Dynamics in Ionic Solutions - American Chemical Society

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J. Phys. Chem. B 2000, 104, 1338-1348

Dynamics in Ionic SolutionssRevisited R. Argaman and D. Huppert* Raymond and BeVerly Sackler Faculty of Exact Sciences, School of Chemistry, Tel AViV UniVersity, Ramat AViV 69978, Israel ReceiVed: September 7, 1999; In Final Form: NoVember 19, 1999

We used steady-state absorption, emission, and time-resolved fluorescence measurements of coumarin 153 in butyl acetate-LiClO4 solutions to study the static and dynamic aspects of ion-probe interactions. We analyzed the low concentration data in terms of two distinct solvate configurations. The first distinct solvate was a probe molecule surround by n solvent molecules in the first solvation shell; in the second distinct solvate, one of the surrounding solvent molecules was replaced by a Li+ cation. We used a diffusive model to describe quantitatively the dynamics of the ion/solvent exchange reaction. At low concentration (e0.5 M), our model accounts for steady-state spectroscopic data and the viscosity dependence of the dynamics.

Introduction Considerable effort has gone into studying the solvation dynamics of probe molecules. Most of the experimental studies have been performed by electronic excitation of organic probe molecules in neat solvents. The solvation of probe molecules in ionic solutions has attracted less attention.1-8 The solvation dynamics of ions differ from that of solvent molecules; while the dynamics in neat solvents primarily involve reorientation of solvent molecules, in ionic solutions the ion-probe interaction arises from translational ion motions. In previous studies, we measured the steady-state fluorescence spectra and the time-dependent fluorescence Stokes shift of probe molecules such as coumarin 153 and coumarin 102. Most of these were in ionic solutions of a single salt, LiClO4, in a wide range of organic solvents. These measurements lead to several conclusions concerning the solvation statics and dynamics of probe molecules in ionic solution. (1) Salt induces a red frequency shift in the probe molecule absorption and emission spectra. The frequency shift is a linear function of the salt concentration but tends to saturate (smaller slope) at high salt concentrations (>0.1 M). For lower polar solvents (for example, ethyl acetate), the Stokes shift is larger than for medium polar solvents (e.g., acetonitrile). At very high polar solvents the Stokes shift decreases further, and for water we were not able to observe spectral shifts due to the presence of strong electrolytes. (2) Time-resolved fluorescence measurements show that the dynamics are rather slow, with a linear dependence on salt concentration. The larger the salt concentration, the faster the ionic solvation dynamics. For a 0.5 M salt solution in a nonassociative solvent with low viscosity (η ≈ 0.5 cP), the solvation dynamics occur in about 1 ns. The relaxation of the fluorescence Stokes shift of coumarin 153 due to the presence of ions in solution was explained using a qualitative analogy to the Debye-Falkenhagen theory9 (DF) describing the relaxation of the ionic atmosphere around a central ion.10,11 The DF theory predicts that the ionic atmosphere relaxation time, τ, will be proportional to s/ΛoC and will be of the order of (Dκ2)-1, where s is the static dielectric constant, Λo is the equivalent conductance at infinite dilution, C is the ion concentration, D is the ion diffusion constant, and κ is the

inverse Debye length proportional to the square root of the solution ionic concentration. These relations refer to ion-ion interaction, while the probe molecule (coumarin 153) can be approximated at best to a dipole interacting with the ionic atmosphere surrounding it. This simplified picture is only true when the ions in the first solvation layer do not interact specifically with the probe molecule and so their contribution to the solvation energy can be accounted for by their electric charge. Furthermore, in low dielectric solvents, counterions tend to form ion pairs with total zero net charge and a large dipole moment. At high salt concentrations, higher aggregates such as trimer, tetramer etc., can exist in appreciable fractions especially in low dielectric constant solvents with < 20.12,13 Van der Zwan and Hynes4 did a theoretical study of the influence of the ion atmosphere dynamics on reaction rates as well as time-dependent fluorescence of a dipolar solute. Their results suggest that dynamics of the ionic atmosphere can sometimes significantly affect reaction rates, and also that the connection between these rates and time-dependent fluorescence can be used to comprehend these effects. The relaxation times predicted by the Debye-Falkenhagen theory are shorter by more than an order of magnitude than the observed time-dependent Stokes shift relaxation times. Chapman and Maroncelli5 measured the statics and dynamics of the salt effect of several probe molecules in electrolyte solutions. They used a number of electrolytes and several organic solvents. The experimental results agree qualitatively with our basic findings. The main difference between our previous studies and Chapman and Maroncelli’s work lies in the electrolyte concentration range we dealt with; we used salt concentrations of 0.01-0.4 M, while they used 0.1-2 M. In addition, they used a large number of bivalent ions. Their interpretation of the static and dynamic salt effects is rather different from ours. They propose a solvation model based on equilibrium among distinct solvates characterized by the number of cations in the first solvation shell of the probe. They pointed out that in the case of a model of distinct solvates it might be preferable to measure the spectral kinetics in a way directly related to the growth and decay of these distinct species. In this study, we measured the solvation dynamics of coumarin 153 in ionic solution of a medium polar liquid, butyl

10.1021/jp9931713 CCC: $19.00 © 2000 American Chemical Society Published on Web 01/20/2000

Solvation Dynamics in Ionic Solutions

J. Phys. Chem. B, Vol. 104, No. 6, 2000 1339

acetate ( ) 5.114), and used a two-species model to describe the experimental results. In this model, the ion contribution to solvation energy of the excited state can be described as the ion/solvent exchange reaction KD

P1Sn + I 98 P1Sn-1I + S where P1Sn denotes an excited probe molecule surrounded by n solvent molecules in the first solvation shell, I is an ion replacing a solvent molecule, and the product is an excited probe molecule with one cation located in the first solvation shell, denoted as P1Sn-1I. We used a diffusive chemical reaction model15,16 to describe the dynamics involved in ionic solvation of excited probe molecules. This model accounts for the viscosity dependence of the solvation dynamics and for the nonexponential nature of this process, which we found in concentrated salt solutions. At high salt concentration, >0.5 M, we find a systematic mismatch between the specific ion exchange model and the experimental results. The experimental absorption band shifts more to the red than the predicted shift of the model. According to Maroncelli and co-workers,5 it can be qualitatively explained by a solvate with two ions in the first solvation shell, PSn-2I2. To account for the additional red shift, we examined two models: (1) we extended the distinct solvate model and incorporated a solvate with two ions in the first solvation shell; (2) a nonspecific contribution of the outer ions to the solvation of the coumarin in the framework of the ionic atmosphere model.

