- Email: [email protected]
Picosecond lifetime determination of the second excited singlet state of xanthione in solution
I1 1. nwnber -1,.5
Votun~r
PlCOSECOND
CIiEMlfCAL PHYSICS LETI-ERS
LIFETIME
OF XANTHIONE
DETERMINATION
OF THE SECOND EXCITED SINGLET
9 Novcn~bcr 1961
STATE
IN SOLUTION
Roccived 3 July 1984; in final form 18 August 1984
fiferimes and quantum yields of the S2 state of xantbionc in benzene and isoloctanc sotution at room mcnsurcd. The Sz iifctimn wcrc found to bc I8 2 2 ps in bcnzcnc and 43 % ‘I! ps in iso-ocrane. The non-radiative decay rate constant is 5.6 x lO’* s-l in benzene and 2.3 X IO** s-t in iso-octane. The lluorescencc
temperature
have
been
1. introduction Many aromatic thiokctones exhibit fluorescence front the second excited singlet state, S,. to the ground slrttc. Xanthionc is probably the most extensively used thionc for the study of the decay dynamics of excited statcfs higher lhan S, [I ] _ Using a Nd3* glass modelocked laser-driven light-gate technique, Anderson et ai. f2] have measured a lifetime of f 2 4 3 ps for the S, fluorescence of xsniltione in benzene. Very recently, Mahaney and Huber [I ] derived the S7 lifetimes, r, and the rate constams for non-~dialjv~dccay, k ,,r. from the S, fluorescence quantum yield and the integrated absorption of xantitione in several solvents. For xsnthione in benzene solution. they found 7 = t 8 ps and k,, = 5.0 X 1O1o s-l _ 111the present communication we report lifetimes and quantum smthione
for the S2 -+ So fluorescence
yields
in benzene
temperature.
of
and
iso-octane solution at room Front these data. the radiative and non-
radirttive decay
rare constants
arc calculated.
2. Experimental
Santl~iom. was synthesized (Aldrich) of 340
in p-divsanc
tetraphosphorus
(Aldrich
decasulfidc
by reflusing 99%)
xanthone
with an excess
(Merck) [3]. The crude
xanthione was purified by column chromatography over silica gel (Machercy Nagel MN-Kieselgel 60) using dicf~Iorome~ltane (Janssen Chimica 99.8%) as the eluent followed by recrystallization from zz-butanol (UCB reagent grade)_ Iso-octane (Merck for fiuoromerryj and benzene (Aldrich spectrophotometric grade) were purified by standard procedures f4] _Solvent purity was checked by gas chromatography. No fluorescence could be detected front any of the purified solvents under the excitation conditions used in this work. 3 3 Itntrtttncttlatiott _._. Fluorescence spectra and quantum yields were obtained with a computerized Spex Fluorolog 1902 using double monochromat~rs in both excitation and emis-
sion. or with a Spex Fluorolog 2 12/Datamate. The optical densities were measured with 3 Perkin-Elmer . Lambda 5 UV/VIS spectrophotometer. The S2 + So quantum yields were determined by a refative method using quinine sulfate in 0.1 N HlS04 (q$ = 0.545) as standard IS]. Correction for the refractive index of the solvents was applied. The absorbances at tile excitation waveiength were lower than 0.1. Fluorescence decay times were measured using a Spectra Physics frequency-doubled cavity-dumped mode-locked synchronously pumped R6G dye-laser system with timecorrelated single-plroton-counting detection [6--8]_ The fluorescence lifetime apparatus and the associated 0 009-26 14/84/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
CHi31ICAL PHYSICS LETTERS
Volume 1 1 1, number 4.5
9 November
1964
ps/channel. For the fluorescence lifetime determinations of xanthione in solution, the optical density at the excitation wavelength, 296 nm. was higher than 2 in 1 mm pathlength optical cells (Hellma QS). The solutions
were
front-face
not degassed
configuration
and were
measured
in the
in a temperature-controlled
(22
+ O.Z°C) cell holder. 1 mm pathlength optical cells were used to minimize any time uncertainties due to the finite thickness of the sample_
2.3. Data mm&sis
Fig. 1. Picosecond ldser cwitdtion system: BS. bcarn splitter, CDD, wvity-dumper driver; M, mirror; FL, focusing lens; I-DC. frequency-doubling crystal; PD. photodiode. SPD. synctuonization
pllotodiode.
optical and electronic components are described in detail elsewhere [9]. The following modifications of the time-correlated fluorometer were made: After a recommendation of Dr. I. Yamazaki (Institute of Molecular Science, Myodaiji, Okazaki. Japan), the synchronization photodrode was removed from the cavity dumper and set to monitor the beam of the mode-locked Ar-ion laser (fig. 1). This modification resulted in improved long-term stability of the pulse shape and intensity_ The alignment and adjustment of the cavity dumper also became much easier. Frequency doubling was aclzieved wit11 an angle-tuned Inrad model 463-l 117 KDP “B” crystal. The dye-laser light was focused on the crystal through a lens. Since the frequencydoubied light is horizontally polarized, no polarizer was inserted in the emission path. Magicangle detection gave the same results but at a reduced count double
rate.
