95

J. Phys. Chem. B 2008, 112, 14959–14970

14959

Solvation and Solvatochromism in CO2-Expanded Liquids. 3. The Dynamics of Nonspecific Preferential Solvation Chet Swalina, Sergei Arzhantsev, Hongping Li,† and Mark Maroncelli* Department of Chemistry, Penn State UniVersity, 104 Chemistry Building, UniVersity Park, PennsylVania 16802 ReceiVed: June 25, 2008; ReVised Manuscript ReceiVed: September 5, 2008

Subpicosecond time-resolved fluorescence of trans-4-dimethylamino-4′-cyanostilbene (DCS) is used to measure solvation dynamics in the gas-expanded liquid (GXL) system CH3CN + CO2 at 25 °C along the liquid-vapor coexistence curve. These measurements are supplemented by measurements of the steady-state solvatochromism of DCS and of its rotation and isomerization times. Molecular dynamics computer simulations and a semiempirical spectral model that reproduces the observed solvatochromism in this system are used to interpret the experimental results. Simulations indicate that at compositions of xCO2 > 0.5, the cybotactic region surrounding DCS is enriched in CH3CN molecules, and the extent of this enrichment is greater in S1 than that in S0. Solvation dynamics are dominated by the CH3CN component. These dynamics are biphasic, consisting of a subpicosecond inertial component, followed by a slower picosecond component, related to the redistribution of CH3CN molecules between the cybotactic region and the bulk solvent. I. Introduction Gas-expanded liquids (GXLs), conventional organic solvents pressurized with a near-critical gas such as CO2, are currently being explored as pressure-tunable media in a variety of applications.1-3 In parallel with applications-oriented research, computer simulations are being used in fundamental studies of their phase behavior, structure, and transport properties.4-14 The nature of the solvation environment provided by this new class of solvents is being probed through electronic15-19 and vibrational20-22 spectroscopic measurements on reporter solutes. Recently, two groups have also combined spectroscopic measurements and computer simulations in an effort to obtain a molecular-level view of solvation in GXLs.15,23-26 Eckert, Hernandez, and co-workers23,24 measured the electronic absorption and emission spectra of the solvatochromic probe coumarin 153 (C153) in two GXLs, acetone + CO2 and methanol + CO2, and simulated the observed spectral shifts using classical molecular dynamics simulations. In closely related work, our group25,26 has measured and simulated the absorption and emission shifts of both C153 and an anthracene-based chromophore in CO2-expanded cyclohexane, acetonitrile, and methanol. The central result of both studies was to show that the local environment surrounding a solute such as C153 is significantly enriched in the polar liquid component compared to the bulk solvent but that the extent of this preferential solvation is much smaller than naı¨ve analyses of solvatochromic shifts suggest. The present paper extends our previous experiment-simulation studies of solvation and solvatochromism in GXLs9,25,26 to consider the time dependence of solvation. Here, we report measurements of solvation dynamics in CH3CN + CO2 at 25 °C along the liquid-vapor coexistence curve using Kerr-gated emission measurements27 on the solvation probe trans-4dimethylamino-4′-cyanostilbene (DCS). DCS is a probe of nonspecific solvation28 whose large dipole change upon excita* To whom correspondence should be addressed. E-mail: maroncelli@ psu.edu. † Current address: Department of Chemistry, Zhengzhou University, No. 100 Science Road, Zhengzhou, Henan 450001, China.

tion (∼14 D29) and isomerization-limited lifetime (99.995%) and was passed through activated charcoal and O2 traps prior to use. The spectroscopic cell used for steady-state and timecorrelated single-photon counting (TCSPC) experiments was a three-window stainless steel high-pressure cell described previously.26 Temperature (298.2 ( 0.2 K) and pressure ((35 kPa) regulations, as well as operating procedures, were the same as those described in ref 26. Absorption spectra were recorded using a Hitachi UV-3000 UV-vis spectrophotometer and corrected emission and excitation spectra measured using a Spex Fluorolog F212 fluorometer. Fluorescence lifetimes and anisotropy decays were collected using a TCSPC system and analysis methods described previously.44 The excitation and emission wavelengths used here were 386 and 510 nm, respectively, and the instrumental response was approximately 25 ps (fwhm). For Kerr-gated emission (KGE) measurements, a two-window stainless steel cell having a 2 mm path length was used. This cell was the same as the one used previously for supercritical fluid experiments,45 except for the addition of a 40 mL stainless steel cylinder to the top of the cell to accommodate the larger liquid volumes needed for the present experiments. The temperature of this cell was monitored by a thermocouple embedded in the cell wall and regulated to 298.2 K using a combination of cartridge heaters and heating tape wound around the expansion cylinder and controlled by an Omega CN77333 temperature controller. The overall temperature stability was (0.2 K. Approximately 1 mL of a solution of DCS in acetonitrile was loaded into the evacuated cell through a syringe connected to one of the input ports. CO2 was then added to the cell using a syringe pump (ISCO 100DM). Pressures were measured using an Omega PX 602 transducer with an accuracy of (35 kPa. Mixture compositions were determined from the measured temperature and pressures and the coexistence data of Kordikowski et al.46 Good mixing was ensured using a highpressure flow pump (Eldex Laboratories model A-30-S), which circulated liquid from the bottom of the cell back to the top. The sample inside of the cell was also constantly stirred by a small X-shape stirring bar. The femtosecond KGE spectrometer employed here has been described in detail elsewhere.27 Excitation and gating pulses were provided by the 150 fs output of an amplified Ti:Sapphire laser (Coherent, RegA9050 /Mira900), and the gated emission spectrum was detected by a spectrograph + cooled CCD camera combination. The instrumental response, measured using the Raman scatter from neat acetonitrile, was 450 fs (fwhm). The 2D data sets (intensity versus time and wavelength) collected in these experiments were corrected for temporal dispersion and spectral sensitivity using an in-house program. The data were then fit to partially remove the temporal broadening caused by the finite instrument response time using two different methods. In the first method, the spectra were integrated in wavelength to obtain their zeroth and first frequency moments as functions of time. These two time-dependent functions were then simultaneously fit to sums of exponentials convoluted with the instrument response in order to determine the time evolution of the average (first moment) frequency νj(t). In the second method, fluorescence decays at 200 wavelengths were individually fit to a model function consisting of a sum of four exponentials using an iterative reconvolution procedure. Timeresolved spectra were then reconstructed, and νj(t) data were determined by fitting spectra at a series of times to log-normal line shapes. Details of these procedures are provided in ref 27.

