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J. Phys. Chem. B 2010, 114, 10160–10170
MD Study of Solvation in the Mixture of a Room-Temperature Ionic Liquid and CO2 Youngseon Shim†,‡ and Hyung J. Kim*,†,§ Department of Chemistry, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213, Department of Chemistry, Seoul National UniVersity, Seoul 151-747, Korea, and School of Computational Sciences, Korea Institute for AdVanced Study, Seoul 130-722, Korea ReceiVed: June 1, 2010; ReVised Manuscript ReceiVed: July 2, 2010
Solvation structure and dynamics of a saturated solution of carbon dioxide in the room-temperature ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate (BMI+PF6-) at 313 K and 0.15 kbar are investigated via molecular dynamics computer simulations by employing a diatomic probe solute. It is found that the mixture shows preferential solvation, which is mainly controlled by the solute-BMI+PF6- electrostatic interactions and thus dictates differing roles for CO2 as the solute charge distribution varies. The local structure and density of BMI+PF6- and CO2 in the vicinity of the solute become enhanced and reduced, respectively, as its dipole moment increases. As a result, equilibrium solvation dynamics of a nonpolar solute in the mixture have a strong CO2 character, whereas those of a dipolar solute are very similar to, albeit faster than, solvation dynamics in pure BMI+PF6-. Related nonequilibrium solvent response couched in dynamic Stokes shifts and accompanying solvation structure relaxation, in particular, CO2 structure reorganization, shows interesting dependence on the solute charge distribution. Ion transport in the mixture is much faster than in pure BMI+PF6-, indicating that the addition of cosolvent CO2 reduces the viscosity of the ionic liquid, significantly. The effective polarity of the mixture, measured as solvation-induced stabilization of a dipolar solute, is found to be comparable to that of neat BMI+PF6-, consonant with solvatochromic measurements. 1. Introduction Room-temperature ionic liquids (RTILs) based on bulky and asymmetric organic cations have received extensive theoretical and experimental attention as “green” reaction media with a broad range of potential applications in chemical synthesis, separation, and extraction.1-4 Because of their unique properties, in particular, nonvolatility, high ion density, good thermal stability, and wide electrochemical window, RTILs also provide an attractive alternative to aqueous and organic electrolytes for electrochemical devices, such as batteries, solar cells, and supercapacitors.5-8 Furthermore, when mixed with various nanoparticles, many RTILs form gelatinous materials, which have an important implication for fabrication and application of RTIL-based soft materials with novel properties.9-13 One of the undesirable aspects of RTILs as reaction media is their high viscosity. Because of bulky size and strong electrostatic interactions of their constituent ions, the typical viscosity of RTILs is higher than that of water by several orders of magnitude at room temperature. One way to overcome this difficulty is to use polar or nonpolar solvents of low viscosity as a cosolvent in the mixtures with RTILs. Nontoxic supercritical carbon dioxide has drawn significant attention as a cosolvent, which can also serve as an effective upper phase in biphasic reaction systems14-16 to extract organic compounds from a lower RTIL phase. There have been many experimental investigations to understand solubilities of CO2 in RTILs and phase behaviors of their mixtures.14,17-25 Considerable efforts via molecular dynamics (MD)26-28 and Monte Carlo29-31 simulations have also been directed toward this. However, little attention has been * Corresponding author. Permanent address: Carnegie Mellon University. E-mail:
[email protected]. † Carnegie Mellon University. ‡ Seoul National University. § Korea Institute for Advanced Study.