Figure 1. Steady-state emission spectra of C153 in neat butyl acetate and with a LiClO4 concentration of (right to left) 0.05, 0.2, and 0.35 M.

Experimental Section Time-resolved fluorescence was detected using a timecorrelated single photon counting (TCSPC) technique. As a sample excitation source we used a CW mode-locked Nd:YAGpumped dye laser (Coherent Nd:YAG Antares and a cavity dumped 702 dye laser) providing a high repetition rate of short pulses (2 ps at full width at half-maximum (fwhm)). The TCSPC detection system is based on a multichannel plate Hamamatsu 3809 photomultiplier, Tennelec 864 TAC and 454 discriminator. A personal computer was used as a multichannel analyzer and for data storage and processing. The overall instrumental response was about 50 ps (fwhm). Measurements were taken at 20 ns full scale. The samples were excited at 300 nm (the second harmonic of Rhodamine 6G dye laser). At this wavelength, the sample is excited to S2, the second excited electronic state. The transition dipole moment S0 f S2 is perpendicular to S0 f S1. Therefore, a polarizer set at an angle complementary to the “magic angle” was placed in the fluorescence collection system. Coumarin 153 (C153) was purchased from Exciton. Butyl acetate, puriss grade, was purchased from Fluka. All chemicals were used without further purification. Steady-state fluorescence spectra of the samples were recorded on a SLM-AmincoBowman 2 luminescence spectrometer and corrected according to manufacturer specifications. All experiments were performed at room temperature (24 ( 2 °C). Results The normalized steady-state fluorescence spectra of C153 in butyl acetate solutions containing various concentrations of LiClO4 are shown in Figure 1. The emission band maximum shifts to the red in the presence of moderate salt concentration. Figure 2 shows the absorption spectra of C153 in butyl acetate with different LiClO4 concentrations. Note that the peak hight

Figure 2. Steady-state absorption spectra of C153 in neat butyl acetate and with a LiClO4 concentration of (right to left) 0.1, 0.2, and 0.35 M.

of the absorption spectra is not normalized as shown in Figure 1. We prepared all solutions with the same dye concentration, so we were able to observe even small differences (∼1%) in the height of the absorption bands as a function of the salt concentration. It can be seen from Figure 2 that as the salt concentration increases the peak height decreases, the band position shifts to red, and the bandwidth increases. The important feature seen in Figure 2 is that an isosbestic point exists at low salt concentrations. As we will show in the next section, the isosbestic point supports the model of ion/solvent exchange. The position of the band maximum of either the absorption or emission spectrum depended on the electrolyte concentration. For a certain electrolyte concentration, the shift of the fluorescence band was about twice as large as that of the absorption band. In the next section we will analyze both the absorption

1340 J. Phys. Chem. B, Vol. 104, No. 6, 2000

Argaman and Huppert

Figure 3. Emission spectra of C153 in butyl acetate with 0.1 M LiClO4. Excitation wavelengths are 470 nm (dashed curve), 410 nm (band maximum, solid curve), and 360 nm (dotted curve).

and emission spectra’s position and shape (shown in Figures 1 and 2) using a two distinct solvates model. Figure 3 shows the emission spectra of C153 in a solution of butyl acetate containing 0.1 M LiClO4, excited at three different wavelengths: (a) red edge excitation at 470 nm; (b) excitation at 410 nm, the band maximum; (c) blue edge excitation at 360 nm. Note that the spectrum shifted to the red when excited at low energy. Figure 4a depicts the time-resolved emission of C153 in neat butyl acetate at several wavelengths. Figure 4b shows the time-resolved emission curves of C153 in 0.5 M electrolyte solution. The emission curves at short times (less than 200 ps) were almost identical to the corresponding curves in neat solvent shown in Figure 4a. At times longer than 200 ps, a new decay was seen at the short wavelengths (520 nm). The slow component is attributed to the solvation of coumarin by the salt. The two distinct solvates model described below accounts for the observed spectroscopic data at low and medium salt concentrations. The Model The model we propose to describe the solvation of a probe molecule in dilute ionic solution is based on two distinct solvates, PSn and PSn-1I. PSn denotes a probe molecule surrounded by PSn-1I solvent molecules in the first solvation shell and Li+ describes a probe molecule into which a single cation is incorporated in the first solvation shell. In our case, a positive Li+ ion situated close to a negative charge of the coumarin dye caused a bathochromic shift of 1000 cm-1 and 1400 cm-1 in the absorption and fluorescence bands, respectively. Absorption, steady-state emission and time-resolved emission spectroscopy of C153 in ionic solutions can be described by Scheme 1. The two solvates P0Sn and P0Sn-1I are in equilibrium in the ground state. Upon photon excitation, both ground state species can be directly excited. As we will show, this model accounts for the absorption and emission properties of C153 in dilute electrolyte solutions. From our analysis of the absorption band shift and shape as a function of electrolyte concentration described in the next

Figure 4. Time-resolved emission spectra of C153 at different wavelengths: (a) neat butyl acetate (top to bottom) 520, 500, 480, and 460 nm; (b) butyl acetate with 0.5 M LiClO4 (top to bottom) 640, 580, 560, 540, 520, 500, 480, and 460 nm.

