10900
J. Phys. Chem. B 2001, 105, 10900-10904
Distance Dependence of the Electron-Transfer Rate Across Covalently Bonded Monolayers on Silicon Jun Cheng,† David B. Robinson, Ronald L. Cicero, Todd Eberspacher, Carl J. Barrelet, and Christopher E. D. Chidsey* Department of Chemistry, Stanford UniVersity, Stanford, California 94305-5080 ReceiVed: June 21, 2001; In Final Form: August 14, 2001
Alkyl monolayers covalently bonded directly to n-type Si(111) surfaces have been prepared by UV illumination of the H-Si(111) surface while immersed in CH2dCH-(CH2)n-3CH3 (n ) 5-8) under high vacuum. The characterization by ellipsometry, infrared spectroscopy, and X-ray photoelectron spectroscopy shows that 1-alkenes form dense monolayers on the silicon surface. The electron-transfer rates from the surface of the electrode through the alkyl monolayers to decamethylferricenium acceptors in tetrahydrofuran have been measured. The rates are proportional to the decamethylferricenium concentration and also to the dopant density as determined from capacitance measurements. The rates show an exponential distance dependence with a decay constant of 1.00 ( 0.05 per CH2, similar to known behavior with alkanethiol monolayers on metal electrodes. The dependence of the rates on applied potential has a logarithmic slope of about 0.25F/RT at potentials negative of the flat-band potential derived from capacitance measurements. This slope is qualitatively consistent with the expected potential dependence of the activation energy of electron transfer. The slope increases as expected at potentials positive of the flat-band potential, where a space-charge region forms.
I. Introduction The study of the kinetics of electron transfer across electrochemical interfaces can be greatly facilitated by the use of organic monolayers. This has been clearly demonstrated for metal electrodes.1-7 By acting as a tunneling barrier, monolayers cause electron transfer to be the rate-limiting process in the flow of current across the interface. The thickness of the monolayer can be varied, revealing an exponential dependence of the rate on tunneling distance. In this situation, the rate law can be separated into a distance-dependent tunneling prefactor and a potential-dependent activation factor. Several methods of preparation of monolayers on silicon electrodes have been developed recently.8-13 The electrochemical properties of some of these have been reported.13-16 We have previously demonstrated that alkyl monolayers formed from 1-octene covalently attached to an n-type silicon (111) surface make electron tunneling to decamethylferricenium rate limiting in a tetrahydrofuran electrolyte. The work presented here shows that alkyl monolayers formed in this way exhibit a distance dependence similar to that seen at metal electrodes (Figure 1). This result allows for a similar separation of the rate law to that found for metal electrodes, which should facilitate study of electrochemical kinetics at silicon electrodes. Much progress has been made in recent years in understanding the kinetics of electron transfer at silicon electrodes. Lewis et al. studied the rate law for electron transfer between a silicon electrode and various viologens and have found that it can be factored in terms of electrode dopant density, concentration of redox species, and a potential-dependent factor with an exponential form when a carrier depletion region exists in the * To whom correspondence should be addressed. E-mail: chidsey@ stanford.edu. † Present address: Dionex Corporation, 445 Lakeside Drive, Sunnyvale, CA, 94088-3603.
Figure 1. Schematic drawing of interfacial electron transfer through an alkyl monolayer on a Si(111) electrode.
electrode.17-19 The rate law for the system described here can be factored in a similar way although the potential-dependent factor has a less rapidly changing exponential, apparently because a carrier depletion region is not formed in the electrode over most of the potential range for which a significant electrontransfer current is measured. The alkyl monolayers we describe offer the benefit of control of electron-transfer rate by controlling electron tunneling. II. Experimental Section A. Monolayer Coated n-Silicon (111) Electrode Preparation. Monolayers were prepared according to the procedure specified in ref 16 except as follows. For the Si(111) attenuated total internal reflection plate, each side was illuminated for 2 h. The Si(111) wafers used for the data presented in Table 1 and Figures 2, 4, and 5 were from Siltec and were specified to have resistivities of 0.1-0.9 Ω‚cm. Those used for Figures 3 and 6 were specified to have resistivities of 1-5 Ω‚cm. Instead of a quartz cuvette, preparation of samples used for the data presented in Figures 3 and 6 used a quartz-windowed chamber
10.1021/jp0123740 CCC: $20.00 © 2001 American Chemical Society Published on Web 10/16/2001
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J. Phys. Chem. B, Vol. 105, No. 44, 2001 10901
TABLE 1: Characterization of Alkyl Monolayers on Silicon (111) monolayer formed from CH3(CH2)n-3CHdC H2
thicknessa (Å)
asymmetric methylene stretchb (p-pol, cm-1)
ratio of C(1s) to Si(2p) XPS peak areas
n)5 n)6 n)7 n)8 n ) 10
6 7 8 9 11.5
2927.3 2924.5 2922.2 2919.5 2920.0
0.46 0.55 0.67 0.77 1.00
a The experimental standard deviations for these determinations were 1 Å as determined from more than three independent measurements. b The reproducibility of peak positions in nominally identical samples was found to be 0.5 cm-1.
