Realistic cluster modeling of electron transport and trapping in solvated TiO2 nanoparticles.

We have developed a cluster model of a TiO(2) nanoparticle in the dye-sensitized solar cell and used first-principles quantum chemistry, coupled with a continuum solvation model, to compute structures and energetics of key electronic and structural intermediates and transition states. Our results suggest the existence of shallow surface trapping states induced by small cations and continuum solvent effect as well as the possibility of the existence of a surface band which is 0.3-0.5 eV below the conduction band edge. The results are in uniformly good agreement with experiment and establish the plausibility of an ambipolar model of electron diffusion in which small cations, such as Li(+), diffuse alongside the current carrying electrons in the device, stabilizing shallowing trapping states, facilitating diffusion from one of these states to another, in a fashion that is essential to the functioning of the cell.

[1]  Yizhak Marcus,et al.  Thermodynamics of solvation of ions. Part 5.—Gibbs free energy of hydration at 298.15 K , 1991 .

[2]  S. C. Parker,et al.  Lithium Insertion and Transport in the TiO2-B Anode Material: A Computational Study , 2009 .

[3]  R. Friesner,et al.  Continuous Localized Orbital Corrections to Density Functional Theory: B3LYP-CLOC. , 2010, Journal of chemical theory and computation.

[4]  A. J. Frank,et al.  Electrons in nanostructured TiO2 solar cells: Transport, recombination and photovoltaic properties , 2004 .

[5]  N. A. Deskins,et al.  Intrinsic Hole Migration Rates in TiO2 from Density Functional Theory , 2009 .

[6]  Laurence M. Peter,et al.  The Grätzel Cell: Where Next? , 2011 .

[7]  D. Morris,et al.  Ionic radii and enthalpies of hydration of ions , 1968 .

[8]  R. Friesner,et al.  Localized Orbital Corrections for the Barrier Heights in Density Functional Theory , 2009 .

[9]  Shane Ardo,et al.  Photodriven heterogeneous charge transfer with transition-metal compounds anchored to TiO2 semiconductor surfaces. , 2009, Chemical Society reviews.

[10]  Mou‐shiung Lin,et al.  Interface energetics for n-type semiconducting strontium titanate and titanium dioxide contacting liquid electrolyte solutions and competitive photoano , 1982 .

[11]  L. Eriksson,et al.  Comparative study of DFT methods applied to small titanium oxygen compounds , 1996 .

[12]  T. Kitamura,et al.  Effects of Lithium Ion Density on Electron Transport in Nanoporous TiO2 Electrodes , 2001 .

[13]  A. J. Frank,et al.  Influence of Electrical Potential Distribution, Charge Transport, and Recombination on the Photopotential and Photocurrent Conversion Efficiency of Dye-Sensitized Nanocrystalline TiO2 Solar Cells: A Study by Electrical Impedance and Optical Modulation Techniques , 2000 .

[14]  A. Klamt,et al.  COSMO : a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient , 1993 .

[15]  Yagi,et al.  Electronic conduction above 4 K of slightly reduced oxygen-deficient rutile TiO2-x. , 1996, Physical review. B, Condensed matter.

[16]  F. Finocchi,et al.  Density functional study of stoichiometric and O-rich titanium oxygen clusters , 2000 .

[17]  Jun Liu,et al.  Size Effects on Li+/Electron Conductivity in TiO2 Nanoparticles , 2010 .

[18]  Henrik Lindström,et al.  Electron Transport in the Nanostructured TiO2-Electrolyte System Studied with Time-Resolved Photocurrents , 1997 .

[19]  S. W. Leeuw,et al.  First principles predictions for intercalation behaviour , 2004 .

[20]  J. Bisquert Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions of states. , 2008, Physical chemistry chemical physics : PCCP.

[21]  S. D. de Leeuw,et al.  Effect of diffusion on lithium intercalation in titanium dioxide. , 2001, Physical review letters.

[22]  J. Datta,et al.  Relative standard electrode potentials of I3−/I−, I2/I3−, and I2/I− redox couples and the related formation constants of I3− in some pure and mixed dipolar aprotic solvents , 1988 .

[23]  R. Friesner,et al.  Localized orbital corrections applied to thermochemical errors in density functional theory: The role of basis set and application to molecular reactions. , 2008, The Journal of chemical physics.

[24]  G. Boschloo,et al.  Conductivity Studies of Nanostructured TiO2 Films Permeated with Electrolyte , 2004 .

[25]  G. Kroes,et al.  Theoretical Study of Stable, Defect-Free (TiO2)n Nanoparticles with n = 10−16 , 2007 .

[26]  M. Grätzel Dye-sensitized solar cells , 2003 .

[27]  N. A. Deskins,et al.  Distribution of Ti3+ Surface Sites in Reduced TiO2 , 2011 .

[28]  Richard A Friesner,et al.  Correcting Systematic Errors in DFT Spin-Splitting Energetics for Transition Metal Complexes. , 2011, Journal of chemical theory and computation.

[29]  Yixiang Cao,et al.  A localized orbital analysis of the thermochemical errors in hybrid density functional theory: achieving chemical accuracy via a simple empirical correction scheme. , 2006, The Journal of chemical physics.

[30]  G. Boschloo,et al.  Spectroelectrochemical Investigation of Surface States in Nanostructured TiO2 Electrodes , 1999 .

[31]  S. Kerisit,et al.  Dynamics of Coupled Lithium/Electron Diffusion in TiO2 Polymorphs , 2009 .

[32]  Anders Hagfeldt,et al.  A detailed analysis of ambipolar diffusion in nanostructured metal oxide films , 2002 .

