ANALYST, MAY 1991, VOL. 116 443 Investigation of the Quenching of Peroxyoxalate Chemiluminescence by Amine Substituted Compounds Joseph K. DeVasto and Mary Lynn Grayeski" Chemistry Department, Seton Hall University, South Orange, NJ 07079, USA The role of amine compounds in quenched peroxyoxalate chemiluminescence was investigated. The mechanistic steps examined included (1) fluorescence quenching; (2) base hydrolysis of the oxalate; and (3) a competitive interaction between the quencher and fluorophore for the peroxyoxalate reaction inter- mediate(s). The results showed no evidence of amines causing fluorescence quenching. Base hydrolysis of the oxalate is significant only at high concentrations of amines. When the concentration of amines is greater than or equal t o the level of oxalate, the amines can compete with the fluorophore for reaction with the intermediate(s).Because competitive effects were demonstrated, one analytical implication is that caution must be exercised in applications where more than one fluorophore is present. At low concentrations of fluorophores relative to the oxalate, chemiluminescence emission of both fluorophores will be observed. At higher levels, the fluorophores can compete for reaction with the intermediate(s). Finally, an important analytical implication of this study is that the quenching response can be used t o quantify amines without the need for derivatization. The limitation is that the linear response is approximately one order of magnitude. Keywords: Peroxyoxalate chemiluminescence; aliphatic/aromatic amines; quenched chemiluminescence Rauhut et al.1 first reported significant differences in quantum yields and chemiluminescence (CL) lifetimes when adding basic compounds to a peroxyoxalate reaction containing bis(2,4-dinitrophenyI) oxalate (DNPO) and 9,10-diphenyl- anthracene. Quenched peroxyoxalate CL was also observed in the reaction of hydrogen peroxide with bis(pentach1oro- phenyl) oxalate (PCPO) using sodium salicylate as a base catalyst .? A number of substituted anilines, and organosulphur and ionic compounds have been analysed by high-performance liquid chromatography and flow injection with quenched peroxyoxalate CL detection.3.-' A competitive quenching mechanism between easily oxidizable analytes and the peroxy- oxalate reaction intermediate was initially proposed.A later report4 suggested that the quencher is involved in radiation- less deactivation of the fluorophore-charge-transfer complex. The purpose of this study was to examine the role of aliphatic and aromatic amines in quenched peroxyoxalate CL, and to develop an analytical technique for measuring amine compounds by means of this quenching phenomenon. The advantage of this approach is that a derivatization step is not required prior to detection of the aliphatic amines. 'This is particularly important for tertiary aliphatic amines for which derivatization reactions are limited. The mechanistic pathways that a quencher (Q) can follow in the reaction with bis(2,4,6-trichlorophenyl) oxalate (TCPO) and hydrogen peroxide are: TCPO + H202 + intermediate(s) (I) + 2[2,4,6-trichlorophenol (TCP)] (1) Q TCPO + OH- + 2TCP ( 1 4 I + fluorophore (FL) + [I'-FL'+] (2) I + Q + non-CL ( 2 4 [I'-FL'+] + FL" ( 3 ) FL" + FL + hv (4) FL" + Q -+ FL ( 4 4 The asterisk signifies the excited state of the fluorophore.Equations (1)-(4) [excluding (la), (2a) and (4a)l are the proposed light producing pathways. Hydrogen peroxide and * To whom correspondence should be addressed. TCPO react to form a high energy intermediate(s) that undergoes an electron charge transfer with a fluorophore. The charge-transfer process leads to radical ion annihilation and formation of an excited state fluorophore that fluoresces. The addition of an amine (or other quencher) can cause the reaction to proceed along dark pathways such as (i) base hydrolysis of the oxalate [equation (la)], (ii) competitive interaction of the quencher and fluorophore for the inter- mediate [equation (2a)l and (iii) fluorescence quenching of the fluorophore [equation (4a)l.Experimental Chemicals Triethylamine (TEA), N-propylamine (N-PA), N-isopropylcyclohexylamine (N-IPCA), 2-ethylaniline (2- EA), 4-toluidine (4-TOL), N,N-dimethylaniline (N,N-DMA) and 30% hydrogen peroxide