Figure 2. Typical cyclic voltammograms obtained on uncoated n-type H-Si(111) and CH3(CH2)2CHdCH2 coated Si(111) (n ) 5) electrodes in 2 mM Me10FcPF6/2 mM Me10Fc/1M LiClO4/THF and in 1M LiClO4/ THF at a scan rate of 500 mV/s. Capacitance measurements on these samples give a dopant density of 6 × 1015 cm-3.
Figure 4. Semilog plots of forward scans of cyclic voltammograms measured on n-type H-Si(111) and CH3(CH2)n-3CHdCH2-coated Si(111) (n ) 5-8) electrodes in 2mM Me10FcPF6/2 mM Me10Fc/1 M LiClO4/THF at a scan rate of 500 mV/s. Currents are cathodic at potentials more negative than the open-circuit potential (the potential of the notch in the H-Si(111) curve) and anodic at more positive potentials. Oscillations at low currents are due to instrumental line noise.
Figure 3. Concentration dependence of the current for a CH3(CH2)5CHdCH2 coated Si(111) (n ) 8) electrode in the specified, equal concentrations of Me10FcPF6 and Me10Fc in THF containing 0.1M LiClO4 at a scan rate of 100 mV/s. Capacitance measurements on these samples give a dopant density of 7 × 1014 cm-3.
Figure 5. Distance dependence of the data from Figure 3. The solid lines give the best fits and result in an average β of 1.00 ( 0.05 per methylene.
that had been evacuated and backfilled with purified argon and that contained samples covered with a thin film of the liquid alkene that had been filtered through alumina and degassed. Samples prepared by this modified procedure have been found to be indistinguishable from those prepared in a quartz cuvette. B. Characterization of Monolayers. 1. Ellipsometry. Ellipsometric measurements were performed with a Gaertner variable angle ellipsometer L116B using a helium-neon laser at an incident angle of 70°.10 The monolayer thickness was calculated using an index of refraction of 1.46 for the hydrocarbon monolayer.20 Effective substrate optical constants were measured for freshly prepared H-Si(111).
2. X-ray Photoelectron Spectroscopy (XPS). X-ray photoelectron spectra were obtained on a Surface Science Model 150 XPS spectrometer equipped with an Al KR source, a quartz monochromator, a concentric hemispherical analyzer, and a multichannel detector. No electron flood gun was employed. The pressure in the analytical chamber during analysis was approximately 5 × 10-8 Torr. A takeoff angle of 35° from the surface was used. Spectra of C(1s) (275-295 eV binding energy), O(1s) (525-545 eV binding energy), Si(2p) (90-110 eV binding energy), and survey scans (0-1100 eV binding energy) were recorded with a 250 × 1000 µm spot size.
10902 J. Phys. Chem. B, Vol. 105, No. 44, 2001
Cheng et al. decamethylferrocene (Me10Fc) by following a published procedure.22 Capacitance was measured by AC impedance using a 10 mV AC signal at frequencies between 33 and 1000 Hz. At higher frequencies, the impedance signal was limited by solution resistance. III. Results and Discussion
Figure 6. Mott-Schottky plot for a CH3(CH2)5CHdCH2 coated Si(111) (n ) 8) 5 Ω‚cm electrodes in 0.1 mM Me10FcPF6/0.1 mM Me10Fc/0.1M LiClO4/THF. Capacitances are averaged over several frequencies and varied by approximately 10%. At the most positive potentials shown, the measurements involved very low currents and are less accurate.
