Computational simulations of latent heat thermal energy storage systems - with innovative and first-principles based simulation for the underlying unsteady melting (and solidification) processes

This thesis develops an effective modeling and simulation procedure for a specific thermal energy storage system commonly used and recommended for various applications (such as an auxiliary energy storage system for solar heating based Rankine cycle power plant). This thermal energy storage system transfers heat from a hot fluid (termed as heat transfer fluid - HTF) flowing in a tube to the surrounding phase change material (PCM). Through unsteady melting or freezing process, the PCM absorbs or releases thermal energy in the form of latent heat. Both scientific and engineering information is obtained by the proposed first-principle based modeling and simulation procedure. On the scientific side, the approach accurately tracks the moving melt-front (modeled as a sharp liquid-solid interface) and provides all necessary information about the time-varying heat-flow rates, temperature profiles, stored thermal energy, etc. On the engineering side, the proposed approach is unique in its ability to accurately solve – both individually and collectively – all the conjugate unsteady heat transfer problems for each of the components of the thermal storage system. This yields critical system level information on the various time-varying effectiveness and efficiency parameters for the thermal storage system.

HIGH VOLTAGE ELECTROPHORETIC DEPOSITION FOR ELECTROCHEMICAL ENERGY STORAGE AND OTHER APPLICATIONS

High voltage electrophoretic deposition (HVEPD) has been developed as a novel technique to obtain vertically aligned forests of one-dimensional nanomaterials for efficient energy storage. The ability to control and manipulate nanomaterials is critical for their effective usage in a variety of applications. Oriented structures of one-dimensional nanomaterials provide a unique opportunity to take full advantage of their excellent mechanical and electrochemical properties. However, it is still a significant challenge to obtain such oriented structures with great process flexibility, ease of processing under mild conditions and the capability to scale up, especially in context of efficient device fabrication and system packaging. This work presents HVEPD as a simple, versatile and generic technique to obtain vertically aligned forests of different one-dimensional nanomaterials on flexible, transparent and scalable substrates. Improvements on material chemistry and reduction of contact resistance have enabled the fabrication of high power supercapacitor electrodes using the HVEPD method. The investigations have also paved the way for further enhancements of performance by employing hybrid material systems and AC/DC pulsed deposition. Multi-walled carbon nanotubes (MWCNTs) were used as the starting material to demonstrate the HVEPD technique. A comprehensive study of the key parameters was conducted to better understand the working mechanism of the HVEPD process. It has been confirmed that HVEPD was enabled by three key factors: high deposition voltage for alignment, low dispersion concentration to avoid aggregation and simultaneous formation of holding layer by electrodeposition for reinforcement of nanoforests. A set of suitable parameters were found to obtain vertically aligned forests of MWCNTs. Compared with their randomly oriented counterparts, the aligned MWCNT forests showed better electrochemical performance, lower electrical resistance and a capability to achieve superhydrophpbicity, indicating their potential in a broad range of applications. The versatile and generic nature of the HVEPD process has been demonstrated by achieving deposition on flexible and transparent substrates, as well as aligned forests of manganese dioxide (MnO2) nanorods. A continuous roll-printing HVEPD approach was then developed to obtain aligned MWCNT forest with low contact resistance on large, flexible substrates. Such large-scale electrodes showed no deterioration in electrochemical performance and paved the way for practical device fabrication. The effect of a holding layer on the contact resistance between aligned MWCNT forests and the substrate was studied to improve electrochemical performance of such electrodes. It was found that a suitable precursor salt like nickel chloride could be used to achieve a conductive holding layer which helped to significantly reduce the contact resistance. This in turn enhanced the electrochemical performance of the electrodes. High-power scalable redox capacitors were then prepared using HVEPD. Very high power/energy densities and excellent cyclability have been achieved by synergistically combining hydrothermally synthesized, highly crystalline α-MnO2 nanorods, vertically aligned forests and reduced contact resistance. To further improve the performance, hybrid electrodes have been prepared in the form of vertically aligned forest of MWCNTs with branches of α-MnO2 nanorods on them. Large- scale electrodes with such hybrid structures were manufactured using continuous HVEPD and characterized, showing further improved power and energy densities. The alignment quality and density of MWCNT forests were also improved by using an AC/DC pulsed deposition technique. In this case, AC voltage was first used to align the MWCNTs, followed by immediate DC voltage to deposit the aligned MWCNTs along with the conductive holding layer. Decoupling of alignment from deposition was proven to result in better alignment quality and higher electrochemical performance.

