Development of Analyzer for Photoluminescence Quenching in a Solid Matrix
Hidenobu SHIROISHI, Kazuhisa SUZUKI, Michiko SEO, Sumio TOKITA and Masao KANEKO
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1 Introduction
Electron transfer reactions at the photoexcited state of a sensitizer molecule are attracting attention for various applications such as energy conversion devices [1  3], photochemical sensors [4  6] and photochemical synthesis. Solid matrixes, e.g., macromolecules, clays and zeolites are useful as a matrix to construct practical devices. Photoinduced electron transfer in a solid matrix is different from that in a solution since diffusion and convection of molecules are suppressed in the matrix.
The excited state of a molecule created by absorption of irradiation returns to the ground state via emission or nonradiative processes. The emission from the excited state of the molecule is influenced by the microenvironment around the molecule and coexisting molecules. This feature is utilized in an emission probe method. We can obtain information about the microenvironment around the probe, electron transfer or energy transfer processes, and coexisting molecules by this method. This method is also useful for quantitative analysis because the sensitivity of emission spectrometry is higher than that of absorption spectrometry.
Photochemical quenching processes in polymer matrixes have been reported by our group [7  11] and others [4, 13]. In such a system, the excited state of the molecule is quenched not only by the collision with the quencher molecule (dynamic mechanism) but also by a static mechanism arising from the overlap of the molecular orbital (or electron tunneling effect) for which both reactants do not diffuse during the quenching event. The analysis of SternVolmer plots is effective to determine the quenching mechanism. However, not all quenching mechanisms could be determined only by analyzing SternVolmer plots because experimental data can sometimes be fitted by more than one model, and convergence can be attained with different parameters when using a nonlinear least square method. In these cases, we have to search a series of parameters with which the equation for the model can reproduce the experimental decay curves. To the contrary, kinetic parameters of a photochemical quenching can be estimated by analysis of the emission decay curves. It is now useful to develop a new system with which the quenching mechanism in a solid matrix can be analyzed using both methods effectively.
In the present study, a program for the analysis of the photochemical quenching mechanism in a solid matrix, called "QchanG4", was developed using Visual Basic. We have derived theoretical equations of emission decay curves in a solid matrix for thirteen models. This program can analyze the quenching behavior with emission decay curves and SternVolmer plots using a GaussNewton method.
2 Quenching mechanisms in a solid matrix
Figure 1 shows the schematic representation of a photochemical energy diagram and the kinetic parameters of each process. The return from a photoexcited state to the ground state is represented by three separated processes: (1) Radiationless deactivation (k_{nr}), (2) Photoluminescence (k_{e}), and (3) Quenching (k_{q1} and k_{q2}). The following decay functions I(t) in each model were normalized in such a way that I(0) = 1.
Figure 1. Photochemical energy diagram and kinetic parameters of photochemical processes. k_{nr} (s^{1}) is a nonradiative rate constant, k_{e} (s^{1}) is an emission rate constant, k_{q1} (s^{1}) is a staticquenching rate constant, k_{q2} (mol^{1}dm^{3}s^{1}) is a dynamicquenching rate constant.
2. 1 Dynamic Quenching Mechanism
Model 1
This is a conventional dynamic quenching model where the SternVolmer plot shows a linear relationship [12]. The decay rate of the photoexcited probe molecule is expressed as:
where [^{*}P] is the concentration of the emission probe in the excited state, [Q_{t}] (mol dm^{3}) is the concentration of the quencher. Emission lifetime at [Q_{t}] = 0, t_{0} (s) is represented as:
The emission decay curves in a solid matrix are often observed as a multiexponential function:
where t_{0,n}(s) is the emission lifetime at [Q_{t}] = 0, and A_{n} is the preexponential factor of nth component. The function of the emission decay curves for model 1 is derived from eqs. 1  3 as eq. 4.
2. 2 Singlestep equilibrium models
These models consider singlestep equilibrium between the emission probe and the quencher. Assuming that the association between the probe and the quencher is not too strong to change the molecular orbital of the excited state of the probe, the photochemical reactions considered in these models are shown below.
where K is the equilibrium constant of the incorporation of the quencher into the quenching sphere, and (P  Q) shows P and Q present in a quenching sphere in which a static quenching takes place with the rate constant k_{q1}.
Model 2
Model 2 takes into account all of the above reactions. The concentration of free quencher ([Q]) is expressed as follows:
where [P_{t}] is the total concentration of the probe. The function of the decay curves for model 2 is given by eq. 15 from eqs. 3, 5  13.
Model 3
In this model, the static quenching rate constant (k_{q1}) is much larger than the reciprocal number of emission lifetime at [Q_{t}] = 0 (t_{0,n}). In this case, the function of emission decay curves is represented as:
Model 4
