J. N. Demas University of Virginia Charlonesviile. 22901
Luminescence Decay Times and Bimolecular Quenching An ultrafast kinetics experiment
For the past three years, our physical chemistry students have carried out an experiment on submicrosecond luminescent decay time measurements and excited state bimolecular quenching. This experiment complements and supplies essential data for another experiment on luminescence spectroscopy which has been described in detail elsewhere ( I ) . The experiment involves measuring the bimolecular quenching constant for deactivation of the excited tris(2.2'bipyridine)ruthenium(II) ion, [Ru(bipy)a2+], by dissolved oxygen with decay time measurements. This intensely orange-yellow complex gives a bright orange luminescence upon uv or visible excitation. The mean lifetime, T,in the absence ofquenchrrs is-600 ns in runm temperature fluid solutions. The Imr lifetime makes the complex quite sensitive to deartivation-(quenching) by many dissolved metal complexes, organics, and 0 2 . The sensitivity to oxygen quenching coupled with the intense long-lived emission makes the system extremely interesting from a teaching standpoint. The decays are long enough to he measured on a very inexpensive apparatus, yet fast enough to fall into the range that most students would consider "ultrafast" kinetics. Since the flash duration is somewhat longer than the 7's encountered, the 7's must he extracted from the flash and decay profiles (deconvolution) which introduces the students to this very. important concept which . is central to most fluorescence decay measurement~onscintillators, laser dyes, and proteins (2, 3). The interesting of statiiversus dynamic quenching can also be explored. Additionally, students are given exposure to one of the forefront areas of inorganic photochemistry ( 4 ) which is sufficiently new that an imaginative student still has the possibility of doing a research quality special project or senior thesis. The decay time apparatus can he exceedingly easily and inexpensively constructed. If an oscilloscope and high voltage power supplies are available, construction cost is only -5100-150 which is a bargain for physical chemistry experiments. In snite of the low cost, however, the apparatus can accurately measure r's as shok as 100 ns and permits estimates at least as low as 50 ns. Indeed, except for the method of data recording, the instrument is equivalent to our recent research apparatus. To our knowledge this decay time apparatus is the first reasonably priced one suitable for measuring longer-lived fluorescence decay times,
form an excited species D*, (2) the radiative decay of D* with the emission of light, (3) the first-order and pseudo first-order quenching of D* by intramolecular interactions or solvent and impurity quenching, and (4) the bimolecular quenchingof D* by added quencher Q. The mean lifetime of D* is then = 11 Kk.
i
+ k,) + kzlQll
(5)
where [Q] is the quencher concentration. Equation (5) rearranges to (114 = (Ilro) + kdQ1 TO =
Mk.
+ k,)
(6)
where rois the decay time of D* in the ahsence of Q. Thus a plot of 117 versus [Q] should he linear with a slope of k2. Alternatively the data may he expressed by the SteruVolmer equation (7017) - 1 = K,,IQl K," = kzio
(7)
where K,, is the Stern-Volmer quenching constant. Also K., ran he dt.termined From specrrotluorimetric measurements d'total luminesrenre intensity, 0, when the concentration of quencher, [Q], is varied. where $is the intensity in the absence of quencher. Equation (8) is the intensity form of the Stern-Volmer equation. Besides diffusional or dynamic quenching there is an additional quenching mechanism possible, static or associational quenching. In static quenching the quencher is chemically associated with the luminescent donor to form a non-luminescent association oair. Thus. the emission intensitv falls with increasing qurnrher concentration herause the tree donor interce~tsa derrrasinr fracuw of the incident lirht. 11 can he shoLm ( ~ ~ ~ e n d i when x - ~ )hoth static a n d dynamic quenching are present that 0018 - 1 = (K,,
