Energetics and Volume Changes in Electron Attachment to Pyrazine in

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J. Phys. Chem. B 2007, 111, 6684-6689

Energetics and Volume Changes in Electron Attachment to Pyrazine in Supercritical Xenon† Richard A. Holroyd* and Jack M. Preses Chemistry Department, BrookhaVen National Laboratory, Upton, New York 11973

Masaru Nishikawa Faculty of Engineering, Kanagawa Institute of Technology, 1030 Shimo-Ogino, Astugi, 243-0292, Japan

Kengo Itoh Department of Pure and Applied Science, UniVersity of Tokyo, 153-8902, Japan ReceiVed: September 11, 2006; In Final Form: NoVember 8, 2006

The attachment of electrons to pyrazine occurs reversibly over a wide range of pressures at and above room temperature in supercritical xenon. The rate constant for attachment increases with pressure at low pressures, passes through a maximum, and levels off at values of 1-3 × 1012 m-1 s-1 at high pressure. The activation volumes for attachment (∆Va*) are quite small but show maxima near the compressibility maxima. In contrast, ∆Va* is always negative for this reaction in sc-ethane and exhibits minima near the compressibility maxima. The rate constants for electron detachment change little with pressure but increase with temperature. Activation volumes for detachment are small. To explain the small volume change observed for this reaction, it is proposed that at the higher pressures clustering around the neutral pyrazine is comparable to that around the ion; i.e., the partial molar volumes are comparable. The free energy change (∆Gr) of this reaction decreases between 40 and 60 bar and then is fairly constant at higher pressures. The dependence of ∆Gr on pressure is consistent with clustering around the neutral pyrazine at higher pressure. Also, the electron affinity of the clusters, pyrazineXen, increases with n to a few tenths of an eV.

Introduction Studies of the effect of pressure on electron attachment/ detachment equilibria in nonpolar hydrocarbon liquids revealed that large volume decreases (from -0.08 to -0.3 L/mol) occur in such reactions.1 These large volume changes are associated with electrostriction of the solvent around the product ion, an effect that is proportional to the compressibility of the solvent. Supercritical fluids are even more compressible than liquids, and greater effects are therefore expected. Indeed, a conductivity study of electron attachment to pyrazine in supercritical ethane showed that quite large volume changes occur. In sc-ethane, the volume changes for reaction 1 are between -1 and -45 L/mol.2

e- + pyrazine a pyrazine-

(1)

With increasing pressure, the equilibrium (eq 1) shifts to the right; the free energy of reaction decreases by about 0.1 eV over a 10 bar pressure interval. The volume changes calculated by the compressible continuum model for electrostriction around the pyrazine ion predict these volume changes quite well.2 By implication, that study suggested that the partial molar volume of neutral pyrazine, V h (Pyz), in supercritical ethane is small in magnitude in comparison to that of the ion. However, studies of other aromatics in supercritical fluids have shown that values of V h (solute) are generally negative and can be significantly large in magnitude in regions of high compressibility especially close to the critical temperature.3-5 For example, for naphthalene †

Part of the special issue “Norman Sutin Festschrift”.

in ethylene at 12 °C, V h (naph) ranges from -15 to 0 L/mol, h (solute) on the depending on pressure.3 The dependence of V isothermal compressibility (χT) has been shown to follow the empirical equation5,6

V h (solute) ) a(T)χT + b(T)

(2)

The partial molar volume will be negative for cases where the intermolecular forces are attractive. These forces may be significantly different in supercritical xenon from those in scethane due to differences in size, shape, and interaction energy, as suggested by theory.7 The electrostriction of the solvent suggests that the ions will have a large solvation shell. This has been demonstrated by measurements of ion mobilities in supercritical solvents.8 The cluster of solvent molecules around the ion results in a lower mobility than that expected for a bare ion. The mobility results were interpreted in terms of a Stokes-like hydrodynamic compressible continuum (HCC) model. That study showed that the size of positive ion clusters first increases with density below the critical density, peaks near critical densities, and then is either level or decreases slightly with density in the high-density region. The diameter of these clusters ranged from 1.2 to 1.8 nm. Information about the size of clusters around negative ions is relevant to the present study. Negative ions are reported to have a higher mobility than positive ions and therefore less of a cluster of solvent molecules attached.8 The mobility of C6F6has been studied in supercritical xenon; HCC calculations indicate the diameter of the clusters at 294 K is between 1 and 1.4 nm depending on pressure.9

