Reactive Dynamics in Confined Liquids: Ultrafast Torsional Dynamics

J. Phys. Chem. B 2009, 113, 1623–1631

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Reactive Dynamics in Confined Liquids: Ultrafast Torsional Dynamics of Auramine O in Nanoconfined Water in Aerosol OT Reverse Micelles Ismael A. Heisler, Minako Kondo, and Stephen R. Meech* School of Chemical Sciences and Pharmacy, UniVersity of East Anglia, Norwich NR4 7TJ, U.K. ReceiVed: October 10, 2008; ReVised Manuscript ReceiVed: NoVember 20, 2008

The effects of confinement on the ultrafast torsional reaction of auramine O in aqueous solution are investigated through ultrafast fluorescence up-conversion with 50 fs time resolution. The aqueous solution is confined in nanoscale water droplets by an ionic surfactant. The torsional motion is orders of magnitude slower in the confined droplets than in bulk aqueous solution. The dynamics become faster with increasing radius of the nanodroplet but never reach the bulk value, even when the radius is as large as 10 nm. Time-dependent fluorescence spectra were constructed and subsequently analyzed using a one-dimensional generalized Smoluchowski equation. An accurate description of the data was achieved using a time-dependent diffusion coefficient. This is suggested to arise because the medium friction reflects dynamics on a broad range of time scales spanning the reaction dynamics. The friction recovered suggests strongly hindered motion in the confined droplet and can be qualitatively related to solvation dynamics measured in AOT, consistent with auramine O torsional dynamics being accompanied by intramolecular charge redistribution. w0 ) [H2O]/[AOT]

1. Introduction In this work we address the influence of confinement on the dynamics of a chemical reaction in dispersed aqueous nanodroplets. In the bulk state water molecules form an extended intermolecular hydrogen-bonding network which is highly dynamic, with both bond lengths, H-bond partners, and network structure fluctuating on picosecond and subpicosecond time scales.1,2 Because of the existence of this network, water is expected to be uniquely sensitive to the presence of a surface or to confinement in three dimensions. The effects of confinement have particular significance because the aqueous environment plays a critical and active role in many biological processes. Molecular dynamics simulations and experiments have shown that the presence of an aqueous layer at the interface of a protein is crucial to processes such as protein folding3 and that the dynamics of this interfacial layer may be very different from those of bulk water.4 Similarly, the living cell is a very crowded environment, and the aqueous medium in which a wide variety of chemical transformations occur is often near a confining interface.5 Thus, the effects of confinement on the properties of water are of central importance in biophysics and have been very widely investigated.6 One of the most convenient and widely studied examples of confined water is the reversed or water-in-oil micelle formed by dispersed water nanodroplets in heptane stabilized by the surfactant bis(2-ethylhexyl) sulfosuccinate (Aerosol OT or AOT), usually in the form of its sodium salt. This ternary system yields size selectable spherical water droplets of narrow size distribution and mean radius rw determined through the relation7,8

rw ) 0.18w0 where * To whom correspondence [email protected].

may

be

addressed.

E-mail:

and the total water content can reach 50 wt %. Among the earliest studies of dynamics in AOT confined water droplets were the picosecond and subpicosecond measurements of excited-state solvation dynamics reported by Bhattacharyya and co-workers6,9-11 and Levinger and co-workers,12-16 respectively. These authors measured the time-dependent fluorescence Stokes shift of a solute molecule dissolved in the water nanodroplet and analyzed the data to yield the solvation time correlation function, which is closely related to the dynamics of the surrounding solvent medium.17,18 It was found that solvation dynamics were appreciably slower in AOT stabilized micelles than in bulk aqueous solution and occurred on a range of time scales, from subpicosecond to tens of picoseconds and longer.6,12-14 Measurements on the subpicosecond time scale showed that dynamics were severely hindered relative to bulk solution but became significantly faster with increasing rw.12,14 It was also observed that solvation dynamics were sensitive to the nature of the counterion12 and proposed that the slowest dynamics may reflect exchange between the different environments rather than extremely slow solvation times.6 An alternative route to probing the microscopic properties of the dispersed water phase of AOT micelles is the measurement of rotational diffusion times of fluorescence probe molecules through their anisotropy decay.19-21 These measurements revealed an rw-dependent and biexponential anisotropy decay. The longer reorientation time could be ascribed to rotation of the fixed probe in the entire micelle and the shorter one to orientational dynamics of the probe in the micelle’s water nanodroplet. Even for the largest micelle the fastest dynamics are significantly slower than for bulk water and dependent on the charge of the probe, suggesting hindered rotation even in the larger droplets.19 These measurements rely on the use of fluorescence probe molecules to determine the properties of the confined water. One difficulty with this is that the location of the probe is difficult to determine. Whether the probe is located in the

10.1021/jp808989f CCC: $40.75  2009 American Chemical Society Published on Web 01/15/2009

1624 J. Phys. Chem. B, Vol. 113, No. 6, 2009

Figure 1. Molecular structure of Auramine O and AOT.

