Theoretical and Experimental Studies of Electrode and ...869860/FULLTEXT01.pdfTheoretical and...

Theoretical and ExperimentalStudies of Electrodeand Electrolyte Processes inIndustrial ElectrosynthesisRasmus K. B. Karlsson

Doctoral Thesis, 2015KTH Royal Institute of TechnologyApplied ElectrochemistryDepartment of Chemical Engineering and TechnologySE-100 44 Stockholm, Sweden

TRITA CHE Report 2015:66ISSN 1654-1081ISBN 978-91-7595-781-4

Akademisk avhandling som med tillstånd av KTH i Stockholm framlägges tilloffentlig granskning för avläggande av teknisk doktorsexamen 18 december kl.10.00 i sal F3, KTH, Lindstedtsvägen 26, Stockholm.

Abstract

Heterogeneous electrocatalysis is the usage of solid materials to decrease the amountof energy needed to produce chemicals using electricity. It is of core importancefor modern life, as it enables production of chemicals, such as chlorine gas andsodium chlorate, needed for e.g. materials and pharmaceuticals production. Fur-thermore, as the need to make a transition to usage of renewable energy sourcesis growing, the importance for electrocatalysis used for electrolytic production ofclean fuels, such as hydrogen, is rising. In this thesis, work aimed at understandingand improving electrocatalysts used for these purposes is presented.A main part of the work has been focused on the selectivity between chlorine gas,or sodium chlorate formation, and parasitic oxygen evolution. An activation ofanode surface Ti cations by nearby Ru cations is suggested as a reason for the highchlorine selectivity of the “dimensionally stable anode” (DSA), the standard anodeused in industrial chlorine and sodium chlorate production. Furthermore, theoret-ical methods have been used to screen for dopants that can be used to improvethe activity and selectivity of DSA, and several promising candidates have beenfound. Moreover, the connection between the rate of chlorate formation and therate of parasitic oxygen evolution, as well as the possible catalytic effects of elec-trolyte contaminants on parasitic oxygen evolution in the chlorate process, havebeen studied experimentally.Additionally, the properties of a Co-doped DSA have been studied, and it is foundthat the doping makes the electrode more active for hydrogen evolution. Finally,the hydrogen evolution reaction on both RuO2 and the noble-metal-free MoS2electrocatalyst material has been studied using a combination of experimental andtheoretically calculated X-ray photoelectron chemical shifts. In this way, insightinto structural changes accompanying hydrogen evolution on these materials isobtained.

Keywords: Electrocatalysis, metallic oxides, ruthenium dioxide, titanium dioxide,DSA, doping, selectivity, ab initio modeling, density functional theory

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Sammanfattning

Heterogen elektrokatalys innebär användningen av fasta material för att minskaenergimängden som krävs för produktion av kemikalier med hjälp av elektricitet.Heterogen elektrokatalys har en central roll i det moderna samhället, eftersom detmöjliggör produktionen av kemikalier såsom klorgas och natriumklorat, som i sintur används för produktion av t ex konstruktionsmaterial och läkemedel. Vikten avanvändning av elektrokatalys för produktion av förnybara bränslen, såsom vätgas,växer dessutom i takt med att en övergång till användning av förnybar energi blirallt nödvändigare. I denna avhandling presenteras arbete som utförts för att förståoch förbättra sådana elektrokatalysatorer.En stor del av arbetet har varit fokuserat på selektiviteten mellan klorgas och bipro-dukten syrgas i klor-alkali och kloratprocesserna. Inom ramen för detta arbete harteoretisk modellering av det dominerande anodmaterialet i dessa industriella pro-cesser, den så kallade “dimensionsstabila anoden” (DSA), använts för att föreslåen fundamental anledning till att detta material är speciellt klorselektivt. Vi före-slår att klorselektiviteten kan förklaras av en laddningsöverföring från rutenium-katjoner i materialet till titankatjonerna i anodytan, vilket aktiverar titankatjonerna.Baserat på en bred studie av ett stort antal andra dopämnen föreslår vi dessutomvilka dopämnen som är bäst lämpade för produktion av aktiva och klorselektivaanoder. Med hjälp av experimentella studier föreslår vi dessutom en koppling mel-lan kloratbildning och oönskad syrgasbildning i kloratprocessen, och vidare haren bred studie av tänkbara elektrolytföroreningar utförts för att öka förståelsen försyrgasbildningen i denna process.Två studier relaterade till elektrokemisk vätgasproduktion har också gjorts. En ex-perimentell studie av Co-dopad DSA har utförts, och detta elektrodmaterial visadesig vara mer aktivt för vätgasutveckling än en standard-DSA. Vidare har en kombi-nation av experimentell och teoretisk röntgenfotoelektronspektroskopi använts föratt öka förståelsen för strukturella förändringar som sker i RuO2 och i det ädelme-tallfria elektrodmaterialet MoS2 under vätgasutveckling.

Nyckelord: Elektrokatalys, metalloxider, ruteniumdioxid, titandioxid, DSA, dop-ning, selektivitet, ab initio-modellering, täthetsfunktionalteori

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Publications

This thesis is based on the following publications:

1. Christine Hummelgård, Rasmus K. B. Karlsson, Joakim Bäckström, SeikhM. H. Rahman, Ann Cornell, Sten Eriksson, and Håkan Olin. Physical andelectrochemical properties of cobalt doped (Ti, Ru)O2 electrode coatings.Mater. Sci. Eng., B, 178:1515–1522, 2013.

2. Hernan G. Sanchez Casalongue, Jesse D. Benck, Charlie Tsai, Rasmus K.B. Karlsson, Sarp Kaya, May Ling Ng, Lars G. M. Pettersson, Frank Abild-Pedersen, Jens K. Nørskov, Hirohito Ogasawara, Thomas F. Jaramillo, andAnders Nilsson. Operando characterization of an amorphous molybdenumsulfide nanoparticle catalyst during the hydrogen evolution reaction. J. Phys.Chem. C, 118(50):29252–29259, 2014.

3. Rasmus K. B. Karlsson, Heine A. Hansen, Thomas Bligaard, Ann Cornell,and Lars G. M. Pettersson. Ti atoms in Ru0.3Ti0.7O2 mixed oxides form ac-tive and selective sites for electrochemical chlorine evolution. Electrochim.Acta, 146:733–740, 2014.

4. Staffan Sandin, Rasmus K. B. Karlsson, and Ann Cornell. Catalyzed anduncatalyzed decomposition of hypochlorite in dilute solutions. Ind. Eng.Chem. Res., 54(15):3767–3774, 2015.

5. Rasmus K. B. Karlsson and Ann Cornell. Selectivity between oxygen andchlorine evolution in the chlor-alkali and chlorate processes - a comprehen-sive review. Submitted to Chem. Rev., 2015.

6. Rasmus K. B. Karlsson, Ann Cornell, and Lars G. M. Pettersson. The elec-trocatalytic properties of doped TiO2. Electrochim. Acta, 180:514-527,2015.

7. Rasmus K. B. Karlsson, Ann Cornell, Richard A. Catlow, Alexey A. Sokol,Scott M. Woodley, and Lars G. M. Pettersson. An improved force field forstructures of mixed RuO2-TiO2 oxides. Manuscript in preparation.

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8. Rasmus K. B. Karlsson, Ann Cornell, and Lars G. M. Pettersson. Structuralchanges in RuO2 during electrochemical hydrogen evolution. Manuscript inpreparation.

Author contributions

• Paper 1:

– I prepared the electrodes together with Joakim Bäckström, and per-formed all electrochemical measurements, as well as all data analysisof those measurements. I also contributed to the overall design andplanning of the study, and wrote parts of the paper.

• Paper 2:

– I performed all XPS calculations and wrote parts of the paper.

• Paper 3:

– I performed all calculations and wrote most of the paper.

• Paper 4:

– I contributed to the initial design and continuous planning of the study.However, all experiments were performed by Staffan Sandin. I alsowrote parts of the paper.

• Paper 5:

– I wrote most of the review paper.

• Paper 6:


• Paper 7:


• Paper 8:


Contents

1 Introduction 11.1 State of the art electrodes . . . . . . . . . . . . . . . . . . . . . . 5

1.1.1 Anodes for chlor-alkali and sodium chlorate production . 51.1.2 Cathodes for HER . . . . . . . . . . . . . . . . . . . . . 7

1.2 Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.1 Process conditions . . . . . . . . . . . . . . . . . . . . . 81.2.2 Electrolyte contamination . . . . . . . . . . . . . . . . . 91.2.3 Electrode structure and composition . . . . . . . . . . . . 10

1.3 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Computational methods 152.1 Theoretical descriptions of matter . . . . . . . . . . . . . . . . . 15

2.1.1 Force fields . . . . . . . . . . . . . . . . . . . . . . . . . 152.1.2 Quantum mechanics . . . . . . . . . . . . . . . . . . . . 182.1.3 Density functional theory . . . . . . . . . . . . . . . . . . 202.1.4 Approximate self-interaction correction with DFT+U . . . 262.1.5 Quantum mechanics for periodic systems . . . . . . . . . 262.1.6 The frozen-core approximation . . . . . . . . . . . . . . . 292.1.7 Describing the wave function: Plane waves, linear combi-

nation of atomic orbitals and real-space grids . . . . . . . 302.2 The theory of X-ray photoelectron spectroscopy . . . . . . . . . . 312.3 Theoretical electrochemistry . . . . . . . . . . . . . . . . . . . . 32

2.3.1 The computational hydrogen electrode method . . . . . . 332.4 Electrocatalysis from theory . . . . . . . . . . . . . . . . . . . . 37

2.4.1 Brønsted-Evans-Polanyi relations . . . . . . . . . . . . . 37

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2.4.2 Sabatier analysis . . . . . . . . . . . . . . . . . . . . . . 382.4.3 Scaling relations . . . . . . . . . . . . . . . . . . . . . . 39

3 Experimental methods 433.1 Preparation of mixed oxide coatings using spin-coating . . . . . . 433.2 Electrochemical measurements . . . . . . . . . . . . . . . . . . . 44

3.2.1 Cyclic voltammetry . . . . . . . . . . . . . . . . . . . . . 443.2.2 Galvanostatic polarization curve measurements . . . . . . 44

3.3 Combined determination of gas-phase and liquid-phase composi-tions during hypochlorite decomposition using mass spectrometryand ion chromatography . . . . . . . . . . . . . . . . . . . . . . 46

4 Results and discussion 474.1 Co-doped Ru-Ti dioxide electrocatalysts . . . . . . . . . . . . . . 474.2 Selectivity between Cl2 and O2 . . . . . . . . . . . . . . . . . . . 48

4.2.1 The uncatalyzed and catalyzed decomposition of hypochlo-rite species . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.2 Theoretical studies of the connection between oxide com-position and ClER and OER activity and selectivity . . . . 53

4.3 Semiclassical modeling of rutile oxides . . . . . . . . . . . . . . 664.4 XPS modeled using DFT . . . . . . . . . . . . . . . . . . . . . . 69

4.4.1 The active site for HER on MoS2 . . . . . . . . . . . . . 704.4.2 Structural changes in RuO2 during HER . . . . . . . . . . 73

5 Conclusions and recommendations 795.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.2 Recommendations for future work . . . . . . . . . . . . . . . . . 80

6 Bibliography 85

7 Acknowledgments 99

List ofsymbols andabbreviations

kB The Boltzmann constant

∆Gr The reaction free energy

εxc The per-particle exchange-correlation energy density ofa system

k The k-vector

ri The position of a particle,(x,y,z)

Ψ The wave function

ψi (r) A one-particle Kohn-Sham or-bital

ρ(r) The total electronic density atposition r

τ (r) The gradient in the kinetic en-ergy density

ψn (r) A pseudo wave function

pai A projector function in the

PAW method

b Tafel slope

E Energy or electrode potential

e The charge of an electron

E0 The ground-state energy

EB Electron binding energy inXPS

Exc [ρ (r)] The exchange-correlationfunctional (the sum of the twocorrection terms ∆T [ρ (r)] and∆Vee [ρ (r)])

F [ρ(r)] A functional of the electronicdensity

H The atomic Hamiltonian

He The electronic Hamiltonian

hKSi The one-electron Kohn-Sham

Hamiltonian

I Electrical current

j Current density, current perarea

me The mass of the electron

mk The mass of atomic nucleus k

N The total number of electronsin a system

q∗ Electrochemically active sur-face area

qi The charge of an ion i

rab The distance between particlesa and b

S Entropy

T Temperature

t Time

Ti Kinetic energy of electron i

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U Electrode potential

Ueq The reversible potential for acertain reaction

uik (r) Unit-cell periodicity vector

v(r) The external potential

VN The nuclear-nuclear repulsionenergy

Vee The electron-electron interac-tion energy, also known as theHartree energy

ve f f [ρ (r)] The effective potential (thesum of electron-nuclei andclassical charge density in-teractions and the exchange-correlation potential)

vext The external potential (theelectron-nuclei interaction)

vH The Hartree potential, the func-tional derivative of the classicalcharge density interaction

vxc The functional derivative of Exc

Z Atomic number

AFM Atomic force microscopy

AOM Angular overlap model

BEP Brønsted-Evans-Polanyi

BZ Brillouin zone

CC Coupled-cluster

CHE Computational hydrogen elec-trode

CI Configuration interaction

ClER Chlorine evolution reaction

CUS Coordinatively unsaturatedsite, e.g. on the rutile (110)surface

CV Cyclic voltammetry

DFT Density functional theory

DFTB Density-functional tight-binding

DSA Dimensionally stable anode

DSC Differential scanning calorime-try

EXX Evaluation of the exchange en-ergy exactly using the Hartree-Fock method on Kohn-Shamorbitals

FF Force field

GA Genetic algorithm

GGA Generalized gradient approxi-mation

GTO Gaussian-type orbital

HER Hydrogen evolution reaction

HF Hartree-Fock

IC Ion chromatography

IR The change in potential acrossan electrolytic cell due to elec-trolyte resistance (I×R)

KS Kohn-Sham

LCAO Linear combination of atomicorbitals

LDA Local density approximation inDFT

ML Monolayer

CONTENTS ix

MP Møller-Plesset

MS Mass spectrometry

OER Oxygen evolution reaction

ORR Oxygen reduction reaction

PAW Projector-augmented wave

PEM Polymer electrolyte membrane

PGM Platinum-group metal (Ru, Rh,Pd, Os, Ir or Pt)

PW Plane wave

QMC Quantum Monte Carlo

RPA Random phase approximation

SE Schrödinger equation

SEM Scanning electron microscopy

SHE Standard hydrogen electrode

TEM Transmission electron mi-croscopy

TST Transition-state theory

XPS X-ray photoelectron spec-troscopy

XRD X-ray diffraction

ZPE Zero-point energy

x CONTENTS

Chapter 1

Introduction

Modern life would be impossible without heterogeneous catalysis. Heterogeneouscatalysts are used to reduce the energy required for production of the fertilizersnecessary to supply humanity with food, to make cleaner fuel for transportation,and to make emissions less harmful. The heterogeneous catalysts that are usedtoday are applied mainly in thermal processes, where a solid catalyst is used todecrease reaction barriers for chemical reactions. However, heterogeneous elec-trocatalysts are also increasingly important. Electrocatalysts have long been usedin chlor-alkali and sodium chlorate production, two inorganic electrosynthesis pro-cesses that have long histories[1]. Electrosynthesis is the usage of electrical energyto produce chemicals. Electrocatalysts are also used in fuel cells, which might beincreasingly important in future transportation. The focus of this thesis is on theunderstanding and improvement of electrocatalysts applied for electrosynthesis,specifically on electrocatalysts used for the anodic processes of chlorine gas andchlorate production, and for the cathodic process of hydrogen evolution.Chlorine is a fundamental building block in modern chemical industry[2]. Theworld-wide production capacity exceeds 50 million metric tons[3, 4]. Chlorine gasis used in production of most (more than 85%) pharmaceuticals, and is involvedin the production of a large part of all other modern chemicals and materials[2, 4].A few important products that require chlorine gas are shown in Table 1.1. Fur-thermore, chlorine, and its oxide sodium chlorate, have long been used as oxidantsfor e.g. bleaching fabrics or pulp and paper. Today, bleaching of pulp and paperproducts is usually performed using chlorine dioxide (ClO2) which is produced us-ing sodium chlorate[5]. This application drives the production of sodium chlorate,which exceeds three million metric tons[6].Both chlorine gas and sodium chlorate are produced through electrolysis of sodiumchloride solutions. A main difference between the processes is the usage of somesort of divider, in chlorine production, between the anode, where chlorides are

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2 CHAPTER 1. INTRODUCTION

Table 1.1: Some important uses for chlorine gas[4].

Product Chlorine usePolyvinyl chloride (PVC) and Raw materialseveral other plastics

TiO2 In precursor TiClxHighly pure Si for solar cells and electronics In precursor SiCl4

Highly pure HCl As reactantPharmaceuticals Final product, reactants or intermediates

oxidized to form chlorine gas according to

2Cl−→ Cl2 +2e− (1.1)

and the cathode, where hydrogen gas is evolved according to

2H2O+2e−→ H2 +2OH−. (1.2)

The anode used in both processes is the so-called Dimensionally Stable Anode(DSA), with is Ti coated with a mixed rutile oxide of ca 30% RuO2 (possiblytogether with other dopants) and 70% TiO2. If a divider is used, the pH at theanode side is kept low and chlorine gas is liberated. Without a divider the pH inthe electrolyte can reach close to neutral values, allowing sodium chlorate to formin the following reactions, starting with hydrolysis of formed chlorine

Cl2 +H2O H++HOCl+Cl−, (1.3)

HOCl+H2O OCl−+H3O+, (1.4)

followed by chemical formation of chlorate,

2HOCl+OCl−→ ClO−3 +2H++2Cl−. (1.5)

The detailed mechanism of reaction 1.5 has still not been determined[1]. To maxi-mize the chemical formation of sodium chlorate, chlorate plants have low-volumeelectrolysis cells connected to larger reactors where the chemical conversion canbe maximized. In the divided cell, highly concentrated sodium hydroxide (alkali)can be extracted from the cathode side, explaining why this process is known asthe chlor-alkali process. The overall reaction occurring in the divided (chlor-alkali)cell is

2NaCl+2H2O→ Cl2 +H2 +2NaOH, (1.6)

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Table 1.2: Typical conditions for chlor-alkali production in membrane processes[3, 4, 8].

Cell voltage / V 2.4-2.7Current density / kAm−2 1.5-7

Temperature / ◦C 90NaCl concentration in the anolyte / gdm−3 200

Anolyte pH 2-4NaOH concentration in the catholyte / wt-% 32

Table 1.3: Typical operating conditions in sodium chlorate production [5, 9, 10].

Cell voltage / V 2.9-3.7Current density / kAm−2 1.5-4

Temperature / ◦C 65-90NaCl concentration / gdm−3 70-150

NaClO3 concentration / gdm−3 450-650NaOCl concentration / gdm−3 1-5

Na2Cr2O7 concentration / gdm−3 1-6Electrolyte pH 5.5-7

whereas in undivided (sodium chlorate) cells the overall reaction is

NaCl + 3 H2O NaClO3 + 3 H2 (1.7)

The type of “divider” used separates the different chlor-alkali processes into threesubtypes: the mercury cell process, the diaphragm process and the membrane pro-cess. Only the last type is currently acceptable from the environmental and eco-nomic points of view[7], and the other processes are to be discontinued in theEuropean Union. Due to the high yearly production rates of both chemicals, withchlor-alkali production alone consuming an estimated 150 TWh of electricity peryear[4], it is clear that high selectivity and energy efficiency in both processesis required.[1] Typical operating conditions for the membrane chlor-alkali andsodium chlorate processes are found in Tables 1.2 and 1.3, respectively.[3–5, 8–10]A challenge in both processes is parasitic oxygen evolution. The possible pathwaysfor this oxygen evolution include direct anodic water oxidation, competing withreaction 1.1,

2H2O→ O2 +4H++4e−, (1.8)

direct anodic chlorate formation

6ClO−+3H2O→ 2ClO−3 +4Cl−+6H++1.5O2 +6e−, (1.9)


as well as decomposition of hypochlorites (HOCl or OCl–) according to

2HOCl→ 2HCl+O2. (1.10)

The decomposition of hypochlorites might be due both to bulk electrolyte and elec-trode surface reactions. The reduction in current efficiency due to these parasiticreactions ranges from 1-5%. While measures such as usage of selective electrodes(see the following section) and anolyte acidification can reduce the oxygen sidereaction to enable a current efficiency of close to 99% in the chlor-alkali process,this is not possible in sodium chlorate production, where 5% losses in currentefficiency are common. Research also indicates that the oxygen evolution side-reaction not only lowers the current efficiency of the processes, but that it is alsodirectly connected to the rate of deactivation of the DSA.[1]The cathode reaction in both chlor-alkali and sodium chlorate production is hydro-gen evolution, reaction 1.2. The interest in this reaction has been rising in recentyears, as it is a way of producing hydrogen for use as fuel (or in production of otherfuels, e.g. by Fischer-Tropsch synthesis) in a renewable fashion[11]. In both indus-trial electrosynthesis of chlor-alkali and sodium chlorate, and in water electrolysisfor production of hydrogen, the hydrogen evolution takes place in a strongly al-kaline solution, which places limitations on the cathode material. Although earlyindustrial electrosynthetic hydrogen production was carried out already in 1927,electrosynthetic hydrogen makes up only a very small part (about 5%) of the totalhydrogen produced today. Production of hydrogen based on fossil hydrocarbonsis the dominant production method, as it requires less energy. The theoretical en-ergy consumption required for production using methane is 41 MJ/kmol H2 whilethe theoretical energy consumption for electrolytic hydrogen is about six timeshigher at 242 MJ/kmol H2[12]. Today, industrial electrolytic cells for chlor-alkaliand water electrolysis often use steel; Ni or Ni alloys; or RuO2 deposited on Nias hydrogen evolution reaction (HER) cathodes[3, 5, 12, 13]. However, due tothe more demanding conditions, mainly steel or Ti cathodes are used in chlorateproduction[5]. Ni-based cathodes are not acceptable in chlorate production as Ni isa well-known catalyst for decomposition of HOCl[1]. As interest in electrochem-ical hydrogen production has risen, so has the research into “activated cathodes”,which are cathodes with an activity exceeding that of Ni[13] .A primary goal of the present thesis has been to further the understanding for howthe electrode composition determines the selectivity, activity and stability in theseprocesses. To this end, the first comprehensive literature review of the selectivityissue in industrial chlor-alkali and sodium chlorate production has been carriedout as a part of the present thesis project[1]. As the review discusses the presentknowledge regarding the effect of anode structure and composition, electrolytecontamination, and process parameters on the selectivity in great detail, the readeris advised to read the Discussion section of that review for a thorough discussionof these aspects. A brief overview will still be provided in Section 1.2 of this

1.1. STATE OF THE ART ELECTRODES 5

chapter. Based on the findings in the review, the selectivity issue in the chlorateand chlor-alkali processes has been investigated in a broader sense, by perform-ing also studies of how electrolyte contamination affects the decomposition ofhypochlorite[14]. Still, a main focus has been put on the influence of electrodestructure and composition[15–20], and I will therefore summarize the present sta-tus of anodes in chlor-alkali and sodium chlorate production and of activated cath-odes for HER in Section 1.1. I have made use of first principles modeling to gaina further understanding of the connection between composition, activity and se-lectivity, and to clarify the connection between experimental X-ray photoelectronspectroscopic (XPS) results and the actual electrode structure. As the applicationof such theoretical methods to problems in heterogeneous (electro)catalysis andmaterials science is recent, Chapter 2 contains a thorough overview of these meth-ods, and their application in the study of solid materials, (electro)catalysis andX-ray photoelectron spectroscopy. Experimental methods employed in this thesisare reviewed in Chapter 3. The results are presented and discussed in Chapter 4,and some conclusions and an outlook for future work is presented in Chapter 5.