SCHEME 1

paragraph, we found the value of the ground-state equilibrium constant K0eq to be 1.1. Chapman and Maroncelli5 estimated that the concentrations of both ground state P0Sn-2I2 and excited state P1Sn-2I2 are small (less than 7%) for similar salt solutions containing less than 0.5 M electrolyte. The concentration of


J. Phys. Chem. B, Vol. 104, No. 6, 2000 1341 TABLE 1: Characteristic Parameters for Two Log-Normal Fits of the Absorption Spectraa LiClO4 [M]

hPSn

hPSn-1I

0 0.01 0.05 0.1 0.2 0.35 0.5

1 1 0.96 0.92 0.83 0.75 0.64

0 0 0.05 0.1 0.2 0.28 0.37

a Absorption spectra were fitted to a sum of two log-normal (see eq 1). The parameters of the PSn band are γ ) 0.38, νp ) 24 200 cm-1, and ∆ ) 3750 cm-1, and for the PSn-1 band γ ) 0.38, νp ) 23 200 cm-1, and ∆ ) 3750 cm-1, where the overall superimposed band maximum intensity is 1.

TABLE 2: Characteristic Parameter for a Single Log-Normal Fit of the Absorption Banda

Figure 5. Absorption spectra of C153 in butyl acetate: (from right to left) neat solvent, solutions with 0.1, 0.2, and 0.35 M LiClO4. Dotted lines are the experimental data and solid lines are the computer fit.

solvates with three ions or more in the first solvation shell is negligible. Therefore, to minimize the number of free parameters and for simplicity and clarity of the model, we used only P0Sn-1I and P1Sn-1I as distinct solvates containing just one ion to quantify our experimental observations. Data Analysis a. Absorption Spectra. To connect the ground-state equilibrium with the absorption band position and shape as a function of ion concentration, we assumed that the shape of the spectrum of P0Sn-1I was identical with the spectrum in the pure solvent except for an overall frequency shift. To generate the line shapes of the absorption spectra of P0Sn and of P0Sn-1I, we used a log-normal distribution,

I(ν) ) h

{

exp[-ln(2){ln(1 + R)/γ}2] R > -1 0 R e -1

(1)

with

R ≡ 2γ(ν - νp)/∆ where h is the peak height, νp is the peak frequency, γ is the asymmetry parameter, and ∆ represents the band’s width. The fits to the experimental absorption bands along with the experimental spectra are shown in Figure 5 for several concentrations of electrolyte solutions. The relevant parameters are given in Table 1. The band shift in the ground state between P0Sn and P0Sn-1I was ∼1000 cm-1. The equilibrium constant was 1.1, similar to Maroncelli’s5 findings for coumarin 102 in acetonitril with NaClO4 as the electrolyte. As can be seen in Figure 5, the model calculations fit the experimental data. As the salt concentration increases the absorption peak height decreases and the band shifts to the red. It is worth mentioning that when we fitted the absorption spectra to only one log-normal, we found a red shift of the maxima, as well as a broadening of their bandwidth and a reduction in the asymmetry parameter as a function of increase in salt concentration (see relative values in Table 2). There is a substantial change in width and spectral shape as one proceeds

concentration [M]

h

γ

νp [cm-1]

∆ [cm-1]

0 0.05 0.1 0.2 0.35 0.43 0.6 0.8 1

1.00 0.995 0.987 0.982 0.978 0.974 0.971 0.964 0.963

0.378 0.363 0.349 0.329 0.303 0.269 0.255 0.249 0.251

24 161 24 112 24 065 23 981 23 860 23 825 23 674 23 536 23 398

3760 3797 3826 3877 3947 4033 4061 4074 4118

a h is the height of the peak maximum, γ is the asymmetry of the peak, νp is the location of the peak maximum, and ∆ is the peak width.

from the pure solvent to the saturated salt solution. The difference (0-1 M) in the spectral full width at half-maximum is 358 cm-1 a change of 9.5%. In the band shape asymmetry, there is a change of 33.6% (the difference in the log-normal asymmetry, γ, see eq 1) and the peak shifts by 763 cm-1 from pure solvent to 1 M salt solution, which is 41.5% of the cyclohexane-DMSO shifts (for C153 in acetonitrile-NaClO4 solutions the shift is only 360 cm-1). These very large spectral changes support the model of two distinct solvates of C153. b. Excited-State Dynamics. 1. Neat SolVent. When a probe molecule is excited in solution it experiences a large change in the charge distribution. The dipole moment of C153 increases from 6.5 D17 in the ground state to 14.2 D18 in the excited state. The solvent molecules reorient to accommodate the change of the charge distribution of the excited state. Analysis of the timeresolved fluorescence spectrum of a probe dye in neat solvent provides the solvent correlation function. Solvent dynamics have been studied extensively and have been found to be bimodal.19-21 A large fraction of the change in solvation energy is gained on the very short time scale of a few tens of femtoseconds. This component is attributed to the inertial motion of the solvent molecules in the first solvation shell. The fast component is followed by a longer component which decays nonexponentially, and its decay time is solvent dependent. This component is attributed to the diffusive orientational motion. The time-resolved emission of C153 in neat butyl acetate was analyzed by a procedure given by Maroncelli,22 to obtain the solvent correlation function. Time-correlated single photon counting has a limited instrumental response function of ∼50 ps, which limits the time resolution to about 20 ps. Therefore, only the long components were accurately time-resolved in this study. The solvation dynamics were analyzed using a sum of exponentials. The relevant parameters are given in the first line of Table 3.


Argaman and Huppert

TABLE 3: Time-Resolved Fluorescence Analysis of Coumarin 153 Measured at 470 nma LiClO4 [M]

a1

τ1b [ps]

a2

τ2c [ps]

a3

τ3 [ns]

0 0.075 0.1 0.2 0.35 0.5

0.08 0.05 0.11 0.15 0.15 0.22

20 20 20 20 20 20

0.92 0.37 0.26 0.23 0.27 0.24

208 250 250 250 250 250

0.58 0.63 0.62 0.58 0.54

7.18 5.43 2.9 1.92 1.48

a The solvation dynamics deduced from the time-resolved decay curves measured at 470 nm. The multiexponential fits are according 3 to the following equation: I(t) ) ∑i)1 ai exp(-t/τi) with ai g 0 and 3 ∑i)1 ai ) 1. The experimental curves were multiplied by et/τf, where τf is the lifetime of the dye molecule. b The time-correlated single photon counting technique has a limited instrumental response of ∼50 ps (fwhm); the true values of the short component are probably much shorter. c The error in the evaluation of the second component is estimated to be 20%.