surfactant head-group region, in the double layer which forms the interface, solvated wholly in the bulk nanodroplet, or in a distribution of these sites may significantly influence the results. More recently, static and time-resolved IR spectroscopy has been employed to observe the dynamics of dispersed water nanodroplets unperturbed by a probe molecule.22-29 The steady-state IR absorption of the water OH stretch is blue-shifted relative to bulk water.30,31 Three groups investigated H-bond dynamics through time-resolved IR spectroscopy, recording vibrational lifetimes, transient spectra, and orientational relaxation of the OH (or OD) oscillator.22-29 The results were discussed in terms of a core-shell model for the nanodroplet, in which the spectrum is assumed to comprise contributions from two components: a bulk water like core and interfacial (shell) water which has distinct and slower dynamics. Many results were consistent with this model, and the core water was thus found to show negligible effects of confinement.27,28 However, Piletic et al. found that the core-shell model (specifically in terms of an admixture w0 ) 2 (shell) and bulk water (core) dynamics) accurately reproduced only the steadystate spectra and vibrational population relaxation, but not measurements of spectral diffusion and orientational relaxation.24 This suggested that a more complex situation exists in the micelle and leaves open the possibility of an intrinsic confinement effect. Significantly, Fayer and co-workers subsequently investigated the influence of surfactant head-group charge.32 Dynamics were found to be similar for water nanodroplets of equal radius stabilized by either nonionic or ionic surfactants. This result suggested that confinement is a key factor in determining the dynamics of spherical water nanopools.32 Much of the importance of confined water comes about because it is the medium in which many chemical and biochemical reactions take place. Thus, it is important to understand how the observed slower dynamics influence the rate of chemical reactions in water nanodroplets. As a step in this direction we present here a detailed investigation of the excitedstate torsional reaction of the dye molecule auramine O (AO, Figure 1) in AOT inverse micelles. This builds on preliminary work by Hirose and co-workers33 and us.34 AO was selected as a suitable probe molecule because its excited-state chemistry has been very well characterized in bulk liquids and it is very water-soluble and exhibits a relatively simple reaction with a rate coefficient that is sensitive to the environment.35-38 Here we study the excited-state dynamics of AO in water, in AOT stabilized nanodroplets as a function of rw, and in a viscous solvent. The observations are made using the fluorescence upconversion method with sub-60 fs time resolution and are analyzed in terms of a one-dimensional generalized Smoluchowski model. The excited-state reaction of AO has been studied for more than 50 years, starting with the work of Oster and Nishijima,

Heisler et al. who observed a reciprocal relationship between fluorescence yield and η/T.39 This was interpreted as indicating intramolecular twisting about the carbon-phenyl bond in the excited state, promoting fast internal conversion. A flat potential energy surface for the twisting motion was assumed, allowing for diffusive reorientation of the ring, consistent with the observed η/T dependence. A more detailed picture of the excited-state dynamics of AO was obtained through ultrafast transient absorption and fluorescence measurements. Changenet et al. showed that the decay is to a nonemissive intermediate state, probably of internal charge transfer or charge shift character, which subsequently decays to the ground state.36 Van der Meer et al. made a detailed study of the initial excited-state reaction through solventdependent time-resolved fluorescence measurements. They successfully modeled the reaction assuming diffusive motion on a barrierless one-dimensional excited-state potential energy surface, using a Smoluchowski equation approach.38 Here we investigate the effect of confinement on this well-characterized excited-state reaction. The remainder of this paper is structured as follows. In the next section sample preparation and fluorescence up-conversion experiments are described. Following that, wavelength and timeresolved fluorescence data for AO in reverse micelles are presented as a function of rw and contrasted with aqueous and decanol solutions. The time-dependent fluorescence spectra are then calculated and modeled with a generalized Smoluchowski equation including an additional excited-state decay function. 2. Experimental Section 2.1. Sample Preparation. AO was purchased from SigmaAldrich as dye content > 80%. It was verified that the impurities did not affect the steady-state fluorescence and absorption spectra by comparing them to the spectra obtained from purified AO. 1-Decanol (99%), AOT (minimum 99%), and heptane (for HPLC, g99%) were also purchased from Sigma-Aldrich. AOT was purified by filtration with cold methanol and then recrystallization and dried over P2O5. Since the water-surfactant molar ratio of the sample solution is critical to determining the micelle size, the residual water content in AOT was measured by Fourier transform IR spectroscopy.40 This revealed ∼0.25 mole of water per mole of surfactant. This is a very low quantity of residual water for the micelle size in which we are interested in this experiment, and therefore the contribution to the micelle size is considered to be negligible. The other solvents were used without further purification. AO in bulk water and decanol samples were prepared by diluting concentrated AO in water and decanol stock solutions, respectively. For AOT micelle samples, 0.8 mol dm-3 AOT in heptane stock solution and 2 × 10-3 mol dm-3 AO aqueous solution were thoroughly mixed. The concentration of AO used was constant and chosen to yield less than one AO molecule per micelle for all the w0 studied. For time-resolved fluorescence measurements the sample was contained in a 1 mm fused silica cuvette and had an optical density of 0.3 at the 415 nm excitation wavelength. For steadystate measurements a 1 cm cuvette was used, and the sample was diluted 10 times. 2.2. Time-Resolved Fluorescence Setup. The femtosecond time-resolved fluorescence up-conversion setup used is shown in Figure 2. This setup has already been discussed in previous literature41,42 and so here we only highlight relevant details of our spectrometer. The Ti:sapphire oscillator produced pulses centered at 830 nm with a time duration of 20 fs at a 76 MHz repetition rate. The laser output was focused onto a 50 µm thick

