WO2018164640A1

WO2018164640A1 - Electrode, electrochemical cell and methods of forming the same

Info

Publication number: WO2018164640A1
Application number: PCT/SG2018/050104
Authority: WO
Inventors: Xiaodong Chen; Yuxin Tang; Yanyan Zhang
Original assignee: Nanyang Technological University
Priority date: 2017-03-08
Filing date: 2018-03-07
Publication date: 2018-09-13

Abstract

Various embodiments may provide an electrode. The electrode may include a first electrode layer including an electrode material and a carbon-based conductive additive. The electrode may also include a second electrode layer in contact with the first electrode layer, the second electrode layer also including the electrode material and the carbon-based conductive additive. A concentration of the carbon-based conductive additive in the first electrode layer may be higher than a concentration of the carbon-based conductive additive in the second electrode layer.

Description

ELECTRODE, ELECTROCHEMICAL CELL AND METHODS OF FORMING THE

SAME

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority of Singapore application No. 10201701881P filed on March 8, 2017, the contents of it being hereby incorporated by reference in its entirety for all purposes.

TECHNICAL FIELD

[0002] Various aspects of this disclosure relate to electrodes. Various embodiments of this disclosure relate to electrochemical cells. Various aspects of this disclosure relate to methods of forming electrodes and/or methods of forming electrochemical cells.

BACKGROUND

[0003] Development of high-performance lithium-ion batteries (LIBs) having high capacity and fast charging capability is the imperative direction to meet ever-growing energy consumption due to demand from various applications ranging from portable electronics to electric vehicles. However, there is a trade-off between the power density and energy density of LIBs. The energy loss is more severe at high rates. One of the key problems lies in the lithium (Li)-ion transport. The Li-ion diffusion process inside the active material as well as across the whole electrode is slow. Hence, materials which allow for fast Li-ion diffusivity reduced diffusion path tortuosity, and superior electron transport are highly desirable for high-performance LIBs.

[0004] In order to address the abovementioned, there may be a need to look at the fundamental process for Li-ion diffusion during an electrochemical reaction. FIG. 1 A illustrates a lithium (Li)- ion cell undergoing a charging process. Li-ions are depleted at a cathode electrode surface and accumulated at an anode side. FIG. IB shows (i) a plot of lithium (Li)-ion concentration (Cu₊) as a function of distance illustrating the concentration distribution of lithium ions in the electrolyte and anode; and (ii) a plot of operation lithiation potential (r\_c) relative to reference lithium metal potential (Eu⁺ - Ε^φϋ) as a function of distance illustrating the variation of polarization -induced potential across the electrolyte and the anode. Eu⁺ is the operation lithiation potential for the anode, Eo is the standard lithiation potential for the anode, and &u is the reference potential of lithium metal. Since the cell potential is determined by the surface composition of electrodes, the increased Li-ion concentration on the anode surface compared to bulk Li-ion concentration results in premature discharge termed as the concentration polarization induced overpotential (¾_c).

[0005] Li-ion transport can be considered as a linear diffusion described by Fick's laws in a conventional electrode. According to the solution of one-dimensional second Fick's law for a symmetric film with a finite thickness (21) and constant Li-ion diffusivity (D), the normalized concentration (C) can be described as function of depth (x) and time (t) using equation (1).

(1)

[0006] According to this equation, normalized charging time (Dt/P) determines the shape of concentration profile as shown in FIG. 1C. FIG. 1C is a plot of normalized concentration as a function of normalized distance showing the lithium (Li)-ion concentration profile for a symmetric film with 21 thickness and constant lithium diffusivity D at a time t. The normalized charging time may be defined as Dt/P.

[0007] In particular, the concentration profile drops sharply at small normalized charging time, while an increase of the normalized charging time can result in more homogeneous Li-ion distribution.

[0008] The simplified diffusion model indicates that concentration polarization is more serious at high charging rates, and it can be reduced or minimized by increasing the characteristic diffusion length (VZ)t) and decreasing the material thickness. By integrating concentration profile over the thickness, the performance, termed as degree of charge (DoC), of an electrode material can be estimated as the ratio of Li-ions in the electrode at time t and at infinite time from Equation (2):

(2)

[0009] FIG. ID is a plot of degree of charge (DoC, in percent or %) as a function of time (in seconds or s) showing the relationship between of charge (DoC) and charging time. FIG. ID clearly indicates that the degree of charge gradually decreases with the decrease in charging time. Further, the degree of charge decreases with decrease of Li-ion diffusivity and/or increase in electrode thickness.

[0010] Hence, Li-ion diffusion is kinetically limited in the conventional electrode system, which results in reaction polarization (concentration and activation polarization) in the anode electrode. There is a gradient reaction along the diffusion direction due to the limited characteristic Li-ion diffusion length especially at high rates. Although the major limitation is Li-ion diffusion, the electronic transport within the electrode may also be crucial for high-rate LIBs application since electrons and Li-ions react within the active material during electrochemical reaction concurrently. Therefore, it is desirable to increase or maximize Li-ion penetration into electrode material by reducing or minimizing effective Li-ion diffusion barrier at maintaining good electronic conductivity to solve the concentration polarization issues. FIG. IE is a plot of current density i (in milliamperes per square centimeter or mA/cm²) as a function of charging current distribution illustrating the total current distribution (Io) distribution in each lithium (Li)-ion battery component according to Faraday's law. 102a indicates the gradient distribution of lithium (Li) current (Iu+) within the anode, and 102b indicates the gradient distribution of electronic current (I_e-) within the anode. Since the total current distribution (I₀) distribution is constant in the electric loop, the electronic current (I_e-) shows a reverse gradient with respect to the lithium (Li) current (Iu+) within the anode. Therefore, according to Ohm's law and Fick's second law, in order to address the reaction polarization issues, it may be required to reduce ionic and electronic resistance at electrolyte/ electrode and electrode/current collector interfaces respectively, as well as to reduce/minimize Li-ion diffusion barrier and increase/maximize electronic conductivity along the charge carrier transport directions

SUMMARY

[0011] Various embodiments may provide an electrode. The electrode may include a first electrode layer including an electrode material and a carbon-based conductive additive. The electrode may also include a second electrode layer in contact with the first electrode layer, the second electrode layer also including the electrode material and the carbon-based conductive additive. A concentration of the carbon-based conductive additive in the first electrode layer may be higher than a concentration of the carbon-based conductive additive in the second electrode layer.

[0012] Various embodiments may provide an electrochemical cell. The electrochemical cell may include an electrode as described herein. The electrochemical cell may also include a further electrode. The electrochemical cell may additionally include an electrolyte layer between the electrode and the further electrode, the electrolyte layer including an electrolyte.

[0013] Various embodiments may provide a method of forming an electrode. The method may include forming a first electrode layer including an electrode material and a carbon-based conductive additive. The method may also include forming a second electrode layer in contact with the first electrode layer, the second electrode layer also including the electrode material and the carbon-based conductive additive. A concentration of the carbon-based conductive additive in the first electrode layer may be higher than a concentration of the carbon-based conductive additive in the second electrode layer.

[0014] Various embodiments may provide a method of forming an electrochemical cell. The method may include providing an electrolyte layer between the electrode as described herein, and a further electrode. The electrolyte layer may include an electrolyte.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The invention will be better understood with reference to the detailed description when considered in conjunction with the non-limiting examples and the accompanying drawings, in which:

FIG. 1A illustrates a lithium (Li)-ion cell undergoing a charging process.

FIG. IB shows (i) a plot of lithium (Li)-ion concentration (Cu+) as a function of distance illustrating the concentration distribution of lithium ions in the electrolyte and anode; and (ii) a plot of operation lithiation potential (η₀) relative to reference lithium metal potential (Eu⁺ - Ε^φυ) as a function of distance illustrating the variation of polarization -induced potential across the electrolyte and the anode.

FIG. 1C is a plot of normalized concentration as a function of normalized distance showing the lithium (Li)-ion concentration profile for a symmetric film with 21 thickness and constant lithium diffusivity D at a time t. FIG. ID shows a plot of degree of charge (DoC, in percent or %) as a function of time (in seconds or s) showing the relationship between of charge (DoC) and charging time.

FIG. IE is a plot of current density i (in milliamperes per square centimeter or mA/cm²) as a function of charging current distribution illustrating the total current distribution (I₀) distribution in each lithium (Li)-ion battery component according to Faraday's law.

FIG. 2A is a cross-sectional schematic of an electrode according to various embodiments.

FIG. 2B is a cross-sectional schematic of an electrochemical cell according to various embodiments.

FIG. 2C is a cross-sectional schematic of an electrode according to various embodiments.

FIG. 3 A is a schematic illustrating a titanium dioxide (Ti0₂) (B) supercell containing lithium (Li) atoms at A2 sites.

FIG. 3B is a plot of the density of states (DOS) (in 1 /electron-volts (eV)/cell) as a function of energy (in electron-volts (eV)) illustrating the density of states (DOS) computed using hybrid functional calculations for lithiated titanium oxide (Ti0₂) (B).

FIG. 4A shows a schematic illustrating the lowest migration pathway of lithium (Li ions) in titanium oxide (Ti0₂) (B).

FIG. 4B is a plot of energy (in electron volts or eV) as a function of reaction coordinate showing the lowest energy diffusion energy barrier for diffusion of lithium (Li) ions in titanium dioxide (Ti0₂) (B) computed for migrations between two lowest energy sites using density functional theory (DFT) and DFT with Hubbard correction (DFT+U).

FIG. 4C shows a schematic illustrating an alternative migration pathway of lithium (Li) ions in titanium oxide (Ti0₂) (B) using Perdew-Burke-Ernzerhof (PBE) calculations.

FIG. 4D is a plot of energy (in electron volts or eV) as a function of reaction coordinate showing the energy barrier corresponding to FIG. 4C.

FIG. 4E shows a schematic illustrating another alternative migration pathway of lithium (Li) ions in titanium oxide (Ti0₂) (B) using Perdew-Burke-Ernzerhof (PBE) calculations.

FIG. 4F is a plot of energy (in electron volts or eV) as a function of reaction coordinate showing the energy barrier corresponding to FIG. 4E. FIG. 5A is a plot of the density of states (DOS) (in 1 /electron-volts (eV)/cell) as a function of energy (in electron-volts (eV)) illustrating the density of states (DOS) of a graphene titanium oxide (Ti0₂) (B) hybrid system according to various embodiments.

FIG. 5B is a schematic illustrating the lowest energy carbon (C) / titanium dioxide (Ti0₂) (B) interface structure according to various embodiments.

FIG. 5C is a schematic illustrating lithium (Li)-ion diffusion along the graphene surface (ab-plane) and through six-membered hexagonal ring (c-direction) according to various embodiments. FIG. 5D is a plot of energy (in electron-volts or eV) as a function of reaction coordinate illustrating lithium-ion diffusion barriers for ab-plane and c-direction pathways according to various embodiments.

FIG. 6A shows cross-sectional schematics of functionally-graded electrodes according to various embodiments, while shows a cross-sectional schematic of a conventional homogenous electrode before vacuum annealing.

FIG. 6B shows cross-sectional schematics of the functionally-graded electrodes according to various embodiments, as well as the homogenous electrode after vacuum treatment.

FIG. 7 shows (top, from left to right) a digital image of different inks (with a concentration of 3.5 mg/mL) of pure graphene oxide (GO), 30% GO / hydrogen titanate nanotubes (H-TNT), 11% GO / H-TNT, 3% GO / H-TNT, and pure TNT; and (bottom, from left to right) a digital image of different layers of pure reduced graphene oxide (RGO), 30% RGO / titanium dioxide (Ti0₂), 11% RGO / Ti0₂, 3% RGO / Ti0₂, pure Ti0₂ and copper foil according to various embodiments. FIG. 8 A is a plot of intensity (in arbitrary units or a.u.) as a function of angle (in degrees) showing the X-ray Diffraction (XRD) patterns of the as-prepared reduced graphene oxide (RGO), pure titanium dioxide (Ti0₂) (B), and various reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) composite films according to various embodiments.

FIG. 8B is a plot of intensity (in arbitrary units or a.u.) as a function of angle (in degrees) showing the X-ray Diffraction (XRD) patterns of graphene oxide (GO) nanosheets and reduced graphene oxide (RGO) nanosheets.

FIG. 8C is a plot of transmittance (in arbitrary units or a.u.) as a function of wavenumber (in per centimeter or cm^"1) showing the Fourier transform infrared (FTIR) spectra of graphene oxide (GO) nanosheets and reduced graphene oxide (RGO) nanosheets. FIG. 8D is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the Cls and Ols X-ray photoelectron spectroscopy (XPS) spectra for pure titanium dioxide (Ti0₂) (B) and reduced graphene oxide / titanium dioxide (RGO/Ti0₂) (B) films according to various embodiments.

FIG. 9A is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the broad scanning spectrum of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in air according to various embodiments.

FIG. 9B is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Cls of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in air according to various embodiments.

FIG. 9C is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ols of titanium dioxide (T1O2) (B) nanotubes formed by annealing in air according to various embodiments.

FIG. 9D is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ti2p of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in air according to various embodiments.

FIG. 9E is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the broad scanning spectrum of titanium dioxide (T1O2) (B) nanotubes formed by annealing in vacuum according to various embodiments.

FIG. 9F is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Cls of titanium dioxide (Ti02) (B) nanotubes formed by annealing in vacuum according to various embodiments.

FIG. 9G is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ols of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in vacuum according to various embodiments.

FIG. 9H is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ti2p of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in vacuum according to various embodiments.

FIG. 91 is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the broad scanning spectrum of titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) nanotubes formed by annealing in vacuum according to various embodiments.

FIG. 9 J is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Cls of titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) nanotubes formed by annealing in vacuum according to various embodiments.

FIG. 9K is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ols of titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) nanotubes formed by annealing in vacuum according to various embodiments.

FIG. 9L is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ti2p of titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) nanotubes formed by annealing in vacuum according to various embodiments.

FIG. 10A is a field emission scanning electron microscope (FESEM) image of a pure titanium dioxide (Ti0₂) (B) film according to various embodiments.

FIG. 1 OB is a magnified field emission scanning electron microscope (FESEM) image of a pure titanium dioxide (T1O2) (B) film according to various embodiments.