2. Electrolyte Solution. When an electrolyte solution is irradiated by a short laser pulse at frequency ν′, which coincided with the absorption band of the coumarin dye, both solvates, P0Sn and P0Sn-1I, are excited. The relative probability of a photon being absorbed by P0Sn-1I is given by

a(ν′) )

agν′(ν′) (1 - a)fν′(ν′) + agν′(ν′)

(2)

where a ) [P0Sn-1I]/([P0Sn] + [P0Sn-1I]) is the concentration fraction of the P0Sn-1I species in the ground state. fν′(ν′) and gν′(ν′) are the line shape functions of the ground-state absorptions of P0Sn and P0Sn-1I, respectively. Immediately after excitation, the solvent in the first solvation shell of the P1Sn-1I species and the solvent molecules in outer shells experience solvent reorientation to accommodate the excited-state charge distribution of the coumarin. For butyl acetate, the slowest component of the solvation was ∼200 ps. The 200 ps solvation component was unaffected by the presence of salt ions up to 0.5 M. Table 3 gives the amplitudes and decay times of the various time components, measured at 470 nm. In addition to the solvent solvation energy, the ion situated in the first solvation shell contributed further stabilization which led to a 1400 cm-1 shift of the P1Sn-1I fluorescence band relative to the P1Sn band. Since the ion is spherically symmetric, the ion rotation has no effect on the solvation energy. If the ion is positioned at the correct site and no translational motion is taking place after excitation, then the change in solvation energy is gained instantaneously after excitation and therefore is not detected in the time-resolved experiment. When a photon is absorbed by P0Sn to create P1Sn, the large increase in the dipole moment (of about 8 D) causes a large increase in the equilibrium constant. As a consequence, an ion/solvent exchange process takes place at the first solvation layer of the coumarin dye. The following scheme illustrates the dynamics immediately after excitation of the solvate PSn.

The zeroth-order description of the kinetics of the above scheme is based on the phenomenological rate equations of chemical kinetics. The mathematical solution of the appropriate coupled rate equations is given in ref 23. If k1 . k-1, kf, then P1Sn

fluorescence intensity decays as a single exponential while an exponential growth of the fluorescence intensity of P1Sn-1I takes place. The decay rate of the P1Sn species varies linearly with ion concentration. In the diffusive model, the replacement of a solvent molecule by a cation occurs at a certain rate, whenever I and P1Sn are in close proximity. As we will show below, if the exchange rate constant is larger than the diffusion rate constant, the dynamics of reaction is nonexponential. Within the framework of the diffusive model, the well-known way of solving the model is along the lines of the Smoluchowski equation.15 We adopted the solution given in a paper by Szabo.16 The survival probability of P1Sn surrounded by an equilibrium distribution of ions denoted by I with the initial condition F(0) ) 1, is

F(t) ) exp(-c

∫0tk(τ)dτ)

(3)

where c is the concentration of the ion and k is the timedependent rate constant, given by

k(t) )

[

4πDa0k0 k0 γ2Dt 1+ e erfc((γ2Dt)1/2) k0 + 4πDa0 4πDa0

]

(4)

where a0 is the contact radius, γ is given by

(

γ ) a-1 0 1+

k0 4πDa0

)

(5)

and erfc is the complementary error function. k0 is the rate constant of the reaction at contact. At long times, the rate constant is time independent and is given by

k)

4πDa0k0 k0 + 4πDa0

(6)

We have found in the past that the rate of salt contribution to solvation of coumarin dyes in electrolyte solutions depends linearly on the solvent viscosity, η.1-3 Within the framework of the diffusion-controlled reactions, the observed rate at long times depends linearly on the ion diffusion constant, D. The Stokes-Einstein expression relates η to D by

D)

kT 6πrη

(7)

where r is the radius of the diffusing species. For a quantitative description of the time-resolved emission as well as the steadystate emission spectrum, we used the diffusive reaction rate expressions given by eqs 3 and 4. c. Time-Resolved Fluorescence. The experimental data analysis above reveals that the absorption and the emission spectra of PSn are structureless broad bands and had bandwidths of 3800 and 2800 cm-1, respectively. PSn-1I spectra have band shapes similar to that of PSn; these were red shifted by about 1000 and 1400 cm-1 for the absorption and emission bands, respectively. One cannot exclusively excite one species since the shift between the bands is rather small compared to the width of each band. Therefore, the time-resolved fluorescence signal at a given time t and frequency ν strongly depends on the excitation frequency ν′. We calculated the signal If(ν′,ν,t) according to the following equation:



Figure 6. Time-resolved emission at 470 nm of C153 in butyl acetate with LiClO4: (top to bottom) 0.05, 0.1, 0.2, 0.35, and 0.5 M. Dashed lines are experimental data and solid lines are computer modeling fit.

TABLE 4: Relevant Parameters of the Simulation to the Time-Resolved Fluorescence of Coumarin 153 LiClO4 [M]

ηa [cp]

Db [m2/s] × 10-9

a(ν′)c

0 0.075 0.1 0.2 0.35 0.5

0.63 0.66 0.68 0.73 0.82 0.92

0.7 0.68 0.63 0.56 0.5

0 0.04 0.11 0.2 0.37 0.43

a

Viscosities were deduced from relative viscosities measurements and comparison to known absolute literature values.14 Measurements were taken at 23 °C. b Diffusion constants were estimated from the Einstein-Stokes relation and the known viscosities of the solutions. c a(ν′) is the relative absorption cross section of P0S n-1I irradiated at 300 nm, given by eq 2.