10.1021/jp065922o CCC: $37.00 © 2007 American Chemical Society Published on Web 01/11/2007

Energetics/Volume Changes in Supercritical Xe

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6685

This study is the first of its kind to investigate electron equilibria in supercritical xenon and also the first to be studied over a wide pressure range. Our purpose is to measure the volume and energetic changes occurring in such an equilibrium in Xe and also to see if any difference exists between this solvent and supercritical ethane where such reactions have already been studied. Experimental Methods In the pulse conductivity technique used, the sample was exposed to X-rays generated by impinging a pulse of electrons from the Van de Graaff accelerator on a lead target. A pulse length of 60 ns was used, and the amplifier had a rise time of 10 ns. Individual rate constants for electron attachment (ka) and detachment (kd) were determined by fitting the amplified current decay to the solution10,11 of the coupled differential equations for the formation and decay of electrons and solute anions:

dn dn ) υD - kan[solute] + kd[solute-] - kimpn[impurity] dt dx (3) d[solute-] ) kan[solute] - kd[solute-] dt

Figure 1. Representative current traces at 20, 30, and 40 °C at pressure of 52 bar with [pyz] ) 2.2 µm.

(4)

where n is the concentration of electrons and υD their drift velocity. Xenon (MG Industries, scientific grade) was purified by passage first through an inert gas Pall filter. The electron lifetime was then checked by the pulse conductivity technique. Generally, the lifetime was initially less than 1 µs. Then the xenon was irradiated with a train of X-ray pulses. This improved the lifetime by orders of magnitude. The Xe was then returned to the vacuum line and passed again through the Pall filter to remove additional impurities formed by the X-ray exposure. This cycle was repeated until a satisfactory lifetime of >50 µs was obtained. We speculate that reactive molecular impurities were transformed to less reactive species by irradiation and removed by the filter. Then ethane (0.3 wt %) was added for the purpose of thermalizing electrons that can remain “hot” for several nanoseconds in Xe. The ethane prevents reactions of hot electrons from occurring and has no effect on the mobility.9 Although ethane is known to quench excimers,9 it is assumed that it has no effect on the electron reactions studied here. At this point, the rate of electron attachment to residual impurities, kimp[impurity], was determined as a function of Xe pressure. The pyrazine (Aldrich 99%) was added by freezing a measured amount of the vapor into the conductivity cell. The sample was placed in a thermostatted Al box and the temperature in the cell controlled to 0.05 K with an Omega CN77530-C2 controller. Pressure was measured with a Setra 212 transducer accurate to 0.45 bar. Density of Xe was obtained using the NIST Database 12.12 Compressibility and volumes of electrostriction were calculated using the compressible continuum model described elsewhere.2 After each experiment, the pyrazine was removed from the sample by passing it through the Pall filter. In this way, the Xe/ethane sample could be used several times. Gas chromatography (GC) analysis afterward showed that most of the ethane added was still present. Results Typical conductivity traces observed for pyrazine in supercritical xenon are shown in Figure 1. As the temperature increases, the equilibrium current that is observed at longer