1.1 The state of the art of electrodes used for the in-organic electrosynthesis of chlorine, sodium chlo-rate and hydrogen

1.1.1 Anodes for chlor-alkali and sodium chlorate production

As has already been mentioned, DSA are used for the oxidation of Cl– in bothprocesses. Dimensionally stable anodes were invented by Henri Beer in the 1950-1960s[21]. Previously, graphite anodes had been applied, but these electrodes wereconsumed during use, requiring frequent adjustment of the anode position. Beerrealized that since titanium forms a highly corrosion-resistant TiO2 oxide layerwhen used as an anode, it could be used as a stable anode support material inchlor-alkali electrolysis[22]. The current DSA coating developed in several steps.First, Beer suggested that deposition of noble metals onto titanium should serve toactivate the anode. If a part of the active coating would be removed from the sur-face, the anode would not be destroyed since corrosion-resistant TiO2 would form.Beer tried depositing noble metals, such as platinum, on the surface of titanium,to activate the electrode, and patented the procedure[23]. However, the stability ofthis coating was found to be insufficient during industrial testing[21, 22, 24]. As anext step, the deposition method was changed from electrodeposition to a methodconsisting of painting a noble metal salt solution onto titanium. The painted ti-tanium was then heated in air at temperatures between 400−500 ◦C, convertingthe salt into what was thought to be metallic form. Different coating solutions,


containing e.g. platinum, ruthenium, iridium and rhodium were in this way ap-plied on titanium. This change took place in the early 1960s. One coating whichwas frequently used was a mixture of 70% platinum and 30% iridium. This metalcombination had actually been known to be stable in these processes already sincethe early 1900s[25]. Except for coatings containing platinum, the heating proce-dure that was used to prepare such coated titanium anodes actually converted thenoble metal into metal oxide form. Electrodes with this coating were preferableto the old graphite electrodes and to platinum coatings, but the anodes were stillnot stable enough in the mercury cell process. Furthermore, the prices of irid-ium and platinum were also high in comparison with other noble metals, such asruthenium[21, 26]. By the middle of the 1960s, Beer proposed that a coating ofruthenium oxide could be preferable to the Pt/Ir coating. It was eventually foundthat mixing a platinum-group metal (PGM) oxide with a film-forming metal oxidecould create a mixed oxide with improved stability. The mixture that was mostpromising was that of ruthenium oxide and titanium oxide[21].The first metal oxide patent, for a coating of 50% ruthenium oxide and 50% ti-tanium oxide was filed by Beer in 1965 (“Beer 1”)[27]. Anodes coated with thismixture were claimed to be more durable in mercury cell processes and to have astronger adhesion of the coating layer to the titanium. Two years later, a secondpatent was filed (“Beer 2”)[28]. It introduced that the coating should be made upof 30% RuO2 and 70% TiO2. This combination had several advantageous proper-ties. It gave a high activity and was well suited for use in chlor-alkali and chlorateproduction. The usage of 70% titanium dioxide in the coating reduced the priceof the coating. Furthermore, the mixed oxide of ruthenium oxide and titanium ox-ide showed a high stability, enabling operation at higher temperatures and currentdensities compared with those possible when using graphite electrodes. Titaniumoxide has a low electric conductivity but, in the mixed oxide, RuO2 increases theelectric conductivity of the coating. Another important advantage, especially ofthe Beer 2 combination, is that the selectivity for chlorine evolution over oxygenformation is increased when the ruthenium amount in the coating is decreased[29–35]. Combined with the self-healing properties of the supporting titanium material,these properties made the “Beer 2” DSA a great step forward in anode technologyfor the chlor-alkali and chlorate industries.[1, 21, 22, 26, 36]The “Beer 2” DSA is considered the standard industrial DSA composition. How-ever, electrode manufacturers usually make further modifications of the electrode,although the details of these modifications are usually kept secret. For exam-ple, coatings containing a reduced amount of ruthenium oxide replaced with tinoxide have been developed to improve the stability of the coating further. Inother coatings, some ruthenium is replaced with iridium oxide, also to improvestability.[1, 26]Nevertheless, the standard 30% RuO2 - 70% TiO2 coating has been studied in de-tail, and it is now known that it is made up of small electrode particles of rutile

1.1. STATE OF THE ART ELECTRODES 7

structure, with sizes ranging from 10 nm to 30 nm[37–39]. The particles likelyconsist of a solid solution of RuO2 and TiO2, meaning that Ti and Ru cations aremixed on the atomic scale[40–42]. On the micrometer scale, the coating has astructure similar to that of dry mud, with large cracks separating more dense areas(the “cracked mud” or “mud crack” structure)[38, 39, 43]. These cracks have beenfound to facilitate chlorine bubble detachment, resulting in improved activity[44].The nanoscale structure of the particles, specifically regarding whether any pre-ferred arrangement of Ru and Ti cations exists in the surface layer of these parti-cles, is still unknown.

1.1.2 Cathodes for HER

Today, steel or Ti cathodes are used for HER in chlorate cells[5], while Ni orRuO2-coated cathodes are used in chlor-alkali cells[3, 12]. Ni cathodes are alsoused in industrially-sized water electrolysis plants. In both chlor-alkali and waterelectrolysis, the cathode is exposed to highly concentrated caustic solutions at ahigh temperature, as this accelerates the kinetics of the process and maximizes theelectrical conductivity of the electrolyte[12, 13]. Under such conditions, Ni com-bines an acceptable activity with a sufficient stability. Nevertheless, Ni electrodesexhibit overpotentials of several 100 mV. This overpotential can be reduced signif-icantly by measures that increase the surface area of the electrode (e.g. in so-calledRaney Ni). This does not change the per-site activity of the electrode, but improvesthe activity by exposing a larger number of active sites[13]. Furthermore, RuO2deposited on Ni combines acceptable stability with a lower overpotential than thatof smooth Ni, making it an alternative to Raney Ni[3].The metal with the highest activity for HER is Pt[45, 46], but its limited stability inalkaline conditions and high cost prevents is use in industrial cells. However, an al-ternative process for water electrolysis is based on cells using polymer electrolytemembranes (PEM) similar to those used in fuel cells[12, 47]. In this case, thecathode material can be graphite, usually with Pt deposited on the graphite. Hereit is also possible to apply other activated cathode materials, e.g. sulphides, oxidesor alloys of several elements (see Trasatti [13]), that have insufficient stability inalkaline solutions. MoS2 deposited on graphite is one such material. While it hasbeen known that a variety of sulphides, including MoS2, are active for HER[13],an increased interest in this material probably originated in the theoretical study ofHinnemann et al. [48], which indicated that edge sites in MoS2 should exhibit asimilar electrocatalytic activity as Pt. This might enable electrolytic hydrogen pro-duction at lower overpotentials than those of Ni without use of noble metals. Thecorrelation between the activity of MoS2 and the edge length was experimentallyvalidated by Jaramillo et al. [49]. The details of the mechanism of HER on thismaterial is discussed in one part of the present thesis[20]. However, MoS2 has ofyet not been studied in a PEM electrolyzer, and electrolysis at industrially relevant


current densities (several kAm−2) is yet to be realized[47].As mentioned above, RuO2 deposited on Ni is used in both alkaline water electrol-ysis and chlor-alkali production[3, 13]. However, RuO2 is not thermodynamicallystable versus reduction under normal HER conditions. This has been associatedwith the decomposition of the cathode, especially under shutdown conditions[50].Indeed, Trasatti [13] points out that degradation during shutdown is actually a mainfactor limiting the stability of cathodes. Still, the degree to which RuO2 is reducedis debated in literature, with some even suggesting a bulk conversion of the oxideinto metallic form[51]. However, other studies have come to the conclusion thatthe reduction that occurs is due to incorporation of H into the coating, and thatformation of metallic Ru does not occur[52, 53]. This topic has been studied inthe present thesis, by comparing calculated XPS shifts with experimental ones ofNäslund et al. [51].

1.2 The present understanding of the selectivity inchlor-alkali and sodium chlorate production

The factors that control the selectivity between parasitic oxygen evolution and thedesired chlorine gas, or sodium chlorate, production, can essentially be dividedinto three groups: effects resulting from process parameters (including tempera-ture and concentrations of the main intermediates and reactants), effects resultingfrom contaminants in the electrolyte (such as those possibly released from theelectrodes or construction materials) and finally effects of the electrode structureand composition. In this section, only the more well-understood effects will bepresented, and a detailed discussion is provided in [1].

1.2.1 Process conditions

Overall, the effects of process conditions are likely the most well-studied, in com-parison with electrolyte impurity and electrode composition effects. The mainanodic reaction is chloride oxidation, reaction 1.1. Oxygen evolution by wateroxidation, reaction 1.8, or hypochlorite oxidation under chlorate conditions, arelikely important anodic side reactions. Electrochemical chlorate and perchlorateformation will be disregarded for the moment, as these can be controlled by keep-ing the hypochlorite or chlorate concentration at the electrode low[9].Water oxidation according to reaction 1.8 is clearly pH dependent, and this reactioncan be controlled by keeping the pH low. Furthermore, HOCl formation fromCl2 is prevented if the pH is kept low. This is the basis for anolyte acidification,which is practiced in chlor-alkali membrane cells[54]. Still, oxygen does formin industrial cells, although there is some dispute regarding which reaction (or

1.2. SELECTIVITY 9

reactions) is the main source. On the other hand, for industrial chlorate productionkeeping the pH low to control the rate of oxygen formation is not possible as anoptimal pH value between pH 6-7 exists for the homogeneous chlorate formationreaction 1.5[30, 55–58].

Furthermore, the chlorine evolution reaction is concentration dependent. Increas-ing the chloride concentration is one of the main ways (together with pH control,and as will be discussed, current density increase) that the selectivity for the de-sired products can be maximized[31, 35, 57–65]. This is due partly to improvedthermodynamics, but perhaps mainly due to increased mass transfer rates of chlo-ride to the surface as well as competitive adsorption of chlorides on the electrodesurface[62, 66].

For modern DSA, the Tafel slope is about 40 mV/decade for chlorine evolution[67],while the Tafel slope for OER has been found to be about 60 mV/dec in acidic so-lutions and ca 120 mV/dec in neutral solutions[68]. With increasing current den-sity, the overpotential for OER should thus increase more rapidly than the over-potential for ClER. A high current density should result in a high selectivity forchlorine evolution, as is indeed noted in practice[35, 43, 55, 57, 61, 62, 66, 69–72].However, the picture seems to be more complicated in chlorate production, sinceit has been found that the optimal chlorate efficiency is found close to the so-calledcritical potential, close to E = 1.4V vs SHE[73].

The effect of temperature is complex. Increasing the cell temperature increases therate of both main and parasitic reactions, and it has been connected to increasedoxygen selectivity under chlorate conditions[57, 69, 71, 72].

When it comes to concentrations of intermediates, increased hypochlorite con-centrations have been found to yield increased oxygen selectivity[57, 60, 64, 69,71, 74–77], likely due to decomposition of hypochlorite, while increasing con-centrations of chlorate have been found to yield decreased oxygen selectivity[10,57, 58, 69]. Both of these species should be avoided in chlor-alkali production,and in chlorate production the hypochlorite concentration is kept relatively low(at 1 g/dm3 to 5 g/dm3[5, 9, 10]) while the chlorate concentration is kept high(450 g/dm3 to 650 g/dm3[5, 9, 10]). However, the concentration of chlorate iskept high primarily to allow crystallization of NaClO3.

1.2.2 Electrolyte contamination

The effects of electrolyte contamination, e.g. by metals, is less well-studied. Fur-thermore, most contaminants have been studied either in pure electrolytes (e.g.including only hypochlorite species and chloride) or otherwise under conditions(e.g. temperature and concentrations) that depart from those used industrially.The main effects that have been studied revolve around competitive adsorption onthe electrode, with phosphates[58, 78, 79], sulphates[79, 80] and nitrates[78] all


having been found to result in increased rates of parasitic oxygen evolution andeffects on the decomposition rate of hypochlorite species. F– has been found toresult in decreased selectivity for oxygen[58, 78, 81], probably due to competitiveadsorption. There is likely no reason to consider F– addition to industrial cells (infact, it has been claimed that F– might lead to electrode deactivation[82]), since thesame effect most probably is achieved by increasing the chloride concentration. Ashypochlorite concentrations should be kept low in chlor-alkali production, oxygenevolution due to decomposition of hypochlorite is a less severe problem in thatprocess. The situation is more challenging in chlorate production. Co[83–91],Cu[83, 84, 90, 92, 93], Ni[83, 87–90, 92] and Ir[88, 94, 95] are all metals thathave been found to catalyze hypochlorite decomposition, and might thus lead tooxygen evolution in both processes.

1.2.3 Electrode structure and composition

The effects of electrode structure and composition can essentially be divided intotwo parts, as pointed out by Trasatti [36]: effects due to changes in electrode activesurface area (the exposed number of active sites) and actual catalytic effects. Thefirst aspect is most likely the one that is most well understood. Increasing the activesurface area, though necessary for achieving a high electrode activity, is connectedwith an increased selectivity for parasitic oxygen formation[43]. Similar effectshave been noted when decreasing coating particle sizes[96]. The effect is fun-damentally the same as that of increased current density, as an increased activesurface area results in a decreased local (per-site) current density. It is likely thatcontrol of the surface area is one aspect that electrode manufacturers make use ofalready today. Doping a pure oxide often results in increased surface area[97, 98],but not necessarily in clear changes in actual catalytic activity (such as e.g. changesin Tafel slope[13]).Nevertheless, exceptions do exist. One such case is DSA itself, where a reductionin the Ru content of the mixed oxide down to about 20 to 30 mol−% has beenfound to result in increased selectivity for chlorine evolution[29–35]. While this islikely partially an effect of the surface area also decreasing when reducing the Rucontent[97], measurements of exchange current densities and Tafel slopes for OERon RuO2-TiO2 electrodes indicate that the Tafel slope increases and the exchangecurrent density decreases as the Ru content is lowered, even at temperatures of80 ◦C[99], both in alkaline[99, 100] and acidic[32, 39, 100] solutions. While somestudies note increased Tafel slopes only below 30% Ru[99, 100], others find a moregradual increase in Tafel slopes when reducing the Ru content in the range 80 %to 20 % Ru[39]. Changes in Tafel slope reflect true electronic effects on cataly-sis, rather than surface area effects, while the exchange current density might beaffected by changes in true surface area[13]. In the case of ClER, Tafel slopeshave generally been found to be constant down to 20% Ru[100], in some cases

1.2. SELECTIVITY 11

even to less than 20% Ru at high temperature (90 ◦C)[101]. This could indicatethat the selectivity of the Ru-Ti mixed oxide, which can be likened to Ru-dopedTiO2 at lower Ru concentrations, is altered due to an electronic effect, related tocharge transfer between the Ru and Ti components. XPS measurements indeedindicate that charge transfer occurs[102, 103]. Furthermore, an increase in surfacearea does not seem to be enough by itself to account for the maintained activity ofClER (and OER) as the Ru percentage in the coating is reduced, as e.g. Burrowset al. [100] found a difference in overpotential between 80% and 20% Ru of 5 mV,while the change in overpotential according to Tafel kinetics for such a decrease inactive site numbers (if Ru is the only active site) should be more than 20 mV (seeKarlsson et al. [16]). Nevertheless, as there is a lack of experimental methods tofully account for changes in surface area when determining the activity of electro-catalysts, it is challenging to fully decouple true catalytic effects from effects ofsurface area[104].

The same problem exists in studies of other mixed oxide combinations. Severalstudies exist of selectivities of ternary Ru-Ti oxides (i.e. where an additionaldopant has been added to the coating), or of RuO2 combined with other transi-tion metals, and there are many more studies that do not examine the selectivityspecifically. For example, doping RuO2 with SnO2 has been found to result in animproved chlorine evolution selectivity[43, 77, 105, 106], and this has again beencoupled with changes in Tafel slopes[43] indicating an electronic effect.

During the past decade, a deeper understanding of the connection between elec-tronic effects and selectivity has been gained from studies using density functionaltheory. When it comes to the electrocatalysis of oxygen and chlorine evolution onoxide surfaces, the studies of Rossmeisl et al. [107] (focusing on the OER) andHansen et al. [108] (focusing on ClER and OER) are possibly the most importanttheoretical contributions since the early 1970’s. The workers found likely reac-tion mechanisms for both ClER and OER on rutile oxide surfaces through firstprinciples calculations. Furthermore, scaling relations (linear relations betweenadsorption energies of different adsorbates, e.g. intermediates in reactions[109],see Section 2.4.3) were identified that enabled the activity for both ClER and OERto be coupled to one single descriptor, the adsorption energy ∆E(Oc) of O on therutile coordinatively unsaturated site (CUS). In this way, the relative activities ofdifferent oxides could be accounted for in a single theoretical framework. Thepresent thesis will use these results as a basis for a consideration of the selectivityof mixed oxides. The results of Rossmeisl et al. [107] and Hansen et al. [108] werelater reconsidered by Exner et al.[110–113], essentially confirming their results. Aquestion that still remains regards the effect of solvation[107, 110, 114], a factorthat is challenging to account for in first principles studies. While both Rossmeislet al. [107] and Siahrostami and Vojvodic [114] found, by modeling water explic-itly, that the hydration itself should have a minor effect on activity trends for OER,Exner et al. [110] found large effects when using an implicit water model.


An additional complication when it comes to the selectivity between oxygen evo-lution and chlorine evolution in chlor-alkali production is that electrodes with de-creased oxygen selectivity have been found to instead yield increased chlorate pro-duction rates[8, 31, 56, 73, 115]. Whether this is purely a pH effect (a decreasedrate of reaction 1.8 resulting in a higher pH at the anode) or due to direct formationof chlorate at the anode is so far not known.

The electrocatalytic properties of electrodes have mostly been studied using elec-trochemical measurements of OER and ClER activities, sometimes with directmeasurements of selectivity. However, the possibility that electrodes might cat-alyze chemical decomposition of hypochlorite in the chlorate process has not beenstudied in much detail. Kuhn and Mortimer [116] suggested this possibility whenusing unpolarized RuO2 electrodes, while Kokoulina and Bunakova [63] and Ko-towski and Busse [117] did not find that unpolarized RuO2-TiO2 electrodes cat-alyzed the decomposition.

To summarize, while the connection between the active surface area of the elec-trode and the selectivity for e.g. ClER is well understood, the connection betweenthe electronic structure of the electrode material and the activity, and selectivity, islacking.

1.3 Aims

As has been made clear in the preceding sections, there are still significant gapsin the understanding of both oxygen-forming reactions in chlor-alkali and sodiumchlorate production, and of the hydrogen evolution reaction on cathodes for waterelectrolysis. The aim of this thesis has been to further the understanding of thesetechnical aspects of electrocatalysis for industrial electrosynthesis. The stability ofelectrodes has also been examined, primarily by XPS simulation to strengthen theconnection between electrode structure and deactivation processes. In this work,both experimental and theoretical methods have been applied. Some key issuesthat have been examined include:

• Why do mixed RuO2-TiO2 coatings exhibit increased chlorine evolution se-lectivity in comparison with pure RuO2?

• How are the electrochemical properties of DSAs and of TiO2 altered bydoping with other elements?

• Which materials catalyze decomposition of hypochlorite?

• Which is the mechanism of HER on Mo sulphide cathodes?

• What structural changes occur during HER on RuO2?

