or 330 ppm for p-cresol, 320 ppm for m-cresol, and 510 ppm for o-cresol. The nozzle was heated to -75 "C to minimize condensation in the aperture or on the walls. We see from the labeled spectrum that spectral lines are clearly visible from all three isomers and that they can be distinguished by using this technique. In order to estimate the limits of discrimination we used the diffusion tube technique to create a low concentration, -0.5 ppm, of one isomer in approximately25 ppm of a second isomer from a second heated diffusioa tube. During these experiments the lines and the nozzle were heated to -90 O C to prevent condensation on the walls. In the case of a mixture of 1:50 of p-:o-cresol or p-:m-cresol the p-cresol spectrum was easily observed with a SIN of at least 12-20/1 so that a discrimination of at least 300-500 was observed with a SIN of a t least 2. The uncertainty in these measurements is on the order of 25%;however, they do provide an indication of the capabilities of this technique. In the region studied, namely the origin peak at 282.97 nm, m- and o-cresol do not ionize in the free jet. However, some background ionization is present even off resonance for the case of all three isomers studied due to several possible factors. These factors may include thermalized background cresol molecules which may be present in the chamber due to incomplete pumping. The warm molecules may absorb and ionize where the cold molecules would not, thus creating a background. In addition, there are always some background ions due to ionization of diffusion pump oil. These problems could be minimized by enclosing the ionization region in a liquid nitrogen cold trap to trap out contamination, A third possibility is that the molecules are not cooled completely and there is always some off-resonant ionization inherently present due to a small population of high rotational states. This should be reduced by using higher reservoir pressures. We used 7 atm of Ar reservoir pressure in order to reduce this problem but found no significant improvement over the spectrum at 1 atm back pressure. One other possibility is that there may be a low background continuum absorption always present as observed in the case of naphthalene (38)which may always limit our inherent background discrimination. In the case of mixtures of m-:p-cresol in -1:50 mixture studied at 277.87 nm and in a mixture of o-:p-cresol in -1:50 mixture studied at 275.42 nm we also observed discrimination limits on the order of 300-5001. Of course, this could be further enhanced by the use of a preseparation technique such as gas chromatography (GC); however, the real-time sampling advantage would be lost. The beauty of the laser technique is that it can provide unique identification while providing spectral discrimination. It should be noted that in the case of the 1:50 mixture of p-:o-cresol the height of the p-cresol peaks in the spectrum are not 50X those of the 0-cresol peaks. At the laser energy used to obtain a useful signal from o-cresol at low concentrationthe p-cresol mass peaks are severely space charge broadened, meaning a loss of ions, and the spectral vibronic peak is also broadened. However, the latter effect does not significantly affect the discriminationattainable with the peaks chosen for study in this experiment. Another important question regards the limits of sensitivity of the technique for real air sampling. The use of the TOFMS device allows mass discrimination against other contaminanta in the air. We therefore monitor the parent peak of p-cresol as a function of concentrationusing the diffusion tube method to create low concentrations of cresoI in nitrogen or compressed air. The concentration can be changed by adjusting the flow rate of gas over the tube. We were easily able to detect -0.4 ppm of p-cresol using this technique with a SIN of -20/1. Lower concentrations could be produced but the signal was not found to fall off linearly with concentration at