were obtained from Aldrich. Analytical-reagent grade dibasic sodium phosphate was received from J. T. Baker and TCPO was obtained from A. Mohan (New Jersey Department of Health, Trenton, NJ, USA). Spectrophotometric grade acetonitrile (Aldrich) and analytical-reagent grade anhydrous sodium perchlorate (GFS Chemicals) were used for determining the oxidation potentials of the fluorophores. The fluorophores used in the fluorescence and CL studies, viz., 1-aminoanthracene, 1-aminopyrene, anthracene, pyrene, perylene, rubrene and 1-aminonaphthalene, were purchased from Aldrich.2,4,6-TrichlorophenoI (TCP) was obtained from Eastman Chemicals, and HPLC grade acetonitrile (Fisher) was used throughout. All chemicals were used as received without additional purification. Static Chemiluminescence: Competitive and Quenching Experiments A Turner Instruments Model TD-20e luminometer was used for CL measurements. In the competitive interaction experi- ments, the reagents were added to a 1.6ml polypropylene cuvette in the following order: (i) 1OOpl of H202 (490 mmol dm-3); (ii) 100 pl of Na2HP04 buffer ( 5 mmol dm-3) (pH 6.2); and either (iiia) 40 pl of acetonitrile for a blank run, (iiib) 20 p1 of solution for a single fluorophore444 1.5 1.0 -0 \ 9 ANALYST, MAY 1991, VOL.116 . run plus 20 pl of acetonitrile or (ziic) 20 pl of each fluorophore solution with no acetonitrile added for runs with mixtures of two fluorophores. For the quenched CL experiments, steps (i) and (ii) were repeated and either (a) 20 pl of 1-aminopyrene (1 pmoldm-3) plus 20pl of quencher solution, ( b ) 201-11 of fluorophore solution plus 20p1 of acetonitrile, (c) 201-11 of quencher solution plus 20pl of acetonitrile or (d) 40p1 of acetonitrile were added to the cuvette. The TCPO (2mmoldm-3) was injected last (50 pl) for either set of experiments into the reaction cuvette with the Turner apparatus.With the final addition of TCPO the total volume was 290 pl for each CL measurement. The CL signal was monitored for 120 s with a Fisher Series 5000 strip-chart recorder, and the CL intensity areas were determined by electronic integration (0-120 s) with the Turner luminometer. The CL reagents were prepared in acetonitrile except for the aqueous phosphate buffer. Relative Fluorescence Quenching Experiments Fluorescence quenching was measured by using a Fluorolog 2 + 2 spectrofluorimeter with a 450W Xe continuous source (Spex Industries). The fluorescence intensity of l-amino- pyrene (1 pmol dm-3) was determined by adding 0.2 ml of the fluorophore to a cuvette containing 1.0 ml of sodium phos- phate buffer (5 mmol dm-3) (pH 6.2) and 1.7 ml of acetonit- rile. Relative fluorescence quenching was measured by adding 0.2 ml of the quencher (at several concentrations examined in the quenched CL experiments) plus 0.2 ml of 1-aminopyrene (1 pmol dm-3) to 1.0 ml of phosphate buffer ( 5 mmol dm-3) (pH 6.2) and 1.5 ml of acetonitrile.Spectral peak areas were determined at an excitation wavelength of 360nm and an emission wavelength range of 390-500nm with a 1 nm bandpass. Base Hydrolysis and Apparent pH The formation of TCP from TCPO was measured at 298 nm by ultraviolet (UV) absorbance5 using a Varian 2200 UV spec- trophotometer. Absorbance readings were recorded 2 min after injecting the last reagent under two sets of run conditions. The injection volumes for each set of runs were: 0.5 ml of TCPO (2 mmol dm-3) + 1.0 ml of Na2HP04 buffer (5 mmol dm-3) (pH 6.2) + 1.0 ml of H202 (490 mmol dm-3) + (0.2 ml of 1-aminopyrene (1 pmol dm-3) + 0.2 ml of acetonitrile; and the same sequence as for the first run but with 0.2 ml of quencher solution substituted for acetonitrile.The background absorbance readings of the fluorophore, H202, buffer and quencher solution components were subtracted from the values obtained from the two sets of runs. All reagents were prepared in acetonitrile (except for the aqueous buffer). The quartz cuvette was placed in the instrument prior to injecting the final reagent (TCPO) in order to improve the experimental precision. Measurements of apparent pH were made on CL solutions that contained quenches at concentrations ranging from 0.0069 to 6.9 mmol dm-3. The injection order and concentra- tions of CL reagents were: 10 ml of H202 (490 mmol dm-3); 10ml of Na2HP04 