For
emission,
monochromator
a Jobin-Yvon
DH 20 Vis
was used. The start
signal for the time analyzer (Canberra model 2044) was taken from a fast photodiode (Spectra Physics model 403B) monitoring a fraction of the undoubled dye-laser beam. The time analyzer was operated in the normal configuration, the voltage ramp being initiated by the photodiode signal and terminated by a signal from the XP2020Q photomultiplier operated at 2300 V. The output pulse of the time analyzer was fed into a Canberra model 1467 biased amplifier_ The Canberra models 1467 and 2044 allow a linear expansion of the multichannel analyzer timescale down to about 1
The observed fluorescence decay curve at the emisof the true desion wavelength_ &,,, , is a convolution cay and the measured instrument response function (irf). The convoluted fluorescence decay function of xanthione in benzene or iso-octane was used to mimic the irf at tlte wavelength of sample emission &,, [lo] _ The least-squares iterative reconvolution method [ 11 121, based on the algorithm of Marquardt [ 131. was used to determine the decay parameters. A careful residual analysis was done after a decay law was fitted to the fluorescence decay data [ 141. The most widely used technique for examining residuals in time-correlated single-photon-counting experiments involves the plotting of the weighted residuals Ri [eq. (3) below] against time or channel number. The patterns of such a plot are helpful in choosing the correct functional fomi of the decay law and determining the need for additional terms in the decay function_ There should be no discernible trend in the plot of the residuals, Xi, versus channel number i: only a random scatter of points about the line Ri = 0. Observations that have extremely large residuals (outhers) can also be detected by examining such a residual plot. In detecting heteroscedasticity [ 151 (error temrs with unequal variances), it is helpful to plot the (squared) residuals versus the predicted responses pi (i.e. the calculated values). A graph of Ri versus Yi should reflect a random scatter of points about a line with zero slope. Systematic patterns would indicate an inadequate model for the decay law. Examining the plot of the autocorrelation function can also indicate if a chosen model for the decay function is adequate 1161. Although residual plots can be easily analyzed and interpreted, their interpretation is somewhat subjective and sometimes biased. Therefore. several numcrical statistical tests were used to make the residual analysis more reliable. 341
CHEMICAL
Volume I1 1, number 4,s
The first numerical test is the calculation reduced &i-square statistic. xt, given by X’, = -&
7
9 November 1981
of the
‘Vj(yi - FiTi)’ ,
(0
where ‘vi, the weighting factor, is the reciprocal of the number of counts Yj in data channel i, II is the number of data points, p is the number of adjustable fitting parameters and Y =/I - p_ pt is given by pr =J/(t’)y(f
PHYSICS LEI-I-CRS
- r’) dt’ ,
u is the standard deviation of the runs distribution. The sequence of the signs of the residuals is considered random at the 50% confidence level if iZ I< 0.6745 (for the other confidence levels, see discussion of zx2 )To test for serial correlation between residuals, the Durbin-Watson test statistic d [20] was calculated:
(7)
(2)
0 where f(f) is the irf and g(f) is the true decay function. The weighted residual in channel i is given by
Ri = ,~f~'l(Yi - Yi)_ xX was converted
(3)
to a standard
normal deviate
Zx2
[17,181 zx2
=
(IJ/2p(x2,
and the required
-
1)
)
probability
(4) determined
from
a table
of standard normal probabilities, e.g. 12x2 I< 1.96 for testing at the 95% confidence level, ,Zx2 I< 2.58 (99%) and !Zxz I < 3.3 (99.9%)). Although the chi-square test is a powerful test for goodness-of-fit, it does not take any account of the signs of the residuals, of their distribution and of their correlation. Therefore. additional tests are necessary to examine those propcrries of the residuals which chi-square ignores. The randomness of the signs of the residuals versus
channel number were investigated with the “ordinary runs test” [ 15,18,19] [eqs. (5) and (6) below]_ In the ordinary runs test, the number of sequences of residuals with the same sign (=ordinary runs), r. is counted and compared with the number expected, I*, for a set of random numbers_ When the number of runs with plus. 12, _and minus. II,. signs are both greater than twenty. the normal approximation
can
be made and the hypothesis of randomness can be tested from a table of standard normal probabilities: z=(r--+;)/u. where
(5)
For a monoexponential decay with 32 > 100,the residuals are regarded as uncorrelated at the 0.05 (onetail) significance level if d > 1.69; if d < 1.65, the residuals are considered to be correlated. When d lies between these values, no conclusions can be drawn. Checking that the residuals are normally distributed is important, especially if confidence intervals are to be calculated_ The most popular graphical approach to determine the normality of a distribution is the normal probability plot [ 15.2 1]_ In a normal probability plot, the II ordered residuals Ri (RI-CR,< ___ CR,,) are plotted versus the inverse cumulative normal distribution function F-‘(i/(lz + 1)). If the residuals are normally distributed, these points should lie roughly on a straight line. The other tests for assessing the normality of the residuals include the determination of the percentage of the residuals within the [2,---2] interval, and the calculation of the mean and standard deviation of the residuals. These values should be reasonably close to the predicted values of 95.4470. 0.0 and I-0, respectively.
3. Results The fluorescence decay from S, of xanthione in iso-octane at 295 K is shown in fig. 2. The fluorescence lifetime was calculated from eq. (2) with g(t) = ff X csp (+/I-), where (Yis the pre-exponential normalization factor and T is the S2 fluorescence lifetime of xanthione in iso-octane. For the excitation pulse-shape function f(t), the convoluted fluorescence decay of xanthione in benzene was taken. The solid line in fig. 2 is the calculated best curve to the experimental fluorescence decay. The result of the analysis indicates that the lifetime of the S7 fluorescence of xanthione in
Voluinc
111. number 4.5
CHEhIICAL
PHYSICS
9
LETTERS
November 1984
3.205 Ri
0 'I
-3.205
F
50
100 CHANNEL
SO
200
250
NUMBER
Fig_ 2. Espcrimcnttl fluore\ccncc dewy curve (point plot) of _unthione m iso-octnnc The dccw function calculated brrween chnnncls 7 and 254 is shown as a solid line. Ike instrument response function (point plot) is the convoluted decw of ;canthione in bcnzcne. hcxc = 296 nrn; &,,, = 460 nm; chnncl width = 7.1 ps, x2 = 1.05:Z X2 = 0.53: ordinary runs Z = 0.49: Durbin-Watson d = 1.93. 95.56% of the weighted residuals are in the [ -2.71 interval. Their 1ne.m and shndard deviation 3ie 0.10 and 1.01. respcctivcly. Also shown are the autocorrclation function C, and the wei+ted residuals Ri versus channel number and versus the calculated decay function Yi.