Reactive Dynamics in Confined Liquids

Figure 2. Femtosecond fluorescence up-conversion experimental setup: PC ) prism compressor; B1 ) 50 µm BBO crystal; B2 ) 100 µm BBO crystal; DM ) dichroic mirror; DS ) delay stage; CM1 ) GSM012 chirped mirrors; CM2 ) GSM216 chirped mirrors; RO ) reflective objective; F1 ) GG455 Schott filter; F2 ) UG11 Schott filter; AL ) achromatic lens; C ) 1 mm cell; M ) monochromator; PMT ) photomultiplier tube; Ph C ) photon counter.

type I BBO crystal with a 150 mm focal length concave mirror to produce up to 15 mW 415 nm second harmonic excitation pump beam. Before the crystal the beam went through a fused silica prism compressor so that the pulses were transform limited at the crystal position, producing maximum second harmonic power. Gate (fundamental) and pump (second harmonic) beams were separated with a dichroic mirror. A pair of chirped mirrors (Femtolasers GSM216) was introduced into the gate beam to compensate for the dispersion introduced by the dichroic mirror and the focusing lens. Another pair of chirped mirrors (Femtolasers GSM012) was introduced into the pump beam path to compensate for the dispersion introduced by the sample cell window. The pump beam was focused with a 150 mm concave mirror to the center of a 1 mm path length cell which contained the sample. The collection of the fluorescence emitted from the sample and posterior imaging onto the sum-frequency crystal constitutes one of the main experimental challenges in ultrafast time-resolved fluorescence up-conversion.43 In our setup a microscope reflective objective was used, with a magnification of 15× and a back focal length of 160 mm. The advantage of working with such objectives is that they collect light with a fairly large angle (∼48°), have good magnification factors, and do not introduce delay times between different fluorescence wavelengths, which is particularly important for ultrafast time resolution. Finally, fluorescence and gate beams were crossed and focused onto a 100 µm BBO type I crystal, and the intensity of the up-converted light was detected by a photomultiplier and monochromator combination and measured with a photon counter. One of the filters (GG455, Schott) was placed after the objective (before the up-converting crystal) to attenuate the strong scattering from the pump beam, and another (UG11, Schott) was placed at the entrance slit of the monochromator. The delay stage and photon counter were controlled through LabVIEW software, and the best time resolution for the experiment was determined to be around 40 fs by recording the up-conversion of Raman scattering from pure heptane at 470 nm. 3. Results and Discussion 3.1. AO Photophysics in Water Nanodroplets. In Figure 3 normalized steady-state absorption and emission spectra for

J. Phys. Chem. B, Vol. 113, No. 6, 2009 1625

Figure 3. Absorption and emission spectra of AO in decanol (cyan), water (magenta), and in micelles for rw ) 1 nm (black), 2 nm (red), 10 nm (blue). The emission spectrum for the aqueous solution is noisier because of the low intensity (see text). A peak due to Raman scattering has been subtracted.

AO in AOT micelles are compared to those for bulk aqueous and decanol solutions. Decanol was chosen as a contrast to bulk water because it has a relatively low polarity and high viscosity. Absorption and emission spectra in decanol are to the blue of those for bulk water, consistent with the relative polarities of the two solvents. In addition, decanol shows increased absorption below 350 nm, consistent with formation of a minor fraction of the deprotonated form of AO (which is not excited by the 415 nm excitation pulse). All other spectra show the fully protonated form of AO. The absorption of AO in the smallest micelles is to the blue even of decanol but shifts to the red with increasing rw until, at rw ) 10 nm, the absorption spectra for bulk water and the micelle are essentially coincident. Thus, a progression from a dominant blue-shifted population in the smallest micelles (probably associated with interfacial sites) to one where a bulk water like environment dominates can be inferred from the absorption spectra. A similar trend is seen in the emission spectra, where decanol has the smallest Stokes shift, again consistent with its lower polarity. The Stokes shift is larger than for decanol in all the micelles and increases with increasing rw, until at rw ) 10 nm the spectrum has a similar peak wavelength to the aqueous solution, although the latter (which is poorly resolved) appears broader. It is significant that the fluorescence yield for AO in bulk water is considerably smaller than in the reverse micelle, even for rw ) 10 nm. This difference is more clearly illustrated through time-resolved data. The decay kinetics are wavelengthdependent (see below), but in Figure 4a we compare the fluorescence decay recorded at the peak of the emission intensity as a function of rw and solvent. The mean lifetime was determined and plotted (Figure 4b) where it is compared with the steady-state fluorescence yield (relative to the rw ) 1 emission). The key conclusion from Figure 4 is that the excitedstate decay of AO in water is dramatically slowed when the solution is dispersed as nanodroplets in AOT micelles. As the size of the micelle increases, both mean lifetime and fluorescence yield decrease, but neither approaches the value observed for bulk water; this behavior is thus in contrast to the electronic absorption spectra (Figure 3) discussed above which showed similar spectra for bulk water and the largest micelle. It is noteworthy that both steady-state and time-resolved data show little further decrease in yield beyond rw ) 5. It was established that the changes seen in Figure 4 are assignable to AO probing the rw-dependent properties of the