Swalina et al. Like most stilbenes,47 DCS undergoes a trans-cis isomerization when exposed to visible light.48-50 As discussed in ref 28, the presence of this photoreaction means that care is required to obtain absorption spectra and quantum yields uncontaminated by the presence of cis isomer. Luckily, the cis isomer does not fluoresce measurably so that the spectral dynamics of most interest here are not affected. B. Simulation Models and Methods. Molecules in this study were modeled as rigid collections of interaction sites with the interactions between sites being of the Lennard-Jones (12-6) plus Coulomb form. Models previously reported in the literature for the neat liquids were used to represent the individual components in the mixtures. The CO2 model used was the threesite EPM2 model of Harris and Yung.51 The acetonitrile model, also a three-site model, was that developed by Edwards et al.52 For a given mixture composition, simulations were performed at the volumes determined from the experimental densities at coexistence. As shown in ref 9, under these conditions, the models reproduce known equilibrium and dynamical properties of the experimental mixtures with good accuracy. For the solute DCS, the same all-atom representation used previously in simulations of supercritical fluoroform45 was employed. The structure of DCS was assumed to be the same in the S0 and S1 states. This structure was obtained from geometry optimization at the RHF/6-31G(d) level; however, the stilbene framework was constrained to be planar instead of the slightly twisted conformation actually predicted by this level of theory.28 (We note that some high-level calculations53 predict significant geometry change, and a twisted intramolecular charge-transfer state formation occurs subsequent to excitation. However, as discussed at length in ref 28, experimental data rule out this possibility.) Atomic charges for the S0 state were obtained by fitting the electrostatic potential to the relaxed MP2/6-311G(d,p)//RHF/ 6-31G(d) electronic density using the method of Singh and Kollman.54 S1 s S0 atomic charge differences were calculated using semiempirical AM1/CI calculations. In contrast to ref 45, the AM1/CI charge differences were not used directly but instead were scaled by a factor of 1.72, the factor required to reproduce the experimental Stokes shift of DCS in CH3CN.28 The need for such scaling results from an insufficient dipole moment change predicted by AM1/CI calculations (8.3 compared to 14 D estimated from experiment29), as was previously discussed in ref 45. The S1 atomic charges were then obtained by summing the S0 and S1 s S0 charge differences. Finally, the parameters specifying the Lennard-Jones interactions of the solute were taken from the OPLS-AA force field.55 The coordinates of DCS, the Lennard-Jones parameters, and various charges are provided in the Supporting Information (Tables SI-3 and SI-4). After completing extensive simulations using aforementioned scaled AM1/CI charge differences, we became aware of another procedure to obtain S0/S1 atomic charges which relies solely on ab initio calculations. The calculations are based on the second-order approximate coupled cluster model56 with the resolution of the identity approximation (RICC2).57,58 Charges obtained using this method require no scaling and yield quantitative results for the S0 f S1 dipole moment change and semiquantitative values for the Stokes shifts of DCS. Comparisons of the energies and dynamics simulated using the scaled AM1/CI and the RICC2 charge sets for DCS in neat CH3CN, neat CO2, and in a xCO2 ) 0.95 mixture are provided in the Supporting Information. On

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J. Phys. Chem. B, Vol. 112, No. 47, 2008 14961

the basis of the similar solvation energies and dynamics found using these two charge sets, we have concluded that, despite the large and ad hoc adjustment required, scaled-AM1/CI charges are suitable for modeling DCS in the CH3CN + CO2 mixtures considered. Thus, all results reported here are based on these AM1/CI charge differences. Simulations were performed using a modified version of the DL_POLY program.59 The systems simulated corresponded to DCS in neat CH3CN and CO2 as well as in CH3CN + CO2 mixtures with xCO2 ) 0.262, 0.461, 0.660, 0.840, and 0.950. Each system consisted of a single DCS molecule solvated by a total of 1000 solvent molecules. Simulations were performed in the NVT ensemble at a temperature of 298 K using a Nose´-Hoover thermostat.60 Volumes were determined from the experimental liquid densities at coexistence,46 assuming a fixed solute partial molar volume of 207 cm3/mol.26 In the case of neat CO2, the volume was that appropriate to a pressure of 6.5 MPa.9 Cubic periodic boundary conditions were applied, and longrange interactions were treated with the standard Ewald method. Rigid body equations of motion were integrated using a leapfrog scheme with a 2 fs time step. Systems were equilibrated for at least 500 ps after inserting the DCS solute into a pre-equilibrated solvent mixture. In the case of equilibrium simulations, trajectory data were collected for a period of 5 ns in 200 ps blocks, and the blocks were averaged to obtain estimates of statistical uncertainties (reported as standard errors of the mean). Nonequilibrium (NVE) simulations of the S0 f S1 solute perturbation consisted of 1000 trajectories, each of 50 ps duration, initiated from samples selected from a 5 ns equilibrium simulation of S0. The main observable of interest in this work is the spectral response function defined in terms of the temporal evolution of fluorescence frequencies as

ν¯ (t) - ν¯ (∞) Sν(t) ) ν¯ (0) - ν¯ (∞)

(1)

These spectral dynamics primarily reflect changes in the energy gap, ∆U, resulting from differences between solute-solvent interactions (U) in the ground and excited states. Assuming the instantaneous frequency shift caused by these interactions to be given by

hν - hνgas ) ∆U ≡ U(S1) - U(S0)

)

h(ν¯ - ν¯ gas)em ) 〈∆U〉eq 1

(4b)

Contributions to U arise from short-range repulsion, dispersion, electrostatic, and induction interactions.61 Previous simulations in GXL mixtures26 and in neat solvents62 have demonstrated that solvent-induced spectral shifts of molecules like DCS can be successfully modeled by considering only independent contributions from electrostatic and dispersion interactions