iso-octane is 43 f 2 ps. The sample fluorescence and the irf were both measured with 10000 counts in the maximum. In order to verify thatf(t) could be replaced by the convoluted fluorescence decay of xanthione in benzene. we calculated the correctf(t) [IO] ; f(i)
= C(i)
-
C(i -
I) exp(--E/ml)
,
(8)
where i is the channel number_fis the correct irf. C is the measured convoluted fluorescence decay of the excitation pulse-shape mimic compound (xanthione in benzene), E is the multichannel time increment per channel
and 7m is the monoexponential
lifetime
of the
mimic compound_ After computingf(i) with T,,, = 5, IO. 15, 18,20 and 25 ps, and after substitution of f(i) in eq. (2), a value of 44 +- 3 ps was obtained for the S, fluorescence lifetime, 7, ofxanthione in iso-octane. The statistical parameters used to judge the goodness-of-fit (see section 2.3) remained acceptable when T,,, was varied from 5 to 25 ps. In order to calculate
the correct irf, the mimic decays were collected to 40000 counts in the maximum. The normal probability plot (not shown) for the experiment given in fig. 2 is similar to that shown in fig. 4. This plot together with the mean and standard deviation of the residuals indicates that the residuals are normally distributedThe fluorescence quantum yield (of) of xanthione in iso-octane was found to be 3.2 X 10T3 _The rate constants for radiative (kf) and non-radiative (k,,) decay were calculated from kf = I$&
and
k,, = A-,(Qr’ - 1) _
(9)
and were found to be 7.4 X 10’ and 2.3 X 1Ol” s-1, respectively_ The decay of the fluorescence emission from SZ of xanthione in benzene at 295 K is given in fig. 3. The correct irf was calculated from the convoluted fluorescence decay of xanthione in iso-octane with 7n, = 43 ps. The calculated best fit to the fluorescence 343
n
1
3.432
-if-
]
-3.4321
. .
.
I I
0
-..
_ IS
I,
I1
50
I
I
I
I,
I
100
I,
I,,
,
150
CHANNEL
,,,,I,
200
250
NUMBER
I-if. 3 EspcrimcntJ fluorcsccncc decay curbc fpotnt plot) of .\.mthionc in bcnmnc The dccny function wlcul~tcd bctwccn Amncl\ 2 .Ind 254 i), shown ;IS rl solid line The tnstrumcnt rcsponsc function (point plot) W.IS wlcul~tcd from the convoluted dCCay of x.mthionc in iso-octane with ml = 43 ps. kxc = 296 nm; km = 460 nm; ch,tnnel width = 7.1 ps; x2 = 1.23; Zx2 = 2.63; UrdillJry runs Z = -0.4 1: Durbin-Watson d = 1.82. Also shown a~!fcthe sutocorr&tion function f?,, and the weighted rcsiduals& bcrsus ch.mncl number and versus the cllculatcd dcc~y function Yt_ NORMAL 3
0
R 0
PROBABILITY
PLOT
43
2.57
E
1.72
R E D
0
96
R E
0
00
s I 0
-0.86
U A L
-1.72
S -2.57
F-Ill/
h+i)
1
Volume 111, number 4.5
CHEMICAL
decay of xanthione in benzene was obtained for 7 = 18 i 2 ps. The mimic decays were collected to 50000 counts in the peak channel. The normal probability plot for the experiment of fig. 3 is given in fig. 4. This plot indicates that the weighted residuals are normally distributed. The values for the mean (0.11) and standard deviation (1.10) are in good agreement with the predicted values of 0.0 and I-0, respectively_ The quantum yield for S1 + So fluorescence of xanthione in benzene was found to be 1.2 X 10e3.
The calculat-
ed values for kf and A-,,,are 6.7 X IO7 and 5.6 X 10” s-l.