paid to solvation properties of the RTIL-CO2 mixtures with the computational methods. In this article, we study equilibrium and nonequilibrium solvation of a model diatomic solute of differing size and dipole moment in the mixture of BMI+PF6- and CO2. Static and dynamic properties of the mixture, for example, structure and transport coefficients, are compared with those of the pure systems, that is, neat BMI+PF6- and supercritical CO2. As for nonequilibrium, time-dependent Stokes shifts following an instantaneous change in the solute charge distribution and accompanying solvent structure relaxation are investigated. The outline of this article is as follows: In Section 2, we give a brief description of the models and methods employed in this study. Equilibrium and nonequilibrium solvation structure and dynamics in the mixture of BMI+PF6- and CO2 are analyzed and compared with those in neat fluid systems in Section 3. Effective solvent polarity and transport properties of the mixture are also investigated there. Section 4 concludes. 2. Simulation Methods The simulation cell is composed of a rigid diatomic solute immersed in a solvent mixture, consisting of 128 pairs of BMI+ and PF6- ions and 418 CO2 molecules. This composition of CO2 mole fraction xCO2 ) 0.76 corresponds to a saturated solution of carbon dioxide in BMI+PF6- at 313 K and 0.15 kbar.17-19,21-23 We used the fully flexible all-atom description of refs 32 and 33 for BMI+. For PF6-, we used the LennardJones (LJ) parameters and charge assignments of ref 34 and intramolecular vibrational force constants of ref 35. The LJ parameters, partial charges, and C-O bond length of CO2 were taken from the three-site EPM2 model.36 Rigid linear geometry was employed for CO2 so that its charge distribution yields an axial quadrupole moment of 2qOrCO2 ) 4.13 DÅ as the first nonvanishing multipole moment, where qO() -0.3256e) and
10.1021/jp105021b 2010 American Chemical Society Published on Web 07/22/2010
Solvation in the Mixture of a RTIL and CO2 rCO() 1.149 Å) are the oxygen charge and C-O bond length and e is the fundamental charge. The solute atoms, separated by either 3.5 or 5.5 Å, interact with the solvent through LJ and Coulomb potentials. The solute LJ parameters, σ ) 4 Å and ε/kB ) 100 K (kB: Boltzmann’s constant), are identical for each constituent atom and remain fixed for all solute models considered here. The diatom mass is adjusted so that the solute moment of inertia is 612.5 amu Å2 irrespective of the bond length. Three different solute charge distributions are considered: neutral pair (NP) with no dipole moment, dipolar pair (DP) with dipole moment 16.7 D, and an intermediate charge distribution denoted as HDP with 8.35 D. Hereafter, we represent different solutes by their dipole moment and bond length; for instance, HDP3.5 refers to the model solute with dipole moment 8.35 D and bond length 3.5 Å. The DL_POLY program37 was used in all simulations. The long-range electrostatic interactions were computed via the Ewald method,38 resulting in essentially no truncation of these interactions. The trajectories were integrated via the Verlet leapfrog algorithm using a time step of 2 fs. We first performed NPT ensemble simulations to determine the solvent densities. For neat BMI+PF6-, we obtained F ) 1.348 g cm-3 at 313 K and 1 atm, in good agreement with measurements.39,40 The MD result for supercritical CO2 at 313 K and 0.15 kbar was F ) 0.764 g cm-3. This compares very well with the experimental value 0.779 g cm-3.41 In the case of the mixture, a simulation in the NPT ensemble at 313 K and 0.15 kbar yielded F ) 1.232 g cm-3 at xCO2 ) 0.76. We note that the expansion factor defined as the ratio of the volume of the mixture to that of neat BMI+PF6- at 313 K is 1.3 for our system, in good accord with the experimental value 1.349.42 NVT simulations were carried out with 10 ns equilibration after annealing from 800 K, followed by a 30 ns trajectory from which averages were computed. As for nonequilibrium solvation, 400 configurations sampled every 20 ps were used as initial configurations to simulate nonequilibrium trajectories for 50 ps in the mixture (and 10 ps in pure BMI+PF6-). 3. Results and Discussion 3.1. Solvation Structure. Here we consider solvation structure of probe diatomic solutes in the BMI+PF6--CO2 mixture and compare with that in neat fluid systems. We also analyze how solvation structure varies with the solute size and charge distribution. We begin with structure in pure solvents, BMI+PF6- and supercritical CO2, in Figure 1. To avoid any confusion, we mention at the outset that for N atoms of BMI+ ions we consider only those that are directly bonded to the butyl chain in the present article for simplicity. We notice that in both solvents there is significant structure-making as the solute charge separation increases. For example, N and P atom sites of BMI+ and PF6- (Figure 1a,b) move closer to the (-) and (+) sites of the solute, respectively, as the solute dipole moment increases. As a result, the solvent distributions near the solute become more structured and their local densities become enhanced with the growing solute dipole moment.43-45 Analogous to normal polar solvents,46-50 solvation structure variation with the solute charge distribution in RTILs was referred to as electrostriction in refs 44 and 45. It is interesting that nondipolar CO2 is also characterized by a substantial electrostrictive effect. This is attributed to electrostatic interactions between the solute dipole and CO2 quadrupole moments. We notice that the extent of structural changes in BMI+PF6- with solute dipole moment, gauged by variations in the heights of maxima and minima of
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Figure 1. Solute-solvent radial distribution functions g(r) (units for r: angstroms) in neat solvents. Distributions of N directly connected to the butyl chain of BMI+ around the (-) site of DP3.5 and DP5.5 in pure BMI+PF6- at 313 K and 1.348 g cm-3 are presented in (a) and (c), respectively, whereas those of anion P around the corresponding (+) site are shown in (b) and (d). Radial distributions of carbon and oxygen atoms of CO2 around the negative site of DP3.5 in supercritical CO2 at 313 K and 0.764 g cm-3 are displayed in (e) and (f). For comparison, g(r) around the NP solutes are also presented.