∆U ) ∆Uel + ∆Udsp

(3)

where 〈∆U(t)〉1 represents an ensemble average of ∆U at time t after changing the solute charge distribution from that of S0 to that of S1. The 〈x〉eq i denotes an equilibrium ensemble average of x in the presence of solute electronic state i ) 0 or 1. In this notation, the solvent-induced spectral shifts of the absorption

(5)

which is the viewpoint adopted here. In so doing, we assume that changes to inductive interactions, which are typically small in comparison to electrostatic and dispersion interactions,61 are effectively incorporated into the former terms, both by virtue of the use of “solution-phase” charges for solvent molecules in calculating ∆Uel (i.e., by using charges previously parametrized to reproduce solution-phase properties with a nonpolarizable model) and by the empirical parametrization of ∆Udsp described below. The electrostatic contribution is calculated using

∆Uel )

∑∑ R

j

∆qRqj rRj

(6)

where the indices R and j denote solute and solvent atoms, respectively. The ∆qR’s are S1 s S0 differences in effective solute charges, and the qj’s are solvent charges.63 Dispersion interactions are modeled by assuming that the (S1 - S0) change between a given solute site R and the solvent is proportional to the ground-state value of this interaction.64 Using the LennardJones terms in the potential to represent the S0 dispersion contribution

∑∑ R

j

4εRjσ6Rj

(7)

r6Rj

we assume

∆Udsp ) -

〈∆U(0+)〉1 - 〈∆U(∞)〉1 eq 〈∆U〉eq 0 - 〈∆U〉1

(4a)

(2)

〈∆U(t)〉1 - 〈∆U(∞)〉1 〈∆U(t)〉1 - 〈∆U〉eq 1

h(ν¯ - ν¯ gas)abs ) 〈∆U〉eq 0

Udsp(S0) ) -

the experimentally observed spectral response function may be modeled as

Sν(t) T S∆U(t) )

and steady-state emission spectra (assumed equilibrated) are given by

∑∑ R

j

fRC(0) Rj

C(0) Rj ≡

4εRjσ6Rj r6Rj

(8)

where εRj and σRj are the Lennard-Jones well depth and size parameters between solute site R and solvent site j. On the basis of our previous calculations of solvent-induced spectral shifts in GXLs,26 we chose the factor fR to be the same for all solute atoms in the π system of DCS and zero elsewhere. This factor, which has a value of ∼0.2, is used as the single model parameter to be adjusted to achieve agreement between simulated and observed spectral shifts. Instead of performing the nonequilibrium simulations required to calculate S∆U(t) according to eq 3 for each CH3CN + CO2

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Swalina et al.

composition, we first approximated S∆U(t) from equilibrium trajectory data assuming a linear solvation response

(i) S∆U(t) = C∆U (t) ≡

〈δ∆U(0)δ∆U(t)〉ieq 〈(δ∆U)2〉ieq

(9)

where δ∆U ) ∆U - 〈∆U〉eq denotes a fluctuation in ∆U and (i) (t) is the solvation time correlation function observed in an C∆U ensemble in equilibrium with solute state i. For any CH3CN + (0) (t) CO2 composition in which the linear response condition C∆U (1) (t) breaks down, we have also calculated S (t) directly = C∆U ∆U from a nonequilibrium simulation. III. Experimental Results Representative absorption and emission spectra of DCS in CH3CN+CO2 mixtures are shown in the top panel of Figure 1. Absorption spectra of DCS in these mixtures are relatively structureless, whereas the emission spectra show some vibronic structure at the highest CO2 concentrations. Also shown in Figure 1 are estimates of the “t ) 0 emission” spectra, the spectra expected after vibrational relaxation but before solvent relaxation occurs. These spectra were calculated using a procedure described in ref 28. As shown here, all three types of spectra shift to the blue with increasing CO2 concentration. The first moment frequencies, plotted in the bottom panel of Figure 1, increase by 760 cm-1 in absorption and 1400 cm-1 in emission over the experimentally accessible range of 0 e xCO2 e 0.85. (This range is limited by the low solubility of DCS in CO2-rich mixtures.) The solvent-induced contribution to the Stokes shift is given by the difference between the t ) 0 and steady-state emission curves, which decreases from 3300 to 2500 cm-1 over the experimental range. Time-resolved emission spectra at the extreme compositions are shown in Figure 2. These spectra were obtained by spectral reconstruction after iterative fitting of the Kerr-gated decay data. By virtue of this fitting procedure, the effects of the finite instrumental response (450 fs fwhm) are partially removed from the spectra. To within the uncertainties of these data, we observe only a continuous shift of a relatively featureless spectrum, without any obvious changes in shape or width. The extent of the dynamic Stokes shift observed here varies from ∼2800 cm-1 in neat acetonitrile to ∼2000 cm-1 at xCO2 ) 0.85 (Table 1). As shown in the bottom panel of Figure 1, the observed Stokes shifts, indicated by the separations between the dashed lines, are smaller than the estimated values by an average of 30%. This shortfall in the observed shift probably results from a combination of the limitations of the KGE instrument and from inaccuracies in the estimation of the t ) 0 spectra ((300 cm-1). Figure 3 shows time evolution of the first moment frequencies νj(t) used to estimate the experimental solvation response functions. To within uncertainties, these νj(t) curves can be represented as biexponential functions of time using

ν¯ (t) ) ν¯ (∞) + ∆ν¯ {f1 exp(-t/τ1) + (1 - f1)exp(-t/τ2)} (10) Results of such fits are summarized in Table 1. As shown there, the component times tend to increase with increasing xCO2. In all cases, there is a subpicosecond component, which is probably broadened somewhat by our limited time resolution, together with a slower component whose time constant increases to several picoseconds at the highest CO2 concentrations.

Figure 1. Top Panel: Steady-state absorption, emission, and estimated time-zero spectra of DCS at three compositions, xCO2 ) 0, 0.45, and 0.84 (left to right). Bottom Panel: First moment frequencies of the steady-state absorption, emission, and estimated time-zero emission spectra. The curves drawn on this figure are fits used to interpolate between data points (open symbols). “∆νest” indicates the magnitude of the estimated dynamic Stokes shift. The smaller filled symbols connected by dashed lines show values of ν(0) and ν(∞) measured in time-resolved experiments.