Figure 2. Rate constant for electron attachment to pyrazine at (2) 20, (9) 30, and (bO) 40 °C versus pressure. Dotted lines are least-squares fits. Solid line at top is rate constant for attachment to C6F6.9

times, which is a measure of the detachment rate (kd), increases. Analysis of such curves as described in the Experimental Methods Section leads to values of the attachment rate, ka, as well as to values of kd. The variation of ka with temperature and pressure is shown in Figure 2. The rate increases with pressure at low pressure, passes through a maximum at intermediate pressures, and is fairly constant at higher pressures. The magnitude of the attachment rate to pyrazine is less than it is in sc-ethane;2 otherwise, the results are similar. The attachment rate decreases with increasing temperature at low pressure. Included for comparison in Figure 2 is the rate constant for attachment to C6F6 at 20 °C.9 Whereas the rate increases rapidly for C6F6 near 62 bar, the rate of attachment to pyrazine at 20 °C is decreasing at this pressure. The differences observed for ka in supercritical ethane and xenon lead to quite different behavior of the activation volumes, ∆Va*. Values of ∆Va* were calculated from the relation

∆Va* ) -RT(∂ ln ka/∂P)T

(5)

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Holroyd and Preses

Figure 3. Activation volume for attachment to pyrazine versus pressure at (2) 20, (9) 30, and (b) 40 °C.

Figure 5. Activation volume for electron detachment from pyrazineanion versus pressure at indicated temperatures in °C. Arrows indicate regions of maximum compressibility.

Figure 4. Rate constant for electron detachment from pyrazine- anion versus pressure at (2) 20, (90) 30, and (bO) 40 °C.

The results obtained for supercritical xenon are shown in Figure 3. The values of ∆Va* for pyrazine are generally small. In supercritical xenon, ∆Va* is negative at low pressures but becomes positive, exhibiting a small peak, at intermediate pressures and lower temperatures. In contrast, for electron attachment to pyrazine in sc-ethane, ∆Va* is negative at all pressures and shows a minimum at intermediate pressures. ∆Va* for C6F6 in sc-xenon also shows a minimum, which is much deeper, reaching values near -28 L/mol. The rate constant for detachment from pyrazine anion changes little with pressure, as shown in Figure 4. This is in sharp contrast to that observed for this reaction in ethane where kd changes by 2 orders of magnitude over a 10 bar interval. The rate of detachment in xenon increases with temperature by a factor of 10 from 20 to 40 °C. This increase in rate with increasing temperature is reasonable for such equilibria as there are typically large activation energies associated with electron detachment.11 Because of the small variation of kd with pressure, values of ∆Vd*, calculated with an equation analogous to eq 5, are small, generally less than (1 L/mol (see Figure 5). At 20 and 30 °C, small peaks in ∆Vd* are observed in the vicinity of the compressibility maxima; the maxima are indicated by the arrows in Figure 5. The values for the free energy change for reaction 1 were calculated from

∆Gr ) -RTln(ka/kd)

(6)

The experimental results are shown in Figure 6b by the filled

Figure 6. (a) Pressure dependence of the calculated number of Xe atoms, m, in solvation shell at temperatures in °C as indicated (mMax ) 20, see text for details). (b) Observed free energy for attachment to pyrazine shown by solid points for (2) 20, (9) 30, and (b) 40 °C. Solid lines indicate calculated values of P- - V0 at temperatures in oC as indicated. Open points are derived values of the electron affinities of pyrazine clusters at (4) 20, (0) 30, and (O) 40 °C.

points for three temperatures. At 20 °C, values of ∆Gr are available only at low pressures because kd is too small at higher pressure. At higher temperatures, the equilibrium could be studied over a wide pressure range. At high pressures, there is very little change in ∆Gr. Decreases with increasing pressure are observed at low pressure. The overall change is less than 0.1 eV at any one temperature.

Energetics/Volume Changes in Supercritical Xe

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6687 and has been neglected, because electrons are in an extended state in sc-Xe. There is ample evidence that electrostriction causes clustering of atoms or molecules around an ion in supercritical fluids. Support for this comes both from the lower than expected mobility of ions,8 and from the study of other equilibria, like reaction 1, in supercritical ethane. The volume changes can be explained by the electrostriction volume calculated by the compressible continuum model for electron attachment to CO2,13 pyrimidine,14 pyrazine, and methylpyrazine.2 Thus, it follows from the results and eq 8 that there must be clustering around the neutral pyrazine solute molecules comparable to that around the ion in xenon to explain the behavior of volume changes with pressure. Then the reaction in sc-Xe should be considered as

