March; 1962
OXYGEKQCEXCHIKG
OF
absorpticln between 550 and 700 mu,the isosbestic point at 410 and the minimum at 840 mp, There thus is little doubt that the short-lived substance of Fig. 1 and 2 is the acid form of the triplet state. It is of particular interest t o establish this link between the flash-excitation and rigid solvent studies, in view of the striking discrepancy between flash and low-temperature cross-illumination spectra in the case (of fluorescein. No lo’w-temperature cross-illumination spectra of the neutral acridine orange base are available. By analogy with the situation in acetic acid it is suggested that the initial spectrum of Fig. 3 is due to the triplet state of the neutral base. While at first glanlce this spectrum appear to be quite different from that of the protonated dye triplet, particularly with regard to the peak a t 410 mp, it is possible ithat the acid triplet also has a strong absorption in this region, overlapped by the original dye peak. The extent of dye conversion is uncertain. Results in Other Solvents.-In pyridine containing TEA (0.007 M ) or aqueous HCl M) results were obtained similar to those in pure TEA or acetic acid, respectively, with regard both to the spectral changes and appearance of short- and long-lived states. Toluene containing TEA (0.01 M ) and ethanol containing sodium methylate (0.02 M ) acted similarly as basic solvents. Kinetic s.-In previous solution studies, we have found that three rate constants are required to account for the decay of triplet states directly to the ground state.6 If the decay occurs via further intermediates, additional constants are necessary. The low absorption of the transients makes our present data too incomplete for such analysis, beyond t,he preliminary rate constants already givena6 Further work involving longer cells and higher flash energies is in progress. I n particular, it is necessary to establish the spectra of the longlived products. However, we wish to stress the general outlines of the phenomena which now appear. Lindqvist’s work on fluorescein in aqueous solution has shown that the bimolecular decay processes of triplet
FLUORESCENCE IN EOLFTIOV
445
mp.
‘
I000
800 700
- 0
$00
599
450
400
I
I
I
350 I1
0.9 -
0.807-
w
06-
V
2
05-
a
0
2
04-
4
0.3 -
0.2-
cm-’
Fig. 3.-Absorption spectra of A 0 in TEA: dashed line, ground state spectrum; solid line, spectrum immediately after flashing; concn. is 4.2 X 10-6 M .
states may lead either directly to the ground state, or, via dismutation, to free radicals. Our results, within the limits imposed by experimental uncertainties, are consistent with this, although the possibility still remains that the long-lived intermediates in the A 0 case may be formed directly from excited singlets. In organic solvents the further possibility of oxidation-reduction reactions between triplet and solvent must, of course, be considered. However, the similarity within the two groups of reactions of A 0 in the various acidic and basic solvents suggests that, as in the fluorescein case, the radicals which we now identify with the longlived products are formed by dismutation processes involving only dye molecules. The excited molecule does not appear to undergo proton transfer reactions within the range of acidity or basicity covered by the two groups of solvents used here.
OXYGEN QUENCHIXG OF FLUORESCENCE IN SOLUTION: AX EXPERIMENTBL STUDY OF THE DIFFUSION PROCESS BY WILLIAMR. WARE Research Laboratory of U n i o n Carbide Consumer Products Company, Division of U n i o n Carbide Corporation, Parma 30, Ohio Recsived September 16, 1961
Unusually large Stern-Volmer constants for the quenching of fluorescence of aromatic hydrocarbons by oxygen in solution are well known. The rate constants for the quenching reaction have been determined by fluorescence lifetime measurements for several hydrocarbons in a series of solvents covering a wide range of viscosities. The diffusion coefficient for oxygen in several solvents also ma8 determined. The rate constants are consistent with a diffusion-controlled reaction when the unusually large diffusion coefficient for oxygen is taken into account.
Introduction Large Stern-Vo1mer for the quellching Of polynuclear aromatic hydroWirbOns bY Oxygen have been known for many
years.1.2 The Stern-Volmer constant is a product (1) P. Pringsheim, “Fluorescence and Phosphorescence,” Inters&nce Publishing &., New York, N. y,, 1949, p. 333. (2) E. J. Bowen, Trans. Faraday SOC., 6 0 , w (1954).
