J. Phys. Chem. B 2001, 105, 7027-7032
7027
Solvent Anions in Supercritical Carbon Dioxide: Formation of Complexes with Polar Solutes† I. A. Shkrob* and M. C. Sauer, Jr. Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: March 27, 2001; In Final Form: May 7, 2001
It is shown that high-mobility multimer (CO2)n•- anions in supercritical (sc)-CO2 form stable complexes with water, aliphatic alcohols, alkyl halides, and alkyl nitriles. The complexation rate is 10-50% of the diffusion controlled rate or faster. The complexes are formed both with the monomer and with the dimer polar solutes. The equilibrium constants of the monomer complexation range from 10 to 350 M-1; the reaction heat is -(15-21) kJ/mol, and the reaction entropy is negative. The stability of the complex increases with the dipole moment of the polar group and decreases with the substitution at the R-carbon. None of these polar solutes directly reacts with quasifree electrons in sc-CO2.
1. Introduction study,1
we reported the occurrence of two In a previous reducing species in supercritical (sc)-CO2 (Fc ≈ 0.468 g/cm3; Tc ≈ 31 °C).2 One of these species is a short-lived (10 cm2/(V s)), quasifree electron, and the other is a multimer solvent radical anion, (CO2)n•-. The mobility of the latter species is 2-10 times higher than the mobilities of regular solute anions but >103 times lower than that for the quasifree electron. The high electron binding energy of this solvent anion, 1.6 ( 0.2 eV,1 indicates that the negative charge is shared by several solvent molecules; the core of this anion could be the C2O4•- dimer.3 We speculate that the anomalously high mobility of this solvent anion is due to resonance charge transfer between the clusters of the solvent molecules, as observed in liquid C6F64 and acetonitrile.5 Such solvent clusters have widely different geometries and sizes,6 while the electron binding energy for gas-phase {CO2}n•- anions (n ) 2-14) strongly depends on both of these factors.3 Neat sc-CO2 is a poor solvent for most compounds of practical interest, and the addition of polar cosolvents, such as aliphatic alcohols and nitriles, is commonly used to improve the solubility.7 In this study, we consider the effect of the polar cosolvent on the negative charge dynamics in sc-CO2. For many nonpolar solvents, addition of polar solutes drastically changes the electron dynamics.8-10 The best documented change occurs upon the addition of aliphatic alcohols (ROH) to saturated hydrocarbons. Because of the formation of hydrogen bonds between the monomer molecules, alcohols in nonpolar solvents tend to form dimers, tetramers, and higher multimers.8-12 For example, for ethanol in cyclohexane, the dimerization constant at 25 °C is 11 M-1, and the equilibrium constant for association of the dimer with the monomer is ≈123 M-1.11 The dimerization enthalpies are typically ≈-20 kJ/mol, which is comparable to the enthalpy of the hydrogen bond formation (≈-23.5 kJ/mol).11,12 Quasifree electrons in hydrocarbons rapidly attach to these alcohol dimers.9a The {ROH}2 * To whom the correspondence should be addressed. † Work performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Science, US-DOE, under Contract Number W-31-109-ENG-38.
