44
Anal. ch8m. 1991, 63,44-48
(24) Yoshda, H.; Morita, I.; Tamai. G.; Masujima, T.; Tsuru, T.; Takai, N.; Imia. H. Chromatographia 1984, 19, 466-472. (25) Hagestam, I.H.; Plnkerton. T. C. Anal. Chem. 1985, 5 7 , 1757-1763. (26) Gish, D. J.; Hunter, B. T.; Feibush, B. J . Chromatogr. 1988, 433, 264-268. (27) Haglnaka. J.; Yasuda, N.; Wakai, J.; Matsunaga, H.; Yasuda, H.;Kimura, Y. Anal. Chem. 1989, 6 1 , 2445-2448.
(28) Floyd, T. R.; Hartwick. R. A. In High Perfwmsnce Liquid Chromarography: Advances and Perspectives; Horvith, C., Ed.; Academic Press: New York, 1986; Vol. 4, pp 45-90.
RECEIVED for review March 21, 1990. Revised manuscript received July 12, 1990. Accepted October 8, 1990.
Electrodesorption from Single-Crystal Electrodes: Analysis by Differential Electrochemical Mass Spectrometry Thomas Hartung, Udo Schmiemann, Inge Kamphausen, and Helmut Baltruschat* Institute of Physical Chemistry, University of WittenlHerdecke, Stockumer Str. 10, 5810 Witten, FRG
A newly designed thin-layer cell allows the use of differential eiectrochemlcaimass spectrometry (DEMS) for the identification of volatile electrochemical desorption products from single-crystal electrodes. The sensitivity is in the range of a percent of a monolayer. This Is demonstrated for the case of preadsorbed benzene on a Pt( 111) electrode. Contrary to the case of a polycrystalline electrode, benzene Is mainly desorbed as such without H/D exchange; only a minor part is hydrogenatedto cyclohexane, whlch is the main desorption product from a polycrystalline electrode. Oxidation of the adsorbate occurs In two well-separated steps: In the double-layer reglon a partially oxldlred adsorbed intermediate is formed, whlch Is oxldized to CO, in the oxygen adsorption region.
INTRODUCTION In heterogeneous electrocatalysis, an understanding of the interaction of molecules with the electrode surface is of primary importance. In recent years, a number of methods have been developed that allow the identification of adsorbates not only ex situ by means of typical ultrahigh vacuum (UHV) techniques (1-3) but also in situ, e.g., various IR techniques (4, 5), radio tracer techniques (6),the extended X-ray absorption fine structure technique (EXAFS) (7),and differential electrochemical mass spectrometry (DEMS) (8). It is clear that different crystallographic orientations of surface atoms have an influence on the catalytic and double-layer properties of single-crystal electrodes. Since the pioneering work of Hamelin et al. (9)and Clavilier ( l o ) ,the importance of using single-crystal electrodes for fundamental electrochemistry has been recognized in many electrochemical groups. For the study of adsorbates, the applicability of IR methods ( 11 ) to well-defined single-crystal electrodes and the first in situ characterization of an adsorbate layer by scanning tunneling microscopy (STM) (12) were major recent achievements. Here we will report the extension of DEMS to single-crystal electrodes. Hitherto, a porous gas diffusion electrode was used as the interface between the electrolyte and the vacuum. Volatile reaction products (or desorption products) evaporate into the mass spectrometer where they are detected on-line with a time constant of less than a second. If the ion current is recorded in parallel to a usual cyclic voltammogram, socalled mass spectrometric cyclic voltammograms (MSCVs) are obtained (8, 13). In the case of desorption experiments, these
MSCVs can be regarded as "electrodesorption spectra" in analogy to thermodesorption spectra. We recently reported the development of a new thin-layer cell that for the first time allowed the use of smooth electrodes (14). Here we will describe the use of a single-crystal electrode in such a cell and the analysis of electrodesorption products, using the anodic and cathodic desorptions of preadsorbed benzene from Pt(ll1) as a model system. The adsorption and electrooxidation of benzene and its homologues on polycrystalline platinum have been examined in a number of papers. Gileadi and Bockris measured the adsorption isotherms by using electrochemical and radiotracer methods (15). Hubbard et al. (16) determined the packing densities of various hydroquinones by the thin-layer technique, and by comparison with the oxidation charge, they concluded that other oxidation products beside COz are formed if adsorption was performed from solutions of higher concentrations. The oxidation of preadsorbed toluene on a porous Pt electrode was studied by DEMS. During the first oxidation cycle, adsorbed intermediates are formed that are in a higher oxidation state. From the number of electrons released per formed COz molecule, one can conclude that COz is the only oxidation product ( I 7). Far less attention has been paid to the cathodic desorption of unsaturated organic compounds from Pt electrodes. Using a long optical path thin-layer cell, Gui and Kuwana studied the hydrogenative desorption of various phenols from polycrystalline platinum (18). The desorption and hydrogenation of toluene, benzene, and acetone were studied in this laboratory (13,14,17).For both benzene and acetone, an extensive H/D exchange was found. The adsorption of difluorobenzene was studied by IR spectroscopy (19). To our knowledge, no such in situ characterization of adsorbed unsaturated compounds has been reported for the case of single-crystal electrodes. The adsorption of benzene on Pt single-crystal surfaces in UHV has been studied by various authors. On Pt(ll1) surfaces, adsorbed benzene only forms ordered layers if coadsorbed with CO (20). A complete H / D exchange has been found for the reaction of C6Hs adsorbed on the P t ( l l 0 ) face with gaseous D, (21).