1.3. AIMS 13

• Can simple force fields based on Buckingham potentials be used to simulatethe structure and energetics of TiO2-RuO2 mixed oxides?


Chapter 2

Computational methods

2.1 Theoretical descriptions of matter

In the present thesis, both first principles (using density functional theory) andsemiclassical modeling (using force fields) of atoms, molecules and matter havebeen carried out. In the following sections, both types of modeling will be de-scribed in some detail, with a focus specifically on the fundamentals of first prin-ciples modeling using density functional theory. I thereby set the stage for themodeling results that are presented in the current thesis, which include an appli-cation of force fields to study mixed rutile RuO2-TiO2, and of density functionaltheory to further the understanding for the HER on RuO2 and MoS2 and for theelectrocatalytic properties of doped TiO2.

2.1.1 Force fields

2.1.1.1 Fundamentals of force fields

Force fields (FFs) based on interatomic potentials have one main advantage overfirst-principles methods in their significantly lower computational cost. They there-fore see a main application in the description of e.g. proteins and other macro-molecules. However, there are also several force fields for the description of in-organic materials, including oxides. In the present thesis, the FFs that have beenused are based on the combination of Coulombic interactions and Buckinghaminteratomic potentials with a shell model on the oxygen anions. The Coulombicinteractions describe the electrostatic contribution to the interaction, and are givenby

15

16 CHAPTER 2. COMPUTATIONAL METHODS

UCoulombi j =

qiq j

4πε0ri j, (2.1)

where the i and j indices correspond to two different ions, qi is the charge of ioni, ε0 is the vacuum permittivity and ri j is the distance between ions i and j. TheCoulombic interactions are pairwise interactions between all ions in the system,and to evaluate this efficiently in three dimensions a special Ewald summation isapplied[118]. The dipolar polarizability of the O 2p electrons is described by ashell model, in which each oxygen is modeled as being composed of a positivecore (with, in this case, a charge of +0.513) and a negative shell (with a chargeof −2.513 in the present work). The distance between the shell and the core isdetermined by an additional potential, which is simply a classical spring with acertain spring constant (k = 20.53eV/2). An additional short-ranged potential isthen added to describe bonding between ions. Several forms of this interactioncan be used, but in the present thesis the Buckingham interatomic potential, whichdescribes the interaction between O shells and Ru and Ti cores or other O shells,has been used. It has the following form

UBuckinghami j = Aexp

(−

ri j

ρ

)− C6

r6i j, (2.2)

with three adjustable parameters A, ρ and C6. The first term in the expression canbe seen as representing the repulsion between electronic densities at close range,with A giving the strength of the repulsion and ρ how far it reaches, while thesecond term is the attractive component (with C6 giving the strength of the attrac-tion). The Buckingham potentials for O-O interactions and oxygen shell modelparameters in the present thesis are the same as in the work of Bush et al. [119].A part of the present thesis has been focused on finding improved Buckinghamparameters for Ru-O and Ti-O interactions. Buckingham potentials and Coulombinteractions are radial, and thus best describe spherical ions. This is not a suit-able description for transition metals with incompletely filled d-shell, in which thenon-spherical d-orbitals play an important role. A recent improvement is the intro-duction of an additional interatomic potential based on the angular overlap model(AOM)[120, 121]. This model, which is related to ligand field theory, allows forthe simulation of the angular distribution of d orbitals. It adds two new parameters,ALF and ρLF , which determine the energies of the d orbitals (εd) according to

εd = ALF S2, (2.3)

and an additional parameter for the spin state (high or low spin) of the system.In equation 2.3, S is the overlap between a transition metal d orbital and an O2−

ligand. Thus, ALF is a scaling coefficient that describes the relationship between

2.1. THEORETICAL DESCRIPTIONS OF MATTER 17

the overlap and the d orbital energy. The ρLF parameter is used to describe theexponential distance dependence of the overlap

S = exp(−r/ρLF) . (2.4)

The AOM is described in more detail in Woodley et al. [121].

2.1.1.2 Using genetic algorithms to find the globally optimal FF

While FFs can be used to successfully model structures and properties of materi-als, a chief difficulty exists in the parametrization of the FF. Typically, this processrequires chemical insight and several attempts before yielding values that achievethe desired accuracy. This is the case even when using partially automatic meth-ods, such as those where the potential parameters are varied to minimize the forceon, e.g., the experimental structure that is used as the “target structure” for theparameters. While such deterministic methods facilitate the fitting of interatomicpotentials, they still require that the initial parameters are well chosen. Further-more, if a successful FF is not found, with this method it is not possible to makecertain that the failure is because there simply is no set of FF parameters that wouldbe successful, or if it is due to a failure on the part of the investigator in exploringthe complete parameter space.In such a situation, to make sure that the complete parameter space has beensearched, a global optimization method is needed. One such optimization methodis optimization by use of a suitably designed genetic algorithm (GA)[122]. Geneticalgorithms are similar to the Monte Carlo method[123] or the method of simulatedannealing[124, 125], both of which invoke thermodynamic arguments for explor-ing a parameter space in a way that is more efficient than a random search. As thename implies, GAs are inspired by natural evolution. The GA works in the follow-ing way. First, a number of chromosomes, e.g. in the present case an array of FFparameters, is generated randomly. These chromosomes are then evaluated usinga fitness function, which ranks the quality of all chromosomes, e.g. based on theirability to model a certain structure accurately. The fittest chromosomes are carriedover to the next generation. However, a crossover operator is usually also applied.This crossover operator combines the chromosomes with the highest fitnesses inthe population to generate a new chromosome that possibly can exceed the qualityof the “parent” chromosomes. Furthermore, a mutation operator is usually alsoapplied, which e.g. changes one value in the chromosome of a certain individualrandomly. This process is then repeated for a certain number of generations, andthe chromosome with the highest fitness after the conclusion of this process is thentaken as the globally optimal solution.Some challenges in the application of this method are immediately obvious. Firstoff, there is no guarantee that the search has converged to the actual global opti-


mum in a certain search space. There are ways to check whether the solution hasconverged close to the optimum, e.g. by repeating a certain search for more gener-ations, or by repeating it with another random seed to see if the best chromosomeis similar to the one previously found. The second problem is that there are nogood rules for how to choose the values for the parameters in the GA, e.g. whatmutation rate (how many percent of the individual chromosomes in a certain gen-eration should be mutated) or what crossover rate to use (i.e. how many of the bestindividuals should be used for crossover to generate new chromosomes). Whichparameters to use is problem-dependent. Studies exist of which GA parameters areoptimal for a certain class of problems[126, 127], but when being applied to a newproblem, several attempts with different GA parameter values are necessary. Infact, there are even methods which attempt to optimize the GA parameters whilethe GA is being used to solve a main problem, which indicates the difficulty indeciding parameters[128]. Finally, as in any global optimization method, for thesolution to be found quickly the evaluation of the fitness function must require ashort time. This is the case when applying GAs for optimization of FF parameters,as one structural relaxation using a force field based on Coulomb interactions andtwo-body potentials such as those of the Buckingham type usually requires just afew seconds on a single modern processor core.

Despite these problems, GAs have been used with success for many optimizationproblems, including the determination of low energy crystal structures[129] andfitting of parameters for force fields[130]. It is used in the present thesis to attemptto find a globally optimal force field, to describe both structural and energeticproperties of DSA, based on Buckingham potentials and the AOM model.

2.1.2 Quantum mechanics

After the discussion of semi-classical modeling of molecules and matter in the lastsection, we will now continue the discussion by focusing on quantum mechanics.This theory, which was developed to describe the behavior of small particles, suchas atoms, electrons and photons, had to also account for the wave-like characteris-tics of matter. This was achieved through the description of a particle using a wavefunction, Ψ. The wave function contains all information that can be known about asystem, such as that of electrons around atoms. For example, for the one-electronwave function, the square (or complex conjugate |Ψ|2 = Ψ∗Ψ, for complex wavefunctions) of the wave function at a certain point is the probability of finding theelectron around that point, and the integral of the square of the wave function overall space is unity (the probability of finding the electron somewhere in space is1). If matter is described as a wave, then there should be a similar kind of waveequation for matter as for waves in classical physics. The equation that was foundto describe the properties of matter is the Schrödinger equation (SE),


HΨ = EΨ, (2.5)

wherein the Hamiltonian (H) operates on the wave function to provide the en-ergy E of the wave function. H mainly appears in two forms. The first one,yielding the time-independent Schrödinger equation, describes the properties ofsystems with no external electric or magnetic fields, and systems for which rel-ativistic effects (which become important for the heavier elements) can be disre-garded . The second one, which is capable of describing such systems, is the time-dependent Schrödinger equation. In the present thesis, only the time-independentSchrödinger equation is considered.[131, 132]

The form of the Hamiltonian for the time-independent SE is the following[132]:

H =−∑i

h2

2me∇

2i −∑

k

h2

2mk∇

2k−∑

i∑k

e2Zk

rik+∑

i< j

e2

ri j+∑

k<l

e2ZkZl

rkl, (2.6)

wherein indices i and j correspond to electrons, indices k and l correspond to nu-clei, h is h/2π and h is Planck’s constant, me is the mass of the electron, mk isthe mass of nucleus k, e is the charge of an electron, Z is an atomic number andrab is the distance between two particles with indices a and b. The Hamiltoniancan thus be understood as being composed of five components: the kinetic energyof the electrons, the kinetic energy of the nuclei, the electron-nuclei attraction, theelectron-electron repulsion and the nuclei-nuclei repulsion. The Schrödinger equa-tion (or indeed, any complete equation for the interaction between three or moreparticles[133]) is analytically unsolvable for more than two interacting particles.Even a simple system such as a single water molecule is a thirteen-particle system(three nuclei and 10 electrons). It is quite clear that even the approximate solutionof the Schrödinger equation for any realistic atomic, molecular or solid system isa daunting task.

A first approximation that is essentially always made is that the wave function canbe separated into two components, one describing the energy of the electrons atfixed positions of the nuclei and one describing the energy of the nuclei. Thisassumption, known as the Born-Oppenheimer approximation, allows the motionof electrons to be decoupled from the motion of the nuclei. This assumption holdsin many cases, but fails e.g. at avoided crossings. Within the Born-Oppenheimerapproximation, the contribution to the total energy of a system can be calculatedseparately for the electronic system and the nuclei. The electronic Hamiltonianthen becomes

He =−∑i

h2

2me∇

2i −∑

i∑k

e2Zk

rik+∑

i< j

e2

ri j, (2.7)


and the electronic SE becomes

(He +VN)Ψe = EeΨe, (2.8)

where VN is the nuclear-nuclear repulsion energy, which is constant for a certainatomic geometry. This is a significant decrease in complexity, but further approxi-mations are needed to be able to simulate atoms, molecules, and solids.

Not only is the evaluation of even the electronic Hamiltonian a challenging prob-lem, the exact description of the wave functions Ψ themselves is also not obvi-ous. The SE is only able to provide the energy for a certain wave function, butsays nothing about how the correct wave function for a certain system might befound. However, it can be proven that any arbitrary trial wave function that is aneigenfunction of the electronic Hamiltonian will, through the Hamiltonian, alwaysbe associated with (or, more precisely, be the eigenfunction of) an energy that ishigher than or equal to the ground state energy E0. This implies that one can rankthe suitability of different trial wave functions by how low the associated energy is.This is the variational principle. Designing and selecting mathematical descrip-tions of the wave function with high enough variational freedom is still a topic ofresearch in quantum chemistry and physics.

The further approximations applied to enable the solution of the SE is what sepa-rates different levels of theory within quantum mechanics. Furthermore, the meth-ods can be separated into molecular orbital based methods and density functionalmethods. The first group includes methods such as Hartree-Fock (HF), Møller-Plesset perturbation theory (MP), Coupled Cluster (CC) and Configuration In-teraction (CI), ordered by increasing level of accuracy (CC and CI can achievesimilar accuracies) and cost. Density functional methods achieve a balance be-tween low computational cost and accuracy, which motivates their wide use forstudy of molecules, solids and heterogeneous reactions, the interaction betweenthe molecules and solids.

2.1.3 Density functional theory

In the electronic Hamiltonian, equation 2.8, the energy of a system is dependenton the unique positions ri = (x,y,z) of every electron in the system1. In turn, thewave function is, through the SE, a function of the interaction between every elec-tron and nucleus in the system. The strength of density functional theory is therecognition that the properties of a chemical system does not need to be describedas a function of every electronic position. Instead, the total electronic density ρ (r)(the integrated number of electrons at every point, a function of the electronic po-sitions) can be used directly. The total electronic density is a unique description

1Where not explicitly stated, the discussion in this section is based on [132, 134–141].


of a given system. This is intuitively understandable. The integral of the elec-tron density is the total number of electrons. Chemical bonds are found in areasbetween the nuclei where the electronic density is higher than that far from thenuclei. The shape of the electronic density indicates the character of the bondsand the electronic structure of the atoms. Cusps in the electronic density indicatethe positions of the nuclei. The derivative of the electronic density at a cusp in-dicates the atomic number of the nucleus. However, while the idea is simple tounderstand, the mathematical implementation is much more challenging.

2.1.3.1 The Hohenberg-Kohn theorems

Density functional theory rests upon two theorems of Hohenberg and Kohn [137].The theorems prove that there is a unique functional (a function of a function)F [ρ (r)] such that

E0 ≡ˆ

v(r)ρ (r)dr+F [ρ (r)] , (2.9)

where ρ (r) is the ground state electron density and v(r) is an external potential(the potential of the interaction between nuclei and electrons). The functionalF [ρ (r)] is thus universal and independent of v(r).[137]The second Hohenberg-Kohn theorem is a variational theorem. Since the firsttheorem proves the unique relation between a certain electronic density and anexternal potential, the density also determines an energy. Thus, upon varying thedensity, an energy that is higher than or equal to the true ground state energy isobtained. Hence, the variational principle of quantum mechanics is also applicableif the electronic density is the fundamental quantity.

2.1.3.2 The Kohn-Sham equations

The next key step in the development of density functional theory (DFT) was pre-sented in the paper by Kohn and Sham [138] in 1965[132, 134, 135, 138]. Kohnand Sham realized that the task of solving the SE within the context of densityfunctional theory could be made much simpler if one started by describing (i.e.by using the Hamiltonian for such a system) a system of non-interacting electronswith the same ground state electronic density as a real system of interacting elec-trons. The advantage now is that several of the terms in the Hamiltonian for anon-interacting system are known exactly, and can be described using expressionsfrom classical physics. The exact energy functional can then be written as

E [ρ (r)] = Tni [ρ (r)]+Vne [ρ (r)]+Vee [ρ (r)]+∆T [ρ (r)]+∆Vee [ρ (r)] (2.10)


where the first three terms are the kinetic energy of the non-interacting electrons(indicated by index ni), the nuclear-electron interaction

Vne [ρ (r)] =nuclei

∑k

ˆZk

|r− rk|ρ (r)dr, (2.11)

and the electron-electron repulsion (or rather, self-repulsion of the charge distribu-tion) in a classical picture

Vee [ρ (r)] =12

ˆ ˆρ (r)ρ (r′)|r− r′|

dr′dr, (2.12)

respectively. Vee [ρ (r)] is also known as the Hartree energy. Now, to be able toevaluate the first term, the kinetic energy of the non-interacting electrons (Tni),Kohn and Sham introduced a set of one-particle orbitals for the non-interactingelectrons. These one-particle orbitals are known as Kohn-Sham orbitals, and havethe property that

ρ (r) =N

∑i

ψi (r)∗ψi (r) =N

∑i|ψi (r) |2 (2.13)

Then one can write the one-electron kinetic energy as

Tni [ρ (r)] =N

∑i

ˆψi (r)∗

(−1

2∇

2)

ψi (r)dr. (2.14)

The last two terms of equation 2.10 are corrections to describe real interactingelectrons. The term ∆T [ρ (r)] is the correction to the kinetic energy due to theinteraction between electrons. The term ∆Vee [ρ (r)] includes all other quantummechanical corrections to the energy due to electron-electron repulsion. Thesecorrections include the energetic corrections due to

• quantum mechanical exchange interaction (interactions due to the Pauli ex-clusion principle, stating that no two electrons can have exactly the samequantum numbers)

• quantum mechanical electronic correlation (that the movement and positionof one electron is correlated with the movement and positions of all otherelectrons)

• the correction for the self-interaction energy (the classical self-repulsion en-ergy as written in equation 2.12 is non-zero even for systems of just oneelectron, i.e. the electron-electron repulsion is overestimated)


The exchange interaction correction can be calculated exactly, as is done in Hartree-Fock theory. Furthermore, the self-interaction energy is completely corrected forin Hartree-Fock theory. On the other hand, apart from a part of the same spincorrelation, most of the correlation is disregarded at the Hartree-Fock level.

To continue, the two correction terms ∆T [ρ (r)] and ∆Vee [ρ (r)] are brought to-gether into one, the so-called exchange-correlation functional Exc [ρ (r)]. Now,if the Kohn-Sham orbitals are introduced into equation 2.10, the energy can beevaluated using the following expression

E [ρ (r)] =N

∑i

ˆψi (r)∗

(−1

2∇

2)

ψi (r)dr−ˆ

ρ (r)

(nuclei

∑k

Zk

|r− rk|

)dr+

ˆρ (r)

(12

ˆρ (r′)|r− r′|

dr′)

dr+Exc [ρ (r)] (2.15)

The equations can be expressed as a set of one-electron equations

hKSi ψi (r) = εiψi (r) , i = 1,2, ...,N (2.16)

where, εi are the KS orbital energy eigenvalues and

hKSi =−1

2∇

2i −

nuclei

∑k

Zk

|ri− rk|+

ˆρ (r′)|ri− r′|

dr′+ vxc (2.17)

and vxc is the functional derivative of Exc:

vxc =δExc

δρ (r). (2.18)

The last three terms of equation 2.17 are often collected into a term known as theeffective potential, ve f f [ρ (r)], as these terms are direct functionals of the elec-tronic density, while the kinetic energy requires the Kohn-Sham orbitals. Further-more,

ˆρ (r′)|r− r′|

dr′ (2.19)

is known as the Hartree potential, vH (the functional derivative of equation 2.12 )and

nuclei

∑k

Zk

|ri− rk|(2.20)


is known as the external potential vext .

The set of all one-electron eigenvalue equations is known as the Kohn-Sham equa-tions. The set of KS equations (equation 2.16) is solved to yield the energies andwave functions (after deciding on some suitable description of the wave functions)of each one-electron orbital. Then, the ground state density can be calculated usingequation 2.13, before calculating the total energy for the interacting system usingequation 2.15.

This line of reasoning is the basis for the vast majority of all applications of DFTin electronic structure studies, and is called Kohn-Sham density functional theory.Alternative density functional theories not following the KS scheme exist, suchas reduced density matrix functional theory[134], but these methods are not ingeneral use yet.

The KS equations represent a significant simplification, as a large part of theground state energy is captured using classical expressions, while still yieldinga formally exact connection between the ground state density and the ground stateenergy, since all corrections are captured in Exc. The equations can be extended totake electronic spin into account [132], but this is not treated in further detail here.

2.1.3.3 The solution of the Kohn-Sham equations in practice

The Kohn-Sham equations are evaluated iteratively. The iterative process startswith a trial electronic density ρ (r). This density can be obtained e.g. starting fromlinear combination of atomic orbitals of all atoms in the system, as is done in theDFT code GPAW (the DFT code that has been used to obtain all results presentedin the current thesis)[142]. The next step is to calculate the part of the total energydue to the effective potential Ve f f [ρ (r)] (the last three terms of equation 2.17).Then, the KS equations are solved to yield the new KS orbitals, which in turn(using equation 2.13) yield a new electronic density. The process is then repeateduntil self-consistency in the electronic density is achieved.

2.1.3.4 Exchange-correlation functionals

Hohenberg and Kohn [137] proved that a universal functional F [ρ (r)] exists, butthe proof says nothing about how this functional might be constructed or how itmight look. The KS equations show how a part of the expression can be con-structed exactly, and placed all corrections into the exchange correlation func-tional Exc. Since 1965, a large number of different approximate Exc expressionshave been designed. This is the reason why DFT is approximate in practice, eventhough it is formally exact. One of the greatest challenges involved in DFT cal-culations is the choice of a proper Exc for the type of problem studied. A number


of papers exist where the accuracy of different functionals is benchmarked, givingsome direction in this task[143–147].Exchange-correlation functionals are generally categorized based on their depen-dence on ρ (r). The simplest group, the local density approximation (LDA) func-tionals,consists of the functionals that depend only on the local electronic densityat every point. These functionals can be described using the general expression

ELDAxc =

ˆεxc (ρ (r))ρ (r)dr (2.21)

where εxc is the exchange-correlation “energy density” per particle for a system.In practice, most LDA functionals use εxc of the homogeneous electron gas (atheoretical model system where electrons interact with a uniformly spread positivecharge yielding a completely homogeneous electronic density).The next level in Exc sophistication, and computational cost, is the group of func-tionals depending on both the electronic density and the gradient in electronic den-sity. These functionals are known as generalized gradient approximation (GGA)functionals. Some of the more well-known GGA functionals include the functionalof Perdew et al. [148] (“PBE”, widely used in physics), “BLYP” (the Becke ex-change functional [149] combined with the Lee-Yang-Parr correlation functional,widely used in chemistry) and “RPBE” (revised PBE, the Exc functional of Ham-mer et al. [150]). RPBE is of special interest for the study of heterogeneous catal-ysis as this functional was designed to yield accurate chemisorption energies, al-though at the cost of a worse description of the properties of solids. It achievesan accuracy in chemisorption energies of between 0.2 to 0.3 eV[150, 151]. Forthis reason, combined with the relatively low computational cost of DFT calcu-lations at the GGA level, RPBE has seen wide use in the study of heterogeneous(electro)catalysis[108, 152–154].The next logical step in complexity after the GGA is the inclusion of not onlythe local electronic density and its gradient (first derivative), but also the secondderivative of the electronic density (or, alternatively, the gradient in the kinetic-energy density τ (r) = ∑

occi

12 |∇ψi (r) |2). These functionals are called meta-GGA

functionals. One example is “TPSS” of Tao et al. [155]. These functionals yield,in general, a slightly improved accuracy in comparison with GGA functionals.Next is usually the combination of a correlation functional with a fraction a ofexact exchange from Hartree-Fock theory:

Exc = (1−a)EDFTxc +aEHF

x (2.22)

These functionals are known as “hybrid functionals”. The most popular DFT func-tional, B3LYP [156, 157], is a hybrid functional. While a clear improvement inaccuracy is often found when using hybrid functionals, the improvement is ob-tained at a significantly increased computational cost due to the evaluation of


HF exchange. As mentioned above in the description of the universal Exc, theexchange-correlation functional should also correct for the self-interaction errorinherent in using the classical expression for the electron density self-repulsion(equation 2.12). This is not done in most LDA, GGA or meta-GGA function-als, but the inclusion of HF exchange in hybrid functionals enables at least partialself-interaction error correction[158].