456
WTLLTAY R.
of the second-order rate constant for the quenching reaction and the fluorescence lifetime of the excited state in the absence of the quencher. Recent lifetime studies3.4made with anthracene in benzene permit one to calculate the actual rate constant, and in this case the value is approximately three times as large as one would estimate from theorye6-* However, such a calculation involves estimating the diffusion coefficient for oxygen in benzene, which makes the comparison very uncertain. The mechanism for the reaction of oxygen with these hydrocarbons is very c ~ m p l e x , gbut ~ ~ ~ it seems reasonable, in view of the large rate constants, to consider separately the process involving the encounter of an excited molecule with oxygen and the subsequent steps which may include the formation of a moleoxidelo or a charge transfer complex,ll and which occur probably with almost every encounter. The purpose of this paper is to examine the first of these two aspects of the process. One would expect the reaction to be diffusion controlled, but the large rate constants raise many questions, since there are several possibilities: (a) the Stokes-Einstein relationship is not suitable for estimating diffusion coefficients from viscosity data; (b) the theory relating the rate constants to the diffusion coefficient may be inadequate; (e) oxygen interacts a t a distance and the quenching is thus more efficient than ordinary diffusioncontrolled reactions; (d) reasonably stable complexes are formed giving the appearance of large rate constants. It appeared desirable to determine the rate constants for quenching by a dynamic method and to do this for several hydrocarbons in a series of solvents covering a wide range or properties. The variation of the fluorescence lifetime with quenchex concentration is the most direct and satisfactory approach, since if a Stern-Volmer mechanism is followed the rate constant is directly obtained from a slope 1/7’ =z 1/7 d- h % O d (1) Lifetime studies also can be used in conjunction with fluorescence intensity measuremeiits, since the lifetime of the excited state, which depends upon the solvent, is required to interpret the SternVolmer constants. In addition it was considered desirable to measure the diffusion coefficient for oxygen in several solvents inasmuch as the polarographic studies of Jordan, Ackerman and Berger12 in waterglycerol mixtures indicated large departures from the Stokes-Einstein relationship for oxygen. (3) W. S. Metcalf, J . Chem. Soc., 3729 (1960). (4) W. R. Ware, J . A m . Chem. Soo., 83, 4374 (1961). (5) F.C. Collins and G. E. Kimball, J . Colloid Sci., 4,425 (1949). (6) J. Q. Umberger and V. K. LaMer, J . A m . Chem. Soc,, 67, 1099
(1946). (7) E. Williamson and T‘. K. LaMer, ibid., 70, 717 (1948). ( 8 ) A. Weller, 2. physik. Chem. (Frankfurt) 13,335 (1957). (9) R. Livingston and S. Rao, J . Phvs. Chem., 63, 794 (1959). (10) R. Livingston, “Photochemistry in Liquid and Solid States,” F. Daniels, Ed., John Wiley and Sons,Ino., New York, N. Y., 1960. (11) R. 8. Mulliken and H. Tsubomura, J . Am. Chem. Soc., 82, 6966 (1960). (12) J. Jordan, E. Aokerman and R. L. Berger, ibid., 78, 2979 (1966).
WARD
Experimental Fluorescence lifetimes were measured with a Rollefson type hase shift instrument. Details of its design and operation iave been described el~ewhere.4~13This device makes use of the fact that the fluorescence excited by a sinusoidally modulated light source also will be modulated but with a phase shift 6 such that tan 4 = 2?rf/B(kl
+ k,Cj)
(2)
where f is the modulation frequency, the hi’s and kj’s are first- and second-order rate constants for the disa pearance of the excited species, the kj’s being multiplied gy appropriate quencher concentrations Cj. Since low light intensities are used, the Cj’s are constant during a determination. The assumptions involved in this method are discussed elsewhere.4Ja A modulation frequency of 5.2 Mc. was used and the useful sec. range of the instrument started at about 1.8 X with an uncertainty of about 20%. At 4 X 10-9 sec. the uncertainty was about 4% and above this value it slowly decreased to 2%. Cells 0.8 X 0.8 cm.2 were used and provision was made to saturate the solutions with either purified helium, dry air, or dry oxygen, and to allow equilibrium to be set up at atmospheric pressure. The lifetime for each hydrocarbon in each solvent was determined after purging with helium and after saturating with oxygen. In some cases air also was used to check the linearity between l / ~and ’ [OZ]and the extrapolation