3. Infrared Spectroscopy. Infrared absorption spectra were obtained on silicon (111) trapezoidal plates designed for attenuated total internal reflection (ATR) spectroscopy (Harrick Scientific, 45°, 50 × 20 × 1 mm) with a Mattson model RS10000 spectrometer and additional external optics.10 Light was focused onto one of the 45° bevels of the ATR plate. The plate rested on three steel balls and against three cylindrical posts to allow reproducible positioning. After exiting the crystal, the IR light was directed to a liquid N2-cooled mercury cadmium telluride detector with an associated preamp. The resultant signal was returned to the spectrometer. The external optics were surrounded by a Plexiglas box which was purged with filtered, water- and carbon dioxide-depleted air. Individual p-polarized ATR intensity spectra were collected for the oxidized silicon, silicon hydride, and monolayer-coated surfaces at 2 cm-1 resolution. Absorption spectra were derived from ratios of monolayer intensity spectra to the spectrum of the freshly oxidized silicon ATR plate. C. Electrochemical Measurements. Electrochemical measurements were made in either a glass cell clamped to the sample with a Chemraz O-ring or in a cell in which a bored cone of Teflon is pressed down against the sample. The electrode areas were measured by electroplating silver onto the electrodes and carefully measuring the dimensions of the plated area with a traveling telescope. Ohmic contacts were made by using Ga:In eutectic (Alfa) between the back of the silicon and a copper plate, which was connected to the working electrode connection of a PAR 273 potentiostat. The potentiostat was interfaced to a personal computer and modified to provide smooth potential ramps for cyclic voltammetry.21 Platinum counter and reference electrodes were used for electrochemical measurements, except for E0_determinations, which were referenced to standard reference electrodes. Measurements using the Teflon cell were performed in an N2-purged glovebox, and those in the glass cell were perfomed under argon following cannula transfer of the electrolyte solution from a Schlenk flask. All measurements were performed in the dark at ambient temperature with a scan rate of 500 mV/s. The electrolyte (LiClO4) was dried at ca. 150 °C under vacuum. The solvent, tetrahydrofuran (THF), was distilled under argon immediately before use from the blue solution formed by sodium and benzophenone. Decamethylferricenium hexafluorophosphate (Me10FcPF6) was prepared from
A. Alkyl Monolayer Characterization. The structures of the alkyl monolayers have been characterized by ellipsometry, X-ray photoelectron spectroscopy, and infrared spectroscopy (Table 1) and are consistent with results presented in previous work.10,16 The thicknesses measured by ellipsometry are near the expected values for densely packed monolayers, with each C-C bond contributing about one angstrom to the thickness. XPS provides elemental analysis of the monolayers. The ratios of the areas of the carbon peaks to those of silicon show a reasonable correlation to the chain length, suggesting uniform coverage as a function of length. The oxygen levels observed by XPS are quite low, as expected for alkyl monolayers. Infrared spectroscopy provides a measure of the density of gauche defects in a monolayer. The peak at 2920 cm-1 is assigned to the asymmetric CH2 stretch. The stretch is known to increase in frequency as the density of gauche defects increases, possibly indicating an increase in free volume within the film.23 The shift of peak position as n decreases from 10 to 5 suggests that the short-chain monolayers form structures with more gauche defects than the longer chains. It has been shown previously that monolayers of short-chain thiols on gold are more defective than those of long-chain thiols, but that even short-chain thiol monolayers form barriers between the electrode and electrolyte.23 B. Monolayer Blocking Characteristics. Previous work has shown that monolayers formed from 1-octene on Si(111) limit the electron-transfer current to decamethylferricenium in tetrahydrofuran.16 Figure 2 shows typical cyclic voltammograms obtained at an n ) 5 alkyl-coated Si(111) and an uncoated H-Si(111) electrode in contact with a tetrahydrofuran solution of 1 M lithium perchlorate and a redox couple composed of 2 mM decamethylferricenium hexafluorophosphate and 2 mM decamethylferrocene. Comparison of the curves in Figure 2 for the coated and uncoated electrodes indicates a significant difference in the electron-transfer rate. The uncoated electrode shows a large current with a diffusion-limited peak, while