The importance of developing new, clean and renewable sources of energy will continue to grow in the foreseeable future and so will the need for the education of researchers in this field of research. The interest and challenges of the field continue to shift from simple homogeneous solutions to increasingly more complex heterogeneous systems and interfaces. Over the past decade there have been numerous theoretical and experimental breakthroughs many of which still exist only in the primary literature. The aim of this book is to gather in one volume the description of modern, sometimes exploratory, experimental and theoretical techniques applied to the dynamics of interfacial electron and electronic excitation transfer processes studied in the context of solar energy conversion. The intended treatment will be fundamental in nature and thus applicable to a broad range of hybrid photovoltaic and photocatalytic materials and interfaces. The book will focus on the dynamic aspects of the electron injection, exciton and carrier relaxation processes, as well as coherence effects, which continue to provide the impetus and the greatest challenge for the development of new methodologies.
About the Author
Piotr Piotrowiak is Professor of Physical Chemistry at Rutgers University-Newark. He graduated with a Magisterium in Chemical Physics from the University of Wrocław, Poland, in 1982 and a Ph.D in Physical Chemistry from the University of Chicago in 1988. He held a Postdoctoral Associate position at Argonne National Laboratory in the Electron Transfer and Energy Conversion Group between 1988 to 1991 and was an Assistant Professor at the Univeristy of New Orleans from 1991 to 1996. He then went on to hold An Associate position in 1996. He has been a visiting fellow at Tokyo Metropolitan University and visiting scientist in the protein engineering department at Genentech Inc., in San Francisco. He has been an active member of many scientific committees and international conferences including the International Symposium of the U.S. Civilian Research and Development Foundation for the Independent States of the FSU, Kiev, Ukraine, in October 2003; the International Organizing Committee for the XX IUPAC Symposium on Photochemistry, Granada, Spain, July 2004; Session Chair, Physical Chemistry of Interfaces and Nanomaterials, International SPIE Optics and Photonics Symposium, San Diego, California, July 2006; Symposium co-Chair, Physical Chemistry of Interfaces and Nanomaterials, International SPIE Optics and Photonics Symposium, San Diego, California, August 2007; Session Chair, Gordon Conference on Electronic Structure and Dynamics, Waterville, Maine, July 2009; Member of the NSF-MRI ARRA review panel for undergraduate institutions, Arlington, Virginia, November 2009; Invited speaker at the Special Symposium on the 50th Anniversary of the Laser, 239th ACS National Meeting, San Francisco, California, March 2010. His main research interests are the development of ultrafast microscopy methods applied to electron and excitation transfer at interfaces and in inhomogeneous systems, time-resolved laser spectroscopy of reactive intermediates, interactions between host-guest systems and redox proteins.
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Solar Energy Conversion
Dynamics of Interfacial Electron and Excitation Transfer
By Piotr Piotrowiak
The Royal Society of ChemistryCopyright © 2013 The Royal Society of Chemistry
All rights reserved.
Computational Modeling of Photocatalytic Cells
STEVEN J. KONEZNY AND VICTOR S. BATISTA
Department of Chemistry, Yale University, P.O. Box 208107, New Haven, CT 065208107, USA
Solar energy conversion into chemical fuels is one of the "holy grails" of the 21st century. Significant research efforts are currently underway toward understanding natural photosynthesis and artificial biomimetic systems. Photocatalytic cells absorb solar energy and use it to drive catalytic water oxidation at photoanodes:
2H2O -> 4H+ + 4e- + O2(g) (1.1)
effectively extracting reducing equivalents from water (i.e., protons and electrons) that can be used to generate fuel, for example H2(g) by proton reduction:
4H+ + 4e- -> 2H2(g) (1.2)
The water oxidation half-reaction, introduced by Equation (1.1), is the most challenging obstacle for solar hydrogen production, since it requires a four-electron transfer process coupled to the removal of four protons from water molecules to form the oxygen–oxygen bond. In Nature, this process is driven by solar light captured by chlorophyll pigments embedded in the protein antennas of photosystem II and the energy harvested is used to oxidize water in the oxygen-evolving complex. The development of photocatalytic solar cells made of earth-abundant materials that mimic these mechanisms and photocatalyze water oxidation has been a long-standing challenge in photoelectrochemistry research, dating back to before the discovery of ultraviolet water oxidation on n-TiO2 electrodes by Fujishima and Honda 40 years ago. However, progress in the field has been hindered by a lack of fundamental understanding of the underlying elementary processes and the lack of reliable theoretical methods to model the photoconversion mechanisms.