buffer (5mmoldm-3) (pH6.2); 2ml of 1-aminopyrene (1 pmol dm-3); 2 ml of quencher solution; and 5 ml of TCPO (2 mmol dm-3).Acetonitrile (2 ml) was substi- tuted for the quencher solution when the apparent pH of the CL reaction was measured. The apparent pH was determined with an Orion Research Model 611 pH meter 2min after adding the last reagent. Oxidation Potentials Oxidation potentials of 1-aminoanthracene and l-amino- pyrene were determined by cyclic voltammetry with an IBM EC/225 voltammetric analyser. Half-wave potentials were determined by using a platinum disc working electrode, a platinum wire auxiliary electrode and an Ag-Ag+ reference electrode. The supporting electrolyte was 0.5 mol dm-3 sodium perchlorate in acetonitrile, and the sweep rate was 10 mV s-1.Results Quenched peroxyoxalate CL in a buffered solution was investigated by measuring the CL response while varying the concentration of amines over several orders of magnitude (Figs. 1 and 2). The CL signal was quantified by determining the quenching ratio IQ : 10, where IQ is the CL intensity with the quencher and Z0 is the intensity without a quencher in the CL reaction. Figs. 1 and 2 show that the aliphatic amines have a more significant quenching effect on the CL reaction in the 0.035-0.69 mmol dm-3 concentration range. Also, an increase in CL intensity is observed for 2-EA and 4-TOL at a concentration of 0.035 mmol dm-3. 1.0 . . 0.6 s 0.2 0.4 t nn 0.5 t ir I € T I I, 0 I I 1 I 1 10 100 1 000 10 000 Concentration/lO-7 mol dm-3 Fig.2 Quenched eroxyoxalate CL ratios for the aromatic amines 2-EA (a), 4-TOL 6) and N,N-DMA (A). Point representation and concentration of the fluorophore as in Fig. 1ANALYST, MAY 1991, VOL. 116 445 Figs. 3 and 4 show typical quenched CL profiles of TEA and 2-EA, respectively. Two peaks are observed when a 0.69 mmol dm-3 TEA solution is added to the CL reaction without 1-aminopyrene (Fig. 3, B). No double peak is observed, however, when the fluorophore is included in the CL reaction. Also, double peaks are not observed when aromatic amines are added to the CL reaction. A decrease in the CL rate of decay occurs at relatively low concentrations (less than 0.069mmoldm-3) of aromatic amines, and an increase in CL emission is observed.The quenched CL response is linear [analysis of variance (ANOVA) regression; F = 0.9751 over a relatively narrow concentration range, viz., 0.0174.17 mmol dm-3 for TEA, and 0.045-0.17 mmol dm-3 for N-IPCA or N-PA. The CL response curve was calculated by taking the reciprocal value of the quenched CL signal versus concentration. The lowest levels of aliphatic amines measured (n = 4) by quenched CL were 0.017 k 0.001mmoldm-3 TEA, 0.045 k 0.002 mmol dm-3 N-IPCA and 0.045 k 0.003 mmol dm-3 N-PA. Fluorescence Quenching A relative comparison of fluorescence spectral peak areas of 1-aminopyrene was made with and without an amine in solution in order to determine fluorescence quenching (Table 1). No fluorescence quenching is observed when the amines are added to 1-aminopyrene in an acetonitrile- phosphate buffer solution. Also, there is no evidence of a shift in the spectral peaks of 1-aminopyrene at any concentration of the quenchers studied.D 3 6 9 Time/m i n Fig. 3 Quenched peroxyoxalate CL with 0.69 mmol dm-3 TEA. Static CL curves: A, acetonitrile blank (CL solution without fluorophore or TEA); B, CL solution with TEA and no fluorophore; C, CL solution with 1-aminopyrene; and D, CL solution with 1-aminopyrene plus TEA. The sensitivity of the luminometer was increased 100-fold when recording CL curves A and B relative to curves C and D C ~~~ 3 6 9 Fig. 4 Quenched peroxyoxalate CL with 0.69 mmol dm-3 2-EA. Static CL curves A-D are as given for Fig. 3 with curves A and B measured at a 100-fold increase in sensitivity relative to curves C and D Timeimin Hydrolysis The apparent pH of the quenched peroxyoxalate CL reaction was measured and compared with the CL reaction without a quencher.There is no significant increase in apparent pH of the quenched CL reaction, except for aliphatic amines added at concentrations greater than or equal to 0.069 mmol dm-3. A similar experiment was conducted using UV absorbance to measure the change in the concentration of TCP in the CL reaction when adding TEA at several