Over the last fifteen years, there has been a rapid growth in the use of high resolution X-ray computed tomography (HRXCT) imaging in material science applications. We use it at nanoscale resolutions up to 50 nm (nano-CT) for key research problems in large scale operation of polymer electrolyte membrane fuel cells (PEMFC) and lithium-ion (Li-ion) batteries in automotive applications. PEMFC are clean energy sources that electrochemically react with hydrogen gas to produce water and electricity. To reduce their costs, capturing their electrode nanostructure has become significant in modeling and optimizing their performance. For Li-ion batteries, a key challenge in increasing their scope for the automotive industry is Li metal dendrite growth. Li dendrites are structures of lithium with 100 nm features of interest that can grow chaotically within a battery and eventually lead to a short-circuit. HRXCT imaging is an effective diagnostics tool for such applications as it is a non-destructive method of capturing the 3D internal X-ray absorption coefficient of materials from a large series of 2D X-ray projections. Despite a recent push to use HRXCT for quantitative information on material samples, there is a relative dearth of computational tools in nano-CT image processing and analysis. Hence, we focus on developing computational methods for nano-CT image analysis of fuel cell and battery materials as required by the limitations in material samples and the imaging environment. The first problem we address is the segmentation of nano-CT Zernike phase contrast images. Nano-CT instruments are equipped with Zernike phase contrast optics to distinguish materials with a low difference in X-ray absorption coefficient by phase shifting the X-ray wave that is not diffracted by the sample. However, it creates image artifacts that hinder the use of traditional image segmentation techniques. To restore such images, we setup an inverse problem by modeling the X-ray phase contrast optics. We solve for the artifact-free images through an optimization function that uses novel edge detection and fast image interpolation methods. We use this optics-based segmentation method in two main research problems - 1) the characterization of a failure mechanism in the internal structure of Li-ion battery electrodes and 2) the measurement of Li metal dendrite morphology for different current and temperature parameters of Li-ion battery cell operation. The second problem we address is the development of a space+time (4D) reconstruction method for in-operando imaging of samples undergoing temporal change, particularly for X-ray sources with low throughput and nanoscale spatial resolutions. The challenge in using such systems is achieving a sufficient temporal resolution despite exposure times of a 2D projection on the order of 1 minute. We develop a 4D dynamic X-ray computed tomography (CT) reconstruction method, capable of reconstructing a temporal 3D image every 2 to 8 projections. Its novel properties are its projection angle sequence and the probabilistic detection of experimental change. We show its accuracy on phantom and experimental datasets to show its promise in temporally resolving Li metal dendrite growth and in elucidating mitigation strategies. Keywords: X-ray computed tomography, 4D X-ray computed tomography, phase contrast optics, fuel cells, Li-ion batteries, signal processing and optimization.

Parmi les différents systèmes de stockage d’énergie électrique étudiés depuis plus de 2 siècles, le stockage électrochimique de type batterie Li-Ion est vraisemblablement le plus pertinent et le plus efficace. Des verrous demeurent cependant pour avoir des batteries Li-Ion répondants aux besoins actuels, et une des limitations provient des matériaux d’électrodes. Le silicium est un candidat de choix pour répondre aux problématiques batteries posées, cependant sa tenue au cyclage est courte et les méthodes de synthèse sont souvent très contraignantes. Associant deux laboratoires de recherche acteurs majeurs dans le domaines des nanosciences (le LRN à l’URCA) et des matériaux et batteries (le LRCS à l’UPJV) le projet pluridisciplinaire NanoSiBL d’une durée de 36 mois se fixe pour objectif d’apporter des solutions aux deux points précédents par : 1, la réalisation d’électrodes négatives en Silicium par une voie de synthèse bas coût originale et innovante développée au LRN (l’électrodépôt en milieu liquide ionique), 2 un accroissement de la durée de vie de l’électrode grâce à deux types de structuration (soit une électrode constituée de nanofils/nanotubes de Si monolithique soit une électrode nanostructurée composite de Si/TiO2). L’expertise dans le domaine des batteries du LRCS devrait permettre sur ce deuxième point de déterminer la géométrie et configuration idéale de l’électrode en termes de performance. Basé des méthodes d’élaboration par électrochimie bas coût et originale, NanoSiBL a pour objectif, grâce au partage de compétences et de technologie entre physiciens et chimistes impliqués, d’initier une nouvelle thématique