J. Phys. Chem. B 2000, 104, 11585-11590
11585
Solvent Clustering around Pyrazine Ions in the High-Compressibility Region of Supercritical Ethane Richard A. Holroyd* 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, Tokyo, 153-8902, Japan ReceiVed: July 30, 2000; In Final Form: September 21, 2000
Pyrazine and methylpyrazine attach electrons reversibly in supercritical (SC) ethane in the interesting region near critical densities. Very rapid shifts in the attachment equilibrium occur over very narrow pressure ranges. Reaction volumes for electron attachment to these solutes range from -1.0 to -45 L/mol, depending on conditions. The agreement of the values of ∆Vr with the calculated values from the compressible continuum model is excellent, indicating that the model predicts the electrostriction volume by ions in SC ethane quite accurately, and also suggesting that the partial molar volumes of neutral pyrazine and methylpyrazine are small by comparison to that of the ions.
Introduction
Experimental Section
Previous studies of electron attachment to solutes in supercritical (SC) ethane have shown that the rate constants for attachment increase rapidly with pressure in regions of high compressibility.1,2 These rapid changes correspond to large negative activation volumes. In the case of NO as solute, ∆Va† reached a minimum value of -29 L/mol at 306 K and 49.5 bar and in the case of C2F4, ∆Va† reached -11 L/mol in this region. Only partial solvent restructuring is expected at the activated state. The complete volume change, ∆Vr, occurring in such electron attachment reactions can be obtained by measuring the equilibrium constants, Keq, for reversible reactions of the type
Ethane (MG Industries, scientific grade) was purified by passage through the appropriate Pall filter. The quantity of ethane needed was measured, by liquid volume at 195 K, and condensed into the pressure cell, as described elsewhere.3 The lifetime, given by [kimp(impurity)]-1, and mobility of excess electrons in the purified ethane were checked prior to addition of solutes under the various experimental conditions. The pyrazine (Aldrich 99%) was degassed at 195 K and sublimed at 288 K in vacuo, retaining the middle fraction. Methylpyrazine (Aldrich, puriss) was similarly degassed at 195 K prior to vacuum distillation at room temperature, and a middle fraction was retained. GC/MS analysis indicated only a minor impurity present (0.3%) which was identified to be 1,2,4-trimethylpiperazine. Solutions of these solutes in ethane were prepared by measuring the pressure of a vapor sample in a calibrated volume, maintained at 306 K, and then freezing the sample into the conductivity cell, cooled to 77 K. The temperature of 306 K was used to minimize the possibility of wall absorption, which could lead to an underestimation of solute concentrations. In the pulse conductivity technique used, the sample is exposed to X-rays generated by impinging a pulse of electrons from an accelerator on a lead target. The Van de Graaff pulse length of 60 ns was used and the current amplifier had a rise time of 10 ns. At the LEAF facility a 30 ps pulse length was used with an EG&G amplifier (model 5185) with a rise time of 2 ns. Individual rate constants for electron attachment (ka) and detachment (kd) were determined by fitting the amplified current decay to the solution of the coupled differential equations for the formation and decay of electrons and solute anions
e- + solute a solute-
(1)
as a function of pressure. Carbon dioxide3 and pyrimidine4 are examples of such solutes, and from changes in Keq with pressure the reaction volumes have been obtained. Values of ∆Vr range from -9.0 to -0.4 L/mol in the case of pyrimidine. These attachment reactions also occur with a large decrease in entropy, and ∆Sr is proportional to ∆Vr.4 However, the measurements could only be made at pressures above the critical region of ethane. Close to the critical density, where the compressibility is highest, values of Keq were too small to measure with these solutes, that is, the reactions were unfavorable. The volume changes in these reactions are a measure of the difference in partial molar volume of the ions and the corresponding neutral molecules. The present study was undertaken to obtain volume changes in the near critical region. As is shown here, pyrazine and methylpyrazine attach electrons reversibly in this region and the results provide data on volumes and the extent of solvent clustering around ions. Pyrazine, an isomer of pyrimidine, was thought to be a good choice because its redox potential is 0.21 eV higher than that of pyrimidine in solution,5 and gas-phase data indicate its electron affinity is higher than that of pyrimidine by 0.25 eV.6
dn/dt ) Vd dn/dx - kan(solute) + kd(solute-) kimpn(impurity) (2) d(solute-)/dt ) kan(solute) - kd(solute-)
10.1021/jp002713+ CCC: $19.00 © 2000 American Chemical Society Published on Web 11/04/2000
(3)
11586 J. Phys. Chem. B, Vol. 104, No. 48, 2000
Holroyd et al.