dimers associate with more alcohol molecules to yield cyclic tetramers and higher multimers that also trap quasifree electrons.11 The {ROH}4•- species exhibits almost the same absorption and EPR spectra as the solvated/trapped electron in neat liquid/glassy alcohols.8,9 Aprotic molecules with large dipole moments, such as acetonitrile (3.92 D in the gas phase),13 also form multimers in nonpolar solutions14-17 that are efficient electron traps (section 1.1 in the Supporting Information).19 As far as the association of polar solutes is concerned, supercritical CO2 is similar to other nonpolar solvents (see section 1.2 in the Supporting Information).20-22 While there is every reason to expect that in sc-CO2, as in hydrocarbons, alcohol molecules form clusters that are capable of trapping quasifree electrons, our results indicate that this trapping does not occur. The solvent itself provides abundant electron traps that are deeper than those provided by these alcohol clusters. In liquid water and alcohols, monomer CO2 efficiently scavenges solvated electrons:23 in these liquids, a single (solvated) CO2 molecule is a better electron trap than several ROH dipoles. These unfavorable energetics suggest that, in sc-CO2, the electron binds to the solvent more strongly than to the alcohol clusters; that is, no {ROH}n•- anions should be formed. Gas-phase studies25 and ab initio calculations26 indicate that, in mixed {(CO2)n-m(ROH)m}•- cluster anions, the electron always resides on the CO2 moiety (section 1.3 in the Supporting Information). Dimitrijevic and Jonah found no characteristic VIS absorption bands of the solvated electrons trapped by the {ROH}n clusters in pulse radiolysis of alcohol/sc-CO2 mixtures (molar fraction < 0.05).24 Nevertheless, as shown below, addition of alcohols does change the negative charge dynamics in sc-CO2: While the quasifree electron does not attach to the {ROH}n clusters, the monomer and dimer solute molecules form complexes with the solvent anion. The gas-phase studies25 indicate that, for n ) 1 and, possibly, for n ) 6 mixed {(CO2)n-m(ROH)m}•- clusters, the complexation of (CO2)n•- with the alcohol molecule(s) is exothermic. Because the solvent anion constantly samples different geometries and sizes of the {CO2}n•- clusters when it migrates by resonant charge transfer in the supercritical solvent, it is possible that in some of these clusters the interaction with the solute molecule is sufficiently strong to temporarily halt the electron
10.1021/jp011139e CCC: $20.00 © 2001 American Chemical Society Published on Web 06/21/2001
7028 J. Phys. Chem. B, Vol. 105, No. 29, 2001
Shkrob and Sauer
hopping. Below, it is demonstrated that several classes of polar molecules can reversibly bind to the solvent anion. To save space, figures and diagrams with a designator “S” after the number (e.g., Figure 1S) are given in the Supporting Information. 2. Experimental Section Supercritical CO2 (research grade, from Scott Specialty Gases) was contained in a conductivity cell with a 2 cm optical path and an internal volume of 5 cm3 (see ref 1 for more detail). Five microliters of a 1 vol % solution of benzene in n-hexane was added to the reaction mixture using an HPLC injector (the flow diagram is shown in Figure 1S). No dc conductivity signal from n-hexane alone was found; no effect of n-hexane (1 ms. For electric fields > 5 kV/cm (in which the geminate ion recombination is shorter than the excitation pulse),1 the decay kinetics after 30 ns can be fit in a model where the solvent anion with mobility µ1- transforms to a solute or impurity anion with
Figure 1. Transient dc conductivity kinetics for photoionization of 0.11 mM benzene in sc-CO2 at F ) 0.76 g/cm3 and T ) 41 °C (the data shown in Figures 2-7 are obtained under the same experimental conditions). The conductivity is given in units of nanoSiemens per centimeter ()10-7 Ω-1 m-1). Trace i is obtained without methanol (the solid line is the least-squares fit obtained by numerical solution of eqs 1-3). For the other three traces, the concentrations of methanol are 0.7, 2.7, 5.6, and 14 mM.