PMMA-CNT matrices for vacuum electronic, biosensing and energy applications

Carbon nanotubes (CNTs) are interesting materials with extraordinary properties for various applications. Here, vertically-aligned multiwalled CNTs (VA-MWCNTs) are grown by our dual radio frequency plasma enhanced chemical vapor deposition (PECVD). After optimizing the synthesis processes, these VA-MWCNTs were fabricated in to a series of devices for applications in vacuum electronics, glucose biosensors, glucose biofuel cells, and supercapacitors In particular, we have created the so-called PMMA-CNT matrices (opened-tip CNTs embedded in poly-methyl methacrylate) that are promising components in a novel energy sensing, generation and storage (SGS) system that integrate glucose biosensors, biofuel cells, and supercapacitors. The content of this thesis work is described as follows: 1. We have first optimized the synthesis of VA-MWCNTs by our PECVD technique. The effects of CH4 flow rate and growth duration on the lengths of these CNTs were studied. 2. We have characterized these VA-MWCNTs for electron field emission. We noticed that as grown CNTs suffers from high emission threshold, poor emission density and poor long-term stability. We attempted a series of experiments to understand ways to overcome these problems. First, we decrease the screening effects on VA-MWCNTs by creating arrays of self-assembled CNT bundles that are catalyst-free and opened tips. These bundles are found to enhance the field emission stability and emission density. Subsequently, we have created PMMA-CNT matrices that are excellent electron field emitters with an emission threshold field of more than two-fold lower than that of the as-grown sample. Furthermore, no significant emission degradation was observed after a continuous emission test of 40 hours (versus much shorter tests in reported literatures). Based on the new understanding we learnt from the PMMA-CNT matrices, we further created PMMA-STO-CNT matrices by embedding opened-tip VA-MWCNTs that are coated with strontium titanate (SrTiO3) with PMMA. We found that the PMMA-STO-CNT matrices have all the desired properties of the PMMA-CNT matrices. Furthermore, PMMA-STO-CNT matrices offer much lower emission threshold field, about five-fold lower than that of as grown VA-MWCNTs. The new understandings we obtained are important for practical application of VA-MWCNTs in field emission devices. 3. Subsequently, we have functionalized PMMA-CNT matrices for glucose biosensing. Our biosensor was developed by immobilized glucose oxidase (GOχ) on the opened-tip CNTs exposed on the matrices. The durability, stability and sensitivity of the biosensor were studied. In order to understand the performance of miniaturized glucose biosensors, we have then investigated the effect of working electrode area on the sensitivity and current level of our biosensors. 4. Next, functionalized PMMA-CNT matrices were utilized for energy generation and storage. We found that PMMA-CNT matrices are promising component in glucose/O2 biofuel cells (BFCs) for energy generation. The construction of these BFCs and the effect of the electrode area on the power density of these BFCs were investigated. Then, we have attempted to use PMMA-CNT matrices as supercapacitors for energy storage devices. The performance of these supercapacitors and ways to enhance their performance are discussed. 5. Finally, we further evaluated the concept of energy SGS system that integrated glucose biosensors, biofuel cells, and supercapacitors. This SGS system may be implantable to monitor and control the blood glucose level in our body.

Energy and conductance state modeling of power electronic converters for DC microgrids

This document will demonstrate the methodology used to create an energy and conductance based model for power electronic converters. The work is intended to be a replacement for voltage and current based models which have limited applicability to the network nodal equations. Using conductance-based modeling allows direct application of load differential equations to the bus admittance matrix (Y-bus) with a unified approach. When applied directly to the Y-bus, the system becomes much easier to simulate since the state variables do not need to be transformed. The proposed transformation applies to loads, sources, and energy storage systems and is useful for DC microgrids. Transformed state models of a complete microgrid are compared to experimental results and show the models accurately reflect the system dynamic behavior.