FIG. IOC is a field emission scanning electron microscope (FESEM) image of a 3% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. The arrows indicate the positions of reduced graphene oxide.

FIG. 10D is a magnified field emission scanning electron microscope (FESEM) image of a 3% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

FIG. 10E is a field emission scanning electron microscope (FESEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. The arrows indicate the positions of reduced graphene oxide.

FIG. 1 OF is a magnified field emission scanning electron microscope (FESEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. FIG. 10G is a field emission scanning electron microscope (FESEM) image of a 30% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. FIG. 1 OH is a magnified field emission scanning electron microscope (FESEM) image of a 30% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

FIG. 101 is a field emission scanning electron microscope (FESEM) image of a pure reduced graphene oxide film according to various embodiments.

FIG. 10J is a magnified field emission scanning electron microscope (FESEM) image of a pure reduced graphene oxide film according to various embodiments.

FIG. 10K is a field emission scanning electron microscope (FESEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments, with the areas encircled by dashed lines indicating the reduced graphene oxide (RGO) nanosheets. FIG. 11A shows a transmission electron microscopy (TEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (T1O2) (B) film according to various embodiments.

FIG. 1 IB is a high-resolution transmission electron microscopy (HRTEM) image of the reduced graphene oxide (RGO) sheet indicated by area "A" in FIG. 11A of the film according to various embodiments.

FIG. 11 C is a high-resolution transmission electron microscopy (HRTEM) image of the titanium oxide (Ti0₂) (B) nanotubes indicated by area "B" in FIG. 11A of the film according to various embodiments.

FIG. 1 ID is a cross-sectional field emission scanning electron microscope (FESEM) image of a reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) electrode.

FIG. HE is a magnified cross-sectional field emission scanning electron microscope (FESEM) image of a reduced graphene oxide (RGO) / titanium dioxide (T1O2) (B) electrode.

FIG. 12A is a plot of number of counts Kent (normalized to 1.0) as a function of energy (in kiloelectron-volts or keV) showing scanning transmission elemental microscopy (STEM) - energy-dispersive X-ray spectroscopy (EDX) spectrum of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

FIG. 12B is a magnified transmission electron microscopy (TEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments showing excellent attachment between the reduced graphene oxide sheets and the titanium dioxide (Ti0₂) nanotubes.

FIG. 12C shows an energy-dispersive X-ray spectroscopy (EDX) mapping of titanium present in a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

FIG. 12D shows an energy-dispersive X-ray spectroscopy (EDX) mapping of oxygen present in a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

FIG. 12E shows an energy-dispersive X-ray spectroscopy (EDX) mapping of carbon present in a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

FIG. 12F shows a transmission electron microscopy (TEM) image of an electrode according to various embodiments.

FIG. 12G shows a cross-sectional titanium (Ti) elemental mapping of the multi-segmented reduced graphene oxide (RGO) nanosheets / titanium dioxide (Ti0₂) (B) nanotube films according to various embodiments.

FIG. 12H shows a cross-sectional oxygen (O) elemental mapping of the multi-segmented reduced graphene oxide (RGO) nanosheets / titanium dioxide (T1O2) (B) nanotube films according to various embodiments.

FIG. 121 shows a cross-sectional carbon (C) elemental mapping of the multi-segmented reduced graphene oxide (RGO) nanosheets / titanium dioxide (Ti0₂) (B) nanotube films according to various embodiments.

FIG. 13A is a plot of weight (in percent or %) as a function of temperature (in degrees Celsius or °C) showing the thermogravimetric analysis (TGA) curves for graphene oxide (GO), reduced graphene oxide (RGO), titanium dioxide (Ti0₂) (B), and various reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) films according to various embodiments heated in air.

FIG. 13B is a three-dimensional plot of weight (in percent or %) as a function of temperature (in degrees Celsius or °C) and time (in minutes or min) showing the thermogravimetric analysis (TGA) curves of graphene oxide (GO) and hydrogen titanate nanotube (H-TNT) according to various embodiments in nitrogen gas atmosphere. FIG. 14A is a plot of intensity (in arbitrary units or a.u.) as a function of Raman shift (in per centimeter or cm^"1) showing the Raman spectra of graphene oxide, reduced graphene oxide (RGO), pure titanium dioxide (Ti0₂) (B) and various ratios of reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) according to various embodiments.

FIG. 14B is a plot of conductivity (in Siemens per centimeter or S/cm) as a function of sample number showing the electrical conductivity of reduced graphene oxide (RGO), pure titanium dioxide (Ti0₂) (B) annealed in air and vacuum, and various ratios of reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) according to various embodiments measured using four-probe resistance testing.

FIG. 14C is a plot of ionic conductivity Du+ (in square centimeter / second or cm²/s) as a function of cycle number illustrating the ionic conductivity of pure titanium dioxide (Ti0₂) (B), reduced graphene oxide (RGO), and various ratios of reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) according to various embodiments measured using electrochemical impedance spectroscopy (EIS) measurements.

FIG. 14D is another plot of ionic conductivity Du+ (in square centimeter / second or cm²/s) as a function of cycle number illustrating the ionic conductivity of pure titanium dioxide (Ti0₂) (B), reduced graphene oxide (RGO), and various ratios of reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) according to various embodiments measured using electrochemical impedance spectroscopy (EIS) measurements.

FIG. 15A shows images of functionally-graded electrodes according to various embodiments, and an image of a conventional homogenous electrode.

FIG. 15B is a plot of discharge capacity (in milliampere-hours per gram or mAh/g) as a function of cycle number showing the rate-dependent electrochemical performance of the upgraded electrode and the downgraded electrode according to various embodiments, as well as the rate- dependent electrochemical performance of the homogenous electrode.

FIG. 15C is a plot of discharge capacity (in milliampere-hours per gram or mAh/g) as a function of cycle number showing the battery performance of three upgraded electrodes according to various embodiments, as well as the battery performance of the homogenous electrode.

FIG. 15D is a plot of electronic conductivity (S cm^"1) / ionic conductivity Du+ (in square centimeter / second or cm²/s) as a function of reduced graphene oxide (RGO) content (in percent or %) showing the correlation between electronic conductivity/ ionic conductivity and RGO content according to various embodiments.

FIG. 15E is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the cyclic voltammogram (CV) curves of the upgraded electrode according to various embodiments as anode at a scan rate of 0.1 mV/s for different cycles.

FIG. 15F is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the cyclic voltammogram (CV) curves of the homogenous electrode as anode at a scan rate of 0.1 mV/s for different cycles.

FIG. 15G is a plot of discharge capacity (in milliampere-hours per gram or mAh g) / coulombic efficiency (in percent or %) as a function of cycle number showing the capacity retention of a composition upgraded anode (gradient sample) according to various embodiments and a homogeneous anode (homogenous sample) through 100 cycles at 1 C rate.

FIG. 15H is a plot of voltage (in volts or V) as a function of discharge capacity (in milliampere- hours per gram or mAh/g) showing the charge/discharge curves of different cycles of a composition upgraded anode according to various embodiments at 1C.

FIG. 151 is a plot of voltage (in volts or V) as a function of discharge capacity (in milliampere- hours per gram or mAh/g) showing the charge/discharge curves of different cycles of a homogenous anode according to various embodiments at 1C.

FIG. 15 J is a plot of lithiation potential (volts or V with reference to Li/Li+) as a function of capacity (in milliampere-hours per gram or mAh/g) showing the charging/discharging curves of the upgraded anode according to various embodiments with increasing current densities.

FIG. 15K is a plot of lithiation potential (volts or V with reference to Li/Li+) as a function of capacity (in milliampere-hours per gram or mAh/g) showing the charging/discharging curves of the homogenous anode according to various embodiments with increasing current densities. FIG. 15L is a plot of lithiation potential (volts or V with reference to Li/Li+) as a function of capacity (in milliampere-hours per gram or mAh/g) showing the charging/discharging curves of the downgraded anode according to various embodiments with increasing current densities.

FIG. 16A is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the cyclic voltammogram (CV) curves of the upgraded anode according to various embodiments at different scan rates from 0.1 to 10 mV/s. FIG. 16B is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li+) showing the cyclic voltammogram (CV) curves of the upgraded anode according to various embodiments, with the curves corresponding the curves shown in FIG. 16A that are within a range of current densities of -1.2 to 0.6 A/g.

FIG. 16C is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the cyclic voltammogram (CV) curves of the homogenous anode according to various embodiments at different scan rates from 0.1 to 10 mV/s.

FIG. 16D is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li Li+) showing the cyclic voltammogram (CV) curves of the upgraded anode according to various embodiments, with the curves corresponding the curves shown in FIG. 16C that are within a range of current densities of -1.2 to 0.5 A/g.

FIG. 17A is a plot of the logarithm of peak current (in amperes or A) as a function of the logarithm of scan rate (in millivolts per second or mV/s) showing the relationship between the cyclic voltammogram (CV) peak current and the scanning rate for the upgraded electrode according to various embodiments and the homogenous electrode.

FIG. 17B is a plot of polarization potential (in volts or V) as a function of scan rate (in millivolts per second or mV/s) showing the redox peak separation during the charging and discharging processes of the upgraded electrode according to various embodiments and the homogenous electrode.

FIG. 18A is a plot of voltage (in volts or V) as a function of time (in minutes or min) showing a galvanostatic intermittent titration technique (GITT) profile of composition upgraded anode according to various embodiments during charging and discharging as a function of time.

FIG. 18B is a plot of voltage (in volts or V) as a function of time (in minutes or min) showing a demonstration of a single titration according to various embodiments.

FIG. 18C is a plot of lithium ion diffusivity (in square centimeter per s or cm²/s) as a function of lithiation potential (volts or V with reference to Li Li⁺) showing the calculated lithium ion diffusion coefficient for the upgraded anode according to various embodiments and the homogenous anode with varying lithiation potential based on the galvanostatic intermittent titration technique (GITT).

FIG. 18D is a plot of voltage (in volts or V) as a function of time (in minutes or min) showing a galvanostatic intermittent titration technique (GITT) profile of a homogenous anode.

FIG. 19A is a plot of current (in amperes or A) as a function of potential (in volts or V) showing the cyclic voltammogram (CV) curve of composition upgraded electrode according to various embodiments at 0.1 mV/s for 1st cycle and the demonstration of cathodic peak intensity.

FIG. 19B is a plot of peak current (in milliamperes or mA) as a function of square root of scan rate

(in root of millivolts per s or (mV/s)^{1 2}) showing the linear fitting of the cathodic peak intensity against the square root of scan rate for the composition upgraded anode according to various embodiments and the homogeneous anode.

FIG. 20 is a three-dimensional plot of the virtual part of the complex-value impedance Z" (in ohms or Ω) as a function of the real part of the complex- value impedance Z' (in ohms or Ω) and the lithiation potential (volts or V with reference to Li/Li⁺) showing the Nyquist plots for the composition upgraded electrode according to various embodiments and the homogeneous electrode.

FIG. 21 is a plot of resistance (in ohms or Ω) as a function of the lithiation potential (volts or V with reference to Li/Li⁺) showing the electrochemical impedance spectroscopy (EIS) measurement of the upgraded electrode according to various embodiments and the homogenous electrode. FIG. 22 is a schematic showing lithium (Li)-ion and electron transport into the composition upgraded titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) electrode according to various embodiments.

FIG. 23 is a schematic showing lithium (Li)-ion and electron transport into the homogenous titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) electrode.

FIG. 24 is a schematic showing a method of forming an electrode according to various embodiments.

FIG. 25 is a schematic showing a method of forming an electrochemical cell according to various embodiments.

DETAILED DESCRIPTION [0016] The following detailed description refers to the accompanying drawings that show, by way of illustration, specific details and embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized and structural, and logical changes may be made without departing from the scope of the invention. The various embodiments are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.

[0017] Embodiments described in the context of one of the methods or electrode/electrochemical cell are analogously valid for the other methods or electrode/electrochemical cell. Similarly, embodiments described in the context of a method are analogously valid for an electrode/electrochemical cell, and vice versa.

[0018] Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments. Features that are described in the context of an embodiment may correspondingly be applicable to the other embodiments, even if not explicitly described in these other embodiments. Furthermore, additions and/or combinations and/or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.

[0019] The word "over" used with regards to a deposited material formed "over" a side or surface, may be used herein to mean that the deposited material may be formed "directly on", e.g. in direct contact with, the implied side or surface. The word "over" used with regards to a deposited material formed "over" a side or surface, may also be used herein to mean that the deposited material may be formed "indirectly on" the implied side or surface with one or more additional layers being arranged between the implied side or surface and the deposited material. In other words, a first layer "over" a second layer may refer to the first layer directly on the second layer, or that the first layer and the second layer are separated by one or more intervening layers.

[0020] The electrode or electrochemical cell as described herein may be operable in various orientations, and thus it should be understood that the terms "top", "topmost", "bottom", "bottommost" etc., when used in the following description are used for convenience and to aid understanding of relative positions or directions, and not intended to limit the orientation of the electrode or electrochemical cell. [0021] In the context of various embodiments, the articles "a", "an" and "the" as used with regard to a feature or element include a reference to one or more of the features or elements.

[0022] In the context of various embodiments, the term "about" or "approximately" as applied to a numeric value encompasses the exact value and a reasonable variance.

[0023] As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

[0024] A functionally graded material may relate to a composite material having a variation in composition and structure gradually over a volume, enabling full utilization of material properties of multiple constituent components. Since Li-ion and electron fluxes are transported from opposite directions, a functionally graded electrode may allow the overcoming of the reaction polarization in conventional homogeneous electrodes (see FIG. IB), by building a reverse gradient transport barrier along the transport direction. In various embodiments, each electrode component may utilize individual electronic and ionic properties of the constituent components, thereby increasing or maximizing the characteristic diffusion length via reducing electrolyte, e.g. Li-ion, diffusion barrier.

[0025] FIG. 2A is a cross-sectional schematic of an electrode 200 according to various embodiments. The electrode 200 may include a first electrode layer 202 including an electrode material and a carbon-based conductive additive. The electrode 200 may also include a second electrode layer 204 in contact with the first electrode layer, the second electrode layer also including the electrode material and the carbon-based conductive additive. A concentration of the carbon-based conductive additive in the first electrode layer may be higher than a concentration of the carbon-based conductive additive in the second electrode layer.