g(r), appears to be more pronounced for the smaller solute of bond length 3.5 Å than for the larger solute of 5.5 Å. We turn to solvation structure in the BMI+PF6--CO2 mixture in Figure 2. One of the most salient features is that the radial distribution of CO2 around the solute in the mixture shows a behavior totally different from that in supercritical CO2. To be specific, the density of CO2 near the solute decreases with increasing solute dipole moment in the mixture (Figure 2e-h), whereas the completely opposite trend was obtained in pure CO2 (Figure 1e,f). In contrast, the structure of BMI+ and PF6around the solute increases with the growing solute charge separation both in the pure ionic liquid and in the mixture. This is a clear indication of preferential solvation in the mixture. Because Coulombic interactions of the solute with monopolar ions are much stronger than those with quadrupolar CO2, the electrostrictive behavior of the mixture is governed primarily by BMI+ and PF6-. Therefore, as the solute charge separation increases, BMI+ and PF6- ions are pulled in closer to the solute, and as a result, CO2 molecules are pushed out of the first solvation shell. The ion density near the solute thus increases with solute dipole moment at the expense of CO2 in the mixture. We note that in the past significant attention was paid to preferential solvation structure and associated dynamics in mixtures of normal solvents, such as hydroxylic and nonhydroxylic solvents and polar and nonpolar solvents.51-58
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Figure 3. Comparison of N(r) around the NP3.5 (-) and DP3.5 ( · · · ) solutes in the mixture (blue) and pure solvents (red): (a) (-)-N of BMI+, (b) (+)-P of PF6-, (c) (-)-C of CO2, and (d) (-)-O of CO2.
in its r dependence and in magnitude. The shoulder structure at r ) 4 to 5 Å arises from the presence of a pronounced first solvation shell around DP (cf. Figure 2a,b). In contrast, N(r) in the presence of NP3.5 in the mixture (solid blue line in panels a and b) is much smaller in magnitude than that in pure BMI+PF6- (solid red line), revealing a marked reduction in the local density of RTIL ions near the nondipolar NP in the former compared with the latter. The situation for CO2 is completely the opposite. Its local density around DP3.5 decreases dramatically in the mixture (dotted blue line in Figure 3cd) compared with supercritical CO2 (dotted red line), whereas both solvent phases are characterized by similar N(r) around NP3.5. 3.2. Effective Solvent Polarity. We now consider effective polarity of the BMI+PF6--CO2 mixture, defined as the solvatochromic shift of the Franck-Condon (FC) excitation energy of chromophores. To do so, we examine the energy difference ∆Eafb between solute electronic states a and b in solution Figure 2. Solvent g(r) around the NP and DP solutes in BMI+PF6-CO2 mixture at T ) 313 K and xCO2 ) 0.76. The same atom pairs of the solute and solvents as in Figure 1 are considered, that is, solute (-) site and cation N in (a) and (c), (+) and anion P in (b) and (d), (-) and C of CO2 in (e) and (g), and (-) and O of CO2 in (f) and (h).