low concentrations due to cresol molecules adsorbed to the walls even though the valve temperature was -90 "C. We estimate a theoretical lower limit of detection of at least 2C-40 ppb in air. Our present limits of sensitivity are limited by background ionization of thermal cresol in the chamber and other stray background ions from pump oil or other contaminants as discussed. Elimination of this problem would significantly lower our limits of sensitivity. In summary, we have shown the ability to uniquely discriminate the isomers of cresol based on the sharp vibronic structure produced by using R2PI spectroscopy with the supersonic molecular beam technique. The precision of these wavelength measurements has been found to be excellent and the use of various carrier gases has been discussed as a means of improving spectral resolution. The use of sampling from 1 atm of air directly from the environment has been demonstrated as well as the ability to discriminate the isomers of cresol in a mixture under these conditions. Discrimination limits of at least 1:300-500 have been achieved between the various isomers of cresol with a theoretical detection limit of -20 ppb. Our hopes for the future of this technique will address the problems of quantitation. The present major obstacles are due to the various experimental variables, most significantly the fluctuation in laser intensity. These fluctuations are due to both pulse-to-pulse variations and longer term changes in laser intensity. Because of the measured I2 power dependence at the laser intensity used in these experiments, the fluctuations are magnified so that at present our quantitative measurements are accurate to no better than 25%. LITERATURE CITED Amirav, A.; Even, U.; Jortner, J. J. Chem. Phys. 1079, 7 7 , 2319. Amirav, A.; Even, U.; Jortner, J. Anal. Chem. 1082, 5 4 , 1666. Amirav, A.; Even, U.; Jortner, J. J. Phys. Chem. 1081. 85, 309. Dietz, T. G.; Duncan, M. A.; Liverman, M. G.; Smalley, R. E. Chem. Phys. Lett. 1980, 7 0 , 246. Dietz, T. 0.; Duncan, M. A.; Liverman, M. G.; Srnaliey, R. E. J. Chem. Phys. 1080, 73, 4816. Smaiiey, R. E.; Wharton, L.; Levy, D. H. Acc. Chem. Res. 1077, 10. 139. Mikami, N.; Hiraya, A.; Fujiwara, I.; Ito, M. Chem. Phys. Lett. 1980, 7 4 , 531. McClelland, G. M.; Saenger, K. L.; Vaientini; J. J.; Herschbach, D. R. J, Phys. Chem. 1070, 83, 947. Fitch, P. S. H.; Haynam, C. A,; Levy, D. R. J . Chem. Phys. 1980, 7 3 , 1064. Warren, J. A.; Hayes, J. M.; Small, G. J. Anal. Chem. 1082, 5 4 , 138. Brown, J. C.; Hayes, J. M.; Warren, J. A.; Small, G. J. I n "Lasers in Chemical Analysis"; Hleftje, G. M., Travis, J. C., Lytle, F. E., Eds.; Humana Press: 1981; Chapter 12. Hayes, J. M.; Small, G. J. Anal. Chem. 1082, 54, 1202. Hayes, J. M.; Chlang, I.; McGiade, M. J.; Warren, J. A.; Small, G. J. "Laser Spectroscopy for Sensitive Detection"; Geibwachs, J. A,, Ed.; Society Of Photo-Optical Instrumentation Engineers: Belllngham, WA, 1981; Vol. 286, p 117. Lubman, D. M.; Kronick, M. N. Anal. Chem. 1082, 5 4 , 660. Lubman, D. M.; Kronick, M. N. Anal. Chem. 1082, 54, 1546. Frueholz, R.; Wessel, J.; Wheatley, E. Anal. Chem. 1980, 5 2 , 281. Lubman, D. M.; Naaman, R.; Zare, R. N. J. Chem. Phys. 1080, 7 2 , 3034. Seaver, M.; Hudgens, J. W.; DeCorpo, J. J. Int. J. Mass Spectrom. Ion. Phys. 1080, 34, 159. Boesl, U.; Neusser, H. J.; Schlag, E. W. Chem. Phys. 1081, 55, 193. Klimcak, C.; Wessel, J. Anal. Chem. 1080, 52, 1283. Brophy, J.; Rettner, C. T. Opt. Lett. 1070, 4, 337. Rhodes, G.; Opsai, R. 8.; Meek, J. T.; Reiily, J. P. Anal. Chem. 1083, 55, 280. Zandee, L.; Bernstein, R. 8. J. Chem. Phys. 1079, 7 0 , 2574. Zandee, L.; Bernstein, R. B. J. Chem. Phys. 1979, 7 1 , 1359. Lichtln, D. A.; DattaGhosh, S.; Newton, K. R.; Bernsteln, R. B. Chem. Phys. Lett. 1080, 7 5 , 214. Cooper, C. D.; Williamson, A. D.; Mllier, J. C.; Compton, R. N. J. Chem. Phys. 1080, 7 3 , 1527. Johnson, P. M. Acc. Chem. Res. 1080, 13, 20. Lubrnan, D. M.; Kronlck, M. N. Anal. Chem. 1982, 5 4 , 2289. Lubman, D. M.; Kronlck, M. N. Anal. Chem. 1083, 55, 1486. Knapp, 0. E.: Moe, H. S.; Bernstein, R. B. Anal. Chem. 1050, 22, 1408. Rorden, R. J.; Lubman, D. M. Rev. Scl. Instrum. 1083, 5 4 , 641.
Anal. Chem. 1904, 56. 1967-1970 Lubman, D. M.; Rettner, C. T.; Zare, R. N. J . Phys. Chem. 1982, 86, 1129. Altshuller, A. P.: Cohen, J. R. Anal. Chem. 1980, 32, 802. Dunn, T. M., prlvate communication. Kantrowltz, A.; Grey, J. Rev. Sci. Insfrum. 1951, 22, 328. Anderson, J. B.; Andres, R. P.;Fenn, J. B. A&. Chem. Phys. 1988, 10, 275. McClelland, G. M.; Saenger, K. L.; Valentlnl, J. J.; Herschbach, D. R. J . Phys. Chem. 1979, 83. 947.