[0026] In other words, various embodiments may relate to a functionally graded electrode 200 with different layers or segments 202, 204 having a different concentration or amount of carbon- based conductive additive.

[0027] Various embodiments may address or mitigate the various issues faced by conventional electrodes. Various embodiments may utilize a functional-layer-graded approach to improve the electrolyte diffusivity, e.g. Li-ion diffusivity within the electrode. Various embodiments may have advantages over conventional homogenous electrodes. Various embodiments may increase or maximize electrolyte penetration into electrode material by reducing or minimizing electrolyte diffusion barrier. Various embodiments may reduce ionic resistance at the electrolyte/ electrode interface, and electronic resistance at the electrode/current collector interface. Various embodiments may reduce or minimize Li-ion diffusion barrier, and/or increase or maximize electronic conductivity along the charge carrier transport directions.

[0028] An electrode material as described herein may refer to a material suitable for an electrode. The electrode material may alternatively be referred to as a matrix material. In various embodiments, the electrode material may be any one selected from a group consisting of titanium dioxide (Ti0₂), lithium titanate, silicon, a metal oxide, a layered oxide (e.g. LiCo0₂, Li n0₂, LiNio.₅Mn₀.₅0₂, or LiNii/3Co₁/3Mm/30₂), a spinel oxide (e.g. LiMn₂0₄ or LiNi₀.₅Mm.₅O₄), and an olivine polyanion L1MPO4 (where M may be Fe, Co, Ni, or Mn). In various embodiments, the electrode material may be an anode material.

[0029] In various embodiments, the electrode material may be titanium dioxide (Ti0₂). The titanium dioxide may have a monoclinic crystal structure (e.g. Ti0₂ (B)) or a tetragonal crystal structure (e.g. anatase form).

[0030] Titanium dioxide with a monoclinic crystal structure (Ti0₂ (B)) may enable fast Li-ion kinetics and may possess safe lithiation potential.

[0031] A carbon-based conductive additive as described herein may refer to an additive containing carbon. In various embodiments, the carbon-based conductive additive may be any one selected from a group consisting of reduced graphene oxide, graphene, carbon black, and carbon nanotubes.

[0032] In various embodiments, the electrode 200 may be referred to as a hybrid electrode as the electrode 200 includes different materials. In various embodiments, the electrode material may be titanium dioxide, and the carbon-based conductive additive may be reduced graphene oxide (RGO). Reduced graphene oxide may include graphene sheets with some oxygen functional groups in or on the reduced graphene oxide surface. An electrode having reduced graphene oxide may have better electrode performance compared to an electrode including carbon black or carbon nanotube, due to the planar structure of the reduced graphene oxide. The carbon-based conductive additive may be dispersed or embedded in the electrode material.

[0033] In various embodiments, the second layer 204 may be on the first layer 202. [0034] In various embodiments, the electrode 200 may further include a current collector. The current collector may include an electrically conductive material, such as a metal, e.g. copper. In various embodiments, the current collector may be in contact with the first electrode layer so that the first electrode layer 202 is between the current collector and the second electrode layer 204. In various embodiments, the first electrode layer 202 may be on or over the current collector, and the second electrode layer 204 may be on the first electrode layer 202. In various embodiments, during operation of the electrode 200, electrons may pass or flow from the current collector through the first electrode layer 202 to the second electrode layer 204.

[0035] In various embodiments, the electrode 200 may further include one or more further electrode layers over the first electrode layer 202 and the second electrode layer 204. The one or more further layers, the first electrode layer 202 and the second electrode layer 204 may form a stacked arrangement. The one or more further electrode layers may also include the electrode material.

[0036] In various embodiments, a topmost further electrode layer of the one or more further electrode layers may be devoid of the carbon-based conductive additive. In other words, the topmost further electrode layer may not contain the carbon-based conductive additive. One or more intervening further electrode layers (of the one or more further electrode layers) between the topmost further electrode layer and the second electrode layer may further include the carbon- based conductive additive. A concentration of the carbon-based conductive additive of an intervening further electrode may be higher than a concentration of the carbon-based conductive additive of another intervening further electrode over the intervening further electrode, and the concentration of the carbon-based conductive additive of the second electrode may be higher than the concentration of the intervening further electrode. In other words, the concentration of the carbon-based conductive additive may increase from the topmost further electrode layer (which contains 0% carbon-based conductive additive) to the first electrode layer. In the current context, a concentration of the carbon-based additive may refer to an amount of the carbon-based additive per unit volume of the electrode layer including the carbon-additive, or may refer to an amount of the carbon-based additive per unit amount of the electrode material. For instance, a "concentration" may refer to a weight ratio or volume ratio of the carbon-based additive to the electrode material. [0037] It may also be envisioned that the topmost further electrode layer also contains the carbon-based conductive additive.

[0038] An electrode in which the concentration of the carbon-based conductive additive increases from the topmost further electrode layer (which contains a relatively lower predetermined percentage of carbon-based conductive additive) to the first electrode layer (which contains a relatively higher predetermined percentage of carbon-based conductive additive) may be referred to as a composition upgraded electrode. A composition upgraded electrode may have a lower energy barrier for electrolyte, e.g. lithium (Li) ion diffusion, and may have a higher electronic conductivity compared to a conventional homogenous electrode.

[0039] In various embodiments, at low potentials, ion diffusivity may be higher in the composition upgraded electrode compared to the conventional homogenous electrode.

[0040] In various embodiments, the electrode material may be included in a plurality of first nanostructures. The first nanostructures may be of any suitable shape. For instance, the first nanostructures may be any one selected from a group consisting of nanotubes, nanowires, nanoparticles, and nanosheets.

[0041] In various embodiments, the carbon-based conductive additive may be included in a plurality of second nanostructures. The second nanostructures may be of any suitable shape. For instance, the second nanostructures may be any one selected from a group consisting of nanotubes, nanowires, nanoparticles, and nanosheets.

[0042] In various embodiments, the first nanostructures may be cross-linked to the second nanostructures. There may be bonds between a first nanostructure and a second nanostructure. The bonds may be van der Waals bonds.

[0043] Various embodiments may provide an electrochemical cell. The electrochemical cell may include an electrode 200 as described herein. FIG. 2B is a cross-sectional schematic of an electrochemical cell according to various embodiments. The electrochemical cell may include the electrode 200 as described herein. The electrochemical cell may also include a further electrode 250. The electrochemical cell may additionally include an electrolyte layer 252 between the electrode and the further electrode, the electrolyte layer including a suitable electrolyte. For instance, the electrolyte may be or may include a lithium salt (e.g. lithium hexafluorophosphate (LiPF₆) or lithium tetrafluoroborate (L1BF4)) in an organic solvent (such as ethylene carbonate, dimethyl carbonate, or diethyl carbonate).

[0044] The electrode 200 may be an anode, while the further electrode 250 may be a cathode. The anode may be defined as the negative electrode during the discharge cycle, while the cathode may be defined as the positive electrode during the discharge cycle.

[0045] In various embodiments, the further electrode 250 may be a conventional electrode, such as a homogenous lithium cobalt oxide electrode.

[0046] In various embodiments, the electrochemical cell may further include a separator layer. The separator layer may be configured to prevent the electrode 200 and the further electrode 250 from coming into physical contact with each other.

[0047] The electrochemical cell may be also referred to as a battery. The electrochemical cell may be a lithium (Li) ion battery. The electrochemical cell may have a battery capacity of more than 100 mAh/g, more than 120 mAh/g, or more than 125 mAh/g at a charging / discharging rate of 20 C (6.7 Ag^"1, 1 C = 335 mA/g). Various embodiments may have a capacity much higher than that of a homogenous electrode having the same composition. For instance, a lithium battery (LIB) including a multi-segmented reduced graphene oxide (RGO) / Ti0₂ (B) hybrid anode may have a battery capacity of about 128 mAh/g at a charging / discharging rate of 20 C (6.7 A/g), which is higher than a capacity of a lithium battery (LIB) having a homogenous reduced graphene oxide (RGO) / Ti0₂ (B) electrode (about 74 mAh/g). The improvement may be due to the enhancement of Li-ion diffusivity in the functionally graded electrode through reducing the effective Li-ion diffusion barrier (since Li-ion diffusivity is the exponential function of the energy barrier). Various embodiments may provide an effective solution for improving high-rate LIB performance.

[0048] Various embodiments may relate to a reduced graphene oxide (RGO) / titanium oxide (Ti0₂) (B) electrode. The electrolyte may include Li-ions. First principle analysis of Li-ion dynamics in RGO/Ti0₂ (B) system may be carried out as a guidance for experimental implementation. The intercalation pseudocapacitive type of Ti0₂(B) materials with relatively high capacity (335 mAh/g), which enable fast Li-ion kinetics and possess safe lithiation potential (> 1.0 V), may be one of the most promising high-rate anode materials to replace commercialized benchmark Li₄Ti₅0₁₂ (175 mAh/g). On the other hand, graphene oxide (GO)-based nanosheets has been identified as an excellent conductive additive for building the conductive networks for numerous electrode materials.

[0049] The corresponding electrode performance of an electrode including reduced graphene oxide may be comparable or higher than that for the electrodes with carbon nanotube/carbon black additive. The electrode performance may be mainly attributed to the unique plane-contact electric networks from large surface area of two-dimensional planar structure.

[0050] Fruitful progress has been made on the introduction of RGO nanosheets into T1O2 or other electrode materials for achieving high-rate LIBs performance (> 10 C). Nevertheless, the electrochemical insight towards understanding of Li-ion transport within graphene-based electrodes may still be limited, and the maximization or increase of ionic diffusivity within the electrodes may be crucial for achieving high-rate performance.

[0051] The arrangement of graphitic carbon planes may significantly affect Li-ion diffusion tortuosity in the electrode materials, thus leading to a difference in electrochemical performance. Various trajectories and change of the electronic properties of Li-ion diffusion barriers may be investigated by a first-principles approach with the density functional theory (DFT) to obtain further insight into the lithiation dynamics in the graphene/Ti0₂(B) hybrid system.

[0052] FIG. 2C is a cross-sectional schematic of an electrode 280 according to various embodiments. The electrode 280 may include a current collector 282. The electrode 280 may also include an electrode body 284 in contact with the current collector 282. The electrode body 284 may include an electrode material and a carbon-based conductive additive. A concentration of the carbon-based additive in a first region may be lower than a concentration of the carbon-based additive in a second region. A distance between the first region and the current collector 282 may be greater than a distance between the second region and the current collector 282.

[0053] In other words, the electrode 280 may include a current collector 282 and an electrode body 284 in contact with the current collector 282. A region of the electrode body 284 further from the current collector 282 may have a lower concentration of carbon-based conductive additive.

[0054] In various embodiments, the electrochemical cell shown in FIG. 2B may include electrode 280 instead of electrode 200.

[0055] The concentration of the carbon-based conductive additive may increase gradually from the first region to the second region. The electrode body 284 may also include one or more further regions between the first region and the second region. The different regions may not form layers or segments that are distinct or distinguishable from one another. In other words, the proportion of the carbon-based conductive additive relative to the electrode material may increase gradually from the first region distal to the current collector 282 to the second region proximal to the current collector. The increase in the proportion or concentration of the carbon-based conductive additive may form a continuous concentration gradient.

[0056] In various embodiments, the first region may extend in a plane parallel to the current collector 282. The second region may also extend in a plane parallel to the current collector.

[0057] In various embodiments, the first region may be a lateral region while the second region may be a separate lateral region. A lateral region may be a region that extends (laterally) from a first lateral side of the electrode body 284 to a second lateral side of the electrode body 284 opposite the first lateral side.

[0058] The electrode material may be any one selected from a group consisting of titanium dioxide (Ti0₂), lithium titanate, silicon, a metal oxide, a layered oxide, a spinel oxide, and an olivine polyanion. The carbon-based conductive additive may be any one selected from a group consisting of reduced graphene oxide, graphene, carbon black, and carbon nanotubes.

[0059] FIG. 3A is a schematic illustrating a titanium dioxide (Ti0₂) (B) supercell containing lithium (Li) atoms at A2 sites. At low Li-ion concentrations in TiC (B), Li atoms may tend to locate at the A2 sites, forming very strong bonding with the host material. The resulted Li-Ti0₂(B) interaction may have a very high ionicity as Li atoms donate electrons to Ti0₂(B) resulting in the formation of Ti³⁺ states.

[0060] FIG. 3B is a plot of the density of states (DOS) (in 1 /electron-volts (eV)/cell) as a function of energy (in electron-volts (eV)) illustrating the density of states (DOS) computed using hybrid functional calculations for lithiated titanium oxide (Ti0₂) (B). The Fermi level is shown as a dashed line in FIG. 3B.

[0061] According to the density functional theory (DFT) hybrid functional calculations, Ti³⁺ states maybe located about 1.1 eV below the conduction band. At dilute Li-ion concentrations, Li may act as a defect and the formed Ti³⁺ states may behave as trapping states for electrons and have a limited effect on electronic conductivity. Further increase of Li-ion concentration and formation of a network of Ti³⁺ states may improve the overall electronic conductivity of the system, which agrees with the experimental results on the enhancement of electronic conductivity after lithiation. In the bulk Ti0₂(B), three lithium diffusion pathways may be considered, as shown in FIGS. 4A- F.

[0062] FIG. 4A shows a schematic illustrating the lowest migration pathway of lithium (Li ions) in titanium oxide (Ti0₂) (B). FIG. 4B is a plot of energy (in electron volts or eV) as a function of reaction coordinate showing the lowest energy diffusion energy barrier for diffusion of lithium (Li) ions in titanium dioxide (Ti0₂) (B) computed for migrations between two lowest energy sites using density functional theory (DFT) and DFT with Hubbard correction (DFT+U). At low Li-ion concentration, Li-Li interaction may not affect the diffusion mechanism, and Li-ion diffusion may be anisotropic. For both DFT and DFT+U calculations (the latter method corrects the Ti d-like states), the lowest migration pathway shown in FIG. 4A may correspond to Li-ion migration between A2 sites with a migration barrier of about 0.3 eV as shown in FIG. 4B.

