solvent reorganization energies measured by an electron transfer reaction in supercritical ethane

Journal of Supercritical Fluids 13 (1998) 155–161

Solvent reorganization energies measured byan electron transfer reaction in supercritical ethane

Kenji Takahashi a, Sadashi Sawamura a, Charles D. Jonah b,*a Division of Quantum Energy Engineering, Hokkaido University, Sapporo 060, Japan

b Chemistry Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, USA

Received 19 June 1997; received in revised form 7 November 1997; accepted 3 December 1997

Abstract

The intermolecular electron transfer reaction between a biphenyl anion and pyrene in supercritical ethane wasstudied using pulse radiolysis. Second-order electron transfer rates were found to be of the order of 1011 M−1 s−1.The rate constants appear to be approximately constant over the pressure range 55–133 bar and slower than thepredicted diffusion-controlled rate constants. Two possibilities are discussed that could explain the present results:diffusion constants that are not well predicted by the hydrodynamic equation; or a solvent reorganization energy ofapproximately 0.35 eV and dependent on pressure. The reorganization energy Er of non-polar supercritical ethanewas estimated from the observed rate constant using the modified Marcus equation. Er may be larger than normallyexpected for non-polar solvents because of density fluctuations. © 1998 Elsevier Science B.V.

Keywords: Solvent reorganization energy; Electron transfer; Non-polar fluid; Marcus theory; Density fluctuation

1. Introduction reactions in non-polar fluids. According to theirresults, the Er in non-polar solvent is not zero but

It is well known that density fluctuations [1] can be represented as the sum of two terms thatand clustering of solvent molecules [2–8] are arise from liquid polarization and density reorgani-observed in supercritical fluids (SCFs). The local zation, with the latter component being of muchdensity of SCFs around a solute may be signifi- greater importance. For this reason we felt thatcantly greater than the bulk density of fluid, not electron transfer (ET) reactions in non-polar SCFsonly in polar fluids [9] but also in non-polar fluids might show a new aspect of the solvent reorganiza-[10]. The local environment around a solute is tion energy in non-polar fluids. Whereas radicalsignificantly changed near the critical pressure [11]. reactions have been studied in SCFs [13–16 ], weRecently, Matyushov and Schmid [12] have theo- are unaware of any ET reactions that have beenretically studied solvent reorganization energy Er studied in SCFs.arising from charge separation and recombination In this work we present the intermolecular ET

reactions in non-polar SCFs. Biphenyl (BPh) anionand pyrene (Py) were used as an electron donor* Corresponding author. Tel: +1 630 252 3471; fax: +1 630 252

4993; e-mail: [email protected] and acceptor respectively. We chose to use ethane

0896-8446/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved.PII S0896-8446 ( 98 ) 00047-3

156 K. Takahashi et al. / Journal of Supercritical Fluids 13 (1998) 155–161

as a non-polar solvent because we could form the absorption spectrum and assuming that the extinc-tion coefficients of BPh and Py were the same asBPh anion in the solution; the anion was relatively

unreactive to the solvent and an SCF could be those in ethanol. No shift of the absorptionspectrum was detected over the pressure rangeformed conveniently. We were unable to form the

BPh anion in CO2 or CF3H. The solvent reorgani- studied.We used the pulse radiolysis method to studyzation energies were estimated using the measured

ET rates and the hydrodynamic diffusion ET reactions in SC ethane. A conventional pulseradiolysis system was used [18]. Electron pulsesconstants.from the Argonne Electron Linear Accelerator,about 30 ps in duration, 20 MeV energy, irradiatedthe solution. Both a short-flash lamp and a pulsed2. Experimental75 W xenon lamp were used as light sources fordetermining the transient absorption, dependingExperiments were run with a cylindrical stain-

less-steel high-pressure cell (Takagi equipment Co., on the time scale. The electron beam and theanalyzing light were collinear, and traversed theLtd., 4 cm in O.D., 9.5 cm in length). The 1 cm

thick Suprasil windows were mounted to the cell cell in opposite directions. Between the cell andthe electron beam port, a very thin mirror wasusing Teflon O-rings. The optical path length is