Heisler et al.

Figure 5. Relative fluorescence yield for AO in water:ethanol mixtures as a function of the mole fraction of water and the weighted mean dielectric constant (ε ) xwaterεwater + (1 - xwater)εethanol).

Figure 4. (a) Time-resolved emission profiles recorded at the peak of the emission spectrum for AO in water (magenta), decanol (cyan), rw ) 1 nm (black), 2 nm (red), 5 nm (green), and 10 nm (dark blue). (b) Average fluorescence lifetimes 〈τ〉 ) [∑iAiτ/∑iAi] (filled symbols) and relative fluorescence quantum yield (open symbols) measured as a function of rw.

water nanodroplet and not some other property of the sample. This was achieved by comparing the relative yield of AO fluorescence as a function of rw when either [AOT] or [H2O] was varied with the other fixed. The results were identical, confirming that Figure 4 indeed indicates an rw dependence of the fluorescence of AO. Although AO dispersed in nanodroplets has a much slower decay than in bulk water, it is still on average faster than in the viscous solvent decanol (Figure 4a). The much faster decay time for AO in bulk water than in decanol is apparently consistent with the strong viscosity dependence described previously by Oster and Nishijima39 and more fully characterized by van der Meer and co-workers in alcohol solutions.38 Thus, the result in Figure 4a might be interpreted in terms of a micelle “microviscosity” intermediate between those of decanol and water. However, as previously noted,34 AO in ethanol has a longer decay time than in aqueous solution, even though the viscosities are similar. This suggests the existence of an additional AO excited-state decay channel which operates in aqueous solution. This was investigated through measurements of the relative fluorescence yield for AO in water:ethanol mixtures. As the water content increases, the absorption spectrum undergoes a small monotonic shift to lower energy. The fluorescence spectrum also shifts to lower energy with increasing water content and undergoes a shape change similar to that seen between decanol and water (Figure 3), with intermediate compositions showing a mixture of the two spectra. However, the most striking result is the large decrease in fluorescence yield with increasing mole fraction of water (Figure 5). The

effect is too large and in the wrong direction to be ascribed to a medium viscosity effect (since water has a slightly higher viscosity than ethanol) and so represents a quenching channel specific to water. Two factors suggest that this quenching requires an aqueous environment around the AO molecule rather than an interaction with a single water molecule. First, the quenching is most evident at high water content and correlates with the shift in the ground-state (absorption) spectrum. Second, the quenching shows an almost linear dependence on aqueous composition of the bulk solvent, as measured by mole fraction or estimated dielectric constant (Figure 5). We will return to the potential significance of this additional quenching process in the analysis of the excited-state dynamics below. The fluorescence decay of AO was found to be wavelength dependent in all environments studied (bulk water, bulk decanol, AOT micelles with rw ) 1 and 5 nm); an example for rw ) 1 nm is shown in Figure 6a. A similar result was reported by van der Meer et al. in their study of AO in alcohol solvents.38 The mean decay time on the blue edge of the emission spectrum is much faster than on the red (Table 1). At all wavelengths the decay profile required at least a three-exponential fitting function for an accurate description, with three decaying components at all wavelengths except the longest (590 nm), which required an ultrafast risetime for an accurate fit. Fitting parameters are collected in Table 1. Such complex wavelength-dependent decay kinetics are often encountered in solvation dynamics.18 Thus, one possible explanation is that the permanent dipole of AO changes between ground and excited states, and the environment reorients to stabilize the new electrostatic interactions. However, solvation dynamics are often characterized by a well-resolved risetime in the fluorescence profile measured on the red edge of the emission, mirroring the ultrafast decay on the blue edge.18 The risetime observed here on the extreme red edge of the emission spectrum is a relatively minor component and is faster than the fastest decaying component. Thus, it is unlikely that these observations can be explained by solvation dynamics alone. An alternative and plausible explanation is that the AO molecules occupy a distribution of sites in the micelles, each characterized by a different decay time. In this model the decay time may range from bulk water (ca. 200 fs) to much longer times in the rigid head-group environment. However, only the fastest relaxation on the highest energy edge of the emission is similar to the relaxation time for AO in bulk water, while the


J. Phys. Chem. B, Vol. 113, No. 6, 2009 1627

Figure 6. (a) Wavelength dependence of the fluorescence decay of AO in rw ) 1 nm AOT micelles. (b) Calculated time-dependent emission spectra fit to a log-normal function.