The landscape of research in solar photocatalysis has been rapidly changing in recent years, with a flurry of activity in the development and analysis of catalysts for water oxidation and fundamental studies of photocatalysis based on semiconductor surfaces. Significant effort is currently focused on the development of more efficient catalysts based on earth-abundant materials and various strategies for the design of molecular assemblies that efficiently couple multielectron photoanodic processes to fuel production. The outstanding challenge is to identify robust materials that could catalyze the necessary multielectron transformations at energies and rates consistent with solar irradiance.
A promising approach for photocatalytic water oxidation involves designing high potential photoanodes based on surface-bound molecular complexes and coupling the anodic multielectron reactions to fuel production at the cathode with long-range free energy gradients. Such a design problem requires fundamental understanding of the factors affecting photoabsorption, interfacial electron transfer to the photoanode, charge transport, storage of oxidizing equivalents for catalysis at low overpotentials and irreversible carrier collection by fuel-forming reactions at the cathode. The characterization of these processes by computational techniques clearly requires methods for modeling the complete photocatalytic mechanism as well as methods for understanding and characterizing the elementary steps at the detailed molecular level, including visible light sensitization of semiconductor surfaces by molecular adsorbates, charge transport and redox catalytic processes. This chapter reviews recent advances in the field, with emphasis on computational research focused on modeling photocatalytic cells and the elementary processes involved at the molecular level. The reviewed studies are part of an interdisciplinary research program including synthesis, electrochemistry and spectroscopy in a joint theoretical and experimental effort to advance our understanding of structure/function relations in high potential photoanodes based on functionalization of nanoporous TiO2 thin films with transition metal catalysts.
The chapter is organized as follows. Section 1.2 reviews recent computational efforts focused on modeling current–voltage characteristics of functional dye-sensitized solar cells (DSSCs) under operational conditions, with emphasis on the effect of the nature of the molecular adsorbates and redox couple on the overall efficiency of photoconversion. Section 1.3 reviews recent developments of methods for inverse design of molecular adsorbers with suitable solar-light photoabsorption. Section 1.4 reviews the development of theoretical models of charge transport in nanoporous metal oxide thin films, with emphasis on the fluctuation-induced tunneling conduction (FITC) model as applied to the description of the temperature dependence of dc and ac conductivities and direct comparisons to experimental data. Section 1.5 is focused on reliable methods for modeling the redox properties of molecular adsorbates, with emphasis on the reduction of systematic errors introduced by either the level of theory (i.e., the choice of density functional theory (DFT) functional, basis set and solvation model) or the electrochemical measurement conditions, including the nature of the solvent, electrolyte and working electrode. Section 1.6 presents a summary of the conclusions and outlook.
1.2 Photoelectrochemical Device Modeling
Modeling can provide a fundamental insight into the effects of individual system components on the overall device functionality. A parameter-space analysis by systematic variation in device composition can lead to the discovery of assemblies with optimum performance. Insight into observed trends can be extracted from the parameters of equivalent-circuit current–voltage simulations. Here, we illustrate this systematic approach by analyzing of a series of high-potential porphyrin photoanodes, metal oxides and redox couples, suitable for photocatalytic cells. We show that DSSCs based on porphyrin dyes demonstrate superior performance owing to increased open-circuit voltage and the short-circuit current when using the relatively high-potential bromide–tribromide redox couple as a regenerative electron mediator rather than the standard iodide–triiodide couple. The resulting potentials progress toward sufficiently positive values suitable for water oxidation chemistry.
