J. Phys. Chem. B 2009, 113, 13291–13299
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Solvation Structures of cis- and trans-1,2-Dichloroethylene in Supercritical CO2 Investigated by Raman Spectroscopy and Attractive Energy Calculations Daisuke Kajiya† and Ken-ichi Saitow*,†,‡,§ Natural Science Center for Basic Research and DeVelopment (N-BARD), Hiroshima UniVersity, 1-3-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8526, Japan, Department of Chemistry, Graduate School of Science, Hiroshima UniVersity, 1-3-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8526, Japan, and PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan ReceiVed: April 8, 2009; ReVised Manuscript ReceiVed: August 20, 2009
Vibrational Raman spectra of the CdC stretching modes of cis- and trans-1,2-dichloroethylene (C2H2Cl2) were measured in supercritical carbon dioxide (CO2). The spectra were collected at a fixed solute mole fraction by varying the fluid density by a factor of 20. As the density increased, the peak frequencies of the CdC stretching modes shifted toward the low-energy side at isotherms of reduced temperature, Tr ) T/Tc ) 1.02, 1.06, and 1.20. By analyzing these density dependences using the perturbed hard-sphere theory, we decomposed the shifts into attractive and repulsive components. The repulsive shifts of cis-C2H2Cl2 were almost equivalent to those of trans-C2H2Cl2. However, the attractive shifts of nonpolar trans-C2H2Cl2 were significantly greater than those of polar cis-C2H2Cl2 at all densities and temperatures. To evaluate the difference in the isomers, we calculated the attractive shifts of the CdC stretching modes of each isomer, composing of dispersion, dipole-induced-dipole, and dipole-quadrupole interactions between solute C2H2Cl2 and solvent CO2 molecules. These three interactions were quantified by considering molecular configurations and orientations, and solvation structures around the isomers were elucidated by 3D schematic diagrams. As a result, it was shown that the anisotropic solvation structure around trans-C2H2Cl2 was responsible for the larger attractive shifts in the supercritical CO2. The difference of solvation structures between the isomers was significant at Tr ) 1.02 but became minor as the temperature increased to Tr ) 1.20. I. Introduction Supercritical fluid changes density continuously from gaslike to liquidlike fluids in the absence of a vapor-liquid phase transition.1-3 Using this property, solute-solvent interactions in supercritical solutions have been investigated by absorption spectroscopy,2,4-9 computer simulation,3,10-14 and thermodynamics experiments15-17 over a wide range of densities. Since Raman scattering measurements enable us to probe the short-range structure around a vibrating molecule, the vibrational Raman spectrum has been measured to study the local structure of supercritical solutions.18-25 In particular, the peak frequency of the Raman band has been measured in various systems, i.e., naphthalene in supercritical CO2;18 acetone and acetonitrile in supercritical Ar, CO2, CHF3, and CF3Cl;19 HCl in supercritical Ar;20 and C6D11H in supercritical CO2.21 From these studies, the peak frequencies shift significantly toward the lower energy side when the solute molecules are dissolved in polar supercritical fluids, whereas those frequencies show a weak density dependence in the nonpolar fluids. A principal contribution to these larger shifts was ascribed to the large dipole moment of solvent molecules in the supercritical state. We investigated the structures of neat supercritical fluids by dynamic light scattering,26-29 terahertz absorption,30,31 vibrational Raman spectroscopy,32-36 and small-angle X-ray scattering.37 * Corresponding author. Telephone and Fax: +81-82-424-7487. E-mail address:
[email protected]. † Natural Science Center for Basic Research and Development (NBARD), Hiroshima University. ‡ Department of Chemistry, Graduate School of Science, Hiroshima University. § PRESTO, Japan Science and Technology Agency.