[0063] According to the Arrhenius law, other Li migration pathways in FIGS. 4C-F may have a minor impact in Li-ion diffusion as they have significantly larger migration barriers. FIG. 4C shows a schematic illustrating an alternative migration pathway of lithium (Li) ions in titanium oxide (Ti0₂) (B) using Perdew-Burke-Ernzerhof (PBE) calculations. FIG. 4D is a plot of energy (in electron volts or eV) as a function of reaction coordinate showing the energy barrier corresponding to FIG. 4C. FIG. 4E shows a schematic illustrating another alternative migration pathway of lithium (Li) ions in titanium oxide (Ti0₂) (B) using Perdew-Burke-Ernzerhof (PBE) calculations. FIG. 4F is a plot of energy (in electron volts or eV) as a function of reaction coordinate showing the energy barrier corresponding to FIG. 4E.

[0064] The Li-ion diffusion pathway in FIG. 4A may be the most feasible, which is consistent with reported b-channel diffusion in Ti0₂(B). The intrinsic low diffusion energy barrier may render fast pseudocapacitive rechargeable behavior for Ti0₂(B).

[0065] Although Li-ion insertion in Ti0₂(B) may reduce the band gap energy according to the calculations, low electronic conductivity may still limit high-rate performance. Taking into account typical distribution of Li-ions during charging (FIG. 1C), the enhancement of electronic properties for Ti0₂(B) films may be limited to the top layers due to small Li-ion diffusion lengths at high charging rates. [0066] A Li-ion concentration gradient may result in the gradient dependence of electronic conductivity. This may be caused by the formation of Ti³⁺ ions as Ti³⁺ concentration is dramatically decreased from front layers to the current collector. To address this challenge, the addition of RGO (approximated as graphene in first-principles simulations) may be applied to facilitate the electron transport Ti0₂(B) films at high rates, especially for the bottom layers, i.e. the layers closer to the current collector. Only the effect of graphene in the reduction of electron diffusion length may be considered in the simulation. There may be no noticeable changes observed in the electronic properties of Ti0₂(B) when graphene forms an interface with Ti0₂(B) (see FIGS. 5A - B).

[0067] FIG. 5 A is a plot of the density of states (DOS) (in 1 /electron-volts (eV)/cell) as a function of energy (in electron-volts (eV)) illustrating the density of states (DOS) of a graphene titanium oxide (Ti0₂) (B) hybrid system according to various embodiments. FIG. 5B is a schematic illustrating the lowest energy carbon (C) / titanium dioxide (Ti0₂) (B) interface structure according to various embodiments. The graphene may have a weak van der Waals bonding with Ti0₂ (001) surface. No direct charge transfer from C to Ti0₂ (B) may be observed. FIG. 5C is a schematic illustrating lithium (Li)-ion diffusion along the graphene surface (ab-plane) and through a six- membered hexagonal ring (c-direction) according to various embodiments. 502a may indicate the diffusion of the Li ion along the graphene surface, while 502b may indicate the diffusion of the Li ion through the graphene hexagonal ring. FIG. 5D is a plot of energy (in electron-volts or eV) as a function of reaction coordinate illustrating lithium-ion diffusion barriers for ab-plane and c- direction pathways according to various embodiments.

[0068] Due to the weak Li-C interaction, a single layer graphene may not contribute significantly to the capacity. Nevertheless, other than electron transport, graphene may also provide connectivity between different parts of Ti0₂(B), and may hence affect Li-ion transport in the electrode. It is found that Li diffusion on graphene surface may be fast with a low migration barrier of 0.3 eV (see FIG. 5D) since it is mainly determined by Li jumping from one hexagonal site to another through the bridge configuration (see FIG. 5C). In contrast to the surface diffusion, Li penetration through six-membered carbon rings may be prohibitive due to ultra-high migration barrier of about 7.4 eV (see FIG. 5D). Thus, it is clear that high graphene concentration may reduce diffusivity for Li-ions due to the increased diffusion length. A functional-layer-graded RGO/Ti0₂(B) structure may be designed based on taking into account this point and that Li insertion induces gradient enhancement of electronic conductivity of Ti0₂(B). The RGO/Ti0₂(B) structure may have a gradual decrease of RGO concentration from bottom-layer (layer nearest to current collector) to top-layer (topmost layer furthest from current collector) to minimize or reduce energy barrier for Li-ion diffusion as well as to maximize or increase the effect of Li on electronic properties of Ti0₂(B).

[0069] FIG. 6 A shows cross-sectional schematics of functionally-graded electrodes 600a, 600c according to various embodiments, while 600b shows a cross-sectional schematic of a conventional homogenous electrode before vacuum treatment. FIG. 6B shows cross-sectional schematics of the functionally-graded electrodes 600a, 600c according to various embodiments, as well as the homogenous electrode 600b after vacuum treatment. 600a is an electrode having a gradual decrease of RGO concentration or volume/weight ratio from the bottom-layer (layer nearest to current collector) to the top-layer (topmost layer furthest from current collector). 600c is an electrode having a gradual increase of RGO concentration or volume/weight ratio from the bottom-layer (layer nearest to current collector) to the top-layer (topmost layer furthest from current collector). The electrode 600a may be referred to as an "upgraded electrode" or a "composition upgraded electrode", which may mean the concentration or weight / volume ratio of RGO in each layer increases from the layer furthest from the current collector to the layer nearest to the current collector. The electrode 600c may be referred to as an "downgraded electrode" or a "composition downgraded electrode", which may mean the concentration or weight / volume ratio of RGO in each layer decreases from the layer furthest from the current collector to the layer nearest to the current collector. The electrode 600b may be referred to as a "homogenous electrode" or a "composition homogenous" electrode, which may mean that the concentration or volume/weight ratio of RGO in the different layers remains substantially unchanged. As shown in FIGS. 6A-B, there may be changes in the RGO concentration or volume/weight ratio after vacuum annealing, which would be described in more detail later.

[0070] Electrodes having different configurations 600a-c as shown in FIG. 6A may be fabricated by layer-by-layer coating. The electrodes 600a-c may include cross-linking Ti0₂ (B) nanotubes and well-dispersed RGO nanosheets. The electrodes 600a, 600c may include functionally graded layers, each layer including graphene oxide (GO) structures and hydrogen titanate nanotubes (H-TNT) structures. The electrode 600a may have a higher concentration or ratio of GO at the electrode layer nearest the current collector, with each subsequent layer having a lower concentration or ratio of GO as the respective subsequent layer becomes further from the current collector. The electrode 600c may have a lower concentration or ratio of GO at the electrode layer nearest the current collector, with each subsequent layer having a higher concentration or ratio of GO as the respective subsequent layer becomes further from the current collector. The electrode 600b may have layers with substantially the same concentration or ratio of GO.

[0071] As mentioned above, the functionally graded layers of electrode 600a, 600c may be fabricated using colloidal suspensions of graphene oxide (GO)/ hydrogen titanate nanotubes (H- TNT) of varying compositions. FIG. 7 shows (top, from left to right) a digital image of different inks (with a concentration of 3.5 mg/mL) of pure graphene oxide (GO), 30% GO / hydrogen titanate nanotubes (H-TNT), 11% GO / H-TNT, 3% GO / H-TNT, and pure TNT; and (bottom, from left to right) a digital image of different layers of pure reduced graphene oxide (RGO), 30% RGO / titanium dioxide (Ti0₂), 11% RGO / Ti0₂, 3% RGO / Ti0₂, pure Ti0₂ and copper foil according to various embodiments.

[0072] A ratio of x % GO / H-TNT may refer to a suspension of a weight ratio or x % of graphene oxide to 100 % of H-TNT. The numbers referred to in FIGS. 6A-B, 7 may refer to the weight ratio. A ratio of x % RGO / Ti0₂ as referred herein may refer to a composition of reduced graphene oxide and titanium dioxide formed from a suspension of x % GO / H-TNT.

[0073] The colloidal suspensions may be stabilized by electrostatic repulsion forces for H-TNT surface (-22 ± 3 mV) and the negatively charged group (COO- ions) of exfoliated GO nanosheets (-9 ± 3 mV), according to the Deyaguin-Landau-Verwey-Overbeek theory. The Ti0₂, RGO, and RGO / Ti0₂ layers shown in the bottom image may be obtained after vacuum annealing the corresponding suspensions at 400 °C for 2 hours. After layer-by-layer coating, the multi- segmented GO/H-TNT films may be the upgraded type (based on 0, 3, 11, and 30% GO/H-TNT films) electrode 600a, the conventionally homogeneous (based on 11, 11, 11, and 11% GO/H-TNT films) electrode 600b, and the composition downgraded type (based on 30, 11, 3, and 0% GO/H- TNT films) electrode 600c as shown in FIG. 6A. The electrodes 600a-c shown in FIG. 6B may be obtained after vacuum annealing. A selection of an average ratio of 5.4% for the whole electrode may be based on the industry standard with the conductive carbon additive less than 10% (normally ~5%). The weight ratio of RGO in each RGO/Ti0₂ (B) layer may gradually increase from 0, 1.7%, 5.4%, to 14.1% for each successive layer nearer to the current collector for the upgraded electrode 600a, and may gradually decrease from 14.1%, 5.4%, 1.7%, to 0 for each successive layer nearer to the current collector for the downgraded electrode 600c. The weight ratio of RGO may be about 5.4% throughout the homogenous electrode.

[0074] The crystal structure and morphology evolution of elongated H-TNT nanotubes, GO nanosheets as well as the corresponding multilayered electrodes after annealing have been investigated. It has been found that the orthorhombic titanate phase of H-TNT may be transformed to monoclinic Ti0₂(B) phase after thermal treatment.

[0075] FIG. 8 A is a plot of intensity (in arbitrary units or a.u.) as a function of angle (in degrees) showing the X-ray Diffraction (XRD) patterns of the as-prepared reduced graphene oxide (RGO), pure titanium dioxide (T1O2) (B), and various reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) composite films according to various embodiments. As highlighted above, the films may be prepared by annealing the various corresponding suspensions. When the RGO content is increased to 5.4%, the (110) peaks for the Ti0₂ (B) may be increased, which may be due to the merging of the Ti0₂(B) and RGO peaks with similar peak positions. FIG. 8B is a plot of intensity (in arbitrary units or a.u.) as a function of angle (in degrees) showing the X-ray Diffraction (XRD) patterns of graphene oxide (GO) nanosheets and reduced graphene oxide (RGO) nanosheets. With reference to FIG. 8B, the reduction of GO to RGO in FIG. 8A may be indicated by the disappearance of the characteristic diffraction peak of GO at ~ 10°. In addition, the layer distance of graphene oxide may decrease from 0.88 to 0.35 nm based on Bragg's law calculations. This may correspond to the removal of water molecules and oxygen functional groups between the oxidized graphene layers, which may be shown by Fourier transform infrared spectroscopy (FTIR).

[0076] FIG. 8C is a plot of transmittance (in arbitrary units or a.u.) as a function of wavenumber (in per centimeter or cm^"1) showing the Fourier transform infrared (FTIR) spectra of graphene oxide (GO) nanosheets and reduced graphene oxide (RGO) nanosheets. The RGO nanosheets may be annealed in vacuum at 400 °C for 2 h. The GO spectrum may show several characteristic peaks at 1053 cm^"1 corresponding to the C-O-C vibration in the epoxy group, 1221 cm^"1 and 1622 cm^"1 corresponding to C-0 vibration and bending of O-H in C-OH group, and 1728 cm^"1 corresponding to carboxyl stretching. Additionally, the broad peak at around 3250 cm^"1 and the peak at 1415 cm^" ¹ may be due to water molecules absorbed as a result of the high hydrophilicity of GO. After thermal annealing, the intensity of the peaks may decrease dramatically, which shows the successful reduction of GO to RGO.

[0077] The surface chemical states as well as chemical composition of Ti0₂(B) and RGO/Ti0₂(B) may be analyzed by X-ray photoelectron spectroscopy (XPS). FIG. 8D is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the Cls and Ols X-ray photoelectron spectroscopy (XPS) spectra for pure titanium dioxide (Ti0₂) (B) and reduced graphene oxide / titanium dioxide (RGO/Ti0₂) (B) films according to various embodiments.

[0078] When the RGO nanosheets are introduced to Ti0₂(B) nanotubular network, the intensities of carbon related peaks (Cls) for the C-O, C=0, and 0-C=0 bonds may be increased. Similarly, the peaks related to oxygen-related groups (Ols) for hydroxyl group (Ti-OH) and C=0 bonds from the RGO nanosheets may also increase. For Ti2p peaks, no significant change may be observable, indicating the same chemical state of titanium for both Ti0₂(B) and RGO/Ti0₂(B) samples. However, the Ti2p peaks are shifted to a higher binding energy (see FIGS. 9A-L) when the Ti0₂(B) samples are annealed in air, suggesting the formation of Ti³⁺ states for both Ti0₂(B) annealed in vacuum and RGO/Ti0₂(B) annealed in vacuum. This may be consistent with previous results on vacuum treated Ti0₂, which may be attributed to the improvement of electronic conductivity of vacuum treated Ti0₂(B) sample. According to electronic conductivity measurement, the electronic conductivity for vacuum treated Ti0₂(B) may be about one order higher than the that of Ti0₂(B) samples annealed in air (l.lx lO^"6 S cm^"1).

[0079] FIGS. 9A-L show the XPS spectra for the Ti0₂-based electrode with different formation conditions according to various embodiments. All spectra are calibrated to the binding energy of adventitious carbon (284.5 eV). The annealing in air or vacuum may be carried out at a temperature of about 200 °C for about 2 hours.

[0080] FIG. 9A is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the broad scanning spectrum of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in air according to various embodiments. FIG. 9B is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of CI s of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in air according to various embodiments. FIG. 9C is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ols of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in air according to various embodiments. FIG. 9D is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ti2p of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in air according to various embodiments.

[0081] FIG. 9E is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the broad scanning spectrum of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in vacuum according to various embodiments. FIG. 9F is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of CI s of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in vacuum according to various embodiments. FIG. 9G is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ols of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in vacuum according to various embodiments. FIG. 9H is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ti2p of titanium dioxide (Ti0₂) (B) nanotubes formed by annealing in vacuum according to various embodiments.