DC MICROGRID STABILIZATION THROUGH FUZZY CONTROL OF INTERLEAVED, HETEROGENEOUS STORAGE ELEMENTS

As microgrid power systems gain prevalence and renewable energy comprises greater and greater portions of distributed generation, energy storage becomes important to offset the higher variance of renewable energy sources and maximize their usefulness. One of the emerging techniques is to utilize a combination of lead-acid batteries and ultracapacitors to provide both short and long-term stabilization to microgrid systems. The different energy and power characteristics of batteries and ultracapacitors imply that they ought to be utilized in different ways. Traditional linear controls can use these energy storage systems to stabilize a power grid, but cannot effect more complex interactions. This research explores a fuzzy logic approach to microgrid stabilization. The ability of a fuzzy logic controller to regulate a dc bus in the presence of source and load fluctuations, in a manner comparable to traditional linear control systems, is explored and demonstrated. Furthermore, the expanded capabilities (such as storage balancing, self-protection, and battery optimization) of a fuzzy logic system over a traditional linear control system are shown. System simulation results are presented and validated through hardware-based experiments. These experiments confirm the capabilities of the fuzzy logic control system to regulate bus voltage, balance storage elements, optimize battery usage, and effect self-protection.

Modeling of diesel particulate filter filtration and regeneration for transient driving schedules

Due to their high thermal efficiency, diesel engines have excellent fuel economy and have been widely used as a power source for many vehicles. Diesel engines emit less greenhouse gases (carbon dioxide) compared with gasoline engines. However, diesel engines emit large amounts of particulate matter (PM) which can imperil human health. The best way to reduce the particulate matter is by using the Diesel Particulate Filter (DPF) system which consists of a wall-flow monolith which can trap particulates, and the DPF can be periodically regenerated to remove the collected particulates. The estimation of the PM mass accumulated in the DPF and total pressure drop across the filter are very important in order to determine when to carry out the active regeneration for the DPF. In this project, by developing a filtration model and a pressure drop model, we can estimate the PM mass and the total pressure drop, then, these two models can be linked with a regeneration model which has been developed previously to predict when to regenerate the filter. There results of this project were: 1 Reproduce a filtration model and simulate the processes of filtration. By studying the deep bed filtration and cake filtration, stages and quantity of mass accumulated in the DPF can be estimated. It was found that the filtration efficiency increases faster during the deep-bed filtration than that during the cake filtration. A “unit collector” theory was used in our filtration model which can explain the mechanism of the filtration very well. 2 Perform a parametric study on the pressure drop model for changes in engine exhaust flow rate, deposit layer thickness, and inlet temperature. It was found that there are five primary variables impacting the pressure drop in the DPF which are temperature gradient along the channel, deposit layer thickness, deposit layer permeability, wall thickness, and wall permeability. 3 Link the filtration model and the pressure drop model with the regeneration model to determine the time to carry out the regeneration of the DPF. It was found that the regeneration should be initiated when the cake layer is at a certain thickness, since a cake layer with either too big or too small an amount of particulates will need more thermal energy to reach a higher regeneration efficiency. 4 Formulate diesel particulate trap regeneration strategies for real world driving conditions to find out the best desirable conditions for DPF regeneration. It was found that the regeneration should be initiated when the vehicle’s speed is high and during which there should not be any stops from the vehicle. Moreover, the regeneration duration is about 120 seconds and the inlet temperature for the regeneration is 710K.

Development and testing of an asymmetric capacitor with a nickel-carbon foam positive electrode

Electrochemical capacitors (ECs), also known as supercapacitors or ultracapacitors, are energy storage devices with properties between batteries and conventional capacitors. EC have evolved through several generations. The trend in EC is to combine a double-layer electrode with a battery-type electrode in an asymmetric capacitor configuration. The double-layer electrode is usually an activated carbon (AC) since it has high surface area, good conductivity, and relatively low cost. The battery-type electrode usually consists of PbO2 or Ni(OH)2. In this research, a graphitic carbon foam was impregnated with Co-substituted Ni(OH)2 using electrochemical deposition to serve as the positive electrode in the asymmetric capacitor. The purpose was to reduce the cost and weight of the ECs while maintaining or increasing capacitance and gravimetric energy storage density. The XRD result indicated that the nickel-carbon foam electrode was a typical α-Ni(OH)2. The specific capacitance of the nickel-carbon foam electrode was 2641 F/g at 5 mA/cm2, higher than the previously reported value of 2080 F/g for a 7.5% Al-substituted α-Ni(OH)2 electrode. Three different ACs (RP-20, YP-50F, and Ketjenblack EC-600JD) were evaluated through their morphology and electrochemical performance to determine their suitability for use in ECs. The study indicated that YP-50F demonstrated the better overall performance because of the combination of micropore and mesopore structures. Therefore, YP-50F was chosen to combine with the nickel-carbon foam electrode for further evaluation. Six cells with different mass ratios of negative to positive active mass were fabricated to study the electrochemical performance. Among the different mass ratios, the asymmetric capacitor with the mass ratio of 3.71 gave the highest specific energy and specific power, 24.5 W.h/kg and 498 W/kg, respectively.