Figure 1. Molecular structures of cis- and trans-C2H2Cl2 and values of their dipole moments.39
In vibrational Raman spectroscopy, we discussed the density dependences of attractive and repulsive interactions between solvent molecules.33-35 As a recent advance, we have conducted studies on intermolecular interaction between solute and solvent and measured the vibrational Raman spectrum of solute molecules in a supercritical fluid.38 The solute molecules investigated were cis- and trans-isomers of 1,2-dichloroethylene (Figure 1); these isomers have many similar properties such as molecular formula and volume, whereas a significant difference exists in polarity, i.e., µ(cis-isomer) ) 1.9 D and µ(trans-isomer) ) 0 D.39 We investigated how the polarity and molecular structure of the isomers affect the interactions between solute and solvent molecules by changing the fluid density. We found that the polar solute molecule show weaker attractive interactions, whereas the nonpolar solute molecule show stronger ones in all densities at the isotherm of reduced temperature Tr ) T/Tc ) 1.02.38 In the present study, the Raman spectral measurements of the isomers were extended to higher temperatures to discuss the differences in their attractive shifts. To investigate why nonpolar trans-C2H2Cl2 has the larger attractive energy than that of polar cis-C2H2Cl2, we conducted theoretical calculations of the attractive shifts of the CdC stretching modes of
10.1021/jp903240v CCC: $40.75 2009 American Chemical Society Published on Web 09/14/2009
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the two isomers. We found that the configurations and orientations of CO2 molecules around the isomers play important roles in the determination of attractive energies between solute and solvent molecules. That is, the anisotropic solvation structure is very significant for the trans-isomer, whereas it becomes isotropic for the cis-isomer. The difference of anisotropy between isomers became minor with increasing temperature. II. Experimental Section The Raman spectrometer constructed is described elsewhere.35,36,38,40 In brief, the light source was a DPSS laser (Laser Quantum, Torus 532-300 mW) operated with an excitation wavelength of 532 nm, at a single frequency output with a power of 200 mW in front of an optical cell. The laser was incident on the cell, and a camera lens collected scattered light at an angle of 90°. Using a monochromator (Jovin Yvon-Spex, HR640) and a photomultiplier tube (Hamamatsu Photonics, R464SS), Raman spectra were recorded by the photon counting method. The frequency of each Raman spectrum was calibrated by that of the exciting laser. Since the frequency repeatability of the present spectrometer was confirmed to be within (0.02 cm-1 over a 4-h period, stability was so high that we could obtain precise Raman spectral shifts of the CdC stretching mode. Supercritical solutions were prepared by the following procedures. An accurate volume of cis- or trans-C2H2Cl2 was introduced into a high-pressure container. The container was then filled with high-pressure CO2 by measuring the weight of the container during CO2 injection. The high-pressure solution generated in the container was transferred into a Raman optical cell. To raise the optical purity, the solution was filtered through a PTFE membrane filter with a pore size of 0.1 µm in the highpressure container. The densities of the supercritical solution were adjusted by releasing the high-pressure supercritical solution from the Raman cell. The mole fraction was determined on the basis of electronic absorption spectra of the solute cisand trans-C2H2Cl2 dissolved in supercritical CO2. The absorbance was measured using a homemade in situ absorption spectrometer. From the linear relationship between absorbance and concentration of a reference solution, we quantified the concentrations and mole fractions of solute molecules (Supporting Information Figure S1). Thus, it was ensured that the concentrations of supercritical solutions are set to be constant for all Raman spectral measurements as a solute mole fraction of 4 × 10-3. Figure 2 shows the thermodynamic states for Raman spectral measurements plotted on P-T (Figure 2a) and P-F (Figure 2b) phase diagrams. The temperature was kept at three isotherms of reduced temperatures, Tr ) 1.02 (310.2 K), 1.06 (322.4 K), and 1.20 (365.0 K), by a set comprising a proportional-integralderivative (PID) controller, heaters, and a thermocouple. Pressure was monitored with a strain gauge backed up with a strain amplifier (Kyowa Dengyo). Both temperature and pressure fluctuations were within (0.1% during measurements. Densities were calculated from the empirical state equation41 using measured P and T values. Chemical purities of CO2 (Chugoku Sanso), trans-C2H2Cl2, and cis-C2H2Cl2 (Tokyo Kasei Kogyo) were 99.99, 98.0, and 99.0%, respectively. The critical constants of CO2 are reported41 to be Tc ) 304.1 K, Pc ) 7.38 MPa, and Fc ) 0.468 g cm-3. The reduced density Fr is given by Fr ) F/Fc.
Figure 2. Thermodynamic states for Raman spectral measurements on (a) pressure-temperature and (b) pressure-density phase diagrams of supercritical CO2. Blue open circles and red open squares represent cis-C2H2Cl2 and trans-C2H2Cl2, respectively. C.P. indicates the gas-liquid critical point. The solid line in part a is the liquid-vapor coexistence curve. The quantity Fr is expressed as Fr ) F/Fc.
III. Results Figure 3 shows the Raman spectra of cis- and trans-C2H2Cl2 in the wide spectral region between 300 and 3500 cm-1 at room temperature; the vibrational modes of these isomers have been assigned.42 We measured the CdC stretching modes of cis- and trans-C2H2Cl2 centered around 1590 and 1580 cm-1, respectively, by changing the density and temperature of supercritical CO2. Figure 4a and b shows typical Raman spectra of the CdC stretching modes of cis- and trans-C2H2Cl2 as functions of density. All spectra were analyzed using a Gaussian function to obtain peak frequencies, ν. Figure 5 shows the density dependence of shifts of the peak frequencies, ∆ν ) ν - ν0, where ν0 is a frequency obtained from the extrapolation of peak frequencies to density ) 0. As the density of supercritical CO2 increases, the peak frequencies shift toward the lower energy side. The shifts of trans-C2H2Cl2 are significantly larger than those of cis-C2H2Cl2 at Tr ) 1.02, 1.06, and 1.20. These observations are consistent with previous studies performed at Tr ) 1.02.38 In the present study, we also checked carefully whether or not the Raman band of the CdC stretching mode is dependent on solute concentration. As a result, it was ensured that shifts are independent of solute concentration, ranging from 1 × 10-3 to 8 × 10-3 (Supporting Information, Figure S2). Thus, Raman spectra were collected at a constant mole fraction of 4 × 10-3 for all measurements.43
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J. Phys. Chem. B, Vol. 113, No. 40, 2009 13293
Figure 3. Typical examples of Raman spectra of (a) cis-C2H2Cl2 and (b) trans-C2H2Cl2 in the wide spectral regions. The data were measured using neat liquids at room temperature.