Figure 2. Attachment rate constant ka versus pressure for pyrazine (4 33 °C; O 37 °C; 0 45 °C) and methylpyrazine (b) at 37 °C. Solid lines are least-squares fits at 37 °C.
Figure 1. Current traces for 0.29 µm pyrazine in ethane at 33 °C. Pressures in bar as indicated.
where n is the concentration of electrons and Vd their drift velocity. During measurements, the sample temperature was controlled to 0.05 K using an Omega (CN77530-C2) temperature controller. Pressure was read with a Setra model 212 transducer, accurate to 0.45 bar. Density and compressibility values for ethane were calculated using an equation of state (EOS) developed by Younglove.7 Volumes of electrostriction, Vel, and energies of polarization in SC ethane were calculated according to a compressible continuum model.1 In this model the pressure due to the charge on the anion is calculated as a function of distance. Then the density, Fr, at each distance is computed from the EOS and the dielectric constant, r, obtained from the Clausius-Mosotti equation. The electric field at each point is then reevaluated on the basis of the new r, and this cycle is repeated till a constant Fr is obtained. Then Vel is given by
Vel ) 4π
∫r∞ (1 - Fr/Fo)r2 dr
(4)
ion
where Fo is the bulk density. Results Rate Constants. Typical conductivity traces observed for pyrazine in SC ethane are shown in Figure 1. As the pressure increases from 45 bar, the rate at which the current decays, a measure of the attachment rate ka, increases. Also the equilibrium current at longer times, a measure of kd, decreases. Analysis of such curves leads to values of ka and kd, as described above. Concentration between 0.14 and 0.28 µm were used for pyrazine and 0.05 and 0.08 µm for methylpyrazine. The observed rate
constants for attachment to pyrazine and methylpyrazine increase with pressure at low pressures and then level off at a nearly constant value throughout most of the SC region (Figure 2). The magnitude of ka is nearly temperature independent, especially at high pressures. Solid lines are second-order leastsquares fit to the data at 310 K. These rate constants are quite high, close to the diffusioncontrolled rate kD. The expression for kD, when combined with the Einstein relation, De ) µekBT/e, becomes
k∆ ) (4πraµekBT/e)N0F/1000
(5)
in units of m-1 s-1, where F is the ethane density in g/mL. The diffusion constant of the neutral species can be ignored. The electron mobility, µe, is around 100 cm2/V s in the near critical region and decreases with pressure. The density increases with pressure, and these terms tend to offset one another so that the diffusion rate constant remains fairly constant, as shown in Table 1. The mean estimated value at 310 K is 1.5 × 1014 m-1 s-1. The rate constants observed at high pressure for pyrazine and methylpyrazine are below this value. A rate constant of 1.9 × 1013 m-1 s-1 was observed for electron attachment to pyrazine in 2,2,4-trimethylpentane at 22 °C.8 This value is also below the diffusion-controlled rate for that solvent. Activation volumes for attachment were determined from the slopes of plots of ka versus pressure according to the relation
Va‡ ) -RT(∂ ln ka/∂P)T
(6)
The results obtained for these solutes at 310 K are shown in Figure 3. The activation volumes indicate that some electrostriction occurs at the activated state. The results are similar for pyrazine and methylpyrazine. The minimum value is -4 L/mol near 51 bar. A similar small change in activation volume was observed for electron attachment to pyrimidine.4 The overall
TABLE 1: Attachment Rate Constants solute
temp (K)
pyrazine
310
methylpyrazine
310
a
ra in eq 5 assumed to be 0.5 nm.
