Photophysics of Hole Injection in Liquid ... - ACS Publications

In liquid cycloalkanes, single-photon excitation of solute radical cations leads to rapid transfer of a valence band electron and formation of a free ...
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J. Phys. Chem. B 1999, 103, 4773-4780

4773

Photophysics of Hole Injection in Liquid Cycloalkanes† I. A. Shkrob,* M. C. Sauer, Jr., and A. D. Trifunac Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: January 4, 1999; In Final Form: February 24, 1999

In liquid cycloalkanes, single-photon excitation of solute radical cations leads to rapid transfer of a valence band electron and formation of a free solvent hole (“hole injection”). Quantum yields for this process upon 2.3 and 5 eV laser excitation of several aromatic radical cations in trans-decalin are reported and the photophysics of the hole injection in cycloalkane liquids is discussed.

1. Introduction Ionization of cyclohexane, methylcyclohexane, and cis- and trans-decalins yields long-lived solvent holes.1-6 Due to their polaronic nature,2,6 these holes exhibit drift mobility 5-20 times higher than the mobility of molecular ions in the corresponding liquids. The lifetime of these fast-diffusing holes is 0.1-2 µs so that the species can be observed using time-resolved conductivity, an opportunity that does not exist for other solvents, where hole mobilities were found to be comparable to the mobilities of molecular ions.1 With dc conductivity, as low as 1-10 nM of the solvent holes can be observed,5-8 which makes this technique preferable to other detection means. Apart from the direct ionization of cycloalkane solvent, the holes can be produced by rapid transfer of the solvent valence band (VB) electron to electronically excited solute radical cation A•+* (“hole injection”):6-8

A•+ + hν f A•+*

(1a)

A•+* + solvent f A + hole+

(1b)

Radical cation A•+ can be photoexcited by the same UV pulse that ionizes the solute (A)5a or by a second laser pulse, of different color, triggered after the ionizing UV pulse.7a The second method gives more experimental control (e.g., the laser wavelength can be tuned to the absorption band of A•+) and eliminates complications due to geminate recombination of ions (the second pulse can be delayed to >1 µs, when the geminate recombination is essentially over). Using transient dc conductivity 5-8 and optical absorbance, 9 we have demonstrated that hole injection is a common photoreaction of aromatic radical cations in both polar and nonpolar solvents and that this reaction is initiated by absorption of a single photon by A•+ and proceeds very rapidly (1 µs). L1 and L2 lasers produced 8 ns and 3 ns fwhm pulses, respectively. L1 is equipped with a 20 dB laser amplifier; it is capable of producing 2.3 eV pulses to 0.4 J. The output power was controlled by delaying the Q-switch relative to the simmer pulse. Due to thermal lensing in the amplifier, the beam diameter increases from 1.6 mm at 10 mJ to 4 mm at 350 mJ. To prevent the loss of photon fluence through aperture A2, the beam was compressed a factor of 2-3 using a 50 cm focusing lens. L2 produces 2.3 eV pulses at 1-90 mJ; the beam diameter is 2.5 mm regardless of the output power. The 2.3 and 5 eV beams were coincident inside a 1 cm path cylindrical conductivity cell with 0.6 cm spacing between planar Pt electrodes (Figure 1). The beams were superimposed so that the column of the 2.3 eV light completely enveloped the column of the 5 eV light. In a typical arrangement, the 5 eV beam passed through a 3 mm diameter aperture (A1) at the front of the cell and the 2.3 eV beams entered through a 3.5-4.7 mm aperture (A2) at the rear. This arrangement allowed us to change the flux of 2.3 eV photons between 0 and 2.5 J/cm2, while the flux of the 5 eV photons was varied between 0.05 and 0.1 J/cm2. If not stated otherwise, the 5 eV photon flux was 0.1 J/cm2. The photon fluences given below are average fluxes through the corresponding apertures. All three lasers were operated at 1 Hz, and the delay times between the laser pulses were controlled with accuracy to (3 ns. The measurements were carried out at 21 °C. The conductivity cell was operated at 7.5 kV/cm and had a cell factor of 12. We used either a glass-blown quartz cell or a cell made of machinable ceramic. Since the Suprasil windows frequently break down when the fluence of 2.3 eV photons exceeds 1 J/cm2, the cell windows were epoxied to the body of the cell (Torr-Seal), and could be removed for replacement by soaking in boiling acetic acid. The photocurrent through 50 Ω was amplified 100 times using two fast CLC449 and CLC100 amplifiers; the signal was acquired with a DSA-601 transient digitizer. The cell was enclosed in an aluminum box that shielded it from electromagnetic interference produced by the lasers. It was found that powerful 2.3 eV laser pulses (>0.5 J/cm2) produced false “conductivity” signals in the circuitry when the light-ablated metal surfaces stood in its path, by disturbing the common ground; to prevent this, the apertures were made of plastic. No transient conductivity signals from 2.3 eV pulses alone, without a preceding 5 eV pulse, were observed. 3. Results Measuring the Quantum Yields. 5 eV laser excitation of an aromatic solute yields the lowest singlet and triplet states; these states absorb the second 5 eV photon and autoionize yielding a geminate pair of the aromatic radical cation (A•+) and electron. The electron is rapidly scavenged by CO2, yielding CO2•- anion. The radical cation can absorb a 5 eV photon yielding a mobile solvent hole, via reaction 1. At 1 µs, essentially all of the geminate pairs have recombined, and 5-10% of the initial ions become “free” of each other’s Coulomb attraction (“free ions”).2 Within the same time period, solvent holes generated by the 5 eV pulse react with the aromatic solute and impurity (Figure 2a). The residual dc conductivity signal is due to 0.01-0.3 µM of long-lived free ions whose recombination is slow. 5 In room temperature trans-decalin, the combined mobility µi ) µ+ + µ- of these molecular ions is