PyzXen + e- a (PyzXen)-

(1a)

To estimate the extent of this clustering around the neutral pyrazine molecule, we calculated the volumes of electrostriction, Vel, using the compressible continuum model; the details of the h model are given elsewhere.15 Vel is assumed to be equal to V (PyzXen-). The radius used for the calculation is 0.31 nm, estimated from the molar volume of pyrazine rather than the cluster radius because the excess electron is considered to be on the π* orbital of a pyrazine molecule. The calculated values of Vel are indicated by the solid lines in Figure 7. The values of V h (PyzXen) were then calculated from the observed values of ∆Vr, the calculated values of V h (PyzXen-) ) Vel, and eq 8a

h (PyzXen-) - V h (PyzXen) ∆Vr ) V Figure 7. (top) Volume change for electron attachment/detachment reaction with pyrazine at( 90) 30 °C. Solid black line is Vel; dashed line is V h (Pyz). Maximum in χT is at 72.7 bar. (bottom) Volume change for electron attachment/detachment reaction with pyrazine at (b) 40 °C. Solid black line is Vel; dashed blue line is V h (Pyz). Maximum in χT is at 81.8 bar.

Volume changes for this reaction were calculated from the usual equation:

∆Vr ) (∂∆Gr/∂P)T

(7)

The results are shown in Figure 7 by the points. Values of ∆Vr are small because ∆Gr changes little with pressure. The variation of ∆Vr with pressure, as shown in Figure 7, is quite similar to the activation volume ∆Va*, because kd changes little with pressure. Discussion Volume Changes. The volume changes ∆Vr estimated by eq 7 for reaction 1 in supercritical xenon are generally small, negative in the lower pressure region, and actually become positive in the vicinity of the compressibility maximum. At pressures above the compressibility maximum, they are practically zero. This is in sharp contrast to the values of ∆Vr observed for the same reaction in supercritical ethane, which are always negative, ranging from -1 to -45 L/mol.2 The volume change in a reaction is given by the difference in partial molar volumes of products and reactants:

h (Pyz-) - V h (Pyz) ∆Vr ) V

(8)

Here, the partial molar volume of the electron is presumed small

(8a)

These values are shown by the dashed lines in Figure 7. In the high pressure region, above the compressibility peak, the partial molar volumes of neutral and ionic pyrazine clusters are nearly equal. Thus, the driving force, that is, the volume decrease observed for this reaction in supercritical ethane, is absent here, and increasing pressure does not shift the equilibrium. At lower pressures, these terms differ and pressure does shift the reaction, as expected for the negative volume change. This trend can be explained as being due to the growth of neutral clusters with increasing pressure. In the lower pressure region, cluster formation is incomplete and electron attachment to the molecule causes electrostriction of the medium; at higher pressures, the cluster is already fully developed and the addition of a charge causes no further cluster build-up. The calculated values of V h (PyzXen) range from 0 to -9 L/mol and follow the compressibility as required by eq 2 (See Figure 8). A least-squares fit of V h (PyzXen) versus χT gives

V h (PyzXen) ) -15.1χT - 0.93

at 30°

V h (PyzXen) ) -18.4χT - 0.19

at 40°

The coefficients a(T) are negative, showing the attractive nature of the intermolecular forces. The pressure dependence of V h (PyzXen) is similar to that observed for naphthalene in supercritical ethene.3 That clustering occurs around a neutral molecule in supercritical fluids is generally well-known and expected for attractive systems.16-18 To estimate the number of Xe atoms in the neutral clusters, we use the dynamic cluster model (DC).19 This is a Langmuirtype model that assumes that atoms in the solvent shell are in dynamic equilibrium with the bulk. The rate of atoms leaving the shell is proportional to the number already there, and the