mobility µ2- < µ1- following pseudo-first-order kinetics (solid bold trace in Figure 1). For concentrations C1 and C2 of these two anions the conductivity signal is given by
σ(t) ) F(µ1sC1 + µ2sC2)
(1)
where F is the Faraday constant, µ1s ) µ1- + µ+, and µ2s ) µ2- + µ+, where µ+ is the mobility of the countercation. The decay kinetics of these anions are given by
dC1/dt ) -k1C1 - ξµ1sC1(C1 + C2)
(2)
dC2/dt ) +k1C1 - ξµ2sC2(C1 + C2)
(3)
The first term gives the rate of the anion transformation (with rate constant k1); the second gives the rate of ion recombination in the bulk. If this recombination obeys the Debye-Langevin equation, the coefficient ξ ) F/0, where 0 is the permittivity of vacuum and is the static dielectric constant of the solvent. Equations 2 and 3 were solved numerically, and the least-squares optimization of fitting parameters yielded σ0 ) F µ1sC0, the free ion conductivity extrapolated to t ) 0 (where C0 ) C1(t)0)), the rate constant k1, and the ratio µ2s/µ1s of the ion mobilities. For F > Fc, this ratio rapidly increases with the solvent density F; at F/Fc ≈ 1.62 and T ) 41 °C, µ2s/µ1s ≈ 0.3. When the temperature increases (F ) const), µ1- increases with the activation energy of 46 kJ/mol, while µ2- and µ+ do not change. Time-of-flight conductivity measurements show that µ+ and µ2- vary little for different solute ions, and for F/Fc > 1.2, µ+ ≈ µ2-.1 In “neat” sc-CO2, the lifetime k1-1 of the solvent anion is ≈10 µs because of electron transfer to 0.5 ppm of O2 impurity present in this solvent. Though this reaction is reversible, at the low concentration of O2 (≈10 µM) present in the solution as impurity, the equilibrium is completely shifted toward the product, CO4•- (the equilibrium constant is (2.8 ( 0.4) × 107).1 When a nonpolar electron acceptor S is added to the reaction mixture, the rate constant k1 linearly increases with [S] because of scavenging of the solvent anion by S.1 Simultaneously, the initial “spike” and the conductivity signal σ0 (observed immediately after the “spike”) decrease, whereas the “tails” of the σ(t) kinetics (t > 50 µs) do not change.1 This behavior indicates that some quasifree electrons are scavenged by the solute before
Solvent Anions in Supercritical Carbon Dioxide
Figure 2. Plot of Z ) 1/f1 - 1 versus [L] for (a) methanol and (b) ethanol. In part a, the concentration dependence of the rate constant k1 of the anion scavenging is shown in the same plot. In part b, three series of measurements in which the concentration of n-hexane (added as a cosolvent) was varied between 1 vol % and 4 vol % are plotted together. Note that while for methanol the Z-dependence is linear within the experimental error, for ethanol this dependence is curved. The line in Figure 2b is the least-squares fit using formula 5.
being trapped by the solvent. Consequently, the initial fraction f1 of the solvent anions with mobility µ1- > µ2- decreases with the solute concentration [S], as does the conductivity signal σ0. Because the total yield of the free ions does not change, the long-term neutralization kinetics (observed for t . k-1) also do not change. The families of the scavenging kinetics for various [S] were fit using eqs 1-3. The ratio µ2s/µ1s was fixed at the infinite dilution value ([S] ) 0) and the fraction f1 of the solvent anions optimized. In this way, the concentration dependence of f1 was found; these dependencies were fit by f1 ) (1 + Re[S])-1, where Re ) k2eτe is the product of (i) the rate constant k2e of the electron attachment to the nonpolar solute and (ii) the electron lifetime τe (which is 3-6 times longer than the geminate lifetime of the electron-cation pair).1 The relative decrease in the “spike” is given by the same Stern-Volmer equation; the two coefficients Re are within a factor of 2 from each other. These results set the background for the present study. 3.2. Kinetics in the Presence of Polar Solutes. When 1-50 mM of a polar solute L is added to the reaction mixture, the effect of such addition is different from that of the addition of a nonpolar electron acceptor (Figure 1 shows such kinetics for methanol). While there is a systematic decrease in the conductivity signal σ0 observed after the excitation pulse, there is little change in the “spike”. This indicates that the direct attachment of quasifree electrons to the polar solutes does not occur. Simultaneously, the rate constant k1 of the solvent anion transformation decreases with [L] (unless there is an electronscavenging impurity in the solute, as is the case with 1-butanol and higher alcohols). This decrease is observed both in the reaction with the O2 impurity (Figure 2a) and in the reaction with the added electron acceptor, CCl4 (Figure 3S).
J. Phys. Chem. B, Vol. 105, No. 29, 2001 7029
Figure 3. (a) Transient dc conductivity kinetics (t > 50 ns) for the solvent anion complex with acetonitrile in sc-CO2 (see Figure 1 for the experimental conditions). The concentration of acetonitrile (from top to bottom): 0 (bold trace), 2.5, 2.9, 3.2, 3.7, 5.6, 8, and 10 mM. (b) Z plot for acetonitrile. Three series of measurements in which the concentration of n-hexane (added as a cosolvent) was varied between 2 and 5 vol % are plotted together.