respectively_
4. Discussion Fluorescence decays of xanthione could be adequately described by a monoexponential decay function_ The lifetimes were independent of the analysis wavelength in the 420-470 nm region. The measured lifetime of xanthione in benzene is in excellent agreement with the lifetime derived from the fluorescence quantum yield and the integrated absorption [ 11, and with the lifetime determined by Anderson et al. [2] _The measured lifetime of xanthione in iso-octane agrees very well with lifetimes of this compound in non-polar solvents (mcthylcyclohexane and 3-methylpentanc) [l] calculated from fluorescence yields and absorption spectra. It has been shown [l] that the S2 fluorescence lifetimes of xanthione and tctramethylindancthione [22] vary similarly between hydrocarbon and inert perfluoroalkanc solvents_ The calculated S, lifetime of xanthionc (460 ps) and the measured S2 lifetime of tetramcthylindancthionc (880 ps) in pcrfiuoroalkanc solvents and our results for xanthione m hydrocarbon solvents arc indicative of a very efficient quenching of the S2 state in hydrocarbon sol-
calculatedf(i) is quite noisy and consequently curve fitting results will be poor. We recommend a peak channel of at least 40000 counts in order to get satisfactory curve fitting results. If Trn is much longer than the lifetime 7 of the unknown, i.e. T, S 7, it will be
very difficult to get a usable reconstructedf(i). As shown in this report, it is possible to obtain reliable results when 7nl > 7. If 7 5 T,, the convoluted decay of the mimic compound can be used as irf, without the need to computationally
excitation pulse-shape mimic compound with a known monocxponential lifetime T,,, is available, it is in principle possible to calculate the exact irf, f(i), from the expcrimcntal convoluted decay, C(i), of the mimic compound and its decay time [cq. (S)]. This tcchniquc can be very successfully applied if some prccautiotts arc taken. The rcconstructcd/‘(i) an
bccornc progressively tuorc noisy with dccrcnsing number ol’counts in the peak chatmet of the convolut-
extract
the correct
irf_
This is the case when nanosecond lifetimes are measured with picosecond mimic compounds_ If 7 = 7, _ the calculated lifetime of the unknown will closely track the assumed T,,~_ If T = 7nl, whatever lifetime is assumed for T,,, in the calculation off(i) will always yield 7,11. If ml and 7 are not too similar. the residual analysis may begin to reveal errors in 7, [lo]. Current research in our laboratory is trying to define further the possibilities and limitations of the escitation pulseshape mimic technique.
Acknowledgement This research was supported in part by grants from the University Research Fund and the FKFO. MvdZ wishes to thank the IWONL for a predoctoral fellowship. NB is a Research Associate of the National Fund for Scientific Research (Belgium). The authors also thank Dr. A.R. Holzwarth and Mr. J. Wendler of the Max-Planck Institute (Miilheim a.d. Ruhr) for helpful discussions_
References [ 1] hl. hL11lancyand J.R. liuber. Cbcm. PIlys. Letters 105 (1984)
VCIl ts. If
9 November 1984
PHYSICS LETI-ERS
395. and rcfcrcnccs
Ulcrcin.
121 R.\\‘. Andcrson Jr., R.M. Huollstrdsscr and II J. Pownall. Clwm. Pbys. Lcttcrs43 (1976) 224. 1’ 1l.J. 001115 .d R.J.F. Nivxd, Syntlic~s 3 (1973) 149. 141 D.D. Pcrritl. W.L P. Arnmrcgo and D.R. Pcrrm. Puritication ol’labordiury cllcmkds (Pcrg.nnun. O\furd. 1966) 151 J.N. Dcms ml GA. Crusby, J. Phys. C11m. 75 (1971)
[ 31 J.W. Sclwxcn,
991; J.V. hlorrk
hl A. MillI~nC~ 2nd 3.1~. llubcr. J. PIIYS. Cl~cnt. 80 (1976) 969.
cd decay curve C(i). Even for a pcnk C(i) of 10”. the 34s
VllllllllC
I I I,
numl1cr4.5
CIIISMICAL
161 K C. Spws. L.E. Cr,uacr end L.D. Ilr~l‘llitnd. Rev. SCI. Inrtruln.49(197R)25$. 171 W.R. Mm, 111;Crhmn ml dctcclion al lllc excited SIJIC. Vol I A. cd. AA. L~IIOIJ (Dckker, New York, 1971) J.N. Dcm.~\. Crcltcd state IIfctlmc mc.wlrements (Awdem~c Prcq New York. 1983). hl. vm den Zcycl. N. Uocnb and F.C. dc Scllryvcr, I11opliys. Clwm.. lo be publislwd. I) R J.miee. 11 R M Dummcr. RI. Vcrrdll and R.P. Slccr, Rev. Sci Instrum 54 (1983) I 121. I A I:. hlcKmnon, A.G S7abc1dnd D R. Mdlcr. J. Pllys. Clwm. 8 I (1977) 1564. I) V. O’Connor, W R W.~rc and J.C. Andre, J. Pllys. cllcIll 83 (I 979) 1333 D W. Mquardt. J Sot Indurt. Appl MJtII. I I (1963) 431. N. Ilocns. bl. wn den Zcgel dnd P.C. dc Scllryver, lo bc publ~slwd. ll.l-. Guna .md R.L hldwn, RcgrcGm .m.dysis and ir\ .~ppl~cx~ion. il data-oriented .Ipproxli (Dckkcr, NLW York, 1980).
I’IIYSIcs
I.li’l”l’lsRs
llhl
9 Novcmlwr
I984
A. Grinvuld rind I.Z. Stclnlwg. Awl. Ilioclicm. 59 (I 974) 5R3, 1171 R, CIwrdll und DA Ruddell, in: IXcmvolutic~n ilntl rcconvolullon of snnlyticnl signals - ,Ipplicutlon to Iluorcwcnce qwctrorcopy (E.N.S.I.C.-I.N.P.L., Nancy. 1982) pp. 445-461. 118 R. C,ttrcr,dI ,md D.A. Duddcll, m: Tulleresolvsd lluorcsccncc spectroscopy in b!oclicmistry rind biology. cds R.R. Cund.dl and R.C. DJIC (Plenum Prc\q. New York, I9831 pp. I73 - 19.5. 119‘1 1. Dickinson Gibbons. Nnnp;~r~wictr~c nwlllods for qudntitativc an&w (11011. Rmclw! and Winston. New York. 1976). 120 J. Durbin aid G.C. W,wm, IGniietrlk,l 37 (1950) 409.38 (1951) 159.58 (1971) I. 121 D hl Cllilko. SAS Tcc1mic.d Report A-106 (I 978). 17-2 A. Macwjwski aid R.P Slccr. Cl~cm Ploy\. Lctlcrr, IO0 (I 983) 540.