6688 J. Phys. Chem. B, Vol. 111, No. 24, 2007

Holroyd and Preses

Figure 8. (a) (9) Partial molar volume of neutral pyrazine versus compressibility at 30 °C. (b) (b) Partial molar volume of neutral pyrazine versus compressibility at 40 °C

rate of atoms arriving is proportional to the number of available open sites. The DC model worked well to explain the spectral shifts in absorption spectra in supercritical solvents16,20 and also explained the pressure dependence of the photoionization energy shifts of anthracene in supercritical ethane and xenon.21,22 The model leads to eq 9, which allows one to calculate m, the number of atoms in the shell at density F.

m)

FmMax

(9)

F1(mMax - 1) + F

F1 is the density at which only one xenon atom, on average, is in the solvent shell. The value of F1 used here is 4.4 × 1020 cm-3, which was calculated from the relation20

1 ) 4π F1

∫r

( )

φ(r) r exp dr kBT

r2 2

1

(10)

A Lennard-Jones potential was used for φ(r):

[( ) ( ) ]

φ(r) ) 412

σ12 r

12

-

σ12 r

6

(11)

The limits of integration were r1 ) 0.31 nm and r2 ) rPyz + 2rXe ) 0.71 nm. The energy parameter 12 used was 332.2 K × kB, and the size parameter was σ12 ) 0.456 nm. The LennardJones parameters for pyrazine were estimated from critical constants according to  ) TckB/1.31 and σ3 ) 0.31/FC.23 The critical constants for pyrazine were evaluated by the Lydersen method.24 For Xe, the Lennard-Jones parameters were obtained

from Reid et al.25 A maximum number, mMax, of xenon atoms can fit in the first shell. This maximum number can be calculated by the equation given by Otomo from geometrical considerations.20 For a radius of pyrazine of 0.31 nm, estimated from the molecular volume and a radius of Xe of 0.20 nm,26 one obtains the maximum number mMax ) 20. The DC model predicts that the number of atoms in the first solvation shell should increase monotonically as the density increases. The result of a calculation of m for mMax ) 20 using eq 9 gives the curves shown in Figure 6a plotted versus pressure. At 20 °C there is a sharp rise in the number m near 62 bar because this is the peak compressibility region where the density increases abruptly. The number m approaches 10 at high pressure at all temperatures. At higher temperatures, the rise is less sharp and occurs at higher pressure but again the rise occurs in the region of maximum compressibility. Energetics. The free energy change for electron attachment to a solute in a liquid is given by ∆Gr(l) ) ∆Gr(g) + P- ∆Gs(e-), where the polarization energy P- is often approximated by the Born equation. This equation works well and has been used to evaluate ∆Gs(e-) in various liquids.1,27 Alternatively, this equation can be used to evaluate the electron affinity (EA) of the solute. When we began studies of this type in supercritical fluids, we found the continuum model of Born did not work because electrostriction causes density build-up around the ion. Calculations using a compressible continuum (CC) model indicated the dielectric constant to be enhanced as far out from the ion as 1 nm. The magnitude of the polarization energy calculated with the CC model differed considerably from that calculated using the Born equation.28 When the CC model was used to calculate P-, the free energy changes for reaction 1 in supercritical ethane2 were quite accurately predicted. Because of clustering in sc-Xe, the electron reacts with a species PyzXen where n may be 0 to 10. Then the free energy change for this reaction (1a) in Xe, ∆Gr, is related to the free energy change in the gas phase, ∆Gg, by -

∆Gr ) ∆Gg + ∆Gs(PyzXen ) - ∆Gs(PyzXen) - ∆Gs(e-) (12) The difference between the free energy of solution of the anion, ∆Gs(PyzXen)- and the free energy of solution of the neutral ∆Gs(PyzXen) is the electrostatic polarization energy of the media by the ion, P-.29 ∆Gs(e-), the energy of the electron in solution, is taken as the conduction band energy in xenon, V0. Because the entropy change in the gas phase is assumed to be small, as configurational change on electron attachment to aromatics is small, ∆Gg can be approximated by ∆Hg ) -EA, where EA is the electron affinity. Then eq 12 becomes -

∆Gr ) -EA + P - V0

(12a)