pressure (bar)
ka(exptl) (m-1 s-1)
µe (cm2/V s)
F (g/mL)
kDa (m-1 s-1)
46.9 54.0 104.7 49.4 54.8 85.4
6.65 × 1.39 × 1013 1.21 × 1013 2.58 × 1013 5.24 × 1013 5.91 × 1013
150.0 68.0 22.4 124.0 68.0 29.5
0.101 0.218 0.360 0.119 0.242 0.342
1.53 × 1014 1.5 × 1014 8.16 × 1013 1.49 × 1014 1.66 × 1014 1.02 × 1014
1012
Solvent Clustering around Pyrazine Ions
J. Phys. Chem. B, Vol. 104, No. 48, 2000 11587
Figure 3. Volumes of activation for electron attachment to (O) pyrazine and (b) methylpyrazine. Figure 5. Energetics of electron attachment to pyrazine. Points are experimental values of ∆Gr (referred to left-hand energy axis) at temperatures indicated. . Points obtained at LEAF at 37 C. Solid lines are least-squares fitted curves. Dotted lines are calculated values of E(P-CC) (referred to right-hand energy axis). Note that the vertical axes are offset by 0.17 eV.
Figure 4. Electron detachment rate constants for pyrazine- for temperatures and pressures indicated.
reaction volumes are much larger in magnitude, however (see below), indicating that the activated state is similar to the reactant structurally. Since entropy changes are proportional to volume change for these reactions, this is equivalent to saying that the entropy of activation is small. The minimum in Va‡ occurs near the pressure where the compressibility of ethane is a maximum, which is 53 bar at 37 °C. The detachment rate constants, in contrast to the attachment rates, decrease rapidly with pressure, by 2 orders of magnitude over approximately a 10 bar range (see Figure 4). The lifetimes of pyrazine anions change with conditions from 0.3 to 20 µs. At any given pressure kd increases with increasing temperature. Values of the free energy for reaction 1, ∆Gr, were calculated from the values of the attachment and detachment rate constants according to
∆Gr ) -RT ln(ka/kd)
(7)
The results for pyrazine and methylpyrazine are shown in Figures 5 and 6, respectively. The points are experimental and the solid lines are fitted curves to the data. The free energy decreases very rapidly with increasing pressure from values near -0.38 to -0.53 eV for both. At 33 °C the drop-off is steepest near 49 bar and leads to very large volume changes (see the Discussion). Above 70 bar these equilibria could not be measured because the detachment rate becomes too small.
Figure 6. Energetics of electron attachment to methylpyrazine. Points are experimental values of ∆Gr (referred to left-hand energy axis) at temperatures indicated. Solid lines are least-squares fitted curves. Dotted lines are calculated values of E(P-CC) (referred to right-hand energy axis). Note that the vertical axes are offset by 0.17 eV.
Discussion Volume Changes. The volume changes for electron attachment to pyrazine and methylpyrazine were calculated as a function of pressure from the slopes of the fitted lines of ∆Gr versus pressure shown in Figures 5 and 6 according to
∆Vr ) (∂∆Gr/∂P)T
(8)
The results are shown by the points in Figures 7 and 8. These are the largest volume changes we have observed. For electron attachment to CO2, minimum values of -20 L/mol at 33 °C and -12 L/mol at 37 °C were observed at the lowest pressures that could be studied.3
11588 J. Phys. Chem. B, Vol. 104, No. 48, 2000
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Figure 7. Volumes for pyrazine. Points are experimental values of ∆Vr. Lines are values of Vel calculated using the compressible continuum model.
Figure 8. Volumes for methylpyrazine. Points are experimental values of ∆Vr. Lines are values of Vel calculated using the compressible continuum model.
