Anal. Chem. 1980, 52, 307-311
307
Chemiluminescence Method for the Determination of Nitrogen Dioxide Yasuaki Maeda, Kenji Aoki, and Makoto Munemori* Environmental Chemistry, College of Engineering, University of Osaka Prefecture, Mozu-umemachi, Sakai, Japan
A chemiluminescence method for the determination of NO, based on the reaction of luminol with NO2 is described. This chemiluminescence reaction needs no metal ion catalyst. Luminoi in alkaline solution is specHicaiiy reactive to NOz, so that other nitrogen-containing compounds such as ammonia, organic nitrite, organic nitrate, NO, and hydrocarbons do not Interfere. Ozone and sulfur dioxide interfere positively and carbon dioxide negatively. Carbon dioxide interference was completely removed by increasing the pH. Ozone and sulfur dioxide interferences were also removed by adding sodium sulfite to iuminoi solution. The limit of determination is approximately 50 parts per trillion NO, and relative standard deviations for the measurements of 3.8 ppm and 5.5 ppb NO, are 0.54% and 4.6%, respectively.
Nitrogen oxides, especially in the form of NO and NOz, are very important in view of air pollution (1-3). Nitrogen dioxide is usually determined by the colorimetric methods developed by Saltzman ( 4 ) and by Jacobs and Hochheizer ( 5 )and nitric oxide is determined by the chemiluminescence method developed by Fontijn (6). For the direct and instantaneous determination of nitrogen oxides a t low concentration levels such as in the case of ambient air monitoring (7-9), the chemiluminescence method seems to be preferred because of its high sensitivity and rapid response. This method is based on the chemiluminescence reaction of NO with ozone (10, 11) and can be applied also to the determination of NOz if NOz is reduced to NO with the catalytic converter (12-15) prior to the reaction with ozone. In this reduction, however, other nitrogen-containing compounds such as organic nitrite, organic nitrate, and ammonia are also converted to NO and in consequence interfere with the determination of NOz (16). Breitenbach has succeeded in removing the interference from ammonia by using Mo-C catalytic converter which permits selective conversion of NOz to NO in the presence of ammonia (17). Even with this converter, however, the interference from organic nitrite and nitrate cannot be removed a t all (18). In addition, when the determination is carried out on dirty gases such as exhaust gas, the selectivity of the converter catalyst is reduced by deposition of heavy metals on the catalyst surface. In our investigation it was found that luminol in an alkaline solution reacts with gaseous NOz a t atmospheric pressure to produce intensive chemiluminescence and NO does not interfere with this reaction. On the basis of this reaction a new chemiluminescence method for the selective determination of NOz has been established. I t is well known that luminol (5-amino-2,3-dihydro-1,4-phthalazine dione) produces intensive chemiluminescence when it reacts with oxidizing agents in alkaline solution in the presence of a metal catalyst (19, 20). This reaction has been used in aqueous phase for the determination of oxidizing agents such as HzOz (21),C10- (22), Cl:! (231, and Iz (24) and for the determination of metal ions such as Fez+ (25),Cuz+ (26),and Cr3+ (27) in the presence of hydrogen peroxide. Anderson has applied the HZO2-luminol 0003-2700/80/0352-0307$01.00/0
reaction to the determination of NO, NOz, SOz, and O3 after pretreatment (28,29). Thus, most of the analytical applications of the luminescence reaction of luminol hitherto developed utilize the catalytic oxidat.ion of luminol. The luminescence reaction described here, however, requires no catalyst.