+ BKeq)[Q1+ K.vBKeJQ12
(9)
where K., is the association constant, K,, is the Stern-Volmer ~ Dmea) constant of eqn. (7) and 0 varies from 1to ( C D ~ for surements made under ooticallv dilute to o~ticallvdense conditions. E ~ Qand co are the extinction coefficient of the association nair and free D a t the excitation wavelenpth, respectively. is the free quencher concentration rather than the formal quencher concentration, Qo. Both eqns. (7) and (9) are correct using Qo in place of [Q] as long as Qo is much greater than the initial donor concentration, a condition which frequently holds. Also since in many cases CD QQ or the measurements are done under optically dilute conditions, 0 is frequently unity. Equation (9) is in fact the general one, and eqn. (8) is the special case of K,, = 0. It is also noteworthy that if'only static quenchingis present (i.e. K,, = O), a linear intensity Stern-Volmer plot results, except that now the slope equals OK,,. In this case intensity data give no warning that the normal Stern-Volmer kinetics (eans. . . (1)-(4)) . . . .. are invalid unless 7 measurements are also made. Thus, rand intensity measurements complement each other. Even if hoth K,, and K., are nonzero, by comparing
h]
Theory
Bimolecular luminescence quenching can usually be described by the following kinetic scheme (5) D+hu-D'
(1)
where step (1) represents the excitation of ground state D to
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Volume 53, Number 10. October 1976
/ 657
intensity and r data both K, and OK, can he evaluated. Then by estimating& which is easy if the solution is optically dilute (,9 = 1) or if em f ~one , cam simply and directly calculate the K., without recourse to any of the conventional methods. An instructive difficulty in the current experiment arises because the flash duration (-0.8 rs) is longer than the decay times to be measured (-0.1-0.6 rs). Thus, there is no region completely free of pumping from the flash, and the usual technique of plotting the logarithm of intensity versus time to evaluate T is not feasible. I t is thus necessary to deconvolute the combined flash and decay data. Numerous methods of der&voluti~~n are available (6-10). The rnethd adopted was the Phase-Plane plot ( 1 0 1 , because it is very economical in computing time A d can he easily programmed into any programmable desk calculator. The calculations are, in fact, so straightforward and simple that they could he carried out on any electronic calculator. The method also gives direct graphical methods of interpreting the accuracy of the fit. The Phase-Plane and all other deconvolution methods rest on the integral equation relating the ohserved flash profile, F(t), and the observed sample decay D(t)
-
where D(t) and F(t) are measured under the same experimental condition and have a common zero time. See Appendix B for a derivation of eqn. (10). By transforming the data into a new space, a linear plot results.
The linearity of the Phase-Plane plot and the agreement hetween I X r J and DCalr(r)can be used to iudee whether the data are accurately represented by a singleexp&ential decay. Curvature and systematic error in the fit are evidence for nonlinear instrumental distortion (e.g. phototube saturation, amplifier nonlinearity) or of more complex decay kinetics (e.g. multiple exponential decays, the difference of exponential~). Apparatus