concentrations (Table 2). As the concentration of the aliphatic amine increases, an increase in the level of TCP relative to the CL reaction without TEA is observed. When absorbance measurements were made on the CL reaction with and without the addition of aromatic amines, there was no increase observed in the concentration of TCP.Competitive Interaction The competitive role of the quencher and fluorophore for the CL reaction intermediate(s) was examined by comparing the CL response of the reaction with one fluorophore with the CL response of the reaction with a mixture of two fluorophores. If the sum of the signals for the individual fluorophores is equivalent to the CL response of the mixture, then there is no competition between the fluorophores for interaction with the intermediate. If the CL signal of the mixture is not equivalent, the interaction with the peroxyoxalate intermediate(s) would be favoured for one fluorophore relative to the other. Two sets of conditions were evaluated in the competitive interaction experiments: (i) the concentrations of the fluoro- phores were lower than the concentration of TCPO by approximately 2-5 orders of magnitude (except for pyrene) ; and (ii) the total concentration of amino substituted fluoro- phores was within one order of magnitude of the concentra- tion of TCPO.These conditions include the entire range of concentrations of amines used in the quenching experiment. If the two fluorophores react competitively with the intermediate(s), the reactivity of one fluorophore might be favoured based on its oxidation potential or concentration. Both of these parameters were evaluated for various fluoro- phores (Table 3). Sums of the CL signals were determined for pairs of fluorophores by using a central composite experi- mental design.The results showed that the CL signal ( n = 3 injections) for a mixture of two fluorophores is equivalent Table 1 Relative fluorescence quenching. The values are relative to the fluorescence intensity of 1-aminopyrene, which is equal to 1 .00 in the absence of a quencher; relative standard deviation = 6.1% (n = 7) Quencher 6.9 mmol dm-3 0.69 mmol dm-3 0.34 mmol dm-3 TEA 1.06 1.08 1 .oo N-PA 1.04 1.03 1.01 N-IPCA 0.95 - - 2-EA 1.02 0.98 1.03 4-TOL 1.06 0.96 - N, N-DMA 0.97 0.98 - ~ ~~~~~ Table 2 TCP product formation during the peroxyoxalate CL reaction plus quencher TEA concentra- tion/mmol dm-3 TCP/mmol dm-3 0 0.54* 0.0069 0.55 0.034 0.56 0.069 0.57 0.34 0.60 0.69 0.60 6.9 0.66 * Average of duplicate injections; relative standard deviation = 1.3%.446 ANALYST, MAY 1991, VOL.116 Table 3 Oxidation potentials (Etox) and concentrations of fluoro- phores in the CL reaction. Final CL reagent concentrations in the static cell: TCPO, 0.34 mmol dm-3; H?O2, 170 mmol dm-3; and phosphate buffer, 1.7 mmol dm-3 Concentration/ E40d pmol dm-37 Fluorophore V versus Ag-Ag+ * Anthracene +0.79 7.4 3.7 0.7 Pyrene +0.86 69.7 34.8 7.0 1-Aminoanthracene +0.10 0.08 0.04 0.008 1- Aminop yrene t-0.19 0.07 0.04 0.007 Perylene +0.55 0.01 0.005 0.001 Rubrene +0.52 0.02 0.01 0.002 1- Aminonaphthalene +0.24 1.4 0.7 0.14 * References 6 and 7. t Three concentration levels were studied with pairs of fluorophores mixed in solution. (within a 95% confidence interval) to the sum of the CL signals for the individual fluorophores when measured at concentrations much lower than that of TCPO.The second set of conditions was examined by increasing the total concentra- tion of the fluorophores and decreasing the level of TCPO by one order of magnitude. 1-Aminonaphthalene (13 vmol dm-3) and 1-aminopyrene (0.71 pmol dm-3) were measured in the experiment with TCPO (0.034 mmol dm-3), H202 (170 mmol dm-3) and phosphate buffer (1.7 mmol dm-3) (pH 6.2). The CL signal of the mixed fluorophores (n = 3) is not equivalent to the sum of the CL responses of each fluorophore when compared within 95% confidence intervals. Discussion Role of the Quencher The role of amines in a buffered peroxyoxalate reaction was examined through a number of possible quenching mechan- isms. The non-chemiluminescent reaction pathways investi- gated included: fluorescence quenching of the fluorophore [equation (4a)l; base hydrolysis of the oxalate [equation (la)]; and competitive interaction of the amine and fluorophore for the