Figure 2. Normalized time-resolved emission spectra at the extremes of the composition range studied. Spectra (right to left) are shown at the series of the nine times indicated. The spectra here have been corrected for the spectral response of the KGE spectrometer and each wavelength fit to a sum-of-exponentials representation in order to partially remove the effects of instrumental broadening.

IV. Experiment-Simulation Comparisons Figure 4 compares the observed frequencies and solventinduced Stokes shifts to simulated values. Simulations provide frequency shifts from the gas phase. Unfortunately, the gasphase frequencies of DCS are not available from experiment. They can be estimated from the solvatochromic fits described in ref 28 (“R2” in Table 5 of that paper), but doing so requires a large extrapolation which is uncertain due to the changing

Solvation and Solvatochromism in CO2-Expanded Liquids TABLE 1: Summary of Experimental Stokes Shift Dynamicsa xCO2 0.00 0.26 0.46 0.66 0.86

νj(∞)/103 ∆νj/103 cm-1 cm-1 18.92 19.06 19.42 19.51 19.97

2.77 2.03 2.10 1.79 2.03

f1

τ1/ ps

τ2/ ∆νjest/103 ps cm-1 fobs

1 0.6 0.42 0.78 0.66

0.22 0.28 0.09 0.40 0.45

3.35 3.36 3.21 2.92 2.49

0.61 0.60 3.0 2.8

0.83 0.60 0.66 0.61 0.81

J. Phys. Chem. B, Vol. 112, No. 47, 2008 14963 TABLE 2: Experimental Rotation Times and Fluorescence Lifetimesa

/ ps 0.20 ( 0.33 ( 0.31 ( 0.78 ( 1.08 (

0.06 0.10 0.07 0.19 0.11

ν(∞), ∆νj, f1, τ1, and τ2 are parameters from biexponential fits of the νj(t) data to eq 10. ∆νjest is the solvation Stokes shift estimated from analysis of steady-state data, fobs ) ∆νj/∆νjest is an estimate of the portion of the shift not observed due to limited time resolution, and is the best estimate of the integral solvation time including the contribution of unobserved components. a

Figure 3. Observed time evolution of the first moment frequency νj(t) at four compositions, xCO2 ) 0, 0.26, 0.46, 0.66, and 0.86.

Figure 4. Observed (thick curves) and simulated (symbols) solvationinduced Stokes shifts (top panel) and gas-to-solution shifts of absorption and emission frequencies (bottom panel). Simulation uncertainties are indicated but are mostly smaller than the symbol size. The experimental curves come from fits to the data in Figure 1. The single error bar in the top panel indicates the estimated uncertainty in the experimental solvation Stokes shift of (300 cm-1. Uncertainties in the experimental absorption and emission shifts are larger ((1000 cm-1; see text).

vibronic structure of the emission spectra. As a result, direct use of these solvatochromic estimates of the gas-phase frequencies to calculate solvation Stokes shifts via ∆νsolv ) (νgas - ν)em - (νgas - ν)abs yields poor agreement with the more reliable estimates obtained from ∆νsolv ) ∆νjest ) νjt)0 - νjem, where νjt)0 and νjem are the first moment frequencies of the estimated time-zero and steady-state emission

xCO2

τrot /ps

τfl /ns

0 0.20 0.40 0.60 0.86

50 ( 5 32 ( 10 32 ( 6 27 ( 5 21 ( 6

0.47 0.41 0.33 0.25 0.18

a

Rotation times, τrot, were determined from anisotropy decay data using three different fitting methods as described in ref 44. The uncertainties in these times reflect the variations in the results of such fits. Uncertainties in fluorescence lifetimes, τfl, are (10%.

spectra (Figure 1). For this reason, we adjusted the values of the estimated gas-phase frequencies by 1250 cm-1 in order to obtain agreement with the best estimate of ∆νsolv in neat CH3CN. The spectral shifts shown in the bottom panel of Figure 4 use these shifted gas-phase frequencies. As a result of this procedure, the uncertainties in the individual absorption and emission shifts are large, (1000 cm-1, whereas the uncertainty in the solvation Stokes shift is (300 cm-1. The spectral shifts simulated as described in section II.B depend upon a single adjustable parameter f, the fractional increase in solute-solvent dispersion interactions in S1 relative to S0. Use of the value f ) 0.24 produces simulated shifts (points) in good agreement with experiment, as shown in Figure 4. This value, which can be interpreted to mean that the polarizability of atoms in the π system of DCS increases by 24% upon electronic excitation, seems plausible. Within the context of the present spectral model, we find that over nearly the entire range of compositions, dispersion interactions account for 90% of the shift of the absorption spectrum from its gasphase value (Figure SI-4, Supporting Information). Dispersion is not as dominant in the emission shifts, which we find to be composed of nearly equal contributions from dispersion and electrostatic interactions. In stark contrast to these absorption and emission shifts, the difference between them, that is, the solvation-induced Stokes shift, is dominated by electrostatic interactions. Typically >95% of the Stokes shift is caused by differences in electrostatic interactions between S0 and S1. For this reason, we will ignore dispersion contributions when considering solvation dynamics below. Finally, we note that the simulations predict a marked drop in the Stokes shift and νjem between xCO2 ) 0.85 and 1 as a result of the much weaker electrostatic interactions in CO2 compared to those in CH3CN. Although the limited solubility of DCS in CO2 precludes experimental observation of this drop, very similar behavior is predicted and observed in the case of C153 in CH3CN + CO2 mixtures.26 As a preliminary check of the dynamics of the simulation model, we measured rotation times of DCS in several mixtures using time-correlated single-photon counting. These results are summarized in Table 2 and plotted in Figure 5. The top panel of Figure 5 contains the measured rotation times (filled symbols) compared to rotation times observed in equilibrium simulations of DCS in the S0 and S1 states. The latter values are 1/e times of the second-rank rotational correlation functions

C2z(t) )

〈 23 cos [uˆ (0) · uˆ (t)] - 21 〉 2

z

z

(11)

where uˆz is a unit vector along the long principal axis of DCS, which is approximately the direction of its emission transition moment. Both the simulated and observed rotational correlation

14964 J. Phys. Chem. B, Vol. 112, No. 47, 2008

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Figure 6. Comparison of simulated solvation correlation functions (S1 state, solid curves) and experimental spectral response functions (dashed curves) at three compositions, xCO2 ) 0, 0.46, and 0.86. The inset shows the integral times of these functions versus xCO2.