Recently, the gas-phase electron affinity of pyrazine was determined to be -0.01 eV by photoelectron spectroscopy.30 An earlier study indicated the electron affinity to be -0.08 eV.31 In any case, eq 10a indicates that the free energy change depends on -EA and the difference P- - V0. We used the compressible continuum model to calculate Pbecause previous studies2,15 indicated the importance of considering the build-up in density around the negative ion. A radius of 0.31 nm, derived from the molar volume (see above), was used for pyrazine. V0 for xenon was calculated by an equation and parameters used by Altmann and Reininger to fit their experimental data.32 The difference in these two energy terms, P-(CC) - V0 should be a measure of ∆Gr (see eq 12a) if we use the EA of pyrazine, which is close to 0. However, P-(CC)

Energetics/Volume Changes in Supercritical Xe

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6689 higher than that of pyrazine itself. The results obtained in scXe are quite different from those in sc-ethane where the volume change of the reaction is negative. Clustering around neutral pyrazine is expected in ethane because partial molar volumes of similar aromatics are large and negative at least in the highly compressible near-critical region.3-5 However, the results in ethane showed that the partial molar volume of neutral pyrazine is small in magnitude, at least in comparison to that of the ion, at the low pressures where the equilibrium was observed. To the extent that such clusters exist, it is suggested they may not change the EA of pyrazine. A full explanation will require further study.

Figure 9. Derived electron affinity of (PyzXem) as a function of the number m of Xe atoms in the cluster (2) 20, (9) 30, and (b) 40 °C.

- V0 changes considerably with pressure, as shown in Figure 6b. The dependence is almost sigmoidal (solid curves) and does not reproduce the experimental free energy changes (shown by solid points). At low pressures, there is near agreement, but at high pressures, the value predicted is ≈0.3 eV higher than that observed experimentally. We conclude that this disagreement is due to the fact that the EA values that should be used in eq 10a are those for the clusters, not the value for a bare pyrazine molecule. The photoelectron spectroscopy work of Song et al.30 showed that pyrazine anion clusters with 1 to 10 Ar atoms are stable; in contrast, the EA of pyrazine is negative. Furthermore, the electron affinity of such clusters increases nearly linearly with the number of atoms in the solvation shell. The increase is about 0.3 eV for 10 atoms in the solvation shell. It is reasonable to expect that a similar effect would occur for Xe atoms. It is clear from the observed volume changes and the DC model that pyrazine molecules have a number of Xe atoms in the first solvation shell in supercritical Xe. Reasoning by analogy to the effect of Ar on the EA of pyrazine, we would expect a similar effect for Xe, that is, the EA of pyrazine should increase by several hundred millielectronvolts as Xe atoms are added to the solvation shell. The electron affinity should be equal to P-(CC) - V0 - ∆Gr from eq 12a. By using values of ∆Gr measured in sc-Xe, we obtain the results shown by the upper open points in Figure 6b, indicating the EA is higher by around 0.3 eV at high pressure. Furthermore, the increase in EA with pressure thus estimated parallels the increase in m with pressure. The EA values of the pyrazine clusters calculated this way are plotted versus m, the average number of Xe atoms in the solvation shell, in Figure 9. The value of m was calculated for each pressure with eq 9. Data for all three temperatures are shown. The EA increases monotonically with pressure from values close to 0 for small values of m to above 0.3 eV at m ) 10. Conclusions There is little volume change on electron attachment to pyrazine above critical pressure, indicating that clustering around the neutral molecules in Xe is comparable to that around the ion at high pressure. Calculations using the dynamic cluster model show that a solvent shell of Xe atoms exists and approaches 10 atoms at high pressure. The observed free energy changes for reaction 1 can be rationalized using the compressible continuum model to calculate P- provided we assume that in sc-Xe the clustered pyrazine molecule has an electron affinity