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5.2 × 10-4 cm2/(V s). 2 The dc conductivity σi of the solution is proportional to the product Ci µi, where Ci is the concentration of free (molecular) ions. Following the photoconversion of A•+ to solvent holes by a 2.3 eV laser pulse at t ) td, the difference conductivity signal ∆σ(τ) ) σ(t) - σi is given by ∆σ(τ) ∝ Ch(τ)(µh - µ+), where τ ) t - td, Ch is the concentration of free solvent holes formed in reaction 1, and the µh is the hole mobility, estimated as (8.7 ( 0.2) × 10-3 cm2/(V s)5a or 9 × 10-3 cm2/(V s).2 Since µ+ , µh (µ+ ≈ 1.5 × 10-4 cm2/(V s)), ∆σ(τ)/σi ≈ (µh/µi)Ch(τ)/Ci. The µh/µi ratio is measured more accurately than the mobilities µh and µi themselves, and has been determined as 17.3 by Warman.2 Using this ratio, from ∆σ(τ)/σi one can determine Ch(τ)/Ci. The decay of the 2.3 eV laser induced conductivity ∆σ(τ) follows scavenging kinetics of free solvent holes. Let us first assume that these kinetics are pseudo first order, with the rate constant of k1 (as is the case for most of hole scavengers in trans-decalin) Keeping in mind that the duration of the 2.3 eV pulse can be comparable to k1-1, a convolution of a Gaussian time profile of the laser pulse with an exponential must be used to fit the decay kinetics,7

∆σ(τ)/∆σ0 ) Ch(τ)/Ch0 ) f(k1;τ)

(2)

where

f(k1;τ) ) (π/tp)1/2

∫-∞τ dη exp(-[η/tp]2) exp[-k1(τ - η)]

) exp(-k1τ + [k1tp/2]2){1 - 1/2 erfc(τ/tp - k1tp/2)} (3) Here tp is the Gaussian width of the laser pulse; the irradiance J(t) ) (π/tp)1/2Jp exp(-[t/tp]2), where Jp is the total fluence. For L1 pulse, tp ≈ 6 ns. Symbols Ch0 and ∆σ0 in eq 2 denote the initial concentration of free holes produced in reaction 1 and the corresponding conductivity signal. To determine ∆σ(τ), two methods were used. With the first method, the 2.3 eV laser was fired for every second 5 eV pulse, and the “on” and “off” σ(t) kinetics were collected and subtracted. With the second method the tail of the conductivity signal from the 5 eV pulse alone was fit as the second order decay curve (the free ion signal σi at t ) td was determined from these fits), and this curve was subtracted from the σ(t) signal obtained with both of the 5 and 2.3 eV laser pulses. Both of these methods gave similar results. The ∆σ(τ) kinetics were fit using eqs 2 and 3, and k1 and ∆σ0/ σi were determined; from the latter ratio, the Ch0/Ci ratio was found. Given that the lifetime of photoexcited solute radical cation A•+* is much shorter than tp and practically no attenuation of the 2.3 eV light occurs on the passage through the cell (the OD at 2.3 eV is less than 10-4), the conversion of the ground-state radical cation A•+ upon single-photon excitation is given by9

Ch0/[A•+] ) 1 - exp(-βJp)

(4)

where β ) 2.4 × 10-2 φ/Eph, φ is the quantum yield of free solvent holes in reaction 1,  is the extinction coefficient of A•+ in M-1 cm-1, Eph is the photon energy in eV, and Jp is the photon fluence in J/cm2. (If the absorbance of A•+ is ,1 and the decay time of A•+* is much shorter than the duration of the laser pulse tp, the rate of photoconversion is given by d[A•+]/dt ∝ φ{[A•+]}{J(t)/Eph}; integration of this equation yields formula 4).9 In principle, given the spatial inhomogeneity of the 2.3 eV beam, eq 4 should be averaged over the entire cell volume.9

Figure 2. Dc conductivity in laser photolysis of (a) 10 µM and (b,ii) 1 µM triphenylene in CO2-saturated trans-decalin at 25 °C; trace (b,i) is the conductivity of the solution without aromatic sensitizer. 5 eV pulse (0.1 J/cm2) was applied at t ) 0, 2.3 eV pulse L1 was applied at 1 µs, 2.3 eV pulse L2 was applied at 2 µs (80% and 60% saturation, respectively, see Figure 3a). In Figure 2b,i, the traces induced by 5 eV light alone are shown by dashed curves (no L2 pulses are shown in Figure 2b,i). In Figure 2a, the broken line is the second-order fit to σ(t) for t > 1 µs (the kinetics were sampled to 20 µs, not shown). The dot-dashed line in Figure 2a is the σ(t) signal induced by both L1 and L2 pulses; the solid lines are for 5 eV and L1 excitation, and 5 eV and L2 excitation.