The explanation of these large volume changes for reaction 1 must take into account that ∆Vr is the difference between partial molar volumes of products and reactants.
in radii changes the calculated values of Vel by less than 1%. The agreement between Vel and ∆Vr is generally good, indicating that the model predicts the electrostriction volumes reasonably well and supporting the premise that the partial molar volumes of pyrazine and methylpyrazine are small by comparison to that of the ions. By contrast, the classical continuum model predicts Vel values larger in magnitude than those calculated by the CC model. This is contrary to the conclusion of Zhang et al. for the electrostriction contribution for positive ions in CHF3.15 For example, we find for pyrazine that at 37 °C and 52.7 bar the CC model predicts Vel ) -19.5 L/mol while the continuum model (given by eq 9 in ref 3) predicts -72.9 L/mol. Energetics. Electron attachment reactions are much more favorable in dense fluids, largely because of the polarization energy of the anion. As pointed out before,3 the Born equation underestimates the magnitude of the polarization energy in supercritical ethane because it does not take into account the clustering of solvent molecules around the ion. Thus we use the compressible continuum model to estimate this term. This involves integrating the pressure due to the ion, as shown in eq 11.
∆Vr ) Vj(pyz-) - Vj(pyz) - Vj(e-)
(9)
As before4 Vj(e-) is presumed to be small. This assumption is based on the idea that the electron mobility is quite high, indicating that localization is unlikely. Also the wave function is expected to be extended. These properties allow little reorganization of the solvent to occur. The volume change becomes
∆Vr ) Vj(pyz-) - Vj(pyz)
(10)
The partial molar volume of aromatic compounds can be large and negative in nonpolar SC fluids where the compressibility is large. For example, Vj for naphthalene in ethylene is -15 L/mol near the critical point.9 On the other hand Vj for CO2 in ethane is small and positive for pressures between 50 and 75 bar at 32.5 °C.10 The value of Vj depends on the compressibility but also on the sign and strength of the solute-solvent interactions.11 For symmetrical molecules with no dipole like pyrazine there would be only the polarizability. A recent study12 of UV absorption spectrum of benzene in SC CO2 concluded that the local density of CO2 around benzene was the same as the bulk density. Since pyrazine has an even lower polarizability than benzene13 it is reasonable to assume that the attractive forces will be weak and that Vj(pyz) in ethane is small. The dominant volume terms are the partial molar volumes of the anions, and these are essentially given by the electrostriction term. Electrostriction volumes around pyrazine and methylpyrazine anions were calculated by our compressible continuum model (see the Experimental Section). The radius, rion, used in eq 4 is 0.257 nm for pyrazine and 0.277 nm for methylpyrazine. These radii are based on Bondi’s volume increments.14 The lines in Figures 7 and 8 show calculated values of Vel as a function of pressure at the various temperatures used. The lines in the two figures are very similar; the difference
E(P-CC) ) 2π
∫r∞ (or[E(r)]2r2) dr - e2/8πorion + ∞ V(r) 4π∫r [1/Vr(r)∫V(∞) P dV]r2 dr ion
(11)
ion
where r is the dielectric constant and E(r) the electric field at a distance r from the ion. The second term is the energy of the ion in a vacuum. The third term is a small correction that takes into account the compression of ethane. The free energy of reaction in solution is related to the free energy of reaction in the gas phase, ∆Gr(gas), by
∆Gr ) ∆Gr(gas) + E(P-CC) - Vo
(12)
where Vo is the energy of the electron in the fluid ethane. The electron is not expected to be trapped in ethane under the experimental conditions, since the mobility is high. Values of Vo reported for ethane decrease somewhat over the density range
Solvent Clustering around Pyrazine Ions
J. Phys. Chem. B, Vol. 104, No. 48, 2000 11589
of interest.16 Since a limited density range is involved, the decrease is only about 0.02 eV, which is comparable to the uncertainty of the Vo measurements, and therefore, a constant value of Vo ) -0.14 eV is assumed here. ∆Gr(gas) is given by -EA - T∆Sr(gas) since ∆Hr(gas) ) -EA. The entropy term is approximately 0.05 eV and for pyrazine EA is reported to be -0.08 eV.6 The EA for methypyrazine is unlikely to be very different. In support of this we find the difference between ∆Gr for pyrazine and methylpyrazine in ethane to be within 0.02 eV. Thus in this case eq 12 becomes