Figure 5. Top Panel: Observed (filled squares) and simulated (open symbols) rotation times. Simulated values are 1/e times of P2z correlation functions from equilibrium simulations of DCS in both the S0 (triangles) and S1 (circles) states. Bottom Panel: Observed rotation times and fluorescence decay (isomerization) times plotted versus simulated solvent viscosity. Also shown as small symbols are the simulated S1 rotation times. The lines shown here are fits to τ ) cηp with p ) 0.77 for τfl, 0.59 for τrot, and 0.95 for the simulated rotation times (dashed line).

functions, which are of limited S/N, are adequately fit by single exponential functions of time. The simulated rotation times do not differ by more than uncertainties between S0 and S1, except for xCO2 ) 0.84 and 0.95, where preferential solvation and differences in electrical interactions apparently retard rotation of the S1 solute relative to S0. The experimental data are best compared to the simulated S1 values. Ignoring the experimental datum at xCO2 ) 0.2, which appears to be in error, the simulated rotation times are about 20% larger than the experimental values at low xCO2 and in better agreement at high xCO2. This behavior is consistent with what was observed previously when comparing rotation times of a larger solute to simulated viscosities.9 In the bottom panel of Figure 5, we plot the experimental rotation times and fluorescence lifetimes of DCS versus these simulated viscosities. (Experimental viscosities are not available; therefore, we use the simulated values from ref 26.) The lifetimes of DCS, which vary between 180 and 500 ps here, are expected to be approximately equal to the isomerization times under these conditions.48,49 Both the experimental rotation and isomerization times are seen to be well correlated to the simulated viscosities of these solutions, as might be anticipated. However, the slopes in this log-log representation are less than unity, 0.77 for τfl and 0.6 for τrot. The fact that the simulated rotation times (small points and dashed line) exhibit a slope of 0.95 probably indicates that, although these dynamics behave approximately as expected from simple hydrodynamic models, the composition dependence of viscosity and thus solute dynamics in the simulation model are slightly stronger than those in the experimental solvent. Finally, Figure 6 compares the solvation response functions observed in experiment with the appropriate solvation correlation

Figure 7. Top Panel: Simulated solvation correlation functions, C(1) ∆U(t), in equilibrium with S1 DCS at the five solvent compositions indicated. Bottom Panel: Comparison of the equilibrium correlation functions C∆U(t) in S0 (lowest curve) and S1 with the nonequilibrium response function (S∆U(t), dashed) in the xCO2 ) 0.95 mixture.

functions obtained from simulation (see below). The experimental functions Sν(t) were obtained from the νj(t) data in Figure 3 using the steady-state estimates of νj(t ) 0) from Figure 1. The simulated functions are more clearly biphasic than are the experimental functions. This difference, like the shortfall in the observed Stokes shift, is probably due to the limited time resolution of the KGE experiment. Nevertheless, the relative amplitudes of the slower phase of the dynamics, as well as the integral response times (inset), are reasonably reproduced by the simulations. These results, together with the other comparisons made in this section, are sufficient to provide confidence in the potentials and spectroscopic model employed here. Although the simulations may not be quantitatively accurate in all respects, they are sufficiently realistic to warrant using them to derive mechanistic interpretations of solvation in CH3CN + CO2 mixtures. Such interpretations occupy the remainder of this paper.

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TABLE 3: Solvation Response Characteristics from Equilibrium Simulationsa xCO2