6 cm and the cell capacity is 4.2 cm3. The temper- placed to lead the analyzing light to the detectorsystem. The energy of the electron beam is suffi-ature of the cell was maintained constant to

±0.1°C at 35°C using an Omega temperature cient to pass through the mirror and Suprasilwindow and ionize the solution in the cell. Thecontroller (Model CN1001RTD), a cartridge

heater and a platinum resistance thermometer. The electron beam generated transient signals whenpassing through the Supracil windows. These tran-thermometer was installed into the cell so that it

is in contact with the fluid. Pressures were gener- sients were smaller than the optical absorptionscaused by the transient chemical species producedated using a JASCO HPLC pump (Model

PU-980). The fluid pressure was monitored with in the cell. The light was detected using a photo-multiplier (Hamamatsu R928) and monochroma-Cole–Parmer digital pressure meter (Model

7350-38) and pressure transmitter (Model K1, tor system or photodiode (CD 10) and bandpassfilter system. The signal from the detector was3000 psi).

Small amounts of stock solutions of BPh digitized using a Tektronix SCD 5000.(Aldrich 99%) and Py (Aldrich 99%) in ethanol,respectively 0.2 M and 0.01 M, were put into theoptical cell using microsyringes and the solvent 3. Results and discussionwas removed by heating the cell. After the evapora-tion of the ethanol, the cell was connected to the Fig. 1 shows typical transient spectra obtained

for the solution of BPh and Py in SC ethane. TheHPLC pump through a series of valves. To mini-mize the presence of oxygen, the entire apparatus concentration of BPh is considerably larger than

that of Py, so that most of the electrons formedwas purged with ethane at low pressure. After thepressure was set, the sample was mixed by a by the ionizing radiation from the solvent will

react with the BPh. The peak near 640 nm ismagnetic stirring bar. In a given experimental run,the molarity was held constant while the pressure attributed to absorption of BPh− and its magni-

tude decreases with time. The absorption aroundwas varied. At higher concentrations, experimentscould not be run at lower pressures because of the 480 nm, which builds up at the same rate as the

640 nm absorption decays, is assigned to Py−,limited solubility.The density of supercritical (SC ) ethane was which is formed by the intermolecular ET reaction.

Fig. 2 shows transient kinetics at 640 nm andcalculated with the Peng–Robinson cubic equationof state [17]. The solubilities of BPh and Py in SC 480 nm corresponding to BPh− and Py− respec-

tively. Under the present experimental conditionsethane were estimated by measuring the UV

157K. Takahashi et al. / Journal of Supercritical Fluids 13 (1998) 155–161

the concentration of BPh− produced can be esti-mated as ca. 10−6 M by assuming that the extinc-tion coefficient of BPh− in SC ethane is the sameas that in ethanol. Although the extinction coeffi-cient of BPh− might depend on the pressure [13],the concentration of the BPh− does not affect themeasured rate constants because we are measuringpseudo-first-order processes. The concentration ofPy was adjusted to 100, 200, 300, 400 and 500 mMand the ET reaction was studied under pseudo-first-order reaction conditions. (At the lowest pres-sure, the entire concentration range could not beused because of limited solubility. The limitedconcentration range sharply limited the accuracyof the rate constant.) The pseudo-first-order reac-tion rates were calculated by simultaneously fittingthe decay of BPh− and growth of Py−. The second-order rate constants were extracted from thepseudo-first-order rates, and are displayed as aFig. 1. Transient absorption spectra monitored at 3 ($) 6 (+)

10 (#) and 15 ns (,) after the pulse. The concentrations of function of the pressure of SC ethane in Fig. 3(a).BPh and Py are 9 mM and 0.7 mM respectively. The pressure The experimental measurements show a decaywas 130 bar and temperature 35°C. of the Py−. We measured this decay as a function

of dose (concentration of Py−) and found that therate was independent of dose. This shows that itis not a second-order reaction, with species pro-duced in the bulk of the solvent. It could be areaction of the Py− with the cation formed in thesame ionization event (geminate decay), but wedid not attempt to establish that.