Figure 5. Density dependence of shifts of peak frequencies for Raman bands of the CdC stretching modes for (a) cis-C2H2Cl2 and (b) transC2H2Cl2. The data were collected at three temperatures.
using the hard-sphere model.45 The quantity ∆νA was derived empirically by subtracting ∆νR from the experimentally obtained net amount ∆ν. Here, the repulsive and attractive shifts indicate the amounts of energy that solvent molecules exert along the vibrational coordinate of a solute molecule. In the conditions that solvent and solute molecules are regarded as a sphere and a pseudodiatomic molecule consisting of two hard-sphere atoms, respectively, the repulsive shift ∆νR is expressed as45
∆νR ) C1 exp(m1F*) + C2 exp(m2F*) - C3 exp(m3F*) ν0 (2)
Figure 4. Density dependence of Raman spectra of the CdC stretching modes of cis- and trans-C2H2Cl2 measured in supercritical CO2. Blue and red correspond to cis-C2H2Cl2 and trans-C2H2Cl2, respectively. Solid lines are curve fits using the Gaussian function. The term Fr is the reduced density represented by Fr ) F/Fc.
To study attractive and repulsive interactions between solute and solvent molecules, shifts were decomposed into attractive and repulsive components by the perturbed hard-sphere theory44,45
∆ν ) ∆νR + ∆νA
(1)
where ∆ν, ∆νR, and ∆νA are the net, repulsive, and attractive frequency shifts, respectively.46 The quantity ∆νR was calculated
with Ck ) kRRθz(1 - z)k-1 exp bk and RR ) re[-(3g/2f) + (GR/FR)], where mk and bk refer to empirical parameters depending on the sizes of solute and solvent molecules. The quantity F* is represented by F* ) FSσS3, where FS is the number density and σS is the diameter of the solvent hard sphere. The quantity θ is given by θ ) kBT/fre2, where kB is the Boltzmann constant and re is the equilibrium bond length of the CdC bond. The value of z is expressed as z ) re/σ with two hard-sphere cavities of diameter σ. f and g are the intramolecular quadratic harmonic and cubic anharmonic force constants of the CdC bond, respectively, and FR and GR are the linear and quadratic constants, respectively, indicating forces that solvent molecules exert along the normal coordinate of the solute. All parameters required for the calculations are listed in Table 1. Figure 6 shows the obtained attractive shifts ∆νA and repulsive shifts ∆νR of the CdC stretching modes of cis- and trans-C2H2Cl2 as functions of the density of supercritical CO2 at Tr ) 1.02, 1.06, and 1.20.55,56 The packing fraction corresponding to the density is shown in the upper axis and is defined as 4π(σS/2)3FS/3. The peak frequencies of the repulsive com-
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TABLE 1: Parameters for Calculation of Repulsive Shifts by the Hard-Sphere Model parameters
cis-C2H2Cl2
trans-C2H2Cl2
7.65 -1.468 10.9 0.023 0.40 0.40 0.40 0.133 2.66 4.41 4.37 -0.61 -1.62 -2.51
7.57 -1.494 10.9 0.023 0.40 0.40 0.40 0.132 2.66 4.41 4.37 -0.61 -1.62 -2.51
a
f (N/cm) g (N/cm2 × 109)b GR/FR ) 1/4L (nm-1)c L ) 0.0571σave (nm)c σave ) (σ + σS)/2 (nm)d σ (nm)d σS (nm)d re (nm)e m1c m2c m3c b1c b2c b3c e
a Reference 51. Reference 54.
b
Reference 52.
c
Reference 45.
d
Reference 53.