to l / ~ The . second-order rate constants for quenching were determined from equation 1. Dilute solutions (10-4 to 10-6 M ) of anthracene, 9,10-dichloroanthracene, 9J0-diphenylanthracene and perylene were used. Oxygen solubilities were determined under identical experimental conditions using a Perkin-Elmer gas chromatograph and probably were accurate to 10%. Agreements with literature values for oxygen solubility14were quite good in most cases. Viscosities, where needed, were determined by conventional techniques. Solvents for these experiments either were reagent grade or were purified by distillation and all were chromatographed on silica gel columns prior to use. Very pure samples of anthracene, perylene and 9,lO-dichloroanthracene were available from previous w01-k.~ A pure sample of diphenylanthracene was obtained by silica gel chromatography. The measurement of diffusion coefficients, especially in solutions of low viscosity, is made very difficult by problems of mixing and convection. I n addition, diffusion from a source of constant concentration provides one of the few sets of boundary conditions which leads to a simple relationship for linear diffusion. After considerable experimentation, the following apparatus was devieed to measure the diffusion coefficient. A hollow vacuum stopcock 8 cm. high was used as the diffusion cell. The straight sidearm was replaced by a capillary having an i.d. of approximately 1.5 mm. which was about 15 cm. long and terminated in a small stopcock. The vacuum stopcock plug was modified by replacing the handle with gas inlet and outlet tubes. At the beginning of an experiment the capillary was filled wlth an oxygen-free solution containing 9,10-diphenylanthracene (10-4 M ) as an oxygen indicator. The bulb at the bottom of the stopcock contained a small amount of the same sohtion saturated with oxygen by a stream of solvent-saturated oxygen slowly passing through. The boundary was set up by turning the stopcock until the hole (normally used to pump out the bulb) was coincident with the capillary and the interface thus exposed to the oxygen-solvent atmosphere of the hollow chamber. The assumption is made that the rate of equilibration at the interface exceeds by a considerable amount the rate of diffusion, and thus essentidly at once there is set up a small element of the solution at the interface in the capillary that is saturated. The time required for this to take place is small compared to the diffusion process. Then linear diffusion takes place with the oxygen concentration C given by
C = COexp
{SF
(3)
(13) E. A. Bailey and G. I(. Rollefson, J . Chem. Phys., 21, 1315 (1953). (14) Gmelins “Handbuch der anorganischen Chemie,” 8 Auf. Verlag Chemie GMBH. 1958.
OXYGENQUENCHING) OF FLUORESCENCE IN SOLWTION
March, 1962
where 2 is the distance from the interface, t the time, and D the diffusion coefficient. The oxygen concentration is followed by making use of the fact that oxygen quenches the fluorescence of the added hydrocarbon. Thus c = kw-1 (&/I 1) (4) where ,.CI is the Stern-Volmer constant and I o / l the ratio of unquenched to quenched fluorescence intensity. Provision was made t o illuminate the capillary with a narrow beam of light and to measure the fluorescence intensity a t right angles with a suitable photomultiplier-filter arrangement. The entire atopcock arrangement was mounted with the capillary horizonta,l on a slider on an optical bench and could be moved past the collimated light beam to vary the distance from the interface a t which time dependent data were taken. Compensation was made for variations in light intensity and corrections made for reflections from the capillary. The method was tested by checking the various aspects of equation 3. It is required that log (.70/.7 - l ) us. l / t plots be linear, that, the same value of D be obtained at several distances, and finally that the extrapolation point for the family of curves a t various distances agree with the experimental value for the ordinant a t infinite time, as determined by letting the oxygen-saturated solution into the capillary. The method was satisfactory and in fact with viscous solutions it even was possible to fill the hollow stopcock completely and obtain fair data, although mixing was a problem, No attempt was made to control the temperature other than to work in an air-conditioned room that was constant to about one degree. The values presented in Table I for a series of sodvents at 25 to 26' are considered accurate to within 15%# which was adequate for the purposes of this work.
