Generation Dependent Ultrafast Charge Separation and

Article pubs.acs.org/JPCB

Generation Dependent Ultrafast Charge Separation and Recombination in a Pyrene-Viologen Family of Dendrons Zheng Gong,† Jianhua Bao,† Keiji Nagai,‡ Tomokazu Iyoda,‡ Takehiro Kawauchi,*,‡ and Piotr Piotrowiak*,†,§ †

Department of Chemistry, Rutgers University, 73 Warren Street, Newark, New Jersey 07102, United States Iyoda Supra-Integrated Material Project, Exploratory Research for Advanced Technology (ERATO), Japan Science and Technology Agency (JST), and Frontier Research Center, Tokyo Institute of Technology, 4259-S2-3 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan § Institute of Advanced Materials, Devices and Nanotechnology, Rutgers University, 607 Taylor Road, Piscataway, New Jersey 08854, United States ‡

S Supporting Information *

ABSTRACT: The ability of a dendritic network to intercept electrons and extend the lifetime of a short-lived photoinduced charge separated (CS) state was investigated in a homologous family of methyl viologen (MV2+) dendrons spanning four generations, G0 through G3. The CS state in the parent pyrene−methylene−viologen G0 system with a single acceptor exhibits an extremely short lifetime of τ = 0.72 ps. The expansion of the viologen network introduces slower components to the recombination kinetics by allowing the injected electron to migrate further away from the donor. The long-lived fraction of the population increases monotonically in the order G3 > G2 > G1 > G0, while the respective recombination rates decrease. In the highest generation of the dendron ∼14% of the CS state population experiences a 10-fold or greater lifetime extension. Long range tunneling across multiple viologen units and sequential site-to-site hopping both contribute to the overall effect. The large excess energy deposited in the apical viologen upon charge separation and the presence of an extended network of low lying π-orbitals likely facilitate shuttling the electron further down the dendron.

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collected in a 2012 review by Astruc.26 This group has successfully employed apical and basal dendritic methylviologen arrays as rectifying conical junctions on metallic electrodes, with the network of viologen moieties proving the conduit for the electrons.15 In the current paper we build on the ability to synthesize functionalized and well-characterized dendritic structures based on the methylviologen repeat unit and use them to investigate the generation dependent capture of electrons produced by a short-lived photoinduced charge separated state formed at the apex of the dendron. The studied here P−C1−(MV2+)x dendrons consist of a pyrene (P) headgroup which is attached to the apical viologen via a single −CH2− group (C1) and serves as the light absorbing electron donor, and a 1−2 branched network of methyl viologens (MV2+), acting as a hierarchical array of electron acceptors (Figures 1 and 2). The top-down and lateral electronic communication between the viologen centers is mediated by mesitylene bridging units with low lying π-orbitals (Figures 1

INTRODUCTION Dendrons and dendrimers are a class of hierarchically structured macromolecules whose branched topology leads to unique properties that set them apart from other oligomers and polymers.1,2 This structural and functional uniqueness has spurred extensive fundamental studies of dendritic systems3−7 and lead to creative use in catalysis,8−10 nanotechnology,11−15 sensing,16,17 light harvesting,18,19 and drug delivery. It has been recognized from the very inception of this field of chemistry that dendritic networks should enable one to control the flow excitons and charges in a way that is not possible in linear arrays or random polymers. As a result, the propagation of electrons and excitons in dendritic networks has attracted considerable interest among theorists who explored various branching motifs and lattices in order to probe the questions of directionality, electronic coupling20−22 and topological effects23−25 in these systems. Dendrimers and dendrons usually consist of entirely organic or mixed, organic/metaloorganic building blocks and often include photoactive or redox active moieties which can perform the desired function. Representative examples of diverse applications of dendrimers which rely on their redox properties and electron transfer have been © 2016 American Chemical Society

Received: February 23, 2016 Revised: April 15, 2016 Published: April 17, 2016 4286

DOI: 10.1021/acs.jpcb.6b01844 J. Phys. Chem. B 2016, 120, 4286−4295

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The Journal of Physical Chemistry B

Figure 1. Members of the P−C1−MV2+ dendron family. The number of viologen units (V2+) is indicated in parentheses.