[0082] FIG. 91 is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the broad scanning spectrum of titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) nanotubes formed by annealing in vacuum according to various embodiments. FIG. 9J is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of C Is of titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) nanotubes formed by annealing in vacuum according to various embodiments. FIG. 9K is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ols of titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) nanotubes formed by annealing in vacuum according to various embodiments. FIG. 9L is a plot of intensity (in arbitrary units or a.u.) as a function of binding energy (in electron volts or eV) showing the fine scanning spectrum of Ti2p of titanium dioxide (T1O2) (B) / reduced graphene oxide (RGO) nanotubes formed by annealing in vacuum according to various embodiments.

[0083] The XPS results may be consistent with previous results on vacuum treated Ti0₂. The improvement of electronic conductivity of vacuum treated Ti0₂(B) samples is discussed later. The results show that GO/H-TNT precursor composites may be converted to RGO/Ti0₂(B) nanotube composite electrodes after vacuum treatment.

[0084] The microstructure of the annealed multi-segmented electrode may be observed by field emission scanning electron microscope (FESEM) and transmission electron microscopy (TEM).

[0085] FIG. 10A is a field emission scanning electron microscope (FESEM) image of a pure titanium dioxide (Ti0₂) (B) film according to various embodiments. FIG. 10B is a magnified field emission scanning electron microscope (FESEM) image of a pure titanium dioxide (Ti0₂) (B) film according to various embodiments.

[0086] FIG. IOC is a field emission scanning electron microscope (FESEM) image of a 3% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. The arrows indicate the positions of reduced graphene oxide. FIG. 10D is a magnified field emission scanning electron microscope (FESEM) image of a 3% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

[0087] FIG. 10E is a field emission scanning electron microscope (FESEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. The arrows indicate the positions of reduced graphene oxide. FIG. 10F is a magnified field emission scanning electron microscope (FESEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

[0088] FIG. 10G is a field emission scanning electron microscope (FESEM) image of a 30% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. The arrows indicate the positions of reduced graphene oxide. FIG. 10H is a magnified field emission scanning electron microscope (FESEM) image of a 30% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

[0089] FIG. 101 is a field emission scanning electron microscope (FESEM) image of a pure reduced graphene oxide film according to various embodiments. FIG. 10J is a magnified field emission scanning electron microscope (FESEM) image of a pure reduced graphene oxide film according to various embodiments.

[0090] FIG. 10K is a field emission scanning electron microscope (FESEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments, with the areas encircled by dashed lines indicating the reduced graphene oxide (RGO) nanosheets. The 0%, 3%, 11%, and 30% RGO / Ti0₂ herein may refer to the weight ratio of the RGO before vacuum annealing, and may correspond to 0%, 1.7%, 5.4%, and 14.1% weight ratios of RGO respectively after thermal annealing. Other percentage values of RGO in Ti0₂ may also be possible. The percentage value of RGO may increase with each successive layer. For instance, another example may be 1%, 3%, 5.4%, and 12.2%, and yet another example may be 1.7%, 4%, 6.2% and 9.7%.

[0091 ] The thermally annealed samples exhibit the crosslinking elongated nanotubular Ti0₂(B) nanotubular network, with a Ti0₂ nanotube being typically of several tens of micrometers in length and hundreds of nanometers in diameter.

[0092] The RGO nanosheets may be uniformly distributed within the Ti0₂(B) nanotubular network. With the gradual increase of RGO content to 30%, the RGO distribution within the nanotube film may become denser. However, the films may not show aggregation of RGO nanosheets.

FIG. 11A shows a transmission electron microscopy (TEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. FIG. 1 IB is a high-resolution transmission electron microscopy (HRTEM) image of the reduced graphene oxide (RGO) sheet indicated by area "A" in FIG. 11A of the film according to various embodiments. FIG. 11C is a high-resolution transmission electron microscopy (HRTEM) image of the titanium oxide (Ti0₂) (B) nanotubes indicated by area "B" in FIG. 11A of the film according to various embodiments.

[0093] The TEM images show that the hollow inner surfaces of the Ti0₂(B) nanotubes along the axial direction may have a strong integration with RGO nanosheets. From the high-resolution TEM (HRTEM) images in FIGS. 11B-C, the lattice fringe of RGO nanosheets is about 0.39 nm, which may correspond to (002) planes of graphite materials, and the lattice fringe of the Ti0₂(B) nanotube has an interatomic spacing of around 0.62 nm and 0.36 nm, which may correspond to the characteristic (001) and (110) planes respectively. Brunauer-Emmett-Teller (BET) surface measurements show that the surface area of the Ti0₂ nanotube electrode may be 130 m²/g with a pore size peak of around 3 ran to 5 ran, corresponding to inner hollow spaces for the nanotubes.

[0094] FIG. 1 ID is a cross-sectional field emission scanning electron microscope (FESEM) image of a reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) electrode. FIG. 1 IE is a magnified cross-sectional field emission scanning electron microscope (FESEM) image of a reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) electrode. The electrode shown in FIGS. 11D-E may have a homogenous composition of RGO/Ti0₂ structures.

[0095] The cross-sectional SEM images in FIGS. 11D-E reveal that the thickness of a four- layer homogeneous RGO/Ti0₂(B) electrode may be around 24 ± 3 μιη, which may be similar to those of the composition up/downgraded electrodes.

[0096] In addition, scanning transmission elemental microscopy (STEM) with energy- dispersive X-ray spectroscopy (EDX) elemental mapping has been applied to further investigate the RGO/Ti0₂(B) hybrid nanostructures.

[0097] FIG. 12A is a plot of number of counts Kent (normalized to 1.0) as a function of energy (in kiloelectron-volts or keV) showing scanning transmission elemental microscopy (STEM) - energy-dispersive X-ray spectroscopy (EDX) spectrum of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. FIG. 12B is a magnified transmission electron microscopy (TEM) image of a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments showing excellent attachment between the reduced graphene oxide sheets and the titanium dioxide (Ti0₂) nanotubes. FIG. 12C shows an energy-dispersive X-ray spectroscopy (EDX) mapping of titanium present in a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. FIG. 12D shows an energy-dispersive X-ray spectroscopy (EDX) mapping of oxygen present in a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments. FIG. 12E shows an energy-dispersive X-ray spectroscopy (EDX) mapping of carbon present in a 11% reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) film according to various embodiments.

[0098] The homogeneous distribution of Ti, O, and C elements as shown in FIGS. 12C-E may unambiguously indicate the intimate contact of RGO and Ti0₂(B) nanotubes (FIG. 12A), which may increase the electrical conductivity of multilayered Ti0₂(B) nanotube based electrode. This may be due to the uniform formation of graphene oxide and titanate nanotube hybrid gel solution with anti-aggregation property stabilized by electrostatic repulsion forces.

[0099] FIG. 12F shows a transmission electron microscopy (TEM) image of an electrode according to various embodiments. FIG. 12G shows a cross-sectional titanium (Ti) elemental mapping of the multi-segmented reduced graphene oxide (RGO) nanosheets / titanium dioxide (Ti0₂) (B) nanotube films according to various embodiments. FIG. 12H shows a cross-sectional oxygen (O) elemental mapping of the multi-segmented reduced graphene oxide (RGO) nanosheets / titanium dioxide (Ti0₂) (B) nanotube films according to various embodiments. FIG. 121 shows a cross-sectional carbon (C) elemental mapping of the multi-segmented reduced graphene oxide (RGO) nanosheets / titanium dioxide (Ti0₂) (B) nanotube films according to various embodiments. The area enclosed by the box in FIG. 12F may correspond to the areas indicated by FIGS. 12G-I.

[00100] From the cross-sectional C element mapping of FIG. 121, a change of carbon distribution from top to bottom may be observed, but it is not easy to see the gradient change of carbon content. This may be due to the following two reasons: 1) The RGO nanosheets are laid down on the nanotube network, and the RGO nanosheets may be parallel to the current collector with less exposed cross-sectional area, giving the low-carbon signal; and 2) the cross-sectional surface may be rough, which affect the received scattering electron signal.

[00101] Measurements using thermogravimetric analysis (TGA), Raman spectroscopy, and four-probe resistance testing/electrochemical impedance spectroscopy (EIS) have been conducted to gain further insights into the composition distribution, the reduced chemical states, and the electronic/ionic conductivity of RGO respectively of the RGO/Ti0₂(B) hybrid electrode.

[00102] The weight loss for each RGO/Ti0₂(B) layer has been tested in air using TGA (see FIG. 13 A). The precursors of GO and H-TNT have also been tested in nitrogen gas using TGA (see FIG. 13B) to determine their weight ratio. FIG. 13A is a plot of weight (in percent or %) as a function of temperature (in degrees Celsius or °C) showing the thermogravimetric analysis (TGA) curves for graphene oxide (GO), reduced graphene oxide (RGO), titanium dioxide (Ti0₂) (B), and various reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) films according to various embodiments heated in air. [00103] FIG. 13B is a three-dimensional plot of weight (in percent or %) as a function of temperature (in degrees Celsius or °C) and time (in minutes or min) showing the thermogravimetric analysis (TGA) curves of graphene oxide (GO) and hydrogen titanate nanotube (H-TNT) according to various embodiments in nitrogen gas atmosphere.

[00104] The weight ratio of reduced graphene oxide present in titanium dioxide (Ti0₂) (B), and various reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) films after annealing is shown in Table 1 below:

[00105] Therefore, the total weight ratio of RGO in different configurations of the multi- segmented RGO/Ti0₂(B) electrode may be around 5.4%. Raman spectroscopy has also been used to identify the reduction state of RGO in each segment. FIG. 14A is a plot of intensity (in arbitrary units or a.u.) as a function of Raman shift (in per centimeter or cm^"1) showing the Raman spectra of graphene oxide, reduced graphene oxide (RGO), pure titanium dioxide (Ti0₂) (B) and various ratios of reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) according to various embodiments. The Raman spectrum indicates the characteristic peaks of Ti0₂(B) at 406, 505, and 631 cm^"1 and the D and G bands of RGO at 1598 and 1338 cm^"1.

[00106] As expected, D/G intensity ratio (ID/IG) may increase from 0.90 for GO to 0.95/0.96 for RGO and RGO/Ti0₂(B) films with different concentrations of RGO after vacuum annealing, indicating that the reduction states of RGO in the hybrid films may be identical or similar.

[00107] FIG. 14B is a plot of conductivity (in Siemens per centimeter or S/cm) as a function of sample number showing the electrical conductivity of reduced graphene oxide (RGO), pure titanium dioxide (Ti0₂) (B) annealed in air and vacuum, and various ratios of reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) according to various embodiments measured using four-probe resistance testing. By introducing the RGO nanosheets as an electrically-conductive linker to the Ti0₂(B) nanotube network and the current collector, the uniform distribution of RGO nanosheets may greatly enhance the electronic conductivity of RGO/Ti0₂(B) hybrids by a few orders of magnitude.

[00108] Moreover, the ionic conductivity of each RGO/Ti0₂(B) segment has been analyzed by electrochemical impedance spectroscopy (EIS) measurements after the cell is stable at different charging rates (see FIGS. 14C-D). FIG. 14C is a plot of ionic conductivity Du+ (in square centimeter / second or cm²/s) as a function of cycle number illustrating the ionic conductivity of pure titanium dioxide (Ti0₂) (B), reduced graphene oxide (RGO), and various ratios of reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) according to various embodiments measured using electrochemical impedance spectroscopy (EIS) measurements. FIG. 14D is another plot of ionic conductivity Du+ (in square centimeter / second or cm²/s) as a function of cycle number illustrating the ionic conductivity of pure titanium dioxide (Ti0₂) (B), reduced graphene oxide (RGO), and various ratios of reduced graphene oxide (RGO) / titanium dioxide (Ti0₂) (B) according to various embodiments measured using electrochemical impedance spectroscopy (EIS) measurements.

[00109] Herein, it is found that the ionic conductivity for RGO may be about five orders lower than that of pure Ti0₂(B). The ionic conductivity of 3% RGO/Ti0₂(B) may be close to that of pure Ti0₂(B) due to low loading of RGO (1.7%). When the RGO content increases, Li-ion conductivity of single RGO/Ti0₂(B) layer may decrease, which is consistent with the first- principles data for Li migration barriers.

[00110] Single layers of the RGO/Ti0₂ (B) with different weight ratios of RGO and Ti0₂ (B) may be constructed to build the multi-segmented RGO/T1O2 (B) hybrid electrodes with different configurations, and the electrochemical performance of the fabricated electrode may be evaluated.

[00111] FIG. 15A shows images of functionally-graded electrodes 1500a, 1500c according to various embodiments, and an image of a conventional homogenous electrode 1500b. 1500a is an electrode having a gradual decrease of RGO concentration or volume/weight ratio from bottom- layer (layer nearest to current collector) to top-layer (topmost layer furthest from current collector). 1500c is an electrode having a gradual increase of RGO concentration or volume/weight ratio from bottom-layer (layer nearest to current collector) to top-layer (topmost layer furthest from current collector). The electrode 1500a may be referred to as an "upgraded electrode" or a "composition upgraded electrode", which may mean the weight ratio of RGO in each layer increases from the layer furthest from the current collector to the layer nearest to the current collector. The electrode 1500c maybe referred to as an "downgraded electrode" or a "composition downgraded electrode", which may mean the weight ratio of RGO in each layer decreases from the layer furthest from the current collector to the layer nearest to the current collector. The electrode 1500b may be referred to as a "homogenous electrode" or a "composition homogenous" electrode, which may mean that the concentration or volume/weight ratio of RGO in the different layers remains substantially unchanged. The intensity scale on the right of FIG. 15A indicates the concentration/ratio of RGO of the different layers.

[00112] FIG. 15B is a plot of discharge capacity (in milliampere-hours per gram or mAh/g) as a function of cycle number showing the rate-dependent electrochemical performance of the upgraded electrode 1500a and the downgraded electrode 1500c according to various embodiments, as well as the rate-dependent electrochemical performance of the homogenous electrode 1500b. FIG. 15C is a plot of discharge capacity (in milliampere-hours per gram or mAh/g) as a function of cycle number showing the battery performance of three upgraded electrodes according to various embodiments, as well as the battery performance of the homogenous electrode. FIG. 15D is a plot of electronic conductivity (S cm^"1) / ionic conductivity Du+ (in square centimeter / second or cm²/s) as a function of reduced graphene oxide (RGO) content (in percent or %) showing the correlation between electronic conductivity/ ionic conductivity and RGO content according to various embodiments.