Another noteworthy feature related to preferential solvation is that radial distributions of BMI+ and PF6- ions around NP do not show any discernible structure in the mixture. Their g(r) tend to increase gradually from 0 to the bulk value, viz. 1, in a nearly monotonic fashion as r increases. In contrast, the presence of a first solvation shell of RTIL ions around NP in pure BMI+PF6- is clearly noticeable in Figure 1a,b. As in the neat BMI+PF6- case, variations of solvent structure with the solute dipole moment in the mixture tend to be more pronounced in the presence of the smaller solute than those for the larger solute. To gain additional insight into preferential solvation, we analyzed the numbers N(r) of various atoms of the solvent molecules and ions inside a spherical volume of radius r from the solute (+) and (-) sites. The results are shown in Figure 3. N(r) associated with cations and anions around DP3.5 exhibits a similar behavior between pure BMI+PF6- and mixture, both
∆Eafb ) Eb - Ea
(1)
For convenience, these states are assumed to be degenerate in energy in vacuo so that 〈∆Eafb〉 measures the solvation-induced shift in the FC energy associated with the afb transition, where 〈 · · · 〉 denotes an ensemble average over solvent configurations in equilibrium with a. With a ) DP or HDP and b ) NP, 〈∆Eafb〉 gauges the widely used empirical polarity scale determined via solvatochromic measurements.59 The results for the mixture as well as for neat BMI+PF6- and CO2 are compiled in Table 1. For comparison, 〈∆Eafb〉 in pure CH3CN studied previously in ref 44 is also presented there. We first consider neat solvents. 〈∆EDP3.5fNP3.5〉 for BMI+PF6is 85.3 kcal/mol, whereas the result for highly dipolar CH3CN is 76.5 kcal/mol. This suggests that BMI+PF6- is effectively more polar than CH3CN, consonant with many solvatochromic measurements42,60-68 and simulations43,44,69,70 of RTILs. Therefore, despite their low dielectric constant,71,72 RTILs’ power of solvating dipolar solutes measured as stabilization energy is comparable to (and often higher than) that of strongly dipolar solvents. This leads to significant solvent reorganization and
Solvation in the Mixture of a RTIL and CO2
J. Phys. Chem. B, Vol. 114, No. 31, 2010 10163
TABLE 1: MD Resultsa solvent CH3CN
b
CO2c BM+PF6- d
mixturec
a/b
〈∆Eafb〉
〈(δ∆Eafb)2〉
〈(∆E˙afb)2〉
ωs
τs
β
τ0
NP3.5/DP3.5 DP3.5/NP3.5 NP3.5/DP3.5 DP3.5/NP3.5 DP5.5/NP5.5 NP3.5/DP3.5 NP5.5/DP5.5 DP3.5/NP3.5 DP5.5/NP5.5 HDP3.5/NP3.5 NP3.5/DP3.5 NP5.5/DP5.5 DP3.5/NP3.5 DP5.5/NP5.5 HDP3.5/NP3.5
0.46 76.5 -0.24 28.7 17.3 0.16 -1.2 85.3 59.7 26.1 -0.16 -0.1 87.3(0.025e) 56.2(0.075e) 22.2(0.070e)
46.4 41.3 14.7 17.4 12.3 61.1 42.4 42.5 33.6 10.6 35.4 21.0 51.3 39.4 15.0
4640 6870 741 1320 603 62600 40800 94700 57600 20200 9760 5380 84600 41900 12600
10.0 12.9 7.1 8.7 7.0 32.0 31.0 47.2 41.4 43.6 16.6 16.0 40.6 32.6 29.0
0.18 0.27 0.22 0.87 1.2 ∼24 ∼80 ∼202 ∼214 ∼140 1.0 1.4 ∼37 ∼51 ∼40
0.18 0.13 0.1 0.1 0.12
1.5 1.8 1.1 1.9 0.54
0.17 0.17 0.19
1.1 4.0 5.4
a Energy, time, and frequency are measured in kilocalories per mole, picoseconds, and inverse picoseconds, respectively. ωs and τs are the solvent frequency and solvation time, and τ0 and β are the time scale and exponent of the stretched exponential decay function exp(-t/τ0)β. b MD results from ref 44 (T ) 300 K and P ) 0.001 kbar). c MD results at T ) 313 K and P ) 0.15 kbar. d MD results at T ) 313 K and P ) 0.001 kbar. e Ratio of the CO2 contribution and total 〈∆Eafb〉.