ponents shift toward the higher energy side as the density increases. This means that the energies of solute-solvent repulsive interactions increase with increase in the density and/ or the solvent packing fraction. Since the molecular properties of the isomers for the calculations are almost the same (Table 1), the repulsive shifts of both isomers result in the same. With regard to the attractive shifts, the peak frequencies of attractive components show the shifts toward the lower energy side as the density increases. The energies of solute-solvent attractive interactions increase with increase in solvent density. The attractive shifts of trans-C2H2Cl2 are larger than those of cisC2H2Cl2 at all densities and temperatures. Since the dipole moments of cis- and trans-C2H2Cl2 are reported to be 1.9 and 0 D, respectively,39 nonpolar trans-C2H2Cl2 shows greater attractive interactions than polar cis-C2H2Cl2 in supercritical CO2. IV. Discussion In order to discuss the observed difference in the isomers, we verified the empirically obtained attractive shifts of the CdC
Kajiya and Saitow stretching modes of the cis- and trans-isomers by the following calculations. The attractive shift is formulated by the attractive shift parameter CA and the solvent density FS as44
∆νA /ν0 ) CAFS /ν0
(3)
CA is composed of the following four terms.49,50,57
CA ) CA,dis + CA,D-D + CA,DID + CA,D-Q
(4)
where CA,dis, CA,D-D, CA,DID, and CA,D-Q are attractive shift parameters corresponding to the dispersion (dis), dipole-dipole (D-D), dipole-induced-dipole (DID), and dipole-quadrupole (D-Q) interactions between solute and solvent molecules, respectively. These components are expressed as49,50,57
CA,dis ) -
a
CA,D-D ) -
)
(
(5)
)
∂µ0 4 4π 1 µ0 ∆Q µS2 3 3 σ 3kBT ∂Q a
CA,DID ) -
(
4π 1 3 ∂R0 I ∆Q RS 3 σ 3 2 a ∂Q
(
(6)
)
∂R0 ∂µ0 4π 1 2µ0 ∆QRS + ∆QµS2 3 σ3 ∂Q ∂Q a
(7) CA,D-Q ) -
(
)
∂µ0 ∂q0 4π 1 2 µ ∆QqS2 + q0 ∆QµS2 3 σ 5 kBT 0 ∂Q ∂Q a (8)
where the subscripts 0 and S show solute and solvent molecules, respectively. R, I, µ, and q are the molecular polarizability, ionization energy, dipole moment, and quadrupole moment,
Figure 6. Calculated repulsive shifts and attractive shifts empirically obtained from measurements of CdC stretching modes of C2H2Cl2. (a and b) Solvent density dependence for the cis- and trans-isomers, respectively.
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TABLE 2: Parameters for Calculation of Attractive Shifts solute cis-C2H2Cl2
e
I0 (J × 10-18)a µ0 (D)a σ0 (nm)b j (L mol-1 cm-2)c A µred (g × 10-24) ∂R0/∂Q (nm2)d (∂R0/∂Q)| (nm2)d (∂R0/∂Q)⊥ (nm2)d
1.55 1.9 0.5 2200 8.5 0.037 0.076 0.018
solute trans-C2H2Cl2 I0 (J × 10-18)a µ0 (D)a σ0 (nm)b ∂R0/∂Q (nm2)d (∂R0/∂Q)| (nm2)d (∂R0/∂Q)⊥ (nm2)d
1.55 0 0.5 0.037 0.076 0.018
solvent CO2 RS (nm3 × 10-3)e RS,| (nm3 × 10-3)e RS,⊥ (nm3 × 10-3)e IS (J × 10-18)a µS (D)a qS (D nm)f
2.65 4.05 1.95 2.21 0 -0.45
a Reference 39. b Reference 53. Reference 60. f Reference 61.
c
Reference 58.
d
∂Q)0,⊥RS,|, and (∂R/∂Q)0,⊥RS,⊥ (see the Appendix). By considering all anisotropic components, we acquired CA parameters by summation of eqs 9-11 and calculated the attractive shifts of the CdC stretching modes of both isomers as a function of density (Figure 7). Dotted lines show the calculated attractive shifts, and the disagreements seen in the isotropic cases disappear. According to the disagreement in the isotropic case and the agreement in the anisotropic case, it is considered that the relative configuration and orientation between solute and solvent molecules play important roles in the attractive interactions.66,67 We quantified solvation structures around the solute molecule using CA. Because various configurations and orientations of solvent molecules can produce the same CA value, forming the dotted line in Figure 7, the possible configurations and orientations were examined by changing θ and φ.68 The obtained results are displayed in Figure 9. These data show the solvation structures around cis- and trans-C2H2Cl2 as a 3D diagram. Briefly, we describe the 3D diagrams involving four important meanings before the discussion of solvation structure. First, the green regions and sticks indicate positions and orientations of CO2 molecules, respectively, to produce the same dotted lines. Second, the solvation structure becomes isotropic, as the green region becomes larger. The anisotropy in the solvation structure
Reference 59.