Acknowledgment. This research was carried out at Brookhaven National Laboratory and supported under contract DEAC02-98-CH10886 with the U.S. Department of Energy and supported by its Division of Chemical Sciences, Biosciences and Geosciences, Office of Basic Energy Sciences. M.N. and K.I. are supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology. The authors thank K.-W. Huang for analysis of gas samples. References and Notes (1) Holroyd, R. A.; Nishikawa, M. Radiat. Phys. Chem. 2002, 64, 19. (2) Holroyd, R. A.; Nishikawa, M.; Itoh, K. J. Phys. Chem. B 2000, 104, 11585. (3) Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J. Phys. Chem. 1986, 90, 2738. (4) Jeon, Y.-P.; Roth, M.; Kwon, Y. J. J. Phys. Chem. A 2000, 104, 5396. (5) Liu, H.; Macedo, E. A. Ind. Eng. Chem. Res. 1995, 34, 2029. (6) Kim, S.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 1206. (7) Petsche, I. B.; Debenedetti, P. G. J. Phys. Chem. 1991, 95, 386. (8) Itoh, K.; Holroyd, R. A.; Nishikawa, M. J. Phys. Chem. A 2001, 105, 703. (9) Holroyd, R. A.; Wishart, J. F.; Nishikawa, M.; Itoh, K. J. Phys. Chem. B 2003, 107, 7281. (10) Tachiya, M. Private communication. (11) Holroyd, R. A. Ber. Bunsen Ges. 1977, 81, 298. (12) Friend, D. G. NIST Thermophysical Properties of Pure Fluids, Version 3.0 Database 12; NIST, 1992. (13) Nishikawa, M.; Itoh, K.; Holroyd, R. A. J. Phys. Chem. A 1999, 103, 550. (14) Holroyd, R. A.; Nishikawa, M.; Itoh, K. J. Phys. Chem. B 1999, 103, 9205. (15) Nishikawa, M.; Holroyd, R.; Itoh, K. J. Phys. Chem. B 1998, 102, 4189. (16) Kajimoto, O. Chem. ReV. 1999, 99, 355. (17) Debenedetti, P. G.; Mohamed, R. S. J. Chem. Phys. 1989, 90, 4528. (18) Egorov, S. A. J. Chem. Phys. 2000, 113, 1950. (19) Kajimoto, O.; Futakami, M.; Kobayashi, T.; Yamasaki, K. J. Phys. Chem. 1988, 92, 1347. (20) Otomo, J.; Koda, S. Chem. Phys. 1999, 242, 241. (21) Nakagawa, K.; Otoda, N.; Kimura, A.; Nurdiawati, D.; Tanaka, K.; Kimura, K.; Ejiri, A. J. Electron Spectrosc. and Relat. Phenom. 1996, 78, 415. (22) Otsuki, Y.; Shimoyama, I.; Mochida, T.; Nakagawa, K. J. Supercrit. Fluids 1998, 13, 163. (23) Panagiotopoulos, A. Z. Mol. Phys. 1987, 61, 813. (24) Klincewicz, K. M.; Reid, R. C. AIChE J. 1984, 30, 137. (25) Reid, R. C.; Prausnitz, J. M.; Poling, J. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. (26) Coker, D. F.; Berne, B. J.; Thirumallai, D. J. Chem. Phys. 1987, 86, 5689. (27) Holroyd, R.; Itoh, K.; Nishikawa, M. Chem. Phys. Lett. 1997, 266, 227. (28) Holroyd, R.; Nishikawa, M.; Itoh, K. J. Phys Chem. B 2005, 109, 2478. (29) Szwarc, M.; Jagur-Grodzinski, J. Ions and Ion Pairs in Electron Transfer Reactions of Radical Anions, Carbanions and Solvated Electrons. In Ions and Ion Pairs in Organic Reactions; Szwarc, M., Ed.; John Wiley & Sons: New York, 1974; Vol. 1. (30) Song, J. K.; Lee, N. K.; Kim, S. K. J. Chem. Phys. 2002, 117, 1589. (31) Mathur, D.; Hasted, J. B. Chem. Phys. 1976, 16, 347. (32) Altmann, K. N.; Reininger, R. J. Chem. Phys. 1997, 107, 1759.