However, under the conditions of our experiment, replacing Jp in eq 4 with average photon flux 〈Jp〉 through the cell leads to insignificant underestimation of β ( 16

0.9 0.7 0.8 0.8

a 40 µM solutions in CO2-saturated trans-decalin at 25 °C, except for triphenylene (10 µM solution). b Extinction coefficient of A•+ at 2.3 eV, in 103 M-1 cm-1 (ref 9). c 2.3 eV excitation in cyclohexane. d 5 eV excitation in trans-decalin. e From ref 10; IPg of trans-decalin is 9.25 eV.

Figure 4. Concentration dependence of the ∆σ/σi ratio at t ) 2 µs induced by a 5 eV pulse at t)0 with an L2 pulse and no L1 pulse (empty squares; 60% saturation) and by a 5 eV pulse with both L2 (at 2 µs) and L1 pulses (empty triangles; the L1 pulse occurred at t ) 1 µs; 80% saturation) in triphenylene solutions of trans-decalin saturated with CO2. The L2 pulse was at 2 µs. Filled circles indicate the concentration dependence of the pseudo-first-order rate constant k1 of the ∆σ(τ) decay.

Figure 3. Photon fluence dependence of hole injection at 2.3 eV laser excitation for (a) 10 µM triphenylene, (b) 40 µM naphthalene, (c) 40 µM biphenyl, and (d) 40 µM perylene in CO2-saturated trans-decalin (td ) 1 µs). Jp is the average 2.3 eV photon flux through aperture A2. Several data series obtained for different focusing of the 2.3 eV beam are spliced together.

of ∆σ0/σi ratio with the concentration [A] of the aromatic solute, as seen in Figure 4. Aromatic Radical Cations. The simplest way to account for the observed ∆σ0/σi and [A•+]/Ci ratios is to assume that aromatic radical cations present at t ) td are generated in two processes: (i) ionization of aromatic solute during 5 eV photoexcitation and (ii) delayed formation of A•+ through scavenging of solvent holes formed upon this 5 eV excitation (via reaction 1). The remaining molecular cations present at t ) td are due to scavenging of the solvent holes by impurity. With these assumptions, denoting the fraction fA of aromatic radical cations and the fraction fH ) 1 - fA of the solvent holes formed promptly upon the 5 eV excitation, one obtains

[A•+]/Ci ) fA + fHY

(5)

Y ) k2[A]/k1 and k1 ) k1° + k2[A]

(6)

where Y is the yield of A•+ formed through hole scavenging, k1 is the observed decay constant, k2 is the rate constant of hole

scavenging by the aromatic solute, and k1° is the pseudo-firstorder rate constant for hole scavenging by impurity. The validity of eq 5 rests on the assumption that only free solvent holes formed upon 5 eV photoexcitation are scavenged by the solutes; this is reasonable since the geminate stage for these mobile species is essentially complete in ca. 30 ns. In purified trans-decalin, k1° ≈ 106 s-1 and k2 ≈ 1.7 × 1011 -1 M s-1 (for triphenylene). With increase in [A], a larger fraction of the solvent holes is scavenged by the aromatic solute and eventually almost all of the cations in the solution are A•+. In the opposite extreme, when most of the solvent holes are scavenged by impurity, the ∆σ0/σi ratio rapidly decreases with decrease in [A] approaching fA. As shown in Figure 4, this prediction is not entirely supported by the experiment: When the concentration of triphenylene is lower than that of scavenging impurity (at [A] )1 µM, k2[A]/k1° ≈ 0.15) the ∆σ0/σi ratio decreases to 55% of its magnitude for [A] > 10 µM (Figure 4). Taken at the face value, this suggests that fA ≈ 0.5 (which is, incidentally, correct). However, in concentrated triphenylene solutions (>10 µM), there is no change in the ∆σ0/σi ratio with [A], which is inconsistent with eq 5. The culprit becomes obvious when one examines the conductivity traces obtained in neat trans-decalin (Figure 2b). Though the conductivity is 5-10 times weaker than in triphenylene solutions (in the neat solvent, the ionization proceeds through a simultaneous absorption of two 5 eV photons), a weak ∆σ(τ) signal induced by 2.3 eV photons at 1 µs is clearly discernible. Apparently, a subset of impurity cations can be excited by 2.3 eV photons to yield free solvent holes via reaction 1. When 1-2 µM of triphenylene is added, the prompt yield of the solvent holes at 5 eV increases 5-fold; the concentration of the impurity cations (formed through scavenging of these holes) increases accordingly. Thus, at low