This behavior may be accounted for by postulating reversible complexation
(CO2)n•- + M h {(CO2)n•-M}
(4)
of the solute monomer M and the solvent anion (CO2)n•-. Let us assume that the mobility of this complex is the same as the mobility of other solute ions and that the equilibrium reaction 4 is set within the duration of the excitation pulse. Then, by the end of the pulse, both the solvent anion and the complex are present in the reaction mixture, and the fraction of the solvent anion f1 ) (1 + K1[L])-1, where K1 is the equilibrium constant of reaction 4. The decay of σ(t) because of a reaction with electron-acceptor solute S would occur with the pseudo-firstorder rate constant k1 ) k2[S]f1 + kC[S](1 - f1), where k2 and kC are the corresponding rate constants for the solvent anion and the complex, respectively. It is reasonable to expect that kC is lower than k2, because the solute complex is less mobile and the reaction with the solvent anion is more exothermic. In such a case, k2 will systematically decrease with [L] (e.g., see Figures 1 and 2a for methanol and Figure 3a for acetonitrile). The equilibrium fraction f1 of the solvent anions may be found by using the fitting procedure described in section 3. Let us introduce the quantity Z ) 1/(f1 - 1). If reaction 4 is the only complexation reaction of the solvent anion and the dimerization of solute is negligible, Z ) K1[L]. Figures 2-4 show the dependencies of Z versus [L] for several polar molecules. Some of these dependencies are linear (e.g., for methanol and tert-butanol), but most exhibit superlinearity. For all systems shown in Figure 4, the concentration plot of Z may be fit using an empirical formula
Z ) K1′[L] + K2′[L]2
(5)
7030 J. Phys. Chem. B, Vol. 105, No. 29, 2001
Shkrob and Sauer For Kd[L] , 1, [M] ≈ [L], and [D] ≈ Kd[L]2. In addition to reaction 4, we consider two more complexation reactions
(CO2)n•- + D h {(CO2)n•-M2}
(7)
{(CO2)n•-M} + M h {(CO2)n•-M2}
(8)
with equilibrium constants K2 and K3, respectively. Because of the detailed equilibrium between all of these species, K2 ) K1K3/Kd and Figure 4. Z plots for various polar solutes in sc-CO2 at 41 °C ([CO2] ) 17.3 M): acetonitrile (dotted circles), water (straight crosses), methanol (dotted squares), ethanol (filled triangles), 1-propanol (open triangles), 1-pentanol (leaning crosses), 2-propanol (open diamonds), cyclohexanol (filled diamonds), and tert-butanol (combined triangles).
TABLE 1: Summary of the Equilibrium Parameters for Complexation of the Solvent Anion in sc-CO2 by Ethanol and Acetonitrile, Reaction 4 (T ) 41 °C, G/Gc ) 1.62) solute
-∆H° a
-∆G° a
-∆S0 b
ethanol acetonitrile
21 ( 1.5 16 ( 1
12.7 ( 3 14 ( 2
27 ( 5 6(4
a Standard potential at 314 K, kJ/mol. b Standard reaction entropy at 314 K, J mol-1 K-1.