Even further increases in accuracy with more complex functionals, such as func-tionals based on the random phase approximation[159–161], are possible. Thislevel of treatment is experimental and quite computationally demanding, and isthus not in general use.

2.1.4 Approximate self-interaction correction with DFT+U

It is well known that both LDA and GGA functionals predict too small band gapsfor many materials with partially filled d− or f−orbitals, predicting that suchmaterials should be metallic conductors rather than insulators. Included in thisgroup of materials are several transition metal monoxides, e.g. NiO[162]. Thereason for this deficiency is that common LDA and GGA functionals do not fullycorrect for the self-interaction energy, and thus favor an unphysical delocalizationof the electron density[158]. An approximate way of correcting for this error is theDFT+U method, which is also known as the Hubbard-U method, where a U valueis chosen to alter the occupation of a certain set of orbitals, e.g. the d orbitals. InGPAW, when applying the DFT+U method, the total energy is evaluated as[142,162]

EDFT+U = EDFT +∑a

U2

Tr(ρa−ρaρ

a) , (2.23)

where U is the chosen Hubbard-U value, Tr is the trace operator (the sum of themain diagonal elements of a matrix) and ρa is the atomic orbital occupation matrix(e.g. the d-orbital density matrix). As discussed by Himmetoglu et al. [158], theapplication of such an energy expression results in a potential that favors integeroccupation (localization) of electrons in e.g. the d orbitals. The DFT+U methodis often applied when modeling metal oxides[163–165].

2.1.5 Quantum mechanics for periodic systems

Heterogeneous catalysis concerns reactions on the surface of a solid catalyst. Twodifferent kinds of methods are usually used for modeling surfaces: cluster-basedmethods and periodic methods.


2.1.5.1 Cluster-based methods

In cluster-based methods, the surface is modeled as a bunch of atoms (a cluster) oflarge enough size to capture the properties relevant for the study. By using a clusterof atoms in vacuum as the model, wave-function-based methods can easily beapplied. This allows for using methods such as coupled cluster, which give resultsapproaching chemical accuracy (errors of the order of kBT at room temperaturei.e. ca 0.025 eV or about 1 kcal/mol), albeit at significant cost. However, edgeeffects due to the finite size of the cluster may affect the results if not correctedfor[166]. Furthermore, for adsorption energy calculations, the state of the clustermight have to be adjusted (e.g. by saturating bonds) to yield an adsorption energythat is similar to that of a proper periodic surface[167]. For other properties, suchas the band structure and properties depending on it, convergence towards a properdescription of a solid by using larger and larger clusters is very slow[168].

2.1.5.2 Periodic methods

Periodic descriptions of a material or a surface allow the properties of a macro-scopic solid to be reproduced using a small unit cell that is repeated infinitely farin the surface-parallel dimensions. With such a model, properties of the periodicsolid, such as the complete band structure, are captured correctly at the level oftheory chosen. It is possible to make such a model by using Bloch’s theorem andBloch functions[135, 169–171]

ψik (r) = uik (r)exp(ik · r) , (2.24)

where i is a certain band index, uik (r) are functions describing the periodicity ofthe system and exp(ik · r) is a plane wave. Bloch functions are the one-electronsolutions of the Schrödinger equation in a periodic potential, such as that set up byatomic nuclei in a periodic solid. They are thus useful as eigenfunctions in periodicKS DFT. Each component of the k-vector is associated with a wave function, butunique wave functions are only found for values in the interval of−π/a≤ k≤ π/awhere a is the periodicity (lattice constant) of the cell in a certain direction ofthe reciprocal unit cell. Values of k in this range are said to describe the “firstBrillouin zone (BZ)”, which spans reciprocal space. In a linear combination ofatomic orbitals picture, each value of the k-vector describes different combinationsof atomic basis functions. These combinations cover the range from completelybonding to completely antibonding[170]. By integrating over the first BZ, proper-ties of a periodic system can be determined. One example is the electronic chargedensity[171]:

ρ (r) =1

VBZ∑

i

ˆBZ

fik|ψik (r) |2dk, (2.25)


where VBZ is the volume of the first BZ and fik is the number of electrons in stateik (the occupation number, 0 ≤ fik ≤ 1). The sum is evaluated over i bands, andthe integral over the first BZ is an integral over all k-points. Another example isthe kinetic energy, which in a periodic KS scheme can be evaluated as[135]

Ekin,s [{ψ}] = ∑i

ˆk

ˆrψ∗ik (r)

(−1

2∇

2)

ψik (r)drdk (2.26)

The range of k-points in the first BZ is of course continuous, but an integral overan infinite number of k-points (not to mention the additional sum over all i bands)is not practical to evaluate. However, one can make use of the fact that wavefunctions ψik at k-points spaced only a short distance apart in the first BZ are verysimilar. Then, the integral over all k-points can be approximated as a weighted sumover a number of k-points. Using more k-points gives an improved approximationof the integral. There are several methods that attempt to find ways of selecting(or sampling) the k-points efficiently, to reduce the number of k-points needed.One method is that of Monkhorst and Pack [172]. The number of k-points neededalso depends on the volume of the first BZ. As the BZ spans reciprocal space,an increased real space volume of a unit cell will yield a smaller BZ. Therefore,fewer k-points will be needed to yield the same spacing between points in recip-rocal space. A doubling of the real unit cell size will thus mean that half as manyk-points need to be sampled for maintained accuracy of description. However, thenumber of k-points that needs to be sampled can also be reduced by using symme-tries in the BZ. From a computational cost point of view, it is more advantageous touse more k-points rather than a larger unit cell, since the cost scales linearly withk-points but (usually) more than linearly with increasing the number of atoms.

Surfaces are commonly treated in a periodic picture. The surface is then modeledas a slab of e.g. four layers of atoms which is separated by vacuum from itsown image in the neighboring cell. Usually e.g. the bottom layers of the slabare fixed to the bulk geometry, and the number of layers of atoms in the slab ishigh enough to reach convergence in the property of interest. The slabs must beseparated by a large enough vacuum distance so that they do not interact. Thesmallest distance that can be used is found by performing several calculations withlarger and larger slab distances and seeing at which distance the property of study(e.g. an adsorption energy) no longer changes. The distance between the slabs isthen said to be converged.

Treatments based on the Bloch theorem can also be applied to study defects (suchas vacancies or interstitial atoms) in a material or on a surface. In a similar wayas when using periodic slabs to model surfaces, it is important that the unit cell ischosen to be large enough that the defect in a unit cell is located far away from itsown repeated image so that the defects do not interact, if that is the situation to bemodeled.


2.1.6 The frozen-core approximation

Chemistry is in general associated with interactions between valence orbitals inatoms. Therefore, for many purposes, calculations can be made less computation-ally demanding if the electrons in the core regions of the atoms are frozen to theconfigurations assumed in the free atom. When this is done, the full system issimulated within a frozen-core approximation. This can be achieved in many dif-ferent ways, for example by using pseudopotentials of different types (e.g., norm-conserving[173] or ultrasoft[174]), or by using projector-augmented wave (PAW)setups. These approximations differ in the accuracy that can be achieved, withPAW setups in general achieving a higher accuracy than e.g., pseudopotentials[175].However, what is common in all practical implementations of the frozen-core ap-proximation is that only the orbitals that are unimportant for the property understudy should be kept frozen. The choice of which electrons to keep in the frozencore must be made based on careful benchmarking versus chemical and physicalproperties.

The PAW description will now be explained in more detail, as it is used for thefrozen core in GPAW. Although the PAW method can be extended beyond a frozen-core description[176], it is only used as such in GPAW. A key advantage with thePAW description is that smooth functions (called pseudo wave functions, ψn (r))can be used in regions outside the atomic cores, while the orbitals in the atomiccore are frozen and described by a pre-generated atomic setup, consisting of coreorbitals φ

a,corei . However, in contrast to pseudopotential descriptions, the all-

electron wave function (through ψn (r)) for the system is still available, and can bereconstructed using a linear transformation

ψn (r) = T ψn (r) (2.27)

where the transformation operator T is given as

T = 1+∑a

∑i

(|φ a

i 〉−⟨φ a

i

∣∣)〈pai | (2.28)

where φ ai (r) are atom-centered all-electron wave functions, φ a

i (r) are the smoothpartial wave functions corresponding to that all-electron wave function, and pa

iare projector functions characterizing the transformation from the all-electron tothe smooth description. In this notation, n is a certain band index, a is a certainatom index and i is given by the n, l and m quantum numbers. The atomic coreall-electron wave functions φ a

i (r) are calculated for the isolated atom, using acertain radial cutoff distance ra

c (defining the atomic augmentation sphere). Thevalence states are described by smooth functions (partial waves, φ a

i ), that mustagree with the all-electron (wave) functions at all distances larger than ra

c . Theprojector functions are also smooth, and one is needed for each valence state partial


wave. These parameters are determined in an atomic calculation where the atomicsetup is generated. The quality of these setups is important for the accuracy of thefinal result.[177, 178]

2.1.7 Describing the wave function: Plane waves, linear combi-nation of atomic orbitals and real-space grids

To describe the wave function in an efficient way, several different mathematicalforms can be applied. In many DFT codes used for modeling of heterogeneouscatalysis, the basis set (the combination of mathematical functions used to repre-sent the wave function) is the combination of plane waves (PWs)

χk (r) = eik·r (2.29)

with different kinetic energies, given by

E =12

k2, (2.30)

when using atomic units. The basis set is limited based on a cutoff, which is theplane wave with the highest energy that is included in the set. Higher energies areassociated with more rapid oscillations in the basis function. PWs are thus suitablefor describing periodic systems where the electronic density varies slowly, such asin a metallic solid material. However, the atomic core regions of a system arechallenging to describe using PW basis sets, as these regions are characterizedby localized and rapidly oscillating orbitals, requiring a large range of k-values.Furthermore, the singularity in the electronic density at the position of the nucleusis also hard to describe. For these reasons, PWs are used together with a frozencore described by a pseudopotential or a PAW.[134]Another common basis set is that of linear combination of atomic orbitals (LCAO).This type of basis is very common in quantum chemistry. In this type of basis set,the functions are chosen to be able to describe atomic orbitals accurately, with eachone-electron orbital being given as a sum of a number of atomic orbital functionswith different weights ai

ψ =N

∑i=1

aiφi. (2.31)

These orbitals are well suited to describe localized states, and fewer terms canbe used to accurately represent atoms or molecules than if e.g, PWs are used.Nevertheless, if diffuse atomic orbital functions are used, delocalized states canalso be described in a LCAO basis set. A common type of function used in LCAObasis set is the Gaussian, i. e., an expression including a e−ζ r2

factor. Such basissets are known as Gaussian-Type Orbital (GTO) basis sets. It is also possible to

2.2. THE THEORY OF X-RAY PHOTOELECTRON SPECTROSCOPY 31

use numerical basis sets, where the individual basis functions are represented bynumerical values on a radial grid rather than as an analytical function. The LCAOmode in GPAW makes use of numerical localized pseudo-atomic orbitals.[132,134, 179]An alternative to using a specific basis set to describe e.g. the wave functions is theusage of a three-dimensional real-space grid, where physical quantities such as e.g.the electronic density or the KS wave functions are represented by values at indi-vidual grid points[142, 180]. The accuracy in the description is then dependent onthe distance between grid points in the system. Furthermore, it is simple to paral-lelize a calculation, as e.g. the calculation of a derivative in the electronic densityis a local operation between neighboring grid points, allowing a straightforwarddivision of a whole system into smaller parts handled on different processors.GPAW[142] allows calculations to be carried out using either PW or LCAO ba-sis sets, or using real-space grids, in all three cases combined with a frozen-coredescription of the nuclei based on the PAW method.

2.2 The theory of X-ray photoelectron spectroscopy

Thus far, I have indicated that it is possible to calculate energies of atoms, moleculesand materials using density functional theory. Once the energy can be calculated,also other properties are accessible. In the current section, I will indicate howDFT can be used to calculate X-ray photoelectron spectroscopic binding energiesand chemical shifts (the difference between the binding energy and a chosen stan-dard binding energy). In this way, a direct connection between a certain structureand the chemical shift can be obtained, and this has been used to further the un-derstanding for the HER on RuO2 and MoS2 (described further in Section 4.4).X-ray photoelectron spectroscopy describes the process where a core electron ina molecule or material is ionized completely by an incoming X-ray, so that theelectron is sent out and can be detected. In experiments, the kinetic energy, givenby

Ekin = hν−EB, (2.32)

where hν is the X-ray photon energy and EB is the binding energy of the electronthat is expelled, is measured.[181]The binding energy determined in an XPS measurement is the same as the differ-ence in total energy between the ground state system (without a core-hole) and theionized system (where an electron is removed from the core region):

EB = Ecore−ionized−Eground−state (2.33)

In DFT calculations in the PAW basis, this difference between total energies isaccessible in a relatively simple way. A special PAW setup must, however, be


prepared, which includes one less electron in a certain orbital (e.g. in one of the3d orbitals of Ru if the 3d XPS binding energies of RuO2 is to be calculated).The calculation for the core-ionized system is carried out with this setup, whilethe ground state calculation is carried out with the standard setup. This methoddoes not include the effects of spin-orbit coupling, the splitting of binding energiesinto two components that occur in ionization of electrons from orbitals with a netangular momentum l (all orbitals other than s). However, chemical shifts are notexpected to be significantly affected by spin-orbit coupling.

In the present thesis, X-ray photoelectron shifts have been calculated using pe-riodic descriptions of the considered systems. To avoid unphysical interactionsbetween core-holes, periodic cell sizes of at least 13 to 15 Å were used. Moreover,the spins in the core-ionized system should be unrestricted, as the singly occupiedcore level can result in polarization of the spins, affecting the total energy.

As is the case for other properties, DFT results for binding energies and chemicalshifts do not achieve chemical accuracy. Absolute values for binding energiescalculated using DFT GGA functionals have been found to differ from experimentby up to 1 eV, depending on the functional used[182], but chemical shifts differmuch less[183].

2.3 Theoretical models for heterogeneous electrochem-ical reactions

Apart from using DFT to calculate XPS chemical shifts, I have also performedDFT calculations to model heterogeneous electrochemical reactions. In practice,theoretical studies based on DFT modeling have so far had the most success in de-scribing heterogeneous gas-solid reactions. The reason is the relative simplicity ofsuch systems compared with typical electrochemical systems. In the case of gas-solid reactions, understanding can be obtained even when a reaction is modeled asoccurring in vacuum since the interactions between molecules in the gas can beassumed small. Furthermore, the rates are controlled by temperature and pressure,which can be taken into account using well-known expressions from thermody-namics and kinetic rate theory. Another advantage is that several experimentalmethods exist that give detailed information about reactions at surfaces under vac-uum conditions.[109, 153]

Conversely, most heterogeneous electrochemical reactions occur in the interfacebetween a solid catalyst and a liquid electrolyte. The electrolyte is often a concen-trated solution, with high concentrations of one or more ionic compounds. Reac-tants in an electrochemical reaction interact strongly with other molecules close tothe surface, leading e.g. to solvation of the reactants by water. A first principles de-scription thus needs to include a description of not only the solid material and the

2.3. THEORETICAL ELECTROCHEMISTRY 33

reactant, but also of the electrolyte. To make matters even more complex, the elec-trolyte cannot be assumed to be a static conformation of molecules, but a properdescription should sample many different configurations of molecules and the en-ergetics for reactions under all such conditions. One way of attacking this problemis by kinetic Monte Carlo methods or (ab initio) molecular dynamics[184].Not only is the system itself more complicated, but the reaction is controlled notonly by temperature and pressure but also by the electrochemical potential. Thismeans that a number of different phenomena also need to be included in a model.These phenomena include the polarization of the electrodes, the charge transferbetween the surface of the electrode and the reactants and also the electric fieldformed between the two polarized electrodes. If the polarization of the electrodesis to be treated rigorously, a complete model should thus include not only a sur-face slab for a single electrode, but rather a system containing both a workingelectrode, a counter electrode and the electrolyte[152]. Upon applying a bias, theeffect of the electric field in the electrolyte between the electrodes, and thus alsothe charged double layers at the electrodes, could be simulated self-consistently.However, this would require a quite large simulation cell, beyond what is practicaltoday. Furthermore, the non-equilibrium situation with two electrodes each havinga different potential (and thus different Fermi levels) is not possible to study withconventional ab initio methods[152]. Not only is the size of the system a chal-lenge, but a method of describing the polarization and charge transfer efficientlyis still lacking[184]. Several methods of modeling the polarization of the elec-trode have been put forward, but it is not clear which offers the best compromisebetween accuracy and cost. Going back to the charge transfer process, Marcustheory is able to describe some details of outer sphere charge transfer[185], butits suitability for describing electrochemical bond formation or bond breaking hasbeen questioned.[184]To add to all these challenges, the actual structure, under polarization, of both theelectrolyte and the surface is in general not well known experimentally (althoughmethods are beginning to become available [184, 186]), as the systems are morechallenging to study experimentally as well.

2.3.1 The computational hydrogen electrode method

The method that has been applied to study electrocatalytic reactions in the presentwork is the computational hydrogen electrode (CHE) method of Nørskov et al.[152]. It is not the first attempt to model electrochemical reactions at the atomiclevel, but it is one of the simpler methods and, more importantly, has been shown tohave predictive power regarding electrocatalyst activities. It makes significant ap-proximations for the electrochemical reaction and the electrolyte, but has still beenfound to yield acceptable results that enable understanding of trends in electrocat-alytic activity. The method is based on periodic calculations, and thus allows for


G / eV

Reaction coordinate

1.37

0

U=0 V

U=1.37 V1.37 eV

1/2 Cl2 + e-

Cl*+e-

Cl-

elec

troc

hem

ical

chemical

Figure 2.1: Illustration of the CHE method at zero applied potential and at theequilibrium potential.

proper modeling of the solid catalyst. The model was first applied to the oxygenreduction reaction (ORR)[152], and this reaction will be used for sake of demon-stration here as well. The ORR was modeled using the following mechanism (an-other associative mechanism was also considered in the paper of Nørskov et al.[152], but is not included here), where * indicates an electrode surface adsorptionsite:

12

O2 +∗ −−→ O∗ (2.34)

O∗ +H++ e− −−→ HO∗ (2.35)

HO∗ +H++ e− −−→ H2O+∗ (2.36)

The binding energies of the O* and HO* intermediates can also be calculated forthe corresponding non-electrochemical conditions:

H2O+ ∗ −−→ HO∗ + 12

H2(g) (2.37)

H2O+ ∗ −−→ O∗ +H2(g) (2.38)

The model then makes the following approximations:

2.3. THEORETICAL ELECTROCHEMISTRY 35

1. The reference potential is set to that of the standard hydrogen electrode(SHE). Then, at U = 0V, 298 K, pH=0, and equilibrium between electrolyteand 1 bar of H2 in gas phase the following relation applies:

G(H++ e−

)≡ G

(12

H2

), (2.39)

which means that the free energy change for reaction 2.37 is equal to thenegative of the free energy change for reaction 2.35:

∆G2.37 = G(HO∗)+G(

12

H2

)−G(H2O)−G(∗) =

−∆G2.35 = G(HO∗)+G(H++ e−

)−G(H2O)−G(∗) . (2.40)

In the same way, the free energy change for reaction 2.38 is the same as thenegative of reactions 2.35 + 2.36:

∆G2.38 =−(∆G2.35 +∆G2.36) . (2.41)

This means that the free energies of electrochemical reaction steps, wherethe electron transfer is associated with hydrogen transfer, can be obtainedfrom the corresponding heterogeneous reactions. This is not limited to(H++ e−

), but any electrochemical reaction associated with a well known

experimental equilibrium voltage can be handled the same way. As an ex-ample, the free energy change of the electrochemical reduction of Cl2:

12

Cl2 + e− −−⇀↽−− Cl−, (2.42)

which is at equilibrium at standard conditions and U =1.37V vs SHE, canbe obtained directly from the free energy change of the associated heteroge-neous reaction

∆G = G(Cl∗)−G(∗)−G(

12

Cl2

). (2.43)

This is illustrated in Figure 2.1.

2. The electrolyte is modeled by introducing one or more monolayers (ML) ofH2O on the surface in the unit cell. In some situations, such as for rutileRuO2 (1 1 0) surfaces[107], the water layer is left out as the effect on theadsorption energies of intermediates is found to be very small[107, 114].