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concentration of the aromatic solute, a substantial fraction of the ∆σ(τ) signal is from the excited impurity cations. Only at higher concentration of the aromatic solute, when most of the solvent holes are scavenged by the aromatic solute, is the ∆σ0 signal mainly from A•+ cations (for this reason, the flux dependences shown in Figure 3 were obtained using high concentration of the aromatic solutes, 40 µM). This scenario is validated in a series of experiments examined below. Three Pulse Experiments. The three-pulse experiment has been alluded to in the preceding (Figures 2a and 4). Above, we assumed that the hole injection is the major photoreaction of A•+ excited with 2.3 eV light. This was supported by measurements of Ch0/Ci: In the limit of complete photobleaching, 7090% of all free cations present in the solution at t ) td (of which most were A•+) were converted to the solvent holes. There is, however, a catch: the µh/µi ratio used in our calculations was obtained with the assumption that ionization of neat transdecalin yields only solvent holes. Since this was shown to be incorrect for other cycloalkanes (e.g., cyclohexane, see ref 6), the actual µh/µi ratio could be higher and then the actual [A•+]/ Ci ratios would be lower. To examine whether the photoexcitation of A•+ yields mainly the solvent holes, the three-pulse experiment described by Figure 2a was implemented. The aromatic solute (triphenylene) was photoionized at 5 eV, the first 2.3 eV pulse (L1) being used for excitation of A•+ at t ) 1 µs, while the second 2.3 eV pulse (L2), of lower intensity, was applied at t ) 2 µs to determine the “permanent” depletion of A•+ at 2 µs caused by the L1 pulse. The intensity of the pump pulse (L1) was sufficient to achieve 80% photobleaching of triphenylene•+, and the intensity of the probe pulse (L2) corresponded to 60% photobleaching; when the two 2.3 eV lasers fired simultaneously at 1 µs, the photobleaching was 90% complete. Figure 2a shows the results of three runs: one is with the 5 eV pulse and L1, one is with the 5 eV pulse, L1, and L2 (the dot-dash curve shown under L2), and one is with the 5 eV pulse and L2 (the solid curve under L2). The difference between these two curves under L2 is a measure of the extent to which L1 changes the concentration of A•+ at 2 µs. To see how this experiment works, consider first the case where the solvent holes are a minor product of A•+ photoconversion, and that the major product does not result in the reformation of A•+ in the time between L1 and L2. Then, following the excitation with L1, less than 20% of triphenylene•+ would remain in the solution. Comparing the ∆σ0 signal induced by L2 pulse with (∆σ0(L1+L2)) and without (∆σ0(L2)) a preceding L1 pulse, one would observe that the former signal is only 20% of the latter. Conversely, consider the case where the solvent hole is the major photoproduct. In this case, a certain fraction Y of the solvent holes will be scavenged by triphenylene re-forming triphenylene•+, and the decrease in the ∆σ0(L1+L2) signal relative to the ∆σ0(L2) signal would be smaller. By varying the delay of the L2 pulse relative to L1 pulse the recovery kinetics of A•+ can be resolved; these kinetics should be complementary to the decay kinetics of the solvent holes (Figure 5a). Since, upon hole scavenging,

d[A•+]/dτ ) k2[A] Ch(τ)

(7)

we obtain (keeping in mind that Ch ∝ ∆σ)

[A•+]τ ∝

∫0τ dτ′ ∆σ(τ′)

(8)

where τ ) t - td(L1). According to eq 8, the recovery kinetics of A•+ can be modeled by numerical integration of the experimental ∆σ(τ) signal induced by the L1 pulse.

Figure 5. (a) Pump-probe three-pulse experiment with 10 µM triphenylene in CO2-saturated trans-decalin (the conditions are as described in Figure 2a). The L2 pulse was delayed relative to the L1 pulse by τ12 which was varied between 30 ns and 2 µs. (b) Recovery kinetics of the signal {∆∆σ/σi}L2 induced by the L2 pulse on the top of σ(t) signal14 induced by the L1 pulse in (i) 10 µM and (ii) 20 µM triphenylene solutions. These kinetics are juxtaposed with the kinetics obtained by integration of normalized ∆σ(τ) induced by the L1 pulse alone, solid lines (cf. eq 8).