The experimental apparatus shown in Figure 1consists of a submicrosecond strobe flashlamo. uv ass filters to isolate the excitation band, the sample holder, a photomultiplier which views the sample through uv absorbing filters which remove the scattered uv excitation, and an oscilloscope for monitoring the transients. The second photomultiplier views the flash directly and generates an external trigger pulse for the oscilloscope; this trigger tube is absolutely essential for the deconvolution procedure to work. Excluding the high voltage power supplies and oscilloscope, the cost of components is -$loo-150. Supplier and recent prices for some components are listed in the table. The flash lamp and phototube wiring diagrams are shown in Figures 2 and 3, respectively. The flashlamp and its firing circuit were contained in a 12 X 4 X 7-in. minihox with all seams made light-tight with black electrical tape. The 150 V was derived from a surplus power supply, and we used 600 V for the flashlamp energy storage capacitor derived from four of these surplus supplies in series. The phototubes were each housed in 5 X 274 X 274-in. minihoxes. T h e trigger phototube viewed the flashlamp directly through a %-in. hole in the flashlamp housing. The flashlamp's excitation radiation passed through a 1 in. diameter hole covered by the filters which were held in place with black tape. The lamp flasher is quite versatile. The repetition ratemay
Thus, the Phase-Plane plot ofZ(t) versus W ( / ) islinear with a slope of -r and an interrcpt of KI.Note that \V(tt and % I / ) are easily evaluated functions ot the ohservahles. Since F(r) and Dtt J are normalls tabular rather than analwical funcrions. the integrals are evaluated numerically (e.g. ~ i m ~ s o nor ' s the trapezoidal rule). See Ref. (10) for a particularly convenient and simple set of equations. Once K and r have been determined, one can calculate the expected D(t), denoted as DCalc(t),from F(t) and eqn. (10) using numerical integration. An especially useful expression for generating W c ( t ) ,from K, i, and F(t) is
N data points are taken at even time intervals, At apart. The F(t) curve is a~oroximatedhvstraieht lines between successive F(t) points; the integratiohs of eqn. (10) are then carried out exactly. Alternatively, the integral of eqn. (10) may be evaluated using the tabular F(t) data and Simpson's or the trapezoidal rule, a procedure which can suffer from convergence problems, however. The agreement between D f t ) and Dcalc(t) can then be quantitated from a goodness-of-fit parameter, G, defined by G
1 N
1 [ D ( t i )- DcdC(ti)12 Ni=,
=-
(13)
G1"is thestandard deviation between the observed and calculated decay curves. 658 / Journal of Chemical Education
Figwe 1. Decay time apparatus. FL-flashlamp and mmrol
[email protected] M C I trigger phototube. PM2-signal phototube. PS-high voltage p w e r supply. F1-w pass 2 X 2-in. glass filter. Corning C.S. 7-60. SFI-solution filter: 1 crn at CuSO,.5HzO (200 gil). S m p l e . SF2-salutim fihw: 1 cm d saturated aqueous NaNO*. FZ-orangered pass 2 X 2-in. glass filter Cornlog C.S. 3-69. O--asciiloscope. RI-load resistor. 1 K or 5 K.
'
SHIELD
Figure 2. Flashlamp firing circuit. E l = 1A bridge rectifier 50 V. C1 = 100 pF. C2, C3 = 1 WF.C4 = 10 pF. C5 = 0.05pF. 200 V C6 = "Plastic Capacitns" 0.01 pF, 2 kV. C7 = "Plastic Capacitors" 0.1-0.5 pF. 2 kV. (see text). D l = 15 V. 1 W Zener. D2. D3.04 =ED1 1200 V, 3 A diodes type HIE 120. Lessexpensive, but perbps slightly less reliableis the mi 1000 V, 3 A HAB100 (1N4145) diode. F l = 1 A fuse, LP =Edgedon. Gemshausen, and Crier Lite Pak FY-5D with FX-6B. FL = flashlamp. R1 = 150 0.2 W. R2 = 500 fl. R3 = 27 0. R4 = 100Kvariable.R5=100K.R6=10K.2W.R7=100K, IOW.S1,2=SPDT. 53 =momentary contact SPST pushbollon. SCR = 2N1777A. T i = 12.6 VAC. 100 mA. U = GE 2N2647. Unless specified, ell resistors are '12 Wand all capacitators are 50 V. Suppliers and Approximate Unit Cart of Components comoonent
