J. Phys. Chem. 1993, 97, 10524-10529
10524
ARTICLES Analysis of the Transient Effect for a Bimolecular Fluorescence-Quenching Reaction between Ions in Aqueous Solution. 2. Temperature Dependence of Kinetic Parameters Andrew D. Scullyt and Satoshi Hirayama Laboratory of Chemistry, Kyoto Institute of Technology, Sakyo- ku, Kyoto 606, Japan
Kenji Fukushima and Toshihiro Tominaga' Department of Applied Chemistry, Okayama University of Science, 1 - 1 Ridai-cho, Okayama, 700, Japan Received: March 19, 1993; In Final Form: June 14, 1993@
The diffusion-influenced electron-transfer reaction between electronically excited 5,10,15,20-tetrakis(4sulfonatopheny1)porphine (H2TPPS6*) and methylviologen (MV2+) in aqueous solution was investigated over the temperature range 10-35 OC using nanosecond time-resolved fluorescence decay measurements. The ionic strength of these solutions was maintained a t 0.004 mol/kg by the addition of N a C l as a n inert electrolyte in order to account for the increase in screening of reactant charges that occurs as the MV2+ concentration increases. The decay of fluorescence from H2TPPS"* is highly nonexponential for all temperatures and MV2+ concentrations used in this work. These nonexponential fluorescence decay curves were analyzed according to the model for the kinetics of diffusion-influenced ionic reactions that was developed by Hong and Noolandi. This has enabled values for the optimized electron-transfer distance, R , the sum of the diffusion coefficients of the reactants, D,and the intrinsic reaction rate coefficient, kat,, to be calculated at each temperature. This reaction was found to obey the Stokes-Einstein relation. The values for R a t each temperature were slightly larger than the estimated contact distance, and a n activation energy of 16.2 f 1.2 kJ/mol was calculated from an Arrhenius-type treatment of the temperature dependence of k,,,.
Introduction The rate of translational diffusion of reactants can influence significantly the rate at which rapid bimolecular chemical reactions can occur in low-viscosity media.I-l9 The analysis of fluorescence decay curves measured by using the technique of time-correlated single-photon counting (TCSPC) has been shownz-13 to be an effective method for studying the kinetics of such reactions in detail. Flannery14 and Hong and NoolandiI5 have developed expressions for the time-dependent rate constant for diffusion-influenced bimolecular chemical reactions between ions, k( t ) , which are based on the Debye-Smoluchowski equation subject to the Collins-Kimball boundary condition (DSCK model).l In practice, nonlinear least-squares analysis using the expression for k ( t ) obtained by Flannery for fluorescence decay curves measured using TCSPC is highly unstable due to severe correlations between the fitted parameters.5-8 Use of the equation for k ( t ) derived by Hong and Noolandi, which is effectively a long-time approximation of the equation developed by Flannery, for the analysis of fluorescence decay curves does not suffer from such instabilities and can provide a useful alternative to Flannery's more complicated equation. Periasamy et al.4demonstrated for a number of fluorescencequenching reactions between ions in aqueous solution that the Hong-Noolandi expression for k( t ) results in satisfactory fitting of the nonexponential fluorescence decay curves which were measured using TCSPC. However, a comprehensive evaluation of the validity of the Hong-Noolandi expression for k ( t )for these systems was prevented due to the use of ionic fluorophores of low valency and relatively high concentrations of the ionic quenchers.
* Author to whom correspondence should be addressed.
Current address: Photophysics Laboratory, School of Chemistry, The University of Melbourne, Parkville 3052, Victoria, Australia. Abstract published in Aduance ACS Abstracts, September 15, 1993.