In Figure 5b, the kinetics obtained with eq 8 and the recovery kinetics determined in the three-pulse pump-probe experiment are compared for two concentrations of triphenylene, 10 and 20 µM. The semblance between the two sets of data is striking. Beyond any doubt, the species that yield solvent holes upon 2.3 eV excitation with the L2 pulse are formed in reaction of solvent holes with triphenylene. From Figure 4, no more than about 20% of the A•+ ions present at the time of the L2 pulse were depleted due to the L1 pulse; most of the A•+ re-formed through the reaction of solvent holes with triphenylene. The fraction of depleted triphenylene•+ decreased with the concentration of triphenylene (Figure 4); at 80 µM, 95% of the triphenylene•+ was recovered. This observation suggests that the depletion of triphenylene•+ is due to scavenging of the solvent holes formed in reaction 1 with impurity. When most of the solvent holes react with triphenylene, the recovery is nearly complete. When the concentration of triphenylene is low (1-2 µM), ∆σ0(L1+L2) ≈ ∆σ0(L2), since the ∆σ0 signals are mainly from photoexcited impurity cations (Figure 4). In the intermediate regime, the recovery of the ∆σ0 signal is incomplete. (This behavior requires a lower efficiency for production of solvent holes from the impurity cation relative to triphenylene•+.) To study the recovery of triphenylene•+ we added a second hole scavenger, 2-propanol, and observed the decrease ∆σ0(L1+L2)/∆σ0(L2) ratio with the fraction Y of the solvent holes scavenged by triphenylene. A simple calculation shows that

∆σ0(L1+L2)/∆σ0(L2) ) 1 - Φ(1 - Y)

(9)

4778 J. Phys. Chem. B, Vol. 103, No. 22, 1999

Shkrob et al.

Figure 6. Ratio ∆σ (L1+L2)/∆σ (L2) (filled circles) and the apparent rate constant k1 (empty squares) for 10 µM triphenylene in CO2saturated trans-decalin containing 0 to 1.1 mM of 2-propanol (same conditions as in Figure 2a). 0

0

where Φ is the fraction of triphenylene•+ photobleached by the L1 pulse. Fitting the ∆σ0(L1+L2)/∆σ0(L2) ratios with eq 9 using kinetic data for 2-propanol (Figure 6) yields Φ ) 0.8, in complete agreement with the value of Φ obtained from the calibration plot in Figure 3. (Scavenging of the solvent hole in trans-decalin by 2-propanol proceeds through the formation of a stable collisional complex with natural lifetime of 30 ns; this complex decays by proton transfer when it encounters another 2-propanol molecule. We have determined the rate constants for this two-step scavenging reaction. It was shown that formula 9 is still applicable when the kinetic data from Figure 6 are used. See the Supporting Information for more details.) In conclusion, the pump-probe experiment demonstrates that, first, the 2.3 eV laser induced photobleaching of the aromatic radical cation yields only solvent holes (i.e., the estimates of µh in room-temperature trans-decalin given in refs 2 and 5a are correct) and, second, that the observed deviations from eq 5 are due to the presence of a photoactive impurity cation. The remaining problem is the determination of the fraction fA of aromatic radical cations formed upon 5 eV excitation. Hole Injection at 5 eV. Previously, by analysis of the 5 eV photon flux dependences for the conductivity signals, we have shown that the formation of the solvent holes in cycloalkanes is a three-photon process while the ionization of the solute is a two-photon process.5b To estimate the quantum yield of reaction 1 induced by 5 eV photons, we need to determine the photon flux dependence of the ratio fH. Assuming that during the 5 eV excitation the only cations formed are solvent holes and A•+, the evolution of the conductivity signal σ(t) is given by

σ(t) ) 10-3F{µh+[h•+]tgh(t) + µi[A•+]tgi(t)}

(10)

where the evolution of the free-ion concentrations [h+] and [A•+] is given by

d[h+]/dt ) - k1[h+] - Rµh[h+][CO2•-]

(11)

d[A•+]/dt ) - k2[A][h+] - Rµh[A•+][CO2•-]

(12)

where [CO2•-] ) [h+] + [A•+], Rµi is the rate constant of homogeneous ion recombination given by the Debye equation; R )10-3F/so, s ) 2.14 is the solvent permittivity, and F is the Faraday constant. At t ) 0, [h+] ) fHc0 and [A•+] ) fAc0, where c0 is the initial concentration of ions (extrapolated to the free ion level). Functions g(t) in eq 10 account for the dc conductivity signal from geminate pairs. The parametrization

Figure 7. Photon fluence dependence (at 5 eV) of the prompt fraction fH of the solvent holes in laser photolysis of (i) 20 µM and (ii) 5 µM triphenylene in CO2-saturated trans-decalin. The fraction fH was determined by numerical fitting of decay kinetics σ(t) using eqs 10-12.

from ref 5a

g(t) ≈ 1 + 0.12(t/tc)-0.75

(13)