If(ν′,ν,t) ∝ [(1 - a(ν′)) fν(ν) F(t) + a(ν′) gν(ν) + (1 - a(ν′))(1 - F(t))gν(ν)] e-kft (8) where fν and gν are the line shape functions of P1Sn and P1Sn-1I luminescence, respectively. F(t) is the survival probability of P1Sn. The time dependence of F(t) due to the ion/solvent exchange reaction was calculated using eqs 3-6. The first term on the right-hand side of eq 8 is the luminescence intensity at frequency ν of P1Sn excited at a frequency ν′. The second term is the luminescence of P1Sn-1I due to direct excitation at a hν frequency ν′, P0Sn-1I f P1Sn-1I. The third term is the luminescence intensity growth of the P1Sn-1I solvate due to the k diffusive reaction taking place in the excited state, P1Sn + I f 1 P Sn-1I. Figure 6 shows the experimental time-resolved emission data measured at 470 nm for various salt concentrations along with the computer fit of the data according to eq 8 (for relative parameters, see Table 4). At this wavelength, the overlap between the P1Sn and P1Sn-1I bands is rather small. The luminescence reflects the decay of the P1Sn population due to the diffusive ligand replacement reaction. The parameters affecting the exchange reaction dynamics are [I], a0, k0, and D, where [I] is the Li+ concentration, a0 is the contact radius for the reaction, and k0 is the intrinsic reaction rate constant at the

contact radius. We used for the diffusion constant a value of D(η[I]) ≈ 10-5 cm2 s-1 for low salt concentrations. This value is based on LiClO4 electrical conductance measurements in THF24 and the viscosity difference between butyl acetate and THF. We estimated the value of a0 on the basis of the size of the bare coumarin dye (3.8 Å) and on our model assumption that the ion/solvent exchange reaction occurs at the interface between the first and second solvation shell. From Petrucci’s electrical conductance measurements,24 the effective radius of a Li+ ion in THF solution is ∼4.5 Å while the crystal ionic radius is only 0.6 Å. Thus, the interaction of the ion with solvent molecules in the first solvation shell is strong and therefore the effective radius, a0, for cation motion includes the first solvation layer. We chose a value of 5.8 Å for the solvated coumarin as a plausible value. We found the intrinsic reaction rate constant to be k0 ) 3.2 × 109 M-1 s-1. The decay at all salt concentration was nonexponential (Figure 6). Equation 4 predicts that at short times the ions close to P1Sn react at a finite rate determined by k0. At longer times, the transport of distant ions limits the effective replacement rate. At long time, the asymptotic rate is given by eq 6. The diffusion rate constant is kD ) 4πN′Da0, where N′ ) NA/1000 is the number of Li+ ions in 1 mL of 1 M solution (NA is Avogadro’s number). For butyl acetate electrolyte solution, kD ≈ 2 × 109 M-1 s-1 and it is slightly smaller than k0. The value of the overall long time rate constant, calculated from eq 6, is 1.2 × 109 M-1 s-1. Thus, the time-dependent reaction rate constant at short time is larger by the factor 3 than at long times. Figure 7a depicts the time-resolved luminescence at selected wavelengths for a solution of 0.5 M LiClO4. At long wavelengths >520 nm, a time growth of the fluorescence intensity was seen due to the ion-solvent replacement reaction. At these wavelengths, the P1Sn-1I luminescence cross section was larger than that of P1Sn since the band maximum of P1Sn-1I was located at 530 nm, while that of P1Sn was at 495 nm. Figure 7b shows the time-resolved luminescence for a solution containing 0.1 M LiClO4. There was very good agreement between the calculated (solid line) and the experimental (dashed line) fluorescence signals at all salt concentrations. The luminescence signals at wavelengths >530 nm for 0.5 M and 0.1 M salt concentrations differed in their relative amplitude of the hν component related to direct excitation P0Sn-1 f P1Sn-1I. This component appears instantaneously after excitation while the fluorescence component due to the exchange reaction has a finite rise time that depends on the electrolyte concentration. The relative fractions of direct excitation for laser excitation at 300 nm were a(0.5 M) ) 0.43 and a(0.1 M) ) 0.11. d. Steady-State Fluorescence. Time integration of the fluorescence expression given by eq 8 provides the steady-state fluorescence intensity at frequency ν. Sweeping the frequency ν across the emission frequencies generates the emission spectrum. Figure 8 shows the steady-state experimental and the calculated spectra (by integration of eq 8) of coumarin solutions with different electrolyte concentrations. The computed integrated fluorescence signals fitted the experimental data very well. Another aspect of the two discrete solvates model is the steady-state fluorescence spectrum dependence on the excitation frequency. Figure 9 shows the fit of the model to the steadystate spectra obtained by exciting at three different wavelengths: (a) at the blue edge of the absorption band, where the absorbance was 25% of the band maximum; (b) at the absorption band maximum; (c) red edge excitation, at 25% of the band maximum.


Argaman and Huppert

Figure 8. Steady-state emission spectra of C153 in several butyl acetate-LiClO4 solutions: (right to left) 0.075, 0.1, 0.2, and 0.35 M. Dashed lines are the experimental data, and solid lines are the calculated data according to eq 8. The excitation frequency was at the absorption band maximum.

Figure 7. Time-resolved luminescence of C153 in butyl acetate with LiClO4 at selected wavelengths of (top to bottom) 640, 580, 560, 540, 520, 500, and 480 nm: (a) 0.5 M solution; (b) 0.1 M solution.

e. Time-Resolved Spectra. In a model where species A converts to B, as time progresses, the emission of species A diminishes while the emission intensity of B increases. If the two bands of species A and B overlap to a certain degree, then at a particular wavelength the emission intensity contribution of bands A and B are equal and hence the time dependence of the fluorescence intensity is constant (except for the natural decay of the excited state). This is illustrated in Figure 10a which shows a simulation of the time-resolved spectra using eq 8 when hν the direct excitation P0Sn-1I f P1Sn-1I is eliminated (the second term in eq 8 is set to zero). Note the isoemissive point at about 19 500 cm-1 (we multiplied the results obtained from eq 8 by et/τf to account for the excited-state lifetime). In our case, an appreciable amount of P1Sn-1I is formed by direct excitation. Figure 10b shows simulations of the time-resolved spectra for a 0.5 M electrolyte, excited at 300 nm, where a(ν′) ) 0.43. Note that the location of the isoemissive point is unchanged but the spectral changes are much smaller. When

Figure 9. Steady-state emission spectra of C153 in butyl acetateLiClO4 0.1 M solution: experimental (dashed lines); calculated (solid lines). Excitation at three different frequencies: at the absorption band blue edge; at the absorption band maximum; at red edge of the absorption band. The latter is the left spectrum.

the peak height is normalized, the time-resolved emission spectra shift to the red as time progresses. Time-resolved spectra are seen as if a single band shifts with time, as one finds for solvation dynamics experiments in a neat solvent. f. Excitation Spectra. The excitation spectra of the luminescence measured at frequency ν was obtained by time integration of eq 8 while holding the emission frequency fixed at a certain frequency ν and sweeping the excitation frequencies, ν′, across the absorption band. Since both the ground-state absorption and the excited-state emission spectra are composed of two overlapping bands, the excitation spectrum, position, and shape are sensitive to the chosen emission frequency. If the



Figure 11. Excitation spectra of C153 in butyl acetate-LiClO4 0.5 M solution: experimental (dashed lines); simulation (solid lines). the emission was collected at the blue edge (right) and at the maximum of the fluorescence band (left).