3. The free energy of intermediates, without applied potential, at standard statecan be calculated as

∆G = ∆Ew,water +∆ZPE−T ∆S (2.44)


where ∆Ew,water is the electronic adsorption energy, including water in thecell, ∆ZPE is the change in zero point energy from the reactant to the in-termediate state and T ∆S is the change in entropy from the reactant to theintermediate state. The expression should also include an enthalpic temper-ature correction, but this contribution is small enough to disregard in manycases2. The electronic adsorption energy of e.g. Cl* can be obtained froman ab initio calculation:

∆Ew,water = E (Cl∗)−E (∗)−E(

12

Cl2

). (2.46)

4. The effect of an applied potential U is introduced by shifting the free energyof each reaction step that involves transfer of an electron by −ne−eU (seeFigure 2.1).

5. The effect of an external electric field on the energy of adsorbates on theelectrode surface is usually neglected as the effect is small[108], but can inprinciple be included as a potential gradient extending from the surface.

6. The free energy of H+ can be calculated at pH different from 0 using thechange in free energy as a function of pH

G(pH) =−kBT ln[H+]

(2.47)

This leads to a model where free energies for electrochemical reactions can beobtained without having to explicitly model neither the polarization of the elec-trodes nor the charge transfer process. However, the method is limited to mod-eling elementary electrochemical reaction steps that are directly associated witha thermodynamic reversible potential. Still, by coupling e.g. chemical surfacereactions and electrochemical adsorption and desorption reactions, multistep pro-cesses can be studied. The advantage of not having to explicitly model polarizationor charge transfer does mean that activation energies, which can be used to obtainrate constants by use of Transition-state theory (TST)[109], cannot be calculatedfor the electrochemical steps. However, Sabatier analysis, which will be intro-duced in the next Section, is still possible based on energetics obtained from theCHE model[188]. This means that predictions regarding which catalysts should beideal for a certain reaction can still be made, but possible differences in activationenergies (and thus kinetics) are not captured fully between different electrocata-lysts.

2As an example, Peterson et al. [187] found that the enthalpic temperature correction,

∆Hcorr =

ˆ(CpdT )intermediate−

ˆ(CpdT )reactant , (2.45)

for adsorption of O on Cu (at 18.5 ◦C) was 0.015 eV, to be compared with e.g. the entropic correctionof 0.192 eV.

2.4. ELECTROCATALYSIS FROM THEORY 37

The CHE model has been applied to several systems. As mentioned, Nørskovet al. [152] applied it to studying the ORR. Their work identified that possibleimprovements in activity beyond Pt might be possible, and the work subsequentlyinspired research into new Pt3X alloys[189]. The superior activity of Pt3X alloysversus pure Pt has been verified experimentally[189–191]. This shows that theCHE method can lead to results that have practical predictive power. Rossmeislet al. used the CHE method to study the oxygen evolution reaction (OER) frommetal [192] and oxide[107] surfaces and Hansen et al. [108] used it for studyingthe chlorine evolution reaction (ClER) on rutile oxides. These studies identified aconnection between the adsorption energy of O on the rutile oxide surface and theactivities for both OER and for ClER.

To summarize, the CHE model enables reaction free energies of electrochemi-cal surface reactions to be determined using adsorption energies obtained fromstandard DFT calculations, and the results obtained have been found to comparefavorably with experiments.

2.4 Understanding of heterogeneous (electro)catalysisfrom electronic structure theory

By using the methods outlined in the preceding sections, the energetics of moleculesand materials can be evaluated accurately. It has also been indicated how the CHEmodel can be used to model the effects of electrode potential on adsorption ener-gies. In the following sections, the connection between these methods and hetero-geneous electrocatalysis will be made, and it will be described how these methodscan be used to understand activity trends of different catalysts. A more thoroughdescription can be found in the introductory textbook by Nørskov et al. [109].

2.4.1 Brønsted-Evans-Polanyi relations

The rate of a chemical reaction is determined by the activation energy for the re-action, the difference between the energy of the transition state and the energy ofthe reactants. In the Arrhenius rate expression there is also the attempt rate, butthe dominating effect is the height of the barrier. In general, then, the energy ofthe transition state needs to be determined to be able to predict the rate of a re-action. The description of how heterogeneous (electro)catalysis can be modeledhas so far only been based on reaction free energies and not on activation energies.The reason why reaction rates can be understood without calculation of activationenergies is that many reactions exhibit so-called Brønsted-Evans-Polanyi (BEP)relationships, where the activation energy of a certain reaction step is linearly de-pendent on the reaction free energy of the step itself (which can be evaluated in the


E

RCl-M

Cl*M1

Cl*M2

Cl-(aq)

Figure 2.2: A qualitative description of the relationship between the reaction en-ergy and the transition state energy for adsorption of Cl– on two different surfaces,M1 and M2. M2 binds the Cl* adsorbate more strongly than M1. ∆Ei indicate thereaction energies and ∆Ei the transition state energies. The dotted lines indicatethe energies of the initial and final states as a function of the Cl-M distance, and thefully drawn lines indicate the actual reaction paths. The transition state is found atthe avoided crossing between the initial state and the final state.

way previously described). This is not unexpected, as the energy of the transitionstate structure is also affected by the bonding to the surface in the same way asthe energies of the intermediates, as is indicated in Figure 2.2[109]. The figuregives a qualitative description of the relationship between the reaction free energyof Cl– adsorption on two different surfaces M1 and M2, where M2 binds the Cl*adsorbate more strongly. As M2 binds the Cl* adsorbate more strongly, the re-action energy is more negative, which in turn results in a lower transition stateenergy. While BEP relations have been found primarily for nonelectrochemicalheterogeneous reactions, similar relationships have also been found for electrocat-alytic reactions[193]. It is assumed that BEP-relations also exist for the OER andClER on rutile oxides, but this has not been verified thus far.

2.4.2 Sabatier analysis

As described in the previous section, the rates of heterogeneously catalyzed reac-tions, including electrocatalytic reactions, are controlled by reaction energies. Thecase of chloride oxidation via the Volmer-Heyrovski mechanism


∗+2Cl−(aq)−−→ Cl∗+e−+Cl− −−→ ∗+Cl2(g)+2e−, (2.48)

will be considered as an example. Different solid materials bind the Cl* interme-diate with different binding energies. The fundamental reason for why this is thecase has been explained using the d-band model for transition metals[109, 194],and similar models have been developed also for TM oxides[165]. To achieve ahigh reaction rate, the catalyst needs to bind the adsorbate strongly enough to sta-bilize the adsorbate sufficiently to facilitate the discharge of Cl–, but on the otherhand, if the Cl adsorbate is bound too strongly, the thermodynamic barrier for thenext step in the reaction, where the Cl adsorbate is to react with solution-phase Cl–

to form Cl2 which diffuses away from the surface, becomes too high. These con-siderations lead naturally to the Sabatier principle, which says that the activity fora certain catalyzed reaction shows a volcano-shaped dependence on the adsorptionenergy of the intermediates (as we shall see in the next section, this is also validfor multistep reactions). In other words, an optimal catalyst should exist for a cer-tain heterogeneously catalyzed reaction. As was described in the previous section,such information alone can give an understanding of both thermodynamics andkinetics (barrier heights) of a reaction[109]. The Sabatier principle is illustratedin Figure 2.3. In studies of electrocatalysis, the Sabatier principle is often used toconstruct volcano plots based on the following precondition for activity based onthe electrode potential[108]. The precondition, in this case for the ClER involvinga Cl adsorbate, is that

U >Ueq + |∆G(Cl∗) |/e (2.49)

for the catalyst to become active (if the precondition is fulfilled, the reaction freeenergy, ∆Gr, of each elementary reaction step is negative). In equation 2.49, U isthe electrode potential, Ueq is the reversible electrode potential for the reaction ande is the charge of the electron. The expression indicates that the electrode potentialhas to be higher than the sum of the reversible potential and the potential requiredto either strengthen or weaken the surface-adsorbate bond so that the thermody-namic barrier is minimized. The optimal catalyst for the ClER involving Cl* thushas an adsorption free energy ∆G(Cl∗) = 0eV.

2.4.3 Scaling relations

The Sabatier analysis turns out to be applicable also to multistep reactions. Thereason is that, fundamentally, similar adsorbates bind the same way to a certaintype of surface (according to the same mechanism of charge transfer between ad-sorbate and surface)[108, 109, 194]. An example, relevant for the ClER on oxidesurfaces, is seen in Figure 2.4. The Figure indicates how the adsorption energiesof a number of adsorbates (including e.g. Cl) depend on the adsorption energy


Too strong binding

Too weak binding

Figure 2.3: Illustration of the Sabatier principle for the case of the ClER via a Cl*adsorbate. The optimal catalyst is the one with the Cl adsorption energy (∆E

(Cl*))

indicated by the dashed line.

of O, on the CUS of rutile oxides. It is seen that there exist linear scaling re-lationships between the descriptor ∆E(Oc) and the adsorption energies of otheradsorbates. The existence of such scaling relationships has been found for severaldifferent reactions (including OER on several oxides[107, 195] and ClER[108] onrutile oxides), and make it possible to describe the activity for a certain reactionbased only on a single descriptor. This is often done as in the study of Hansenet al. [108], by first modeling the stability of different surface intermediates as afunction of experimental parameters (like pH, temperature, and electrode poten-tial) and constructing a general surface Pourbaix diagram (where the most stablesurface intermediate under a certain set of conditions is assumed to be the domi-nating one on the surface) as a function of the descriptor, and then coupling thisdiagram with the precondition for activity based on the electrode potential thatwas discussed in the previous section. In this way, an overall volcano plot for bothClER and OER was constructed for rutile oxides (Figure 2.5). The volcano plotindicates the connection between a materials property that can be calculated usingDFT (∆E(Oc)), and the electrocatalytic properties (activity and selectivity) of ru-tile oxides. This connection has been used in the present thesis to understand theelectrocatalytic properties of doped TiO2.


1.0 2.0 3.0 4.0 5.0 6.0∆ EO∗ [eV]

-2.0

0.0

2.0

4.0

6.0

∆E

[eV

]

RuO2

TiO2

PtO2

Cl(O*)2

IrO2

O2**

Cl*

ClO*

Cl@O*

Figure 2.4: The scaling relations for Cl-containing intermediates on rutile oxidesurfaces, from the study of Hansen et al. [108]. Figure reproduced from Hansenet al. [108] with permission of the PCCP Owner Societies.


0 1 2 3 4 5∆ E (Oc) [eV]

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

U[V

]

Oc

OHc or Clcc

Occ2 RuO2

IrO2

PtO2

Cl2 evolutionO2 evolution

Figure 2.5: The volcano plot for OER and ClER on rutile oxides of Hansen et al.[108]. The dashed and dotted lines enclose areas where either oxygen evolution(blue dashes) or chlorine evolution (black dots) is thermodynamically possible ac-cording to the precondition for activity (e.g. equation 2.49 for Cl2). However,unless the surface intermediate involved in a reaction is prevalent on the surface,the reaction rate is predicted to be low. The thick black line encloses areas wherethe chlorine evolution rate is predicted to become significant, since the precondi-tion for activity is fulfilled and the intermediate involved in the reaction is prevalenton the surface. Figure reproduced from Hansen et al. [108] with permission of thePCCP Owner Societies.

Chapter 3

Experimental methods

The current section gives a brief overview of the experimental methods applied inthe present thesis. Further details are found in Hummelgård et al. [15] (paper 1)and Sandin et al. [14] (paper 4).

3.1 Preparation of mixed oxide coatings using spin-coating

In Hummelgård et al. [15], we studied the effect of modifying a conventional DSAcoating (Ru0.3Ti0.7O2) by addition of Co to obtain a coating with 31% less Ru andthe overall composition Ru0.2Co0.1Ti0.7O2 (based on the composition of the coat-ing solution). The electrodes were prepared by depositing the coating solutiononto polished Ti discs, which were then spun at 1400 rpm on a spin-coating deviceto produce an even coating layer. Afterwards, the electrode was first dried in a fur-nace kept at 80 ◦C for 10 minutes before being calcined at 470 ◦C for 10 minutesin the same furnace. This process was either performed once, or repeated 3 or 7times, before a final calcination for 60 minutes at the highest temperature. Thisspin-coating method makes it possible to control the amount of coating solutionthat is applied in each layer. It was estimated (based on the measured weight in-crease and the concentration-weighted density of the oxide coating[196]) that thisproduced coatings with thicknesses of 0.5 µm, 1.45 µm or 3.4 µm. The coating wasthen characterized by use of atomic force microscopy (AFM), scanning electronmicroscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction(XRD) and differential scanning calorimetry (DSC) as well as by electrochemicalmeasurements.

43

44 CHAPTER 3. EXPERIMENTAL METHODS

3.2 Electrochemical measurements

3.2.1 Cyclic voltammetry

In the study of Hummelgård et al. [15] cyclic voltammetry (CV) was used bothfor the quantification of the electrochemically active surface area (q∗) and to gainfurther information about the processes ongoing on the electrode at different po-tentials. For metal oxide electrodes, the voltammogram is characterized by thepresence of broad diffuse peaks and thus cannot give the same understanding ofthe surface reactions as is possible e.g. for metallic Pt[197]. However, the determi-nation of q∗ based on the CV is a standard measurement in electrochemical studiesof metal oxide electrodes. In the present work, the q∗ is determined by measuringthe CV between two end potentials, and then integrating the current over time toobtain a positive and a negative charge. The average absolute value of these twocharges is used as q∗. In turn, this charge is related to the real surface area of theelectrode[97]. However, the connection is nontrivial for mixed oxide electrodes,and q∗ is mainly utilized to compare the surface areas between different electrodes,rather than to obtain an absolute value of the surface area in e.g. m2/g.

3.2.2 Galvanostatic polarization curve measurements

In the study of Hummelgård et al. [15], we measured polarization curves (electrodepotential plotted versus the logarithm of the applied current density, j) for mixedoxide electrodes. The slope of this curve is the Tafel slope. For industrial synthesis,it is important that the Tafel slope is minimized, since high production rates at highcurrent densities then become achievable at a low total electrode voltage and totalapplied power.

While polarization curves at low applied current densities can be measured with arelatively simple three-electrode setup, the high current densities relevant for in-dustrial electrosynthesis (i.e. several kiloamperes per square meter) require controlof primarily two factors: the control of mass transport of reactants and productsand accurate correction for the effect of the resistance of the electrolyte on themeasured electrode potential.

In the present work, the first factor is controlled by using rotating discs as elec-trodes. These discs can be rotated at high rotation rates (several thousand rotationsper minute), which allows for a controlled rate of mass transfer to the surface ofthe electrode.[197]

Generally, to reduce the impact of the electrolyte resistance, a Luggin capillary isemployed to position the reference electrode close to the surface of the workingelectrode. However, at high current densities, the potential gradient between theopening of the Luggin capillary and the electrode surface becomes too high, pre-

3.2. ELECTROCHEMICAL MEASUREMENTS 45

venting precise measurements of the electrode potential. This potential gradientis known as the IR drop. The IR drop in the electrolyte will cause the measuredelectrode potential to differ from that associated with the surface reaction alone.Therefore, the IR drop has to be corrected for. In the present thesis, the current in-terrupt method was used to correct for the electrolyte IR-drop. The method utilizesthe fact that the voltage component associated with the electrical resistance of theelectrolyte will disappear immediately once the electrical current is switched off.However, the electrode potential will attain a new value more slowly, as the poten-tial decay of the electrode is associated with the conversion of surface species. Thismeans that if the electrode potential is followed after the current is interrupted, thetransient potential decay of the electrode can be recorded and used to determine theelectrode potential just after the current has switched off. This electrode potentialis the IR-corrected electrode potential.If the perfect equipment for analysis of this potential decay were available, a com-plete transient might be measured, and the value just after the current is turnedoff would be measured precisely. However, in practice, the time resolution of theinstrument is often a limiting factor. For potential decay on oxide electrodes suchas DSA, the potential decay occurs over several tens of microseconds, and it isin general not possible to obtain accurate measurements of this decay during thefirst few microseconds. This is mainly associated with the delayed response of thereference electrode used. To reduce this time-lag, a dual-reference electrode setupwas used in the present work. The additional reference electrode was a Pt wireimmersed in the electrolyte, and connected in series with a capacitor. In turn, thePt wire and capacitor were connected in parallel with the reference electrode. Theresponse of the Pt wire then dominates during the first few microseconds[198]. Inthe present work, it was found that this allows a stable signal to be read after ca 4 µsto 5 µs rather than after 10 µs without the dual reference electrode setup. Further-more, to reduce the noise in the measurements, the mean value of several transients(between 24 and 72), measured upon interruption at the same current density, wasused. Between each interruption, the electrode was polarized for several ms, tomake sure that each transient would be measured under the same conditions. Nev-ertheless, the electrode potential just after the interruption of the current is still notmeasured, so some type of fitting must be used to obtain an expression that canyield the potential at t = 0s. In the present work, the expression due to Morley andWetmore [199] was used:

E (t) = E (t = 0)−b× ln(

1+tτ

). (3.1)

In this expression, E (t = 0) is the IR-corrected potential, b is the Tafel slope ofthe reaction occurring during the potential decay and τ is a constant expressed by

τ =bCj, (3.2)

46 CHAPTER 3. EXPERIMENTAL METHODS

where j is the applied current density and C the capacitance (likely made up mostlyby the pseudocapacitance, but with a lesser contribution from the double layer ca-pacitance, on oxides such as RuO2[200]). To obtain an IR-corrected electrode po-tential using this expression, equation 3.1 is fitted to the mean transient recordedafter interruption of the current at a certain current density, using non-linear fitting.However, it is also possible to use more simple types of expressions, such as poly-nomials, and it is even possible to use the first accurately measured potential as anapproximation to the true IR-corrected potential. This was acceptable especiallyat lower current densities ( j < 1kA/m2).

3.3 Combined determination of gas-phase and liquid-phase compositions during hypochlorite decom-position using mass spectrometry and ion chro-matography

A goal of the study of Sandin et al. [14] was to quantify important products dur-ing the chemical decomposition of hypochlorite species. The measurements werecarried out in a system where time-resolved compositions of both the liquid phaseand gas phase could be determined, by using ionic chromatography (IC) and massspectrometry (MS), respectively. The pH of the solution was controlled automat-ically in the range of 5 to 10.5, and the temperature was kept at 80 ◦C. The pHcontrol afforded by our experimental setup allowed a detailed study of the effectof pH on the rate of both uncatalyzed chlorate formation and uncatalyzed oxygenformation. In contrast with industrial chlorate production, the ionic strength of thesolution was lower, but the NaOCl concentration of 80 mM (6 g/dm3) was similarto the industrial concentration. An equimolar amount of Cl– was also present inthe solution.

Chapter 4

Results and discussion

4.1 Cobalt-doped Ruthenium-Titanium dioxide elec-trocatalysts

As has been mentioned, in the study of Hummelgård et al. [15], Co-doped RuO2-TiO2 coatings were characterized using both non-electrochemical and electrochem-ical measurements. Only rutile peaks were found in the XRD spectra, indicatingthat the Co component was either present as an amorphous phase, or as a compo-nent in the rutile lattice. The second explanation is perhaps more likely consideringthe high crystallinity of the film indicated by the XRD spectrum. The later theo-retical study of Karlsson et al. [17] indicated that it should be possible to dopeCo into the rutile lattice of TiO2. Moreover, it was found that the Co-doped RTOcoatings had increased crack densities, mainly for the thinnest coating. Further-more, the grain size, 10 nm, (estimated using the Scherrer equation1[201]) of theCo-doped coating was smaller, than the 20 nm of the RTO coating. Both the in-creased crack density and the decrease in particle size are indicative of increasedstrain in the coating due to lattice mismatch between the CoOx component and theRu-Ti oxide component (RuO2 and TiO2 having very similar lattice dimensions).The difference in particle size resulted in differences in q∗, indicating that the Co-

1The Scherrer equation is written as

L =Kλ

β cosθ, (4.1)

where L is the mean size of the particle, β is the width at half-maximum intensity of the peak (e.g. the(110) XRD peak at approximately 2θ =28° observed in RTO) and K has a value of approximately 1.This empirical expression gives a relationship between particle size and diffraction peak width, basedon the observation that X-ray beams diffracted through randomly oriented crystals become increasinglybroadened as the crystal particle sizes decrease.

47

48 CHAPTER 4. RESULTS AND DISCUSSION

Figure 4.1: The effect on q∗ of the number of coating layers and of Co-doping forRuxTi1–xO2 coatings in the study of Hummelgård et al. [15].

doped RTO had an increased electrochemically active surface area. Furthermore,q∗ also increased with the number of coating layers applied (Figure 4.1).

Anodic polarization curve measurements were conducted in 5 M NaCl and ca-thodic polarization curve measurements in 1 M NaOH (Figure 4.2). Both typesof coatings exhibited similar kinetic parameters, with Tafel slopes close to typicalvalues for RTO and RuO2. The Co-doped coatings exhibited lower overpotentialsat the higher current densities. This was found to be related to the higher q∗ ofthese coatings, which decreases the local current density, and thus the electrodepotential, at a certain total current density. These results show one way that mod-ification of the coating by doping can be used to alter the amount of electricalenergy needed for chlorine or hydrogen evolution. Additionally, Co is a much lessexpensive noble metal than Ru, and the study thus indicates a way that DSAs canbe made using less expensive materials. While no selectivity measurements wereperformed in the study, it is likely that the Co-doped coatings would have exhibiteda lower Cl2 selectivity due to the increased surface area[1]. However, the electrodewould likely be less suitable for chlorate production, as Co is a well-known cata-lyst for decomposition of HOCl/OCl– to form O2[1].