EXPERIMENTAL Apparatus. A chemiluminescence analyzer designed and constructed in this laboratory is schematically shown in Figure 1. It consists of three parts, i.e., gas supply system,reaction vessel, and measuring system. The gaseous sample containing NO2was fed into the reaction vessel (L) and contacted there with the surface of the alkaline solution of luminol which was also fed into the reaction vessel at a constant flow rate with a peristaltic pump (G). Chemiluminescence produced was detected with a Hamamatsu Television R374 photomultiplier (H) through an OV-31 quartz filter (I), and photocurrent produced was amplified by an amplifier (J) and recorded with a Hitachi Model 056 recorder (M). The photomultiplier was operated at 400 V for determination at the ppm level and 780 V at the ppb level. The luminol solution in the reaction vessel was overflowed through D (see Figure 2b), so that the distance between the surface of luminol solution and photomultiplier remained constant and the continuously-renewed surface of definite area of luminol solution was exposed to a stream of sample gas. The reaction vessel was made of a 35-mm length of 30-mm i.d. (40-mm 0.d.) stainless steel tubing and the inner surface was covered with Teflon sheet. The chemiluminescence spectra were obtained using a Hitachi Fluorometer Model MPF-2A. When they were measured, the excitation source was removed and the chemiluminescencereaction was allowed to take place in the cell compartment by introducing a stream of N O p (87.9 ppm) in nitrogen over the surface of an alkaline solution of luminol taken in a beaker. Reagents. Luminol of chemically pure grade was used without further purification. Other chemicals were of reagent grade obtained from Wako Chemical Co. NO2 was supplied from a standard gas cylinder (87.9 ppm in nitrogen, Seitetsu Kagaku Co.) and diluted t o the required concentrations in a range extending from several ppb to several ppm with air purified by passing it through three traps connected in series; silica gel (DJ, activated charcoal (Dz),and molecular sieve in glass tubes. Ozone was generated by an ozonizer (Nihon 5A (D3) Ozone Co.). RESULTS AND DISCUSSION Design and Construction of the Reaction Vessel. Chemiluminescence analyzers for gaseous substances hitherto developed are based on gas phase reactions, e.g., reaction of NO with 03,ethylene with O3 (30),and PAN with ethyl amine (31), and rarely on a gas-solid reaction such as the reaction of O3 with rhodamine B adsorbed on a silica gel disk (32). The present chemiluminescence reaction, however, takes place between gas and liquid phases and, therefore, the reaction vessel required a major design effort. When the reaction vessel for the gas phase reaction shown in Figure 2a was used, the periodic fluctuations in signal were observed at sample gas flow rate below 500 mL/min as shown in Figure 3a. This is due to the periodic change of the surface area of the luminol solution which is exposed to the sample gas. The luminol solution flowed out from C (see Figure 2a) 1980 American Chemical Society
308
ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980 gas su@y s y s t e m
reaction
measuring
c
I I Figure 1. Schematic diagram of chemiluminescence analyzer. (A) Air compressor; (6)standard gas cylinder; (C,, C,) constant pressure regulator; (D, -D3) gas purification tube; (E, -E3) flowmeter; (F) gas mixer; (G) peristaltic pump; (H) photomultiplier; (I) quartz filter; (J) amplifier; (K,-KK,) glass tap; (L) reaction vessel; (M) recorder
U
Ill
Ill
2x nL,m,n
Figure 4. Effect of sample gas flow rate on signal response. (0)Flow rate of luminol solution is 0.5 mL/min. (A) Flow rate of luminol solution is 2.0 mL/min. NOp concentration, 3.8 ppm; luminol concentration, 1X M; KOH concentration, 5 X lo-' M
Ill
Ill
-ti (a)
33: l X 5x sample gas flow rate,