This model is applied when the product of the dynamic quenching rate constant and the total quencher concentration (k_{q2}[Q_{t}]) is negligible. The function of the emission decay curves is expressed by eq. 17.
Model 5
In this model, the k_{q1} is much larger than 1/t_{0,n}, and the diffusion of the molecules in the solid matrix is suppressed so that the dynamic quenching is negligible. I(t) is expressed as follows:
Since the decay curve is independent of the quencher concentration, photochemical parameters cannot be obtained from the analysis of emission decay curves.
2. 3 Multistep equilibrium models (Poisson distribution models)
Eq.19 to 24 were taken into account in the following Multistep equilibrium models.
where k_{qI} is the static quenching rate constant, and equals k_{q1} in models 6 to 9 and k_{qI} = ik_{q1} in the models 10 and 11.
Model 6
Assuming that the distribution of the emission probe and the quencher follows the Poisson distribution, the probability of existing x quenchers in a quenching sphere p(x) is expressed as:
where r (nm) is the radius of the quenching sphere, s (nm) is the radius of the excluded volume of the molecules, and N_{A} is the Avogadro's number.
The function of the emission decay curves is expressed by eq. 25.
The relationship between the equilibrium constant (K_{1}) and the radius of the quenching sphere is represented by the following equation:
Model 7
Eq. 26 can be rewritten when the static quenching rate constant (k_{q1}) is much larger than the reciprocal of the emission lifetime at [Q_{t}] = 0 (t_{0,n}) as follows:
Model 8
When the dynamic quenching rate constant (k_{q2}) is much smaller than 1/t_{0,n}, I(t) is represented as follows:
Model 9 (Conventional static quenching model)
This model can be applied in the case where k_{q1} is much larger than 1/t_{0,n} and k_{q2}[Q] is negligible. I(t) is expressed as:
This equation is socalled Perrin equation [13]. Eq. 29 does not contain the quencher concentration, so that the emission decay curves does not change with increasing quencher concentration.
Model 10
In this model, the static quenching rate constant is proportional to the number of the quencher in the quenching sphere ( k_{qI} = ik_{q1}). I(t) is expressed as
Model 11
Eq. 31 can be applied when the dynamic quenching mechanism is negligible.
2. 4 Twosite dynamic quenching models [4]
In these models reported by Carraway et al., it is assumed that two regions with different diffusion coefficients exist in a solid matrix, which causes different secondorder quenching rates (k_{q21} and k_{q22}).
Model 12
In the model, I(t) is represented as:
where, f_{1} and f_{2} are the fractions of the different regions.
Model 13
This model can be applied in the case where k_{q22} is neglected because of slow diffusion in region 2. I(t) is represented as follows:
The summary of these models is shown in Table 1.
Table 1. Summary of quenching mechanisms and kinetic parameters
 Rate constants and their restriction   Shape of SternVolmer Plot^{b} 
Model  static  dynamic  Equation^{a} 
1) Dynamic mechanism (1site models) 
1    k_{q2}  4  S 
2) Quenching involving static mechanism 
21) 1step equilibrium models 
2  k_{q1}  k_{q2}  15  C 
3  k_{q1} >> 1/t_{0}  k_{q2}  16  U 
4  k_{q1}  k_{q2} = 0  17  D 
5  k_{q1} >> 1/t_{0}  k_{q2} = 0  18  S 
22) multistep equilibrium models 
6  k_{q1}  k_{q2}  25  C 
7  k_{q1} >> 1/t_{0}  k_{q2}  27  U 
8  k_{q1}  k_{q2} = 0  28  C 
9  k_{q1} >> 1/t_{0}  k_{q2} = 0  29  U 
10  ik_{q1}  k_{q2}  30  C 
11  ik_{q1}  k_{q2} = 0  31  U 
3) Dynamic mechanisum (2site models) 
12    k_{q21} k_{q22}  32  D 
13    k_{q21} k_{q22} =0  33  D 
a) The corresponding decay curve equation is shown in the text.
b) S, straight line; U, upward deviating curve; D, downward deviating curve; C, complicated curve
c) The corresponding quenching system to which the mechanism is applicable.
3 Implementation
We used an IBMPC/AT compatible (HITACHI) in which Microsoft Windows 2000 was installed for developing "QchanG4" with the Microsoft Visual Basic version 6(SP5). The program was tested with Windows 98, Me, NT4, 2000 and XP installed in IBM/PCAT compatibles and PC9821.
4 Feature of QchanG4
The commands of QchanG4 are listed in Table 2. Figure 2 shows the screen shot of QchanG4. QchanG4 is equipped with the following two methods for the analysis of the quenching mechanisms.
Figure 2. Screen shot of QchanG4. (a) Main window. (b) Graph window of emission decay curves. (c) SternVolmer plot window. (d) Numerical values calculated by a theoretical equation. (e) Numerical values of experimental emission decay curves.
Table 2. Command in QchanG4.
Menu/Submenu  Description 
File 
 New  Clear All the quenching data. 
 Open  Read the quenching data in QchanG4 format. 
 Save As  Save the quenching data in QchanG4 format. 
 Quit  Quit QchanG4. 
Calc 
 Normalization  Normalize the preexponential parameters (A_{n}). 
 Decay curve Analysis  Analyze the decay curves with GaussNewton method. 
 Calc decay curves with input param.  Calculate the decay curves with input parameters. 
 SternVolmer ananlysis  Analyze the SternVolmer plot with GaussNewton method. 
 Calc SternVolmer with input param.  Calculate the SternVolmer plot with input parameters. 
Settings 
 Set Parameters  Settings for output format and GaussNewton method 
Help 
 Help  Show help file. (English and Japanese) 
 About  Show information about QchanG4. 
4. 1 Usage
4. 1. 1 Analysis of Emission Decay Curves at Various Quencher Concentrations