∆Gr ) E(P-CC) + 0.17
(12a)
or the free energy of reaction is linearly related to the polarization energy and furthermore the change in ∆Gr with temperature and pressure should be reflected in changes in E(P-CC). This is, in fact, the case as is shown in Figures 5 and 6, where calculated values of E(P-CC) are plotted using the righthand Y-axis, which is offset by 0.17 eV. Clearly, changes in E(P-CC) are reflected in changes in ∆Gr, as predicted by eq 12a. To obtain the close fit shown we adjusted the value of the ion radius to 0.32 nm for pyrazine and 0.33 nm for methylpyrazine. The polarization energy is quite sensitive to the radius used (while Vel is not); a smaller radius would lead to values of E(P-CC) that are larger in magnitude than those shown, and the dotted lines would be shifted vertically downward. By contrast, the continuum model for calculating polarization energy fails to describe the pressure dependence here. A sample calculation is shown in Figure 5; the dashed line is calculated for 45 °C using the Born equation and a radius of 0.257 nm. Although there is coincidental agreement with experiment at 69 bar, as the pressure decreases the stabilization energy of the ion decreases much faster than observed because the bulk dielectric constant decreases rapidly. This necessity to use a compressible continuum model to evaluate the energetics of reactions involving ions has been pointed out before.17 Electron Transfer. Methylpyrazine- to Pyrazine. Comparison of the electron attachment to two solutes over the same pressure range provides information about the electron transfer from one solute to another. For example, consider the two electron attachment reactions
e- + pyrazine a pyrazine- ∆Gr(pyz) e- + methylpyrazine a methylpyrazine- ∆Gr(mepyz) methylpyrazine- + pyrazine a methylpyrazine + pyrazine- ∆Gr(pyz) - ∆Gr(mepyz) (13) Subtracting the free energy of one from the other gives the free energy of electron transfer from methylpyrazine- to pyrazine. At 37 °C, in the pressure range from 47 to 54 bar, the free energy for each reaction changes considerably, but the difference, ∆Gr(pyz) - ∆Gr(mepyz), remains nearly constant; the average value is -0.025 ( 0.002 eV. There is no definite change with pressure, indicating that the volume change for this electron transfer is small. This difference of -0.025 eV represents the difference in polarization energies of the two ions plus the difference in electron affinities (see eq 12). Again the calculated values of the polarization energies for both ions change considerably over this pressure range, but the difference E(P-CC)pyz - E(P-CC)mepyz remains constant at -0.026 eV. Since this difference is within experimental error, the same as the difference in free energies, it is concluded that there is no difference in the electron affinities of pyrazine and methylpyra-
Figure 9. Electron transfer from pyrimidine- to pyrazine at 45 °C. (a) ∆Gr versus pressure for (O) e- + pyrazine, (0) e- + pyrimidine, (b) pyrimidine- + pyrazine and (b) volume changes in these reactions.
zine. The reason that this reaction is shifted to favor the electron on pyrazine is because the smaller ion, pyrazine-, is stabilized by polarization more than the larger one. Pyrimidine- to Pyrazine. For electron transfer from pyrimidine anion to pyrazine, a volume change is observed, in contrast to reaction 13. At 45 °C the free energy of electron attachment to pyrazine is available up to 70 bar; at higher pressures this reaction is strongly shifted to the right and equilibrium data are not available. The free energy of attachment to pyrimidine was measured only down to 60 bar;4 at lower pressures, the reaction becomes too unfavorable. Although a comparison over a wider pressure range would be interesting, at least these reactions can be compared in this overlapping intermediate region from 60 to 70 bar. The free energies of attachment to these molecules change with pressure as shown by the open points in Figure 9a. The changes are clearly different for the two, and when ∆Gr for the pyrimidine reaction is subtracted from that for the pyrazine reaction, the free energy for the electron-transfer reaction