EXPERIMENTAL SECTION A thin-layer cell, which allows the use of smooth electrodes for DEMS, was already described in ref 14 and was slightly modified for single-crystal electrodes. The thin-layer volume is formed by the electrode itself and a porous Teflon membrane, which are separated by a Teflon spacer
0003-2700/91/0363-0044$02.50/00 1990 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 63, NO. 1, JANUARY 1, 1991
-2.51
y
I
-501
-1 0
L OD
45
0.5
1D
I
II
I
I
I
1.5 E / Vphe
Figure 1. Voltammogram of the Pt(ll1)electrode in 0.05 M H2S04 (H cell, v = 40 mVls) after depsorptlon of the Iodine layer in 0.1 M KOH and cycling for 30 mln between -0.05 and 1.1 V.
I
mlz-78
63 (e50 gm, inner diameter 6 mm) and give a volume of approximately 1 gL. The connection to a counter and a reference electrode is made through capillaries, one of which also serves as the electrolyte outlet. A third bore is used as the electrolyte inlet. The hydrophobic Teflon membrane is mechanically supported by a steel frit. Volatile species, generated at the electrode, diffuse through the electrolyte and evaporate in the pores of the membrane. They are detected in the mass spectrometer with an overall time constant of approximately 2 s. This allows mass spectrometric cyclic voltammograms to be recorded in parallel to the usual cyclic voltammograms as long as the sweep rate does not exceed 20 mV/s. With the computerized quadrupole mass spectrometer (Balzers QMG 511), up to five m / z values can be recorded in parallel. The Pt(ll1) single crystal (diameter 1 cm) was obtained from Goodfellow, oriented to within 0.25 deg and polished with 1-gm alumina. Special care is necessary in preparing the electrode surface before each experiment. For the annealation of the crystal, we used the method of Wieckowski et al. (22),which leads to atomically flat surfaces with terrace widths of hundreds of micrometers (12, 23, 24). After the crystal is cleaned by cyclic voltammetry in sulfuric acid and rinsed with water, it is annealed in a hydrogen flame and transferred to a flask, where it cools down in an N, atmosphere saturated by iodine. The resulting iodine layer adsorbed on the platinum protects the surface from contaminations during the cooling and during the transfer to an electrochemical cell. Occasionally, the surface smoothness was checked with a home-built STM. Before the electrochemical experiments, this iodine has to be completely desorbed. For this, we used two methods: The first one (used by Wieckowski et al.) consists of displacing the iodine by CO in acidic electrolyte a t potentials close to the onset of the hydrogen evolution. After an electrolyte exchange, the adsorbed CO is oxidized, avoiding potentials a t which the crystal is roughened due to oxygen adsorption. The second one consists of desorbing the iodine in alkaline solutions. With respect to acidic solutions, the potential window between hydrogen and oxygen evolution is shifted cathodically, and potentials can be applied that are negative of that where reversible iodine adsorption occurs (-0.4 V versus NHE (25)). After the annealation, the iodine therefore was desorbed in 0.1 M KOH by sweeping the potential negative to +50 mV (RHE) (=4.73 V (NHE)). After an electrolyte exchange, the crystal was transferred to another cell and introduced into sulfuric acid a t 50 mV (RHE, pH 1). During this transfer, the crystal surface was protected by a droplet of electrolyte. Cycling between4.05 and 1.1 V with 0.4 V/s for 30 min improved the shape of the voltammogram (Figure 1). To our experience, this second procedure gave less problems with iodine contaminations. After checking for cleanliness and surface order by cyclic voltammetry in the hydrogen region, adsorption was performed under potential control at 0.4 or 0.5 V by forcing the electrolyte containing benzene (or, for calibration experiments, CO) through the thin-layer cell, typically 0.5-1 mL in 1min. This was followed by a thorough electrolyte exchange with sulfuric acid. Control
Flgure 2. Electrodesorptionof benzene from Pt(1 11)after adsorption from a 2 X lo4 M benzene solution followed by electrolyte exchange , = 0.2 V; v = 12.5mV/s; cathodic potential with 0.05 M H,SO,; E limit -0.1 V. Broken line: second sweep. (a) Cyclic voltammogram, (b) MSCV for benzene, (c) MSCV for cyclohexane.