inter-établissement axée sur la valorisation de nanostructures de silicium et silicium composite nanostructuré. L’intérêt scientifique de ce projet réside dans la mise en œuvre et le contrôle des propriétés intrinsèques de ces nanostructures à base de silicium pour la réalisation d’électrodes négatives performantes de batterie Li-Ion. Dans la littérature, les électrodes négatives à base silicium ou silicium composite (type Si/TiO2) ont déjà démontré une amélioration par rapport aux électrodes de silicium massif. Néanmoins, le passage à des dispositifs opérationnels reste peu fréquent car les voies permettant de contenir l’expansion en volume du silicium restent à éprouver et car les méthodes utilisées pour élaborer ces nanofils de silicium (Chemical Vapor Deposition, évaporation réactive…) restent très contraignantes, tant au niveau des conditions de croissance (nécessité d’utiliser des précurseurs métalliques et des gaz très toxiques) que des coûts de fabrication (travail sous ultra-vide, nombreuses étapes pour la réalisation des dispositifs avec la nécessité de réaliser des contacts post-croissance…). NanoSiBL propose donc une alternative en réelle rupture technologique avec les méthodes de synthèse actuelles. Les techniques de croissance (électrodépôt en liquide ionique) et de nanostructuration (au sein de membranes polycarbonates ou nanotubes de TiO2) utilisées dans le projet permettront la mise au point d’électrodes à bas coût performantes pour l’application batterie Li-Ion visée. En outre la variété conséquente de géométries possibles proposées par les membranes nanoporeuses qui seront utilisées dans le projet (polycarbonate ou nanotubes de TiO2) permettra d’établir un comparatif essentiel de l’impact de la nanostructuration ou encore de la composition des électrodes pour contenir l’expansion en volume du silicium lors du cyclage et ainsi améliorer la durée de vie de telles électrodes (batterie). / Among the various electric energy storage systems studied for more than two centuries, the electrochemical storage battery type Li-Ion is probably the most relevant and most effective. however locks remain for Li-Ion batteries respondents to current needs, and limitations comes from the electrode materials. Silicon is a prime candidate to meet the challenges posed batteries, however its resistance to cycling is short and synthesis methods are often very restrictive. Combining two research laboratories major players in the fields of nanoscience (the LRN to URCA) and materials and batteries (the LRCS to UPJV) the multidisciplinary project NanoSiBL a period of 36 months set the objective of provide solutions to the above two points: 1, the realization of negative electrodes in silicon by a synthetic route down original and innovative cost developed LRN (electrodeposition in ionic liquid medium), 2 increased lifetime of the electrode through two types of structuring (or one electrode made of nanowires / nanotubes Si monolithic or a composite nanostructured electrode Si / TiO2). The expertise in the field of LRCS of batteries should allow this second point to determine the geometry and ideal configuration of the electrode in terms of performance. Based methods developed by electrochemistry low cost and original NanoSiBL aims, through the sharing of expertise and technology between physicists and chemists involved, to initiate an inter-establishment new theme focused on valuation and silicon nanostructures composite nanostructured silicon. The scientific interest of this project lies in the implementation and control of the intrinsic properties of these nanostructures based on silicon for making efficient negative electrodes of Li-Ion battery. In the literature, the negative electrodes based on silicon or silicon composite (type Si / TiO2) have already demonstrated improvement compared to bulk silicon electrodes. However, the transition to operational devices remains uncommon for ways to contain the expansion in volume of the silicon are experiencing and because the methods used to develop these silicon nanowires (chemical vapor deposition, reactive evaporation ...) remain very restrictive both in terms of growth conditions (the need to use metal precursors and highly toxic gases) that manufacturing costs (labor UHV, many steps for the realization of devices with the need for contacts post- growth…). NanoSiBL proposes an alternative in real technological break with the current methods of synthesis. growth techniques (electrodeposition in ionic liquid) and nanostructuring (in polycarbonates or TiO2 nanotube membranes) used in the project will enable the development of electrodes at low cost efficient for application referred Li-Ion battery. Furthermore the consequent variety of possible geometries offered by the nanoporous membranes to be used in the project (polycarbonate or TiO2 nanotubes) will establish a critical comparison of the impact of the nanostructure or composition of electrodes to contain expansion by volume of the silicon during the cycling and improve the life of such electrodes (battery).