Analysis of a novel waste heat recovery mechanism for an I.C. engine

Typical internal combustion engines lose about 75% of the fuel energy through the engine coolant, exhaust and surface radiation. Most of the heat generated comes from converting the chemical energy in the fuel to mechanical energy and in turn thermal energy is produced. In general, the thermal energy is unutilized and thus wasted. This report describes the analysis of a novel waste heat recovery (WHR) system that operates on a Rankine cycle. This novel WHR system consists of a second piston within the existing piston to reduce losses associated with compression and exhaust strokes in a four-cycle engine. The wasted thermal energy recovered from the coolant and exhaust systems generate a high temperature and high pressure working fluid which is used to power the modified piston assembly. Cycle simulation shows that a large, stationary natural gas spark ignition engine produces enough waste heat to operate the novel WHR system. With the use of this system, the stationary gas compression ignition engine running at 900 RPM and full load had a net increase of 177.03 kW (240.7 HP). This increase in power improved the brake fuel conversion efficiency by 4.53%.

Performance evaluation of a novel asymmetric capacitor using a light-weight, carbon foam supported nickel electrode

Electrochemical capacitors have been an important development in recent years in the field of energy storage. Capacitors can be developed by utilizing either double layer capacitance at the electrode/solution interfaces alone or in combination with a battery electrode associated with a faradic redox process in one electrode. An asymmetric capacitor consisting of electrochemically deposited nickel hydroxide, supported on carbon foam as a positive electrode and carbon sheet as a negative electrode has been successfully assembled and cycled. One objective of this study has been to demonstrate the viability of the nickel carbon foam positive electrode, especially in terms of cycle life. Electrochemical characterization shows stable, high cycle performance in 26 wt. % KOH electrolyte with a maximum energy density of 4.1 Wh/Kg and a relaxation time constant of 6.24 s. This cell has demonstrated high cycle life, 14,500 cycles, with efficiency better than 98%. In addition, the cell failure mechanism and self-discharge behavior of the aforesaid capacitor are analyzed.

Numerical modeling of the failure mechanisms in Si thin film anode for Li-ion batteries

In recent times, the demand for the storage of electrical energy has grown rapidly for both static applications and the portable electronics enforcing the substantial improvement in battery systems, and Li-ion batteries have been proven to have maximum energy storage density in all rechargeable batteries. However, major breakthroughs are required to consummate the requirement of higher energy density with lower cost to penetrate new markets. Graphite anode having limited capacity has become a bottle neck in the process of developing next generation batteries and can be replaced by higher capacity metals such as Silicon. In the present study we are focusing on the mechanical behavior of the Si-thin film anode under various operating conditions. A numerical model is developed to simulate the intercalation induced stress and the failure mechanism of the complex anode structure. Effect of the various physical phenomena such as diffusion induced stress, plasticity and the crack propagation are investigated to predict better performance parameters for improved design.

Laser Thomson scattering measurements of electron temperature and density in a Hall-effect plasma