I
16' ( b)
Figure 2. Reaction vessel. (A) Sample gas inlet, (B) luminol solution inlet, (C) sample gas contacts here with lurninol solution, (D) luminol solution and sample gas outlet, (E) photomultiplier, (F) quartz filter
,
188LLLlli
I 8 8 8 / I / l
16'
1 8 I I I 8 l l
o-~
1 luminol concentrati31, N
102
,
I 1 1 8 I
15,
Figure 5. Effect of lurninol concentration on signal response. NOp concentration, 3.8 ppm; KOH concentration: 5 X lo-' M Table I. Effect of Metal Iono metal ion
signal response
metal ion
none Fe3'
145.0
Mn2+
2.9
Zn2+
cu2+
4.2
Ni"
Co3+ Cr3'
4.2
Pb2+
6.8
c u+
signal response 9.0 66.5 76.0 86.0 141.0
NO, concentration, 69 ppm; luminol concentration, 1 M ; KOH concentration, 5 X M ; and metal ion concentration, 2 x M. a
X
a
b
Figure 3. Signal response. (a) Signal response obtained with reaction vessel shown in Figure 2a. (b) Signal response obtained with reaction vessel shown in Figure 2b in the form of drops, the increase and decrease in the signal corresponded to the repetitive growth and falling of the drop. When the sample gas flow rate exceeded 500 mL/min, the drop was broken into fine particles and the signal intensity was reduced to one tenth. However, when the reaction vessel shown in Figure 2b was used, the fluctuations were completely removed and the steady signals were obtained as shown in Figure 3b. With this reaction vessel, the signal response was independent of the flow rate of luminol solution in the range from 0.25 to 3 mL/min and, moreover, the response was independent of the sample gas flow rate beyond 1000 mL/min as shown in Figure 4. The independence of the signal response from flow rate is the advantage of the present method over the conventional gas phase chemiluminescence method. Most experiments were performed with flow rate of 1 mL/min of luminol solution and of 1000 mL/min of sample gas, and the reaction vessel shown in Figure 2b was used. Effect of Metal I o n s on the Chemiluminescence Reaction. As is well known the chemiluminescence reaction of luminol with hydrogen peroxide in the liquid phase requires
a metal ion catalyst such as Cuz+ or Cr3+. The reaction of luminol with NO2, however, requires no catalyst and, on the contrary, the chemiluminescent emission was decreased when metal ion was added. As shown in Table I, the more reactive the metal ion is toward the luminol-hydrogen peroxide reaction, the more strongly it inhibits the luminol-NOz reaction. The metal ion interference is probably due to luminol complexing with the metal ions (33). Effects of Luminol and Potassium Hydroxide Concentration. To obtain the optimum condition for the chemiluminescence reaction of luminol with NOz, the effects of luminol and potassium hydroxide concentration on the emission intensity were investigated. As shown in Figure 5 , the emission intensity was increased and then decreased after passing through the maximum with an increase in luminol concentration. The maximum intensity was obtained for the luminol concentration from 3 X to 3 X M. The decrease in emission intensity at higher luminol concentration is presumed to be due t o the absorption of the emitted light by luminol molecules. The effect of potassium hydroxide concentration on the emission intensity is shown in Figure 6. In the absence of potassium hydroxide, no chemiluminescence was detected. In M, the the presence of potassium hydroxide more than
ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980
309
Table 11. Signal Response of Nitrogen-Containing Compoundsa signal
compound
3.8 86.9
NO, NO N,O
1'T2
1
KOH
u'
concentration^
10'
1 O0 M
Flgure 6, Effect of KOH concentration on signal response. NO2 M concentration, 3.8 ppm; luminol concentration, 1 X I
concn, ppm response, cm 8.0
1.0x 105
isoamyl nitrite isoamyl nitrate
76.0 58.0
"3
55.6
a Luminol concentration, 1 x tration. 5 x lo-* M.