SS obs. /103 cm-1

SS est. /103 cm-1

ωs /ps-1

0 0.262 0.461 0.660 0.840 0.950 1

3.36 3.25 3.14 3.02 2.71 2.18 0.77

3.36 3.29 3.15 3.12 2.86 2.60 0.77

12.5 11.0 10.1 8.7 7.3 5.9 6.9

aG ω /ps-1 S1Simulations 0.857 0.749 0.689 0.563 0.433 0.401 0.461

a1

τ /ps

a2

τ2 /ps

14.5 13.4 12.4 11.3 9.7 7.8 6.0

0.158 0.253 0.289 0.434 0.477 0.381 0.484

0.76 0.60 0.55 0.63 0.62 0.96 0.31

0.003 0.016 0.038 0.016 0.100 0.212 0.056

14.5 8.5 6.6

0.175 0.468 0.591

0.75 0.43 0.33

0.253 0.087

fd

τd /ps

6.6 5.0 2.9 15 7.6 17 3.0

0.16 0.26 0.32 0.44 0.57 0.60 0.54

0.87 0.85 0.82 1.13 1.84 6.7 0.59

1.5 1.2

0.17 0.71 0.66

0.74 0.80 0.45

S0 Simulations 0 0.950 1

3.36 2.18 0.77

3.32 1.89 0.78

12.5 6.3 6.7

0.845 0.302 0.356

a eq SS obs. is the electrical component of the Stokes shift, SS obs. ) 〈∆Uel〉eq 0 - 〈∆Uel〉1 , and SS est. is the linear response estimate, SS est. ) 〈(δ∆Uel)2〉ieq/kBT. ωs is the solvation frequency (eq 12) measured from the first few points of C∆U(t); aG, ω, a1, τ1, a2, and τ2 are from fits of C∆U(t) to eq 13, and fd and τd are defined by eq 14. Uncertainties in the Stokes shifts are 1-4%, and those in the solvation frequencies are 0.85). What is found in the case of xCO2 ) 0.95 is shown in the bottom panel of Figure 7. In contrast to other (0) (t) and compositions, the equilibrium correlation functions C∆U C(1) ∆U(t) at this composition differ significantly, with the S1 correlation function decaying more slowly at long times. The nonequilibrium response, S∆U(t), lies between the two equilibrium estimates. We note that the departure from linear response predictions is also observed in the magnitude of the simulated Stokes shifts for the most CO2-rich mixture, as listed in Table 3. For all but the xCO2 ) 0.95 composition, the linear response estimates of the Stokes shifts, 〈(δ∆Uel)2〉eq i /kBT, lie within 5% of the observed Stokes shifts eq 〈∆Uel〉eq 0 - 〈∆Uel〉1 . Only at xCO2 ) 0.95 do the estimates based on S0 and S1 simulations differ from one another or from the actual Stokes shift by significantly more than their uncertainties. Given that the experimental data only cover the range where linear response estimates are accurate, we will discuss the equilibrium dynamics first. (1) (t) functions consist of a As shown in Figure 7, the C∆U Gaussian initial component followed by a long-time tail of varying importance. The general trend with composition is that the initial rate of decay of C∆U(t) decreases with increasing CO2 concentration. For mixtures containing only a small amount of CH3CN, the long-time tail accounts for a significant portion of the overall relaxation. This tail is greatly reduced in the case of neat CO2, as it is in the case of neat CH3CN. We use three quantities to characterize the concentration dependence of these correlation functions. The short-time dynamics are characterized by the solvation frequency, defined by the initial curvature of the solvation correlation function

ω2s ) -

( ) d2C∆U dt2

(12) t)0

This frequency, determined from a parabolic fit of the first few

points of C∆U(t), reflects the impact of inertial motions on ∆Uel. The two remaining characteristics are determined by fitting the decays to a Gaussian plus biexponential function

{

}

1 C∆U(t) ) aG exp - ω2t2 + 2

2

∑ ai exp{-t/τi}

(13)

i)1

Although this function does not have the appropriate zero slope at t ) 0, it enables us to obtain the fraction, fd, and average time, τd, associated with the “diffusive” component of the dynamics

fd )

a1 + a2 aG + a1 + a2

τd )

a1τ1 + a2τ2 a1 + a2

(14)

Into this latter component are subsumed all dynamics not accounted for in the initial Gaussian component. These dynamics mainly consist of diffusive reorientational and translational motions of solvent molecules. However, it should be recognized that the dissection into inertial and diffusive contributions implied above is not rigorous. For example, the oscillations seen near 0.3 ps in the lower xCO2 curves in Figure 7, which are not captured by eq 13, reflect underdamped motions continuing after the Gaussian component has decayed. Of the three quantities reported here, only the solvation frequency can be unambiguously assigned to a single type of motion. Nevertheless, we expect τd to provide a reasonable estimate for the time scale of the diffusive response and fd to roughly indicate the relative importance of diffusive versus inertial contributions to solvation. (1) (t) are plotted versus x These three characteristics of C∆U CO2 in Figure 8. All three exhibit monotonic trends with increasing CO2 up to very high CO2 concentrations. Somewhere in the range of 0.95 < xCO2 < 1 there is a dramatic reversal in the diffusive time and a much more modest reversal in ωs. To understand the molecular mechanisms behind these trends, it is useful to first consider the neat solvent end points. Ladanyi and Maroncelli have already analyzed the solvation mechanisms in neat CH3CN and CO2 in considerable detail.65 In that work, solvation of an immobile benzene-like solute was examined. The situation for a large solute like DCS is expected to be quite similar.66 In both CH3CN and CO2, solvation is accomplished predominantly via rotational motions of solvent molecules, with

14966 J. Phys. Chem. B, Vol. 112, No. 47, 2008

Figure 8. Composition dependence of three characteristics of the (1) equilibrium solvation correlation functions C∆U (t). ωs is the solvation frequency, defined by eq 12, and fd and τd are the fractional contribution and the integral time constant associated with the “diffusive” component of the dynamics (eqs 13 and 14).

translational motions accounting for only 10-20% of the response. The nearly two-fold difference in the solvation frequencies of these two solvents, whose inertial characteristics are quite similar, results from differences in the collective nature of the response. In CH3CN, strong correlations between the orientations of pairs of solvent molecules suppress fluctuations in ∆Uel and thereby increase the solvation frequency by factors of 2-3 and the overall speed of the response by even larger factors, compared to what would be expected based on the contributions of independent solvent molecules.65,67 In contrast, weak correlations between the nondipolar CO2 molecules in neat CO2 are such that the solvation response differs only slightly from the response expected from independent solvent molecules.65 Given this description of the neat solvents, what would be expected for intermediate compositions? Simple models relating single-molecule dynamics to the collective solvation response65,67 suggest that both ωs and fd should scale directly with the extent to which solvent molecule orientations are correlated. Given the similar inertial and packing characteristics of CH3CN and CO2, it seems reasonable that addition of CO2 to CH3CN might dilute this correlation approximately in proportion to xCO2 and give rise to the nearly linear variations of ωs and fd with xCO2 observed. In the case of τd, an additional factor, not important for ωs and fd, gives rise to the rapidly increasing time scale of the diffusive component of the response for xCO2 > 0.5. As will be shown in more detail below, the slow portion of the solvation response and therefore τd is sensitive to the time required for redistribution of molecules between the bulk of the solution and the first solvation shell of the solute. Before discussing this solvent restructuring, we first consider the relative contributions of the component species to the dynamics. For this purpose, we decompose the spectroscopic energy difference into contributions from CO2 and CH3CN molecules, ∆U ) ∆UCO2 + ∆UCH3CN, and C∆U(t) into component time correlation functions according to68,69

Swalina et al.

(1) Figure 9. S1 solvation correlation functions, C∆U (t), and their decomposition into contributions, cR(t), from CH3CN and CO2 molecules (eq 15) at two compositions.

TABLE 4: CH3CN Contribution to the Stokes Shifts (%)a xCO2

S0

S1

0.262 0.461 0.66 0.84 0.95

97 95 91 83 69

98 95 94 89 86

a These decompositions are based on the t ) 0 values of the component time correlation functions defined by eq 15.