If there are no electrostatic interactions betweenthe reactants, the rate of an ET reaction can bedescribed by [19]

kobs=kd

1+0.2 expCErA1+DG

ErB2/4RTD

(1)

where kd is a diffusion-controlled rate constant,−DG is the free energy change (0.52 eV for thepresent system [18]) and Er is the reorganizationenergy. The diffusion-controlled rate for a reactionand distance r can be described by Eq. (2) and isplotted in Fig. 3(a).

kd=4prDNa (2)Fig. 2. Transient kinetics at 640 and 480 nm. The pressure is101 bar and temperature was 35°C. The concentrations of Py

where Na is Avogadro’s number, r is the reactionand BPh are 300 mM and 7 mM respectively. The trace at thedistance and assumed as a sum of the donor andbottom of the figure shows the difference between the fit and

the experimental data at 480 nm. the acceptor radii, and D is the sum of the diffusion


On examination of Fig. 3(a), one observes thatthe rate constants appear to be approximatelyconstant and considerably smaller than the diffu-sion-controlled rate constant (solid line, Fig. 3(a))over the pressure range 50–140 bar. The signifi-cance of the apparent increase at the lowest pres-sure, which mirrors the increase in the diffusion-controlled rate constant, is unclear because of thelarge error bar. Two possible explanations for thevariance from the diffusion-controlled rates are:(1) the viscosity of the SCFs does not determinethe diffusion rate and thus the diffusion-controlledrate is not what is expected; or (2) the solventreorganization energy Er is large and may changewith pressure. We will discuss these two possibilit-ies separately.

It is well known that the diffusion constants inmany systems do not correspond to the hydrody-namic diffusion constants and the true diffusionconstants are, in general, smaller than predictedby those equations. Such data are reviewed formany systems in Ref. [21], although, unfortu-nately, not for any systems in SC ethane. If cluster-ing around a solute molecule modifies thediffusivity, one might well expect differences fordifferent solvents (and solutes) [11]. We are observ-ing the reaction between an ion (BPh−) and a

Fig. 3. (a) Points are the ET rate constants in SC ethane as aneutral molecule and the ion might well have afunction of total pressure at 35°C. Error bars are two standardsmaller diffusion constant than the neutral (seedeviations. The solid line is the calculated diffusion-controlledRef. [22] and references cited therein).rate constant kd as a function of pressure (see text). (b)

Calculated solvent reorganization energy based on Eq. (1). See In a recent publication [23], it has been showntext for details. that the rotational diffusion time of a fluorescent

species is considerably slower than one wouldpredict from the calculated viscosity of the fluidcoefficients of the reactants. Values of D were

calculated by hydrodynamic theory in which the at lower pressures. Also, the difference betweenpredicted and measured reorientation timeshydrodynamic radius of BPh− and Py are assumed

to be the same as naphthalene as a model aromatic. decreased as the pressures increased. The authorssuggested that this result could be due to eitherThe values of D, however, might be overestimated

in the low pressure experiments because, near the (1) a cluster of solvent molecules around theexcited state that inhibits the rotation of the mole-critical pressure, clustering around the solutes may

occur. This problem will be briefly discussed later. cule or (2) a clustering of solvent molecules withthe solute molecule where this cluster moves as aThe viscosity of SC ethane was calculated using

an equation proposed by Younglove and Ely [20]. group (and thus more slowly). Certainly, thesecond suggestion would explain the present data.The calculated kd may be an underestimate because

the reaction radius may be larger than the sum of Morita and Kajimoto [10] have reported a clus-tering in non-polar SCFs. Their results show thatthe donor and acceptor radii; however, the relative

dependence of kd on pressure is independent of the solvatochromic shift is much larger than ex-pected from Onsager’s theory. The bathochromicthe reaction radii.