0.05 M and KOH concen-
Table 111. Interferences from Other Gasesa other gas none
co
1,2-dichloroethylene propylene ozone
so, co,
c 5
0.01 2.9 0.0
I
a
0.2
concn, ppm 1.1x l o i 1.0 x l o 4 1.0x 104
0.08 0.3
16.6
x 103 1.2 x l o 4
4.0
rel. signal responseb
1.00
1.00 1.01 1.00 1.52
2.70 1.25 0.68 0.27
NO, concentration, 3.8 ppm; luininol concentration, SigM ; and KOH concentration, 5 X 10.' M. 1X nal for N O , + other gas/signal for NO,. 400
500
wavelength, nm
Flgwe 7. Emission spectra. (A) Chemiluminescence spectrum obtained from the reaction of luminol with NO,. (B) Chemiluminescence spectrum obtained from the reaction of luminol with H202in the presence of Cu2+ (34)
chemiluminescence was detected and intensity was increased with the increase in potassium hydroxide concentration. The intensity reached the maximum at 1.0 M in potassium hydroxide and decreased again. It seems likely that the presence of potassium hydroxide facilitates the dissolution of NOz in luminol solution to favor the access of NOz to luminol and also that the hydroxyl ion supplied by potassium hydroxide takes part in the luminescence reaction itself. At potassium hydroxide concentration higher than 0.1 M, oxygen reacts with luminol to produce chemiluminescence and interferes with the NOz determination. Therefore, the following measurements were carried out with 0.05 M potassium hydroxide. Potassium hydroxide was used in most cases, but sodium hydroxide and lithium hydroxide were equally useful. Reaction Mechanism. It is well known that NOz dissolves rapidly in an alkaline solution to produce nitrite and nitrate ion and, therefore, there is the possibility that the chemiluminescence is produced through the reaction of luminol with nitrite or nitrate ions. To test this possibility, the reactions of luminol in an alkaline solution with potassium nitrite and potassium nitrate were studied using the reaction vessel shown in Figure 2a. As a result, no chemiluminescence was observed even with 0.01 M potassium nitrite or nitrate solution. Accordingly, it is evident that chemiluminescence is produced by the reaction of luminol in an alkaline solution with molecular NOz. In Figure 7 , curve A shows the chemiluminescence spectrum produced from the reaction of luminol with NOz. The spectrum has the maximum emission intensity at 425 nm. Curve B shows the chemiluminescence spectrum for the reaction of luminol with hydrogen peroxide in the presence of Cuz+in an aqueous solution, reported by White (34). These spectra
resemble each other in shape. White has described that the chemiluminescence spectrum he obtained (curve B) was in good accordance with the fluorescence spectrum of aminophthalic ion. The agreement of curves A and B in Figure 7 suggests the emitter is the same when luminol is oxidized by NOz as when it is oxidized by Cuz+and H202. Further investigation, such as products study, is required to clarify the mechanism. Interferences from Other Gases. The determination of NOz is often required in connection with the photochemical smog formation. When photochemical smog is formed, various other pollutants such as NO, 03,SO2,COz, and hydrocarbons coexist with NOz. The effects of these compounds were examined. Table I1 shows the signal response of nitrogen-containing compounds. Compared with NOz, other compounds except for isoamyl nitrite gave small signals to be neglected. When ambient air is analyzed for NOz, the signal response of isoamyl nitrite can be neglected by consideration of its concentration. The small signal with NO is due to NOz present as a contaminant in the NO. Table I11 shows the signal response for 3.8 ppm NOz in the presence of other pollutants. NzO, NO, 1,Z-dichloroethylene,and propylene did not interfere with the determination of NOz. Ozone and sulfur dioxide interfere positively and carbon dioxide negatively. Removal of Sulfur Dioxide Interference. Various kinds of sulfur compound were added to an alkaline luminol solution and the chemiluminescence from the reaction of luminol with NOz was measured. As shown in Table IV, sulfite and dithionite enhanced the signal remarkably. In the case of sulfite, in particular, the enhancement was almost independent of its concentration. The effect of dithionite is probably due to the sulfite which has been produced by hydrolysis of dhhionite. When the alkaline luminol solution added with sodium sulfite (0.01 M) was used, the signal for 3.8 ppm NOz was markedly enhanced (see in Table IV) and moreover the sulfur dioxide interference was completely removed at the enhanced signal level even in the presence of 40 ppm SOz. Removal of Ozone Interference. Ozone reacts with luminol to produce chemiluminescence about 30 times stronger
310
ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980
Table IV. Effects of Sulfur Compounds Added in Luminol Solutiona concn, M 0.01
sulfur
compound none
Na,S
8.0 21.5 0.2 5.3 1.3 39.6 5.3 40.0 38.7 6.8 6.5
0.01 0.1 0.01
Na,S,O,
0.1 Na,SO,
0.01 0.1 0.01 0.1
Na,SO, a 1X
luminol concentration
KOH concentration
signal response, cm
0.1 Na,S,O,
Table VI. Optimal Condition
Na,SO, concentration flow rate of luminol solution flow rate of sample gas When the sample contains CO,. NO, in the presence of ozone.