Such systems inevitably involve solutions of considerably high ionic strength, and, consequently, screening of reactant charges occurs. The significance of these screening effects is evident in the values obtained by these authors for the effective reaction distance, R H N being , intermediate in magnitude between those values expected in the limits of no screening and complete screening of reactant charges, respectively. If both the fluorophore and quencher are low-valency ions, then not only will the ionic strength of the solution be necessarily high, but the distance for reaction will be comparable with the absolutevalue of the Onsager distance, Ir,l. This results in R H Nbeing a complicated function of the rate constant, k,,,, and the center-to-center distance, R , for the intrinsic chemical reaction, as well as the sum of the diffusion coefficients of the reactants, D, and r,. Such a situation inhibits quantitative analysis of the reaction kinetics by using the Hong-Noolandi equation for k ( t ) . We reported recently" the results of fluorescence decay curve analyses using the expression for k(t) that was derived by Hong and No01andi.l~ The reaction examined was the photoinduced transfer of an electron from the electronically excited singlet state of 5,10,15,20-tetrakis(4-sulfonatophenyl)porphine(HzTPPS"*) to the methylviologen dication ( M V + ) in aqueous solution at 25.0 'C. The decay of fluorescence from HzTPPS'* was measured using TCSPC and was highly nonexponential for all solutions containing M V + . These nonexponential fluorescence decay curves were analyzed using the Hong-Noolandi expression for k ( t ) , and the effective reaction distance, R H N was , found to be dependent upon the concentration of added inert electrolyte. In the absence of added electrolyte, the value obtained for R H N was comparable with the absolute value of the Onsager distance, as predicted by Hong and No01andi.I~ The magnitude of RHN decreased significantly as the concentration of electrolyte was increased, until a limiting value for R H Nwas attained at ionic
0022-3654/93/2097-10524$04,00/0 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10525
Transient Effect for Fluorescence Quenching strengths greater than approximately 0.2 mol/kg. The value for RHNin this limit was proposed to represent the effective reaction distance in the case of complete screening of reactant charges and can be regarded as being equivalent to the effective distance for the reaction in the absence of Coulombic interactions between the reactants. On the basis of these results, it was possible to estimate values for k,,,, R, and D for this reaction. The present work extends the scope of our previous studies on this topic by using the results of analysis of fluorescence decay curves measured using TCSPC to examine the effect of temperature on the kinetic parameters associated with the electrontransfer reaction between H2TPPS6* and MV2+ in aqueous solution. These results are discussed in terms of the temperaturedependence of the kinetic parameters for this reaction and provide a further means of evaluation of the Hong-Noolandi equation for k ( t ) as a description of the kinetics of diffusion-influenced bimolecular ionic reactions. The temperatures for these measurements were controlled to within an accuracy of 0.1 OC by a thermoregulated water bath. All other experimental details are the same as described previously.13
MCA CHANNEL NUMBER
0
I00
200
Theory The expression for the time-dependent rate coefficient for the quenching of an electronically excited ionic fluorophore, A*, by an ionic quencher, Q, that was derived by FlanneryI4 from the DSCK model is k(t) = a
+ b exp(c2t) erfc(ct'/2)
(1)
where
Figure 1. Fluorescence decay curves (dots) measured for HzTPPS' in aqueous solution with a MV2+ concentration of 1.0 mM: (a) 35.0 "C, (b) 25.0 "C, (c) 20.0 "C, (d) 15.0 OC, and (e) 10.0 "C. The solid lines are the best-fit curves calculated according to the function given in eq 6. Curve (f) is the instrument response function.
where RHN
=
r C
[1 + (4arSN/kacJl exp(rc/R) - 1
(4)
The parameter RHNmay be interpreted as an effectiue encounter distance at which the reaction proceeds with certainty.15 The timedependence of the concentration of A* in the presence of quencher, Q, is given by
-d[A*lf dt - -[A*],(s,l
+ k(t)[Q])
where TO is the unquenched fluorescence lifetime of A*, [A*Jfis the concentration of A* at time 1, and [Q] is the concentration of quencher. The function that is obtained for the time-dependent decay of fluorescence intensity, F(t),upon substitution of eq 3 for k ( t ) in eq 5 and then integration is
In the above equations, R is the distance required for reaction between species A* and Q in the absence of ionic interactions, D is the sum of the diffusion coefficients of these entities, k,,, is the intrinsic rateconstant for the reaction a t a separation distance R, N is Avogadro's number, and r, is the Onsager distance which is defined as rc =
zAzQe2 4neockBT
In this equation, zAe and zQe are the effective charges on the fluorophore and quencher, respectively; €0and c are the dielectric constants of a vacuum and the reaction medium, respectively; k g is Boltzmann's constant; and Tis the absolute temperature of the system. At sufficiently long times, eq 1 can be approximated by the following equation which was derived by Hong and Noolandils (3)
F(t) = F(0) exp(-At - Bt'/*)
(6)
where
The nonexponentiality of the quenched fluorescence decay curves at early times in the decay that is implied in eq 6 is the so-called2 "transient effect".