Figure 10. Simulated time-resolved fluorescence spectra of C153 in butyl acetate-LiClO4 0.5 M solution using eq 8. The spectra were calculated for 200 ps time intervals: (a) no direct excitation, a ) 0; (b) direct excitation of the PSn-1I solvate, a ) 0.43, the parameters value for excitation at 300 nm.

excitation spectrum is measured at a certain frequency ν at the blue edge of the fluorescence spectrum, the emission of the P1Sn species will be pronounced and hence the excitation spectrum will shift to the blue. Figure 11 shows both the simulation and the experimental excitation spectrum measured at two emission frequencies, at the blue edge and at the maximum of the emission band. High Salt Concentrations The specific ion-solvent exchange model described in Scheme 1 is in a good agreement with the experimental results of the dependence of the spectroscopic measurements on salt concentration up to 0.5 M LiClO4. Using the model we got good fits to the electrolyte concentration dependence of the absorption spectra, the steady-state emission, and the time-resolved emission decay curves and spectra.

Figure 12. Absorption spectra of C153 in butyl acetate-LiClO4 solutions: (right to left) neat butyl acetate, 0.5, 0.6, 0.8, and 1 M solutions.

At relatively high LiClO4 concentrations, >0.5 M up to 1 M, we found a systematic mismatch between the model and the experimental results. The mismatch increases with the increase of salt concentrations. Figure 12 shows the absorption spectra of C153 in butyl acetate solution with high LiClO4 concentrations. As the salt concentration increases, the peak height decreases, the peak position shifts to the red, and the bandwidth increases. One can see that the isosbestic point exists at low salt concentrations (which supports our model of ion/ solvent exchange for low salt concentrations). At concentrations above 0.35 M, each spectral line crosses the other at a different wavelength. We attempt to explain the high salt concentrations results by two different models, the first one is similar to the ion/solvent exchange model.


Argaman and Huppert

Figure 14. Absorption spectra of C153 in butyl acetate: (right to left) neat solvent, 0.35, 0.6, and 1 M of LiClO4. Dashed lines are the experimental data and solid lines are the fitting according to the combined model. With U ) d[I], d ) 450 cm-1 and [I] is the ion concentration in molar units.

Figure 13. Absorption spectra of C153 in butyl acetate: (right to left) neat solvent, 0.1, 0.35, and 1 M of LiClO4; experimental (dashed lines); calculated (solid lines); (a) K1 ) 1.1 and K2 ) 0.057; (b) K1 ) 2.0 and K2 ) 0.45.

We extend the model by taking into account the possibility that more than one positive ion can exchange a solvent molecule in the first solvation shell. The ground state exchange reactions can be described schematically by K1

PSn + I {\} PSn-1I + S K2

PSn-1I + I {\} PSn-2I + S We assumed that the absorption and emission spectral shift due to the second ion/solvent exchange is the same for the first exchange, ∆ν2 ) 2∆ν0, and that the spectral shapes do not change. We tested this model for the ground state, i.e., for the absorption spectra. For K1 and K2, we took two different sets of values. In the first case we used K1 ) 1.1 and K2 ) 0.0057 the values derived by Maroncelli5 and ∆ν0 ) 900 cm-1. The

spectra obtained from those calculation using the two ion exchange model along with the experimental spectra are shown in Figure 13a. One can see that the fitting is getting worse as the LiClO4 concentration increases in three different aspects of the signal fit: its height, shape, and location. It is worth mentioning that the isosbestic point does not exist at electrolyte concentrations higher than 0.35 M, and a red spectral shift occurs. A much better fit is found when a different set of values is chosen for the equilibrium constants K1 ) 2.0 and K2 ) 0.5. In such a case, we obtained a much better agreement with the experimental spectra. The shape and the peak location of the computed signal match the experimental data, but the height is wrong. The results are shown in Figure 13b. The second model is a combination of two different types of contributions to the ion-probe molecule interaction. The first one is described by the specific single ion/solvent exchange model given in detail in the previous sections and the second one is a nonspecific model where the ion’s atmosphere reaction field affects both the absorption and emission spectra.1-4 The model was tested by observing the ground-state absorption spectrum as a function of electrolyte concentration. The red shift due to the specific interaction is gained when an ion replaces one solvent molecule in the first solvation shell of coumarin 153 according to Scheme 1, where the spectral shift in that case is due to the reduction of PSn absorption band and the growth of the PSn-1I spectral band. The nonspecific contribution to the red shift of the absorption spectra is due to the ionic atmosphere interaction with the coumarin molecular dipole. This contribution shifts the absorption bands of both species PSn and PSn-1I. We assumed that the shift is equal for both species. We obtained the best results when we assumed that band shift due to the ionic atmosphere is linear with salt concentration, U ) d[I] (where U is the ion atmosphere contribution to the spectral shift and d is the nonspecific spectral shift at 1 M electrolyte concentration and was found to be 450 cm-1. [I] is the electrolyte concentration in molar units). The calculated absorption spectra along with the experimental one are shown in Figure 14 for a few of the



tested solutions. For the fits shown in Figure 14, the specific ion/solvent exchange parameters are ∆ν0 ) 900 cm-1 and K1 ) 0.95. As can be seen, the agreement of the combined model with the experimental data is very good. Discussion The model we propose to describe the solvation of a probe molecule in ionic solution of low and medium concentrations is based on two distinct solvates, PSn and PSn-1. PSn denotes a probe molecule surrounded by n solvent molecules in the first solvation shell and PSn-1I describes a probe molecule into which a single cation is incorporated into the first solvation shell. In our case, a positive Li+ ion situated close to a negative charge of the coumarin dye caused a bathochromic shift of 1400 cm-1 in the fluorescence band. We used a diffusive model to calculate the exchange reaction dynamics where a solvent molecule in the first solvation layer of a coumarin dye is replaced by an ion. Eigen and Tamm25 derived a multistep process description for the ligand-water exchange reaction around a metal ion. The exchange rate was studied by relaxation techniques. Equation 9 describes a two-step complexation scheme, k12

k23

2+ 2- y z \ z Me2+(aq) + L2-(aq) y\ k21 Me (H2O)L k32 MeL

(a)