N O , concn, PPbU
5 50 200
Table V. Removal of Ozone Interferencea ozone
rel.
of additive,
concn, ppm
signal intensityb
additive
M
urea NaBH, Na,SO,
1 x 10-2 1x
1 x 10-3 1x
1.0 1.0 1.0 1.0
4.0 2.1c
1.8 1.03 1.2 1.6
1x 2.8 1x 8.5 1 x lo-' 1.0 2.8 1x lo-] 1.2 8.5 1 x lo-] 2.0 51.0 a NO, concentration, 3.8 p p m ; luminol concentration, 1x M; and KOH concentration, 5 X M. Sig. nal for NO, + O,/signal for NO,. Signal for NO, reduced to one half. than NOz does as shown in Table 111. Therefore, ozone will strongly interfere with the determination of NOz. This interference causes a serious problem, because in ambient air ozone and NOz are both present a t comparable concentration. In order t o remove this interference, the effect of various additives was studied. I t was found that in this case also the addition of sodium sulfite is the most effective. As shown in Table V, in the presence of 0.1 M sodium sulfite the ozone interference was negligibly small, so far as the concentration of ozone is nearly equal to that of NOz. Removal of Carbon Dioxide Interference. The chemiluminescence response for 3.8 ppm NOz was decreased with the increase in the concentration of carbon dioxide contained in sample gas. This change of response was found to be due to the pH change of the surface layer of luminol solution which results from absorption of carbon dioxide and, therefore, the removal of carbon dioxide interference by increasing potassium hydroxide concentration in luminol solution was studied. When the potassium hydroxide concentration was 1.0 M, the carbon dioxide interference was removed irrespective of its concentration. Analytical Performance and Feasibility. The method herein described for determining NOz is extraordinarily sensitive and the lowest determinable concentration was estimated to be 50 parts per trillion (the exact value has not been experimentally obtained because of the difficulty in preparation of standard gases of such dilution). The signal response was proportional to the concentration of NOz from 0.5 ppb to 100 ppm. Nine measurements for 3.8 ppm NOz gave a signal of 9.7 cm (gain 1, 400 V, see Experimental section) as average on a recorder chart with the relative standard deviation of 0.54%. Five measurements for 5.5 ppb NOz gave the signal of 10.0 cm (gain 100, 780 V) as average with the relative
1 . 0 mL/min 1.0 L/min
Determination of
Table VII. Comparative Analytical Results
NO, concentration, 3.8 p p m ; luminol concentration, M; and KOH concentration, 5 x M.
concn
1 X 10-3 M 5 x 10.' M 1.0 Ma 1x M 1 x 10.' M b
1000
this method
established methodb
4.8 50.5 199.8 998.5
5 49 197 996
Concentration calculated from the dilution ratio of standard gas to air. Obtained by using a Kimoto Denshi Model 258 nitrogen oxides meter. a
standard deviation of 4.6%. Optimal compositions of luminol solution based on the above study are summarized in Table VI. The results obtained by this method were in good agreement with those obtained by an established method as shown in Table VII. The latter were obtained by using a Kimoto Denshi Model 258 nitrogen oxides meter which is based on the chemiluminescence reaction of NO with ozone after reduction of NOz to NO. As shown in Table 111, ozone and sulfur dioxide (in the presence of NOz) produce strong luminescence. These chemiluminescence reactions can be used for determination of these substances. The determination method for these substances and complete remove1 of ozone interference with NOz determination are being investigated in our laboratory.