the coated electrode shows a much smaller current that does not reach a diffusion limit in the same potential range. This shows that the monolayer is able to block access to the electrode by the redox couple, reducing the electron-transfer rate.24 The background current for a coated Si electrode in an electrolyte without the redox couple was measured. It is negligible compared to that from electron transfer to the electron acceptor across the coated electrode. This demonstrates that corrosion processes and double-layer charging make insignificant contributions to the current and that the current can be attributed solely to electron transfer to the redox couple. C. Rate Law. Because the reverse scan of the curve for the monolayer-coated electrode nearly overlaps the forward scan, we conclude that the observed current is not limited by diffusion. In that case, when the potential is significantly negative of the formal potential of the couple, E0', the electron-transfer rate constant is expected to be related to the current density, i, by
i ) -FCAkred
(1)
where F is Faraday’s constant, the charge of one mole of
Distance Dependence of the Electron-Transfer Rate
J. Phys. Chem. B, Vol. 105, No. 44, 2001 10903
electrons, CA is the bulk concentration of electron-acceptor molecules, and kred is the reduction rate constant.25 Figure 3 confirms the concentration dependence of this relationship. The inset shows that the concentration dependence is first-order, within experimental error, and independent of potential.24 D. Distance Dependence. Semilog plots of the absolute value of current vs potential for electrodes coated with monolayers of various lengths are shown in Figure 4. For comparison, a similar plot for an uncoated electrode is shown. Figure 5 plots the current as a function of n for several applied potentials. For each potential, the data can be fit to an exponential decay as a function of n:
i ∝ exp(-βn)
(2)
where β is the decay constant for electron transfer. β is approximately constant over the entire potential range. The value of β is 1.00 ( 0.05 per CH2, closely matching the value predicted26,27 and observed2,3,28-30 for alkyl monolayers on metal electrodes. This suggests that the monolayers keep the acceptor molecules at a distance from the electrode surface greater than the monolayer thickness. Given this exponential distance dependence, there must be relatively few pinhole defects in the monolayer because such defects are known to easily dominate the electron-transfer process and to destroy the observed distance dependence. The fact that the distance dependence is independent of potential suggests that the rate constant for electron transfer can be expressed as the product of a distance-dependent prefactor limited by electron tunneling and an activation factor that depends on the applied potential and the electronic energy levels in the electrode and the acceptor molecule. E. Potential Dependence. To develop an understanding of the potential dependence of the current, we have attempted to learn how the charge carriers are distributed at the interface as a function of potential. When charge carriers are depleted from a semiconductor surface and a space charge region develops in the semiconductor, the capacitance of the interface is relatively low and is described by the Mott-Schottky formula,31 which for n-type semiconductors takes the form
(CA)
-2
)
2 (E - Efb) e0ND
(3)
Here, C/A is the interfacial capacitance per unit area, E is the applied potential, Efb is the flat-band potential (essentially the potential of zero charge within the semiconductor), e is the charge of an electron, is the dielectric constant of silicon (11.9), o is the permittivity of free space, and ND is the dopant density. When charge carriers accumulate at the interface, there is no space charge region, and the capacitance is much higher. For n-type semiconductors, this occurs for potentials more negative than Efb. Figure 6 shows that the interfacial capacitance of alkyl monolayer-coated silicon electrodes conforms to the expected behavior, with a region at more positive potentials that follows the Mott-Schottky formula and a region at more negative potentials where the capacitance is very high and thus the inverse square capacitance is negligible. The results shown are independent of concentration of the redox couple. The intercept of the Mott-Schottky curve on the potential axis indicates a flatband potential of approximately 0 V versus NHE.32 The slope of the curve indicates a dopant density of 7 × 1014 cm-3, a value consistent31 with the specified resistivity range of the wafers used, 1-5 Ω‚cm.