Votun~r
PlCOSECOND
CIiEMlfCAL PHYSICS LETI-ERS
LIFETIME
OF XANTHIONE
DETERMINATION
OF THE SECOND EXCITED SINGLET
9 Novcn~bcr 1961
STATE
IN SOLUTION
Roccived 3 July 1984; in final form 18 August 1984
fiferimes and quantum yields of the S2 state of xantbionc in benzene and isoloctanc sotution at room mcnsurcd. The Sz iifctimn wcrc found to bc I8 2 2 ps in bcnzcnc and 43 % ‘I! ps in iso-ocrane. The non-radiative decay rate constant is 5.6 x lO’* s-l in benzene and 2.3 X IO** s-t in iso-octane. The lluorescencc
temperature
have
been
1. introduction Many aromatic thiokctones exhibit fluorescence front the second excited singlet state, S,. to the ground slrttc. Xanthionc is probably the most extensively used thionc for the study of the decay dynamics of excited statcfs higher lhan S, [I ] _ Using a Nd3* glass modelocked laser-driven light-gate technique, Anderson et ai. f2] have measured a lifetime of f 2 4 3 ps for the S, fluorescence of xsniltione in benzene. Very recently, Mahaney and Huber [I ] derived the S7 lifetimes, r, and the rate constams for non-~dialjv~dccay, k ,,r. from the S, fluorescence quantum yield and the integrated absorption of xantitione in several solvents. For xsnthione in benzene solution. they found 7 = t 8 ps and k,, = 5.0 X 1O1o s-l _ 111the present communication we report lifetimes and quantum smthione
for the S2 -+ So fluorescence
yields
in benzene
temperature.
of
and
iso-octane solution at room Front these data. the radiative and non-
radirttive decay
rare constants
arc calculated.
2. Experimental
Santl~iom. was synthesized (Aldrich) of 340
in p-divsanc
tetraphosphorus
(Aldrich
decasulfidc
by reflusing 99%)
xanthone
with an excess
(Merck) [3]. The crude
xanthione was purified by column chromatography over silica gel (Machercy Nagel MN-Kieselgel 60) using dicf~Iorome~ltane (Janssen Chimica 99.8%) as the eluent followed by recrystallization from zz-butanol (UCB reagent grade)_ Iso-octane (Merck for fiuoromerryj and benzene (Aldrich spectrophotometric grade) were purified by standard procedures f4] _Solvent purity was checked by gas chromatography. No fluorescence could be detected front any of the purified solvents under the excitation conditions used in this work. 3 3 Itntrtttncttlatiott _._. Fluorescence spectra and quantum yields were obtained with a computerized Spex Fluorolog 1902 using double monochromat~rs in both excitation and emis-
sion. or with a Spex Fluorolog 2 12/Datamate. The optical densities were measured with 3 Perkin-Elmer . Lambda 5 UV/VIS spectrophotometer. The S2 + So quantum yields were determined by a refative method using quinine sulfate in 0.1 N HlS04 (q$ = 0.545) as standard IS]. Correction for the refractive index of the solvents was applied. The absorbances at tile excitation waveiength were lower than 0.1. Fluorescence decay times were measured using a Spectra Physics frequency-doubled cavity-dumped mode-locked synchronously pumped R6G dye-laser system with timecorrelated single-plroton-counting detection [6--8]_ The fluorescence lifetime apparatus and the associated 0 009-26 14/84/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
CHi31ICAL PHYSICS LETTERS
Volume 1 1 1, number 4.5
9 November
1964
ps/channel. For the fluorescence lifetime determinations of xanthione in solution, the optical density at the excitation wavelength, 296 nm. was higher than 2 in 1 mm pathlength optical cells (Hellma QS). The solutions
were
front-face
not degassed
configuration
and were
measured
in the
in a temperature-controlled
(22
+ O.Z°C) cell holder. 1 mm pathlength optical cells were used to minimize any time uncertainties due to the finite thickness of the sample_
2.3. Data mm&sis
Fig. 1. Picosecond ldser cwitdtion system: BS. bcarn splitter, CDD, wvity-dumper driver; M, mirror; FL, focusing lens; I-DC. frequency-doubling crystal; PD. photodiode. SPD. synctuonization
pllotodiode.
optical and electronic components are described in detail elsewhere [9]. The following modifications of the time-correlated fluorometer were made: After a recommendation of Dr. I. Yamazaki (Institute of Molecular Science, Myodaiji, Okazaki. Japan), the synchronization photodrode was removed from the cavity dumper and set to monitor the beam of the mode-locked Ar-ion laser (fig. 1). This modification resulted in improved long-term stability of the pulse shape and intensity_ The alignment and adjustment of the cavity dumper also became much easier. Frequency doubling was aclzieved wit11 an angle-tuned Inrad model 463-l 117 KDP “B” crystal. The dye-laser light was focused on the crystal through a lens. Since the frequencydoubied light is horizontally polarized, no polarizer was inserted in the emission path. Magicangle detection gave the same results but at a reduced count double
rate.