TABLE 1: Results of Fitting the Time-Resolved Fluorescence of the rw ) 1 nm Micelle to a Triexponential Function λ/nm

τ1/ps

A1a

τ2/ps

A2

τ3/ps

A3

〈τ〉/ps

465 477 495 523 590

0.18 0.28 0.42 0.47 0.10

0.61 0.59 0.36 0.24 -0.29

1.60 2.23 2.93 3.33 4.29

0.30 0.31 0.24 0.27 0.52

11.10 12.95 14.98 17.01 22.03

0.09 0.10 0.09 0.10 0.19

1.61 2.16 3.13 4.47 9.08

a

Normalised amplitude of each exponential component.

decay profiles measured at lower energies have no 200 fs component (Table 1). This is certainly in contrast to expectations for a simple two-site model, given that bulk water has the shortest lifetime and the most red-shifted emission spectrum (Figure 3). Thus, a simple two-environment “core-shell” picture with the AO molecule occupying either the core or shell region of the micelles does not fit the observed kinetics, although a distribution of sites in the “shell” region remains possible. The most plausible explanation for the wavelength-dependent decay, and one which is consistent with previous studies of AO fluorescence,36,38 is that the complex profile reflects the dynamics of the molecules on the excited-state potential energy surface. To better characterize the fluorescence dynamics, we measured the fluorescence decay kinetics at a range of wavelengths across the emission profile and used these data to reconstruct time-dependent emission spectra.44 The resulting time-dependent spectral profiles are well fit by the log-normal function (Figure 6b). From the log-normal functions we can calculate the timedependent integrated fluorescence intensity, the mean frequency (first moment) of the emission, and the spectral width as a

Figure 7. (a) Time-dependent integrated fluorescence intensity (calculated from the integral of the log-normal function), (b) first moment of the time-dependent emission spectra, and (c) full width at halfmaximum for the time-dependent emission spectra: water (cross), decanol (triangle), rw ) 1 nm (diamond), and rw ) 5 nm (square).

function of time after excitation. These data were created for rw ) 1 and 5 nm AOT micelles, decanol, and water (Figure 7). These data bear out the previous qualitative conclusions. AO in water decays much faster than in any of the other environments, and the spectral red shift goes further and faster than in the other environments. The spectral shift and fluorescence decay are slower in rw ) 1 nm than rw ) 5 nm. Decanol has the slowest spectral shift and decay of fluorescence of all samples, but it does have a significant component which is as fast as the fastest relaxation in micelles. It is interesting to note that for the longer-lived samples the spectral evolution is dominated by relaxation on the subpicosecond time scale. In the next section we will attempt to quantitatively model these results using the one-dimensional generalized Smoluchowski approach, which has been extensively discussed for barrierless torsional dynamics,45,46 including AO,38 and for charge transfer reactions.47,48 3.2. Excited-State Dynamics. The application of diffusive models to analyze dynamics on reactive potential energy


Heisler et al.

surfaces has a long history. The earliest study of AO modeled the reaction as rotational diffusion of the phenyl ring on a flat excited-state potential.39 A more general treatment allows the inclusion of specific features of the (one-dimensional) excitedstate potential energy surface. In this approach the initial population on the ground-state surface is transferred to an unstable position on the excited-state surface. The subsequent evolution of the excited-state population, F(z,t), along the reaction coordinate (z) is given by the generalized Smoluchowski equation45,46

(

)

∂ ∂ ∂ 1 ∂ F(z, t) ) D(t) + S (z) F(z, t) - κΓ(z)F(z, t) ∂t ∂z ∂z kBT ∂z r (1) This equation allows the evolution of population density, F(z,t), on the reaction coordinate (assumed to be the twisting coordinate in AO) to be determined for any potential surface, Sr(z), and diffusion coefficient, D(t), which may be time dependent. In addition to the excited-state evolution, the final term allows for decay from the excited state to the ground state with a rate coefficient κ which may itself be a function of z (we employ the “Gaussian sink model”,46 and so Γ(z) is a Gaussian function). The excited-state dynamics of AO in bulk solution were studied in detail by Glasbeek et al.36,38,49 and Martin et al.,35 who found that the excited state relaxes to a dark intermediate state prior to decay to the ground state. Thus, following van der Meer et al.,38 the anharmonic excited-state potential Sr(z) is obtained from a coupling between the harmonic fluorescent state, Se(z), and a harmonic dark state, Sd(z)

1 1 Sr(z) ) (Se(z) - Sd(z)) - √(Se(z) + Sd(z))2 + 4C2 (2) 2 2 In eq 2 C is the coupling strength. During the evolution from the fluorescent to the dark state, the normalized coordinatedependent transition moment, M2(z), can be calculated from47,48,50