Layered lithium transition-metal oxides (LMOs) are used as the positive electrode material in rechargeable lithium-ion batteries. Because transition metals undergo redox reactions when lithium ions intercalate in and disintercalate from the lattice, the selection and composition of transition metals largely influence the electrochemical performance of LMOs. Recently, a Ni-rich compound, LiNi0.8Co0.1Mn0.1O2 (NCM811), has drawn much attention. It is expected to replace its state-of-the-art cousins, LiCoO2 (LCO) and LiNi1/3Co1/3Mn1/3O2 (NCM111), because of its higher capacity, lower cost, and reduced toxicity. However, the excess Ni, as a transition-metal element in NCM811, can cause structural and cycling instability. Starting from NCM811, I modified the composition of transition metals by two approaches: 1) introducing cobalt deficiency and 2) substituting Ni, Co, and Mn with Zr. Their influences on the phase, structure, cycling performance, rate capability, and ionic transport were investigated by a variety of characterization techniques. I found that cobalt non-stoichiometry can suppress Ni2+/Li+ cation mixing, but simultaneously promotes the formation of oxygen vacancies, leading to rapid capacity fade and inferior rate capability compared to pristine NCM811. On the other hand, Zr can reside on and expand the lattice of NCM811, and form Li-rich lithium zirconates on their surfaces. In particular, 1% Zr substitution can increase the stability of NCM811 and facilitate Li-ion transport, resulting in enhanced cycling durability and high-rate performance. My studies help improve the understanding of the effects of transition metals on the degradation of the Ni-rich layered positive electrode material and provide modification strategies to enhance its performance and durability for Li-ion battery applications.

Ce travail de thèse porte sur la réalisation d’une batterie redox-flow fonctionnant grâce à la circulation de suspensions de matériaux d’insertion du lithium afin d’accroitre leur densité d’énergie. Le recours à des cellules microfluidiques permet de s’affranchir des limitations causées par les membranes échangeuses d’ions. Il s’articule dans un premier temps sur la synthèse contrôlée par voie hydrothermale de nanoparticules de LiCoO2 et leur caractérisation en suspension aqueuses. Cette étape permet de déterminer à la fois les propriétés électrochimiques des suspensions, leur état d’agrégation ainsi que leur comportement rhéologique en vue d’une utilisation redox-flow. Le transfert électronique entre une particule en suspension et les électrodes de la cellule est un aspect fondamental de ce type de batteries. Ce transfert est étudié grâce la technique de collision électrochimique dans laquelle la réponse de chaque agrégat est détecté individuellement par une ultramicroélectrode ce qui permet d’établir de nombreuses propriétés physique-chimiques de ces suspensions. Ce travail propose ensuite de s’affranchir de l’utilisation des membranes et de leurs limitations par le recours aux techniques de la microfluidique. La formation d’un écoulement co-laminaire en microcanal permet d’obtenir une cellule redox-flow opérationnelle. La conception et le fonctionnement de ces cellules est étudié en vue de la mise en circulation de suspensions de nanoparticules dans ce type de systèmes. / The aim of this work is to make a redox-flow battery that runs on lithium insertion material suspensions in order to increase the energy density of such systems. The use of microfluidic technics allows to solve the issues and limitations of ion exchange membrane by removing them. In the first part controlled size LiCoO2 nanoparticles are synthesized by hydrothermal route and dispersed into suspensions. The aggregation state of these suspensions are investigated using diffusion light scattering and transmission electronic cryoscopy. Rheological properties were also characterized for redox-flow use. The electronic transfer between a particle in suspension and the flow cell electrodes is crucial for their performances. This transfer is studied in the second part using the single event collision technic which consist of isolating individual aggregate electrochemical response at the surface of an ultramicroelectrode. This approach allows an extensive investigation of suspensions aggregates size, mobility and insertion reaction kinetic. Finally this works propose to replace the conventional ion exchange membrane by the mean of microfluidic technics. In co-laminar condition the fluid interface acts as a separation membrane to create a membrane-less redox-flow battery. The last part focuses on the fabrication of microfluidic cells and the behavior of suspensions in micro-channels.