experiments were performed in the usual H cells, using the "hanging electrolyte" method. Saturated benzene solutions (0.02 M (26))or diluted benzene solutions were prepared by bubbling either benzene-saturated argon or a mixture of 1% of this benzene-saturated Ar with pure Ar through an electrolyte reservoir. Assuming Henry's law to be applicable, the latter procedure resulted in benzene concentrations of 2 x 10-4 M. Benzene p.a. (Carl Roth GmbH), benzene-d, (99.5 atom % D, Sigma Chemie), D20 (99.8 atom % D, Sigma Chemie), and H2S04 (Suprapure, Merck) were used as received. Solutions were prepared from Millipore water and deaerated with Ar (99.9997%).
RESULTS AND DISCUSSION Cathodic Desorption of Electrosorbed Benzene. After electrosorption of benzene from a 2 x IO4 M solution in 0.1 M H2S04followed by a thorough electrolyte exchange, the potential of the Pt(ll1) electrode was swept negative to -0.1 V (RHE). The voltammogram (Figure 2a) shows that the benzene desorption during the first sweep is nearly complete,
46
ANALYTICAL CHEMISTRY, VOL. 63, NO. 1, JANUARY 1, 1991
1 -0 10-10 A
1-
2'1\
8 24 0
;A
0
I
II
0.3
0.6
I I
0.9E/V
Figure 4. Electrodesorption of preadsorbed C,D, (from a 0.02 M solution) in 0.5 M H2S0,; ,Ed = 0.54 V; v = 12 mV/s. (a) CV, sweep number as indicated. (b) MSCV; insert: m l z = 82, 83, and 80 with a 1 0-fold sensitivity.
12
m l z : 84
0
I\
12
Flgwe 3. Electrodesorption of preadsorbedbenzene from a roughened Pt(l11)electrode; E,, = 0.44 V, same conditions as in Figure 2.