has been used, where tc ) eRc2/kTµs is the Onsager time, Rc ) e2/4πkTsο is the Onsager radius, and µs is the sum of mobilities of the geminate ions (indices “h” and “i” in eq 10 refer to geminate pairs involving the solvent hole and A•+, respectively). Using the known mobilities, we obtain tc ≈ 33 ns for the solvent holes and tc ) 0.55 µs for A•+ cations in trans-decalin, respectively. The traces were simulated using eqs 10-12 for t > 30 ns; parameters c0 and fH were varied to obtain the leastsquares fit, while all other parameters were taken either from the literature or from the experiment. The initial guesses for c0 were obtained by fitting the σ(t) traces for t > 2 µs as secondorder decay kinetics. The σ(t) kinetics were fit for several concentrations of triphenylene (1-80 µM) and fluences of 5 eV photons (from 0.05 to 0.1 J/cm2). The maximum yield c0 of free ions was obtained in 20 µM triphenylene solutions (c0 ≈ 0.25 µM at 0.1 J/cm2); at 5 and 75 µM, c0 was half as low. At a fluence of 0.1 J/cm2, a single value of fH ≈ 0.5 was used to fit the σ(t) traces for all concentrations of triphenylene in excess of 10 µM. In less concentrated solutions, fH increases substantially, from 0.5 at 10 µM to 0.6 at 5 µM to 0.7 at 1 µM to 1.0 in the neat solvent. Given the strong attenuation of 5 eV light by aromatic solute (at 5 eV, triphenylene has an extinction coefficient of 8.7 × 104 M-1 cm-1), the increase in fA observed in weak solutions must be due to increased absorbance of 5 eV light by triphenylene•+. When fH was plotted as a function of the incident flux of 5 eV photons (uncorrected by absorbance of the ground state and singlet triphenylene),5b we found that fH increased linearly with a slope of 7.5 ( 1 cm2/J regardless of the solute concentration (Figure 7). From this slope it can be estimated that φ ≈ 1.6 × 103 M-1 cm-1. From the absorption spectra of triphenylene•+ in boric acid glass,9 we estimate that the extinction coefficient of this cation at 5 eV is < 104 M-1 s-1, which gives φ in excess of 0.16. Thus, for triphenylene•+ the quantum yield of hole injection at 5 eV is at least three times higher than at 2.3 eV(see Table 1). The estimate of fH ≈ fA ≈ 0.5 in concentrated solutions agrees well with the values of fH ) 0.47 ( 0.1 and fH ) 0.6 ( 0.2 extracted from scavenging experiments using triethylamine and 2-propanol, respectively (see the Supporting Information). The observed increase in fH with reduction in [A] explains why eq 5 was inapplicable in the low-concentration regime: Due to increased absorption of 5 eV photons by A•+, the conversion

Hole Injection in Liquid Cycloalkanes

J. Phys. Chem. B, Vol. 103, No. 22, 1999 4779 survival probability

P(t) ) P∞{1 + (τD/πt)1/2}

Figure 8. A correlation between the quantum yield φ of free solvent holes in 2.3 eV photolysis of aromatic radical cations in trans-decalin with their gas-phase ionization potential IPg: Pe, perylene•+, Tp, triphenylene•+, Bp, biphenyl•+, Np, naphthalene•+.

of A•+ to the solvent hole was more complete, and the relative yield of impurity cations converting to solvent holes upon 2.3 eV photoexcitation increased accordingly. 4. Discussion Figure 8 shows the correlation of the quantum yield φ of hole injection with the gas-phase ionization potential IPg of the aromatic solute (the IPg of trans-decalin is 9.25 eV). Since the solute radical cations are roughly the same size, the relative order of the corresponding IPs in the liquid must be similar. 9 As indicated by the plot, φ logarithmically increases with IPg; all of these quantum yields are 5-10 times lower than the quantum yields of irreversible hole injection for the same radical cations in 2-propanol,

A•+* + {ROH}n f A + RO• + H+{ROH}n-1

(14)

(in which φ also logarithmically increases with the IPg).9 The quantum yield for perylene•+ (for which reaction 1 is thermoneutral) is only 7 times lower than the quantum yield for triphenylene•+ for which reaction 1 is exothermic by 0.9-1 eV. In cyclohexane, φ for triphenylene•+ is 20% lower than in transdecalin, while the exothermicity of reaction 1 decreases from 1 to 0.3 eV. Upon 5 eV excitation of triphenylene•+ in transdecalin, φ increased ca. 3 times while the exothermicity of reaction 1 increased from 1 to 4 eV. Thus, despite a correlation between φ and IPg for a series of solutes in a given solvent, the exothermicity of reaction 1 does not seem to have much effect on the yield of free solvent holes. These energetics are incompatible with the hole injection proceeding through extended VB states at the top of the valence band. What then controls the yield of free solvent holes in reaction 1? Given an order of magnitude difference between φ in cycloalkanes (where the hole transfer is reversible) and alcohols (where it is irreversible), it seems likely that φ is controlled by the escape probability P∞ of the geminate pair formed in reaction 1. In ref 7a, we considered diffusion kinetics for a geminate pair of the solvent hole and the aromatic molecule generated upon the hole injection. The initial distribution p(r) of thermalized solvent holes around the aromatic molecule was given by the normalized r2-Gaussian distribution, pG(r) ) (4r2/xπb3) exp(-[r/b]2); the solvent hole was assumed to react with the aromatic molecule at the reaction radius R ≈ 1 nm. One way to visualize this model is to assume that the electron is transferred from a localized VB state (a "preexisting hole trap") in the vicinity of the solvated radical cation A•+; p(r) is the distribution of such traps. The model yields the escape probability P∞ ) erfc(-R/b) and the asymptotic behavior of the

