Quantum Efficiency of Charge Transfer Competing against

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C: Physical Processes in Nanomaterials and Nanostructures

The Quantum Efficiency of Charge Transfer Competing Against Non-Exponential Processes: The Case of Electron Transfer from CdS Nanorods to Hydrogenase James Keller Utterback, Molly B Wilker, David W. Mulder, Paul W. King, Joel David Eaves, and Gordana Dukovic J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b09916 • Publication Date (Web): 06 Dec 2018 Downloaded from http://pubs.acs.org on December 9, 2018

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The Journal of Physical Chemistry

The Quantum Efficiency of Charge Transfer Competing Against Non-Exponential Processes: The Case of Electron Transfer from CdS Nanorods to Hydrogenase James K. Utterback,*,† Molly B. Wilker,†,§ David W. Mulder,‡ Paul W. King,‡ Joel D. Eaves,† and Gordana Dukovic*,† †Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States ‡Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States

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ABSTRACT

Photoexcited charge transfer from semiconductor nanocrystals to charge acceptors is a key step for photon energy conversion in semiconductor nanocrystal-based light-harvesting systems. Charge transfer competes against relaxation processes within the nanocrystals, and this competition determines the quantum efficiency of charge transfer. The quantum efficiency is a critical design element in photochemistry, but in nanocrystal–acceptor systems its extraction from experimental data is complicated by sample heterogeneity and intrinsically non-exponential excited-state decay pathways. In this manuscript, we systematically explore these complexities using TA spectroscopy over a broad range of timescales to probe electron transfer from CdS nanorods to the redox enzyme hydrogenase. To analyze the experimental data, we build a model that quantifies the quantum efficiency of charge transfer in the face of competing, potentially non-exponential, relaxation processes. Our approach can be applied to calculate the efficiency of charge or energy transfer in any donor–acceptor system that exhibits non-exponential donor decay and any ensemble distribution in the number of acceptors provided that donor relaxation and charge transfer can be described as independent, parallel decay pathways. We apply this analysis to our experimental system and unveil the connections between particle morphology and quantum efficiency. Our model predicts a finite quantum efficiency even when the mean recombination time diverges, as it does in CdS nanostructures with spatially separated electron– hole pairs that recombine with power-law dynamics. We contrast our approach to the widelyused expressions for the quantum efficiency based on average lifetimes, which for our system


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overestimate the quantum efficiency. The approach developed here is straightforward to implement and should be applicable to a wide range of systems.

INTRODUCTION Semiconductor nanocrystals have become an attractive platform for harvesting solar energy.1-8 They are exceptionally versatile light absorbers with tunable electronic structure and surface chemistry.2,9-12 Additionally, quantum confinement and large surface area-to-volume ratios in nanocrystals can lead to increased electronic coupling with charge acceptors, thereby increasing the rate of charge transfer and improving its efficiency.13-16 Semiconductor nanocrystals have been employed in solar cells,2-4 and coupling them to redox catalysts is an emerging strategy for photochemically driving multi-electron redox reactions.2,6,7,17-22 Nanocrystals complexed with redox enzymes, in particular, are capable of selectively performing light-driven multi-electron redox reactions such as H2 production, N2 fixation, and CO2 reduction.23-28 In order to convert solar energy into electricity and chemical energy in such systems, photoexcited charge carriers must undergo charge transfer across the nanocrystal–acceptor interface.2,4,5,7,29-32 The upper limit on the efficiency of energy conversion depends on the competition between this charge transfer and the intrinsic relaxation pathways within the nanocrystal.33 The internal quantum efficiency of charge transfer (𝜙)—the probability that a photoexcited donor will undergo decay via charge transfer—is an important measure of the competition between charge transfer and excited-state relaxation. Because charge transfer is a key step in light-harvesting applications, a quantitative understanding the factors that govern 𝜙 is critical for improving such processes. Typically, this quantity must be extracted from models