since the suppression of the hydrogen adsorption is lifted in the first anodic sweep. Parts b and c of Figure 2 show the corresponding MSCVs for benzene and cyclohexane. Benzene (m/z = 78) desorption starts at 0.16 V and is nearly completed a t the negative potential limit. Only minor amounts still desorb during the anodic sweep. The onset of cyclohexane formation (mlz = 84) coincides with the decrease of the benzene signal. Cyclohexane continues to be desorbed during the anodic scan; also, in the second sweep, cyclohexane is formed. However, the integrated ion intensities show that the amount of formed cyclohexane is much smaller than that of desorbed benzene. Taking into account the different fragmentation probabilities, a ratio of 1:5 is estimated. I t is well-known that the surface of a Pt(ll1) crystal is roughened when the anodic potential limit is extended into the oxygen adsorption region (2). The hydrogen adsorption peaks of such a crystal are drastically changed, approaching the shape obtained with polycrystalline electrodes, although the ratio of the height of the two main hydrogen adsorption peaks is still different (the cathodic peak is larger). By use of such a Pt(ll1) crystal, the results shown in Figure 3 are
obtained. Benzene desorption starts a t 0.24 V, Le., a t more positive potentials than in the case of the well-ordered (111) surface. The general shape of the MSCV is similar to those of Figure 2. Totally different, however, is the ratio of formed cyclohexane to the desorbed benzene, which now amounts to 6:l. This shows that the roughened Pt(ll1) electrode is 30 times more active for the electrocatalytic hydrogenation of benzene than the smooth Pt(ll1) electrode and behaves in this respect identical with the polycrystalline electrode (24). Experiments using higher concentrations (2 X M) of benzene yielded identical results on both Pt(ll1) and polycrystalline Pt as those with 2 X M benzene solutions. Varying the adsorption potentials had no influence on desorption potentials or the cyclohexane/ benzene ratio. Using deuterated benzene for the adsorption experiments, we recently observed various degrees of H/D exchange in the benzene desorbed from a polycrystalline Pt electrode. No such H/D exchange occurs on the Pt(ll1) electrode, as shown in Figure 4: By far the highest intensity is obtained for m / z = 84, corresponding to C6Ds. Only minor ion currents are detected at m / z = 82 (13%), 80 (3%))and 83 (4%).The first two originate from the (M - D), (M - 2D) fragment of CP,. The intensity at m / z = 83 is both due to contamination of benzene-d6 with benzene-d, and the (M - D) fragment containing 13C. No potential-dependent mass intensity was detected a t other m / z values, especially 78, 79, and 81. In this experiment, the potential at which hydrogenation starts was avoided. The intensity a t m / z = 84 therefore is solely due to C6D6 (and not C6H12). Again, contrary to the polycrystalline surface, the Pt(ll1) surface is not active for catalyzing a reaction involving hydrogen transfer. In the case of the polycrystalline electrode, we found maximum ion intensities for benzene in which either all or no hydrogen atoms were exchanged (14). One of our explanations for this behavior was that some crystal orientations on the polycrystalline surface might, while others might not, catalyze the HID-exchange reaction. The new finding that the Pt(ll1) electrode does not catalyze this exchange reaction confirms this assumption.
ANALYTICAL CHEMISTRY, VOL. 63, NO. 1, JANUARY 1, 1991
il
47
I
I
1.0
00
-1 0
mlz=44
mlz
1.6-
@
I
44
9 " 1.4'9
--
I
12-
1.0-
00
05
10
15 E/Vrhe
Figure 5. Oxidation of preadsorbed benzene (from a 2 X M solutii) on a roughened Pt(ll1)electrode in 0.05 M H,S04; E, = 0.35 V; v = 12.5 mV/s. (a) CV, sweep number as indicated. (b) MSCV for CO,.
00
05
10
15 E / V r k
Flgure 6. Oxidation of preadsorbed benzene at a smooth Pt(ll1) electrode; v = 25 mV/s; other conditions as in Figure 5. (a) CV; (b) MSCV for COP.
Oxidation of Preadsorbed Benzene. On polycrystalline Pt electrodes, preadsorbed benzene is oxidized to CO, a t potentials where oxygen is adsorbed. Again, a P t ( l l 1 ) electrode roughened by potential cycling behaves quite similarly as can be seen from the voltammogram and the corresponding MSCV in Figure 5. Although the potential is scanned to the onset of oxygen evolution, some of the adsorbate is only oxidized in subsequent sweeps. When comparing the amount of charge with the amount of evolved CO, for each sweep, one can see that more charge is consumed per CO, molecule during the first sweep than in the following ones. As already has been shown more quantitatively for preadsorbed toluene (17)and acetone (13),this means that in the first sweep intermediates are formed that are already partially oxidized but stay adsorbed on the electrode. Complete oxidation in the second sweep requires less electrons per evolved C 0 2 molecules. The same experiment using a Pt(ll1) single crystal gives a completely different result (Figure 6). The oxidation now proceeds in two well-separated steps, the first of which does not yield CO, as oxidation product. A reversal of the potential sweep after the first oxidation peak gives some information on the nature of this peak (Figure 7). A conventional H cell was used in this experiment. No corresponding reduction peak is seen, and the so-called "butterfly" structure around 0.5 V is suppressed. Since in this experiment the surface was not roughened by extending the potential sweep into the oxygen adsorption region, this shows that the electrode is still covered by an adsorbate. The sharp peak a t 0.1 V suggests that the adsorbate is desorbed at this potential and substituted by hydrogen. In the following anodic sweep, this peak is much smaller because most of the species has diffused away from the electrode; this shows that the species really desorbs from the electrode and that the peak is not due to an adsorbed redox system. If the same experiment is performed in the thin-layer cell, this anodic peak is as large as the previous