peroxyoxalate reaction intermediate(s) [equation (2a)l.The results in Table 1 show that there is no significant change in the fluorescence intensity of 1-aminopyrene at the higher concentrations of quenchers used in this study. Therefore, the amines are not causing fluorescence quenching [equation (4a)l of the fluorophore in the peroxyoxalate CL reaction. The effect of TEA on the base hydrolysis of TCPO was determined at several concentrations of TEA in the CL reaction (Table 2). The formation of TCP is increased relative to the CL reaction without TEA at levels greater than or equal to 0.069 mmol dm-3.Aliphatic amines also affect the appar- ent pH of the CL reaction at concentrations greater than 0.069 mmol dm-3. These results indicate that aliphatic amines have sufficient basicity to exceed the buffer capacity of the CL reaction and cause the hydrolysis of TCPO. It has been speculated that the efficiency of the peroxyoxalate CL reaction decreases above pH 8 because of base hydrolysis of the oxalate.8 In this study, base hydrolysis also appears to be part of the quenching mechanism when high concentrations of aliphatic amines are added. There is no evidence of base hydrolysis when aromatic amines are added to the CL reaction. There is also no significant change in the apparent pH of the CL reaction when 2-EA, 4-TOL or N,N-DMA are added at a high concentration (6.9 mmol dm-3).These aromatic amines are relatively weak bases compared with the aliphatic species studied, and do not exceed the buffer capacity of the CL reaction. The possibility of a competitive quenching mechanism was investigated by measuring the CL response of pairs of fluorophores both as a mixture and separately (Table 3). If a competitive mechanism exists, then a decrease in CL intensity should be observed relative to the sum of the intensities for each species measured separately. There is no competitive interaction for the peroxyoxalate reaction intermediate(s) when the concentration of TCPO is several orders of magnitude greater than that of the fluorophores. Also, differences in the oxidation potentials of the two fluorophores do not contribute to a competitive interaction for the reaction intermediate(s) .There is evidence of a competitive mechanism when the total concentration of 1-aminopyrene or 1-aminonaphthalene is within one order of magnitude of the level of TCPO. As the concentration of the peroxyoxalate reaction intermediate(s) is limited relative to that of the fluorophores, one fluorophore acts as a competitive quencher of the CL reaction. The non-fluorescent amines used in the quenching study (Figs. 1 and 2) were added to the peroxyoxalate reaction at concentra- tions that were greater than or equal to the level of TCPO (0.34 mmol dm-3). This implies that a competitive mechanism can occur between the quencher and fluorophore for the peroxyoxalate reaction intermediate(s) if the concentration ratio of quencher:TCPO is greater than or equal to unity. This is based on most of the TCPO reagent being converted into the high energy intermediate(s) in the peroxyoxalate reaction.It is not clear which quenching mechanism operates when the concentration of the amine is significantly less than that of TCPO. An earlier report4 on the role of a quencher in the peroxyoxalate reaction postulated that the fluorophore- charge-transfer complex undergoes radiationless deactiva- tion. This suggests that a trimolecular interaction of the quencher, fluorophore and intermediate is favoured over a bimolecular light-producing fluorophore-intermediate re- action pathway. It should be noted that fluorophores with broad emission bands and some spectral overlap were included in this study.Theoretically, it should be possible to measure the emission from one fluorophore in the presence of another if the two fluorophores are sufficiently spectrally resolved and exhibit efficient CL. This would require the use of a very long wavelength emitter relative to the fluorophores usually measured with this reaction.9 For the fluorophores examined here, the emission levels were very low at all the concentra- tions studied and the total intensity was integrated over all wavelengths in order to collect an adequate signal. Analytical Implications Aliphatic and aromatic amines