(9)

(b)

where Me2+ is a solvated metal ion, L2- is a solvated ligand, Me2+(H2O)L2- is an intermediate solvated ion pair, and MeL is the inner-sphere complex. According to Eigen and Tamm,25 the complexation mechanism involves the initial formation of an ion pair from the hydrated uncomplexed or partially complexed metal ion and the ligand. Then a water molecule from the inner hydration shell of the metal ion species is removed. This process is rate determining in the complex formation since it is much slower than the first step. An overall rate constant for the substitution of one molecule of water coordinated around the metal by the ligand can be written within the multistep process formalism.26 The values of water substitution measured by relaxation methods25 agree with the results by NMR of the rate of exchange of H2O between the first coordination sphere around the cations and the bulk solvent.27 Ultrasonic absorption studies of divalent metal sulfates in water lead to the conclusion that measurements should not be attributed to the relaxation of the ionic atmosphere. This also leads to the conclusion28 that the first step of the association process is a simple and discrete diffusion-controlled process leading to a solvated complex or ion pair. This solvated complex or ion pair, according to Eigen,28 is not one of the many possible configurations of the ionic atmosphere, but a true product of a discrete process. However, he pointed out that, at high electrolyte concentrations, a spectrum of relaxation times with the appearance of a broad absorption spectrum has to appear. Our data analysis of static and dynamic solvation of coumarin dye parallels Eigen’s model for the ion/ligand exchange reaction. In this study, we emphasized the diffusional nature of the ion/ solvent exchange reaction. Our diffusion model replaces the twostep processes of the Eigen model, given by eq 9. This diffusion model accounts for the transport of ions from a distance to the close vicinity of a coumarin dye molecule to form an ion pair of coumarin-solvent-ion. This step is fast for high salt concentrations and slow for low salt concentrations. The ion/ solvent exchange to form the coumarin-ion contact pair is a

slow process. Our findings are similar to the findings of solvent exchange reactions around the ion in water25 and in medium polar solvents.24,30 Electrolytes in media of low permittivity are strongly associated to form ion pairs, triple ions, and higher aggregates.13,24,29,30 Petrucci et al.24,30 used electrical conductance, ultrasonic absorption, and microwave complex permittivities techniques to study ion pairing statics and dynamics of LiClO4 and NaClO4 in tetrahydrofuran solutions. Their ultrasonic relaxation data show linearity between the inverse of the relaxation time, τ-1, and the electrolyte concentration. This was explained assuming that the relaxation process is due to an ion pair, AB, in equilibrium with a triple ion, A2B. Using a chemical kinetic rate equation, k1

the rate of triple ion formation AB + A f A2B was found to be 1.6 × 109 M-1 s-1.24,30 Using a diffusion-controlled expression similar to eq 6 gives kD ) 1.4 × 1010M-1 s-1, a value that is an order of magnitude larger value than the ultrasonic relaxation time. We found a good correspondence between the ultrasonic relaxation rate of Petrucci’s study and the exchange rate of ion/solvent around excited coumarin dye measured and discussed here. For the replacement reaction kD

P1Sn + I f P1Sn-1I in butyl acetate we found a rate constant at contact (a0 ) 5.8 Å) of k0 ) 3.2 × 109 M-1 s-1; this is twice the rate of triple ion formation in THF solutions. The diffusion constants of the Li+ ion in different solvents with similar polarity are approximately inversely related to the solution viscosity. For pure solvents and dilute electrolyte solutions, the viscosities of butyl acetate and THF are ηBA ) 0.732 centipouise and ηTHF ) 0.455 centipouise, respectively. If the hydrodynamic volume of the Li+ ion in both solvents is about the same, then according to the Stokes-Einstein equation, the ratio of the diffusion constants in these solvents is DBA/ DTHF ) 0.62. The range of electrolyte concentration in both Petrucci’s and our study is similar and the solvents' permittivities are also alike, 7 for THF and 5.1 for butyl acetate. In our case, the “ion”, I, can be a symbol for a solvated Li+ ion, and other ionic aggregates such as a solvated LiClO4 contact ion pair and Li(ClO4)2- or Li2ClO4+ triple ions. By simple hydrodynamic considerations, the values of the diffusion constant of all these species vary only by a factor of 3. From electrical conductance measurements and analysis using the Fuoss-Kraus theory, Petrucci deduced the ion pair and triple ion association constants.24 At high concentrations (>0.1 M), the triple ion concentration is dominant. The conductivity of the triple ions, ΛT0, is estimated to be 1/3Λ0 where Λ0 is the limiting conductivity value of LiClO4 ) 156 W-1 cm2 equiv-1. The conductivity data are related to the diffusion constants through the Stokes-Einstein equation. The calculated diffusion constant of the Li+ ion in THF is of the order of DLi+ ) 10-5 cm2 s-1. We used similar values for the simulations in this study. The question arises as to what the rate-limiting step in the ligand exchange mechanism is. Petrucci found activation energies of 1.5 kcal mol-1 for the triple ion formation reaction, a similar value to the activation energy of the viscosity of THF, Eaη ) 1.8 kcal mol-1. These similar activation energy values and the similar values of the diffusion-controlled rate, kD ) 4πN′Da0, and k0, prevent simple differentiation between the ion diffusion step and the exchange process itself. Summary and Conclusions The work we report here consists of steady-state absorption and emission as well as time-resolved fluorescence measurements of C153 in butyl acetate, LiClO4 solutions. In previous