Figure 2. Schematic representation of electron acceptor sites in a 1 → 2 dendron (top), a linear chain of acceptors (middle), and a linear system with multiple spacers and a single acceptor site.

and 3). In order to minimize ion pairing and to promote solubility in organic solvents, the dendrons were prepared as hexafluoroborate (PF6−) salts. In a branched system such as the P−C1−(MV2+)x dendrons, after the initial electron transfer from the photoexcited donor (pyrene) to the LUMO of the apical acceptor (viologen), the electron can travel along and across the dendron through a sequence of random hops between the adjacent, formally degenerate viologen sites. Because of the 1−2 branching of the dendron, the probability of a forward electron transfer from any viologen site is Pfwd = 1/2, while the probability of a return transfer is only Pback = 1/4, as is the probability of a lateral hop, Plat = 1/4. The lateral hops contribute to the fanning out of the distribution of the injected electrons. For the terminal viologens in any dendron generation, the probability of a return hop is 1/2, whereas in a linear chain it is 1. Overall, the probability of

Figure 3. A simplified energy level diagram of the components of the P−C1−MV2+ dendrons. Note that several empty orbitals of each MV2+ unit lie below the LUMO of the pyrene electron donor.

the electron returning to the origin in the minimum possible number of steps decreases with the generation n as Pfr = 1/2 × (1/4)n‑1, whereas in the linear chain it follows a much less steep Pfr = (1/2)n‑1 dependence. Therefore, it would be expected that the effect of expanding a 1 → 2 dendron on the lifetime of the CS state should grow up to ∼2n times faster than in the case of an analogous linear chain of acceptors.25 The relative importance of the appealing electron hopping picture outlined in the preceding paragraph depends on the overall kinetic parameters of the system. In order for the electron to diffuse rapidly through this mode, the activation 4287


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Figure 4. Steady state absorption (left) and fluorescence (right) spectra of G0, G1, G2, and G3 recorded for 1.5 × 10−5 M solutions of the respective compounds in CH3CN.

barrier for the individual hops, ΔG‡hop ≈ λ/4, where λ is the reorganization energy, must be low, on the order of several kBT. As a result, thermal hopping is more effective in low polarity media. Since the P−C1−MV2+ dendrons are charged and can be studied only in polar solvents, the corresponding activation barrier is high and stochastic hopping among neighboring sites alone cannot fully account for the experimentally observed behavior. We propose that long-range electron tunneling to distant viologen sites mediated by superexchange must be considered as the primary mechanism responsible for the generation dependent growth of the long-lived fraction of charged separated states in these systems. The short-range siteto-site hopping plays a secondary role and is assisted by the electric field gradient set up by the charged viologen network, as well as by the substantial excess energy deposited in the first viologen moiety at the apex of the dendron upon the highly exoergic charge separation.

by a mode-locked Ti-sapphire oscillator (Spectra-Physics Tsunami) and used to seed a home-built 1.25 kHz multipass amplifier. The output (500 mW) of the amplifier was split into two beams one of which was directed to pump a noncollinear optical parametric amplifier (NOPA, Topas White, Light Conversion), the output of which was frequency doubled in a BBO crystal to produce 1.5 mW of 345 nm light which was used to excite the sample. The second fundamental beam was used to produce white light continuum in a 2 mm sapphire plate. The excitation beam and the white light continuum were focused with the help of a parabolic mirror and spatially overlapped in a 10 mm quartz cuvette containing the sample. The pump beam was modulated with a mechanical chopper. The pump−probe spectra and the transient profiles were recorded using an Si-photodiode, a monochromator (Oriel MS257), and a digital lock-in amplifier (Stanford Research, SR810). The delay between the pump and probe pulses was varied with the help of a computer controlled translation stage. In most cases, 6 scans were averaged in order to improve the signal-to-noise ratio. The relative polarization of the probe and pump beams was set at the “magic angle”. MO Calculations. The calculations were carried out at the DFT B3LYP/6-31G* and AM1 semiempirical levels using the Spartan’14 software package (Wave function, Inc.).