For
emission,
monochromator
a Jobin-Yvon
DH 20 Vis
was used. The start
signal for the time analyzer (Canberra model 2044) was taken from a fast photodiode (Spectra Physics model 403B) monitoring a fraction of the undoubled dye-laser beam. The time analyzer was operated in the normal configuration, the voltage ramp being initiated by the photodiode signal and terminated by a signal from the XP2020Q photomultiplier operated at 2300 V. The output pulse of the time analyzer was fed into a Canberra model 1467 biased amplifier_ The Canberra models 1467 and 2044 allow a linear expansion of the multichannel analyzer timescale down to about 1
The observed fluorescence decay curve at the emisof the true desion wavelength_ &,,, , is a convolution cay and the measured instrument response function (irf). The convoluted fluorescence decay function of xanthione in benzene or iso-octane was used to mimic the irf at tlte wavelength of sample emission &,, [lo] _ The least-squares iterative reconvolution method [ 11 121, based on the algorithm of Marquardt [ 131. was used to determine the decay parameters. A careful residual analysis was done after a decay law was fitted to the fluorescence decay data [ 141. The most widely used technique for examining residuals in time-correlated single-photon-counting experiments involves the plotting of the weighted residuals Ri [eq. (3) below] against time or channel number. The patterns of such a plot are helpful in choosing the correct functional fomi of the decay law and determining the need for additional terms in the decay function_ There should be no discernible trend in the plot of the residuals, Xi, versus channel number i: only a random scatter of points about the line Ri = 0. Observations that have extremely large residuals (outhers) can also be detected by examining such a residual plot. In detecting heteroscedasticity [ 151 (error temrs with unequal variances), it is helpful to plot the (squared) residuals versus the predicted responses pi (i.e. the calculated values). A graph of Ri versus Yi should reflect a random scatter of points about a line with zero slope. Systematic patterns would indicate an inadequate model for the decay law. Examining the plot of the autocorrelation function can also indicate if a chosen model for the decay function is adequate 1161. Although residual plots can be easily analyzed and interpreted, their interpretation is somewhat subjective and sometimes biased. Therefore. several numcrical statistical tests were used to make the residual analysis more reliable. 341
CHEMICAL
Volume I1 1, number 4,s
The first numerical test is the calculation reduced &i-square statistic. xt, given by X’, = -&
7
9 November 1981
of the
‘Vj(yi - FiTi)’ ,
(0
where ‘vi, the weighting factor, is the reciprocal of the number of counts Yj in data channel i, II is the number of data points, p is the number of adjustable fitting parameters and Y =/I - p_ pt is given by pr =J/(t’)y(f
PHYSICS LEI-I-CRS
- r’) dt’ ,
u is the standard deviation of the runs distribution. The sequence of the signs of the residuals is considered random at the 50% confidence level if iZ I< 0.6745 (for the other confidence levels, see discussion of zx2 )To test for serial correlation between residuals, the Durbin-Watson test statistic d [20] was calculated:
(7)
(2)
0 where f(f) is the irf and g(f) is the true decay function. The weighted residual in channel i is given by
Ri = ,~f~'l(Yi - Yi)_ xX was converted
(3)
to a standard
normal deviate
Zx2
[17,181 zx2
=
(IJ/2p(x2,
and the required
-
1)
)
probability
(4) determined
from
a table
of standard normal probabilities, e.g. 12x2 I< 1.96 for testing at the 95% confidence level, ,Zx2 I< 2.58 (99%) and !Zxz I < 3.3 (99.9%)). Although the chi-square test is a powerful test for goodness-of-fit, it does not take any account of the signs of the residuals, of their distribution and of their correlation. Therefore. additional tests are necessary to examine those propcrries of the residuals which chi-square ignores. The randomness of the signs of the residuals versus
channel number were investigated with the “ordinary runs test” [ 15,18,19] [eqs. (5) and (6) below]_ In the ordinary runs test, the number of sequences of residuals with the same sign (=ordinary runs), r. is counted and compared with the number expected, I*, for a set of random numbers_ When the number of runs with plus. 12, _and minus. II,. signs are both greater than twenty. the normal approximation
can
be made and the hypothesis of randomness can be tested from a table of standard normal probabilities: z=(r--+;)/u. where
(5)
For a monoexponential decay with 32 > 100,the residuals are regarded as uncorrelated at the 0.05 (onetail) significance level if d > 1.69; if d < 1.65, the residuals are considered to be correlated. When d lies between these values, no conclusions can be drawn. Checking that the residuals are normally distributed is important, especially if confidence intervals are to be calculated_ The most popular graphical approach to determine the normality of a distribution is the normal probability plot [ 15.2 1]_ In a normal probability plot, the II ordered residuals Ri (RI-CR,< ___ CR,,) are plotted versus the inverse cumulative normal distribution function F-‘(i/(lz + 1)). If the residuals are normally distributed, these points should lie roughly on a straight line. The other tests for assessing the normality of the residuals include the determination of the percentage of the residuals within the [2,---2] interval, and the calculation of the mean and standard deviation of the residuals. These values should be reasonably close to the predicted values of 95.4470. 0.0 and I-0, respectively.
3. Results The fluorescence decay from S, of xanthione in iso-octane at 295 K is shown in fig. 2. The fluorescence lifetime was calculated from eq. (2) with g(t) = ff X csp (+/I-), where (Yis the pre-exponential normalization factor and T is the S2 fluorescence lifetime of xanthione in iso-octane. For the excitation pulse-shape function f(t), the convoluted fluorescence decay of xanthione in benzene was taken. The solid line in fig. 2 is the calculated best curve to the experimental fluorescence decay. The result of the analysis indicates that the lifetime of the S7 fluorescence of xanthione in
Voluinc
111. number 4.5
CHEhIICAL
PHYSICS
9
LETTERS
November 1984
3.205 Ri
0 'I
-3.205
F
50
100 CHANNEL
SO
200
250
NUMBER
Fig_ 2. Espcrimcnttl fluore\ccncc dewy curve (point plot) of _unthione m iso-octnnc The dccw function calculated brrween chnnncls 7 and 254 is shown as a solid line. Ike instrument response function (point plot) is the convoluted decw of ;canthione in bcnzcne. hcxc = 296 nrn; &,,, = 460 nm; chnncl width = 7.1 ps, x2 = 1.05:Z X2 = 0.53: ordinary runs Z = 0.49: Durbin-Watson d = 1.93. 95.56% of the weighted residuals are in the [ -2.71 interval. Their 1ne.m and shndard deviation 3ie 0.10 and 1.01. respcctivcly. Also shown are the autocorrclation function C, and the wei+ted residuals Ri versus channel number and versus the calculated decay function Yi.