From capacitance and current data, we find that the electrontransfer current is proportional to the dopant density. For example, capacitance data from the samples used in Figures 3 and 4 show that the dopant density is 10 times greater for the samples used in Figure 4. The concentration of ferricenium is 4 times greater for the solutions used in Figure 4 than for the more concentrated solution in Figure 3. The resulting electrontransfer currents for the electrode coated with the octene-derived monolayer in Figure 4 are 40 times greater than for the more concentrated solution in Figure 3, showing that the current scales linearly with dopant density. This result suggests that electron transfer is occurring largely from the conduction band of the electrode to the ferricenium. With the above understanding of the charge distribution at the interface, we examine the potential dependence of the currents shown in Figure 4. The slopes of semilog plots such as those in Figure 4 are traditionally characterized by the dimensionless parameter, R:
R)
-kBT d ln|i| e dE
(4)
The value of R observed at potentials negative of the flat-band potential is about 0.25 for all monolayer thicknesses.33 At potentials negative of the flat-band potential, charge carriers accumulate at the interface, no space charge layer exists, and most of the interfacial potential drop is expected to occur across the monolayer. In this case, the value of R is determined largely by the potential dependence of the activation energy for electron transfer.34-36 This is similar to the situation at metal electrodes. At both metal electrodes and n-type semiconductor electrodes in carrier accumulation, R is expected to be less than 0.5 for potentials significantly negative of the formal potential, as in the current case.1 In the Mott-Schottky region, where potentials are more positive than the flat-band potential, one would expect the current to exhibit a potential dependence dominated by thermal activation of electrons over the space charge barrier, with R approaching 1.0.34 To the extent that the potential dependence of the currents can be determined from the data in this region, the curves in Figure 4 are indeed steeper in this potential region. For example, at 50 mV versus NHE, the heptene monolayer exhibits an R value of about 0.8. IV. Conclusions Monolayers of several thicknesses prepared by UV-induced addition of 1-alkenes to hydrogen-terminated Si(111) surfaces have been shown to block electron transfer across the siliconTHF electrolyte interface, allowing the electron-transfer current to remain kinetically limited well beyond the flat-band potential. The dependence of the electron-transfer rate on monolayer thickness has been shown to be similar to that at gold-aqueous electrolyte interfaces, suggesting that the monolayers block the approach of electron acceptors to the surface and that no significant contribution to the measured electron-transfer rate is made by transfer at pinhole defects in the monolayer. Moreover, this distance dependence is independent of potential, suggesting a clean separation of the rate constant into a tunneling-dependent prefactor and a potential-dependent activation factor. The potential dependence is consistent with the flatband potential derived from capacitance data. These alkenederived monolayers on silicon may facilitate further attempts to gain a better understanding of electron transfer at silicon electrodes. Acknowledgment. This work was supported by the National Science Foundation through grant CHE-9412720. We also thank