You must measure emission decay curves at various concentrations of the quencher to estimate lifetimes and other parameters.

Run QchanG4.exe, and input these parameters into the upper table of QchanG4.

Normalize A values by selecting [Calc]®[Normalization]. Then, emission decay curves and numerical values are displayed in new windows.

Select a model, and input the initial parameters (see Table 3).

The decay curve analysis by the GaussNewton method will start when you select [Calc]®[decay curve analysis]. Since the analysis by GaussNewton method often diverges, you must watch carefully whether there is "*" in the "Error" column. If you obtain it, please try another initial parameters. If you have "not saturated" in the "Error" column, you must input a bigger number in "Iteration" textbox.

After the analysis, the parameters are shown in the lower table; rate constants, equilibrium constant, and the sum of squared residual (S_{e}) or coefficient of determination (R^{2}) defined by:
where S_{yy} is the sum of squared deviation.
Table 3. Parameters used for the analysis.
Parameter  Description  Restriction 
k_{q1} /s  Static quenching rate constant  k_{q1} > 0 
k_{q2} /mol^{1}dm^{3}s^{1}  Dynamic quenching rate constant  k_{q2} >0 
K  Equilibrium constant  K > 0 
F  F value (=f_{2}/f_{1}) using model 12 and 13  F>0 
Probe / M  The concentration of probe (C_{p})  C_{p }> 0 
s /nm  The radius of the excluded volume of the redox center  s>0 
Iteration  The number of maximum iteration  Iteration >0 
Tolerance  The condition to end the regression process  Tolerance >0 
4. 1. 2 Analysis of SternVolmer Plot

You must input the relative emission yields at the various concentrations of the quencher in the upper table.

Input the parameters of the decay curve at 0 mol dm^{3} in the first column in the upper table.

Select a model, and input initial parameters for GaussNewton method.

If you calculate the k_{q2} value based on the decline of t_{0}/t plots vs. [Q_{t}], input the k_{q2} value into the textbox for k_{q2}, and check the "Fix kq2 value".

The calculation will start when you select [Calc][SternVolmer analysis].