iso-octane is 43 f 2 ps. The sample fluorescence and the irf were both measured with 10000 counts in the maximum. In order to verify thatf(t) could be replaced by the convoluted fluorescence decay of xanthione in benzene. we calculated the correctf(t) [IO] ; f(i)
= C(i)
-
C(i -
I) exp(--E/ml)
,
(8)
where i is the channel number_fis the correct irf. C is the measured convoluted fluorescence decay of the excitation pulse-shape mimic compound (xanthione in benzene), E is the multichannel time increment per channel
and 7m is the monoexponential
lifetime
of the
mimic compound_ After computingf(i) with T,,, = 5, IO. 15, 18,20 and 25 ps, and after substitution of f(i) in eq. (2), a value of 44 +- 3 ps was obtained for the S, fluorescence lifetime, 7, ofxanthione in iso-octane. The statistical parameters used to judge the goodness-of-fit (see section 2.3) remained acceptable when T,,, was varied from 5 to 25 ps. In order to calculate
the correct irf, the mimic decays were collected to 40000 counts in the maximum. The normal probability plot (not shown) for the experiment given in fig. 2 is similar to that shown in fig. 4. This plot together with the mean and standard deviation of the residuals indicates that the residuals are normally distributedThe fluorescence quantum yield (of) of xanthione in iso-octane was found to be 3.2 X 10T3 _The rate constants for radiative (kf) and non-radiative (k,,) decay were calculated from kf = I$&
and
k,, = A-,(Qr’ - 1) _
(9)
and were found to be 7.4 X 10’ and 2.3 X 1Ol” s-1, respectively_ The decay of the fluorescence emission from SZ of xanthione in benzene at 295 K is given in fig. 3. The correct irf was calculated from the convoluted fluorescence decay of xanthione in iso-octane with 7n, = 43 ps. The calculated best fit to the fluorescence 343
n
1
3.432
-if-
]
-3.4321
. .
.
I I
0
-..
_ IS
I,
I1
50
I
I
I
I,
I
100
I,
I,,
,
150
CHANNEL
,,,,I,
200
250
NUMBER
I-if. 3 EspcrimcntJ fluorcsccncc decay curbc fpotnt plot) of .\.mthionc in bcnmnc The dccny function wlcul~tcd bctwccn Amncl\ 2 .Ind 254 i), shown ;IS rl solid line The tnstrumcnt rcsponsc function (point plot) W.IS wlcul~tcd from the convoluted dCCay of x.mthionc in iso-octane with ml = 43 ps. kxc = 296 nm; km = 460 nm; ch,tnnel width = 7.1 ps; x2 = 1.23; Zx2 = 2.63; UrdillJry runs Z = -0.4 1: Durbin-Watson d = 1.82. Also shown a~!fcthe sutocorr&tion function f?,, and the weighted rcsiduals& bcrsus ch.mncl number and versus the cllculatcd dcc~y function Yt_ NORMAL 3
0
R 0
PROBABILITY
PLOT
43
2.57
E
1.72
R E D
0
96
R E
0
00
s I 0
-0.86
U A L
-1.72
S -2.57
F-Ill/
h+i)
1
Volume 111, number 4.5
CHEMICAL
decay of xanthione in benzene was obtained for 7 = 18 i 2 ps. The mimic decays were collected to 50000 counts in the peak channel. The normal probability plot for the experiment of fig. 3 is given in fig. 4. This plot indicates that the weighted residuals are normally distributed. The values for the mean (0.11) and standard deviation (1.10) are in good agreement with the predicted values of 0.0 and I-0, respectively_ The quantum yield for S1 + So fluorescence of xanthione in benzene was found to be 1.2 X 10e3.
The calculat-
ed values for kf and A-,,,are 6.7 X IO7 and 5.6 X 10” s-l.