C∆U(t) ) cCO2(t) + cCH3CN(t) with

cR(t) )

〈δ∆U(0)δ∆UR(t)〉 〈(δ∆U(0))2〉

(15)

Component time-correlation functions cR(t) for the xCO2 ) 0.46 and 0.95 solvents in equilibrium with S1 DCS are depicted in Figure 9. The t ) 0 values of these functions represent the relative contributions of the two components to the overall fluorescence Stokes shifts. Percentage contributions of the CH3CN component based on such decompositions for all equilibrium systems are listed in Table 4. It is evident from Figure 9 and Table 4 that for mixtures in equilibrium with either of the two solute states, solvation time-correlation functions are dominated by the CH3CN component. This dominance is due to the much larger electrostatic interactions between DCS and the strongly dipolar CH3CN molecules compared to the quadrupolar solvent CO2. For xCO2 g 0.66, cCO2(t) develops an increasingly negative slowly decaying component. The negative sign of cCO2(t) indicates that the motions of CO2 molecules are anticorrelated with ∆U(0) whereas those of CH3CN are positively correlated with ∆U(0). The anticorrelations for CO2 result from CO2 molecules adopting energetically unfavorable orientations with respect to the solute in order to allow more favorable orientations of CH3CN molecules. The stronger electrostatic interactions between DCS and CH3CN easily compensate for these unfavorable interactions among CO2 molecules. We now consider the solvation structure present in these systems and how it differs between the S0 and S1 solute states. Figure 10 shows contour plots of the equilibrium solvent density surrounding S1 DCS in the xCO2 ) 0.95 mixture,

Solvation and Solvatochromism in CO2-Expanded Liquids

Figure 10. Contour plots of the solvent density surrounding S1 DCS in the xCO2 ) 0.95 solvent. The top panel shows the density of solvent atoms of any type, relative to a uniform density distribution. The molecular structure (purple) shows the 0.004 au isodensity surface of the S0 (RHF/6-31G(d,p)) wave function. The bottom panel shows enrichment factors, the number of CH3CN solvent atoms at a given location divided by the number expected based on the bulk mole fraction of CH3CN in the mixture. The molecular structure here shows the electrostatic potential (ESP; red e -0.03 au, blue ) 0.03 au) mapped onto the isodensity surface. (The ESP on the cyano N atom reaches -0.06 au, but a smaller negative value is used to better display the remaining variations.) In all cases, densities in the dimension not plotted are averaged over lengths appropriate to the given dimension of DCS. From left to right, the averages are over (1, (3, and (8 Å. The grid markings are in units of 1 Å.

where the preferential solvation is the greatest. The top panel of Figure 10 shows the total density of solvent atoms relative to what is expected for a uniform distribution. In this system, there is roughly a 1.5- to 2-fold greater solvent density (blue) in the few Ångstro¨m thick region surrounding the solute compared to the density in the bulk solvent. There is also a hint of a rarefaction (light green) and second densification as one moves outward from the solute. This solvent layering is similar to the packing found around solutes in dense liquid solvents like neat CH3CN, but the degree of structuring is muted here due to the lower packing fraction at this high value of xCO2.9 More relevant to our present concerns is the fact that the cybotactic region of DCS is significantly enriched in CH3CN molecules compared to that of the bulk, as shown in the bottom panel of Figure 10. The enrichment factors plotted here are the relative probabilities of finding an atom of CH3CN in a particular location relative to what would be expected based on the total atom density and the bulk mole fraction of CH3CN. (Note that the densification effect has been removed from these factors). As illustrated in Figure 10, there is a three- to six-fold enrichment of CH3CN atoms surrounding DCS(S1) at this composition. This enrichment generally follows the densification pattern observed in the top panel, that is, it is most pronounced above and below the molecular plane where the net solvent density is greatest

J. Phys. Chem. B, Vol. 112, No. 47, 2008 14967 and somewhat less so around the periphery. Noteworthy is the fact that there is no indication of specific solvation in this system. Even distributions of individual atoms (Figure SI-5, Supporting Information) do not show signs of any specific interactions, for example, with the highly charged cyano N atom of DCS (q(S1) ) -0.55 e), although there is a general orientational preference of the sort expected. This observation appears to differ from the behavior recently reported by Gohres et al.24 who observed high relative densities of acetone molecules localized near to the more negative end of the solute coumarin 153 (C153) in dilute acetone + CO2 mixtures. On the basis of our own simulations of C153 in CH3CN + CO2 mixtures, we believe that even in this case the highly nonuniform distributions observed are induced by the less orderly packing of solvent molecules around the irregularly shaped positive end of C153 compared to that at the more planar negative end, rather than indicating the presence important specific attractive interactions. Because of its near planarity, DCS does not give rise to the same sort of packing localization. Given the lack of specific structure observed here, it is convenient to use less detailed representations to summarize the composition dependence of this structure. Toward this end, Figure 11 shows relative CH3CN and CO2 atom densities averaged over the solute surface for both S0 and S1 at three solvent compositions. The “solvation shell distribution functions” gss(r) plotted here are defined as the probability of finding a solute atom of a given type at a distance r from the nearest solute atom relative to a random distribution.70 The distributions observed here with DCS are quite similar to those found for the C153 probe in these same mixtures.26 The CO2 distributions change little with composition. In contrast, the first peak in gss(r) increases markedly with increasing xCO2, signaling the enrichment of CH3CN in the first solvation shell and, to a much lesser extent, in the second shell. Table 5 lists coordination numbers obtained by integrating these distributions over the first solvation shell, defined as r ) 5.0 Å. As discussed in refs 9 and 26, number densities go through a maximum as a function of xCO2 along the coexistence curve, and this density maximum is directly reflected in the total coordination numbers, Nu. At higher CO2 loadings, the S0 f S1 change is accompanied by an increase of between one and two atoms (1-2%) in the solute’s first coordination shell. The enrichment of this first shell in the more polar component CH3CN is quantified using “enrichment factors”26

xu(1) Nu(1)/Nu ) x(1) x(1)

(16)

where the subscript “u” indicates a first solvation shell quantity and “1” refers to component #1, CH3CN. As shown in Table 5, the first solvation shell of DCS contains roughly two (S0) to three (S1) times as much of the CH3CN component compared to the bulk fluid at the highest value of xCO2 studied. At this composition, the differential enrichment of the S1 and S0 solutes amounts to adding four atoms of CH3CN (and removing one to two atoms of CO2) subsequent to the S0 f S1 transition. We now return to the observable consequences of this restructuring on the solvation dynamics, focusing again on the xCO2 ) 0.95 case. Figure 12 compares changes in coordination numbers and contributions to the solvation response observed in nonequilibrium simulations. These plots clearly indicate that

14968 J. Phys. Chem. B, Vol. 112, No. 47, 2008

Swalina et al.