source
Comments
Most Electronic Components. "Plartic camcitors" ($7-111,RCA 9 3 1 Phototube (517) C7164R Phototube (5210)
Allied Electronics 2400 W. Warhington ~lvd. chicam. . . I L 60612
~ o o general d rupplier. but frequently back-orders with very lona delays A stock item
EM1 9781-R Phototube (555)
' ED1 H I B 1 2 0 ($3 each) E D i H A S 100 (IN4145 5 1 each) 2 in. Diameter Pyrex Window (53). 2 X 24". 7-60 Filter (57). 3-69 158). 3-70 ($111, 3-67 (59) 2K2O HV Power Supply (5330)
RCA Electronic components Harrison. NJ 07029 Gencom Division Emitronics 1°C. 80 Express street Plainview. NY lie03 ' AIOW EleCtronlCI 5207 East Drive Baltimore. M D 71227 ---ESCO Products 1 7 1 Oak Ridge Road Oak Ridge. NJ 07438 Power Design Inc. 1700 Shames Drive Westbury, N Y 11590 EG and G Inc. ~lectro-O~tics ........ 35 Congrerr Street Salem, M A 01970 Herback and Raaeman lnc. a01 F a s t Erie Avenue Philadelphia. PA
Normally a item
Excellent general supplier of lens. filters, windowr, and other optics
Excellent source of many low cant rurpl~5 items. Regular flier iirtr available items
Plaltic OIC~IIOSCOP. Grids ($20/1001, Marking Penr ($11 Phase R corporation Box G-2 New Durham, NH 03855
SIGNAL -&NODE Figure 3. Phototubeworking diagram. R i = 10 M. R2, R3, R4. R5. R6. R7 = 50 150K. C1=0.02uF. C 2 = 0.05 &F. C3 = 0 IrrF A Ir e s i ~ t o r ~W anda Icapac tors 500 V-ceramc d m AII *iring shoua oe on t woe somet The m e d 4s a s q l e eyer of cower 10' wrnpletely wveting me glass envelope except f w a viewing pott. The phddube glass and shield must be electrically isolated from ground. The signal lead is connected to ground through the load resistor. K R8 r 75 ~. ~- K . R9 = 100K.. R10 = 130K. R i i = ~
~
b e v a r i e d c o n t i n u o u s l y from 4.5-100 Hz d e p e n d i n g on t h e s e t t i n g of t h e "HI-LOW" s w i t c h a n d t h e p o t e n t i o m e t e r or single s h o t with manual triggering. F l a s h energy and d u r a t i o n a r e c o n t r o l l e d by t h e size o f t h e e n e r g y storage capacitors C6 a n d C7 a n d t h e c h a r g i n g voltage. I f C7 i s o m i t t e d , t h e p u l s e w i d t h is 4 . 7 us. F o r C7 un t o 0.1 uF a t 600 V. t h e flash i s s t i l l u n d v r l p s in b u r a t i o n ( t i l i e b e t w e e n thr. i,uf p e a k i n t e n s i t y u u i n t s l : however. t h e lou i n t e n i i r v f l a s h t a i l inrreases a t t h e k y h e r energies. Fur ('7 = 0.5 pk'. ;he pulse w i d t h increases t u -2 usec. For t h r c u r r e n t e x ~ e r i m e n ('7 t = 0.1 g F i s adeqtlate. h u t for w e s k r r l u n g e r - l i v e d emissions t h e larger c a p a c i t o r s wndd D r u h ~ h l vh e nreferred. T u c u t c ~ ~ s(t' 6s c o u l d h e u m i r r r d as l o n g as t h e i e r y ' f a s t e s t p u l s e (C7 = 0) w e r e not needed. T h e samole box was cardboard w h i c h was s p r a y p a i n t e d f l a t b l a c k on t i e inside. H o l e s were c u t for e x c i t a t i o n and right angle v i e w i n g by t h e detector. T h e signal phototube dynode string should definitely b e t a p e r e d a n d h a v e b y p a s s c a p a c i t o r s o n t h e l a s t stages as ind i c a t e d in F i g u r e 3 (11). T h e same d y n o d e s t r i n g s h o u l d also b e s u i t a b l e if t h e a p p a r a t u s i s u p g r a d e d with a N2 laser excit a t i o n source a n d a 50-R load resistor. T h e t r i g g e r p h o t o t u b e requirements are not critical. A l i n e a r d y n o d e s t r i n g (R3 = R4 - . . = R l l ) i s adequate, and t h e b y p a s s c a p a c i t o r s c o u l d
- .