respectively_
4. Discussion Fluorescence decays of xanthione could be adequately described by a monoexponential decay function_ The lifetimes were independent of the analysis wavelength in the 420-470 nm region. The measured lifetime of xanthione in benzene is in excellent agreement with the lifetime derived from the fluorescence quantum yield and the integrated absorption [ 11, and with the lifetime determined by Anderson et al. [2] _The measured lifetime of xanthione in iso-octane agrees very well with lifetimes of this compound in non-polar solvents (mcthylcyclohexane and 3-methylpentanc) [l] calculated from fluorescence yields and absorption spectra. It has been shown [l] that the S2 fluorescence lifetimes of xanthione and tctramethylindancthione [22] vary similarly between hydrocarbon and inert perfluoroalkanc solvents_ The calculated S, lifetime of xanthionc (460 ps) and the measured S2 lifetime of tetramcthylindancthionc (880 ps) in pcrfiuoroalkanc solvents and our results for xanthione m hydrocarbon solvents arc indicative of a very efficient quenching of the S2 state in hydrocarbon sol-
calculatedf(i) is quite noisy and consequently curve fitting results will be poor. We recommend a peak channel of at least 40000 counts in order to get satisfactory curve fitting results. If Trn is much longer than the lifetime 7 of the unknown, i.e. T, S 7, it will be
very difficult to get a usable reconstructedf(i). As shown in this report, it is possible to obtain reliable results when 7nl > 7. If 7 5 T,, the convoluted decay of the mimic compound can be used as irf, without the need to computationally
excitation pulse-shape mimic compound with a known monocxponential lifetime T,,, is available, it is in principle possible to calculate the exact irf, f(i), from the expcrimcntal convoluted decay, C(i), of the mimic compound and its decay time [cq. (S)]. This tcchniquc can be very successfully applied if some prccautiotts arc taken. The rcconstructcd/‘(i) an
bccornc progressively tuorc noisy with dccrcnsing number ol’counts in the peak chatmet of the convolut-
extract
the correct
irf_
This is the case when nanosecond lifetimes are measured with picosecond mimic compounds_ If 7 = 7, _ the calculated lifetime of the unknown will closely track the assumed T,,~_ If T = 7nl, whatever lifetime is assumed for T,,, in the calculation off(i) will always yield 7,11. If ml and 7 are not too similar. the residual analysis may begin to reveal errors in 7, [lo]. Current research in our laboratory is trying to define further the possibilities and limitations of the escitation pulseshape mimic technique.
Acknowledgement This research was supported in part by grants from the University Research Fund and the FKFO. MvdZ wishes to thank the IWONL for a predoctoral fellowship. NB is a Research Associate of the National Fund for Scientific Research (Belgium). The authors also thank Dr. A.R. Holzwarth and Mr. J. Wendler of the Max-Planck Institute (Miilheim a.d. Ruhr) for helpful discussions_
References [ 1] hl. hL11lancyand J.R. liuber. Cbcm. PIlys. Letters 105 (1984)
VCIl ts. If
9 November 1984
PHYSICS LETI-ERS
395. and rcfcrcnccs
Ulcrcin.
121 R.\\‘. Andcrson Jr., R.M. Huollstrdsscr and II J. Pownall. Clwm. Pbys. Lcttcrs43 (1976) 224. 1’ 1l.J. 001115 .d R.J.F. Nivxd, Syntlic~s 3 (1973) 149. 141 D.D. Pcrritl. W.L P. Arnmrcgo and D.R. Pcrrm. Puritication ol’labordiury cllcmkds (Pcrg.nnun. O\furd. 1966) 151 J.N. Dcms ml GA. Crusby, J. Phys. C11m. 75 (1971)
[ 31 J.W. Sclwxcn,
991; J.V. hlorrk
hl A. MillI~nC~ 2nd 3.1~. llubcr. J. PIIYS. Cl~cnt. 80 (1976) 969.
cd decay curve C(i). Even for a pcnk C(i) of 10”. the 34s
VllllllllC
I I I,
numl1cr4.5
CIIISMICAL
161 K C. Spws. L.E. Cr,uacr end L.D. Ilr~l‘llitnd. Rev. SCI. Inrtruln.49(197R)25$. 171 W.R. Mm, 111;Crhmn ml dctcclion al lllc excited SIJIC. Vol I A. cd. AA. L~IIOIJ (Dckker, New York, 1971) J.N. Dcm.~\. Crcltcd state IIfctlmc mc.wlrements (Awdem~c Prcq New York. 1983). hl. vm den Zcycl. N. Uocnb and F.C. dc Scllryvcr, I11opliys. Clwm.. lo be publislwd. I) R J.miee. 11 R M Dummcr. RI. Vcrrdll and R.P. Slccr, Rev. Sci Instrum 54 (1983) I 121. I A I:. hlcKmnon, A.G S7abc1dnd D R. Mdlcr. J. Pllys. Clwm. 8 I (1977) 1564. I) V. O’Connor, W R W.~rc and J.C. Andre, J. Pllys. cllcIll 83 (I 979) 1333 D W. Mquardt. J Sot Indurt. Appl MJtII. I I (1963) 431. N. Ilocns. bl. wn den Zcgel dnd P.C. dc Scllryver, lo bc publ~slwd. ll.l-. Guna .md R.L hldwn, RcgrcGm .m.dysis and ir\ .~ppl~cx~ion. il data-oriented .Ipproxli (Dckkcr, NLW York, 1980).
I’IIYSIcs
I.li’l”l’lsRs
llhl
9 Novcmlwr
I984
A. Grinvuld rind I.Z. Stclnlwg. Awl. Ilioclicm. 59 (I 974) 5R3, 1171 R, CIwrdll und DA Ruddell, in: IXcmvolutic~n ilntl rcconvolullon of snnlyticnl signals - ,Ipplicutlon to Iluorcwcnce qwctrorcopy (E.N.S.I.C.-I.N.P.L., Nancy. 1982) pp. 445-461. 118 R. C,ttrcr,dI ,md D.A. Duddcll, m: Tulleresolvsd lluorcsccncc spectroscopy in b!oclicmistry rind biology. cds R.R. Cund.dl and R.C. DJIC (Plenum Prc\q. New York, I9831 pp. I73 - 19.5. 119‘1 1. Dickinson Gibbons. Nnnp;~r~wictr~c nwlllods for qudntitativc an&w (11011. Rmclw! and Winston. New York. 1976). 120 J. Durbin aid G.C. W,wm, IGniietrlk,l 37 (1950) 409.38 (1951) 159.58 (1971) I. 121 D hl Cllilko. SAS Tcc1mic.d Report A-106 (I 978). 17-2 A. Macwjwski aid R.P Slccr. Cl~cm Ploy\. Lctlcrr, IO0 (I 983) 540.