Conventional energy sources are diminishing and non-renewable, take million years to form and cause environmental degradation. In the 21st century, we have to aim at achieving sustainable, environmentally friendly and cheap energy supply by employing renewable energy technologies associated with portable energy storage devices. Lithium-ion batteries can repeatedly generate clean energy from stored materials and convert reversely electric into chemical energy. The performance of lithium-ion batteries depends intimately on the properties of their materials. Presently used battery electrodes are expensive to be produced; they offer limited energy storage possibility and are unsafe to be used in larger dimensions restraining the diversity of application, especially in hybrid electric vehicles (HEVs) and electric vehicles (EVs). This thesis presents a major progress in the development of LiFePO4 as a cathode material for lithium-ion batteries. Using simple procedure, a completely novel morphology has been synthesized (mesocrystals of LiFePO4) and excellent electrochemical behavior was recorded (nanostructured LiFePO4). The newly developed reactions for synthesis of LiFePO4 are single-step processes and are taking place in an autoclave at significantly lower temperature (200 deg. C) compared to the conventional solid-state method (multi-step and up to 800 deg. C). The use of inexpensive environmentally benign precursors offers a green manufacturing approach for a large scale production. These newly developed experimental procedures can also be extended to other phospho-olivine materials, such as LiCoPO4 and LiMnPO4. The material with the best electrochemical behavior (nanostructured LiFePO4 with carbon coating) was able to delive a stable 94% of the theoretically known capacity. / Konventionelle Energiequellen sind weder nachwachsend und daher nachhaltig nutzbar, noch weiterhin langfristig verfügbar. Sie benötigen Millionen von Jahren um gebildet zu werden und verursachen in ihrer Nutzung negative Umwelteinflüsse wie starke Treibhausgasemissionen. Im 21sten Jahrhundert ist es unser Ziel nachhaltige und umweltfreundliche, sowie möglichst preisgünstige Energiequellen zu erschließen und nutzen. Neuartige Technologien assoziiert mit transportablen Energiespeichersystemen spielen dabei in unserer mobilen Welt eine große Rolle. Li-Ionen Batterien sind in der Lage wiederholt Energie aus entsprechenden Prozessen nutzbar zu machen, indem sie reversibel chemische in elektrische Energie umwandeln. Die Leistung von Li-Ionen Batterien hängen sehr stark von den verwendeten Funktionsmaterialien ab. Aktuell verwendete Elektrodenmaterialien haben hohe Produktionskosten, verfügen über limitierte Energiespeichekapazitäten und sind teilweise gefährlich in der Nutzung für größere Bauteile. Dies beschränkt die Anwendungsmöglichkeiten der Technologie insbesondere im Gebiet der hybriden Fahrzeugantriebe. Die vorliegende Dissertation beschreibt bedeutende Fortschritte in der Entwicklung von LiFePO4 als Kathodenmaterial für Li-Ionen Batterien. Mithilfe einfacher Syntheseprozeduren konnten eine vollkommen neue Morphologie (mesokristallines LiFePo4) sowie ein nanostrukturiertes Material mit exzellenten elektrochemischen Eigenschaften hergestellt werden. Die neu entwickelten Verfahren zur Synthese von LiFePo4 sind einschrittig und bei signifikant niedrigeren Temperaturen im Vergleich zu konventionellen Methoden. Die Verwendung von preisgünstigen und umweltfreundlichen Ausgangsstoffen stellt einen grünen Herstellungsweg für die large scale Synthese dar. Mittels des neuen Synthesekonzepts konnte meso- und nanostrukturiertes LiFe PO4 generiert werden. Die Methode ist allerdings auch auf andere phospho-olivin Materialien (LiCoPO4, LiMnPO4) anwendbar. Batterietests der besten Materialien (nanostrukturiertes LiFePO4 mit Kohlenstoffnanobeschichtung) ergeben eine mögliche Energiespeicherung von 94%.