[00113] FIG. 15E is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the cyclic voltammogram (CV) curves of the upgraded electrode according to various embodiments as anode at a scan rate of 0.1 mV/s for different cycles. FIG. 15F is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the cyclic voltammogram (CV) curves of the homogenous electrode as anode at a scan rate of 0.1 mV/s for different cycles. [00114] The cyclic voltammogram (CV) measurements shown in FIGS. 15E-F show that the electrochemical reaction may be due to Ti0₂(B) with the appearance of its broad pair of characteristic peaks (at about 1.5-1.6 V/1.7 V). The lines generated at different cycles for each of FIG. 15E and FIG. 15F may show similar trends.

[00115] At low rate of about 0.5 C to about 2 C (1 C = 335 mA/g), the composition upgraded electrode may show a capacity similar to that of the homogeneous electrode (FIG. 15B). This may also be proven by the long-time performance stability of the upgraded and homogeneous RGO/Ti0₂(B) electrodes at 1 C (see FIGS. 15G-I). FIG. 15G is a plot of discharge capacity (in milliampere-hours per gram or mAh/g) / coulombic efficiency (in percent or %) as a function of cycle number showing the capacity retention of a composition upgraded anode (gradient sample) according to various embodiments and a homogeneous anode (homogenous sample) through 100 cycles at 1 C rate. FIG. 15H is a plot of voltage (in volts or V) as a function of discharge capacity (in milliampere-hours per gram or mAh g) showing the charge/discharge curves of different cycles of a composition upgraded anode according to various embodiments at 1C. FIG. 151 is a plot of voltage (in volts or V) as a function of discharge capacity (in milliampere-hours per gram or mAh/g) showing the charge/discharge curves of different cycles of a homogenous anode according to various embodiments at 1C. The lines generated at different cycles for each of FIG. 15H and FIG. 151 may show similar trends.

[00116] The capacity loss and unstable CV curves for the first few cycles may be due to the irreversible reaction of generating the solid electrolyte interphase (SEI) layer between Ti0₂(B) nanotube and electrolyte (see FIG. 15B). The comparable performance between upgraded electrode and the homogenous electrode may be due to the sufficient time for electron and Li-ion diffusion. However, the battery performance of the composition downgraded electrode may be worse than that for the upgraded and homogenous electrodes. This may be mainly due to the poor electronic conductivity as the pure Ti0₂(B) layer is at the bottom, i.e. adjacent the current collector.

[00117] For example, at 1 C, the capacities may be about 224, 223, and 163 mAh/g for the upgraded, homogeneous and downgraded electrodes respectively. As the charging/discharging rates increase further, the capacity differences between the upgraded and homogeneous anode may increase slightly. However, the capacities of the upgraded and homogenous anodes may become much greater than the capacity of the downgraded anode. [00118] At a high rate (20 C), the electrochemical cell including an upgraded anode may show excellent capacity retention and may achieve a stable high capacity of 128 mAh/g, whereas the homogeneous anode may only maintain the capacity of 74 mAh/g. The capacity of the downgraded anode may be low, delivering only 2 mAh/g. These results clearly indicate that the composition upgraded electrode may provide high capacity and long cycle life at an ultrahigh rate.

[00119] The rechargeable profiles of the electrodes at different rates may be analyzed to understand the lithiation behaviors for the upgraded, homogeneous, and downgraded Ti0₂ (B) electrodes (see FIGS. 15J-L).

[00120] FIG. 15 J is a plot of lithiation potential (volts or V with reference to Li/Li+) as a function of capacity (in milliampere-hours per gram or mAh/g) showing the charging/discharging curves of the upgraded anode according to various embodiments with increasing current densities. FIG. 15K is a plot of lithiation potential (volts or V with reference to Li/Li+) as a function of capacity (in milliampere-hours per gram or mAh/g) showing the charging/discharging curves of the homogenous anode according to various embodiments with increasing current densities. FIG. 15L is a plot of lithiation potential (volts or V with reference to Li/Li+) as a function of capacity (in milliampere-hours per gram or mAh/g) showing the charging/discharging curves of the downgraded anode according to various embodiments with increasing current densities.

[00121] It is found that the rechargeable behavior at various current rates may be similar with nearly constant slope of galvanostatic characteristics, which indicates the pseudocapacitive charge storage behavior for T1O2 (B) materials.

[00122] At low rates (< 2 C), the discharge profile may normally be divided into three obvious regions for a Ti0₂ (B) electrode (see FIG. 15J): I) a region of rapid ohmic potential drop, II) a slow slope lithiation reaction region in Ti0₂ (B), and III) a region of fast potential decrease due to the surface storage of Li-ion.

[00123] As the current density increases, the ohmic potential drop may decrease faster for the homogeneous electrode (FIG. 15K) compared to that of the upgraded electrode (FIG. 15 J). This may be due to large internal resistance for the homogeneous anode, and the polarization drop may be more serious at high current density. This issue may be even worse for the downgraded electrode (see FIG. 15L). For the slope lithiation reaction region, the rate-dependent discharge profile for the upgraded electrode may drop slightly at higher discharging rates, indicating that the upgraded electrode may uptake more Li-ions compared with other two electrodes at the same discharge voltage. Since the surface storage has very fast kinetics like capacitor-storage behavior, no significant difference amongst the electrode may be observed.

[00124] In order to obtain further insights on the electrochemical properties of the upgraded and homogeneous electrodes, the reaction kinetics may be studied and dynamic ionic and electronic measurements may be conducted during the lithiation processes. The CV measurements may be shown in FIGS. 16A-D with a scan rate from 0.1 to lO mV/s, and the correlation of the peak current with the scan rate may be shown in FIG. 17A.

[00125] FIG. 16A is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the cyclic voltammogram (CV) curves of the upgraded anode according to various embodiments at different scan rates from 0.1 to 10 mV/s. FIG. 16B is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li+) showing the cyclic voltammogram (CV) curves of the upgraded anode according to various embodiments, with the curves corresponding the curves shown in FIG. 16A that are within a range of current densities of -1.2 to 0.6 A g.

[00126] FIG. 16C is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the cyclic voltammogram (CV) curves of the homogenous anode according to various embodiments at different scan rates from 0.1 to 10 mV/s. FIG. 16D is a plot of current density (in amperes per gram or A/g) as a function of lithiation potential (volts or V with reference to Li/Li+) showing the cyclic voltammogram (CV) curves of the upgraded anode according to various embodiments, with the curves corresponding the curves shown in FIG. 16C that are within a range of current densities of -1.2 to 0.5 A/g.

[00127] FIG. 17A is a plot of the logarithm of peak current (in amperes or A) as a function of the logarithm of scan rate (in millivolts per second or mV/s) showing the relationship between the cyclic voltammogram (CV) peak current and the scanning rate for the upgraded electrode according to various embodiments and the homogenous electrode. The cathodic peak intensity may be linearly fitted with the square root of the scan rate.

[00128] In general, the CV current (z) is related to scan rate (v) via Equation (3): [00129] The ό-value may be determined by the slope of log(v)-log(z) plot in FIG. 17A. A b- value of 0.5 may suggest rigorous diffusion behavior, whereas a value of 1.0 may indicate a capacitive process. As shown in FIG. 17A, two slopes may be obtained for each electrode, with the two slopes separated at 1.0 mV/s. The 3-values of the upgraded RGO/Ti0₂ (B) electrode may be 0.77 at a scan rate range of 0.1 to 1.0 mV/s (1.8 C) and 0.66 at a scan rate rage of 1.0 to 10.0 mV/s (18 C). These 3-values are higher than 0.5 even at 10 mV/s, which may indicate mixed contributions from both capacitive surface storage and diffusion controlled reaction. This may be due to the high conductivity of the upgraded RGO/Ti0₂ (B) structure and the intrinsic properties of Ti0₂(B) electrode with fast pseudocapacitive charge capability.

[00130] On the other hand, the b- value decreases from 0.74 at low scanning rates (< 1.0 mV/s) to 0.45 at higher rates (> 1.0 mV/s) for the homogeneous electrode, which may be due to the low Li-ion diffusivity as well as large polarization at ultrafast scan rates.

[00131] FIG. 17B is a plot of polarization potential (in volts or V) as a function of scan rate (in millivolts per second or mV/s) showing the redox peak separation during the charging and discharging processes of the upgraded electrode according to various embodiments and the homogenous electrode.

[00132] It is observed from FIG. 17B that the polarization between the redox potential may occur with the increase of scan rates, which may be more serious for the homogeneous electrode due to reaction limitation.

[00133] The ionic conductivity may also be determined by galvanostatic intermittent titration technique (GITT). FIG. 18A is a plot of voltage (in volts or V) as a function of time (in minutes or min) showing a galvanostatic intermittent titration technique (GITT) profile of a composition upgraded anode according to various embodiments during charging and discharging as a function of time. FIG. 18B is a plot of voltage (in volts or V) as a function of time (in minutes or min) showing a demonstration of a single titration according to various embodiments. FIG. 18C is a plot of lithium ion diffusivity (in square centimeter per s or cm²/s) as a function of lithiation potential (volts or V with reference to Li/Li⁺) showing the calculated lithium ion diffusion coefficient for the upgraded anode according to various embodiments and the homogenous anode with varying lithiation potential based on the galvanostatic intermittent titration technique (GITT). Results show that the upgraded electrode may have higher ionic conductivity compared to the homogeneous electrode at different discharging states. FIG. 18D is a plot of voltage (in volts or V) as a function of time (in minutes or min) showing a galvanostatic intermittent titration technique (GITT) profile of a homogenous anode.

[00134] FIG. 19A is a plot of current (in amperes or A) as a function of potential (in volts or V) showing the cyclic voltammogram (CV) curve of composition upgraded electrode according to various embodiments at 0.1 mV/s for 1st cycle and the demonstration of cathodic peak intensity. FIG. 19B is a plot of peak current (in milliamperes or mA) as a function of square root of scan rate (in root of millivolts per s or (mV/s)^1/2) showing the linear fitting of the cathodic peak intensity against the square root of scan rate for the composition upgraded anode according to various embodiments and the homogeneous anode.

[00135] The ionic conductivity determined by GITT may b e consistent with the results from C V testing. The calculated effective Li-ion diffusivities for the upgraded electrode and the homogeneous electrode may be 3.0 x 10^"11 and 1.9 x 10^"11 cm²/s respectively.

-ion diffusion may usually follow the Arrhenius relationship provided by:

wherein AG is the effective energy barrier, kB is Boltzmann constant, and Do is the pre-factor estimated empirically. This means that the lower energy barrier for Li-ion diffusion in the upgraded RGO/Ti0₂(B) electrode may result in fast reaction kinetics along with the reduction of reaction polarization.

[00137] Dynamic ionic and electronic measurements of the upgraded and homogeneous electrodes at different lithiation stages by EIS (see FIG. 20) have been conducted to monitor the evolution of internal resistance (R₀), and SEI layer resistance (RSEI), and charge-transfer resistance (RCT) change. FIG. 20 is a three-dimensional plot of the virtual part of the complex-value impedance Z" (in ohms or Ω ) as a function of the real part of the complex- value impedance Z' (in ohms or Ω) and the lithiation potential (volts or V with reference to Li/Li⁺) showing the Nyquist plots for the composition upgraded electrode according to various embodiments and the homogeneous electrode. FIG. 21 is a plot of resistance (in ohms or Ω) as a function of the lithiation potential (volts or V with reference to Li/Li⁺) showing the electrochemical impedance spectroscopy (EIS) measurement of the upgraded electrode according to various embodiments and the homogenous electrode.

[00138] As shown in FIG. 21, the internal resistance (R₀) and SEI layer resistance (RSEI) for the upgraded electrode may be comparable with that of the homogeneous electrode, indicating that electronic conductivity for the whole cell as well as the ionic conductivity for the SEI layer may be the same or similar for these two electrode systems. However, a huge difference between the upgraded electrode and the homogenous electrode may be observed for the charge-transfer resistance (RCT). The upgraded electrode may have a charge-transfer resistance of about 105 0 , while the homogeneous electrode may have a charge-transfer resistance of about 552 Ω , suggesting a larger reaction polarization for the homogeneous electrode during Li-ion insertion in Ti0₂ (B) matrix, which may be well matched with discharge profiles in FIGS. 15I-J. Also, these observations may correlate well with both first-principles calculations and GITT/CV measurement for Li-ion diffusivity (see FIG. 18C), indicating that the reduction of Li-ion diffusion barrier for the upgraded electrode may be vital for high-rate LIBs performance as the electronic conductivities for these two electrodes are comparable.

[00139] The remarkable performance of the segmented functionally graded electrode may be attributed to the following key characteristics as described below. Proposed Li-ion and electron transport pathways for the composition upgraded and homogeneous electrode are shown in FIG. 22 and FIG. 23 respectively.

[00140] FIG. 22 is a schematic showing lithium (Li)-ion and electron transport into the composition upgraded titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) electrode 2200 according to various embodiments. The composition upgraded electrode 2200 may include a first electrode layer 2202, a second electrode layer 2204 on the first electrode layer 2202, a third electrode layer 2206 on the second electrode layer 2204, and a fourth electrode layer 2208 on the third electrode layer 2206. The first electrode layer 2202 may be on the current collector 2210.

[00141] For the composition upgraded electrode 2200, a high concentration of RGO nanosheets at the bottom layer 2202 may ensure excellent electrical contact between RGO/Ti0₂ (B) film 2202 and the current collector 2210, which may improve electron transport.

[00142] The design of composition upgraded electrode 2200 may reduce electrode/current collector interface resistance and may benefit from the improvement of electronic conductivity originating from gradient Li-ion distribution, thus facilitating electron diffusion from bottom-layer 2202 to top- layer 2208 during lithiation.

[00143] FIG. 23 is a schematic showing lithium (Li)-ion and electron transport into the homogenous titanium dioxide (Ti0₂) (B) / reduced graphene oxide (RGO) electrode 2300. The homogeneous electrode 2300 may include a first electrode layer 2302, a second electrode layer 2304 on the first electrode layer 2302, a third electrode layer 2306 on the second electrode layer 2304, and a fourth electrode layer 2308 on the third electrode layer 2306. The first electrode layer 2302 may be on the current collector 2310.