Then you have a result in the lower table of the main window. If you have "*" in the "Error" column, please try another initial parameter.
5 Analysis of Phosphorescence Quenching in polyethylene glycol using QchanG4
The phosphorescence quenching in polyethylene glycol (MW = 20,000) was analyzed with QchanG4. Tris(2,2'bipyridine)ruthenium(II) (Ru(bpy)_{3}^{2+}) and methylviologen (abbreviated to MV^{2+}) were utilized as an emission probe and a quencher, respectively.
5. 1 Experimental
Ru(bpy)_{3}^{2+} and MV^{2+} were dissolved in a 5wt% polyethylene glycol aqueous solution. Then 100 mm^{3} of the mixture solution was spread onto a precleaned slide glass (Matsunami S0313). The film was dried under vacuum for 3h at 25°C. The concentration of Ru(bpy)_{3}^{2+} in the film is 20 mmol dm^{3}. The sample film was placed in a quartz cell diagonally. The emission was monitored from the backside of the glass plate to minimize the scattering effect. All the measurements were carried out under Ar. Emission spectra were measured with a spectrofluorometer (Shimadzu RF5300 with Hamamatsu photonics photomultiplier R92808), and emission decay was measured with a timecorrelated singlephoton counting apparatus (HitachiHoriba NAES550) equipped with a nitrogen lamp (10 atm) at 20°C.
5. 2 Results and Discussion
Figure 3 shows the corrected emission spectra of Ru(bpy)_{3}^{2+} in polyethylene glycol and water. The maximum of the spectrum in polyethylene glycol shifts to higher energies by 920 cm^{1} than that in the aqueous solution. This would be because the dielectric constant of polyethylene glycol is lower than that of water to destabilize the excited state of the probe. Another possible reason is the luminescence rigidochromism caused by the slow reorientation of adjacent molecules (solvent molecules and counter ions)[14]. The lifetime of Ru(bpy)_{3}^{2+} in polyethylene glycol is similar to that in an aqueous solution (664 ns). Since the lifetime of the phosphorescence in a rigid environment becomes longer than that in a solution, the reason for the blue shift would be attributed to the lower dielectric constant.
Figure 3. Corrected emission spectra of Ru(bpy)_{3}^{2+}. , in polyethylene glycol; , in H_{2}O.
Table 4 shows the result of the lifetime decay analysis for Ru(bpy)_{3}^{2+} in polyethylene glycol. The phosphorescence decay curves in polyethylene glycol were biexponential curves that have been often observed in heterogeneous systems [11, 14].
Table 4. Analysis of lifetime decay curves for Ru(bpy)_{3}^{2+} in polyethylene glycol.
MV^{2+} /10^{3}mol dm^{3}  Component 1  Component 2  c^{2} 
A_{1}  t_{1}  A_{2}  t_{2} 
0.0  0.646  697  0.354  251  1.21 
2.5  0.467  465  0.533  178  1.06 
5.0  0.327  465  0.673  177  1.22 
7.5  0.368  446  0.632  168  1.18 
10.0  0.309  448  0.691  167  1.07 
Table 5 shows the parameters obtained by the analysis of the emission decay curves and the sum of squared residual calculated with the theoretical equations of the SternVolmer plot with the parameter [11].
Table 5. Result of decay curve analysis.
Model  K or F  k_{q1}/10^{}6s  k_{q2}/10^{7}M^{1}s^{1}  k_{q22}/10^{7}M^{1}s^{1}  S_{e}  r /nm  S_{e}(SternVolmer) 
10  244.9  0.81  62.6   0.35  4.6  0.20 
6  278.2  1.48  46.8   0.45  4.8  0.18 
2  570.9  0.80  196.   0.86   0.18 
8  1043.  1.14    0.90  7.5  1.03 
12  0.55   15.2  254.4  7.00   1.12 
7  9.69   15.3   7.10  1.6  0.12 
11  469.3  0.52    7.13  5.7  1.08 
1    15.3   7.46   0.16 
3  4.75   16.1   7.47   0.12 
13  0.55   15.7   7.65   0.71 
4  15420.  2.57    19.49   0.17 
On the basis of the sum of squared residual, phosphorescence behavior in polyethylene glycol can be explained with models 10 and 6 considering Poisson type static quenching and dynamic quenching mechanisms. Although it is difficult to determine the most suitable model between models 10 and 6, the decay curves are well simulated by model 10 (Figure 4). Since the precision of emission intensity is lower than that of lifetime measurement in the film system, model 10 would be suitable to describe the quenching mechanism in polyethylene glycol.
Figure 4. Emission decays of Ru(bpy)_{3}^{2+} in polyethylene
glycol at various MV^{2+} concentrations. Symbols: experimental, ,
0 mol dm^{3}; , 2.5 mmol dm^{3};
, 5 mmol dm^{3}; ,
7.5 mmol dm^{3}; , 10 mmol dm^{3}.
The curves are simulated with (a) Model 10 and (b) Model 6.
The dynamic quenching rate constant in polyethylene glycol is almost the same as that in an aqueous solution, suggesting that the collision frequency in polyethylene glycol is as high as that in water despite the solid matrix.
6 Conclusion
We have developed a photoluminescence quenching analyzer called QchanG4 with Visual Basic. Quenching mechanisms in a solid matrix can be analyzed with the software using emission decay curves and a SternVolmer plot. Model 10 considering Poisson distribution type static quenching and dynamic quenching explains the quenching behavior in polyethylene glycol.
7 Agreements for using the program
The "QchanG4" is freeware. We cannot be responsible for damages that you might receive when using this program. Please feel free to contact us, when you find bugs. We would welcome suggestions for the improvement of the program. The program can be downloaded at the CSJ ftp server.
The authors acknowledge a GrantinAid for JAERI's Nuclear Research Promotion Program (JANP) from Japan Atomic Energy Research Institute.
References
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[ 9] M. Kaneko, S. Iwahata, T. Asakura, Photochem. Photobiol., 55 (1992).
[10] K. Nagai, N. Takamiya, M. Kaneko, J. Photochem. Photobiol. A:Chem., 84, 271 (1994).
[11] K. Nagai, N. Takamiya, M. Kaneko, Macromol. Chem. Phys., 197, 2983 (1996).
[12] O. Stern and M. Volmer, Phys. Z., 20, 183 (1919).
[13] F. Perrin, J. Perrin, C. R. Acad. Sci., Paris, 10, 1978 (1924).
[14] S.E. Mazzetto, I.M.M. Carvalho, M.H. Gehlen, J. Luminescence, 79, 47 (1998).
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