-1 0
I/
cathodic one, since the species cannot diffuse away and readsorbs. No volatile desorption products could be observed in the corresponding MSCVs. This shows that peaks I and I1 do not correspond to parallel reactions: if in peak I only part of the adsorbate was oxidized, the other part should be desorbed as benzene at potentials where H2is evolved. More information on the oxidation process is obtained when the number of electrons released per CO, molecule is calculated: The ion current in the mass spectrometer is proportional to the faradaic current (8) Zi = K* (1/ n ) A I , where n is the number of electrons transferred per produced molecule, A is the current efficiency, and K* includes all parameters of the instrument. K* is dependent on the species
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 1, JANUARY 1, 1991
detected and can be found by a calibration experiment. In the case of COz, the calibration is most easily done by oxidation of preadsorbed CO. Assuming a current efficiency A of 1, i.e., COz is the only oxidation product of preadsorbed benzene, one gets
nor = K" (Q/ Qi) where Q and Qi are the sum of the electronic charges and integrated ion intensities of the first three oxidation cycles. (One single oxidation cycle does not lead to a complete oxidation of the adsorbate.) Due to an integration over the whole potential cycles, contributions from oxygen adsorption cancel. From the results shown in Figures 5 and 6, one gets noX= 6.2 for the roughened Pt(ll1) electrode and nor = 6.6 for the smooth Pt(ll1) electrode. When comparing these values with the theoretical value for benzene oxidation (30 electrons for the molecule or 5 electrons per formed COP),it has to be kept in mind that the experimental values have not been corrected for the change in double-layer capacity and shift of the potential of zero charge during adsorption (or desorption, respectively). In the case of CO adsorption, these effects amount to 20% of the total charge (27)and have been considered in the evaluation of K*. If we assume hypothetically the same contribution for the case of benzene adsorption, we get values of 5.0 or 5.3, respectively. This was implicitly assumed in our previous work on acetone (13) and toluene (17) adsorption. Therefore, these values show that on both polycrystalline and Pt(ll1) electrodes preadsorbed benzene is oxidized to COP, although one cannot exclude formation of other products to some extent. The charge of the first oxidation peak in the case of the Pt(ll1) electrode amounts to one-fourth of the total oxidation charge. The charge necessary for the oxidation of benzene to benzoquinone is 6 electrons or one-fifth of the charge released for complete benzene oxidation (30 electrons). This suggests that the adsorbed intermediates are benzoquinonelike species.
CONCLUSIONS We have shown that it is now possible to use DEMS for single-crystal electrodes and thereby to identify anodic and cathodic desorption products in analogy to thermodesorption mass spectrometry in the case of the metal-gas interface. The sensitivity is estimated to be about 1% of a monolayer (cf. the mass intensity of cyclohexane in Figure 2c, which corresponds to about one-fifth of the adsorbed benzene). Our experiments show that for reactions including hydrogen transfer the smooth Pt(ll1)surface is catalytically much less active than the roughened Pt(ll1) surface and the polycrystalline electrode. Hydrogenation of preadsorbed benzene to cyclohexane occurs to a much smaller extent (1/30), and H/D-exchange reactions do not occur during the desorption of benzene. However, as in the case of the polycrystalline electrode, no partially hydrogenated species were detected. Also different is the catalytical activity for the oxidation of preadsorbed benzene. The oxidation starts a t lower potentials; on the other hand, the formation of the final oxidation
product C 0 2 only starts a t more positive potentials than on the polycrystalline or roughened surface. As opposed to the polycrystalline electrode, two reaction steps of the presumably rather complicated mechanism could thus be separated. These results show that the crystal orientation of Pt electrodes has a marked influence on the electrolytic activities. They also show that measurements using single-crystal electrodes help in understanding the results obtained with polycrystalline electrodes. For a detailed understanding of this influence, experiments using other crystal planes are necessary and in progress.