M2(z) )

C2 C + [Sr(z) - Se(z)]2 2

(3)

which is a decreasing function with increasing motion along z and decreases more sharply for weaker coupling. To compare the model with the experimental data, it is necessary to calculate the time-dependent spectra, given by47,48

Ifl ∝

∫ dz g(ν0(z), ν(z) - ν0(z))M2(z)F(z, t)ν3

(4)

in which g(ν0(z),ν(z) - ν0(z)) is a line-shape function (a lognormal function was used here) which describes the FranckCondon factor, where ν0(z) is the torsional-angle-dependent energy gap between the excited and ground states, that is, ν0(z) ) (Sr(z) - G(z))/h. The objective of the analysis is to determine D(t) by fitting (4) to the experimental time domain data (Figures 6 and 7) using (1)-(3). This requires a number of parameters: the line-shape function; a force constant, k, for the harmonic excited-state surfaces (assumed for simplicity to be the same in Se(z) and Sd(z)); a coupling strength, C; equilibrium energies (minima) for the potential surfaces, Seeq(z) and Sdeq(z). Further, the decay constant (κ) and location and width of the Gaussian sink must

be specified. Thus, there are numerous fitting parameters in the model, but there are also many constraints; the model must fit steady-state absorption and emission spectra as well as the timedependent fluorescence intensity, spectral shift, and width. The approach is illustrated here for the decanol solvent. In the first instance the Seeq(z), Sdeq(z), and g(ν0(z),ν(z) - ν0(z)) are selected on the basis of the steady-state spectra. Other parameters were varied to obtain the best fit to the time domain data, initially assuming only a fixed, time-independent, diffusion coefficient and no decay function. The temporal evolution of the excited-state population on the excited-state potential surface, Sr(z), for such a model is shown in Figure 8a and the resulting z-dependent transition moment in Figure 8b. The fits to the timedependent spectra are shown in Figure 8c-e. The best fit parameters are shown in Table 2, omitting the parameters which were common for all cases, specifically, force constant k ) 3500 cm-1, coupling strength C ) 800 cm-1, and temperature T ) 293 K. Evidently, the simplest form of the model only qualitatively reproduces the data, failing to accurately simulate the spectra (Figure 8c). The quality of the fit was improved somewhat by allowing the population to decay back to the ground state through a sink located at z0 ) 0.8, the minimum of Sr(z), with a width σ ) 0.2. The resulting time-dependent spectra are shown in Figure 8d. Even in this case a quantitative fit was not achieved, with the fit underestimating the rate of decay and spectral width at early times. A much more accurate representation of the spectra was obtained by allowing the diffusion coefficient to be time dependent (Figure 8e (see below)). The spectral shape and intensity in the micelle are a stronger function of time than in decanol solution, so to obtain acceptable fits to their time-dependent emission again required both a decay function (also located at z0 ) 0.8 with σ ) 0.2) and a time-dependent diffusion coefficient. The quality of the fit for rw ) 1 nm is displayed in Figure 9, and the best fit parameters for both micelle systems are collected in Table 2 along with the data for decanol and aqueous solution. Some discussion of the origin of a time-dependent diffusion coefficient is required. For a detailed discussion see the classical papers by Hynes and co-workers,51-54 which have been extended to the case of barrierless dynamics.45,46 The time-independent diffusion coefficient, used to calculate the result in Figure 8c, implies that motion along the coordinate experiences a frequencyindependent friction. This is represented in the relationship between D and η in the Stokes-Einstein-Debye equation for example. However, this static friction is only attained when the particle is dragged or rotated through the medium at a steady rate. If the particle dynamics are very fast for example in regions where the potential surface is steep (as seems to be the case for the picosecond and subpicosecond dynamics on the AO excitedstate surface), this steady-state friction is never attained. In this case the frequency dependence of the friction must be taken into account. Essentially, on these ultrafast time scales only the high-frequency components of the friction can influence motion along the reaction coordinate. At later times, where the dynamics have slowed lower frequency dynamics become important. The formal definition of D(t) for a given potential energy surface was given by Hynes53,54 and Oxtoby and co-workers:55,56

D(t) ) -〈(δz)2〉

˙ (t) ∆ ∆(t)

(5)

in which ∆(t) is the normalized reaction coordinate time correlation function ∆(t) ) 〈δz · δz(t)〉/〈(δz)2〉 and δz ) z - zeq. In (5) 〈(δz)2〉 describes the mean-square fluctuation of the


J. Phys. Chem. B, Vol. 113, No. 6, 2009 1629 TABLE 2: Parameters Used in Fitting Time-Dependent Emission Spectra to the Generalized Smoluchowski Equation D(t)a/ps-1 medium b

decanol decanolc decanold rw ) 1 nm rw ) 5 nm water

Se/cm-1

Sd/cm-1

a1

22 480 22 480 22 480 22 640 22 230 22 120

21 610 21 610 21 610 21 790 21 380 21 270

0.56 0.56 0.83 0.94

τD1 /ps

τD2 /ps

κ/ps-1

D ) 0.01 0.44 0.58 0.44 0.58 0.17 0.32 0.06 0.33 D ) 0.75

4.30 7.50 1.60 1.20

0 0 0.05 0.14 0.26 1.80

a2

a Fitting parameters with bi-exponential D(t), D(t) ) a1 exp(-τD1 / t)+a2 exp(-τD2 /t). b Time independent D and κ ) 0 assumed. c Time dependent diffusion coefficient, D(t), assumed and no sink, that is, κ ) 0. d Time dependent D and sink allowed.