Hall-effect thrusters (HETs) are compact electric propulsion devices with high specific impulse used for a variety of space propulsion applications. HET technology is well developed but the electron properties in the discharge are not completely understood, mainly due to the difficulty involved in performing accurate measurements in the discharge. Measurements of electron temperature and density have been performed using electrostatic probes, but presence of the probes can significantly disrupt thruster operation, and thus alter the electron temperature and density. While fast-probe studies have expanded understanding of HET discharges, a non-invasive method of measuring the electron temperature and density in the plasma is highly desirable. An alternative to electrostatic probes is a non-perturbing laser diagnostic technique that measures Thomson scattering from the plasma. Thomson scattering is the process by which photons are elastically scattered from the free electrons in a plasma. Since the electrons have thermal energy their motion causes a Doppler shift in the scattered photons that is proportional to their velocity. Like electrostatic probes, laser Thomson scattering (LTS) can be used to determine the temperature and density of free electrons in the plasma. Since Thomson scattering measures the electron velocity distribution function directly no assumptions of the plasma conditions are required, allowing accurate measurements in anisotropic and non-Maxwellian plasmas. LTS requires a complicated measurement apparatus, but has the potential to provide accurate, non-perturbing measurements of electron temperature and density in HET discharges. In order to assess the feasibility of LTS diagnostics on HETs non-invasive measurements of electron temperature and density in the near-field plume of a Hall thruster were performed using a custom built laser Thomson scattering diagnostic. Laser measurements were processed using a maximum likelihood estimation method and results were compared to conventional electrostatic double probe measurements performed at the same thruster conditions. Electron temperature was found to range from approximately 1 – 40 eV and density ranged from approximately 1.0 x 1017 m-3 to 1.3 x 1018 m-3 over discharge voltages from 250 to 450 V and mass flow rates of 40 to 80 SCCM using xenon propellant.

Proteins in silico-modeling and sampling

Proteins are linear chain molecules made out of amino acids. Only when they fold to their native states, they become functional. This dissertation aims to model the solvent (environment) effect and to develop & implement enhanced sampling methods that enable a reliable study of the protein folding problem in silico. We have developed an enhanced solvation model based on the solution to the Poisson-Boltzmann equation in order to describe the solvent effect. Following the quantum mechanical Polarizable Continuum Model (PCM), we decomposed net solvation free energy into three physical terms– Polarization, Dispersion and Cavitation. All the terms were implemented, analyzed and parametrized individually to obtain a high level of accuracy. In order to describe the thermodynamics of proteins, their conformational space needs to be sampled thoroughly. Simulations of proteins are hampered by slow relaxation due to their rugged free-energy landscape, with the barriers between minima being higher than the thermal energy at physiological temperatures. In order to overcome this problem a number of approaches have been proposed of which replica exchange method (REM) is the most popular. In this dissertation we describe a new variant of canonical replica exchange method in the context of molecular dynamic simulation. The advantage of this new method is the easily tunable high acceptance rate for the replica exchange. We call our method Microcanonical Replica Exchange Molecular Dynamic (MREMD). We have described the theoretical frame work, comment on its actual implementation, and its application to Trp-cage mini-protein in implicit solvent. We have been able to correctly predict the folding thermodynamics of this protein using our approach.

Development of room temperature operating single electron transistor using FIB etching and deposition technology

The single-electron transistor (SET) is one of the best candidates for future nano electronic circuits because of its ultralow power consumption, small size and unique functionality. SET devices operate on the principle of Coulomb blockade, which is more prominent at dimensions of a few nano meters. Typically, the SET device consists of two capacitively coupled ultra-small tunnel junctions with a nano island between them. In order to observe the Coulomb blockade effects in a SET device the charging energy of the device has to be greater that the thermal energy. This condition limits the operation of most of the existing SET devices to cryogenic temperatures. Room temperature operation of SET devices requires sub-10nm nano-islands due to the inverse dependence of charging energy on the radius of the conducting nano-island. Fabrication of sub-10nm structures using lithography processes is still a technological challenge. In the present investigation, Focused Ion Beam based etch and deposition technology is used to fabricate single electron transistors devices operating at room temperature. The SET device incorporates an array of tungsten nano-islands with an average diameter of 8nm. The fabricated devices are characterized at room temperature and clear Coulomb blockade and Coulomb oscillations are observed. An improvement in the resolution limitation of the FIB etching process is demonstrated by optimizing the thickness of the active layer. SET devices with structural and topological variation are developed to explore their impact on the behavior of the device. The threshold voltage of the device was minimized to ~500mV by minimizing the source-drain gap of the device to 17nm. Vertical source and drain terminals are fabricated to realize single-dot based SET device. A unique process flow is developed to fabricate Si dot based SET devices for better gate controllability in the device characteristic. The device vi parameters of the fabricated devices are extracted by using a conductance model. Finally, characteristic of these devices are validated with the simulated data from theoretical modeling.