Layered crystals with magnetic elements as Co and Fe have been studied. In TlCo2Se2, where Co atoms in one sheet are separated by Tl and Se from the next Co sheet, magnetic interaction within and between the sheets have been studied. Samples doped with 4% 57Fe replaced Co, show a magnetic spiral character with hyperfine fields in a flower shape in the ab-plane. The magnetic moment of 0.46 μB per Co atom derived from the average field is in good agreement with the result from neutron diffraction. In TlCu1.73Fe0.27Se2 the easy axis of magnetisation is the c-axis. The magnetic moment calculated from the Mössbauer data and SQUID magnetrometry is 0.97 μB per Fe atom with TC = 55(5) K. Multilayers of different elements have been studied. The effect of vanadium atoms on iron atoms at the interface of FeNi/V multilayers has been determined and the intermixing at the interface has been calculated to be 2-3 monolayers. For FeNi/Co 1/1 monolayer the magnetic hyperfine field (Bhf) is 45° out-of-plane, while for superlattices containing 2 to 5 monolayers it is in the plane. An study on Fe/Co superlattice were done by experimental, theoretical and simulational methods. The Bhf is highest for the Fe at the second layer next to the interface and gets the bulk value in the centre of thicker Fe layers. Studied magnetic nanoparticles coated with a lipid bilayer (magnetoliposomes) are found to have the magnetite structure but being non-stoichiometric as a result of the manufacturing process. The composition was approximately 32% γ-Fe2O3 and 68% Fe3O4. The oxidation evolution and its effect on magnetic properties of Fe clusters were also studied by means of different techniques. The extraction and insertion mechanism of lithium in the cathode material Li2FeSiO4 has been monitored by in situ x-ray diffraction and Mössbauer spectroscopy during the first two cycles. The relative amount of Fe+3/ Fe+2 at each end state was in good agreement with the results obtained from electrochemical measurements. A possible explanation to the observed lowering of the potential plateau from 3.10 to 2.80 V occurring during the first cycle, involves a structural rearrangement process in which some of the Li ions and the Fe ions are interchanged. The behaviour of small amounts of Fe in brass is investigated using Mössbauer spectroscopy. It was shown that a heat treatment can increase the amount of the precipitates of γ-Fe and ~650° C is the optimal treatment for having the highest amount of this phase.

The batteries used in plug-in hybrid electric vehicles (PHEVs) need to overcome significant technical challenges in order for PHEVs to become economically viable and have a large market penetration. The internship at Argonne National Laboratory (ANL) involved two experiments which looked at a vehicle systems approach to analyze two such technical challenges: Battery life and low battery power at cold (-7 ⁰C) temperature. The first experiment, concerning battery life and its impact on gasoline savings due to a PHEV, evaluates different vehicle control strategies over a pre-defined vehicle drive cycle, in order to identify the control strategy which yields the maximum dollar savings (operating cost) over the life of the vehicle, when compared to a charge sustaining hybrid. Battery life degradation over the life of the vehicle, and fuel economy savings on every trip (daily) are taken into account when calculating the net present value of the gasoline dollars saved. The second experiment evaluates the impact of different vehicle control strategies in heating up the PHEV battery (due to internal ohmic losses) for cold ambient conditions. The impact of low battery power (available to the vehicle powertrain) due to low battery and ambient temperatures has been well documented in literature. The trade-off between the benefits of heating up the battery versus heating up the internal combustion engine are evaluated, using different control strategies, and the control strategy, which provided optimum temperature rise of each component, is identified.

NMR experiments performed under the effect of electric fields, either continuous or pulsed, can provide quantitative parameters related to ion association and ion transport in solution.  Electrophoretic NMR (eNMR) is based on a diffusion pulse-sequence with electric fields applied in the form of pulses. Magnetic field gradients enable the measurement of the electrophoretic mobility of charged species, a parameter that can be related to ionic association. The effective charge of the tetramethylammonium cation ion in water, dimethylsulphoxide (DMSO), acetonitrile, methanol and ethanol was estimated by eNMR and diffusion measurements and compared to the value predicted by the Debye-Hückel-Onsager limiting law. The difference between the predicted and measured effective charge was attributed to ion pairing which was found to be especially significant in ethanol. The association of a large set of cations to polyethylene oxide (PEO) in methanol, through the ion-dipole interaction, was quantified by eNMR. The trends found were in good agreement with the scarce data from other methods. Significant association was found for cations that have a surface charge density below a critical value. For short PEO chains, the charge per monomer was found to be significantly higher than for longer PEO chains when binding to the same cations. This was attributed to the high entropy cost required to rearrange a long chain in order to optimize the ion-dipole