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EXPERIMENTAL METHODS Synthesis. The dendrons were prepared via a microwave heating technique.27 Detailed synthetic and characterization procedures are available in the Supporting Information. Sample Preparation. Acetonitrile (≥99.9%, Fisher Scientific) was used without further purification. Samples for all the measurements were prepared through the similar method: Approximately 1.6 mg of each dendron was dissolved in 1 mL of solvent to obtain a series of concentrated solutions. Then, different amount of concentrated solution (20 μL of P−C1− G0, 50 μL of P−C1−G1, 110 μL of P−C1−G2, 225 μL of P− C1−G3) was pipetted into 3 mL of solvent for dilution separately. The concentration of all the samples was 1.5 × 10−5 M, as verified by their absorption spectra. Finally, 3 mL of the solution was transferred into a standard quartz cuvette. Steady-State Spectroscopy. Absorption spectra were collected at room temperature on a Cary 5000 UV−vis-NIR spectrophotometer. Steady-state fluorescence spectra were recorded on a Varian Cary Eclipse fluorimeter using an excitation wavelength of 325 nm. Pump−Probe Spectroscopy. The charge transfer properties of P−C1−MV2+ dendrons were measured by applying ultrafast laser spectroscopy. 50 fs, 795 nm pulses were produced

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RESULTS The ground state UV absorption spectra of the G0 through G3 dendrons (Figure 4) show in the 310−350 nm region the characteristic pyrene progression, which maintains its sharp vibronic structure and remains unchanged for all generations. The well-defined peak at 345 nm provides a convenient measure for determining and normalizing the concentration of the dendrons in solution. The spectra do not suggest aggregation or a major conformational change for the higher members of the sequence. In the wavelength range between 230 and 290 nm both pyrene and MV2+ absorb light and as the number viologen units grows, the spectrum becomes dominated by the absorption of the latter. The saturation of the viologen peak seen in the spectra of G2 and G3 occurs because the limit of the dynamic range of the spectrometer has been reached. The characteristic intense fluorescence of pyrene 4288


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This implies that the donor−acceptor electronic coupling is relatively insensitive to the mutual orientation of the pyrene and viologen units within the thermally accessible range of geometries. The source of such remarkably fast forward and back electron transfer rates lies primarily in the energetics of the pyrene-viologen donor−acceptor pair. In most photoinduced electron transfer systems, charge separation is only mildly exoergic and lies in the Marcus “normal region”, while the recombination tends to be highly exoergic and lies deep in the “inverted region”. The exceptionally low reduction potential of viologen leads to a rare situation where the charge separated state is placed nearly exactly midway between the excited state of pyrene and the ground state of the system. The driving forces for charge separation, ΔG0 CS = −1.7 eV, and recombination, ΔG0CR = −1.6 eV, are both large and similar in magnitude to the respective reorganization energies, λCS = 1.5 eV and λCR = 1.4 eV (see the Supporting Information). As a consequence, both processes lie slightly in the “inverted region” and are close to the barrier-less optimum set by -ΔG0 = λ. The recombination rate of 1.4 × 1012 s−1 combined with the above thermodynamic parameters yield a reasonable LUMO(MV2+)− HOMO(P) electronic coupling of 125.4 cm−1. Despite the similar Franck−Condon density of states (at the level of classical Marcus theory), charge separation in G0 is considerably faster than the recombination. This could be caused simply by a ∼ 3-times higher LUMO(P)−LUMO(MV2+) electronic coupling, however, it is also likely that the charge separation in G0 is aided by the presence of several low lying empty orbitals of viologen. According to DFT calculations, LUMO through LUMO+3 of MV2+, lie below the LUMO of pyrene (Figure 6). Each of these orbitals is characterized by its own driving force and electronic coupling with the LUMO of pyrene and each of them contributes to the overall charge separation rate. The involvement of multiple low-lying orbitals of the acceptor acting as intermediate states was first highlighted by Miller et al. in the case of quinones.29 The resulting electronic excited states of the reduced acceptor are usually short-lived. Häupl et al. determined that the excited state of MV+• has a lifetime of 700 fs and decays with the formation of vibrationally hot ground state which then thermalizes on a slower, 1−15 ps time scale.30 As a result, when the ET rates are as fast as in G0, Marcus theory should be used with caution. Since the entire electron transfer “round trip” in G0 is completed within less than a picosecond, the system does not reach equilibrium solvation and retains some vibrational excitation throughout the charge transfer sequence. In the absence of full thermal equilibration the Marcus equation may lead to inaccurate and erroneous predictions. Ion Pairing. The ionic nature of the studied here dendrons opens the possibility of ion pairing between the viologen moieties and the counterions. Ion association may influence the kinetics of electron transfer by modulating the driving force and modifying the reorganization energy.31,32 Large specific ion