respectively (Table 2). The quantities σa and Ia are expressed as σa ) (σ0+σS)/2 and Ia ) I0IS/(I0 + IS). Q is the vibrational normal-mode coordinate of the solute, and ∆Q ) Q11 - Q00 is the change in expectation value of the normal-mode coordinate upon vibrational excitation.62 Here we show the calculated results of attractive shifts of the CdC stretching modes using eqs 3-8 (Figure 7). Solid lines represent the calculated attractive shifts CAFS/ν0 and symbols represent the empirically obtained attractive shifts ∆νA/ν0. However, there is disagreement between these values. To consider this disagreement, let us mention CA,dis, CA,D-D, CA,DID, and CA,D-Q, whose parameters involve anisotropic components. That is, ∂R0/∂Q consists of parallel (∂R0/∂Q)| and perpendicular (∂R0/∂Q)⊥ components relative to the CdC bond.59,64 The former value is 4.2 times greater than the latter (Table 2). The term RS consists of parallel RS,| and perpendicular RS,⊥ components relative to the OdCdO bond.64 The effective dipole moment µ and quadrupole moment q are changed by the relative configuration between solute and solvent molecules, depending on the angles θ and φ (Figure 8a and b).60,65 Under these situations, we need to recharacterize the attractive shifts of the CdC stretching modes for the anisotropic condition. Since the dipole moment of CO2, µS, is zero, the four eqs 5-8 are reduced to the following three equations.
CA,dis ) -
π∆QIa 3σa3
j(θ, φ)
(9)
CA,DID ) -
∂µ0 RS 4π 2µ0 ∆Q g(θ) 3 ∂Q 2 3σa
(10)
CA,D-Q )
3qS 4π ∂µ0 ∆Q h(θ, φ) 3σa ∂Q 4
(11)
where j(θ,φ), g(θ), and h(θ,φ) are defined as the orientational factors60,65 and involve (∂R/∂Q)0,|RS,|, (∂R/∂Q)0,|RS,⊥, (∂R/
Figure 7. Attractive shifts of CdC stretching modes of experiments (symbols) and calculations (lines) as functions of density. (a) cisC2H2Cl2. (b) trans-C2H2Cl2. Solid and dotted lines are calculated results based on isotropic and anisotropic configurations, respectively. Attractive shifts are proportional to density.69
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Figure 8. (a) Coordinates and angles between a solute and a solvent molecule. (b) Molecular orientations at θ0 ) θS ) φ0 ) φS ) 0. (c) Parallel and perpendicular directions for molecular polarizabilities and polarizability derivatives.
indicates that configurations of solvent molecules around a solute molecule are not an isotropic but an anisotropic distribution. Third, the configuration does not indicate the freeze condition
Kajiya and Saitow of molecular motion but the position and orientation with high probability around the solute. Fourth, the anisotropy in the solvation structure is combined directly to the molecular anisotropy in the CA parameter. This is because the polarizability and polarizability derivative in the direction, shown in Figure 8c, are combined by CA in eqs 9-11. Here we discuss the solvation structures of 3D diagrams of CO2 around each isomer. As shown in Figure 9, the green region of cis-C2H2Cl2 is 50 times larger than that of trans-C2H2Cl2. Since cis-C2H2Cl2 has a larger green region, it is elucidated that the solvation structure becomes isotropic. On the other hand, trans-C2H2Cl2 has a smaller green region. These results revealed that anisotropic solvation becomes significant in trans-C2H2Cl2 rather than in cis-C2H2Cl2. According to molecular properties in two isomers, nonpolar trans-C2H2Cl2 has only a dispersion interaction, while cis-C2H2Cl2 with the dipole moment has not only a dispersion but also dipole-quadrupole and dipoleinduced-dipole interactions. That is, the differences in molecular interactions between cis-C2H2Cl2/CO2 and trans-C2H2Cl2/CO2 determine whether the solvation structure becomes isotropic or anisotropic. Such a situation was quantified by Raman spectroscopy and attractive shift calculations in the present study. Regarding anisotropic solvation structures, studies using molecular dynamics simulations,70 NMR,71 and Monte Carlo simulations72-74 have been reported on aromatic molecules70-73 and alcohols74 in supercritical CO2. To the best of our knowledge, the present study is the first report where the configurations and orientations of solute and solvent molecules in supercritical fluid as well as high pressure gas and liquid are visualized by Raman spectroscopic study.
Figure 9. 3D diagram of solvation structures around cis-C2H2Cl2 (a-d) and trans-C2H2Cl2 (e-h). Green regions (b, c, f, and g) and sticks (d and h) indicate positions and orientations of CO2 molecules, respectively, to produce the dotted lines in Figure 7 in the x′-, y′-, and z′-coordinates (a and e).