4.2 The selectivity between chlorine and oxygen inchlor-alkali and sodium chlorate production

4.2.1 The uncatalyzed and catalyzed decomposition of hypochlo-rite species

In the study of Sandin et al. [14], we have investigated the kinetics for both uncat-alyzed and catalyzed decomposition of hypochlorous acid species, for the reaction

4.2. SELECTIVITY BETWEEN CL2 AND O2 49

E/VvsAg/AgCl[sat.KCl]

1.04

1.06

1.08

1.1

1.12

1.14

1.16

1.18

1.2

j / Am-2

1 10 100 1000

7 layers, no Co7 layers, Co3 layers, no Co3 layers, Co1 layer,no Co1 layer,Co

Number of layers

(a) Anodic polarization curves.

E/ V

vs

Hg/

HgO

(1M

KO

H)

−1.4

−1.3

−1.2

−1.1

−1

−0.9

-j / Am-2

1 10 100 1000

7 layers, no Co7 layers, Co3 layers, no Co3 layers, Co1 layer, no Co1 layer, Co

Number of layers

(b) Cathodic polarization curves.

Figure 4.2: Polarization curves for Co-doped and undoped RTO coatings withdifferent numbers of applied layers.


0 20 40 60 80 1000

20

40

60

80

100

time / min

Ci /

mM

ClO

3

− Calculated

CH

Calculated

ClO3

− Data

CH

Data

Figure 4.3: The overall rates of hypochlorous acid species decomposition andsodium chlorate formation, together with third-order rate expressions using fit-ted rate constants. cH is the total hypochlorous acid species concentration (cH =cHOCl + cOCl–) as determined using IC. Reprinted with permission from Sandinet al. [14]. Copyright 2015 American Chemical Society.

pathway resulting in oxygen formation and the pathway resulting in chlorate for-mation. A limited study of the effect of the ionic strength was carried out, whereit was found that increasing the NaCl concentration to 2.7 M had no effect on theuncatalyzed rate of oxygen formation.

Focusing first on the uncatalyzed reactions, the overall rate of hypochlorite decom-position was found to be described by the following third-order rate equation:

r =−k [HOCl]2 [OCl–] . (4.2)

The value of k was found to be (2.39±0.12)M−2s−1 in agreement with the valueobtained by Knibbs and Palfreeman [75]. The third-order rate constant for chlo-rate formation was found to be (0.731±0.035)M−2s−1. The agreement betweendata and the third-order rate equations is seen in Figure 4.3. Surprisingly, it wasfound that also the uncatalyzed oxygen formation reaction was best described us-ing a third-order rate expression, as can be seen in Figure 4.5. It was found thatboth chlorate formation and uncatalyzed oxygen formation exhibit rate maxima atapproximately the same pH (Figure 4.4), indicating that both HOCl and OCl– arereactants in both reactions.

These similarities in the pH dependence and reaction orders indicate a possibleconnection between the reactions resulting in oxygen and chlorate formation. Thiswas first suggested for alkaline conditions by Lister and Petterson [202]. Adamet al. [203] proposed a mechanism for the decomposition reaction in the pH range5-8 involving formation of first Cl2O:

2 HOCl Cl2O · H2O (4.3)


pH4 5 6 7 8 9

FO

2m

ax

/ m

M·m

in-1

0

0.02

0.04

0.06

0.08

0.1

0.12

pH4 5 6 7 8 9

Ri,C

lO3- /

mM

·m

in-1

0

1

2

3

4

a)

b)

Figure 4.4: a) The maximum rates of uncatalyzed oxygen (estimated based onflow of oxygen at the MS detector) and b) chlorate formation (based on the initialrate). Both processes have similar pH dependence, signaling a possible connectionbetween the two reaction pathways. Reprinted with permission from Sandin et al.[14]. Copyright 2015 American Chemical Society.

0 20 40 60 800

0.5

1

time / min

CO

2

/ m

M

3rd

order

2nd

order

Data average

Figure 4.5: The experimental data for accumulated oxygen (per electrolyte vol-ume) together with fitted second- and third-order rate expressions indicating thata third-order rate expression is a better description of the data. Reprinted withpermission from Sandin et al. [14]. Copyright 2015 American Chemical Society.


and then formation of HCl2O –2 or H2Cl2O2 according to

OCl– + Cl2O · H2O HOCl + HCl2O –2 (4.4)

or

HOCl + Cl2O · H2O HOCl + H2Cl2O2 (4.5)

The formation of the HCl2O –2 or H2Cl2O2 intermediates is third order with re-

spect to hypochlorite according to the reactions above. As the uncatalyzed oxygenevolution rate could be described as third order with respect to hypochlorite, theformation the intermediate is possibly the rate determining step also for oxygenformation. Adam et al. [203] then proposed a number of reaction steps throughwhich ClO –

3 might form. In general agreement with the suggestion of Lister andPetterson [202], we propose that a small amount of the HCl2O –

2 or H2Cl2O2 inter-mediate might instead be decomposed to form oxygen, in a pathway with a lowerrate than the main chlorate-forming reaction.Additionally, a variety of potential catalysts for the decomposition of hypochlo-rite were evaluated, including AgCl, Al2O3, CeCl3 · 7 H2O, CoCl2, Fe3O4, FeCl3· 6 H2O, IrCl3 · xH2O, Na2Cr2O7 · 2 H2O, Na2Mo4 · 2 H2O, RuCl3 · xH2O and RuO2· xH2O. The amounts of the potential catalysts were chosen to achieve a solutionconcentration of 10 µM, except for the solid materials AgCl (100 ppm) and Al2O3(9 ppm). Of these materials, only CoCl3 and IrCl3 · xH2O were active catalysts foroxygen formation by hypochlorite decomposition, with the Ir compound also be-ing a catalyst for chlorate formation. Both materials precipitated upon addition tothe electrolyte, indicating that the effects might be due to heterogeneous reactions.Co was found to be an active catalyst for oxygen formation at pH 3, 6.5 and 10.5.The effect of iridium chloride addition was dependent on pH, with the selectivityfor chlorate formation being higher at pH 10.5 than at pH 6.5. Furthermore, thebehavior of the oxygen evolution rate at both pH 6.5 and 10.5 indicates a possibleconnection between the selectivity and activity and an Ir redox reaction such as thefollowing,

IrO2 + 2 H2O IrO 2–4 + 4 H+ + 2 e , (4.6)

which would be controlled both by pH and the oxidative potential of the elec-trolyte. Further work on the properties of Ir as a potential chlorate catalyst iswarranted. Neither the Ru chloride nor RuO2 was active for hypochlorite decom-position. This indicates that heterogeneous decomposition of hypochlorite on in-dustrial electrodes might not be an important source of oxygen in industrial chlo-rate production. Nevertheless, as both concentrations of NaCl and NaClO3 weremuch lower than in the industrial process, further experimental work under moreprocess-like conditions is necessary to draw a final conclusion.


4.2.2 Theoretical studies of the connection between oxide com-position and ClER and OER activity and selectivity

4.2.2.1 Computational details

We have performed a fundamental study of the effect on electrocatalytic propertiesof doping TiO2 with both conventional dopants such as Ru or Ir, and also 36 otherdopants, including all fourth, fifth and sixth-row transition metals[17]. A deeperstudy was performed of the TiO2-RuO2 mixed oxide[16]. In both cases, DFT onthe RPBE-level[150] was used to calculate the adsorption energy of O on the CUS:

∆E(Oc) = E (Oc)−E (c)−E(H2O)+E (H2) , (4.7)

This adsorption energy has been found to serve as a descriptor for both OER andClER[108], meaning that this adsorption energy can be used, together with the vol-cano plot of Hansen et al. [108] (Figure 2.5), to predict the activity and selectivityof different rutile oxide materials for ClER and OER. The selectivity was evalu-ated based on the difference between the electrode potential U required for OERand the one required for ClER, for a certain material. We considered both binaryand ternary combinations of TiO2 and other oxide materials, as well as the distancedependence of the effects. This was done by calculating ∆E(Oc) with one or twodopants placed into a unit cell with 8 cations (in the binary systems) or either 8or 16 cations (in the ternary systems). The positions in the 8 cation-cell wheredopants could be placed are indicated in Figure 4.6, where the three-dimensionalstructure of the surface is also indicated.

4.2.2.2 The self-interaction error

A key challenge in modeling mixed oxide materials is the self-interaction error(SIE), which is related to the failure of presently available density functionals tocompletely correct for the classical self-interaction (see Section 2.1.3.2). This errorcauses the electronic density to delocalize in an unphysical way, and this is a partic-ular problem for the description of dopants and defects[159, 164, 204]. The mostpopular way of correcting for this error in theoretical studies of (electro)catalysisis the Hubbard-U method, where the energy of the d orbitals of different atomsin the solid are altered to describe the electronic density correctly. However, thismethod is usually applied in a non-self-consistent manner, where the U value isdetermined in some way and then kept constant during calculation of e.g. adsorp-tion energies. Two main methods of determining the U involve either fitting thevalue to recover some experimental thermochemical data[165, 205, 206], or fittingthe value to recover the correct curvature of the total energy with changes in thenumber of electrons in a system (the so-called linear response U[207–210]). Still,in neither of these methods does the resulting U value correct the description of


O

Ti

Ru

1cus 1br 2a 2b

Oc

Oc

a b

3a 3b 4a 4b

Figure 4.6: a) The model systems studied, as well as the different positions wherethe dopant could be placed in the studies of Karlsson et al.[16, 17]. b) A three-dimensional image of the (110) surface of an Ru-doped TiO2-slab.

all physical properties, and it has been found that the U-value needed to e.g. cor-rect the band gap of a material might be too high to recover the correct enthalpyof formation of the material[165]. Furthermore, it is not straightforward to de-termine which orbitals should be altered with a U-value[209]. It is possible that amethod where the U-value is determined self-consistently using the linear responsemethod[207], at every step in e.g. a relaxation calculation, and for all orbitals out-side of the frozen core, might correct for these deficiencies, but this is not practicedat present. There are other methods that might approach chemically accurate en-ergies (energies with an error of less than 1–2 kcal/mol≈0.04–0.08 eV), includingcalculations where the exchange energy is evaluated exactly using the Kohn-Shamorbitals (EXX) and the correlation energy is evaluated using the random-phaseapproximation (RPA)[211] and quantum Monte Carlo (QMC)[212], but both ofthese methods are presently too computationally demanding to be used in screen-ing studies.

In the present studies[16, 17], we have used the Hubbard+U method, applied on3d or 4d states of either dopants, Ti cations, or both, to ascertain the importance ofa partial SIE correction. For the RuO2-TiO2-system, we first found that as long asspin polarization is neglected, which is acceptable for nonmagnetic materials suchas DSA, the addition of a U value, in the range of 1 eV to 6 eV, on the Ti d statesresulted in only minor effects on adsorption energies[16]. However, in the later


Sc Y Ti Zr Hf V Nb Ta Cr

Mo W Mn

Re Fe Ru

Os

Co Rh Ir Ni

Pd Pt Cu

Ag Au Zn Cd

Hg

Ga In Tl Ge Sn Pb As Sb Bi Se Te

dopant in 1br

4

3

2

1

0

1

2

3

4

∆E

(Oc) U−

∆E

(Oc) U

=0 /

eV

U = 2 eV on TiU = 2 eV on Ti and dopantU = 2 eV on dopant

Figure 4.7: The effect of Hubbard U on the adsorption energy of O.

screening study[17], several dopants which are often associated with magnetism(including Fe, Co and Mn) were included, and all calculations were therefore spinpolarized. We then studied the effect of applying a U = 2eV, similar in magnitudeto the optimal found by García-Mota et al. [165], to either dopants, Ti or all d-states. The effect was here found to be larger for some dopants, see Figure 4.7.The largest effects of applying a U were seen for Sc, Y, Cu, Cd, and Hg. ForCd and Hg, the effect was associated with an instability of the dopant in the TiO2structure. This is seen in Figure 4.8, where the distance between the surface CUSsite and the second layer 2a site for a doped TiO2 (see Figure 4.6) is compared withthe same distance in pure TiO2. In fact, Hg was unstable as a dopant regardlessof the U value. However, the large effects of U on the adsorption energies onSc- or Y-doped TiO2 do not appear to be associated with a change in structure. Ithas been found previously that keeping a high enough number of electrons in thevalence (outside the frozen core) is necessary to achieve accurate results for theseatoms[213, 214], but the adsorption energies were hardly affected by repeating thecalculations with a setup that had a smaller frozen core. The results for these twodopants are thus hard to rationalize. For Cu, it is possible that altering the energyof the d-states has a large effect on the d-state filling, which seems to result in anartificial activation of the dopant.

For a number of dopants, including Cr, Mo, Mn, Re, Fe, Ru and Os, the applicationof a U value results in smaller changes in the adsorption energy and a weakeningof the oxygen-surface bond. The effects are similar to those noted by García-Mota


et al. [165]. The effect for a number of other dopants, such as In, Ge, Sn, Pb, As,Sb, Bi and Se, are quite small.

However, our results indicate that the application of a U =2 eV might result ina less accurate description than that obtained at the RPBE level. First off, theapplication of a U value changes the magnetic properties of the materials in away that is not expected. It is known that Co, Cr, Fe, and Mn-doped TiO2 aremagnetic[215, 216]. For the bare surfaces (without O adsorbate), both RPBE+Uand RPBE calculations predict these materials to be magnetic, while for the sur-faces with an Oc adsorbate only the RPBE-level calculations predict that the ma-terials are magnetic. At the same time, the RPBE+U calculations predict thatO-covered In- or Cd-doped surfaces should become magnetic, even though bothRPBE and RPBE+U calculations predict that bare Mn- or Fe-doped TiO2 sur-faces have the highest magnetic moments. RPBE gives a consistent descriptionof the magnetic properties, for both bare and O-covered slabs. Apart from mag-netic properties, the application of a Hubbard U results in much larger changes inadsorption energy of O for pure TiO2 than what is found by carrying out an ac-tual self-interaction correction using the method of Perdew and Zunger[204, 217](PZ-SIC). Applying a PZ-SIC when calculating the adsorption energy of O onthe (110) surface of rutile TiO2, Valdés et al. [217] found that the adsorption en-ergy was changed by only 0.03 eV. In contrast, the application of a Hubbard Uon Ti d-states results in a weakening of the adsorption energy of ca 0.3 eV, aten times larger change. It is expected that the SIE should be small for systemswith low d-orbital occupancy[218, 219], and this is reflected in the PZ-SIC re-sult, but not in the Hubbard-U result. The U that is found through linear responsecalculations[209] is about 5 eV, an even higher value than what we consideredhere. Such a high value allows the value of the band gap for TiO2 to be calculatedcorrectly, but it actually results in a much worse value for the enthalpy of formationof Ti2O3 from TiO2 (it changes the enthalpy of formation by more than 1.5 eV andchanges the sign of the formation energy)[165], and, as we indicate, it is much toohigh to be consistent with a correction for the SIE. These results, combined withthe good performance of RBPE for chemical energetics[147], lead me to concludethat the usage of RPBE without a Hubbard U correction results in more consistent(and possibly more accurate) results for adsorption energies, even for doped TiO2.I suggest that higher-level calculations, e.g. using RPA+EXX or QMC, are neededto benchmark GGA, GGA+U and hybrid DFAs before a final conclusion about theapplicability of Hubbard U methods for chemisorption energies can be made. Fi-nally, the important observation that linear scaling relations obtained at the GGAlevel are usually maintained at the GGA+U level indicates that our results shouldbe qualitatively correct regardless of the results of such a comparison[165, 209].The results presented hereafter are from calculations on the RPBE level.


Sc Y Ti Zr Hf V Nb Ta Cr

Mo W Mn

Re Fe Ru

Os

Co Rh Ir Ni

Pd Pt Cu

Ag Au Zn Cd

Hg

Ga In Tl Ge Sn Pb As Sb Bi Se Te

dopant in 1br

1

0

1

2

3

4

5

d1cu

s−2a,U−d

1cus−

2a,U

=0,T

iO2 /

U = 2 eV on TiU = 2 eV on Ti and dopantU = 2 eV on dopantWithout U

Figure 4.8: The effect of Hubbard U on the distance between the Ti cations in 1cusand 2a (see Figure 4.6a). The distance parameter, d1cus−2a, is plotted relative to thatof pure TiO2 and without an applied U , indicating deviation from the rutile surfacestructure. For most dopants, the relaxed structure is still rutile-like. Significantsystematic deviations (not depending on the chosen U) are clear for Hg. Significantdeviations are seen also for Cd when a U value is applied on the Cd dopant or whenno U value is used. For Zn and In, deviations are clear when a U value is appliedon the dopant. Ag, Au, Bi, and Te display lesser deviations regardless of U .


0.50.00.51.01.5d1cus−2a,U−d1cus−2a,U=0,TiO2

/

ScYTiZrHfV

NbTaCrMoW

MnReFeRuOsCoRh

IrNiPdPt

CuAgAuZnCdHgGa

InTl

GeSnPbAsSbBi

SeTe

Dopant as active site (1cus case)

0.5 0.0 0.5 1.0 1.5d1cus−2a,U−d1cus−2a,U=0,TiO2

/

ScYTiZrHfV

NbTaCrMoW

MnReFeRuOsCoRh

IrNiPdPt

CuAgAuZnCdHgGa

InTl

GeSnPbAsSbBi

SeTe

Ti as active site (1br case)

Figure 4.9: The distance parameter, d1cus−2a (the distance between the surfaceCUS cation and the cation in the next layer, see Figure 4.6a), plotted relative tothat of pure TiO2, when the dopant atom occupies the active CUS site (left side)and when the dopant atom occupies the surface br site (right side). Note that thepositive direction of the x axis is toward the left on the left side, and toward theright on the right side.

4.2.2.3 Results of the screening study

The stability of dopants in the rutile structure is a key concern as it will determinewhether the dopant-Ti arrangements considered here can be realized in practice. Toquantify this aspect, structural changes based on the d1cus−2a (the distance betweenthe CUS active site and the Ti cation in the next layer, see Figure 4.6a) have beencalculated and are shown in Figure 4.9. Once more, it is seen that the stabilityof Hg and Cd as dopants in rutile TiO2 is limited. However, also Pb, Tl and Yas dopants occupying the CUS site, and Te as dopant occupying the bridge sitedisplay deviations from the rutile structure of more than 0.5 Å. Still, the majorityof dopants display only minor deviations from the rutile structure, indicating that itshould be possible to form structures with dopants in the sites we have considered.

The adsorption energy results obtained from the screening are seen in Figure 4.10.Before discussing the results in detail, there are two important descriptor (∆E (Oc))


values of the volcano plot (Figure 2.5)[108] that should be kept in mind. The firstone is the optimal descriptor value for the OER, of ∆E (Oc) = 2.4eV. The activityfor ClER is also maximized at that descriptor value. The second is the descriptorvalue for maximized ClER activity and selectivity, at ∆E (Oc) = 3.2eV. There aretwo descriptor values that result in optimal activity for ClER since there are twostable surface intermediates that can result in chlorine evolution at U = 1.37eV.Figure 4.10 indicates the descriptor value for doped TiO2 with the dopant placedeither in the active site (the “1cus” case) or in the bridge site next to the active site.In the first case, the dopant is the cation in the active site, whereas in the secondcase, the active site is a Ti cation that might be activated by the nearby dopant.In the left half of Figure 4.10, it is seen that the descriptor value for a numberof dopants, including As, Mn, Co and Pd, is close to optimal for selective andactive ClER (∆E (Oc) = 3.2eV). Sb or V in the same position results in a materialwith optimal activity for OER, while Ru or Ir in that position results in a materialwith electrocatalytic properties similar to those of pure RuO2. Turning next to thesituation of dopants located next to a Ti CUS site (the right hand side of Figure4.10), it is seen that a number of dopants, including Ru, Ir, As and V all result ina descriptor value close to the optimal one for ClER. These dopants all activateTi sites. Finally, a number of dopants, including Sn, Ag and Au, hardly affect theelectrocatalytic properties of TiO2.

The surface of a real mixed oxide electrode presents a multitude of sites, withslightly varying geometry and with different arrangements of the oxide compo-nents. Some active CUS might be occupied by a dopant, and others by Ti. Thus,the overall electrocatalytic activity of a doped TiO2 material is described by thecombination of the activity of dopant CUS sites and Ti CUS sites activated bydopants. The sensitivity to dopant position can be found by comparing the de-scriptor value for the cases when the dopant occupies CUS sites or bridge sites. Asan example, on a real Ru-doped TiO2 electrode (such as a conventional DSA), RuCUS sites will exhibit a similar activity as pure RuO2, that is it will be active forboth ClER and OER. However, Ru bridge sites will activate Ti sites for optimumClER activity and selectivity. Ideally, the dopant should provide the same effectindependent of site since it is difficult to see how the dopant could be steered tothe desired site. Arsenic is thus a very interesting dopant for chlorine-evolvingelectrodes, as TiO2 doped with As should exhibit optimum ClER activity and se-lectivity regardless of whether As occupies the CUS or the bridge site.