is >99.8% quenched in deaerated solutions of all P−C1−Gn dendrons pointing to very rapid and practically quantitative charge separation. The weak residual emission is slightly redshifted (∼10 nm) with respect to the 1-methylpyrene reference. Its intensity continues to diminish for the higher generations of the dendron, suggesting that the electron transfer quenching of the excited state becomes even faster than in G0 as the number of the available acceptor sites increases (Figure 4, inset). Charge Separation and Recombination in the G0 Donor−Acceptor Compound. The initial charge separation and the final electron−hole recombination at the junction between pyrene and the first viologen moiety at the apex of the dendron are crucial for the overall ET kinetics of all generations of the P−C1−(MV2+)x sequence. Furthermore, the rates of these steps should be nearly identical in all generations of the dendron. Photoexcitation of the G0 system at the 345 nm vibronic peak of pyrene28 leads to very rapid charge separation which occurs well within the time resolution of our measurements, τCS < 100 fs, and is manifested by the instantaneous appearance of the transient spectrum which consists of the characteristic broad absorption band of the reduced methyl viologen, MV+• at 550−700 nm and a sharper peak of the oxidized pyrene, P+•, at 430 nm (Figure 5). Charge

Figure 5. Normalized transient absorption spectra of the G0, G1, G2 and G3 generations of the dendron. All spectra were recorded at 0.5 ps delay following 345 nm excitation of deaerated 1.5 × 10−5 M solutions in CH3CN. The 430 nm band is characteristic of P+• while the broad 600 nm band belongs to MV+•.

recombination in G0 is very rapid as well. The decay of the charge separated state is well reproduced by a single exponential with τCR = 0.72 ps (Figure 5 and Tables 1 and 2). The homogeneous decay is somewhat surprising because the pyrene and the viologen moiety of G0 can sample a broad range of dihedral angles which cannot be fully rotationally averaged within the subpicosecond lifetime of the CS state.

Table 1. Fitting Parameters for the Decay of the P+• Signal Monitored at 430 nm τ1

generation P−C1−G0 P−C1−G1 P−C1−G2 P−C1−G3

0.71 0.69 0.78 0.83

± ± ± ±

0.01 0.01 0.01 0.02

A1

τ2

A2

A∞

A2 + A∞

1.0 0.955 ± 0.01 0.905 ± 0.01 0.874 ± 0.02

− 7.6 ± 1.8 8.3 ± 0.9 10.1 ± 2.9

− 0.027 ± 0.006 0.064 ± 0.011 0.081 ± 0.010

− 0.018 ± 0.002 0.031 ± 0.002 0.045 ± 0.008

− 0.05 ± 0.008 0.10 ± 0.013 0.13 ± 0.018

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The Journal of Physical Chemistry B Table 2. Fitting Parameters for the Decay of the MV+• Signal Monitored at 600 nm τ1

generation P−C1−G0 P−C1−G1 P−C1−G2 P−C1−G3

0.76 0.69 0.72 0.78

± ± ± ±

0.01 0.02 0.02 0.03

A1

τ2

A2

A∞

A2 + A∞

1.0 0.967 ± 0.01 0.919 ± 0.01 0.861 ± 0.01

− 6.1 ± 4.4 5.2 ± 1.1 9.0 ± 2.6

− 0.014 ± 0.009 0.059 ± 0.010 0.068 ± 0.011

− 0.019 ± 0.007 0.022 ± 0.002 0.071 ± 0.010

− 0.03 ± 0.016 0.08 ± 0.012 0.14 ± 0.021

Figure 6. Low-lying molecular orbitals of G0 which are involved in the charge separation and recombination. The energy is shown relative to the HOMO of pyrene (B3LYP, 6-31G*, in vacuum, Spartan ’14 by Wave function, Inc.).