where [L] is the total concentration of the polar solute. In the low concentration range ([L] < (1-5) mM), Z ≈ K1′[L]. For alcohols, the apparent equilibrium constant K1′ (≈K1) varies between 82 ( 3 M-1 (for tert-butanol) and 223 ( 7 M-1 (methanol). For ethanol, K1′ ≈ 130 ( 10 M-1, and the driving force ∆G of reaction 4 is -12 ( 3 kJ/mol; for acetonitrile, these values are 350 M-1 and -15.3 ( 2.2 kJ/mol, respectively (Table 1). Thus, the complexation is rather weak, and the dissociation of the complex at low concentrations of alcohol is efficient. This explains why the establishing of the equilibrium is not observed: to obtain a measurable change in σ0 (say, for Z ≈ 0.2), one needs to add 1-2 mM of the alcohol. For diffusion-controlled complexation of the solvent anion (≈1.5 × 1011 M-1 s-1),1 the time to establish the equilibrium would be 1.76 eV produces quasifree electrons.1 The conductivity “spike” from these short-lived electrons follows the line shape of the excitation pulse (Figure
Solvent Anions in Supercritical Carbon Dioxide
J. Phys. Chem. B, Vol. 105, No. 29, 2001 7031
5S). The photoinduced change in the conductivity ∆σ ∝ S0JC1, where S0 is the photodetachment cross section for the solvent anion, J is the light fluence, and C1 is the concentration of the solvent anion. In this work, a 2.33 eV photon pulse (J ≈ 0.14 J/cm2) was used to excite the anions in the reaction mixture 160 ns after the ionizing 5 eV pulse (∆σ/σ does not change with the delay time tp of the 2.33 eV pulse for tp < 1 µs). The concentration plots of the photoinduced change ∆σ and the ratio ∆σ/σ (defined as shown in Figure 5Sa) for two polar solutes, ethanol and acetonitrile, are shown in Figures 6S and 7S. For [EtOH] < 20 mM, ∆σ decreases with [EtOH] in a similar way as the fraction f1 of the solvent anions determined from the analyses of the decay kinetics (also shown in Figure 6S). For [EtOH] < 15 mM, the fraction f1 rapidly decreases from 1 to 0.2, whereas the ratio ∆σ/σ changes very little (Figure 6S). Therefore, the product of reaction 4, like the solvent anion itself, yields quasifree electrons upon the photoexcitation. At higher concentrations, ∆σ/σ begins to decrease (Figure 6S). The concentration of the ethanol at which ∆σ/σ decreases by 50% is ≈45 mM (which corresponds to 22 M-1). The overall concentration dependence cannot be explained if only one anion complex is present in the reaction mixture. Indeed, in such a case
∆σ/σ ∝ (S0 + S1K1[M])/(µ1s + µ2sK1[M])
(10)
where S0 and S1 are the photodetachment cross sections for the solvent anion and the monomer complex, respectively. For S1/S0 > µ2s/µ1s, ∆σ/σ given by eq 10 increases with [M]; otherwise, it decreases with [M]. This ratio could also stay constant (for ethanol, S1/S0 ≈ 0.375, which is close to µ2s/µ1s), but it cannot stay constant and then decrease. Apparently, the decrease is due to reactions 7 and 8 that yield the dimer complex with a cross section S2 considerably smaller than S0. From that, the dimerization constant Kd for ethanol is estimated to be ∼20 M-1. A bell-shaped concentration dependence of ∆σ/σ was observed for acetonitrile (Figure 7S). When the complexation reactions 7 and 8 are taken into account,
∆σ/σ ∝ (1 + [S1/S0]K1[M] + [S2/S0]K2[D])/ (1 + [µ2s/µ1s]{K1[M] + K2[D]}) (11) Because the data on ∆σ/σ provide additional information as to the extent of the dimerization, equilibrium constants K1, K3, and Kd can be estimated separately. Simultaneous least-squares fitting of Z and ∆σ/σ as a function of [L] (Figure 7S) yields the following optimum parameters: K1 ≈ 300 M-1, K2 ≈ 4600 M-1, Kd ≈ 2 M-1, S1/S0 ≈ 0.68, and S2/S0 ≈ 0.53. As expected, the dimerization of acetonitrile is less efficient as compared to that of hydrogen-bonded solutes; it would not be observable if the complexation with the dimer were not very efficient. 3.4. Energetics of Complexation. Temperature dependencies of the isochoric complexation constant K1 (41-60 °C) were obtained for acetonitrile and ethanol. The kinetic traces for acetonitrile are shown in Figures 8S and 9S. The initial slope K1′ ≈ K1 of Z versus [L] was determined using four concentrations of the solute for every temperature point (