stabilization/destabilization effects in chemical reactions involving charge shift and transfer, for example, electron transfer70,73-76 and SN1 reactions,77 in RTILs. We also notice that just like in normal polar solvents,78,79 the solvent shift in BMI+PF6decreases as the size of the probe solute increases. Another interesting feature is that supercritical CO2 is characterized by a significant solvent spectral shift, 〈∆EDP3.5fNP3.5〉 ) 28.7 kcal/mol. This indicates that the solvation strength of nondipolar CO2 is ∼1/3 of that of highly dipolar CH3CN, in concert with spectroscopic measurements.59,80,81 As in the case of the aforementioned electrostriction, this arises from the CO2 quadrupole moment, which stabilizes a dipolar solute through electrostatic interactions.82-85 Turning to the mixture, we notice that its 〈∆EDP3.5fNP3.5〉 () 87.3 kcal/mol) is very close to the pure BMI+PF6- value, 85.3 kcal/mol. The contribution of CO2 is a mere 2.1 kcal/mol, which is 50% of the entire relaxation for both solvents. The solvation time, τs, determined as the area under Ca/b(t), differs by two orders of magnitude between the two solvents (Table 1). It is noteworthy that Ca/b(t) of CO2 in the presence of DP is characterized by a bimodal decay, whereas that for NP is not. As a consequence, solvation dynamics of NP and DP show a significant gap for t
J 300 fs in supercritical CO2; their respective τs values are 0.24 and 1.1 ps. This state of affairs is different from a previous study with a benzene-like probe solute using a different Ewald summation method.115 One general feature we observe is that for a given solute dipole moment, inertial solvation dynamics are slower for larger solutes than smaller ones. The solvent frequency, defined as
ωs2 ) 〈(∆E˙afb(0))2〉/〈(δ∆Eafb(0))2〉
(3)
decreases from 47 ps-1 for DP3.5 to 41 ps-1 DP5.5 in neat BMI+PF6-. The corresponding results in neat CO2 are 8.7 and 7.0 ps-1. To understand this, we employ the approximation involved in ref 87 for 〈(δ∆E˙afb)2〉 in RTILs
〈(δ∆E˙afb)2〉 ≈ 〈(
k T
∑ vR · ∇R∆Eafb)2〉 ) ∑ mBR 〈(∆fRcoul)2〉 R
R
(4) where R labels solvent ions, mR and vR are the mass and velocity is the difference in the Coulomb forces on of ion R, and ∆f coul R R arising from the a- and b-state solute charge distributions. For convenience, we assume that the solute is of spherical shape with a point dipole at the center, and the main contribution to 2 ∆Eafb arises from the first solvation-shell ions. The 〈(∆f coul R ) 〉 -6 2 term will then behave like R , whereas 〈(δ∆Eafb) 〉 varies as R-4, where R is the distance from the solute center to its first solvation shell. We therefore obtain ωs2 ≈ R-2 in the simple approximate description employed here. Because R increases as the size of the solute grows, we deduce that ωs2 will decrease with the increasing solute size. Because solvation dynamics are measured as time evolution of primarily the solute-solvent electrostatic interactions, their relaxation becomes slower with the increasing solute size, even though the time scale of underlying molecular motions is not influenced by the solute size. A similar result can be derived for dipolar and quadrupolar solvents in essentially the same way. Turning to solvation dynamics in the mixture in Figure 5c, we notice that its Ca/b(t) in the presence of DP, that is, CDP/NP(t), has a strong BMI+PF6- character. Specifically, solvent relaxation is biphasic, characterized by subpicosecond inertial dynamics, followed by slow decay occurring on the subnanosecond to nanosecond time scale. As in the neat BMI+PF6- case, long-time solvation dynamics of DP are reasonably described as a stretched exponential function. We nonetheless notice that the addition of CO2 accelerates the slow dynamics of CDP/NP(t). For example, the β value that determines the temporal behavior
Solvation in the Mixture of a RTIL and CO2
Figure 7. Components of Ca/b(t) in the presence of (a) DP3.5 and (b) NP3.5 in the mixture at 313 K.