pairing effects were reported for charge-shift reactions in covalently bridged radical anions33 and long-lived intramolecular photoinduced charged separated states.34 The electrolyte effects are most pronounced in low to medium polarity solvents, ε < 10. Since in constant molarity solutions of the P−C1−Gn dendrons the effective concentration of the viologen units and the PF6− counterions increases with each generation, the ion pairing, if present, would be generation dependent, too. A 1 μM solution of P−C1−G3 is 15 μM in viologen and 30 μM in PF6− ions and may undergo more significant ion pairing than a 1 μM solution of a lower generation of the dendron. In order to assess these effects, which would complicate the interpretation of the results, we carried out pump−probe experiments on 1.5 × 10−5 M CH3CN solutions of G0 containing 1.0 mM of tetrabutylammonium hexafluorophosphate, N(n-C4H9)4+PF6−. The resulting transient absorption decays obtained in the presence of the more than 30-fold excess of the PF6− counterions are indistinguishable from the ones obtained in pure CH3CN as shown in Figure 7. This leads us to conclude that ion pairing is not significant at the studied 1.5 × 10−5 M concentration of dendrons. Our observations are consistent with the reported

Figure 7. Temporal profiles of the G0 charge separated state obtained at 430 nm (P+• absorption, top) and 600 nm (MV+• absorption, bottom) in the absence of additional electrolyte (black) and in the presence of 1.0 mM of N(n-C4H9)4+PF6− (red).

association constant between monomeric viologen MV2+ and PF6− anions of approximately 2 × 103 M−2 in acetone, ε = 21.0.35 At the concentration of 1.5 × 10−5 M employed in this study, the degree of ionic association would remain very low for all generations of the dendron and vary from 0.01% for G0 to less than 1% for the G3. In the considerably more polar acetonitrile, ε = 36.6, the association constant must be even lower and ion pairing should remain negligible under our experimental conditions. Charge Separation and Recombination in Dendrons G1, G2, and G3. As expected, the addition of viologen shells to the dendron leads to the appearance of longer lifetime components in the decay of the charge separated state (Figure 4290


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The G2 and G3 dendrons display more pronounced slowing down of the recombination, both in terms of the decay rates and increasing long-lived populations of the CS state. In order to treat the data in a consistent manner, all charge recombination profiles of G1, G2 and G3 were fitted with a double exponential function A(t) = A1e‑t/τ1 + A2e‑t/τ2 + A∞. Naturally, this is merely an empirical fitting model. In reality, each dendron generation introduces new nonexponential terms to the overall decay dynamics. Importantly, the value of τ1, which corresponds to the recombination of electrons which failed to escape beyond the apical viologen, varies negligibly among all generations (Tables 1 and 2). Indeed, this parameter may be also set equal to the decay rate of the CS state in G0 and kept constant for the higher generations without changing the overall trend of the recovered CS state recombination rates and the respective amplitudes. As in G1, the time constant τ2 corresponds to the electrons which return to the apical viologen and subsequently recombine with the parent P+• hole in a relatively small number of itinerant hops. It reaches ∼10 ps in G3 and accounts for approximately 7% of the overall population of the charge separated state. The fraction A∞ which represents the longest lived charge separated states “lost in the network” increases as well and reaches 6% in G3. Overall, the sum A2 + A∞, i.e. the total fraction of electrons which escaped beyond the apical viologen, increases from 4% in G1 to 9% in G2 and 13−14% in G3. While the generation dependent extension of the average lifetime is the expected behavior, the accompanying steady and pronounced, more than 3-fold increase of the long-lived population of the charge separated states is intriguing and cannot be explained by simple stochastic hopping among degenerate viologen sites. Plausible mechanisms which can lead to the observed behavior are discussed in detail below.

8, Tables 1 and 2). The behavior is evident both when the 430 nm band of P+• or the 600 nm band of MV+• is monitored. In