interactions with the cations. Moreover, it was suggested that short PEO chains may exhibit distinct binding modes in the presence of different cations, as supported by diffusion measurements, relaxation measurements and chemical shift data. The protonation state of a uranium (VI)-adenosine monophosphate (AMP) complex in aqueous solution was measured by eNMR in the alkaline pH range. The question whether or not specific oxygens in the ligand were protonated was resolved by considering the possible association of other species present in the solution to the complex. The methodology of eNMR was developed through the introduction of a new pulse-sequence which suppresses artifactual flow effects in highly conductive samples. In another experimental setup, using NMR imaging, a constant current was applied to a lithium ion (Li ion) battery model. Here, 7Li spin-echo imaging was used to probe the spin density in the electrolyte and thus visualize the development of Li+ concentration gradients. The Li+ transport number and salt diffusivity were obtained within an electrochemical transport model. The parameters obtained were in good agreement with data for similar electrolytes. The use of an alternative imaging method based on CTI (Constant Time Imaging) was explored and implemented. / <p>QC 20140825</p>

Three-dimensional macroporous structures (‘opals’ and ‘inverse opals’) can be produced by colloidal crystal templating, one of the most intensively studied areas in materials science today. There are several potential advantages of lithium-ion battery electrodes based on inverse opal structures. High electrode surface, easier electrolyte access to the bulk of electrode and reduced lithium diffusion lengths allow higher discharge rates. Highly open structures provide for better mechanical stability to volume swings during cycling. Silicon is one of the most promising anode materials for lithium-ion batteries. Its theoretical capacity exceeds capacities of all other materials besides metallic lithium. Silicon is abundant, cheap, and its use would allow for incorporation of microbattery production into the semiconductor manufacturing. Performance of silicon is restricted mainly by large volume changes during cycling. The objective of this work was to investigate how the inverse opal structures influence the performance of silicon electrodes. Several types of silicon-based inverse opal films were synthesised, and their electrochemical performance was studied. Amorphous silicon inverse opals were fabricated via chemical vapour deposition and characterised by various techniques. Galvanostatic cycling of these materials confirmed the feasibility of the approach taken, since the electrodes demonstrated high capacities and decent capacity retentions. The rate performance of amorphous silicon inverse opals was unsatisfactory due to low conductivity of silicon. The conductivity of silicon inverse opals was improved by crystallisation. Nanocrystalline silicon inverse opals demonstrated much better rate capabilities, but the capacities faded to zero after several cycles. Silicon-carbon composite inverse opal materials were synthesised by depositing a thin layer of carbon via pyrolysis of a sucrose-based precursor onto the silicon inverse opals in an attempt to further increase conductivity and achieve mechanical stabilisation of the structures. The amount of carbon deposited proved to be insufficient to stabilise the structures, and silicon-carbon composites demonstrated unsatisfactory electrochemical behaviour. Carbon inverse opals were coated with amorphous silicon producing another type of macroporous composites. These electrodes demonstrated significant improvement both in capacity retentions and in rate capabilities. The inner carbon matrix not only increased the material conductivity, but also resulted in lower silicon pulverisation during cycling.

Titanium dioxide, TiO₂, materials have received much attention in recent years due to their potential use as intercalation negative electrodes for rechargeable lithium-ion batteries. The aim of this doctoral work was to synthesise and characterise new titanium dioxide nanomaterials and to investigate their electrochemical behaviour. Three morphologies of TiO₂(B) phase: micro-sized (bulk), nanowires and nanotubes, were synthesised. All three exhibit properties which make them excellent hosts for lithium intercalation. The nanotubes show the best capability of accommodating lithium in the structure, being able to host over one molar equivalent of lithium at low current rates (5 mA g⁻¹). The lithium insertion mechanism in the TiO₂(B) was studied using powder neutron diffraction. In addition, the nature of the irreversible capacity of the nanotubes was studied and ways of reducing it proposed. Nanotubes of another titanium dioxide polymorph, anatase, were synthesised and characterised. Their electrochemical performance was compared with that of commercially available counterparts with different morphologies and particle sizes. The interrelation between particle size/morphology and electrochemical properties has been established. The insertion of lithium which leads to phase variations was studied using in situ Raman microscopy and neutron powder diffraction. It has been demonstrated that doping of the TiO₂(B) nanotubes with vanadium improves their electronic conductivity which is essential for practical applications. Remarkably good electrochemical performance is exhibited by the 6% V-doped TiO₂(B) nanotubes.