-
SUP IU II Power SuPnlier
: T I
ery timer result ~ o w e r cost t N, laser on the market
p r o b a b l y h e e l i m i n a t e d without d e g r a d i n g performance. T h e dynode strings s h o u l d h e w i r e d d i r e c t l y to t h e p h o t o t u h e sockets. T h e s i e n a l o h o t o t u b e s h o u l d h e c o n n e c t e d to t h e oscilloscope h y ;he shnrtcst p o w h l e l e n g t h u f c o x x ~ acl a h l r .-5 Hz), a stable continuous trace results. This would simulifv ~hotoeraphic recording . . . . . - and permit a low-wst,slow camera to he used. In our casr it permils tracing thedata directly irom thescreen onti) plastic girls wirhspecial mnrking pens. %ese grids mad6 by JTKhl Swpr Tracer have a precision cm graticule and adhesive which permits sticking them to the scope face. Different colored pens are available, and several transients can be clearly displayed on the same sheet. Cost of -$.20 per grid is considerably less than Polaroid film and students waste less. Errors can even be "erased" by wiping with 95% ethanol. We give each group only three grids to eliminate wastage. Further, since the sheets are transparent, the data may he projected onto graph paper with a photographic enlarger and traced with a pencil. The only difficulty with the grids is that a steady hand is required and not everyone can produce accurate traces. The oscilloscope should have at least a 0.25 cm/&s sweep speed. A 5-MHz bandpass and a 0.1-V/cm sensitivity are also rewired. plans for a suitahle low-temperature Dewar and sample tubes for the 77 OK measurements are available on request. Cost for Pyrex which is suitable for thisexperiment is-$5 for the Dewar and -$3 for the sample tubes. The system is quite robust and practically indestructible. In three vears of tvuical student use, we have not had a sinele .. electronic malr~mctlon.The only maintenance is the need to periodically replace the filter solutions because of rorn,sion of the brass walls; an all glass filter cell would eliminate [hi; problem. The only hrenkn~chas been one sample tube which broke when the methanol-water glass fractured. We have warned that anyone breaking the $50 Dewar would pay for it which mav he ris~onsiblef& its lous life. A rather surprising characteristic of the experiment is its remarkable tolerance to light. The experiment is performed in a windowless room without lights hut with the door open into another fullv liebted room. In s ~ i t of e the absence of eood baffling around thephototube, the experiment still work&ell when the instrument dials are easilv read bv. lieht - comiue" through the doorway. The insensitivity is, of course, a consequence of the verv hiah peak Dowers of the flash and the luminescence conpied Gith the small load resistors required by the shortness of the decays.
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The Experiment
The experiment consists of measuring the decay time of Ru(bipy)a2+ in Oz and air-saturated water, and in a deoxygenated solution to obtain ro. Also to demonstrate the tem660 / Journal of ChemicalEducation
TIME ( p r e c i
Figure 4. Luminescence decay time data. F(t): Solid line is the observed flash. The 0'sare me data paints used in the deconvolution. D(t]-AIR: Solid curve is observed decay tor air saturatedaqueousRu(bipyhC12(-1 X 10-W.The 0's are calculated data pointr for r = 37 1 ns. G'I2 = 1.4,D(t)-N2: Solid line is obsewed decay of deoxygenated aqueous Ru(bipyh2+with the calculated pointr 0 ' s for T = 560 0s. GV2 = 1.0.
Figure 5. Phase-Plane plots for the decay data of Figure 4.s'. are far air-saturated solmian and 0's are for deoxygenated solution. Number corresponds to number of intervals followingthe zero time. Unnumbered data polnts fallow each other sequentially. Lines are least-squares filthrough the last 75% of the data Points. perature dependence of r , i t is measured in a rigid glass a t 77
ou
A>.