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J. Phys. Chem. B, Vol. 113, No. 40, 2009 13297 obtained at the higher temperature of Tr ) 1.20, as shown in Figure 11. From the results, it is revealed that the green region of trans-C2H2Cl2 at Tr ) 1.20 becomes 7 times larger than that at Tr ) 1.02. That is, the solvation structure of trans-C2H2Cl2 changes from the anisotropic to the isotropic, as the temperature increase. On the other hand, the green region of cis-C2H2Cl2 does not significantly change with increasing temperature. It is shown that the temperature dependence of solvation structure of cis-C2H2Cl2 is insignificant. Next, we investigated that a difference of solvation structures between cis- and trans-C2H2Cl2 in two temperatures. As shown in Figure 11, the green region of cis-C2H2Cl2 is 50 times larger than that of trans-C2H2Cl2 at Tr ) 1.02. On the other hand, the difference of green region in two isomers is reduced to one-seventh of 50 at Tr ) 1.20. That is, the difference of solvation structures between cis- and transisomers becomes minor with increasing temperature. This tendency is in good agreement with the results shown in Figures 10a-c, because the differences in attractive shifts between the isomers become small as the temperature increases. Consequently, it was verified that the difference of solvation structures between isomers results in minor with increasing temperature in the range covered in the present study. These results and interpretations are based on experimental data. V. Conclusions
Figure 10. Attractive shifted amounts of CdC stretching modes of cis- and trans-C2H2Cl2 at Tr ) (a) 1.02, (b) 1.06, and (c) 1.20.
Finally, we state the temperature dependence of solvation structures. Figure 10a-c show attractive shifts of both cis- and trans-C2H2Cl2 at three temperatures, Tr ) 1.02, 1.06, and 1.20. The differences between the isomers become smaller as the temperature increases. To examine the temperature dependence, we conducted the same analysis by producing a 3D diagram at Tr ) 1.20 by using eqs 3, 4, and 9-11. That is, the slopes of attractive shift as a function of density were analyzed by eq 3. The obtained CA values in each temperature were used to optimize angular parameters for drawing 3D diagrams in the temperatures by eqs 4 and 9-11. As a result, the 3D diagrams of solvation structures around cis- and trans-C2H2Cl2 are
We have measured the vibrational Raman spectra of CdC stretching modes of both cis- and trans-1,2-C2H2Cl2 in supercritical CO2 at three isotherms of Tr ) 1.02, 1.06, and 1.20 in a wide density range. The peak frequencies of the CdC stretching modes shifted toward the low energy side as the density of supercritical CO2 increased, and the shifted amounts were decomposed into attractive and repulsive components by the perturbed hard-sphere theory. The energies of the repulsive shifts of cis-C2H2Cl2 were almost equivalent to those of transC2H2Cl2, whereas the attractive shifts energies of nonpolar transC2H2Cl2 were significantly larger than those of polar cis-C2H2Cl2 at all densities and temperatures. These differences in the isomers were evaluated by calculating the attractive shifts of the CdC stretching modes of both isomers; these were obtained by considering the dispersion, dipole-induced-dipole, and
Figure 11. 3D diagram of solvation structures atround trans- and cis-C2H2Cl2 at Tr ) 1.02 and 1.20. Green regions indicate positions of CO2 molecules, respectively, to produce the experimental results in Figure 7 in the x′-, y′-, and z′-coordinates in Figure 9.
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dipole-quadrupole interactions between solute C2H2Cl2 and solvent CO2 molecules. The configurations and orientations between solute and solvent molecules were quantified, and solvation structures were visualized by 3D diagrams. The anisotropic solvation structure observed in trans-C2H2Cl2 was responsible for larger attractive shifts in the supercritical CO2. It was revealed that solvent CO2 molecules around cis-C2H2Cl2 exist in an area 50 times wider than that around trans-C2H2Cl2 at Tr ) 1.02, but the areas were reduced to one-seventh of 50 by increasing the temperature to Tr ) 1.20. The difference of solvation structures between the isomers was significant at Tr ) 1.02, but became minor as the temperature increased up to Tr ) 1.20. Appendix: Attractive Shift Parameters for Anisotropic Configuration According to the studies by London,65 attractive potential energies V between a solute and a solvent molecules are expressed as60