1348 J. Phys. Chem. B, Vol. 104, No. 6, 2000 studies of the electrolyte contribution to the solvation energy of probe molecules in organic solvents, we adopted a model where nonspecific interaction of an ion atmosphere with a probe molecule occurs. We found that the relaxation times of ion atmosphere predicted by the Debye-Falkenhagen (DF) theory9 are shorter by more than an order of magnitude than the observed time-dependent Stokes shift relaxation times. In addition, we found that the measured solvation energies are larger than those predicted by the DF theory. In contrast to our model, Chapman and Maroncelli5 explained the slow dynamics of ion contribution to probe solvation by ion/solvent rearrangements in the first solvation shell of the probe. In this study, we adopted their interpretation of experimental data. We analyzed our data in terms of two distinct solvate configurations. The first species was a coumarin molecule surrounded by n solvent molecules in the first solvation shell, and in the second species one solvent molecule was replaced by a Li+ cation. We analyzed the absorption, the steady state emission, and the time-resolved emission of coumarin in salt solutions in a way directly related to the existence of these two distinct solvates, both in the ground and excited states. An important feature in our model is the diffusive nature of the exchange reaction of ion/solvent. This description accounts for the diffusive nature of the reaction, and a natural consequence of such a model is the viscosity dependence of the exchange reaction. Ultrasonic techniques have been used to study water exchange times for many ions.25 The exchange times are in the range of a few nanoseconds for monovalent ions such as the alkali ions used in our study. Petrucci24 used ultrasonic techniques to measure relaxation times of THF/LiClO4 solutions. A reaction rate constant of 1.6 × 109 M-1 s-1 for a Li+ to recombine with a LiClO4 ion pair, to form a triple ion, was calculated from ultrasonic relaxation time. We found the intrinsic rate constant for the exchange of a solvent molecule by an ion next to coumarin dye to be 3.2 × 109 M-1 s-1. In conclusion, we demonstrated how steady state and time-resolved spectroscopic methods provide unique information for ligand/solvent exchange processes. Steady-state spectroscopic techniques provide the energetics and equilibria constants of ion solvation while time-resolved spectroscopic techniques provide accurate dynamics. At high salt concentrations above 0.35 M, we find that the model fails to describe quantitatively the changes in the absorption spectrum. To account for the slight difference

Argaman and Huppert between the calculated spectrum and the experimental, we invoke a nonspecific contribution to the red shift by the outer sphere ions. Acknowledgment. We thank Prof. N. Agmon for discussions and comments. This work is supported by a grant from James Franck Binational German-Israeli program in Laser-Matter interaction. References and Notes (1) Huppert, D.; Ittah, V.; Kosower, E. M. Chem. Phys. Lett. 1989, 159, 267. (2) Huppert, D.; Ittah, V. In PerspectiVe in Photosynthesis; Jortner, J., Pullman, B., Eds.; Kluwer: Dordrecht, 1990; pp 301-316. (3) Ittah, V.; Huppert, D. Chem. Phys. Lett. 1990, 173, 496. (4) van der Zwan, G.; Hynes, J. T. Chem Phys. 1991, 152, 169. (5) Chapman, C. F.; Maroncelli, M. J. Phys. Chem. 1991, 95, 9095. (6) Neria, E.; Nitzan, A. J. Chem. Phys. 1994, 100, 3855. (7) Bart, E.; Huppert, D. Chem. Phys. Lett. 1992, 195, 37. (8) Bart, E.; Meltsin, A.; Huppert, D. J. Phys. Chem. 1994, 98, 10819. (9) Debye, P.; Falkenhagen, H. Physik. Z. 1928, 29, 121. (10) Debye, P.; Hu¨ckel, E. Physik. Z. 1923, 24, 185. (11) Onsager, L. Physik. Z. 1927, 28, 277. (12) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworth: London, 1959. (13) Fuoss, R. M.; Kraus, C. A. J. Am. Chem. Soc. 1933, 55, 1019. (14) Weast, R. C. CRC Handbook of Chemistry and Physics, 66th ed.; CRC Press: Boca Raton, FL, 1986. (15) Smoluchowski, M. Z. Phys. Chem. 1917, 92, 129. (16) Szabo, A. J. Phys. Chem. 1989, 93, 6929. (17) Moyland, C. R. J. Phys. Chem. 1994, 98, 13513. (18) Heitele, H. Angew. Chem., Int. Ed. Engl. 1993, 32, 359. (19) Passino, S. A.; Nagasawa, Y.; Fleming, G. R. J. Chem. Phys. 1997, 107, 6094. (20) Nibbering, E. T. J.; Wiersma, D. A.; Duppen, K. Chem. Phys. 1994, 183, 167. (21) Zolotov, B.; Gan, A.; Fainberg, B. D.; Huppert, D. J. Lumin. 1997, 72-74, 842. (22) Horng, M. L.; Gardecki, J. A.; Papazian, A.; Maroncelli, M. J. Phys. Chem. 1995, 99, 17311. (23) Ireland, J. F.; Wyatt, P. A. H. AdV. Phys. Org. Chem. 1976, 12, 131. (24) Jagodzinski, P.; Petrucci, S. J. Phys. Chem. 1974, 78, 917. (25) Eigen, M.; Tamm, K. Z. Elektrochem. 1962, 66, 93, 107. (26) Hammes, G.; Steinfeld, J. I. J. Am. Chem. Soc. 1962, 84, 4639. (27) See the following review: Petrucci, S. In Ionic Interactions; Petrucci, S., Ed.; Academic: New York, 1971. (28) Eigen, M.; De Mayer, L. In Techniques of Organic Chemistry; Weissbeiger, A., Ed.; Wiley (Interscience): New York, 1963; Part II, Vol. VIII. (29) Bjerrum, N. Kg Danske Videnski. Selskab. Skr. 1926, 7, 9. (30) Farber, H.; Petrucci, S. J. Phys. Chem. 1976, 80, 327.

Dynamics in Ionic Solutions - American Chemical Society

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