Room temperature data taken by the author for F(t) and D(t) in deoxygenated and air-saturated solutions are shown in Figure 4. Even though there is no exponential region for either sample, both are quite different from the flash and clearly different from each other. These differences permit successful deconvolution to obtain the 7's. The Phase-Plane plots for these data are shown in Figure 5. After the first few points where experimental scatter is always large, both data sets give excellent conformity to eqn. (11) which confirms that deactivation of the excited state occurs h s either first-order or pseudo first-order processes; that is if the flash were of zero. duration and the measuring system infinitely fast, then the observed decav would he exoonential. Using the a and r obtaine2 for each sample, the calculated decavs, Dcai'(t)'s, were commted from e m . (12) and comnared withthe original data as shown in Figure4. Again the excellent agreement between the observed and calculated curves confirms the presence of a single exponential decay and establishes the absence of significant nou-linear instrumental distortions. Similar data were obtained for the O2 saturated solution and are not reproduced here. r's for the deoxygenated, air, and Opsaturated solutions were 560,371, and 161ns, respectively. The 117versus [Q]plot
Figure 6. Variation of Ru(bipyhzcdecay time with oxygen cancentratlon is given in Figure 6; a least-squares fit yields k2 = 3.4 X 109 M-' s-' and i o = 563 ns. K,(= k270) is 1940M-l. These data are in good agreement with q's of 600 (12,13) and 660 ns (14) and the air-saturated values of 376 (11) and 405 ns (15) reported by others. The K,, is in excellent agreement with the values of 2060 M-' from intensity quenching data and 1890 M-I from r data; the latter value was obtained on a system verv similar to the current one except for the use of ohotographic data recording (16). The agreement between the iand intensity derived K , values establishes that there is little if any static quenching present in this system. Decays for R ~ ( b i p y ) ~ Zin+ a rigid methanol-water glass (411:vIv) a t 77'K are so long that the semilogarithmic plot of intensity versus time yields a good estimate of r as long as the data are taken from the plot after significant curvature is gone. Our InI(t) versus t plots were linear over two mean lives and gave GIi2 0.2 with a maximum value of lnI(t) 5. 8 s were 5.76 and 6.10 rs. Alternatively, the Phase-Plane method can be used. althoueh considerahlv more work is involved. llnlikn -. with the shorter decay times, however, best accuracy is obtained if D(t) decavs to at least a half or a ouarter of its oeak intensity, even though F(t) is very compressed and cannot be accuratelv read. We find that students frequently do not get quite as good results, especiallv on the deconvolutions. In s ~ i t of e warnines they often fail to recognize the great caution.needed in daia tracing because of parallax errors. For -9 mouos. we obtained 576 fSO,363 f 57, and 153 f 19 ns for thk decay times, kp = (3.6 f 0.6) X lo9 M-l s-I, and K., = 2050 f 400 M-I. For the low temperature decay time, students using the Phase-Plane method obtained 4.3 f 0.3 ps while those using the linear semilogarithmic plot obtained 5.8 f 0.3 rs. These values are similar to the 5.0 ps obtained for an ethanol-methanol glass at 77 O K (17) and to a 4.00 r s value measured in the methanol-water glass by two of our students using a laser decay time system. I t seems likely that the 4 r s decay is more accurate, and the longer decay from the semilogarithmic plot arises, because of continued pumping from the long-lived afterglow from the xenon flash.
-
-
Procedure
Students are supplied with a stock solution of aqueous R u ( b i ~ y ) 3 ~(-1-4 + X 10-4 M )in a Pyrex test tube. 7 measurements were made on deoxygenated, air saturated, and oxygen saturated solutions prepared by bubbling for about 5 min with Np, compressed air, or 02, respectively. During measurements bubbling is continued in the upper portion of the tube. The sample emission in all cases was bright enough to be easily viewed in a darkened room; the more perceptive students quickly recognized that the emission intensity falls pronouncedly with increasing Op concentration. The D(t) curves also change dramatically with O2 concentration.
We have found it most convenient to adjust the phototube w l t a r r so that the 0 2 saturated solution eives a full-SCRIP deflection on the 0.1 \i/cm range. The two Lss quenched solutions will then be brighter, and by adjusting the sample position and/or masking the phototube, these signals can be reduced to give full scale deflection on'the same range. For obtaining the flash profile, F(t), a test tube of dilute rhodamine B or fluorescein in ethylene glycol replaces the sample. The fluorescences of these dyes pass the phototube filter, and their 7's (