that are in contact. This idea is based on the reported model49,50,57 and is applied to the present analysis. If the other parameters except for R0 and µ0 would depend significantly on Q or θ0, θS, φ0, φS, and r0S would couple to each other, the use of eqs A1-A6 might be reconsidered. Acknowledgment. K.-i.S. acknowledges the Sumitomo Foundation Award for Young Researchers and a Grant-in-Aid for Young Scientists (B) (13740321) from the Ministry of Education, Science and Culture of Japan. These grants helped us construct the instrument used in the present study. Supporting Information Available: Two tables showing the data of Figure 6 and two figures showing the experimental results of absorbance of C2H2Cl2 in supercritical CO2 (S1) and concentration dependences of peak frequencies (S2). This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes
Vdis ) -
VDID ) -
VD-Q )
j(θ, φ)Ia 4r0S
6
µ02RSg(θ) 2r0S6
3µ0qSh(θ, φ) 4r0S4
(A1)
(A2)
(A3)
with
j(θ, φ) ) (A - B - B' + C)[sin θ0 sin θS cos(φS - φ0) 2 cos θ0 cos θS]2 + 3(B - C) cos2 θ0 + 3(B′-C) cos2 θS + (B + B' + 4C) (A4) g(θ) ) 3 cos2(θ0 + 90) + 1 h(θ, φ) ) cos(θ0 + 90)(3 cos2 θS - 1) 2 sin(θ0 + 90) sin θS cos θS cos(φ0 - φS)
(A5)
(A6)
with A ) R0,|RS,|, B ) R0,|RS,⊥, B′ ) R0,⊥RS,|, C ) R0,⊥RS,⊥. θ and φ are the angles that specify the relative configuration between a solute and a solvent molecule (Figure 8a and b). r0S is the distance between the center of the solute molecule and the solvent molecule. Subscripts | and ⊥ represent the parallel and perpendicular components, respectively (Figure 8c).60,65 On the basis of the methods49,50,57 for obtaining attractive shift parameters of isotropic cases, we calculated the attractive shift parameters CA of anisotropic cases with each molecular configurations and orientation. That is, eqs 9-11 are obtained by differentiating eqs A1-A3, respectively, and by multiplying by 4πσa3/3, and then by substituting σa to r0S. For the derivations of eqs 9-11, there are several approximations. (1) The other parameters except for R0 and µ0 are independent of Q. (2) θ0, θS, φ0, φS, and r0S are not affected in each other and do not couple to each other. (3) The r0S is fixed and is used as the sum of radii of solute and solvent molecules
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Solvation Structures of 1,2-Dichloroethylene (33) Saitow, K.; Otake, K.; Nakayama, H.; Ishii, K.; Nishikawa, K. Chem. Phys. Lett. 2003, 368, 209. (34) Saitow, K.; Nakayama, H.; Ishii, K.; Nishikawa, K. J. Phys. Chem. A 2004, 108, 5770. (35) Saitow, K.; Sasaki, J. J. Chem. Phys. 2005, 122, 104502. (36) Otake, K.; Abe, M.; Nishikawa, K.; Saitow, K. Jpn. J. Appl. Phys 2006, 45, 2801. (37) Nishikawa, K.; Ochiai, H.; Saitow, K.; Morita, T. Chem. Phys. 2003, 286, 421. (38) Kajiya, D.; Mouri, Y.; Saitow, K. J. Phys. Chem. B 2008, 112, 7980. (39) CRC Handbook of Chemistry and Physics, 77th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1996. (40) The resolution of this Raman spectrometer is less than 0.8 cm-1 at full width at half maximum at high resolution conditions. (41) Span, R.; Wagner, W. J. Phys. Chem. Ref. Data 1996, 25, 1509. (42) Shimanouchi, T. Tables of Molecular Vibrational Frequencies Consolidated Volume I; National Bureau of Standards: Washington, DC, 1972; pp 78-80. (43) Almost studies on supercritical solutions have been performed using solutions of saturated or fixed molar concentrations. In these experimental conditions, solute mole fraction changes by fluid density, because the solubility of solute and number density of solvent molecules change depending on fluid density. On the other hand, the mole fraction of solute molecule was set to be constant in the present study, and the density dependence was investigated under the fixed mole fraction. That is, the Raman spectra were measured at fixed mole fractions of solute and solvent molecules in all densities, temperatures, and both solute molecules of cisand trans-isomers. (44) Schweizer, K. S.; Chandler, D. J. Chem. Phys. 1982, 76, 2296. (45) Zakin, M. R.; Herschbach, D. R. J. Chem. Phys. 1986, 85, 2376. (46) The analysis based on the perturbed hard-sphere theory was conducted in Raman spectroscopic studies of some neat supercritical fluids in refs 33-35, 47, and 48 and supercritical solutions in refs 21 and 38 