Figure 4.10 shows that the electrocatalytic properties of TiO2 can be modified sig-nificantly by changing the dopant. Furthermore, by performing fundamental stud-ies of other electrochemical reactions on rutile oxides, it is possible that the resultsin Figure 4.10 could be applied also to understand the electrocatalytic activity ofdoped TiO2 in other reactions, such as e.g. direct hypochlorite or sodium chlorateproduction. The recent study of Viswanathan et al. [220], indicating that rutile


10123456∆E(Oc ) / eV

ScYTiZrHfV

NbTaCrMoW

MnReFeRuOsCoRh

IrNiPdPt

CuAgAuZnCdHgGa

InTl

GeSnPbAsSbBi

SeTe

Dopant as active site (1cus case)

1 0 1 2 3 4 5 6∆E(Oc ) / eV

ScYTiZrHfV

NbTaCrMoW

MnReFeRuOsCoRh

IrNiPdPt

CuAgAuZnCdHgGa

InTl

GeSnPbAsSbBi

SeTe

Ti as active site (1br case)

Figure 4.10: The descriptor value for doped TiO2, when the dopant atom occupiesthe active CUS site (left) and when the dopant activates the Ti active site (the 1brcase, right). The vertical lines correspond to (from left to right on the left-handside, and from right to left on the right-hand side) the descriptor value for pureTiO2 (thin green), the optimal descriptor value for ClER selectivity and activity(thick red), the descriptor value for maximum OER activity (thick blue) and thedescriptor value for pure RuO2 (black). The positive direction of the x axis istoward the left on the left side, and toward the right on the right side.


oxides with a descriptor value of ∆E (Oc) =3.8 to 3.9 eV2 should be selective forelectrochemical H2O2 production, is one example.

Another way of controlling the activity of TiO2 is to use more than one dopant ele-ment. Industrial DSAs often contain not only Ru and Ti, but also other componentssuch as Ir[221]. An example of the effect on the descriptor value of combining twodopants, where dopants are arranged in the same surface layer, to either side of theTi CUS, is seen in Figure 4.11. It is seen that by surrounding a Ti active CUS sitewith two dopants, the descriptor value of that site can be modified to a value that isclose to the mean value of the descriptor values of the respective binary dopant-Tioxides. In this way, two dopants can be combined to further control the activityof doped TiO2. However, how to accurately control the atomic-scale arrangementof these dopants is an open question. If dopants are simply combined in a coatingsolution that is then calcined to yield a final oxide, the final result is most likelyan oxide which exposes a variety of different active sites with different electro-catalytic activities and selectivities. New preparation methods where the atomicstructure can be controlled are needed to fully profit from the results shown inFigure 4.10.

Unless the arrangement of the oxide components is controlled on the atomic level,the dispersion of dopants in the material might be more or less random, anddopants might thus be present further down in the oxide layer rather than only inthe surface layer. Furthermore, on real electrode surfaces, the coverage of adsor-bates will vary with the process conditions of the electrolysis (e.g. current densityand reactant concentration). The effect of altering surface coverage, as well asthe effect of moving a Ru dopant further from the surface of a doped TiO2 slab,is seen in Figure 4.12. It is clear that surface coverage has a strong effect on theelectrocatalytic process. However, there are still arrangements of Ru and Ti thatresult in optimal selectivity for ClER, although the exact arrangement depends onthe surface coverage. It is also seen in the figure that Ru dopants in the secondand third layer also activate Ti surface sites, but that the effect has essentially dis-appeared once the dopant has been moved past the fourth layer. The effect is thusshort ranged, and dopants must be present in the near surface region. This trend islikely similar for the other dopants considered in Karlsson et al. [17].

We also found that this activation effect might be specific to TiO2, or possibly tooxides of cations with low d-electron numbers (such as e.g. ZrO2 or TaO2). For-mally, Ti in TiO2 is d0. A comparison between the change in descriptor value withdopant position for two oxide models, either for Ru-doped TiO2, as has alreadybeen shown in Figure 4.12, or for Ti-doped RuO2 is seen in Figure 4.13. Alsoseen in the figure is the same trend for a model system with an overall Ru:Ti stoi-chiometry close to that in DSA. The DSA model system behaves similarly to theRu-doped TiO2 system, indicating the applicability of our results also to materi-

2Heine A. Hansen, personal communication, 2015.


Pt-Ti-Ir Mo-Ti-Cu Re-Ti-Zn0

1

2

3

4

5

6

∆E

(Oc) /

eV

Average of the adsorption energies of the binary systemsCalculated adsorption energy

Figure 4.11: The effect of surrounding a Ti active site with two different dopants.The bright bars are adsorption energies estimated as the mean value of the ad-sorption energies of the two binary systems, while the dark bars are the calculatedadsorption energies on the ternary slabs. The horizontal lines correspond to (fromtop to bottom) the descriptor value for pure TiO2 (green), the optimal descriptorvalue for ClER selectivity and activity (red), the descriptor value for maximumOER activity (blue) and the descriptor value for pure RuO2 (black).


1cus 1br 2a 2b 3a 3b 4a 4bRu position

1

2

3

4

5

Elec

troni

c ad

sorp

tion

ener

gy /

eV

∆E(Oc ), 50% surface coverage∆E(Oc ), 100% surface coverageOptimal ∆E(Oc )∆E(Oc ) on pure TiO2

∆E(Oc ) on pure RuO2

Figure 4.12: The effect on the Oc adsorption energy at the CUS site of Ru-dopedTiO2. The position of the Ru atom is varied. The system is either a 1x1 system(100% surface coverage) or a 1x2 system with adsorption of O only on one CUSsite (50% surface coverage). The dashed lines for the adsorption energies on purematerials are from calculations on 1x1 surface systems. Figure reprinted fromKarlsson et al. [16], with permission from Elsevier.

als with higher concentrations of dopants near the active site. Furthermore, it isseen in the figure that while the doped TiO2 material is strongly affected by the Rudopant, the RuO2 material is hardly affected at all.

Some insight into the inherent stability of different dopant-Ti arrangements can begained by comparing the total energies of the two arrangements in Figure 4.10. Theresults are seen in Figure 4.14. It is seen that for O-covered surfaces, the situationof the dopant occupying the surface CUS site is often more stable. This indicatesthat during OER, there is a driving force for moving dopants towards the surfaceCUS. Such driving forces also exist for several of the bare surfaces. The existenceof such a driving force could be an explanation for the gradual removal of Ru fromDSA electrodes during use[222, 223]. Experimental studies have shown that thedegradation of DSAs is directly tied to the rate of OER[224–228], during which


1cus 1br 2a 2b 3a 3b 4a 4b

dopant position

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Ele

ctro

nic

adso

rpti

on e

nerg

y /

eV

∆E(Oc ) on Ru-doped TiO2

∆E(Oc ) on Ti-doped RuO2

∆E(Oc ) on DSA

Optimal ∆E(Oc )

∆E(Oc ) on pure TiO2

∆E(Oc ) on pure RuO2

Figure 4.13: Oxygen adsorption energy trends, at 100% surface coverage, as thedopant atom position is varied in Ru-doped TiO2, Ti-doped RuO2 and in the DSAmodel system. The O adsorbate is allowed to adsorb on the “1cus” site in allcases, so that adsorption occurs directly on the dopant atom only in the “1cus”case. Figure reprinted from Karlsson et al. [16], with permission from Elsevier.


2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5E(bare)1cus−E(bare)1br / eV

ScYTiZrHfV

NbTaCrMoW

MnReFeRuOsCoRh

IrNiPdPt

CuAgAuZnCdHgGa

InTl

GeSnPbAsSbBi

SeTe

Bare surfaces

2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5E(Oc )1cus−E(Oc )1br / eV

ScYTiZrHfV

NbTaCrMoW

MnReFeRuOsCoRh

IrNiPdPt

CuAgAuZnCdHgGa

InTl

GeSnPbAsSbBi

SeTe

Surfaces with O

Figure 4.14: The energy difference between the situations where the dopant occu-pies the 1cus position and the 1br position, for surfaces without O (left side) andwith O (right side). Positive values signify that the situation where the dopant oc-cupies the 1br position is more stable than the situation where the dopant occupiesthe 1cus position, indicating a driving force for movement of the dopant from the1cus to the 1br position.

Oc intermediates are present on the surface[107, 108]. The driving force duringchlorine evolution is determined by the intermediates present on the surface duringClER, such as OHc or Clc[108] for materials with a descriptor value E (Oc) >3eV. Our calculations indicate, again using Ru-doped TiO2 as an example, thatthe driving force for moving the dopant to the CUS site when these adsorbates arepresent on the surface is either very small or negative. Further studies are necessaryto fully understand the segregation of dopants in TiO2, but this indicates that it ispossible that also the other dopants considered will be stable in e.g. the bridge siteduring ClER.Finally, we used Bader charges[229] to attempt to explain the activation of Tisurface sites through dopants. The case of Ru as a dopant was again examined,and it was found that the Ru dopant transfers charge to the Ti surface site, whichallows the CUS Ti-Oc bond to become stronger.These results require experimental verification. Therefore, we also suggested amodel electrode that should be possible to manufacture using some method allow-ing atomically precise control of deposition of monolayers of atoms[16]. The twomodel systems that we suggested are seen in Figure 4.15. What we found was thatthe descriptor value (oxygen adsorption energy) on the TiO2-covered RuO2 sur-


(a) The O-covered RuO2 overlayer modelelectrode.

(b) The O-covered TiO2 overlayer modelelectrode.

Figure 4.15: The two model electrodes studied in Karlsson et al. [16]. Green ballsare Ru, grey balls are Ti and red balls are O.

face should be close to that optimal for ClER activity and selectivity. On the otherhand, the RuO2-covered TiO2 surface should have electrocatalytic properties verysimilar to those of pure RuO2. By preparing such model electrodes and performingelectrolysis experiments in chloride-containing electrolyte, it should be possible tocompare the selectivity for ClER that the two model electrodes exhibit. We pre-dict that the ClER selectivity of the monolayer TiO2 on RuO2 electrode should behigher than that of the monolayer RuO2 on TiO2 electrode, and that both electrodesshould be active. This same theoretical prediction was also made independentlyby Exner et al. [112] at almost the same time.

4.3 Semiclassical modeling of rutile oxides

There is now a large literature indicating the value of theoretical modeling based onDFT. DFT is now a mainstream tool for materials science and catalysis. However,the computational cost of DFT calculations still makes some studies, specificallyon the mesoscale, prohibitive. One such problem, that is expensive to tackle on theDFT level, is the study of the segregation of Ru and Ti in DSA. As has been in-dicated in previous sections[16, 17], the local structure of a mixed oxide electrodecoating decides the electrocatalytic properties of the electrode. If the local struc-ture is to be controlled, tools to model the changes in local structure over time, bothduring preparation of the electrode and during use, are required. DSA coatings aremade up by nanoscale particles of typically tens of nanometers size[37], so themodel needs to be able to simulate particles of such size. A RuO2 particle with a

4.3. SEMICLASSICAL MODELING OF RUTILE OXIDES 67

Table 4.1: The Buckingham cation-oxygen shell potentials found through fittingto experimental structures of rutile RuO2 and TiO2.

Cation A / eV ρ / eVA−1 C6 / eVA−6 rcut / ÅRu 172038.5 0.17 0.49 10.0Ti 2665.7 0.28 0 10.0

size of 10 nm contains several hundred thousand atoms. To put this number intoperspective, the largest systems modeled with DFT in the present work containedabout 1000 atoms. As the increase in computer time required for a DFT calculationon a system with N times more atoms usually scales by more than N in practice,it is clear that less computationally demanding methods are needed to simulatediscrete particles of realistic size. Therefore, we attempted to fit a force field thatcould describe the structural and energetic properties of RuO2-TiO2 mixed rutileoxides[18]. All calculations using FFs in this thesis were carried out using theGeneral Utility Lattice Program (GULP)[118, 230–232].

The fitting started from the Buckingham force fields of Bush et al. [119] and Bat-tle et al. [233], which are both based on the same transferable oxygen-oxygenpotential. By refitting both the Ti-O potential and Ru-O potential, an attempt wasmade at finding an improved set of parameters to describe the structures of pureTiO2[234] and RuO2[235]. The approach was based on simultaneous fitting (fit-ting both interatomic parameters and O shell positions concurrently for a staticstructure) as well as relaxed fitting (fitting parameters and shell positions, but alsorelaxing the structure at every step). The parameters found by using this fittingmethodology are seen in Table 4.1. For the structures of the pure materials, thenew FF is an improvement (see Tables in [18]).

However, the goal of the fitting was to find parameters that could describe themixed oxide. For this purpose, three bulk mixed oxide systems were chosen (seeFigure 4.16). The geometric parameters (atomic positions as well as cell param-eters) were relaxed at the PBEsol[236] level. A comparison between the DFTstructure and the structure obtained with the new FF is seen in Table 4.2. It is seenthat the combination of the new Ti-O and new Ru-O interatomic potentials yields aworse result than the combination of the new Ti-O parameters with the Battle et al.[233] Ru-O parameters. The energies of the three systems were calculated usingboth PBEsol and the GLLB-SC[237] functional, which improves the descriptionof the exchange energy and therefore should be associated with a smaller SIE. Theenergetic ordering (the energy differences between the three systems) were consis-tent with both functionals. The energies calculated using DFT as well as with thenew FF are found in Table 4.3. It is clear that none of the FFs recover the correctenergetics. For example, while “system 2” is the least stable system according toDFT, it is the most stable system according to the force fields.


1 2 3

Figure 4.16: The three mixed Ru-Ti bulk oxide systems used to fit and benchmarkthe force field parameters. Green balls are Ru, grey balls are Ti and red balls areO.

Table 4.2: Comparison between volumes and cell parameters for mixed oxidestructures calculated using DFT and using the force field. The results when usingBuckingham potential parameters based on a GA search, using atomic positionand volumes in the DFT systems to evaluate the fitness, are also shown.

System Param. PBEsol New FF New FF for Ti-O, FF from GARu-O from Battle et al. [233] search

System 1

V / A3 249.115 246.224 247.559 250.286x / Å 6.510 6.353 6.381 6.352y / Å 5.893 6.096 6.078 6.204z / Å 6.494 6.358 6.384 6.352

System 2

V / A3 248.390 246.282 247.497 250.281x / Å 6.458 6.351 6.382 6.351y / Å 5.886 6.091 6.077 6.204z / Å 6.535 6.366 6.381 6.353

System 3

V / A3 249.989 246.049 247.251 250.288x / Å 6.423 6.323 6.367 6.350y / Å 6.062 6.112 6.088 6.204z / Å 6.422 6.361 6.378 6.353

Table 4.3: Calculated energies (in eV) of the three mixed oxide systems.

System PBEsol GLLB-SC New IPNew FF for Ti-O,Battle et al. [233]

parameters for Ru-OSystem 1 −212.071 −212.233 −968.624 −961.758System 2 −211.580 −211.693 −968.649 −961.778System 3 −211.927 −212.191 −968.541 −961.694

4.4. XPS MODELED USING DFT 69

It is reasonable to assume that an improved description of the Ru and Ti cationsis required to describe the energetics correctly. Both Ti and Ru are d elements,and the effect of the spatial distribution of the d orbitals is key to describe bothstructure and energetics of their oxides. We therefore attempted to add the AOMto the force field. The first attempt was based on standard deterministic fitting.However, the best FF that could be found in this way only managed to minimizethe energy differences between the three systems. Therefore, several attempts tooptimize the parameters for the AOM using a GA were performed. In the GA,an array of the FF parameters was used as the chromosome, and the fitness ofeach chromosome was evaluated by relaxing the structures of the three mixed ox-ide systems, and comparing volumes with the volumes obtained using DFT, andthe relative energies between the three systems with the corresponding relativeDFT energies. Initial testing of the GA indicated that it was able to find Bucking-ham potentials of comparable quality to those obtained using deterministic fitting.However, when using the GA to fit also the AOM parameters, to attempt to finda FF that could describe both structural parameters and energetics, we found noset of parameters that recovered the correct energetic orderings. Again, the bestsolution found was a set of parameters that minimized the energy differences be-tween the three systems. Although we failed to find a FF that could describe theenergies and structures of RuO2-TiO2 mixed oxides, the new FF (that is the com-bination of the new Ti-O parameters and the Battle et al. [233] Ru-O parameters)is at least able to describe the structure of such oxides more accurately than previ-ous Buckingham-based force fields. The results also indicate that something morethan the AOM model is needed to describe the energetics correctly. It is possiblethat it is necessary to depart from a constant charge description of the cations toachieve this goal, as impressive results for the description of pure rutile TiO2 havebeen obtained with charge-equilibration models[238].

4.4 Understanding X-ray photoelectron spectroscopyusing density functional theory

The HER has been studied on two materials, MoS2 and RuO2, based on com-parisons between experimental and calculated XPS chemical shifts. In the firststudy[20], we used this method to further the understanding of the mechanism ofHER on MoS2, a material that has been devoted study as it is active for HER eventhough Mo is not a noble metal[48, 49]. In the second study, we calculated XPSbinding energies for RuO2 and for a variety of hydrogenated RuO2 structures andRu oxides and hydroxides to reconsider conclusions drawn in previous work[51]regarding structural changes in RuO2 during HER.


4.4.1 The active site for HER on MoS2

The study used an ambient pressure XPS setup, as shown in Figure 4.17. Thesetup consisted of a Nafion membrane, which separated the cathode side, on whichamorphous nanoparticulate MoS3 catalysts were dispersed on a carbon supportmaterial, from the anode side, on which a platinum-carbon catalyst was deposited.The Mo 2p XPS measurements were performed at room temperature, with the an-ode side being exposed to saturated water vapor and the cathode side to a vacuumwith a leakage stream of water gas achieving a partial pressure of water of 10 torr.The evolution of the X-ray photoelectron spectra is seen in Figure 4.18. Two mainpeaks are visible, with the main peak before HER decreasing in intensity, and thepeak shifted by ca −1 eV from the main peak increasing in intensity during HER.Comparison with the spectra for nanocrystalline MoS2 indicated that the changeduring electrolysis corresponds to a conversion of MoS3 to MoS2. The inelasticmean-free path of the electrons being ionized from the Mo sites was estimated tobe 2.2 nm, indicating that the spectral changes correspond to changes in the near-surface region. Previous studies have shown that MoS2 nanoparticles are presenton the support as flat polygons made up of trilayer S-Mo-S structures, where the Sedges are active for HER[49]. The thickness of one S-Mo-S trilayer is about 3 Å, atenth of the penetration depth of the excited electrons, so it is not possible to con-nect the active site structure to the observed XPS shifts directly without modelingthe active site and calculating the shifts for representative structures.

To further the understanding of the active site for HER, we carried out DFT cal-culations to model flat trilayer structures corresponding to both MoS3 and MoS2.Previous theoretical studies have indicated that the experimental conditions de-cide the S coverage on the Mo edges[239, 240]. To attempt to find the moststable S edge coverages at HER conditions, free energy calculations were car-ried out to examine the stability of different Mo edge structures at varying partialpressures of H2S. In these calculations, the electrode potential was accounted forusing the CHE model (further details of this method are found in the work ofBollinger et al. [240]). It was found that, under HER conditions (U = 0V vs RHE,pH2S = 1×10−6 bar, the pressure chosen based on the arbitrary standard for cor-rosion resistance of a material[241]), the most stable Mo-S edge coverage wasθS = 0.5ML and θH = 0.25ML. Thus, under HER, the active edge of the catalystshould correspond to coordinatively unsaturated Mo sites, mirroring the activity ofCUS for OER and ClER on RuO2. XPS calculations were then carried out for Moedges with increasing coverage of S, from θS = 0.5ML (the CUS “MoS2” edgestructure) to θS = 1ML (the coordinatively saturated “MoS3” edge structure).

The calculated XPS shifts for these structures are seen in Table 4.4. In cases wheremultiple unique S anions are present at the edge, the XPS shifts for each uniqueanion is indicated. It is seen that the XPS binding energies for the MoS3 structureis shifted by ca 1.3 eV from the binding energy of the MoS2 structure. S in S


Figure 4.17: a) The ambient pressure XPS setup used in the study of Sanchez Casa-longue et al. [20]. b) A two-electrode CV performed using the setup, indicatinga cathodic current due to hydrogen evolution at cathodic voltages. Reprinted withpermission from Sanchez Casalongue et al. [20]. Copyright 2014 American Chem-ical Society.


Figure 4.18: a) The changes in the S 2p photoelectron spectra as hydrogen evo-lution starts and progresses. b) Photoelectron spectra measured during HER ona nanocrystalline MoS2 material. Reprinted with permission from Sanchez Casa-longue et al. [20]. Copyright 2014 American Chemical Society.


Table 4.4: Calculated S 2p XPS shifts, versus the MoS2 θS = 0.5ML structure, fordifferent θS.

S coverage Coordination of ionized S atom XPS shift vs 50% coverage

50% S monomer 0.062.5% S monomer (surrounded by two S monomers) -0.0562.5% S monomer (surrounded by one S dimer and one S monomer) -0.8062.5% S atom part of an S dimer (surrounded by S monomers) 1.9275% S monomer (surrounded by S dimers) -1.1775% S atom part of an S dimer (surrounded by S monomers) 1.87

87.5% S monomer (surrounded by S dimers) -0.1187.5% S atom part of an S dimer (surrounded by S dimers) 1.16

87.5% S atom part of an S dimer 1.04(surrounded by one S monomer and one S dimer)100% S dimer 1.34

dimers (on saturated Mo cations) are associated with positive XPS shifts of 1.3to 1.9 eV. This corresponds well with the shift between the two peaks that shiftin intensity during HER (Figure 4.18). The peak corresponding to S dimers (andan S coverage above 50%) decreases in intensity, while the peak correspondingto S monomers (and a 50% S coverage) increases in intensity, as HER starts andprogresses. The activity is thus correlated with the presence of CUS Mo sites onthe edges of MoS2. This analysis indicates that when an amorphous MoS3 catalystis used, an activation occurs during which edge sites are converted to the MoS2structure.