of the stretched exponential decay is nearly twice as large in the mixture as in the pure RTIL (Table 1). This acceleration is attributed to dramatic enhancement in RTIL ion translational diffusion in the mixture observed in Section 3.3 above. As a consequence, the solvation time of the DP solutes decreases from τs ≈ 200 ps in neat BMI+PF6- to 40-50 ps in the mixture. This agrees well with recent measurements in the mixtures of BMI+PF6- with nondipolar solvents.86 In contrast, solvation dynamics of NP in the mixture show a significant departure from the corresponding relaxation behavior in pure BMI+PF6-. To be specific, CNP/DP(t) does not exhibit a strong bimodal character, and its long-time decay is no longer given by a stretched exponential in the mixture. In addition, rapid oscillations of CNP/DP(t) present in pure BMI+PF6disappear completely. Overall relaxation of CNP/DP(t) becomes much faster in the mixture than in pure BMI+PF6-; the corresponding solvation time decreases by a factor of 20-50 in the former compared with the latter (Table 1). Despite these differences between CDP/NP(t) and CNP/DP(t), we notice that for a given solute dipole moment, solvation dynamics in the mixture tend to become slower as the solute bond length increases, analogous to neat solvents. The qualitatively differing influence of CO2 on solvation dynamics observed here, which varies with the probe solute electronic structure, is directly related to preferential solvation discussed above. For additional insight, we have decomposed ∆Eafb into the contributions of BMI+PF6- and CO2 and analyzed their correlations. In Figure 7, three components of Ca/b(t) in the mixture, that is, the auto- and cross-correlations of the BMI+PF6- and CO2 contributions, are shown. In the presence of DP3.5, equilibrium solvation dynamics are almost completely determined by BMI+PF6-. This explains why relaxation behaviors of CDP/NP(t) in pure BMI+PF6- and mixture are quite similar, as shown above. In the case of the NP3.5 solute, however, the contributions of BMI+PF6- and CO2 to Ca/b(t), measured as the initial values of their autocorrelations at t ) 0, are comparable. This is due to high concentration of CO2 around NP in the mixture (Figure 2e,f). Resulting solvation dynamics in the mixture thus develop a substantial CO2 character. Specifically, the short-time relaxation of CNP/DP(t) up to ∼0.5 ps is governed predominantly by CO2, whereas RTIL is responsible for its slow dynamics. Also interesting is that in contrast with the DP case, the BMI+PF6- contribution does not show a distinctive bimodal character. This is again ascribed to preferential solvation, in particular, (near) absence of RTIL ions in the first solvation shell of NP and resulting lack of strong modulations of ∆Eafb via hindered translations of RTIL ions close to the solute. We notice that the contribution of crosscorrelation of BMI+PF6- and CO2 is considerably smaller in the presence of NP than in the DP case. Although not shown here, NP5.5 and DP5.5 show essentially the same solvation dynamics behaviors as NP3.5 and DP3.5.
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Figure 8. Solvent response functions Sa/b(t) and its cation and anion contributions in pure BMI+PF6-. The solvent was initially in equilibrium with the b-state charge distribution of the solute of bond length 3.5 Å before it becomes electronically excited to state a at t ) 0. The ensuing relaxation is monitored via FC energy ∆Eafb (eq 5).