and conducted in infrared spectroscopic studies of supercritical solutions in refs 49 and 50. (47) Ben-Amotz, D.; LaPlant, F.; Shea, D.; Gardecki, J.; List, D. Proceedings of the Supercritical Fluids Technology; ACS Symposium Series No. 488; Bright, F. V., McNanlly, M. E., Eds.; American Chemical Society: Washington, DC, 1992; p 18. (48) Cabac¸o, M. I.; Besnard, M.; Tassaing, T.; Danten, Y. J. Mol. Liq. 2006, 125, 100. (49) Lalanne, P.; Tassaing, T.; Danten, Y.; Cansell, F.; Tucker, S. C.; Besnard, M. J. Phys. Chem. A 2004, 108, 2617. (50) Tassaing, T.; Oparin, R.; Danten, Y.; Besnard, M. J. Supercrit. Fluids 2005, 33, 85. (51) Jeyapandian, S.; Raj, G. A. S. J. Mol. Struct. 1972, 14, 17. (52) Herschbach, D. R.; Laurie, V. W. J. Chem. Phys. 1961, 35, 458. (53) Edward, J. T. J. Chem. Educ. 1970, 47, 261. (54) Takahashi, K.; Sugawara, M.; Yabushita, S. J. Phys. Chem. A 2002, 106, 2676. (55) The values of attractive shifts were listed in Supporting Information Tables S1 and S2. (56) According to the perturbed hard-sphere analysis, the repulsive shift is not zero but the nonzero value at the density ) 0. This is indicated by
J. Phys. Chem. B, Vol. 113, No. 40, 2009 13299 the following equation. That is, eq 2 at density ) 0 brings ∆νR/ν0 ) C1 exp(0) + C2 exp(0) - C3 exp(0) ) C1 + C2 - C3 * 0. (57) Ben-Amotz, D.; Lee, M.-R.; Cho, S. Y.; List, D. J. J. Chem. Phys. 1992, 96, 8781. (58) Tanabe, K.; Saeki, S. Bull. Chem. Soc. Jpn. 1974, 47, 2545. (59) Kukina, V. S.; Sverdlov, L. M. Opt. Spectrosc. 1967, 23, 297. (60) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley; New York, 1954; pp 25-30, 947-951, and 955-970. (61) Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids Volume 1: Fundamentals; Clarendon Press: Oxford, 1984; p 580. (62) In the pseudodiatomic approximation, (∂R0/∂Q)∆Q and (∂µ0/∂Q)∆Q can be expressed by (∂R0/∂r)∆r and (∂µ0/∂r)∆r, where ∆r is given by ∆r ≈ -(3/2)hcν0g/f 2.57 The term h is the Planck constant, and c is the speed j /πN)1/2,63 where of light in vacuum. ∂µ0/∂Q is given by ∂µ/∂Q ) (3c2µredA j , and µred are the Avogadro’s number, integrated absorption coefficient, N, A and reduced mass obtained from ν0 ≈ (k/µred)1/2/2π. Parameters required for calculations are listed in Table 2. Since trans-C2H2Cl2 and CO2 molecules do not possess a permanent electric dipole moment, eq 4 can be simplified by writing CA ) CA,dis + CA,DID + CA,D-Q for cis-C2H2Cl2, and CA ) CA,dis for trans-C2H2Cl2. (63) Barrow, G. M. Introduction to Molecular Spectroscopy; McGrawHill: New York, 1962; pp 76-80. (64) For cis- and trans-C2H2Cl2 molecules, the value of polarizability derivative of perpendicular to CdC bond in the plane of C2H2Cl2 molecule is reported to be equal to that perpendicular to the plane of C2H2Cl2 molecule,59 and hence, ∂R0/∂Q ) [(∂R0/∂Q)| + 2(∂R0/∂Q)⊥]/3.19,60 For molecular polarizability of CO2, the relationship is given as RS ) (RS,| + 2RS,⊥)/3.60 (65) London, F. J. Phys. Chem. 1942, 46, 305. (66) When the anisotropic shifts are averaged by θ and φ, the anisotropic shifts become the isotropic shift. (67) The value of CA is obtained from the summation of eqs 9-11, whose equations are functions of angles, θ0, θS, φ0, and φS. One can obtain the CA value as a function of an angle by fixing the other angles. (68) In calculation of anisotropic attractive shift, the radial distance between solute and solvent molecules is fixed and is used as the sum of radii of solute and solvent molecules that are in contact. This idea is based on the model used in refs 49, 50, and 57 and is applied to the present analysis. As for the orientation, the anisotropic attractive shift is calculated by changing each angle. (69) As shown in Figure 7, the slope of attractive shifts changes slightly by the density. According to our estimation, the difference of slopes in the present density range is within 10%. Thus, we approximate the obtained data as linear density dependence. (70) Inomata, H.; Saito, S.; Debenedetti, P. G. Fluid Phase Equilib. 1996, 116, 282. (71) Kanakubo, M.; Umecky, T.; Kawanami, H.; Aizawa, T.; Ikushima, Y.; Masuda, Y. Chem. Phys. Lett. 2001, 338, 95. (72) Stubbs, J. M.; Drake-Wilhelm, D. D.; Siepmann, J. I. J. Phys. Chem. B 2005, 109, 19885. (73) Iwai, Y.; Uchida, H.; Koga, Y.; Arai, Y.; Mori, Y. Ind. Eng. Chem. Res. 1996, 35, 3782. (74) Iwai, Y.; Koga, Y.; Arai, Y. Fluid Phase Equilib. 1996, 116, 267.
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