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DISCUSSION The fast but otherwise straightforward electron transfer dynamics in the G0 pyrene-viologen diad has been adequately addressed in the previous sections of the paper. Here we will focus on the more complex behavior of the extended dendrons, especially on the generation dependent growth of the long-lived fraction of the charge-separated states. In this context, the most salient features of the G0 system are (1) the extremely rapid charge separation−charge recombination cycle which is completed on a time scale faster than thermal equilibration and (2) the possible formation of electronically excited states of the reduced viologen moiety at the apex. In the simplest view, the fate of the electron transferred from the pyrene donor to the apical viologen should be determined by the relative rates of the charge recombination at the apex, kCR(G0), and the electron hopping khop among the degenerate or nearly degenerate viologen sites. The highly exoergic charge recombination in the P−C1−(MV2+)x dendrons is much faster than the random electron hopping at zero driving force. In this limit of kCS(G0) > kCR(G0) ≫ khop, the fraction of electrons which survive to travel further down the dendron is very low. Since kCR(G0) = 1.4 × 1012 s−1, khop of 4−7 × 1010 s−1 is needed in order to account for the 3−5% long-lived fraction of charge separated states observed in G1. This value is comfortably slower than the τ2 recombination component measured for G1, 1/τ2 = (1.3−1.6) × 1011 s−1, which could be simplistically interpreted as corresponding to the sequence of one forward and one return hop between the G0 and G1 layers of viologens in the dendron. Unfortunately, it is also several orders of

Figure 8. Transient absorption decay profiles recorded at (a) 430 nm, the absorption maximum of P+•, and (b) 600 nm, the absorption maximum of MV+•.

G1, the first generation dendron, we detect a small, ∼ 2% population of the CS state which decays with τ2 = 6−8 ps, i.e. approximately ten times slower that in the parent G0. Furthermore, a much longer lived component, which does not decay appreciably within the sampled 25 ps time window and amounts to additional ∼2% of the CS state population, is also detected. Both long-lived components are ascribed to the electrons which managed to escape immediate recombination and traveled beyond the apical viologen site. The dominant component, τ 1 ∼ 0.7 ps, which corresponds to the recombination at the apex, remains remarkably constant and nearly identical as in G0. The slower component τ2 can be interpreted either in terms of sequential hops between the adjacent viologens or a single step long-distance electron tunneling between pyrene and the second layer of viologens. The importance of both scenarios for charge separation and recombination is examined in more detail in the Discussion section of the paper. 4291


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The Journal of Physical Chemistry B magnitude faster than the hopping rates predicted by the classical Marcus theory. At ΔG0 = 0 the effective activation barrier is ΔG‡ = λ/4, where λ is the total reorganization energy. The electronic coupling calculated as 1/2 of the splitting between the LUMO orbitals of MV2+ moieties attached symmetrically to the meta positions of the bridging benzene ring ranges from ∼30 to ∼100 cm−1, depending on the method and the basis set. Combined with the estimated total reorganization energy of 1.4 eV, with the solvent contribution based on the Born model and the intramolecular component taken from DFT calculations at the B3LYP 6-31G* level, these electronic couplings predict very slow hopping, khop ≈ 2 × 105 s−1 and 2 × 106 s−1, respectively. Even an arbitrarily high preexponential factor of 1 × 1015 s−1 yields a rate of 7 × 108 s−1, which would allow only less than 0.1% of the electrons escape from the apical viologen site. These simple estimates may be prone to errors, nevertheless the discrepancy of several orders of magnitude warrants the consideration of other mechanisms which could allow the electrons reach further acceptor sites in the network. The most obvious alternative path for populating distant viologen sites is long-range electron tunneling. As pointed out by others,20,24 an electron donor attached to a linear or branched array of acceptors is electronically coupled to all of them, not solely the one at the apex (Figure 2). Superexchange mediated tunneling to distant acceptor sites is therefore possible. The relevant electronic coupling decreases with distance as e‑β·n, where n is the generation of the acceptor shell and β is the attenuation per repeat unit; however, the system has to overcome the activation barrier only once, not ntimes. If instead of attributing it to hopping, one ascribes the τ2 = 6.1−7.6 ps recombination component measured in G1 to long-range electron tunneling between the second layer of viologens and the pyrene headgroup (Tables 1 and 2), it be can used to extract the magnitude of the corresponding electronic coupling. The resulting |V| = 31.3 cm−1 is consistent with the predominantly conjugated nature of the intervening material. Since in a 1 → 2 branching dendron the number of acceptor sites grows with each generation as 2n, the intrinsic falloff of the forward electron transfer rate is diminished. The resulting expression for the rate of the long-distance tunneling is proportional to e‑β·n × 2n. Figure 9 shows the relative electron transfer rates to the nth shell of acceptors in a 1 → 2 dendron and a linear chain for several values of β. The softer distance dependence in the dendron is evident even for large β. The total rate of forward electron transfer from the excited donor can be obtained by summing the computed relative forward ET rates from the donor to all available acceptor sites in a system of a given generation. The resulting total relative rate has been plotted in Figure 10. It can be seen that adding new acceptor shells to a dendron or expanding a linear chain of acceptors accelerates the depopulation of the initial excited state of the donor. The cw fluorescence spectra of the P−C1− Gn dendrons (Figure 4, the inset) are in qualitative agreement with this prediction. The weak residual fluorescence of pyrene in G0 continues to decrease for higher generations of the dendron, consistent with a small fraction of direct electron transfer to the growing number of distant acceptor sites. A contribution from this long-range mechanism can at least partially account for the observed generation depended yields of the long-lived CS states. Both the electron hopping and the long-range tunneling channels are likely to significantly benefit from the highly