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(38) Beck, S. M.; Monts, D. L.; Liverman, M. G.; Smalley, R. E. J . Chem. Phys. 1979, 7 0 , 1062.
RECEIVED for review March 19,1984. Accepted May 10,1984. We gratefully acknowledge financial support from a Cottrell Research Grant, a Petroleum Research Fund Type G Grant, and a University of Michigan Rackham Award.
Chronoamperometric Determination of Diffusion-Layer Thicknesses at Hydrodynamic Electrodes Kenneth W.Pratt Center for Analytical Chemistry, National Bureau of Standards, Washington, D.C. 20234
A new technlque Is described by whlch dlffuslon-layer thlcknesses at hydrodynamic electrodes are measured wlthout knowlng the electrode area, sdutlon concentration, OT number of electrons In the electrode reactlon. Comparison of the chronoamperometrlc current, obtalned In qulescent solution, wlth the llmitlng current obtalned at the same electrode In hydrodynamic voltammetry ylelds a characterlstk “equlvalent tlme”. Thls parameter Is directly related to the dlffuslon-layer thlckness at the electrode. Experlmental diffusion-layer thlcknesses are measured at rotating dlsk and vlbratlng wlre electrodes uslng thls technlque. The values agree wlh those obtalned from llmllngturrenl measurements to wlhln 5 % at the rotating dlsk and 16% at the vlbratlng wlre electrode. Factors contrlbutlng to these errors are evaluated.
at time t = 0 from a value Eo,where no reaction occurs at the electrode, to El, the value used in the steady-state measurements. These currents are described by eq 1 for the steadystate case and by eq 2, the Cottrell equation, for the transient case
Using the same electrode and solutions in both experiments ensures the equality of n, A, D , and C. Graphs of eq 1 and 2 are presented in Figure 1 by solid lines. The values of ISs and I(t)were calculated by using representative values for n, A, D, C , and 6. For t = tr,the point at which I ( t ) = I,,, the right members of eq 1and 2 are equal. Simplification yields the following expression:
6 = (7rDt?1/2
The analytical sensitivity of hydrodynamic electrodes in voltammetry is governed by the thickness of the diffusion layer, 6, established at the electrode. The value of 6 is used to intercompare the performance of electrodes of different geometries and to optimize a given electrode (I). Experimental values for 6 generally are calculated by using eq 1 nFADC 18,= (1) 6 where I,, n, F, A, D, and C represent the steady-state limiting current, number of electrons in the electrode reaction, Faraday constant, electrode surface area, diffusion coefficient, and bulk concentration of the electroactive species, respectively. Calculation of 6 depends on each of these parameters. Frequently, the exact electrode area is not available, due to surface roughness or partial fouling of the electrode. In contrast to the above method, the technique described here allows the value of 6 to be determined for a hydrodynamic electrode without measuring its surface area. Prior knowledge of the hydrodynamic conditions prevailing a t the electrode is not required. The determination is based on a comparison of the steady-state and transient currents observed at the same electrode in a single solution. The steady-state limiting current, I-, is measured under the hydrodynamic conditions of interest at a potential E,, corresponding to the masstransport limited reaction of the electroactive species a t the electrode. The transient faradaic response of the electrode in quiescent solution, I(t),is then recorded for a potential step
(3) Equation 3 is used to calculate the value of 6, using the experimental value for t ! The value for D may be calculated (2) from the equivalent conductance of the electroactive species at infinite dilution. Neither A, n, nor C needs to be experimentally determined. The value of 6 calculated by using this technique represents the average value for the entire electrode surface. In most cases, the local value of 6 varies a t different points on the electrode, as a result of varying hydrodynamic conditions. Only those electrodes satisfying the condition of uniform accessibility (3), such as the rotating disk electrode (RDE), have equal values of 6 at all points on the electrode surface. Flanagan and Marcoux (4) first introduced the concept of t’, the ”equivalent time”, in a theoretical study of the chronoamperometric response of tubular electrodes. Measurementa of t’values for actual electrodes were not presented. The present contribution represents the first experimental comparison of chronoamperometric data, obtained in quiescent solution, with data obtained by hydrodynamic voltammetry at the same electrode. Other combinations of independent electroanalytical measurements, obtained on a single electrode system, have previously been used in measurements of the value of n (5) and D (6) for electrochemical systems. The present method for the measurement of 6 represents a third member of this family of “paired” techniques. EXPERIMENTAL SECTION Apparatus and Reagents. Experimental studies were conducted using a Pt disk electrode (Model DD20,Pine Instrument
Thls artlcle not subject to U S . Copyright. Published 1984 by the American Chemlcal Society