(15)

where the diffusion time τD ) R2/Dh (∼30 ps) and Dh ) (kT/ e)µh is the diffusion coefficient of the solvent hole. Equating P∞ and φ, we obtain that the average solute-hole distance ravg ) 2b/xπ increases from 0.6 nm for perylene•+ to 1.0 nm for naphthalene•+. Thus, reaction 1 seems to involve mainly the solvent molecules in the second to third solvation shell around A•+. The electronic structure of these molecules could be different from that in the solvent bulk. An example of the effect of solvent-solute interaction on the band structure of the solvent, for the conduction band, is given by electron injection from aqueous halide anions X-.12,13 According to ultrafast pump-probe spectroscopy 12 and quantum dynamics modeling,13 the photoelectron first localizes in a trap in the second solvation shell around X- (50 fs) and then drifts away forming a {X•‚‚H2O‚‚e-} pair (0.2 ps) that dissociates on a picosecond time scale. Naturally, the perturbation of nonpolar cycloalkane solvent by A•+ is much weaker than that of water dipoles around X-. However, even small perturbation might have dramatic consequences when the solvent hole is a polaron: as was argued in refs 2 and 6, the positive charge in cycloalkanes does not reside on a single solvent molecule but is spread over several of them, on the scale of 0.4-0.5 nm. This sharing reduces the barrier for charge hopping between the solvent molecules from 1 to 2 eV to 20-80 meV. 6 It may also facilitate reaction 1, by reducing the barrier for removal of positive charge from A•+: Instead of an electron transfer from a single solvent molecule, the electron density may be transferred from several solvent molecules in concert, and when a sufficiently large group of the solvent molecules is charged the polaron takes off. To verify this mechanism, one needs to study the hole injection in alkane solvents that do not yield polaron-like holes. Since localized holes exhibit low mobility, 2 the dc conductivity method cannot be used for their detection against the background of molecular ions. Therefore, the only practical way to study reaction 1 in such solvents is to observe photobleaching and recovery kinetics of A•+ using transient absorption spectroscopy. 9 Despite many efforts to produce sufficient concentration of free A•+ cations by laser ionization of aromatic solutes in paraffins, isooctane, and cycloalkanes, we did not obtain sufficiently high yield of these cations to make reliable measurements of the photobleaching (the ∆OD was typically 10-3-10-2). Although in some instances we did observe reduction in the ∆OD upon 2.3 eV photoexcitation, it was caused by photoreactions of species other than A•+, such as triplet aromatic molecules. To remove these excited states, the solution must be saturated with O2, which further reduces ∆OD by 5-10 times. Short of enhancing the detection sensitivity to ∼10-5, only electron accelerators can produce detectable concentrations of A•+ to study reaction 1 using transient absorption spectroscopy. Such a study will be carried out in our laboratory. 5. Conclusion Photoexcitation of aromatic solutes with 5 eV photons in trans-decalin yields just two types of positive charge species: the solute radical cation A•+ and the solvent hole. The latter is formed in reaction 1 initiated by absorption of a 5 eV photon by A•+. For triphenylene•+, the quantum yield φ of free solvent holes upon the 5 eV excitation is ca. 0.16. For a fluence of 0.1

4780 J. Phys. Chem. B, Vol. 103, No. 22, 1999 J/cm2 of 5 eV photons, 50-70% of aromatic radical cations are converted to the solvent holes via reaction 1. The solvent holes react with the aromatic solutes yielding A•+ or with impurities yielding impurity cations. Some of these impurity cations absorb 2.3 eV light and yield solvent holes via hole injection. In concentrated solutions of aromatic sensitizers, most of the solvent holes generated upon 2.3 eV excitation are formed through reaction 1. In trans-decalin, hole injection is the only reaction of excited aromatic radical cations A•+*. The quantum yield φ of free solvent holes was determined for several aromatic radical cations in trans-decalin and cyclohexane. All of these quantum yields are less than about 0.1. Though φ correlates with the exothermicity of reaction 1, it appears that φ is controlled mainly by the geminate pair dynamics. We speculate that the polaronic nature of the solvent hole in cycloalkanes leads to higher yields of free solvent holes via reaction 1 as compared to localized solvent holes in other alkanes. Further experiments are needed to explore this hypothesis. Our work lends support to the suggestion of Warman et al. 4 that scavenging of solvent holes in cycloalkanes by high-IP solutes occurs through the formation of a short-lived collision complex (see the Supporting Information). For scavenging of the hole in trans-decalin by 2-propanol, the natural lifetime of this complex is 30 ns and the equilibrium constant is 1.3 × 103 M-1 (at 21 °C). The complex either dissociates or encounters a second 2-propanol molecule, and a proton transfer from the aromatic radical cation to the two alcohol molecules occurs. It is likely that other slow reactions of the solvent holes in cycloalkanes occur via the same mechanism. Acknowledgment. We thank Dr. C. D. Jonah for helpful comments and Dr. K. Anderson for GC-MS analysis of transdecalin. Supporting Information Available: Scavenging of solvent holes in trans-decalin. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Trifunac, A. D.; Sauer, Jr., M. C.; Shkrob, I. A.; Werst, D. W. Acta Chem. Scand. 1997, 51, 158 and references therein.