MULTIDIMENSIONAL OPTIMAL DROOP CONTROL FOR WIND RESOURCES IN DC MICROGRIDS

Two important and upcoming technologies, microgrids and electricity generation from wind resources, are increasingly being combined. Various control strategies can be implemented, and droop control provides a simple option without requiring communication between microgrid components. Eliminating the single source of potential failure around the communication system is especially important in remote, islanded microgrids, which are considered in this work. However, traditional droop control does not allow the microgrid to utilize much of the power available from the wind. This dissertation presents a novel droop control strategy, which implements a droop surface in higher dimension than the traditional strategy. The droop control relationship then depends on two variables: the dc microgrid bus voltage, and the wind speed at the current time. An approach for optimizing this droop control surface in order to meet a given objective, for example utilizing all of the power available from a wind resource, is proposed and demonstrated. Various cases are used to test the proposed optimal high dimension droop control method, and demonstrate its function. First, the use of linear multidimensional droop control without optimization is demonstrated through simulation. Next, an optimal high dimension droop control surface is implemented with a simple dc microgrid containing two sources and one load. Various cases for changing load and wind speed are investigated using simulation and hardware-in-the-loop techniques. Optimal multidimensional droop control is demonstrated with a wind resource in a full dc microgrid example, containing an energy storage device as well as multiple sources and loads. Finally, the optimal high dimension droop control method is applied with a solar resource, and using a load model developed for a military patrol base application. The operation of the proposed control is again investigated using simulation and hardware-in-the-loop techniques.

NANOSCALE ELECTROCHEMISTRY BY IN-SITU TRANSMISSION ELECTRON MICROSCOPY

Nanoscale research in energy storage has recently focused on investigating the properties of nanostructures in order to increase energy density, power rate, and capacity. To better understand the intrinsic properties of nanomaterials, a new and advanced in situ system was designed that allows atomic scale observation of materials under external fields. A special holder equipped with a scanning tunneling microscopy (STM) probe inside a transmission electron microscopy (TEM) system was used to perform the in situ studies on mechanical, electrical, and electrochemical properties of nanomaterials. The nanostructures of titanium dioxide (TiO2) nanotubes are characterized by electron imaging, diffraction, and chemical analysis techniques inside TEM. TiO2 nanotube is one of the candidates as anode materials for lithium ion batteries. It is necessary to study their morphological, mechanical, electrical, and electrochemical properties at atomic level. The synthesis of TiO2 nanotubes showed that the aspect ratio of TiO2 could be controlled by processing parameters, such as anodization time and voltage. Ammonium hydroxide (NH4OH) treated TiO2 nanotubes showed unexpected instability. Observation revealed the nanotubes were disintegrated into nanoparticles and the tubular morphology was vanished after annealing. The nitrogen compounds incorporated in surface defects weaken the nanotube and result in the collapse of nanotube into nanoparticles during phase transformation. Next, the electrical and mechanical properties of TiO2 nanotubes were studied by in situ TEM system. Phase transformation of anatase TiO2 nanotubes into rutile nanoparticles was studied by in situ Joule heating. The results showed that single anatase TiO2 nanotubes broke into ultrafine small anatase nanoparticles. On further increasing the bias, the nanoclusters of anatase particles became prone to a solid state reaction and were grown into stable large rutile nanoparticles. The relationship between mechanical and electrical properties of TiO2 nanotubes was also investigated. Initially, both anatase and amorphous TiO2 nanotubes were characterized by using I-V test to demonstrate the semiconductor properties. The observation of mechanical bending on TiO2 nanotubes revealed that the conductivity would increase when bending deformation happened. The defects on the nanotubes created by deformation helped electron transportation to increase the conductivity. Lastly, the electrochemical properties of amorphous TiO2 nanotubes were characterized by in situ TEM system. The direct chemical and imaging evidence of lithium-induced atomic ordering in amorphous TiO2 nanotubes was studied. The results indicated that the lithiation started with the valance reduction of Ti4+ to Ti3+ leading to a LixTiO2 intercalation compound. The continued intercalation of Li ions in TiO2 nanotubes triggered an amorphous to crystalline phase transformation. The crystals were formed as nano islands and identified to be Li2Ti2O4 with cubic structure (a = 8.375 Å). This phase transformation is associated with local inhomogeneities in Li distribution. Based on these observations, a new reaction mechanism is proposed to explain the first cycle lithiation behavior in amorphous TiO2 nanotubes.