[33]  J. Gale,et al.  A first principles investigation of lithium intercalation in TiO2-B , 2009 .

[34]  J. Yates,et al.  Light-induced charge separation in anatase TiO2 particles. , 2005, The journal of physical chemistry. B.

[35]  N. A. Deskins,et al.  Electron transport via polaron hopping in bulk TiO2 : A density functional theory characterization , 2007 .

[36]  R. Friesner,et al.  Localized orbital corrections for the calculation of ionization potentials and electron affinities in density functional theory. , 2006, The journal of physical chemistry. B.

[37]  A. J. Frank,et al.  Temperature Dependence of the Electron Diffusion Coefficient in Electrolyte-Filled TiO2 , 2006 .

[38]  Richard A Friesner,et al.  A B3LYP-DBLOC empirical correction scheme for ligand removal enthalpies of transition metal complexes: parameterization against experimental and CCSD(T)-F12 heats of formation. , 2012, Physical chemistry chemical physics : PCCP.

[39]  R. Friesner,et al.  Development of Accurate DFT Methods for Computing Redox Potentials of Transition Metal Complexes: Results for Model Complexes and Application to Cytochrome P450. , 2012, Journal of chemical theory and computation.

[40]  Anders Hagfeldt,et al.  Activation energy of electron transport in dye-sensitized TiO2 solar cells. , 2005, The journal of physical chemistry. B.

[41]  Annabella Selloni,et al.  Electronic structure of defect states in hydroxylated and reduced rutile TiO2(110) surfaces. , 2006, Physical review letters.

[42]  B. Ohtani,et al.  Quantitative analysis of defective sites in titanium(IV) oxide photocatalyst powders , 2003 .

[43]  Benjamin H. Meekins,et al.  Got TiO2 nanotubes? Lithium ion intercalation can boost their photoelectrochemical performance. , 2009, ACS nano.

[44]  L. Kavan,et al.  Pseudocapacitive Lithium Storage in TiO2(B) , 2005 .

[45]  S. W. Leeuw,et al.  Diffusion of Li-ions in rutile. An ab initio study , 2003 .

[46]  C. Adamo,et al.  Density functional theory analysis of the structural and electronic properties of TiO2 rutile and anatase polytypes: performances of different exchange-correlation functionals. , 2007, The Journal of chemical physics.

[47]  A. J. Frank,et al.  Transport-Limited Recombination of Photocarriers in Dye-Sensitized Nanocrystalline TiO2 Solar Cells , 2003 .

[48]  Kang‐Ryul Lee,et al.  Syntheses of O‐Methylated‐1,2,4‐dioxazolidines by Ozonolyses of O‐Methylated Dioximes. , 2001 .

[49]  R. Caminiti,et al.  Deep versus Shallow Behavior of Intrinsic Defects in Rutile and Anatase TiO2 Polymorphs , 2010 .

[50]  M. V. Ganduglia-Pirovano,et al.  Oxygen vacancies in transition metal and rare earth oxides: Current state of understanding and remaining challenges , 2007 .

[51]  Zheng-Wang Qu,et al.  Theoretical study of the electronic structure and stability of titanium dioxide clusters (TiO2)n with n = 1-9. , 2006, The journal of physical chemistry. B.

[52]  Annabella Selloni,et al.  Excess electron states in reduced bulk anatase TiO2: comparison of standard GGA, GGA+U, and hybrid DFT calculations. , 2008, The Journal of chemical physics.

[53]  A. Selloni,et al.  Bulk and Surface Polarons in Photoexcited Anatase TiO2 , 2011 .

[54]  G. Watson,et al.  Polaronic trapping of electrons and holes by native defects in anatase TiO2 , 2009 .

[55]  C. Majumder,et al.  Size-dependent electronic structure of rutile TiO2 quantum dots , 2011 .

[56]  S. Bromley,et al.  Theoretical Investigation of the Hydrogenation of (TiO2)N Clusters (N = 1–10) , 2011 .

[57]  B. Conway The evaluation and use of properties of individual ions in slution , 1978 .

[58]  S. W. Leeuw,et al.  Density-functional simulations of lithium intercalation in rutile , 2002 .

[59]  Michael Grätzel,et al.  Recent advances in sensitized mesoscopic solar cells. , 2009, Accounts of chemical research.

[60]  Anders Hagfeldt,et al.  Characteristics of the iodide/triiodide redox mediator in dye-sensitized solar cells. , 2009, Accounts of chemical research.

[61]  V. Sapunov,et al.  A new table of the thermodynamic quantities of ionic hydration: values and some applications (enthalpy–entropy compensation and Born radii) , 2000 .

[62]  Hyman D. Gesser,et al.  Porous titania glass as a photocatalyst for hydrogen production from water , 1981, Nature.

[63]  M. A. Henderson A surface science perspective on TiO2 photocatalysis , 2011 .

[64]  T. Kitamura,et al.  Influence of the electrolytes on electron transport in mesoporous TiO2-Electrolyte systems , 2002 .

[65]  J. Nelson,et al.  Charge transport model for disordered materials: Application to sensitized TiO2 , 2002 .

[66]  Eric A. Schiff,et al.  Ambipolar Diffusion of Photocarriers in Electrolyte-Filled, Nanoporous TiO2† , 2000 .

[67]  G. Pacchioni Modeling doped and defective oxides in catalysis with density functional theory methods: room for improvements. , 2008, The Journal of chemical physics.

[68]  Jun Liu,et al.  Mechanism of Li+/electron conductivity in rutile and anatase TiO2 nanoparticles , 2010 .

[69]  R. Friesner,et al.  Computing Redox Potentials in Solution: Density Functional Theory as A Tool for Rational Design of Redox Agents , 2002 .