1.2.1 Modeling Current-Voltage Characteristics
The current–voltage characteristics, that is the current density J as a function of the applied voltage V, of photoelectrochemical cells are used to extract important parameters related to device performance. In the case of a DSSC, parameters of interest include the short-circuit current JSC [equivalent to] J(V = 0), open circuit voltage VOC [equivalent to] V(J = 0) and the power conversion efficiency. However, owing to the complex nature of DSSC operation, these data alone offer a limited understanding of the underlying physical/electrochemical processes. Device modeling of current–voltage characteristics is needed in order to develop this understanding and establish property–performance relationships. This kind of an analysis is useful not only to DSSCs but to photoelectrochemical cells in general since they share common system components.
The equivalent circuit diagram used to model solar cell current–voltage characteristics is shown at the top of Figure 1.1. The schematic energy level diagram of a DSSC at the bottom of Figure 1.1 shows the various charge transfer processes that occur in photoelectrochemical cells and relates these processes to current pathways via components of the model circuit. An illumination current density JL is induced upon photoexcitation of the adsorbed dye molecule, followed by interfacial electron injection into the conduction band of the metal oxide semiconductor. Direct recombination of the photoinjected carriers with redox species in the electrolyte solution and the dark current along the edges of the cell contribute to the shunt resistance RSH of the cell. Under applied bias, the cell can be modeled as a diode with a current density JD that runs parallel to JL and shunt current density JSH that opposes JL. The cell also has a net series resistance RS, which includes the resistance of the metal oxide and the ionic resistance of the redox pair in the electrolyte.
The output current density J of the solar cell as a function of applied bias voltage in the equivalent circuit model is:
[MATHEMATICAL EXPRESSION OMITTED] (1.3)
where J0 is the reverse saturation current, k is the Boltzmann constant, T is the absolute temperature, q is the electronic charge, A is the device area and f is the ideality factor. Equation (1.3), which was originally developed to describe the non-ideal diode behavior of inorganic semiconductor p–n junctions, has been applied to a wide range of solar cell technologies including hydrogenated amorphous silicon p–i–n cells, Cu(In,Ga)Se2 cells, organic bulk heterojunction cells and DSSCs. In the case of photoelectrochemical cells, J0 is related to the energy level alignment between the bottom of the conduction band of the metal oxide and the excited state donor level of the dye D*. This differs from JL, which is related to the coupling between D* and states in the metal oxide that are closer in energy and therefore typically deeper in the conduction band. This means that a clear strategy for improving device performance is to adjust the energetic position of D* relative to the metal oxide density of states to achieve maximum JL and minimum J0. The benefits of this approach are apparent in Equation (1.3), which gives an estimate of the open circuit voltage of the cell in the regime of high shunt resistance:
[MATHEMATICAL EXPRESSION OMITTED] (1.4)
We note that this model could be extended to incorporate electrochemical processes. For example, the electrochemical kinetics at the electrodes is more appropriately described by the Butler–Volmer equation with non-linear J–V characteristics rather than an ohmic resistor. However, as shown in Section 1.2.2, much insight can be gained when using the equivalent circuit model of Figure 1.1 and Equation (1.3) to do a comparative analysis of a series of device architectures in which the relevant energy levels are systematically varied.
1.2.2 Bioinspired High-Potential Porphyrin Photoanodes
Table 1.1 compares the equivalent circuit parameters that characterize the performance of solar cells based on sensitizers 1, 2 and 3 (Figure 1.2) and N719. The analysis includes solar cells with either I-3/I- or Br-3/Br- redox couples as regenerative electron mediators and TiO2 or SnO2 nanocrystalline substrates. It is shown that the series resistance increases when the TiO2 photoanode is replaced by SnO2, for a given dye and electrolyte, consistent with lower in vacuo room temperature nanoporous-film dark conductivities in TiO2 (~10-10 Ω-1 cm-1; Figure 1.7) compared to SnO2 (~10-6 Ω-1 cm-1; Figure 1.10). In addition, the series resistance RS decreases for iodide relative to bromide for dyes 1–3, consistent with the higher conductivity of iodide when compared to bromide at low concentrations. In addition to changes caused by the intrinsic properties of the ions, the substitution of I- by Br- leads to a reduction in the saturation recombination current J0 and an increase in the open circuit voltage VOC, as observed for solar cells based on sensitizers 1–3. These changes in the current–voltage characteristics are due to a tighter binding of bromide to the porphyrin adsorbates, as shown by the analysis of the electrostatic potentials.