4.4.2 Structural changes in RuO2 during HER

The HER reaction on RuO2 is associated with structural changes, including anexpansion of the rutile lattice as detected using XRD[51–53, 242, 243], and ithas been suggested that these structural changes are due to formation of firstRuO(OH)2 before a final reduction to Ru metal[51]. These structural changesoccur concomitantly with an activation of the electrode for HER[52, 242, 243].The RuO2 electrode is stable while being used as a cathode in e.g. industrial chlor-alkali or chlorate production, but is known to degrade quickly if it is exposed toreverse currents that can occur during shut-down of an electrolyzer[50]. Näslundet al. [51] connected this behavior with their proposed mechanism of step-wisereduction of RuO2 to Ru metal.

The experiments performed by Näslund et al. [51] consisted of XPS measure-ments performed on six different electrodes of RuO2 deposited on Ni substratesthat had been used for HER at a current density of −6.4 kA/m2 and a temper-ature of 90 ◦C in 8 M NaOH for either 0.5 h, 3 h, 6 h, 12 h, 18 h or 24 h. Theelectrodes had been prepared by conventional thermal decomposition of RuCl3


Table 4.5: The observed Ru 3d binding energies found by Näslund et al. [51], aswell as the respective XPS shifts versus the Ru 3d5/2 peak. The proposed identifi-cation for the peaks are also indicated. If the peak at 289 eV was due to a new Ruoxyhydroxide phase, it would be the Ru 3d3/2 doublet peak, and the correspondingRu 3d5/2 peak would be found at approximately 285 eV.

BE / eV Shift vs Ru 3d5/2 / eV Proposed identification of peakca 280 −0.8 Ru metal[51], bare RuO2 CUS sites[246]280.8 0 Ru 3d5/2

282.5 1.8RuO3[247–251],

unscreened core-hole[252], O on RuO2 CUS [253],surface plasmon excitation[254]

284.9 4.2 Ru 3d3/2

ca 289 8.6 Unscreened core hole[102], RuO(OH)2[51],CO3[244]

dissolved in 1-propanol, followed by a high-temperature calcination. The XPSspectra obtained are seen in Figure 4.19. The proposed identification of the peaksin the Ru 3d spectra as well as alternative interpretations are found in Table 4.5. Asis indicated, the peak inversion occurring during electrolysis, as well as the peakappearing at ca 289 eV, was interpreted as due to a new RuO(OH)2 phase, whilethe additional peak appearing at ca 280 eV was interpreted as due to formation ofmetallic Ru. It should be noted that the peaks interpreted as due to RuO(OH)2 haveelsewhere been interpreted as due to carbon contamination[244, 245]. The appear-ance of XPS C 1s peaks due to carbon contamination at these binding energiesis widely known in literature, and is even used to calibrate XPS spectra[20]. Thechanges in the O 1s spectra were, however, also interpreted as due to formation ofRuO(OH)2.[51]

In our work[19], we examined whether the interpretation of Näslund et al. [51]could be supported by calculated XPS shifts for ruthenium (oxy)hydroxides. Wecalculated XPS binding energies for a number of different structures, Figure 4.20,including pure RuO2 and RuO4, O, H, C, CO and CO3 adsorbates on the (110) sur-face of RuO2, hydrogen (both atomic and molecular) introduced into bulk RuO2,structures representative for Ru (oxy)hydroxides as well as metallic Ru and ruthe-nium carbide. As no accurate experimental structural data exists for any Ru (oxy)-hydroxide, we used structural analogs of Ru or related transition metal compounds,and replaced ions in the structure with O and H to find structures representing Ru(oxy)hydroxides. These analogs were obtained from the Materials Project[255] aswell as from the Crystallography Open Database[256–258]. For these structures,we carried out global optimization using minima hopping[259, 260] to find anyrelated Ru structures with higher stability. The details about the structural analogs


Figure 4.19: Ru 3d (left) XPS spectra of RuO2/Ni cathodes and metallic Ru andO 1s (right) XPS spectra of RuO2/Ni cathodes. (a) is a reference RuO2/Ni sample,that has not been exposed to the electrolyte, (b)-(g) are measurements on electrodesused for hydrogen evolution for either 0.5 h, 3 h, 6 h, 12 h, 18 h or 24 h, respectivelyand (h) in the left figure is a spectrum from metallic Ru. Figures reprinted withpermission from Näslund et al. [51]. Copyright 2014 American Chemical Society.


and structural relaxations (local and global) are found in the paper[19].Ru 3d, O 1s and C 1s XPS binding energies were calculated for all the structuresconsidered in the study. The analysis was based on chemical shifts calculated ver-sus either the 3d BE of Ru in bulk RuO2, in the case of Ru 3d and C 1s shifts, andversus the O 1s BE of O in bulk RuO2, in the case of O 1s shifts. Of the structuresconsidered, only the Ru 3d XPS shift of RuO4 is consistent with the 4 eV shift ofthe 289 eV peak, interpreted as corresponding to RuO(OH)2[51]. However, it isvery unlikely that RuO4, a more oxidized, meta-stable, form of RuO2 with a boil-ing point of 40 ◦C[261] would form during cathodic polarization at 90 ◦C. Whilethe peak shifted by ca−0.8 eV could be due to formation of Ru metal, the presenceof other structures and structural motifs, including the bare or H-covered CUS onRuO2 and Ru sites in the Ru Gibbsite (001) surface would also result in an XPSpeak with that shift. Experimental C 1s BEs for e.g. carboxyl groups[245] canexplain the peak shifted by 9 eV from the RuO2 3d5/2 peak. Furthermore, the peakinversion observed in Figure 4.19 might be explained by surface carbons such asCO and CO3, shifted by 4.1 eV and 5.1 eV from the RuO2 3d5/2 peak, respectively.From these results, we are forced to conclude that the appearance of what mightlook like a new spin-orbit split doublet peak at 285 eV and 289 eV might insteadbe due to carbon contamination in the near-surface region of the electrode. Con-sidering that the electrodes were prepared by thermal decomposition of precursorchlorides dissolved in isopropanol, this might not be implausible.Furthermore, it was found that the evolution of the O 1s XPS spectra, indicatinga peak shift of 2 eV, can be explained by the hydrogenation of oxygens in therutile RuO2 structure. The O 1s XPS BEs of OH groups in the rutile structureswere found to be shifted by around 2 eV from the O 1s XPS BE in RuO2. Themuch smaller shift associated with introduction of molecular H2 into RuO2, 0.8 eV,indicates that the XPS intensity changes occurring during HER on RuO2 are dueto introduction of H rather than H2 into the coating. Furthermore, upon relaxingbulk RuO2 structures with H inside, which resulted in conversion of O groups intoOH groups, the structures exhibited similar volume increases as those observedexperimentally during HER on RuO2[51–53, 242, 243].These results can be summarized as follows. During HER, H enters the RuO2structure, and converts the structure into a Ru(OH)3 structure. This explains thevolume increase of the lattice, as well as the observed XPS shifts. The large pos-itive XPS shifts observed by Näslund et al. [51] during HER are likely due tocarbon contamination, either from the environment during the electrolysis, or dueto residual carbon inside the coating from the solvent used in the preparation ofthe electrode. The additional peak appearing at a slightly lower binding energythan the Ru 3d5/2 peak could be due to formation of metallic Ru, but it is morelikely that this peak is due to either Ru sites in hydroxidic regions of the outersurface of the coating, or indeed to bare or H-covered CUS sites on the electrodesurface. This latter result suggests that a reason for the activation of RuO2 that has


1 2 3

4 5

6 7 8

9

Figure 4.20: The relaxed bulk structures of RuO2 (1) , RuO4 (2), RuOOH (3, basedon FeOOH), RuO(OH)2 (4, based on RuOCl2), Ru(OH)3 (5, based on Al(OH)3 inthe Gibbsite structure), the second Ru(OH)3 structure (6, based on arbitrary place-ment of OH around Ru in a periodic cell) and its more stable form found throughminima hopping (7), ruthenium carbide (RuC, 8) and finally ruthenium metal inthe hcp structure (9). Red circles represent oxygen, white circles hydrogen, greenspheres ruthenium and grey spheres carbon. The (001) surface of the Gibbsite-likestructure (5) is obtained by making a cut between two Ru-O-H layers.


been noted during cathodic polarization might be a gradual removal of surface O,remaining from the electrode preparation and exposure to air, opening new activesites for HER.

Chapter 5

Conclusions andrecommendations

5.1 Conclusions

In the study of Hummelgård et al. [15], we found that the doping of DSA with Coresulted in activation of the electrode for hydrogen evolution, an effect largely dueto increased active surface area.

In the study of Sandin et al. [14], we found indications for a mechanistic connec-tion between the homogeneous chlorate formation reaction and the uncatalyzedformation of oxygen during hypochlorite decomposition. Further understandingof this connection might be used to control the selectivity, to enable more selectivechlorate formation. Additionally, it was found that the oxygen evolution is third-order with respect to hypochlorite. The rate of the reaction has a maximum at pH6.5, indicating the involvement of both HOCl and OCl–. We also found indicationsthat higher oxidation states of Ir catalyze chlorate formation.

In the theoretical studies of Karlsson et al.[16, 17], we found that doping ru-tile TiO2 with transition metals, including Ru (as in DSA), As, Bi, Co, Ir, Mn,Pd or Ru, activates Ti surface sites for selective electrochemical chlorine evolu-tion. This is a fundamental explanation for the observed experimental selectivitytrends of Ru-doped TiO2 (DSA). Furthermore, the finding that doping with ar-senic should result in a high selectivity regardless of whether the As dopant re-sides in the surface CUS active site or close to Ti sites is intriguing, as arsenicis very cheap[17, 262]. In other cases, a higher degree of control of the atomiclevel arrangement of dopants is required to achieve the results indicated by ourpredictions. In general, the results show that it seems possible to adjust the elec-

79

80 CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS

trocatalytic properties of TiO2 from optimal OER activity to optimal ClER activityand selectivity.

We also attempted to fit a force field for rutile Ru-Ti mixed oxides[18]. While animproved interatomic potential for TiO2 and for the structure of the mixed oxidewas found, the energetics of the force field when it comes to modeling the relativeenergies of different Ru-Ti arrangements were incorrect.

Finally, in the papers of Sanchez Casalongue et al. [20] and Karlsson et al. [19],computational modeling was used to understand results from XPS studies of HERon MoS2 and RuO2. In the first study, we found that during HER on MoS2, theedge structure changes from the amorphous MoS3 structure, where two S anionsare found on each Mo cation of the edge, to an MoS2 structure. In the secondstudy, we found that the XPS shifts and structural changes which are noted duringHER on RuO2, can be explained by incorporation of H into the rutile RuO2 lattice,converting O groups into OH groups. XPS shifts that had previously[51] beenattributed to formation of Ru metal are more likely associated with either formationof such OH groups, or with removal of O from RuO2 surface sites, while largepositive chemical shifts that had been attributed to formation of a new RuO(OH)2phase could only be attributed to surface carbon contamination.

5.2 Recommendations for future work

The results in the present thesis show that atomistic modeling, both semi-classicaland ab initio, is a tool that now has utility in studies of heterogeneous electrocatal-ysis. As Gurney [263] stated already in 1931,

“As quantum mechanics endows particles with entirely new prop-erties, it enables us to deal with problems which have remained un-solved for many years. In electrolysis we have been unable to vi-sualize the physical processes which underlie some of the most el-ementary phenomena. Thermodynamics gives a consistent accountof them, independent of any mechanism; but when we try to unravelthe actual processes their complexity is baffling. Quantum mechanicsprovides a new line of attack.”

It is just during the last few years that it has been possible to start exploringthis “new line of attack”. By using the screening possibilities afforded by mod-ern ab initio methods, the design of electrocatalysts can go beyond the “try andsee”[13] methodology that has characterized electrocatalyst design (and the de-sign of heterogeneous catalysts) until now[153, 264]. Nevertheless, although thetools are now available to be able to answer the question “What electrode compo-sition should be used?”, the answer to the question “How can such an electrode

5.2. RECOMMENDATIONS FOR FUTURE WORK 81

be made?” still remains to be answered. Here a combination of theoretical andexperimental research is needed.I would also like to make some detailed recommendations for further theoreticalwork. First off, quantum chemical methods could be used to try to explore thechlorate formation mechanism, with an aim to e.g. try to examine the propertiesof the proposed “H2Cl2O2” intermediate. Using a detailed theoretical model forthe chlorate formation mechanism, the possible catalytic effect of ions or solidsmight also be understood. However, the chlorate formation mechanism is likely acomplicated multistep reaction[203, 265], so that computational methods that donot require human intervention to examine different reaction pathways[266] couldaid the search.Continuing next to the computational screening of activity and selectivity of dopedoxides, the next step would be to broaden the possible applicability of the ∆E(Oc)descriptor. It is possible that the same descriptor could be used to account also forformation of higher chlorine oxides (e.g. hypochlorite, chlorate and perchlorate),so that it might be possible to suggest electrodes that could be used for selectivedirect production of these chemicals. As an example, Viswanathan et al. [220]has suggested that rutile oxides with slightly higher ∆E(Oc) than those for optimalClER could also be selective for H2O2 production. The other area that should beexplored is a verification of the accuracy of the results. As has been described insome detail, the SIE in adsorption energy calculations on the DFT GGA level formixed oxide systems is not straightforward to estimate, and more accurate methodssuch as RPA[267] (or improvements on the RPA[161, 211]) or QMC[212, 268,269] might be needed to examine the accuracy of the results. GGA+U calculationsare not likely to correct for the SIE without resulting in a worse description of otherchemical properties. Regardless of whether GGA or GGA+U calculations are tobe used for larger screening studies, usage of higher-level methods (e.g. RPA)for benchmarking is recommended. An area that also deserves more attention isthe effect of hydration of the electrode surface on the activity trends that havebeen identified, although the studies of Rossmeisl et al. [107] and Siahrostami andVojvodic [114] have shown that the effect should be small.Ab initio theoretical studies are limited by the availability of computational re-sources. For this reason, further attempts to use semi-empirical methods such asforce fields are motivated. However, as is indicated by our attempt to fit a newforce field for DSA[18], it is not necessarily simple to design a force field thatcan describe all desired properties. Further work on automatic fitting of forcefields[130], to avoid the need for semi-manual fitting, is desired. As force-fieldsclearly have limitations, another avenue of work that might hold more promiseis semi-empirical methods such as density-functional tight-binding (DFTB)[270].The continual decrease in the cost of computational resources also means that thecost of using accurate methods (e.g. LDA or GGA-level DFT) that are too expen-sive for present-day studies of e.g. nanoparticles soon might become acceptable.


When it comes to experimental studies, the main recommendation is that ourpredictions[16, 17] regarding the selectivity and activity of doped TiO2 should betested in practice. For verification of the theoretical results, tests using the modelelectrodes indicated in Karlsson et al. [16] should be made, while the predictionsresulting from computational screening[17] could serve as inspiration for studiesof other dopants in TiO2, including dopants that appear never to have been studiedfor the purpose of ClER or OER electrolysis.

Although the present thesis has had a main focus on ab initio modeling tools thathave come into general use only recently, it cannot be said that the experimen-tal tools that are available are the same today as they were almost 50 years ago,when the DSA was introduced. In particular, the automatization of laboratoryequipment that is now becoming standard allows for experiments, such as mightbe exemplified by those in our study[14], where changes in both liquid phase andgas phase are measured with high accuracy and time resolution. Furthermore,in studies of electrodes, attempts should be made to separate apparent kineticsfrom true electronic effects, e.g. normalizing the apparent current density by theelectrochemically active surface area[15, 271]. This is unfortunately not the ruleeven today. The possibility of using in-situ methods to study changes on elec-trode surfaces, as done in the study of Sanchez Casalongue et al. [20], shouldalso be explored further. New insight can also be gained from the rapid devel-opment of X-ray spectroscopic methods that has occurred only during the lasttwo decades[181, 272]. The combination of such spectroscopic studies, givinginsight into the atomic-level structure of oxides, with electrochemical studies, iswell exemplified by the study of Sanchez Casalongue et al. [20] and of Krtil andRossmeisl with co-workers[273–275] (although we have questioned some of theirconclusions[17]). It is regrettable that such an approach was not assumed in ourstudy on Co-doped DSA[15], as more interesting results regarding the possibleelectronic effects of Co-doping in DSA and RuO2[273–275] might have been ob-tained. Finally, it should be stressed that much can be gained by combining ex-perimental studies with ab initio simulations, as it is difficult to draw detailedconclusions from e.g. experimental XPS results[51] without the direct connectionbetween structure and e.g. XPS shifts that computational modeling can supply[19].

Lastly, some recommendations for further work specifically focused on the chlo-rate process will also be made. In general, the overall goal can be said to beto improve the understanding of the reactions that occur in the process, i.e. thechlorate formation reaction itself and homogeneous and possibly heterogeneousdecomposition of hypochlorites to form oxygen. Detailed knowledge about thesereactions is presently based mainly on experiments under conditions that differfrom those of the actual process. Future studies should attempt to work underconditions close to the industrial ones. Such work is important especially when itcomes to the effects of electrolyte contamination, as it seems that very few studiesof chlorate formation catalysis or hypochlorite decomposition (to form oxygen)

5.2. RECOMMENDATIONS FOR FUTURE WORK 83

under industrial conditions exist. Another area that requires further study is thedetails of the connection between current density and the selectivity for oxygenevolution, as there seems to be a minimum in the selectivity for O2 at the criticalanode potential[73].


Chapter 6

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Chlorate Manufacture, J. Electrochem. Soc. 131 (1984) 1551–1559.[11] J. Genovese, K. Harg, M. Paster, J. Turner, Current (2009) state-of-the-art hydrogen produc-

tion cost estimate using water electrolysis, Review NREL/BK-6A1-46676, US Department ofEnergy (2009).

[12] P. Häussinger, R. Lohmüller, A. M. Watson, Ullmann’s Encyclopedia of Industrial Chemistry,chap. Hydrogen, 2. Production, Wiley-Blackwell (2012) .

[13] S. Trasatti, Electrocatalysis in hydrogen evolution: Progress in cathode activation, chap. 1, VCHPublishers (1992) pp. 2–85.

[14] S. Sandin, R. K. B. Karlsson, A. Cornell, Catalyzed and Uncatalyzed Decompositionof Hypochlorite in Dilute Solutions, Ind. Eng. Chem. Res. 54 (2015) 3767–3774, doi:10.1021/ie504890a.

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H. Olin, Physical and electrochemical properties of cobalt doped (Ti, Ru)O2 electrode coatings,Mater. Sci. Eng., B 178 (2013) 1515–1522, doi:10.1016/j.mseb.2013.08.018.

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Chapter 7

Acknowledgments

First, let me acknowledge the funding for this project, which was received fromPermascand AB and the Swedish Energy Agency, within the program “Effektivis-ering av industrins energianvändning”.Many people have supported me during these last years. First off, I’d like to thankmy two main supervisors, Ann Cornell and Lars G. M. Pettersson. Your interest,patience, direction and deep knowledge have helped me every step along the way.It has been a pleasure to work with you, and I am thankful to have been able tolearn so much from both of you.I would also like to thank my co-supervisors Joakim Bäckström, Göran Lindberghand Susanne Holmin for their support and helpful discussions. I would also liketo thank John Gustavsson, for introducing me to the experimental side of electro-catalysis research, and Henrik Öberg, for introducing me to the hands-on use ofdensity functional theory. I would also like to thank Christine Hummelgård fora productive and interesting collaboration during the work on Co-doped DSAs.Thanks also to Heine Hansen and Thomas Bligaard for hosting me for a weekat SLAC, and for teaching me much about theoretical electrochemistry. Thanks,Richard Catlow, Alexey Sokol and Scott Woodley for being very gracious hostsduring my two visits to UCL, and I would like to thank you for an interestingfew weeks of arduous interatomic potential-tweaking. I would also like to thankStaffan Sandin for our years of working together on “hypo” decomposition. I havealso enjoyed working with Lars-Åke Näslund on several projects.During this project, I have gained much from regular discussions with staff at bothPermascand and AkzoNobel Pulp and Performance Chemicals. These discussions

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100 CHAPTER 7. ACKNOWLEDGMENTS

have made my work much more interesting by giving me a firm grounding inwhat questions are interesting from the industrial point of view. I’d like to thankLars-Erik Bergman, Erik Zimmerman, Ingemar Johansson, Bernth Nordin, JohnGustavsson, Susanne Holmin and Fredrik Herlitz from Permascand. I’d also liketo thank Johan Wanngård, Kristoffer Hedenstedt, Johan Lif, Nina Simic, MagnusRosvall, Kalle Pelin, Adriano Gomes and Mats Wildlock from AkzoNobel Pulpand Performance Chemicals.Much of the work that has resulted in this thesis has been computational. Through-out these last few years, I have often gotten help from Peter Gille (PDC, KTH) withall kinds of matters ranging from cryptic compiler messages to general Linux-related questions. Thanks, Peter! Furthermore, the helpful community surround-ing the GPAW code has been a great help in my learning and usage of that code. Inconnection with that, I would especially like to thank Ask Hjorth Larsen, Jens Jør-gen Mortensen and Marcin Dulak. The calculations could not have been performedwithout the computing resources of the HPC2N, and I would like to acknowledgethe support provided by their staff. Furthermore, I would like to thank NajeemLawal for providing access to the Goliat computer at the Mid Sweden University.The friendly and supportive spirit provided by past and present colleagues at TEKand EP, KTH and Atomic Physics and Chemical Physics, SU, is much appreciated.You have made these past years a pleasure.I would like to thank Sigbritt, Thore, Jesper and Mathilda for everything they havedone for me, and for all their support.Finally, I want to express my gratitude to my wife Lina. Your support and encour-agement has helped me get to this point. We’ve made it through these last nineyears at KTH hand in hand, through almost every course and “tentaplugg” andnow (soon) through our PhD studies. Tack för allt! Jag har tur som träffade dig.

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