-
are much greater in the case of oxygen, both with regard to the magnitude and to the behavior at high viscosity. It is thought that this is due in part to the combined effect of the relative molecular sizes of oxygen and the solvent plus the fact that oxygen has a lower mass than the solvent molecules and a much lower mass than large molecules which obey the Stokes-Einstein equation. It is interesting in this connection that nitrogen, hydrogen and oxygen have quite large diffusion coefficients in water16 compared to larger solute molecules. Also, the value for carbon dioxideI6of 3.2 X cm.2 set.-' in ethyl alcohol at 17" compares favorably with our value of 4.0 X 10-6 for oxygen in the same solvent a t 25". Mention already has been made of the large departures from StokesEinstein behavior for oxygen in glycerol-water mixtures. Indeed, it would seem unreasonable to expect the Stokes-Einstein equation to hold where the solute molecules are much smaller than those of the solvent since the macroscopic viscosity should become an unsatisfactory parameter under these circumstances. In Table I there also are listed values for the rate constants calculated from diffusion theory using kq
TABLE I
457
= 4n N(Dh
+ Do) + ~0)/1000 (5%
(5)
For comparison, values calculated using the StokesCOMPARISON WITH DIFFUSION THDORY Einstein equation rather than the measured difkq k kq ks fusion coefficients have been included. I n both Dh Do (eq. 5) (S-& (exp.) (exp.) x 106, Anthracene av. b cases a radius of 4 8. wagassumed for the hydroSolvent om.2 Bec.-l X 10-11 M-1 sec.-1 carbon molecules while 2 A. was taken for oxygen. n-Octylalcohol 0.4 1 . 6 0.9 0 . 1 1 . 7 1 . 7 A comparison also is given in Table I between the .7 2.4 1.4 . 2 1 . 8 1.8 Isobutylalaohol experimental values obtained for anthracene and 3 . 3 1 . 9 . 3 2 . 2 2 . 5 Isopropyl alcohol .9 of the values obtained for anthracene, an average Ethyl alcohol 1.4 3.9 2.4 .7 2.5 2.5 perylene and diphenylanthracene. It is clear from 1 . 2 3 . 1 Benzene 2.2 5.7 3.6 3.0 these data that the rate constants and Sternn-Heptane 3.1 5.6 4.0 1.9 3.5 3.1 Volmer constants appeared large because of the Acetone 3 . 7 9 . 0 5 . 7 2 . 3 3 . 9 3.9 gross underestimate of the diffusion coefficients Using Stokes-Einstein equation. b Average of anthrawhich results from the application of the Stokescene, perylene and 9J0-diphenylanthracene. Einstein relationship. In fact, considering the Results and Discussion assumptions involved in the derivation oi the difThe results obtained from lifetime measurements fusion equation the agreement between theory are given in Table 11. In the case of anthracene and experiment is rather good. the Stern--Volmer constants also were determined A transient terms kq(Th Y,,)/v'Z frequently is using conventional techniques in the solvents added to equation 5 . This term arises from the listed. Rate constants for the quenching reaction solution of Fick's equation when steady-state concalculated from the Stern-Volmer constant using ditions are assumed a t low solute concentrations. the measured lifetimes in the absence of queiicher The lifetimes and diffusion coefficients encountered were on the average about 7% higher than those in this work lead to a correction of about 5 to 10% obtained directly (equation l), which is within from this transient term. experimental error but is perhaps significant. A more interesting point concerns the implicaThis will be discussed below. tions of this transient term on the phase shift The difjfusion coefficient for oxygen was meas- measurement. This involves introducing a timeured in seven of the solvents covering the whole dependent terms into the equation viscosity range. The results are given in Table I. Values listed for the diffusion coefficient of the hydrocarbon, Di,,were estimated from the data of Bowen and Metcalf.l6 It can be seen that the in place of kq. The solution is very involved, but diffusion coefficient Do is from 2.5 to 4 times greater it appears that to a first approximation the phase than Dh and that it falls rather slowly with viscosity. shift technique measures only the time-independent While both the hydrocarbon solutes and oxygen part of kq when the rate constants and diffusion cofail to folllow the Stokes-Einstein equation, D = efficients are of the magnitude found in this work. kT/6nq, where q is the viscosity, the departures If this is correct, the fact that the Stern-Volmer 0
+
(15) E. J. Bowen and W. 8.Metcalf, Proc. Boy. Soc. (London), 2068, 437 (1951).
(16) "Internationrtl Critical Tables," MoGraw-Hill Book Go., New York, N. Y., 1926.