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used to fit experimental data. Attaining an accurate measure of 𝜙 in photoexcited nanocrystals is complicated by the fact that they often exhibit excited-state decays that contain multiple decay components over a broad range of timescales due to population heterogeneity as well as intrinsically non-exponential relaxation.29,34-40 In systems where Cd-chalcogenide nanocrystals are coupled to enzymes and other charge acceptors, there is a distribution in the number of acceptors bound to a particular donor in the ensemble, which imparts an additional layer of complexity in the extraction of the 𝜙 from experimental data.33,41-48 In this Article, we investigate the quantum efficiency of electron transfer (ET) in a system that exhibits multi-exponential and power-law excited-state relaxation: complexes of CdS nanorods (NRs) with [FeFe] hydrogenase from Clostridium acetobutylicum (H2ase). This system serves as a case study for evaluating the impact of complex, heterogeneous, and non-exponential relaxation on the calculation of 𝜙. Transient absorption (TA) spectroscopy is used to probe photoexcited electron dynamics in CdS NRs as well as ET in CdS–H2ase complexes. The CdS NR sample contains both structures that are uniform and non-uniform in diameter, and we study ET from both types of nanostructures. While uniform CdS NRs exhibit multi-exponential decay that is common in heterogeneous nanocrystal samples, non-uniform CdS NRs display a powerlaw decay at long times that is a result of diffusion-limited recombination of spatially separated electrons and holes. We derive an expression for the ensemble quantum efficiency of ET, 𝜙 , which accounts for the competition between parallel charge transfer and non-exponential relaxation pathways without assuming a specific functional form of the donor decay nor a specific distribution in the number of acceptors. We use this expression to analyze ET from uniform and non-uniform NRs and develop insights into design principles for controlling the photochemistry of such nanocrystal–catalyst systems. Notably, our model results in a finite value


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of 𝜙 even when the average lifetime diverges, as it does in when the system exhibits power-law decay. We find that using average lifetimes to calculate 𝜙 does not capture the competition between charge transfer and the various donor decay components in our system. We therefore caution against such a treatment when the donor exhibits a multi-exponential excited-state decay. Within the context of parallel decay kinetics, the exact expression for 𝜙 that we describe here can be applied to an empirical non-exponential donor decay function and an arbitrary acceptor distribution, and this general approach can be applied to a broad range of systems.


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METHODS Sample preparation and characterization. Synthesis of CdS NRs and purification and characterization of H2ase have been described previously.49 The CdS NRs studied here are 32 ± 6 nm in length and 4.4 ± 0.6 nm in diameter, on average. All experiments were performed on CdS NRs functionalized with 3-mercaptopropionic acid (3-MPA) in an aqueous buffer solution (12.5 mM Tris-HCl, pH 7). Complexes of CdS NRs and H2ase form by electrostatic interaction between the negatively charged carboxylate end groups of the 3-MPA ligands and a positively charged region on the surface of the enzyme located near the distal iron-sulfur cluster that acts as the electron-injection site.23,24,49 Transmission electron micrograph (TEM) samples were prepared by drop-casting assynthesized CdS NRs onto TEM grids (300 mesh copper grids with carbon film, Electron Microscopy Science). TEM images were taken using a Phillips CM100 TEM at 80 kV with a bottom-mounted 4 megapixel AMT v600 digital camera. The dimensions of the CdS NRs were determined by measuring about 200 particles in TEM using ImageJ software.50 UV-visible absorption spectra were recorded using an Agilent 8453 spectrophotometer utilizing tungsten and deuterium lamps at room temperature sealed under Ar in 2 mm quartz cuvettes. The UV-visible absorption spectrum of the CdS NR sample used for transient absorption measurements in the manuscript is presented in Figure S1 of the Supporting Information. Transient absorption (TA) spectroscopy. TA spectroscopy measurements in the 100 fs to 3 ns time window and the 0.3 ns to 10 µs time window were performed as previously described.49,51 6:1 H2ase:CdS molar ratio mixtures of CdS NRs (730 nM) and H2ase (4.2 µM) were prepared in aqueous buffer solution (12.5 mM Tris-HCl, 5mM NaCl, 5% glycerol, pH 7).