[00144] It may be observed from FIG. 21 that the internal total resistance may be rather similar for the composition upgraded electrode 2200 and the homogeneous electrode 2300, although a high capacity of the composition upgraded electrode 2200 at a high rate of 20 C may be achieved. This indicates that the electronic conductivity may not be the limiting factor for both the composition upgraded electrode 2200 and the homogenous electrode 2300 due to the significant reduction of electron diffusion length by the introduction of conductive RGO nanosheets.

[00145] Li-ion diffusion may be the rate-limiting process compared to electronic conduction in an electrochemical reaction since the Li-ion radius is a few orders of magnitude larger than that of an electron. Hence, the increase of Li-ion diffusivity through the reduction of effective Li-ion diffusion barrier may be crucial for high-rate LIBs without the sacrifice of electronic conductivity in the segmented electrode 2200.

[00146] A lower energy barrier for Li-ion diffusion may be built by increasing RGO from the top- layer 2208 to the bottom- layer 2202 for the composition upgraded electrode 2200 (as compared to the energy barrier of the homogeneous electrode 2300), which may render faster kinetics for Li insertion and extraction in the composition upgraded electrode 2200 at high rates.

[00147] A composition upgraded anode may show a superior capacity (e.g. 128 mAh/g) in comparison to the homogeneous electrode (e.g. 74 mAh/g). This may be attributed to the distribution of RGO and Ti0₂(B) in the multi-segmented electrode for the synchronous achieving ionic and electron transport highway: 1) a lower energy barrier for Li-ion diffusion may be achieved in the upgraded electrode than that of homogeneous electrode, rendering faster kinetics for Li insertion and extraction at high rates; and 2) a high electronic conductivity originating from increasing or maximizing the effect of Li insertion on electronic properties of the upgraded electrode and the reduction of electron diffusion length induced by the introduction of RGO nanosheets.

[00148] The functionally graded material concept may be extended to other hybrid electrodes for reduction or minimization of Li-ion diffusion barriers and increase or maximizing electron transport towards efficient energy devices.

[00149] FIG. 24 is a schematic showing a method of forming an electrode according to various embodiments. The method may include, in 2402, forming a first electrode layer including an electrode material and a carbon-based conductive additive. The method may also include, in 2404, forming a second electrode layer in contact with the first electrode layer, the second electrode layer also including the electrode material and the carbon-based conductive additive. A concentration of the carbon-based conductive additive in the first electrode layer may be higher than a concentration of the carbon-based conductive additive in the second electrode layer.

[00150] In other words, the method of forming an electrode may include forming at least two electrode layers, wherein a ratio or concentration of a carbon-based conductive additive present in a first electrode layer may be higher than a ratio or concentration of a carbon-based conductive additive present in a second electrode layer.

[00151] The steps shown in FIG. 24 may not be in sequence. Step 2404 may occur after, before or concurrently with step 2402.

[00152] In various embodiments, the first electrode layer may be formed on or in contact with a current collector. The method may also include forming the current collector.

[00153] In various embodiments, the method may also include forming one or more further electrode layers. The one or more further electrode layers may be formed over the first electrode layer and the second electrode layer to form a stacked arrangement. The one or more further electrode layers may also include the electrode material.

[00154] In various embodiments, a topmost further electrode layer of the one or more further electrode layers may be devoid of the carbon-based conductive additive. The topmost further electrode layer may include or consist of the electrode material. One or more intervening further electrode layers between the topmost further electrode layer and the second electrode layer may further include the carbon-based conductive additive. [00155] In various other embodiments, the topmost further electrode layer of the one or more further electrode layers, in addition to the one or more intervening further electrode layers between the topmost further electrode layer and the second electrode layer, may include the carbon-based conductive additive. In other words, all the electrode layers of the electrode may include the carbon-based conductive additive and the electrode material.

[00156] In various embodiments, a concentration or ratio (e.g. volume ratio or weight ratio) of the carbon-based conductive additive of an intervening further electrode may be higher than a concentration of the carbon-based conductive additive of another intervening further electrode over the intervening further electrode. The concentration or ratio (e.g. volume ratio or weight ratio) of the carbon-based conductive additive of the second electrode may be higher than the concentration of the intervening further electrode. The electrode layer furthest from the current collector may have the lowest concentration or ratio of the carbon-based conductive additive. The concentration or ratio of the carbon-based conductive additive of an electrode layer nearer the current collector may be higher than the concentration or ratio of the carbon-based conductive additive of an electrode layer further from the current collector.

[00157] In various other embodiments, electrode layer furthest from the current collector may have the highest concentration or ratio of the carbon-based conductive additive. The concentration or ratio of the carbon-based conductive additive of an electrode layer nearer the current collector may be lower than the concentration or ratio of the carbon-based conductive additive of an electrode layer further from the current collector.

[00158] In various embodiments, forming the first electrode layer may include forming a colloidal suspension based including an electrode material precursor and a carbon-based conductive additive precursor. Forming the first electrode layer may also include annealing the colloidal suspension to form the first electrode layer. Forming the first electrode layer may include coating the colloidal suspension on the current collector before annealing the colloidal suspension.

[00159] In various embodiments, forming the second electrode layer may include forming a further colloidal suspension based including the electrode material precursor and the carbon-based conductive additive precursor. Forming the second electrode layer may also include annealing the colloidal suspension to form the second electrode layer. Forming the second electrode layer may include coating the further colloidal suspension before annealing the colloidal suspension. The further colloidal suspension may be coated on the first electrode layer including the colloidal suspension.

[00160] In various embodiments, a ratio (e.g. a volume ratio or weight ratio) of the conductive precursor to the electrode precursor in the colloidal suspension may be higher than a ratio (e.g. a volume ratio or weight ratio) of the conductive precursor to the electrode precursor in the further colloidal suspension.

[00161] Forming a further electrode layer or an intervening electrode layer may include forming a respective colloidal suspension based including the electrode material precursor and the carbon- based conductive additive precursor. Forming the further electrode layer or the intervening electrode layer may also include annealing the respective colloidal suspension. Forming the further electrode layer or the intervening electrode layer may also include coating the respective colloidal suspension before annealing. The respective colloidal suspension may be coated on a preceding electrode layer. For instance, the colloidal suspension forming the third electrode layer may be coated on the second electrode layer including the further colloidal suspension. In various embodiments, annealing may be carried out after coating the colloidal suspensions over the current collector.

[00162] In various embodiments, the electrode material may be any one selected from a group consisting of titanium dioxide (Ti0₂), lithium titanate, silicon, a metal oxide, a layered oxide (e.g. LiCo0₂, Li n0₂, LiNio.5Mno.5Ch, or LiNi₁/₃Coi/₃Mni/₃0₂), a spinel oxide (e.g. LiMn₂0₄ or LiNio.5Mni .5Ο4), and an olivine polyanion L1MPO4 (where M may be Fe, Co, Ni, or Mn). In various embodiments, the carbon-based conductive additive may be any one selected from a group consisting of reduced graphene oxide, graphene, carbon black, and carbon nanotubes.

[00163] In various embodiments, the electrode material may be titanium dioxide (Ti0₂). In various embodiments, the carbon-based conductive additive may be reduced graphene oxide ( GO). In various embodiments, the electrode material precursor may be hydrogen titanate. In various embodiments, the electrode material precursor and the electrode material may be of different phases. In various embodiments, the carbon-based conductive additive precursor may be graphene oxide.

[00164] The graphene oxide may be formed from graphite powder. [00165] The electrode may for instance be electrode 200 as shown in FIG. 2A or electrode 280 shown in FIG. 2C.

[00166] Various embodiments may provide an electrode formed by any method described herein.

[00167] FIG. 25 is a schematic showing a method of forming an electrochemical cell according to various embodiments. The method may include, in 2502, providing or forming an electrolyte layer between the electrode as described herein, and a further electrode. The electrolyte layer may include an electrolyte.

[00168] In other words, various embodiments may relate to forming an electrochemical cell or battery including an electrode as described herein. The electrochemical cell or battery may further include a further electrode.

[00169] In various embodiments, the electrode may be an anode, while the further electrode may be a cathode. The electrode may for instance be electrode 200 as shown in FIG. 2A or electrode 280 shown in FIG. 2C.

[00170] In various embodiments, the further electrode may be a conventional electrode.

[00171] In various embodiments, the method may also include forming or providing a separator layer.

[00172] The electrolyte may be or may include a lithium salt (e.g. lithium hexafluorophosphate

(LiPF₆) or lithium tetrafluoroborate (L1BF4)) in an organic solvent (such as ethylene carbonate, dimethyl carbonate, or diethyl carbonate).

[00173] Experimental Details

[00174] Synthesis of GO and H-TNT Precursors

[00175] GO may be prepared through Hummers method with the natural graphite powder as precursor. Ultrasonic treatment may be used for further exfoliation of graphite oxide nanosheets. Then, the solution maybe centrifuged at 3000 rpm, and the upper brown solution maybe collected. H-TNT may be prepared by a stirring hydrothermal method.

[00176] H-TNT may be prepared by a stirring hydrothermal method. In a typical experiment, P25 powder (100 mg) and sodium hydroxide (NaOH ) pellets (6 g) may be dispersed in 15 mL of deionized (D.I.) water (~10 M NaOH solution) with continuous stirring for 10 minutes for a homogeneous solution, and may then be transferred into 25 mL Teflon-lined stainless-steel autoclave. The autoclave may be kept at 130 °C for 24 h with the stirring speed of 500 rpm. The Na-titanate product may be collected and washed with D.I. water to neutral. Subsequently, the sample may undergo an ion-exchange process that initially Na⁺ is replaced by H⁺ by means of immersing the sample in 0.1 M hydrochloric acid (HC1) solution to obtain the hydrogen titanate nanotube (H-TNT). The suspension may then be centrifuged, and may then be washed with D.I. water for several times, and may finally be dispersed in ethanol solution.

[00177] Fabrication of Multi-Segmented Composition-graded and Conventional Electrodes

[00178] Firstly, the obtained GO and H-TNT samples may be dispersed into pure ethanol (99%) respectively with a concentration of 3.5 mg/mL. In a typical fabrication for composition upgraded RGO/Ti0₂(B) electrode, a 30% GO/H-TNT ethanol suspension may firstly be spread as the bottom layer on a copper foil (current collector) by drop-casting method. During the drying, the ethanol solution may instantly be evaporated, and elongated nanotubes may be solidified and may adhere well to the substrate. This step may be repeated for another three times after drying until four layers of the composite with the weight ratio in the sequence of 30, 11, 3, and 0% GO/H-TNT (top layer) deposited on the current collector.

[00179] For the composition downgraded electrode, the fabrication process may be inverse to the fabrication sequence of the composition upgraded electrode. On the other hand, the conventionally homogeneous electrode may be directly fabricated with four layers with the same ratio of 11% GO/H-TNT thin film. Finally, the above multilayered GO/H-TNT films may be subjected to vacuum annealing at 400 °C for 2 hours to achieve final electrode configuration with composition upgraded, conventionally homogeneous, and composition downgraded electrodes with a loading amount 1.0-1.1 mg/cm².

[00180] Electrochemical Measurement

[00181] The battery performance of half cells may be measured using CR 2032 coin cells with the lithium metal as the reference electrode. The electrolyte maybe 1.0 M LiPF₆ in a 50 : 50 (w/w or weight ratio) mixture of ethylene carbonate and diethyl carbonate. The cells may be assembled in a glove box with 0₂ and H₂0 contents below 1.0 and 0.5 ppm, respectively. Rechargeable cycles may be conducted with the voltage window of about 1.0 - 3.0 V for the half cells at varied current densities on a NEWARE battery tester. [00182] Cyclic voltammogram (CV) test may be conducted from 3.0 to 1.0 V using an electrochemical analyzer (Gamry Instruments. Inc). The electrochemical impedance spectroscopy (EIS) tests may be carried out using an electrochemical station (ZAHNER MESSSYSTEM Electrochemical Workstation) over a frequency range from 1 MHz to 0.1 Hz with a voltage amplitude of 10 mV.

[00183] The galvanostatic intermittent titration technique (GITT) measurements may be conducted on NEWARE battery tester with the test profile including a charge and discharge interval at 1 C for 1 minute and a rest interval of 59 minutes.

[00184] Galvanostatic Intermittent Titration Technique (GITT) Measurements

[00185] GITT test is a reliable test which may be used to study the lithium diffusivity. The battery may first be charged/discharged with a small current for a short time followed by rest for a long time. An assumption may be made that the lithium inside the electrode tries to diffuse to achieve a homogeneous solid solution phase during rest for a thermodynamic equilibrium state.

This diffusion process may be indicated by voltage decrease/increase during rest after charge/discharge. FIG. 18A shows the overall GITT profile of composition upgraded anode during charge and dischar e. The lithium diffusivity (Du⁺) may be obtained from:

wherein t is the charge/discharge time, TUB is the mass of electrode, VM and MB are the molar volume and molar mass of electrode, respectively, A is electrode surface area and AE_S and AEt represent the potential change which is shown in FIG. 18B.

[00186] The calculated lithium diffusivity for both composition upgraded and homogeneous anodes may be shown in FIG. 18C. The composition upgraded and homogeneous anodes show the similar lithium diffusivity in the voltage range of 1.7 to 1.9 V, for example, lithium diffusivity of about 4.9 x 10^"10 cmV¹ at 1.8 V for both the composition upgraded and homogeneous electrodes. There is a small peak in the voltage range of 1.8 to 1.9 V, which may be due to the anatase impurity. As the voltage decreases, the lithium ion diffusivity may decrease for both composition upgraded and homogeneous anodes, because more and more diffusion sites in Ti0₂(B) are occupied due to increasing capacities. However, the lithium ion diffusivity of the composition upgraded anode may be much higher than that in the homogeneous anode, for example, 1.7 x 10^"10 cmV¹ for composition upgraded anode and 3.0 x 10^"10 cm²s^"' for homogeneous anode at 1.2 V.

[00187] Cyclic Voltammogram (CV) Test

[00188] CV curves may also be used to investigate the lithium diffusivity. The relationship between the peak intensity and scan rate may be used to calculate the lithium ion diffusion coefficient.