Figure 9. Relative rate of electron tunneling to the acceptor repeat unit n in a linear chain (circles) and in a 1 → 2 dendron (solid dots) calculated for attenuation factors β of 1.0 (blue), 1.5 (red), 2.0 (green), and 3.0 per repeat unit (black).

Figure 10. Total relative rate of forward electron transfer (depopulation of the initial state) as a function of the generation in a 1 → 2 dendron (top), a linear chain of acceptors (middle) and a single acceptor at an increasing distance (bottom) calculated for β = 2.0 per repeat unit.

exoergic initial charge separation which occurs in less than 100 fs and results in the formation of a vibrationally hot and possibly electronically excited MV+• radical at the apex of the dendron. The large excess energy equivalent to several skeletal quanta of the aromatic rings must be distributed between the donor and the acceptor and ultimately dissipated into the 4292


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The Journal of Physical Chemistry B surrounding medium. Vibrational relaxation (IVR) in molecules of the size of viologen or pyrene takes 0.5−1 ps to complete, while thermal equilibration with the solvent occurs on a slower picosecond time scale.30 Since charge recombination in G0 takes place with τ = 0.72 ps, the first electron hop from the apical viologen competes both with the IVR and solvation and inevitably takes place with a sizable residual driving force. As a result, it can be considerably faster than the Marcus theory predictions based on complete solvation and the equilibrium ΔG0 = 0. One can estimate that every 1300 cm−1 of residual thermal excitation, which is roughly equivalent to one breathing mode quantum of viologen, will accelerate the first electron hop by a factor of ∼20. Naturally, the significance of this “thermal boost” diminishes abruptly for the subsequent hops, however, it is crucial that at this point the recombination at the apex has been avoided and the surviving electron can travel further down the network at a much slower pace. Indeed, if upon charge separation the excess energy is equally partitioned between the P+• and the apical MV+•, the resulting 0.85 eV of thermal excitation of the latter should lead to an instantaneous hopping rate of 2 × 1010 to 2 × 1011 s−1, even with the modest calculated viologen-viologen electronic couplings and assuming full reorganization energy. Such high initial rates would be sufficient to intercept up to ∼15% of the initial charge separated state, consistent with the experimental findings (Tables 1 and 2). This picture is corroborated by the findings of Häupl et al., who reported that the final thermalization of the vibrationally hot MV+• radical ion is in acetonitrile as slow as 16 ps.30 Population of electronically excited states of the apical MV+• upon charge separation would have a similar effect. In this case both the initial driving force and the electronic coupling would be affected. Higher orbitals of the viologen−mesitylene−viologen network are more delocalized and should promote stronger electronic coupling. Lastly, we should note that because of the polyelectrolyte nature of the P−C1−(MV2+)x dendrons, the ΔG0 landscape is not as flat as it would have been in a similar network of neutral acceptors. The branching array of the doubly charged viologens sets up an electric field which modifies the electron affinity of the individual acceptor sites. Kawauchi et al. observed that extending the dendritic network lowers the reduction potential of the viologen core from −0.410 V in G1 to −0.390 V for G3.15 Larger generation dependent changes reaching 60 mV were reported by others in closely related viologen dendrimers.36,37 These changes of the reduction potential were diminished by the screening caused by the 100 mM concentration of supporting electrolyte present in the voltammetry measurements. At the 1.5 × 10−5 M dendron concentration employed in all spectroscopic experiments reported here, the screening is absent. AM1 and DFT calculations corroborate the electrochemical results and show that the addition of a new layers of viologens to the dendron lowers the energy of the LUMO orbitals of all preceding shells. The resulting collective field imparts a tub-like shape to the ΔG0 profile of the dendron, as illustrated by the electrostatic potential map of G3 in Figure 11, and influences the preferred location of the electron. Acceptors in the (n − 1) layer are predicted to exhibit the highest electron affinity, while the apical and terminal viologens are the least favored sites for the injected electron. The slight outward slant of ΔG0 favors electron hops away from the donor, while the return to the apex becomes endoergic and therefore slower. Naturally,