R, J, GLEDHILL
458
Vnl. 66
TABLE I1 RATECONSTAXTS FOR OXYGENQUENCHING 8 -1
Solvent
x 10-4 poise-1'
Anthracene 7a
kqb
9,lO-Dichloi-oanthraoene r kq
9,lO-Diphenylanthracene 7
h
Perylene 5-
Acetone 3.11 5.7 3.9 7.7 1.6 9.7 3.8 6.1 n-Heptane 2.60 5.8 3.5 8.3 2.2 8.9 2.6 5.7 Toluene 1.77 3.1 4.2 10.4 1.7 8.1 2.8 5.5 Methyl alcohol 1.72 5.7 3.2 8.3 2.2 9.7 3.1 6.2 Benzene 1.64 4.2 3.1 1.0 2.4 8.2 2.8 5.2 p-Xylene 1.63 4.2 3.0 11.4 2.0 8.3 2.4 5.7 Ethyl alcohol 0,905 5.8 2.5 8.7 1.7 9.4 2.3 6.0 Dioxane .835 4.8 2.3 10.6 1.4 8.9 1.9 5.9 Isopropyl alcohol ,445 6.0 2.2 8.6 1.6 9.2 2.2 6.1 Isobutyl alcohol .264 5.5 1.8 9.2 1.5 9.0 1.7 6.0 n-Octyl alcohol ,130 5.6 1.7 10.1 1.1 8.8 1.6 5.8 a X loQsec. b X 10-lo M-' sec.-l. -4verage of anthracene, 9,10-diphenylanthracene and perylene.
constant yields a slightly higher rate constant than is obtained with the phase shift technique is understandable, since the former would contain the transient term. As can be seen from Table 11, 9,lO-dichloroanthracene gave lower rate constants than the other hydrocarbons. This is probably a manifestation of a lower probability for quenching once an encounter has taken place, compared to the other three hydrocarbons. A slightly lower diffusion coefficient for dichloroanthraceiie compared to the other hydrocarbons would not produce this effect, since the diffusion coefficient for oxygen is the more important quantity, especially a t lorn viscosity. The disagreement between the experimental reresults and eq. 5 a t very low and very high viscosities is perhaps the result of a combination of two factors; (a) an incorrect estimate of the radii and (b) failure to take into account separation prior to reaction in the case of very rapid diffusion found in solutions of low viscosity.
h 4.1 3.1 3.4 3.0 3.2 2.6 2.7 2.0 2.6 1.9 1.7
ksC av.
3.9 3.1 3.1 3.1 3.0 2.7 2.5 2.1 2.5 1.8 1.7
Two other possible explanations were given in the Introduction for the apparently large rate constants for oxygen quenching. With regard to interaction a t a distance, the essential condition for resonance transfer presumably is not present." Stable non-fluorescent complexes would influence the Stern-Volmer constant measurements but not the lifetime measurement^.^ Since these agree to within a few per cent., this presumably is not an important factor in determining the magnitude of the rate constant. Summary.-The rate constants for oxygen quenching of fluorescence of aromatic hydrocarbons in various solvents have been determined. Both the magnitude and the behavior with solvent viscosity are explained in terms of a diffusion-controlled reaction by making use of measured diffusion coefficients to compare theoretical with experimental values. (17) Th. Fbrster, Discussions Faraday SOC.,27, 7(1959).
PARTICLE-SIZE DISTRIBUTION DETERMIKATION BY TURBIDIMETRY BYR. J. GLEDHILL Communication A-0. 2228 from the Kodak Research Laboratories, Eastman Kodak Company, Rochester, K . Y . Received September BO, 1951
By the application of the Mie theory of light scattering to measurements of the specific turbidity and the dependence of turbidity on wave length, particle-size distributions on a weight basis have been determined for polydispersions of nonabsorbing isotropic spheres in the micron to submicron range. The polydispersions studied fit a log-normal t pe of distribution. A method is described for constructing a graphical calibration grid for a system of known opticaYconstants and known distributional form, from which the weight mean diameter and standard deviation of the distribution corresponding to observed turbidity measurements can be read directly. The particle-size distribution constants obtained by this turbidimetric method agree with those determined from electron-microscopic analysis within an average deviation of 1.370.
but these generally have been limited essentially to Introduction The light scattering of most colloidal suspensions monodispersed systems. However, more recently of spheres in the micron- to submicrnn-size range Meehan and Beattiea have used the Mie theory to can be treated adequately only on a basis of the Tabibian, w. Heller, and J. N. &el, J . Colloid Sei., 11, general ~i~ theory. This is especially true where the refractive index Of the differs signifi(2) J. B. Bateman, E. J. Weneok, and D. C. Eshler, dbid., 14, 308 cantly from that of the medium of suspension. (1959), Such treatments have been in the determi(3) E. J. Meehan and W. H. Beattie, J. Phya. Chem., 64, 100 nation of particle size by light-scattering methods,'** (1960).
,gF;l,";B;I".