[00189] FIG. 19A illustrates the method to determine the peak intensity. In a first case, if the peak intensity shows a linear relationship between the scan rate, the charge/discharge may be characterized as capacitive behavior. In a second case, if the peak intensity displays a linear relationship with the square root of scan rate, the charge/discharge may represent the diffusion control process with the following equation:

I_p = 2.69x x A x Cx D^₊ x n^m xv^m (6) where I_p is peak intensity, A is electrode area, Du⁺ is lithium ion diffusivity, C is the concentration of the electrolyte, n is a number of electrons involved in reaction and υ is scan rate. The slope from the above equation is proportional to the lithium ion diffusion coefficient. FIG. 19B shows the linear relationship between the cathodic peak intensity and the square root of scan rate. Both composition upgraded and homogeneous anodes may involve a diffusion control process during charge and discharge. However, the composition upgraded electrode shows larger slope compared with homogeneous material, which may mean that the composition upgraded electrode exhibits higher lithium-ion diffusivity. The calculated Du⁺ for the composition upgraded and homogeneous electrodes are 3.0 x 10^"11 and 1.9 ^x 10^{"1 1} cmV¹ respectively.

[00190] Materials Characterization

[00191] The crystal structure of GO/H-TNT nanotube composite before and after heat treatment may be studied through thin film X-ray diffraction (XRD, Shimadzu XRD-6000) pattern obtained by using Cu Ka source and scanned from 10° to 70° with the scanning rate of l°/min. The morphology and microstructure of the as-synthesized samples may be investigated by field emission scanning electronic microscopy (FESEM; JEOL JSM-7600F) and transmission electron microscopy (TEM; JEOL, JEM-2100F). [00192] EDX attached to the FESEM may be used to analyze the component elements. X-ray photoelectron spectroscopy (XPS, Al K source) may be used to determine the elemental composition of pure Ti0₂(B) and RGO/Ti0₂(B) composite. All peaks may be calibrated according to the adventitious C-C bond at 284.8 eV. The electrical conductivity (sheet resistance) of the Ti0₂(B) and RGO/Ti0₂(B) composite may be measured with a CMT-SR 2000N 4-point probe station from Advanced Instrument Technology. The lithium ion diffusivity for the RGO/Ti0₂(B) composite layer with different RGO weight ratio may be measured by electrochemical impedance spectroscopy (EIS) tests at 3.0 V after different cycles, which may be carried out in a Solartron electrochemical station. The prepared GO and RGO may be investigated through Fourier transform infrared spectroscopy (FTIR, Perkin Elmer FTIR spectrometer) from 4000 nm to 600 nm wavelength and Raman spectroscopy (WITec CRM200 confocal Raman microscopy) at room temperature with the reference band of 520 cm^"1 for Si.

[00193] Thermo gravimetric analysis (TGA)

[00194] The weight percentage of RGO inside different composites may be investigated by thermogravimetric analysis (TGA, Q500) in air/nitrogen atmosphere at a heating rate of 10 degrees Celsius/minute.

[00195] The GO may undergo three main steps of weight loss when annealed in air: I) the loss of absorbed water (25 ~ 200 °C); (II) the decomposition of labile oxygen-containing functional groups (300 ~ 500 °C) to form the RGO, and (III) the oxidation of RGO to carbon dioxide (> 500 °C).

[00196] Different from GO, there may be no significant weight loss before 500 °C for RGO during vacuum annealing due to the previous weight loss steps (I, II). For the annealed RGO/Ti0₂(B) composite, the minor weight loss at relative low temperature region (around 200 °C) may be due to evaporation of absorbed water, while the significant weight loss after 400 °C may be mainly contributed by the oxidation of RGO to carbon dioxide since the weight loss from pure Ti0₂(B) may be very much lesser (< 1%) after 400 °C.

[00197] In order to investigate the weight loss during the annealing process, the GO and H-TNT nanotube without annealing may be heated to 400 °C followed by an isothermal step for 30 minutes in nitrogen gas to simulate the vacuum annealing weight loss process. As shown in FIG. 13B, the weight loss for precursor GO and H-TNT nanotubes may be around 52% and 12% respectively before the isothermal process. This may mean that the weight of the generated RGO after annealing of GO is less than 50% of original weight of precursor GO, and the calculated weight ratio of annealed RGO/Ti0₂(B) with the initial weight ratio of 30%, 11%, and 3% may be around 14.1%, 5.4%, and 1.7% respectively. The total weight ratio of RGO in different configurations of multilayered RGO/Ti0₂(B) electrodes may be around 5.4%.

[00198] Simulation Methods

[00199] All first principles calculations may be carried out using the Vienna Ab Initio Simulation Package (VASP). For the studied systems, the Perdew-Burke-Ernzerhof (PBE) functional may be used to treat the exchange-correlation effects. However, since PBE has a limited accuracy in the description of van der Waals (vdW) systems, optB86b-vdW functional is used to analyze the stability of graphene-Ti0₂(B) systems. Such functional may allow capturing of the vdW forces based on the first principles level without adding any empirical corrections. In order to analyze electronic properties of Li-doped Ti0₂ and predict a position for Ti³⁺ picks, detailed DFT+U calculations with the method introduced by Dudarev et al. with U=4.2 eV may be introduced for Ti d-like orbitals. Finally, for the lowest energy structures found from DFT+U calculations, hybrid functional calculations may be carried out to predict electronic properties with high accuracy.

[00200] For first principles simulations, the cutoff energies for plane-wave basis may be set to 400 and 500 for final "static" density functional theory (DFT) calculations and optimization of lattice parameters, respectively. The Brillouin-zone integrations may be performed using the Γ- centered Monkhorst-Pack grids of different sizes as provided by Table 2 below :

System Type of calculations Grid size

Li-Ti0₂(B) Atomic relaxation (DFT, DFT+U) 4x4x4

Diffusion calculations 2 2x2

Hybrid functional calculations 2 2 2

Li-C Diffusion calculations 3x3x 1

C-Ti0₂(B) Atomic relaxation 8x4 1 Density of states 16x8x 1

00201] DFT and DFT+U calculations for Li-doped Ti0₂(B) may be carried out using 1 3 2

Ti0₂ supercells, while the hybrid functional calculations may be carried out for 1 2x 1 Ti0₂ supercell. Li interaction with graphene was analyzed using 6 3 graphene supercell. To study the interface between graphene and Ti0₂(B), a model containing 3x3 graphene supercell and 1 x2 TiO₂(001) slab may be created (see FIG. 5B).

[00202] Screening of 36 different interface configurations may be performed to find the lowest energy interface structures. For all systems, the atoms may be relaxed until the internal forces were smaller than 0.015 eV/A. To predict Li migration barriers, the nudged elastic band (NEB) method may be used. However, for Li migration via graphene, simulations by manual screening with fixed C atoms in a direction parallel to Li diffusion may be used. Tests to make sure that migration barrier is not affected by selected computational setup may also be used. The computed results may be analyzed using Vesta and pymatgen codes. The first principle calculations may be performed on an Abel cluster.

[00203] Discussion on State Of Charge (SoC) For Evaluating Battery Performance

[00204] By integrating concentration profile over the thickness, electrode performance termed as state of charge (SoC) may be estimated as the ratio of Li-ion concentration in the electrode at time t and at an infinite time from Equation (2).

[00205] The SoC may be gradually decreased with the decrease in charging time and Li-ion diffusivity (D), and with the increase of electrode thickness (1). Herein, it is concluded that Li-ion diffusion may be kinetically limited in traditionally homogeneous electrode systems, resulting in gradient Li-ion distribution along diffusion direction due to the limited Li-ion characteristic diffusion length, especially at high rates.

[00206] Discussion on Charge Carrier Transport Within Battery Electrode

[00207] As the Li-ion current resulting from Li-ion diffusion in the electrode is proportional to the gradient of Li-ion concentration, it may be derived by taking derivatives of the concentrations defined by Equation (1) with respect to x. The derived ionic current within the electrode at a time may be shown as the line 102a in FIG. IE. From Faraday's law, the current in a closed circuit may be kept constant everywhere throughout the circuit. Setting the constant current as I₀, we have: [00208] ^electrolyte ⁼ Ianode ⁼ ^collector ⁼ IQ 00 where Ieiectroiye is the current in the electrolyte, Ianode is the current at the anode, and Icoiiector is the current flowing through the current collector.

[00209] Within the electrode, the current may include Li-ion current (Iu+) and electronic current

Ianode ⁼ i+ + - ⁼ ) (β)

[00210] The derived current profiles of Li-ion and electron within the electrode is shown in FIG. IE. As the Li-ions are injected from electrolyte/electrode interface while electrons from collector/electrode interface, there may be a dominating Iu+ at the electrolyte/electrode interface and a dominating I_e- at the collector/electrode interface. Therefore, for a conductive agent with homogeneous distribution in the electrode, the voltage drop (V=IR, overpotential) due to electronic current may be the largest near the current collector/electrode interface while voltage drop due to Li-ion current is the largest near the electrolyte/electrode interface. In order to compensate the intrinsic electronic conduction inefficiency near the current collector/electrode interface, a graded electrode design with simultaneous electronic conduction enhancement near current collector/electrode interface and Li-ion conduction enhancement near electrolyte/electrode interface according to various embodiments may be proposed. A graded RGO/Ti0₂(B) composite electrode maybe provided where the ratio of RGO gradually decreases from the collector/electrode interface to the electrolyte/electrode interface. In such a case, the voltage drop due to electronic current may decrease as a result of compensated electronic conductivity especially near the current collector, voltage drop arising from Li-ion current may also drop due to a gradient distribution of Li-ion diffusion coefficients.

[00211] While the invention has been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.

Claims

1. An electrode comprising:

a first electrode layer comprising an electrode material and a carbon-based conductive additive; and

a second electrode layer in contact with the first electrode layer, the second electrode layer also comprising the electrode material and the carbon-based conductive additive;

wherein a concentration of the carbon-based conductive additive in the first electrode layer is higher than a concentration of the carbon-based conductive additive in the second electrode layer.

2. The electrode according to claim 1,

wherein the electrode material is any one selected from a group consisting of titanium dioxide (Ti0₂), lithium titanate, silicon, a metal oxide, a layered oxide, a spinel oxide, and an olivine polyanion .

3. The electrode according to claim 2,

wherein the electrode material is titanium dioxide.

4. The electrode according to claim 3,

wherein the titanium dioxide has a monoclinic crystal structure or a tetragonal crystal structure.

5. The electrode according to any one of claims 1 to 4,

wherein the carbon-based conductive additive is any one selected from a group consisting of reduced graphene oxide, graphene, carbon black, and carbon nanotubes.

6. The electrode according to claim 5,

wherein the carbon-based conductive additive is reduced graphene oxide.

7. The electrode according to any one of claims 1 to 6, further comprising:

a current collector in contact with the first electrode layer so that the first electrode layer is between the current collector and the second electrode layer.

8. The electrode according to any one of claims 1 to 7, further comprising:

one or more further electrode layers over the first electrode layer and the second electrode layer to form a stacked arrangement;

wherein the one or more further electrode layers also comprise the electrode material.

9. The electrode according to claim 8,

wherein a topmost further electrode layer of the one or more further electrode layers is devoid of the carbon-based conductive additive.

10. The electrode according to claim 9,

wherein one or more intervening further electrode layers between the topmost further electrode layer and the second electrode layer further comprise the carbon- based conductive additive.

11. The electrode according to claim 10,

wherein a concentration of the carbon-based conductive additive of an intervening further electrode is higher than a concentration of the carbon-based conductive additive of another intervening further electrode over the intervening further electrode; and

wherein the concentration of the carbon-based conductive additive of the second electrode is higher than the concentration of the intervening further electrode.

12. The electrode according to any one of claims 1 to 11,

wherein the electrode material is comprised in a plurality of first nanostructures; and

wherein the carbon-based conductive additive is comprised in a plurality of second nanostructures.

13. The electrode according to claim 12,

wherein the first nanostructures may be any one selected from a group consisting of nanotubes, nanowires, nanoparticles, and nanosheets.

14. The electrode according to claim 12 or claim 13,

wherein the second nanostructures may be any one selected from a group consisting of nanotubes, nanowires, nanoparticles, and nanosheets.

15. An electrochemical cell comprising:

an electrode according to any one of claims 1 to 14;

a further electrode; and

an electrolyte layer between the electrode and the further electrode, the electrolyte layer comprising an electrolyte.

16. The electrochemical cell according to claim 15, wherein the electrode is an anode and the further electrode is a cathode.

17. The electrochemical cell according to claim 15 or claim 16,

wherein the electrolyte comprises a lithium salt.

18. A method of forming an electrode, the method comprising: forming a first electrode layer comprising an electrode material and a carbon- based conductive additive; and

forming a second electrode layer in contact with the first electrode layer, the second electrode layer also comprising the electrode material and the carbon- based conductive additive;

19. The method according to claim 18,

wherein forming the first electrode layer comprises:

forming a colloidal suspension based comprising an electrode material precursor and a carbon-based conductive additive precursor; and annealing the colloidal suspension to form the first electrode layer.

20. The method according to claim 19,

wherein forming the second electrode layer comprises:

forming a further colloidal suspension based comprising the electrode material precursor and the carbon-based conductive additive precursor; and

annealing the further colloidal suspension to form the second electrode layer.

21. The method according to claim 20,

wherein a ratio of the conductive precursor to the electrode precursor in the colloidal suspension is higher than a ratio of the conductive precursor to the electrode precursor in the further colloidal suspension.

22. The method according to any one of claims 19 to 21,

wherein the electrode material precursor is hydrogen titanate.

23. The method according to any one of claims 19 to 22,

wherein the carbon-based conductive additive precursor is graphene oxide.

24. The method according to any one of claims 18 to 23,

wherein the first electrode layer is formed in contact with a current collector.

25. The method according to any one of claims 18 to 24, further comprising:

forming one or more further electrode layers over the first electrode layer and the second electrode layer to form a stacked arrangement;

26. The method according to claim 25,

27. The method according to claim 26,

28. The method according to claim 27,

29. A method of forming an electrochemical cell, the method comprising:

providing an electrolyte layer between the electrode according to any one of claims 1 to 14, and a further electrode;

wherein the electrolyte layer comprises an electrolyte.