Figure 11. Surface electrostatic potential of the G3 dendron in vacuum (AM1, Spartan ’14 by Wave function, Inc.). The pyrene headgroup at the apex of the dendron (center) is not shown.

calculations in vacuum exaggerate the magnitude of the field effect; nevertheless, they are useful in qualitative terms. The solvent reorganization energy is also influenced by the charged network. The simple Born model used to estimate the λs, assumes full solvation of each ion regardless of the local structure and proximity of other charges. For a dendritic polyelectrolyte this is not a realistic picture. The excluded volume grows with the size of the dendron and it is impossible for each viologen to maintain its own infinite solvation sphere. The more sophisticated SM8 model38,39 of acetonitrile used in conjunction with B3LYP DFT optimization predicts a ∼ 5% reduction of the average solvation energy per each viologen as the number of repeat units increases. As a consequence, the ΔG‡ ≈ λ/4 must decrease correspondingly and the site-to-site hopping within the dendron should experiences a somewhat lower solvation barrier than that predicted on the basis of an individual, fully solvated viologen moiety. The resulting roughness of the ΔG0 and λs landscape of the P−C1− (MV2+)x dendrons influences the effective electron mobility along the network and affects the charge recombination kinetics, especially at the longest time scale.

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CONCLUSIONS Branched multiacceptor structures inherently favor outward flow of electrons and by extension also excitons, away from the apex rather than toward it. This intrinsic directionality has important implications for the envisioned applications of dendrons and dendrimers as excitation and charge collectors.3,18,40−43 We have shown that a diverging dendritic network can significantly prolong the short intrinsic lifetime of the CS state of the P-CH2−MV2+ donor−acceptor diad through a combination of long-range electron tunneling and site-to-site hopping. Which of the two mechanisms dominates is determined by the respective electronic couplings and activation barriers. In the P−C1−(MV2+)x dendrons the exceptionally high driving force and the sub-100 fs photo4293


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The Journal of Physical Chemistry B induced electron transfer produce a “hot” charge separated state with large excess energy. The resulting thermal excitation of the first acceptor facilitates the next electron transfer step. The dynamic competition between the vibrational cooling, forward electron transfer occurring at a diminishing, time dependent driving force and the rapid charge recombination, all of which take place faster than thermal equilibration with the solvent, offers a fascinating and complex problem for a QMMD simulation and further time-resolved experiments. In the present system, the electron donor is linked to the apical viologen by a single −CH2− group. The short link leads to rapid charge recombination which reduces the fraction of electrons which survive to propagate along the dendritic network. In order to maximize the kinetic forward bias set up by the branching and allow the dendron to act as a topological rectifier, one must move the system away from the kCR(G0) ≫ khop limit. This can be achieved by lowering the electronic coupling between the electron donor and first acceptor at the apex of the dendron. While the charge separation rate will be similarly affected, the long S1 lifetime of pyrene leaves a large kinetic margin for achieving nearly quantitative quantum yields of the charge separated state. The work on such systems with reduced kCR(G0) as well as on linear arrays of viologen electron acceptors is in progress.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b01844. The details of the synthesis and characterization of the dendrons, as well as additional computational results (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(P.P.) E-mail: [email protected]. Telephone: +1 973-353-5318. *(T.K.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the NSF-JSPS International Collaboration in Chemistry Program for partial support of this project through NSF Grant 1415881. The instrumentation used in the course of this research was acquired with the help of US DOE Office of Basic Energy Research Grant DE-FG06ER15828 and NSF MRI Grant 0923345 to P.P. T.K. acknowledges generous support by JSPS KAKENHI Grant No. 15K04590. P.P. wishes to acknowledge helpful discussions with Drs. John R. Miller, David Beratan and Michele Pavanello.

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REFERENCES

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