ACKNOWLEDGMENT We thank Kimoto Denshi for making the nitrogen oxides meter available for our present work. LITERATURE CITED Leighton, P. A. "Photochemistry of Air Pollution"; Academic Press: New York and London, 1961; Chapters 3-5. Tuesday, C. S. "Chemical Reaction in Urban Atmospheres", Elsevier: New York, 1971; Session 11. Heicklen, J. "Atmospheric Chemistry", Academic Press: New York, 1976; Chapter 4. Saltzman, Bernard E. Anal. Chem. 1954, 26, 1949-55. Jacobs, Morris B.; Hochheizer, Seymour. Anal. Chem. 1958, 30, 426-26. Fontijn, Arthur; Sabadell, Albert0 J.; Ronco, Richard J. Anal. Chem. 1970, 42,575-79. Warner, P. 0. "Analysis of Air Pollutants", John Wiley & Sons: New York, 1976; Chapters 3, 4, 6. Leithe, W. "The Analysis of Air Pollutants", Ann Arbor Science Publishers: Ann Arbor, Mich., 1971; Chapters 4, 5. Isacsson, Ulf; Wettermark, G. Anal. Chim. Acta 1974, 68, 339-62. Clyne, M. A. A,; Thrush, Brian A,; Wayne, R. P. Trans. Faraday SOC. 1964, 60,359-370. Clough, P. N.; Thrush, Brian A. Trans. Faraday SOC. 1967, 63, 915-925. Sigsby, John E., Jr.; Black, Francis M.; Bellar, Thomas A,; Klosterman. Donald L. Environ. Sci. Technol. 1973, 7, 51-54. Ivanov, D. G.; Petrova, 0. Tezhka. Prom. 1959, 2, 22-24: Chem. Absb. 1961, 55, 157779. Sherwin, E.; Weston, G. J. "Chemistry of the Non-Metallic Elements". Pergamon Press: New York, 1966; p 130. Munemori, Makoto; Maeda, Yasuaki Proc. I V Int. Clean Air Congr. pp 370-72. Glover, J. H. Analyst (London) 1975, 100, 449-464. Breitenbach, 128-131. L. P.; Shelef, M. J . Air Polluf. Control ASSOC. 1973, 23, Winer, Arthur M.; Peters, John W.; Smith, Jerome P.; Pitts, James N., Jr. Environ. Sci. Technol. 1974, 8 , 1118-21. Buzh. I.Talanta 1970, 17, 1221-24. Erdey, L.; Weber, 0.;
Anal. Chem. 1980, 52, 311-314
(20) Gundermann, K-D. Angew. Chem. 1965, 7 7 , 572-580. (21) White, Emil H.; Zafiriou, Oliver; Kagi, Heinz H.; Hill, John H. M. J . Am. Chem. SOC.1964, 86,940-41. (22) Babko, A. K.; Terietskaya, A,; Dubovenko, L. I . Ukr. Khim. Zh.1966, 32, 728-31. (23) Kachibaya, V. N.; Siamashvili, I. L.; Mamukashvili, M. V. Ukr. Khim. Zh. 1971, 26, 1846-49. (24) Babko, A. K.; Markova, L. V.;Lukovskaya, N. M. J. Anal. Chem. USSR 1968, 23, 330-35. (25) Seitz, Rudolf W.; Hercules, David M. Anal. Chem. 1972, 44, 2143-49. (26) Babko, A. K.; Lukovskaya, N. M. Ukr. Khim. Zh. 1962, 17, 50-52. (27) Seitz, Rudolf W.; Suydam. Wallace W.; Hercules, David M. Anal. Chem. 1972, 4 4 , 957-63. (28) Anderson, Howard H.; Moyer, Rudolph H.; Sihbett, Donald J.; Sutherhnd, David C. U S . Patent No. 3659100,Aug. 14, 1970.
311
(29) Anderson, Howard H.; Moyer, Rudolph H.; Sihbett, Donald J.; Sutherhnd, David C. U S . Patent No. 3700896,Oct. 24, 1972. (30) Nederbragl, G. W.; Van der Horst, A,; Van Duijn, J. Nature (London) 1965, 206, 87. (31)Pitts, James N., Jr.; Fuhr, Hartmut; Gaffney, Jeffrey; Peters, John W. hviron. Sci. Techno/. 1973, 7 , 550-52. (32) Regener, V. H. J . Geophys. Res. 1964, 69,3795-3800. (33) Burdo, Timothy G.;Seitz, W. Rudolf Anal. Chem. 1975, 4 7 , 1639-43. (34)White, Emil H.; Bursey, Maurice M. J . Am. Chem. Soc. 1964, 86, 941-42.