Figure 9. (a) Fit to the time-dependent spectra of AO in AOT rw ) 1 nm using the time-dependent diffusion coefficient and decay through a Gaussian sink. Parameters are shown in Table 2. (b) Fit to the mean frequency (first moment) and (c) spectral width as a function of time.

Figure 8. (a) Temporal evolution of the population distribution on the reactive potential energy surface. (b) z-dependent transition moment employed in calculation of the transient emission spectra. (c) Theoretical fit (line) to the experimentally determined log-normal representation of the time-resolved emission spectra (circles). In the model a timeindependent diffusion coefficient was used with no sink decay function. (d) as for (c), but allowing the population to decay through a Gaussian sink. (e) as for (d), but including a time-dependent diffusion coefficient (see text and Table 2).

reaction coordinate and can be completely determined in terms of the force constant, k, and the temperature of the sample, T, through the relation 〈(δz)2〉 ) (βk)-1, where β ) (kBT)-1.51 In our fitting 〈(δz)2〉 ) 0.059. The exact description of how the frequency-dependent friction determines D(t) is in principle possible from molecular dynamics calculations, but a more direct

experimental approach is preferred (and is probably essential for complex media like the inverse micelle). One useful basis for calculating D(t) is the experimentally measured solvation time correlation function, C(t), determined from time-resolved fluorescence Stokes shift experiments for example.44 This is certainly appropriate for charge transfer reactions47,48,51 since C(t) reflects the response of the medium to a sudden change in solute dipole moment, so similar dynamics are expected to promote an electron transfer reaction. Since it has been suggested that the dark state to which AO decays is itself a charge transfer (or charge shift) state,35 C(t) also seems a good starting point for the current calculations. The C(t) functions have been determined for a number of media, including decanol44 and AOT reverse micelles.14 In both cases they are characterized by a multiexponential time profile with a subpicosecond response assigned to nondiffusive orientational (librational) dynamics in the solvent cage, followed by a slower diffusive relaxation, which reflects solvent size and viscosity.


Figure 10. Time-dependent ∆(t) functions (as used in eq 5) (solid lines, decanol (cyan), rw ) 1 nm (black), and 5 nm (green)) compared with the original C(t) (dash lines) for decanol (cyan)18 and for rw ) 0.9 nm (black).14

Thus, a guide to D(t) can be obtained by equating ∆(t) with C(t). Our approach has been to use the experimentally determined solvation dynamics correlation function as a starting point and adjust them to refine the fit to the experimental data. The biexponential ∆(t) obtained from the best fits (in conjunction with the parameters in Table 2) are shown in Figure 10 along with those calculated from the original C(t), and the numerical results are shown in Table 2. The final ∆(t) have in common with the original C(t) a strongly bimodal profile with both subpicosecond and slower components (Figure 10). The most striking difference is that the slower components of the C(t) evidently play a much less significant role in the reaction dynamics than in the solvation. One interpretation of this is that the fast nondiffusive component of the medium response is mainly responsible for motion from the Franck-Condon excited state to the dark state. However, there is no obvious difference in the energetics of the dark and directly excited states in decanol and rw ) 1 nm that would lead to the suppression of the long time component in the latter but not the former (Table 2). The effect of medium on the emissive state energy is in line with the shifts seen in the absorption spectra (Figure 3). The simulations suggest that the dark state is shifted to somewhat lower energy in the aqueous environment, which is consistent with the assignment of charge transfer character.35 An alternative assignment is that the fast component in the medium response regulates population of the dark state through conformational reorganization, but in aqueous solution the dark state (or rather the mixed state) formed is rapidly quenched to repopulate the ground state, such that the slower component of C(t) is not probed by the time-resolved fluorescence of AO. This recalls the strong specific quenching mechanism which was observed for AO in ethanol:water mixtures (Figure 5) and is supported by the numerical results (Table 2). In the micelles the decay parameter κ is 3 times larger in the rw ) 1 nm nanodroplet than in decanol and increases further in the larger micelle. Thus, the present results are consistent with the timedependent diffusion controlling the ultrafast dynamics on the excited-state surface, leading to formation of a charge-separated “dark” state. However, in aqueous environments the “dark” state exhibits an additional specific quenching of the excited state, which is absent in decanol. The quenching effect is very much more marked for AO in water (Table 2). 4. Conclusions The dynamics of the reactive probe molecule AO have been studied in nanoconfined water in an AOT micelle and modeled