ACKNOWLEDGMENT Thanks are due to Paul Linke from the IGV of the KernforschungsanlageJulich for orienting and polishing the Pt(ll1) crystal. We also thank J. Heitbaum for helpful discussions. LITERATURE CITED (1) Feiter, T. E.; Hubbard, A. T. J. Nectroanal. Chem. InterfacialElectrochem. 1979, 100, 473. (2) Wagner, F. T.; Ross, P. N., Jr. J. Nectroanal. Chem. InterfacialElectrochem. 1983, 150, 141. (3) Koib, D. M.; Lehmpfuhl, G.; Zei, M. S. J. Electroanal. Chem. Interfacial Nectrochem. 1984, 179, 289. (4) Bewick, A. J. Electroanal. Chem. Interfacial Electrochem. 1983, 150, 481. (5) Seki, H.: Kunimatsu, K.; Golden, W. G. Appl. Spectrosc. 1985. 3 9 , 437. (6) Horanyi, G. J. Nsctroanal. Chem. Interfacial Electrochem. 1974, 51, 163. (7) Meiroy: 0. R.; Samant, M. G.; Borges, G. L.; Gordon, J. G., 11; Bium, L.; White, J. H.; Albarelli, M. J.; McMliian, M.; Abruna, H. D. Langmuir l 9 8 & 4 , 728. (8) Wolter, 0.; Heitbaum, J. Ber. Bunsenges. Phys. Chem. 1985, 88, 2; 1985, 88, 6. (9) Hamelin, A. I n Modern Aspects of Nectrochemistry; Conway, B. E., White, R. E., Bockris. J. O'M., Eds.; Plenum Press: New York, 1985; Vol. 16, Chapter 1. (10) Ciavilier, J. J. Nectroanal. Chem. Interfacial Nectrochem. 1980, 107, 211. (11) Leung, L.-W. H.; Wieckowski, A.; Weaver, M. J. J. Phys. Chem. 1988, 92* 6985. (12) Yau. S.-L.; Vitus, C. M.; Schardt, B. C. J. Am. Chem. SOC. 1990, 112, 3677. (13) Bansch, 6.; Hartung, T.; Baltruschat, H.; Heitbaum, J. J . Nectroanal. Chem. Interfacial Nectrochem. 1989, 259, 207. (14) Hartung, T.; Baltruschat, H. Langmuir 1990, 6, 953. (15) Giieadi, E.; Duic. L.; Bockris, J. D'M. Electrochim. Acta 1988, 13, 1915. (16) Soriaga, M. P.; Chia, V. K. F.; White, J. H.; Song, D.; Hubbard, A. T. J. Nectroanal. Chem. Interfacial Electrochem. 1984, 162, 143. (17) Zhu, J.; Hartung. T.; Tegtmeyer, D.; Baltruschat, H.; Heitbaum, J. J. Electroanal. Chem. Interfacial Electrochem. 1988, 244, 273. (18) Gui, Y.; Kuwana, T. Langmuir 1988, 2, 471. (19) Pons, S.; Bewick, A. Langmuir 1985, 1, 141. (20) Mate, C. M.; Somorjai, G. A. Surface Sci. 1985, 160, 542. (21) Surman. M.; Bare, S. R.; Hofmann, P.; King, D. A. Surface Sci. 1983, 126, 349. (22) Zurawski, D.; Rice, L.; Hourani, M.; Wieckowski, A. J. Nectroanal. Chem. Interfacial Electrochem. 1987, 230, 221. (23) Schardt, B. C.; Yau, S.-L.; Rinaldi, F. Science 1989, 243, 1050. (24) Vogel. R.; Kamphausen, I.; Baltruschat, H. Poster presented at the 41.9 ISE conference, Prague, 1990. (25) Lu, F.; Saiaita, G. N.; Baitruschat, H.; Hubbard, A. T. J. Nectroanal. Chem. Interfacial Electrochem. 1987, 222, 305. (26) Landolt-Biirnstein, Zahlenwerfe und funktionen; Berlin, 1962: 6. Aulf.. Bd. 11/2b. pp 3-395. (27) Schmiemann, U. Master thesis, University of Witten/Herdecke, 1990.
RECEIVED for review July 6, 1990. Accepted October 2, 1990. Financial support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