Shkrob et al. (2) Warman, J. M. The Study of Fast Processes and Transient species by Electron-Pulse Radiolysis; Baxendale, J. H., Busi, F., Eds.; Reidel: The Netherlands, 1982; p 433. (3) Beck, G.; Thomas, J. K. J. Phys. Chem. 1972, 76, 3856. Hummel, A.; Luthjens, L. H. J. Chem. Phys. 1973, 59, 654. Zador, E.; Warman, J. M.; Hummel, A. Chem. Phys. Lett. 1973, 23, 363; 1973, 75, 914; J. Chem. Phys. 1975, 62, 3897; J. Chem. Soc., Faraday Trans. 1 1979. de Haas, M. P.; Warman, J. M.; Infelta, P. P.; Hummel, A. Chem. Phys. Lett. 1975, 31, 382; Chem. Phys. Lett. 1976, 43, 321; Can. J. Chem. 1977, 55, 2249. Luthjens, L. H.; de Leng, H. C.; van den Ende, C. A. M.; Hummel A. Proc. 5th Symp. Radiat. Chem. 1982, 471. Hummel, A.; Luthjens, L. H. J. Radioanal. Nucl. Chem., Art. 1986, 101, 293. Anisimov, O. A.; Warman, J. M.; de Haas, M. P.; de Leng, H. Chem. Phys. Lett. 1987, 137, 365. Sauer, Jr., M. C.; Schmidt, K. H. Radiat. Phys. Chem. 1988, 32, 281. (4) Warman, J. M.; de Leng H. C.; de Haas, M. P.; Anisimov, O. A. Radiat. Phys. Chem. 1990, 36, 185. (5) (a) Shkrob, I. A.; Yan, J.; Schmidt, K. H.; Trifunac, A. D. J. Phys. Chem. 1996, 100, 11325. (b) Liu, A.; Sauer, Jr., M. C.; Trifunac, A. D. J. Phys. Chem. 1993, 97, 11265. (6) Shkrob, I. A.; Liu, A. D.; Sauer, Jr., M. C.; Schmidt, K. H.; Trifunac, A. D. J. Phys. Chem. B 1998, 102, 3363. (7) (a) Shkrob, I. A.; Sauer, Jr., M. C.; Schmidt, K. H.; Liu, A. D.; Yan, J.; Trifunac, A. D. J. Phys. Chem. 1997, 101, 2120; (b) J. Phys. Chem. B 1998, 102, 3371. (8) Liu, A. D.; Shkrob, I. A.; Sauer, Jr., M. C.; Trifunac, A. D. Radiat. Phys. Chem. 1998, 51, 273. (9) Shkrob, I. A.; Sauer, Jr., M. C.; Liu, A. D.; Crowell, R. A.; Trifunac, A. D. J. Phys. Chem. A 1998, 102, 4976. (10) Lias, S. G.; Bartmess J. E.; Liedman, J. F.; Holmes J. L.; Levin, R. D.; Mallard, W. G. Gas-Phase Ion and Neutral Thermochemistry, J. Phys. Chem. Ref. Data 1988, 17, Suppl. No. 1. (11) Shkrob, I. A.; Sauer, Jr., M. C.; Yan, J.; Trifunac, A. D. J. Phys. Chem. 1996, 100, 6876. (12) Gauduel, Y.; Gelabert, H.; Ashokkumar, M. Chem. Phys. 1995, 197, 167. Long, F. H., Lu, H.; Shi, X.; Eisenthal, K. B. Chem. Phys. Lett. 1990, 169, 165. (13) Borgis, D.; Staib, A. J. Chim. Phys. 1996, 93, 1628; J. Chem. Phys. 1996, 104, 9027; 1995, 103, 2642; J. Phys. Condens. Matter 1996, 8, 9389; Chem. Phys. Lett. 1994, 230, 405. (14) To obtain the recovery kinetics shown in Figure 5b, the σ(t) traces in Figure 5a were fit to σi(t)[1 + {∆σ0/σi}L1f(k1, t-τ1) + {∆∆σ0/σi}L2f(k1, t-τ2)], where σi(t) was determined by second-order fit of the σ(t) kinetics upon 5 eV excitation, {∆σ0/σi}L1 is the ∆σ0/σi ratio for the L1 pulse applied at t ) τ1 (1 µs) and {∆∆σ0/σi}L2 is the increase in the dc conductivity induced by the L2 pulse applied at t ) τ2 (2 µs). The fitting program optimized {∆∆σ0/σi}L2, {∆σ0/σi}L1 and k1 for every trace shown in Figure 5a; the variation in the latter two parameters was lower than 10%. The recovery kinetics in Figure 5b is the plot of optimum {∆∆σ0/σi}L2 vs τ12 ) τ2 - τ1.