10904 J. Phys. Chem. B, Vol. 105, No. 44, 2001 the Center for Materials Research at Stanford University for the use of the XPS made possible through funds from the NSFMRSEC program. D.B.R. acknowledges a National Science Foundation Graduate Fellowship. Jason Henderson at Zyomyx Inc. (Hayward, CA) provided advice and technical assistance with preparation of some samples. References and Notes (1) Chidsey, C. E. D. Science 1991, 251, 919. with the correction: Chidsey, C. E. D. Science 1991, 252, 631. (2) Becka, A. M.; Miller, C. J. J. Phys. Chem. 1992, 96, 2657. (3) Finklea, H. O.; Hanshew, D. D. J. Am. Chem. Soc. 1992, 114, 3173. (4) Terrettaz, S.; Becka, A. M.; Traub, M. J.; Fettinger, J. C.; Miller, C. J. J. Phys. Chem. 1995, 99, 11216. (5) Cheng, J.; Saghiszabo, G.; Tossell, J. A.; Miller, C. J. J. Am. Chem. Soc. 1996, 118, 680. (6) Weber, K.; Hockett, L.; Creager, S. J. Phys. Chem. B 1997, 101, 8286. (7) Sachs, S. B.; Dudek, S. P.; Hsung, R. P.; Sita, L. R.; Smalley, J. F.; Newton, M. D.; Feldberg, S. W.; Chidsey, C. E. D. J. Am. Chem. Soc. 1997, 119, 10563. (8) Linford, M. R.; Chidsey, C. E. D. J. Am. Chem. Soc. 1993, 115, 12631. (9) Haran, A.; Waldeck, D. H.; Naaman, R.; Moons, E.; Cahen, D. Science 1994, 263, 948. (10) Linford, M. R.; Fenter, P.; Eisenberger, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc. 1995, 117, 3145. (11) Bansal, A.; Li, X. L.; Lauermann, I.; Lewis, N. S.; Yi, S. I.; Weinberg, W. H. J. Am. Chem. Soc. 1996, 118, 7225. (12) Royea, W. J.; Juang, A.; Lewis, N. S. Applied Physics Lett. 2000, 77, 1988. (13) Boukherroub, R.; Morin, S.; Bensebaa, F.; Wayner, D. D. M. Langmuir 1999, 15, 3831. Yu, H. Z.; Boukherroub, R.; Morin, S.; Wayner, D. D. M. Electrochemistry Communications 2000, 2, 562. (14) Vuillaume, D.; Boulas, C.; Collet, J.; Davidovits, J. V.; Rondelez, F. Appl. Phys. Lett. 1996, 69, 1646. (15) Bansal, A.; Lewis, N. S. J. Phys. Chem. B 1998, 102, 4058. (16) Barrelet, C. J.; Robinson, D. B.; Cheng, J.; Hunt, T. P.; Quate, C. F.; Chidsey, C. E. D. Langmuir 2001, 17, 3460. (17) Fajardo, A. M.; Lewis, N. S. Science 1996, 274, 969. (18) Fajardo, A. M.; Lewis, N. S. J. Phys. Chem. B 1997, 101, 11136. (19) Haber, J. A.; Lauermann, I.; Michalak, D.; Vaid, T. P.; Lewis, N. S. J. Phys. Chem. B 2000, 104, 9947.
Cheng et al. (20) This refractive index value is set to the value for SiO2 on Si (our reference sample) and is in the range reported for liquid and solid hydrocarbons at room temperature (1.38 for hexane to 1.54 for high-density polyethylene). The resulting film thicknesses are not strongly dependent upon this choice. See also: Allara, D. L.; Nuzzo, R. G. Langmuir 1985, 1, 52. (21) Chidsey, C. E. D.; Loiacono, D. N. Langmuir 1990, 6, 682. (22) Nesmeyanov, A. N.; Materikova, R. B.; Lyatifov, I. R.; Kurbanov, T. K.; Kochetkova, N. S. J. Organomet. Chem. 1978, 145, 241. (23) Porter, M. D.; Bright, T. B.; Allara, D. L.; Chidsey, C. E. D. J. Am. Chem. Soc. 1987, 109, 3559. (24) The standard deviation of the current among the first scans of samples from separate monolayer preparations is 25%. The current density for repeated scans decreases by 35% before reaching a steady state. Data reported here are from the first scan on a given sample. (25) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; John Wiley & Sons: New York, 1980. (26) Cave, R. J.; Newton, M. D. Chem. Phys. Lett. 1996, 249, 15. (27) Cheng, J.; Miller, C. J. J. Phys. Chem. B 1997, 101, 1058. (28) Xu, J.; Li, H. L.; Zhang, Y. J. Phys. Chem. 1993, 97, 11497. (29) Smalley, J. F.; Feldberg, S. W.; Chidsey, C. E. D.; Linford, M. R.; Newton, M. D.; Liu, Y. P. J. Phys. Chem. 1995, 99, 13141. (30) Slowinski, K.; Chamberlain, R. V.; Miller, C. J.; Majda, M. J. Am. Chem. Soc. 1997, 119, 11910. (31) Sze, S. M. Semiconductor DeVices: Physics and Technology; John Wiley & Sons: New York, 1985. (32) Flat-band potentials are specific to a given electrode, monolayer, and electrolyte system and can vary by hundreds of millivolts for different systems. Cohen, R.; Zenou, N.; Cahen, D.; Yitzchaik, S. Chem. Phys. Lett. 1997, 279, 270. (33) Though the slope is largely independent of potential negative of the flat-band potential, there is a fine structure that varies from sample to sample and may be related to differences in the density of states available for tunneling. (34) Gerischer, H. In AdVances in Electrochemistry and Electrochemical Engineering; Delahay, P., Tobias, C. W., Eds.; Interscience Publishers: New York, 1961; Vol. 1; p 139. (35) Gerischer, H. In Physical Chemistry: An AdVanced Treatise; Eyring, Henderson, Jost, Eds.; Academic Press: New York, 1970; Vol. 9A, p 463. (36) Hamnett, A. Semiconductor Electrochemistry. In ComprehensiVe Chemical Kinetics; Compton, R. G., Ed.; Elsevier: New York, 1987; Vol. 27, p 61.