3.5. Nonequilibrium Solvation Dynamics. To understand nonequilibrium solvation dynamics, we have analyzed the normalized dynamic Stokes shift function116-118
Sa/b(t) )
∆Eafb(t) - ∆Eafb(∞) ∆Eafb(0) - ∆Eafb(∞)
(5)
widely used to describe relaxation dynamics associated with solvation. Here ∆Eafb(t) denotes the average FC energy associated with the afb transition at time t after an instantaneous change in the solute electronic state from b to a at t ) 0. The average is taken over the initial distribution of solvent configurations in equilibrium with the b-state solute charge distribution. We first consider the results for pure BMI+PF6in Figure 8. Regardless of the solute charge distributions, Sa/b(t) in pure BMI+PF6- shows ultrafast subpicosecond relaxation, followed by a slow decay analogous to Ca/b(t). As noted above, this is in concert with many dynamic spectroscopy measurements.65-67,99-109 Both the anions and cations play an important role in relaxation dynamics, although the contribution from the former tends to be more significant than that from the latter. This state of affairs is in good accord with previous simulation studies.69,87 There it was also found that while RTIL ions close to the solute are primarily responsible for the ultrafast relaxation of SNP/DP(t), ions in all ranges tend to make contributions to the initial dynamics of SDP/NP(t). This difference is due to the differing RTIL densities around the solute at the onset of solvent relaxation. Figure 9 presents the results for Sa/b(t) in the mixture and its IL CO2 IL (t) and Sa/b (t) (Sa/b(t) ) Sa/b (t) + two components, viz. Sa/b CO2 Sa/b (t)), arising from RTIL and CO2, respectively. Compared with pure BMI+PF6-, solvent response in the mixture shows several distinctive features. SNP/DP(t) exhibits faster relaxation in the mixture than in pure BMI+PF6- (Figure 9a), whereas SDP/NP(t) is considerably slower in the former than that in the latter during the first ∼50 ps of the solvent relaxation (Figure 9b). The SDP/NP(t) result is rather unexpected and counterintuitive because in the case of RTIL transport and Ca/b(t) analyzed above, the mixture displayed faster dynamics than neat BMI+PF6-. We will return to this issue below. As explicitly compared in Figure 9e, SNP/DP(t) and SDP/NP(t) show markedly different dynamic behaviors in the mixture. There we also notice that SDP/NP(t) does not display rapid oscillations of small amplitude that are CO2 (t) present in SNP/DP(t). Another notable difference is that SNP/DP is essentially negligible in the mixture (Figure 9c), whereas 2 (t) plays quite a significant role (Figure 9d). Interestingly, SCO DP/NP for both SNP/DP(t) and SDP/NP(t), the CO2 component is character-
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Figure 9. Sa/b(t) in the BMI+PF6--CO2 mixture. Solvent response to the instantaneous changes of the solute charge distribution, that is, DP3.5 f NP3.5 and NP3.5 f DP3.5, at t ) 0 in the mixture is compared with that in neat BMI+PF6- in (a) and (b), whereas the contributions of BMI+PF6- and CO2 to Sa/b(t) are presented in (c) and (d). SNP/DP(t) and SDP/NP(t) in the mixture are compared in (e), and ∆EDPfNP(t) and its components associated with the latter is displayed in (f).
ized by a rapid initial drop below ) 0, followed by a gradual increase back to ∼0, even though this is much more pronounced in the latter. For further insight, we have analyzed ∆EDPfNP(t) associated with SDP/NP(t) (cf. eq 5). The result is presented in Figure 9f. The CO2 contribution to ∆EDPfNP(t) shows a striking nonmonotonic behavior, the maximum transient value of which is larger than its fully relaxed value at t ) ∞ by one order of magnitude! It increases dramatically from 0 to >20 kcal/mol in 2 to 3 ps before it slowly decays to its equilibrium value of ∼2 kcal/mol (Table 1). To acquire better understanding of nonequilibrium solvation dynamics in the mixture, we consider temporal behaviors of solvent structure subsequent to an instantaneous change in the solute charge distribution at t ) 0. We first examine nonequilibrium solute-solvent radial distribution functions g(r; t) in Figure 10, where the solvent, initially equilibrated to the DP3.5 solute, relaxes to a new state in equilibrium with the NP3.5 charge distribution. This delineates the solvent structural relaxation accompanying SNP/DP(t) in Figure 9c. g(r; t) of BMI+ and PF6- in the first solvation shell, viz. within 5 Å of, respectively, the negative and positive sites of the solute, becomes considerably smaller and wider in