can be quantified by using quenched peroxyoxalate CL detection. An advantage of this technique is that aliphatic amines can be detected without derivatization.This is important in quantifying tertiary aliphatic amines where the choice of a derivatizing reagent is very limited. There are limitations that must be considered in quantifying amines by quenched CL detection. Fig. 1 clearly shows a non-linear quenching response when aliphatic amines are measured over three orders of magnitude in concentration. This is the result of the quencher causing complex kinetics that change the CL peak shape and rate of decay. A probable cause of this phenomenon (Fig. 3, C and D) is that as the concentration of the aliphatic amine increases in the buffered CL reaction, it exceeds the buffer capacity and acts as a base catalyst thus increasing the CL rate of decay.'() A linear response can only be observed over a range less than or equal to one order of magnitude in concentration.The quenched CL response of the aromatic amines (Fig. 2) is also non-linear and shows an increase in CL emission at relatively low concentrations. The cause of the increase in CLANALYST, MAY 1991, VOL. 116 emission was not investigated, but a decrease in the CL rate of decay was observed. It is possible that the aromatic amines are increasing the formation of a second peroxyoxalate reaction intermediate. 1 1 Possible evidence for this mechanism was obtained qualitatively (Fig. 3, B). The CL intensity-time curve has two peaks, which indicates that two intermediates are formed when aliphatic amines are added to the CL reaction without a fluorophore. A burst of light generates the initial peak which might correspond to a reaction pathway in which an arylperoxyoxalic acid intermediate is formed rapidly together with a dioxetane dione or dioxetanone intermediate species.Although double peaks are not observed for the aromatic amines (Fig. 4), it is still possible that a second reaction intermediate is formed but cannot be observed. The addition of aromatic amines might generate a burst of light which is too rapid to measure, o r a second low-level emission peak which cannot be detected above the main CL signal. As competition occurs, the question about mixtures of fluorophores is raised. Is one fluorophore preferentially being measured when several fluorophores are present in a solution? This information was obtained by investigating the competi- tive role of a quencher in the peroxyoxalate CL reaction. A quenched CL signal could occur when determining the concentration of more than one fluorophore in a solution.One fluorophore can act as a quencher if the total concentration is within one order of magnitude of the level of the oxalate in the CL reaction. A quantitative CL signal should result from a mixture of fluorophores when the total concentration of the fluorophores is significantly less than that of the oxalate. This research was supported through Corporation. 447 a grant from Research 1 2 3 4 5 6 7 8 9 10 11 References Rauhut, M. M., Bollyky, L. J . , Roberts, G. B., Loy, M . , Whitman, R. H., Iannotta, A. V.. Semsel, A. M., and Clarke, R. A., J. Am. Chem. Soc., 1967, 89, 6515. Catherall, C. L. R., Palmer, T. F., andcundall, R. B.,J. Chem. Soc., Faraday Trans. 2 , 1984, 80, 823. van Zoonen, P., Kamminga, D. A., Gooijer, C., Velthorst, N. H., and Frei, R. W., Anal. Chem., 1986, 58, 1245. van Zoonen, P., Bock, H., Gooijer, C., Velthorst, N. H., and Frei, R. W., Anal. Chim. Acta, 1987, 200, 131. Givens, R. S . , Schowen, R. L., Matuszewski, B., Alvarez, F., Parekh, N., and Nakashima, K., paper presented at the Federation of Analytical Chemistry and Spectroscopy Societies Symposium. St. Louis. MO, September 1986. Pysh, E. S., and Yang, N. C.. J. Am. Chem. Soc., 1963, 85, 2124. Siegerman, H . , Techniques of Electroorganic Synthesis, Part It, Wiley, New York, 1975, vol. 5. Wcinberger, R., J. Chromatogr., 1984, 314, 155. Mann, B., and Grayeski, M. L., Anal. Chem.. 1990, 62, 1532. Nozaki. 0.. Ohba, Y . , and Imai, K . , Anal. Chim. Acfa, 1988, 205, 255. Alvarez. F. J., Parekh, N. J . , Matuszewski, B., Givens, R. S . , Higuchi, T., and Schowen, R. L., J . A m . Chem. Soc., 1986,108, 6435, Paper 0103 784 B Received August 17th, I990 Accepted December 17th, 1990