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The samples were sealed under Ar in 2 mm quartz cuvettes equipped with Kontes valves. A magnetic stirrer continuously stirred samples during data collection. The pump pulse was directed through a series of neutral density filters, a depolarizer and a synchronized 500 Hz chopper, then focused into the sample with a beam waist of ~240 µm with a pulse energy of ~10 nJ/pulse. The pump power was chosen so as to be in a regime where the CdS NR decay kinetics were independent of pump power. Experiments were conducted at room temperature.

RESULTS AND DISCUSSION TA measurements of excited-state relaxation and ET in CdS–H2ase complexes. To study the competition between ET and non-exponential nanocrystal excited-state decay, we probed the excited-state dynamics of CdS NRs with and without adsorbed H2ase using TA spectroscopy. The photophysics of CdS NRs have been previously studied in great detail.33,35,38,39,44,49,51-55 Here, we summarize the salient points. Photoexcitation at 400 nm gives rise to transient bleach peaks (Figure 1), the magnitudes of which (∆𝐴) are attributed to state filling of the electron in the conduction band states and thus directly probe electron population dynamics.53,56 While some CdS NRs made by colloidal synthesis are effectively uniform cylinders, a fraction of NRs in a sample can have non-uniform diameters along their lengths, manifesting in narrow and wide regions referred to as the “rod” and “bulb,” respectively.35,39,40,57,58 These two morphological features can be seen in the transmission electron microscopy (TEM) image of Figure 1a, and are depicted schematically in the inset of Figure 1b.39 The non-uniform morphology of CdS NRs has a significant impact on the electronic structure of these nanocrystals.35,39,58 The rod and the bulb of non-uniform NRs can act as two distinct electronic states within the same nanostructure where the bulb has a lower transition


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energy compared to the rod due to a lower degree of quantum confinement, producing the two overlapping bleach features in the TA spectrum (Figure 1b).35,39,58 Following previous work,35 we isolate the signals of the rod and bulb from each other by choosing the probe wavelengths shown in Figure 1b.

Figure 1. Electron relaxation in uniform and non-uniform CdS NRs. (a) Representative TEM image of a CdS NRs showing both uniform and non-uniform NRs. (b) TA spectrum of CdS NRs recorded 10 ns after excitation with 400 nm pulses (solid black line). This spectrum was fit to find the rod (dashed blue line) and bulb (dashed red line) spectra, the sum of which reproduce the experimental spectrum. Vertical lines mark 453 nm and 490 nm, the wavelengths that isolate the rod and bulb signals of these CdS NRs, respectively. Inset: Schematic depiction of a non-uniform CdS NR and energy level diagram as a function of position along the NR. Energy offsets are drawn to scale for 70 meV and 20 meV electron and hole offsets, respectively, which are based on the centers of the rod and bulb bleach peaks. (c) TA time traces from 0 ps to 300 ps


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(instrument response function ~150 fs) of CdS NRs monitored at the rod and bulb transitions, showing population transfer from the rod to the bulb. The traces are plotted on a split time axis that is linear for the first 1 ps and logarithmic thereafter. Inset: Schematic depiction the hole trapping and rod-to-bulb electron localization in a non-uniform NR, leading to charge separation. (d) TA time traces from 300 ps to 10 µs of CdS NRs, normalized at 300 ps, plotted on a log-log scale. The rod decay fits eq 6, while the bulb decay fits eq 7. Fits were performed on raw data and the data were smoothed for presentation only.

The dynamics of electrons and holes in uniform and non-uniform CdS NRs have been explored previously and our results here are consistent with those reports.33,35,39,53 After excitation above the band edge at 400 nm (Figure S1), the band-edge bleach features grow in on a

Quantum Efficiency of Charge Transfer Competing against

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