RECEIVED for review June 21, 1979. Accepted November 6, 1979.
Factor Analysis of Some Physical and Structural Properties Influencing the Fluorescence Lifetimes of an Atabrine Homologous Series L. J. Cline Love,* Patricia Cala Tway, and Linda M. Upton Department of Chemistry, Seton Hall University, South Orange, New Jersey 07079
The technique of factor analysis has been applied to a matrix of fluorescence lifetime data as a function of solvents and solutes. The data factor analyzes as log T with two factors. Two properties of the solute, identity and number of carbon atoms attached to the exocyclic nitrogen, were found to reproduce the experimental data within experimental error. Many solvent properties were also studied, but no combination could be found whlch successfully reproduced the data. New insights into possible solvent effects were obtained however.
The fluorescence lifetime, r , of a compound in a solvent is dependent on many factors. This is evident from the definition of T , as given in Equation 1,
1 T =
kf + k i + kz +
(1) kq[Ql
where kf is the rate constant for fluorescence, k l is the rate constant for internal conversion, k, is the rate constant for intersystem crossing, and kq is the rate constant for any quenching reaction by the quencher Q. The value of each of these constants is, itself, dependent on a number of factors, although the exact functionality is seldom known. I t is apparent that in the absence of all decay processes competing with kf, the fluorescence lifetime is a maximum value. As more mechanisms are made available for nonfluorescence deactivation of the molecule, the measured fluorescence lifetime becomes shorter. The fluorescence lifetimes of compounds can be very sensitive indicators of solute characteristics such as structural conformation and of solvent properties. When experiments are performed to study some of the effects on lifetimes of a particular set of compounds in certain environments, attempts are made to hold most of the factors constant, while one or two of them are studied (1-4). Because of the large number of possible factors, some often unknown, this is a difficult task to perform reproducibly and with any degree of certainty. For example, one may hold temperature, purity of environment, excitation wavelength, and compound constant in the hopes 0003-2700/60/0352-031 l$Ol .OO/O
of studying solvent effects. However, many factors do change when a solvent is changed, for example, viscosity, pH, ionization of the sample, solvent polarity, hydrogen bonding, ionic strength, and quenching. Additional information on solvent effects is obtained by studying a homologous series of compounds in different solvents. One can quickly build a matrix of fluorescence lifetimes, with solvents as the columns and compounds as the rows. It is often difficult to understand and explain the trends seen in such a data set because several different factors can contribute to the data simultaneously. Factor analysis is a mathematical technique which enables the chemist t o see and explain trends in a data set multidimensionally ( 5 ) . I t is, in part, a multiparameter curve-fitting method (6). It has been used in chromatography (7, 8 ) , spectroscopy ( 9 ) ,mass spectrometry ( I O - I Z ) , and biological activity (13). Factor analysis allows one to (1)determine the number of abstract factors needed to reproduce the array of data, (2) correlate these abstract factors with actual physical properties of the row and column designees (target transformation), and (3) predict new data using these target transforms. It has been difficult to utilize factor analysis in the past because of the uncertainity in how and when to use it ( 1 4 , 1 5 ) . The error theory of Malinowski (16-18) has solved some of these problems. This theory provides semiquantitative indicator functions which can be used to evaluate results of factor analysis. The use of Malinowski’s indicators lends assurance to the chemist that the problem under consideration is indeed factor analyzable and that the correct number of factors are chosen for the problem. I t was felt that a matrix of fluorescence lifetimes with solvents and solutes as the row and column designees might be amenable to factor analysis. The criteria to use in determining whether a problem is factor analyzable are (1)the components, K , of the matrix should be related to energy, (2) each component should be related to a linear sum of terms which are products of factors r and c, as given below,
Kl., = xrl.,c)h J=1
(2)
where the r factors relate solely to the row designees and the 0 1980 American Chemical Society