Heisler et al. with a one-dimensional generalized Smoluchowski equation previously used to study AO in solution.38 The effect of confinement is a dramatic slowing down in the excited-state torsional motion which leads to excited-state quenching. The effect is strongest in the smallest micelle and decreases with increasing rw. However, even in the largest micelle the AO dynamics do not approach to those seen in bulk water. Evidently, the “core-shell” model is not useful in understanding the conformational dynamics of a large molecule such as AO in inverse micelles. This may be due to the preferential location of AO in the ionic head-group region of the inverse micelle, where water molecules are believed to be strongly immobilized, as was already proposed for AO.57 This possibility is investigated further by modifying the charge in the head group in a separate publication.58 Alternatively, it may be that medium dynamics controlling intramolecular conformational motion in a large molecule are inherently slower than dynamics probed by transient IR spectroscopy measurements of orientational motion of isolated OD bonds or single water molecules. Studies of different reactive probes and in a range of confining media are in progress to address these points. Acknowledgment. We are grateful to EPSRC for financial support. We also thank Profs. Taiha Joo (POSTECH, Korea) and Tahei Tahara (RIKEN Japan) for advice on construction of the up-conversion spectrometer and Dr. David Steytler (UEA) for assistance with the micelle preparation and characterization. References and Notes (1) Eaves, J. D.; Loparo, J. J.; Fecko, C. J.; Roberts, S. T.; Tokmakoff, A.; Geissler, P. L. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 13019. (2) Cowan, M. L.; Bruner, B. D.; Huse, N.; Dwyer, J. R.; Chugh, B.; Nibbering, E. T. J.; Elsaesser, T.; Miller, R. J. D. Nature (London) 2005, 434, 199. (3) Ebbinghaus, S.; Kim, S. J.; Heyden, M.; Yu, X.; Heugen, U.; Gruebele, M.; Leitner, D. M.; Havenith, M. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 20749. (4) Qiu, W. H.; Zhang, L. Y.; Okobiah, O.; Yang, Y.; Wang, L. J.; Zhong, D. P.; Zewail, A. H. J. Phys. Chem. B 2006, 110, 10540. (5) Persson, E.; Halle, B. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 6266. (6) Bhattacharyya, K.; Bagchi, B. J. Phys. Chem. A 2000, 104, 10603. (7) Rees, G. D.; Robinson, B. H. AdV. Mater. 1993, 5, 608. (8) Day, R. A.; Robinson, B. H.; Clarke, J. H. R.; Doherty, J. V. J. Chem. Soc., Faraday Trans. 1 1979, 75, 132. (9) Ghosh, S.; Mandal, U.; Adhikari, A.; Dey, S.; Bhattacharyya, K. Int. ReV. Phys. Chem. 2007, 26, 421. (10) Dutta, P.; Bhattacharyya, K. J. Chem. Sci. 2004, 116, 5. (11) Bhattacharyya, K. Acc. Chem. Res. 2003, 36, 95. (12) Pant, D.; Riter, R. E.; Levinger, N. E. J. Chem. Phys. 1998, 109, 9995. (13) Riter, R. E.; Undiks, E. P.; Levinger, N. E. J. Am. Chem. Soc. 1998, 120, 6062. (14) Riter, R. E.; Willard, D. M.; Levinger, N. E. J. Phys. Chem. B 1998, 102, 2705. (15) Corbeil, E. M.; Riter, R. E.; Levinger, N. E. J. Phys. Chem. B 2004, 108, 10777. (16) Harpham, M. R.; Ladanyi, B. M.; Levinger, N. E. J. Phys. Chem. B 2005, 109, 16891. (17) Gardecki, J.; Horng, M. L.; Papazyan, A.; Maroncelli, M. J. Mol. Liq. 1995, 65-6, 49. (18) Horng, M. L.; Gardecki, J. A.; Papazyan, A.; Maroncelli, M. J. Phys. Chem. 1995, 99, 17311. (19) Dutt, G. B. J. Phys. Chem. B 2008, 112, 7220. (20) Spry, D. B.; Goun, A.; Glusac, K.; Moilanen, D. E.; Fayer, M. D. J. Am. Chem. Soc. 2007, 129, 8122. (21) Visser, A.; Vos, K.; Vanhoek, A.; Santema, J. S. J. Phys. Chem. 1988, 92, 759. (22) Park, S.; Moilanen, D. E.; Fayer, M. D. J. Phys. Chem. B 2008, 112, 5279. (23) Moilanen, D. E.; Levinger, N. E.; Spry, D. B.; Fayer, M. D. J. Am. Chem. Soc. 2007, 129, 14311. (24) Piletic, I. R.; Moilanen, D. E.; Spry, D. B.; Levinger, N. E.; Fayer, M. D. J. Phys. Chem. A 2006, 110, 4985. (25) Tan, H. S.; Piletic, I. R.; Fayer, M. D. J. Chem. Phys. 2005, 122.

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Reactive Dynamics in Confined Liquids: Ultrafast Torsional Dynamics

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