pyrimidine- + pyrazine a pyrimidine + pyrazine- (14) is obtained. The free energy for reaction 14 changes with pressure, as shown by the solid points in Figure 9a. The electron is favored to be on pyrazine. From the change in ∆Gr for this reaction with pressure, ∆Vr(14) is obtained, which changes from -2.3 L/mol at 61 bar to -0.6 L/mol at 68 bar, as shown by the solid points in Figure 9b. Since the electrostriction volumes are expected to be similar for the two ions in reaction 14, because the radii are comparable, the volume changes are attributed to the difference in partial molar volumes of the two neutral molecules Vj(pyr) - Vj(pyz). If, as was argued earlier, Vj(pyz) is small because of its symmetry and low polarizability, these volume changes are attributed mainly to Vj(pyr). It is reasonable to expect this term to be negative close to critical densities because of a large dipole moment. Others18 have used an equation of the form
Vj(pyr) ) aχT + b
(15)
11590 J. Phys. Chem. B, Vol. 104, No. 48, 2000 to represent partial molar volumes of solutes, where a is a negative term that is important in regions of high compressibility and b is a positive contribution important at high pressures and related to the molar volume. A regression of our experimental values of Vj(pyr) on χT shows a good linear fit with a correlation coefficient of 0.997 with a ) -34.3 L -bar/mol and b) 0.16 L/mol. This fit is shown by the dashed line in Figure 9b, which is also extrapolated to lower pressures; thus, Vj(pyr) is projected to reach a minimum value of -2.5 L/mol, where χT reaches a maximum at 45 °C. At lower temperatures, where the compressibility is larger, even lower values of Vj(pyr) may be anticipated, but use of eq 15 may be risky because the parameter a is expected in general to be temperature dependent. Conclusion This pulse conductivity study shows that large volume changes occur on electron attachment to solutes in supercritical ethane in regions of high compressibility, indicating clustering of solvent molecules around the ions. A compressible continuum model successfully predicts the volume changes, as well as the energetics of these reactions. The model also predicts that volumes of electrostriction do not change significantly for ion radius changes from 0.3 to 0.5 nm. This contrasts with the continuum (Born) model that predicts an inverse radial dependence. By contrast, the polarization energy of an ion, a key component of the free energy of attachment reactions, is very dependent on the ion radius. The radii chosen to fit the energetics for these anions are slightly larger than those expected for the neutral molecules. The volume change for electron transfer from an ion to a neutral molecule is largely attributed to the difference in partial molar volumes of the neutrals.
Holroyd et al. Acknowledgment. The authors thank J. Miller and J. Wishart for helpful suggestions. This research was carried out at Brookhaven National Laboratory and supported under contract DE-AC02-98-CH10886 with U.S. Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. K.I. and M.N. are supported by a Grant in Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan. References and Notes (1) Nishikawa, M.; Holroyd, R. A.; Itoh, K. J. Phys. Chem. 1998, 102, 4189. (2) Nishikawa, M.; Holroyd, R. A.; Itoh, K. ICDL Proc. (3) Holroyd, R. A.; Nishikawa, M. Itoh, K. J. Phys. Chem. 1999, 103, 550. (4) Nishikawa, M.; Itoh, K.; Holroyd, R. A. J. Phys. Chem. 1999, 103, 9205. (5) Wiberg, K. B.; Lewis, T. P. J. Am. Chem. Soc. 1970, 92, 7154. (6) Mathur, D.; Hasted, J. B. Chem. Phys. 1976, 16, 347. (7) Younglove, B. A.; Ely, J. F. J. Phys. Chem. Ref. Data 1987, 16, 577. (8) Holroyd, R. A. Unpublished results. (9) Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J. Phys Chem. 1986, 90, 2738. (10) Khazanova, N. E.; Sominskaya, E. E. Russ. J. Phys. Chem. 1968, 42, 676. (11) Debenedetti, P. G.; Mohamed, R. S. J. Chem. Phys. 1989, 90, 4528. (12) Otomo, J.; Koda, S. Chem. Phys. 1999, 242, 241. (13) Calaminici, P.; Jug, K.; Koster, A. M.; Ingamells, V. E.; Papadopoulos, M. G. J. Chem. Phys. 2000, 112, 6301. (14) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; Wiley: New York, 1968; p 450ff. (15) Zhang, J.; Connery, K. A., Brennecke, J. F.; Chateauneuf, J. E. J. Phys. Chem. 1996, 100, 12394. (16) Yamaguchi, Y.; Nakajima, T.; Nishikawa, M. J. Chem. Phys. 1979, 71, 550. (17) Luo, H.; Tucker, S. C. J. Phys. Chem. A 1997, 101, 1063. (18) Kim, S.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 1206.