TABLE 5: First Solvation Shell Characteristicsa Nu

Nu(1)

xu(1)/x(1)

xCO2

S1

S1 - S0

S1

S1 - S0

S1

0 0.262 0.461 0.660 0.840 0.950 1

76.2 79.3 82.5 84.4 85.3 82.2 76.0

0.3 ( 0.1 -0.1 ( 0.2 0.5 ( 0.2 0.4 ( 0.2 0.7 ( 0.2 1.6 ( 0.2 0.3 ( 0.2

76.2 59.4 46.7 35.3 21.1 11.6 0

0.3 ( 0.1 1.7 ( 0.9 0.6 ( 1.0 1.9 ( 1.0 3.0 ( 1.4 4.2 ( 1.0 0

1 1.01 ( 0.01 1.05 ( 0.02 1.23 ( 0.02 1.55 ( 0.07 2.83 ( 0.16 1

S0 1 0.98 ( 0.01 1.04 ( 0.02 1.17 ( 0.02 1.34 ( 0.06 1.86 ( 0.11 1

a Nu is the total number of solvent atoms and Nu(1) the number of component #1 (CH3CN) atoms in the first solvation shell of the solute. xu(1)/x(1) ) Nu(1)/Nux(1) is the enrichment factor describing the enrichment of the solute’s first solvation shell in CH3CN. Uncertainties in Nu and Nu(1) are less than 0.2 and 1, respectively.

Figure 11. Solvation shell distribution functions gss(r) (see text) at compositions of xCO2 ) 0.461, 0.840, and 0.950. Distributions of both components surrounding DCS in the S0 (left) and S1 states (right) are shown.

Figure 13. Comparison of the solvation response S∆U(t) to the analogous function describing the number of CH3CN atoms in the first solvation shell of the solute S∆N(t) in the xCO2 ) 0.95 solvent. Also shown for comparison is the equilibrium solvation function in the S1 (1) state C∆U (t). The lines are single exponential fits to the data between 3 and 50 ps. The time constants obtained from these fits are 22 (SN), 20 (C∆U), and 14 ps (S∆U).

Another noteworthy feature of Figure 12 is that no clear distinction can be made between the time scales for the net change in coordination number and the solvent sorting, that is, the exchange of CO2 for CH3CN. This behavior stands in contrast to what has been previously observed in simulations of ions42,43 and small molecules40 solvated in liquid mixtures, where fast electrostriction and slower solvent sorting occur on well-separated time scales. The distinction probably reflects the fact that the S0 f S1 transition in DCS is a smaller and more delocalized perturbation than the transitions studied in these other cases. We also note that the nonequilibrium data in the bottom panel of Figure 12 show the same essential features as the equilibrium correlation functions in Figure 9, the dominant contribution of CH3CN to the solvation response and the anticorrelation of the CH3CN and CO2 contributions during the solvent resorting period. Figure 13 compares the normalized solvation response function S∆U(t) to the CH3CN number response Figure 12. Nonequilibrium dynamics subsequent to a S0 f S1 solute transition in the xCO2 ) 0.95 solvent. The top panel shows the changes in the numbers of solvent atoms in the first solvation shell, and the bottom panel shows changes in the contributions to the spectroscopic energy difference ∆U. The horizontal lines on the right side of the figure denote equilibrium values in S1.

solvent restructuring has little to do with the rapid ( 0.5, the simulations indicate that the solvent composition in the cybotactic region of DCS is significantly enriched in CH3CN. The extent of this enrichment is greater for the S1 solute compared to that for the S0 solute. At xCO2 ) 0.95, there are approximately three-fold and two-fold enrichments in CH3CN in the first solvation shell in S1 and S0, respectively. This difference requires transport of CH3CN to DCS from the bulk fluid after excitation. The time scale on which this transport occurs is 10-20 ps at the highest values of xCO2, in keeping with what is expected for a diffusive process. The behavior observed in CO2-expanded CH3CN is, in most respects, qualitatively similar to what has been previously reported in conventional liquid-liquid mixtures. Preferential solvation of the sort observed here is prevalent in liquid mixtures whenever the components differ significantly in polarity, especially when hydrogen bonding or other specific interactions exist between the solute and one of the mixture components.74 A qualitative distinction between liquid mixtures and GXLs (when used at liquid-vapor coexistence near room temperature) is that GXLs possess larger and more variable free volumes9 than is the case in conventional liquid mixtures. As discussed in ref 26, this feature renders the relationship between spectral shifts and local compositions more nonlinear and more difficult to interpret in GXLs. The greater free volumes also lead to higher fluidity and faster diffusion in GXLs relative those in to liquid-liquid mixtures. A number of groups have recently measuredsolvationdynamicsinconventionalliquidmixtures,30-37,75 and simulations of several of these systems have also been performed.39-41 Except in cases where the extent of preferential solvation is designed to be negligible,37 these studies usually find biphasic dynamics of the sort observed here: a fast and often unresolved component comparable to what is present in the neat component liquids followed by a process that can be slower than any found in the pure components. As in the present case, the interpretation provided by simulation is that the fast dynamics reflect the response of nearby solvent molecules in whatever solvation environment prevails at the moment of excitation, and the slow response involves a restructuring of the cybotactic region which, in dilute conditions, can be viewed as a diffusive process. Details vary from system to system, which makes direct comparison of these studies to the present one difficult. However, it seems reasonable to expect that the main distinction between solvation dynamics in GXLs and that in conventional liquid mixtures is that the greater fluidity of GXLs should produce faster solvation, especially at compositions where solvent redistribution is important. Acknowledgment. Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for support of this research. Supporting Information Available: Analysis of DCS atomic charge sets, tables of simulation parameters, and additional simulation analyses. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Jessop, P. G.; Subramaniam, B. Chem. ReV. 2007, 107, 2666.

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