The analysis of electrostatic potentials suggest that Br- ions interact more strongly than I- and bind more closely to the aromatic rings owing to their smaller ionic radius (Br-: 1.82 Å, I-: 2.06 Å). The resulting stabilization includes anion π interactions with the permanent quadrupole moments of the aromatic rings. Up to 4 Br- anions per porphyrin are predicted to bind to 1 and 3 with binding energies in the -5 to -13 kcal mol-1 range. Two Br- ions bind to the pentafluorophenyl groups while the other two bind to the carbomethoxyphenyl groups (Figure 1.4). In addition, Br- can bind to Zn in 2, with a binding energy of -12.5 kcal mol-1. However, metal–anion interactions for Zn - I- and Pd - Br- are much weaker (i.e., comparable to thermal fluctuations). In contrast to bromide, iodide ions show much weaker specific interactions with 1–3 probably due to the larger ionic radius.
The analysis of adsorbate ions interactions provided fundamental understanding of the origin of changes in the I–V characteristics induced by changes in the nature of the redox couple. The larger concentration of smaller ions shifts the electron donor and acceptor states and the edge of the conduction band to more negative potentials, preventing recombination and reducing J0 (Figure 1.4). Therefore, the open circuit voltage VOC is increased and the slope of the characteristic curve is reduced as V->0. The illumination current density increases (or decreases) when the donor state is poised where the conduction band has a larger (or smaller) density of states.
The comparative analysis of porphyrin-based photoanodes suggests that new high-potential sensitizers and device architectures can significantly expand the available parameter space of DSSC current–voltage simulation methods. In particular, a suitable choice of electron-withdrawing substitution groups, or transition metal, can shift the porphyrin redox potential and make it sufficiently positive to activate water oxidation catalysts. However, the porphyrin excited state which injects the photoexcited electrons into the metal oxide conduction band typically experiences a similar stabilization when changing the metal center or the substitution groups, giving similar vertical excitation bands as seen in the absorption spectra (Figure 1.3). Therefore, it is natural to expect that adsorbates that generate deep positive holes by excitation with visible light would photoinject electrons only into metal oxides with conduction bands that are more positive than the NHE (e.g., SnO2). Achieving efficient water oxidation and proton reduction by visible light photocatalysis on sensitized metal oxide surfaces thus might require two-photon schemes. A simple example is shown in Figure 1.5 where red photons inject electrons into the photocathode at potentials more negative than the NHE, while blue photons generate holes in porphyrins adsorbed on the photoanode, sufficiently positive as to activate water oxidation catalysts.
1.3 Inverse Design of Photoabsorbers
The search for molecular adsorbates for high potential photoanodes with high photoconversion efficiency is challenging. Most of the work reported to date has been based on direct molecular design using empirical strategies, where typical "guess-and-check" procedures face the challenge of selecting suitable candidates from an immense number of accessible stable molecules. Therefore, there is significant interest in the development of inverse design methods that bypass the combinatorial problem in the development of materials for solar energy conversion.
Excerpted from Solar Energy Conversion by Piotr Piotrowiak. Copyright © 2013 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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Table of Contents
Design and characterization of molecular adsorbates for solar energy conversion; Charge and exciton dynamics in semiconductor quantum dots: a time-domain, ab initio view; Multiscale modelling of interfacial electron transfer; Plasmon-enhanced solar chemistry: electrodynamics and quantum mechanics; Charge carrier generation, separation, recombination and transport in nanostructured materials; Two-dimensional photon echo spectroscopy and energy transfer; Ultrafast imaging and microscopy of energy conversion materials; Ultrafast multiphoton photoemission microscopy of solid surfaces in the real and reciprocal space; Light at the tip: hybrid scanning tunnelling/optical spectroscopy microscopy; Time resolved IR spectroscopy of metal oxides and interfaces; Carrier dynamics in photovoltaic structures and materials studied with time-resolved terahertz spectroscopy; Time-resolved x-ray absorption spectroscopy for solar energy research.