Results and Discussion The fluorescence decay curves measured at a constant ionic strength of 0.004 mol/kg for aqueous solutions of H2TPPSC containing 1.O mM MV2+ over the temperature range 10.0-35.0 OC are presented in Figure 1. The increase in the rate of quenching of fluorescence from H2TPPS'* by MVZ+ that occurs with increasing temperature results in a significant decrease in the
Scully et al.
10526 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 3
0.14
4 27745
6 2482
0
I 7 12466
I
I
0 5 66696
Figure 2. Distribution of reduced residuals corresponding to the analysis of the flUXescence decay curves h w n in Figure 1 using a singleexponential function. Thedistributionsassociatedwith thedecay curves (a)-(e) in Figure 1 are shown from bottom to top. The corresponding values for thd reduced chi-square parameter are (a) xr2= 2.94, (b) X? = 3.09, (c) x? = 2.80, (d) X? = 2.55, and (e) X? = 2.44.
I
1 [MV2+] - (mM) . .
I
I
2
Figure 4. Plots of A MV2+ concentration and the corresponding lines of best fit calculated using eq 7 for temperaturesof (a) 35.0 o c , oc, (b) 25.0 oc,(c) 20,0 oc, (d) 15.0 oc, and (e)
1 " 1
0 2 74564
-11
0.2
r
0
Is
1i
Y
2 63622
m
0.1
0
1
2 646
0 I
I
I
3
15996
[MV2+](mM)
0 I
I
I
2 97778
Figure 3. Distributionof reduced residuals corresponding to the analysis of the fluorescence decay curves shown in Figure 1 using the function given in eq 6. The distributionsassociated with the decay curves (a)-(e) in Figure 1 are shown from bottom to top. The corresponding values for the reduced chi-square parameter are (a) xr2= 1.18, (b) xr2= 1.09, (c) xr2 = 0.99, (d) xr2= 1.09, and (e) xr2 = 0.98.
apparent fluorescence lifetime of H2TPPS6*. The distributions of reduced residuals corresponding to the best-fit curves calculated using either an exponential function or the nonexponential function given in eq 6 are shown in Figures 2 and 3, respectively. The decrease in the apparent fluorescence lifetime with increasing temperature is accompanied by a slight increase in the deviation of the measured fluorescence decay curves from exponentiality. The distributions of reduced residuals shown in Figure 3 demonstrate the quality of fitting by the function given in eq 6 obtained for all nonexponential fluorescence decay curves analyzed in this work. The values recovered for the parameters A and B should vary linearly with MVZ+concentration according to eqs 7 and 8. Plots of the recovered values for A and B as a function of MV2+ concentration are shown in Figures 4 and 5 , respectively. The good linear correlations of these plots for all of the temperatures used in this work provide further support for the validity of the Hong-Noolandi expression for k ( t )as a description of the kinetics of diffusion-influenced bimolecular ionic reactions on the nanosecond time scale. The slight variation with temperature in the ordinate value of the intercept in Figure 4 results mainly from
Figure 5. Plots of B versus MV2+ concentration and the corresponding lines of best fit calculated using eq 8 for temperatures of (a) 35.0 "C, (b) 25.0 "C,(c) 20.0 OC,(d) 15.0 "C,and (e) 10.0 "C.
TABLE I: Results of Analysis According to Equation 6 of the Quenched Fluorescence Decay Curves Measured for H2TPPSC* in the Presence of MV2+ T ("C)" Ircl (nm)b RHN D X 1Olo (m2S-I)~ 10.0 5.630 5.4 f 0.3 3.8 f 0.7 15.0 20.0 25.0 35.0
5.660 5.691 5.725 5.796
5.2 f 0.2 5.2 f 0.2 5.1 0.1 5.3 f 0.2
*
4.8 i 0.5 5.1 0.5 6.5 0.5 7.3 f 0.8
*
"i0.1 "C. bCalculated using the values for t in ref 21, p 457. Calculated from the slopes of the lines of best fit shown in Figures 4 and 5 .
the experimental uncertainty in the temperature dependent fluorescence decay time of H2TPPS6* measured in the absence of MV2+. Values for RHNand D a t each temperature were calculated from the slopes of the plots shown in Figures 4 and 5 , and these values are presented in Table I. One of the implications of the Hong-Noolandi model is that, in the absence of screening of reactant charges, the value for RHN should be approximately equal to the value of (rcJwhen R