shifts can be attributed to the solvent aggregation used to calculate Er is a lower limit. If the reactionradius were larger, the two Er curves would sepa-around a solute even in non-polar ethane. These

results are consistent with the present data. rate further. It seems unlikely that Er could bemuch lower than that calculated in the lower curveThe second alternative, a change in the solvent

reorganization energy Er, would also explain the (considering the possibility of some energy due toa twist in the biphenyl anion); thus we expect thatdata. Eq. (1) shows that a shift in Er alters the

rate constant. Fig. 3(b) shows the two calculated the estimated radius is reasonable. If, however, themobilities are lower than assumed then the lowervalues of Er as a function of pressure using the

assumed values for the diffusion-controlled rate. curve for Er would move up while the upper curvewould move down. This would be consistent withOwing to the quadratic dependence of the rate on

Er, there are two values for Er that would explain the possible increase in Er that could arise fromthe fluctuations in the SC ethane. To estimatea particular experimental rate constant. These

results can be compared with the literature results more precisely the diffusion coefficients we needfurther experimental data.for non-polar liquids, which are summarized in

Table 1. The previous results are smaller than We can examine the magnitude of Er using thetheory of Matyshov and Schmid [12]. Er can beeither curve given in Fig. 3(b) except for the results

by Cortes et al. [25]. (The interpretation of those represented as the sum of two terms, Ep and Ed,where Ep determines the solvent reorganizationresults is uncertain, in that the authors refer to

these values as unphysically large.) There are sev- due to the polarization of the fluid and Ed repre-sents the contribution from repacking the solventeral possible explanations for the relatively large

value of Er determined from the present experi- near the core of the electron donor–acceptor com-plex. Using their results, we have calculated Er forment. As Miller et al. have shown, there can be a

low energy twisting motion of BPh that would ethane. In the calculation the cavity radius wasestimated as 5 A based on an approximation ofcontribute approximately 0.15 eV [26]. If this value

is added to the literature values for Er then the the size of the molecule. The molecular polarizabil-ity was 4.07 A3 [28]. The solvent diameter of 3.7 Alower curve is only slightly higher than suggested

by previous work. In addition, experimental was estimated from an ab initio calculation (6-31g)[29] of the van der Waals volume. The Er calcu-studies [1] have shown the existence of large

fluctuations near the critical point in SCFs. lated is 0.47 eV. This value is very close to the Erof the high pressure region in Fig. 3(b).Theoretical [12] studies have suggested that such

fluctuations could increase the value of Er. In their theory [12], Ed is much larger than Ep.If one replaces the solute–solvent distributionFurthermore, simulations by Ganapathy et al.

have shown that reaction rates will not follow the function by a step function, the value of Ed isgreatly reduced and Er is approximately the sameSmoluchowski rate expression in SCFs if the reac-

tion probability is small [27]. A large solvent as Ep. Our molecular dynamics simulations [30]show that, at low densities, the pair correlationreorganization energy could lead to similar appar-

ent results as a low reaction probability. functions are less like a step function than theyare at higher densities. Thus Ed will be much largerAs stated above, the reaction radius that werelative to Ep at lower densities. This means thatEr will be larger at lower densities than oneTable 1

Solvent reorganization energy in non-polar liquids might expect.To explore the dependence of Er on pressure

Solvent Er/eVwill require further experiments utilizing reactionswith different DG values. It is clear that the pres-Closs et al. [18] iso-octane 0.15

Gould et al. [24] n-C6H12 0.14 sure dependence of Er and solvation dynamics inCCl4 0.16 SCFs will be an important topic of future research.

Cortes et al. [25] n-C6H12 0.33–0.51 New simulations that make use of molecularCCl4 0.31–0.46

dynamics and quantum calculations and the use


of polarizable solutes and solvents will provide No. W-31-109-ENG-38 with the US Departmentof Energy. The US Government retains for itself,important insights into the mechanisms. None of

the proposed experiments will be possible without and others acting on its behalf, a paid-up, non-exclusive, irrevocable worldwide license in saidnew measurements of diffusion constants.article to reproduce, prepare derivative works,distribute copies to the public, and perform pub-licly and display publicly, by or on behalf of the4. ConclusionGovernment.

We have measured ET reactions between ananion and a neutral species in a non-polar super-critical fluid. To our knowledge this is the first

Referencesmeasurement of ET reactions in SCFs. Theseresults provide evidence for new phenomena that

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solvent reorganization energies measured by an electron transfer reaction in supercritical ethane

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