Three – Dimensionally Ordered Macroporous Amorphous C/TiO2 Composite Electrodes for Lithium-ion Batteries

A facile method utilizing colloidal templating and sucrose as a carbon precursor is used to synthesize highly ordered, porous inverse opal structures as C/TiO2 nanocomposites. Material characterization shows amorphous TiO2 and a large pore size of ∼400 nm allowing for enhanced electrolyte penetration. C/TiO2 inverse opals materials as electrodes in Li-ion battery half cells demonstrate discharge and charge capacities of ∼870 mAh g−1 and 470 mAh g−1, respectively, at a current density of 150 mA g−1. The enhanced capacities, which surpass theoretical limits for TiO2 and carbon based on intercalation reactions, are analyzed under voltammetric conditions to assess relative contributions to capacity from diffusion-limited intercalation and capacitive charge compensation reactions. The porous structure contributes to excellent capacity retention, rate performance and improved Coulombic efficiency (99.6% after 250 cycles), compared to individual carbon and TiO2 inverse opals.

6][7][8] As the demand for higher energy density, faster charging capabilities and longer cycle life continues to grow, the need for advanced electrode materials 9,10 and designs becomes increasingly crucial.2][13] However, carbon based materials suffer great danger from dendrite formation due to their low intercalation potential, which can cause poor cycling stability, and safety issues.Conversely, TiO 2 has shown good chemical and physical properties and has garnered attention as a promising material in LIBs [14][15][16] and other electrochemical technologies, nonetheless, TiO 2 suffers from limited Li-ion and electron transport capabilities which results in low capacity retention and poor rate performances. 17,180][21][22][23] Nevertheless, many commercial materials are slurry-based, comprising of active material particles, binders and conductive additives that are randomly arranged and densely packed, affording limited control over their structural attributes. 24They exhibit an adverse relationship between tortuosity and porosity, leading to a trade-off between energy density and power density. 25,265][36][37][38][39] Among these materials, inverse opals (IOs) are a subtype of 3DOMs, formed via a sacrificial template of polymer spheres such as polystyrene. 40,41Os offer the benefit of shorter diffusion lengths for lithium ions and can improve charge transfer rates because of a larger surface area.The porous architecture facilitates rapid Li + movement and diffusion within the electrolyte, all while preserving the structural integrity, thus preventing volume swelling or material degradation.Notably, IOs can be prepared directly onto the current collector and so removes the need for any binders or additives.
In this report, C/TiO 2 composite inverse opal electrodes with a robust 3D structure and high surface area were synthesized using a solvent infiltration method.Structural characterization in the form of X-ray diffraction (XRD) and selected area electron diffraction (SAED) reveals the amorphous nature of the material.We investigate the effect of combining carbon and TiO 2 by conducting a comparative electrochemical analysis of the composite IO electrode alongside their individual IO counterparts.The electrochemical performances of both materials are analyzed by cyclic voltammetry (CV), galvanostatic cycling (GCPL) and rate testing.Our findings demonstrate that the C/TiO 2 IOs offer increased capacities and improved capacity retention over 250 cycles compared to pure TiO 2 and carbon IOs.Our composite electrodes exhibit stable Coulombic efficiency even at high current densities, showcasing very good high-rate performance.Furthermore, post-mortem evaluation underscores the structural stability of the IOs, as they maintain their structural integrity after cycling.

Experimental
Materials preparation.-Thesubstrates used were stainless steel (SS) discs (grade 304) with a diameter of 15.5 mm.The opal template was fabricated using the evaporation induced self-assembly (EISA) method, which involved suspending the SS discs in a 0.2% solution of polystyrene spheres (500 nm diameter) and deionized water and placing in a convection oven at 60 °C overnight.TiO 2 and carbon IO samples were prepared for the purpose of conducting structural and crystallinity comparison analyses, as well as for making electrochemical comparisons with the composite materials.
z E-mail: c.odwyer@ucc.ieECS Advances, 2024 3 010502 C/TiO 2 IO preparation.-A0.1 M solution of titanium(IV) chloride tetrahydrofuran (TiCl 4 .2THF)was prepared in IPA while the carbon precursor solution consisted of sucrose, ethanol (EtOH), deionized water and sulphuric acid (18 M, Sigma Aldrich).These were mixed in mass ratios of 1:35.5:5:0.18,respectively.The dried PS sphere templates were then infilled by drop casting a volume of the carbon precursor (∼15 μl) followed by an equal volume of the TiO 2 precursor.The samples were placed in a convection oven at 70 °C for 25 min before being heated to 100 °C for 5 h in air.After 5 h the samples were placed in a tube furnace under Ar and heated to 500 °C at a ramp rate of 5 °C min −1 .The samples were held at 500 °C for 2 h.
Carbon IO preparation.-Thedried PS spheres were infilled with ∼30 μl of the sucrose solution before being placed in a convection oven at 70 °C for 25 min.The carbon samples were then heated to 100 °C for 5 h in air before being heated to 900 °C under Ar and held for 2 h.TiO 2 IO preparation.-Thedried PS spheres were infilled with ∼30 μl of the TiCl 4 .2THFsolution before being placed in a convection oven at 70 °C for 25 min.The samples were then heated to 500 °C in air at a ramp rate of 5 °C min −1 and held for 1 h.Material characterization.-SEManalysis was performed on FEI Quanta 650 FEG high resolution SEM at an accelerating voltage of 10 kV.EDS analysis was performed using a FEI Quanta 650 FEG high resolution SEM at an accelerating voltage of 20 kV.EDS mapping was performed on Zeiss Supra 40 high resolution SEM at an accelerating voltage of 20 kV.SEM images and feature dimensions were analyzed using ImageJ software.Raman scattering was performed on an Ocean Optics QE65PRO Raman Spectrometer using a 40 mW Ar + laser at 532 nm excitation.The laser was focused onto the samples using a 40× objective lens and spectra were collected using a CCD camera.X-ray diffraction (XRD) was conducted using a PANalytical XPERT PRO PW3050 diffractometer using a Cu anode, Kα radiation with wavelength λ = 0.15406 nm, operation voltage 40 kV, current 20 mA, with the samples being scanned from 2θ = 5°-80°.TEM analysis was conducted using a JEOL JEM-2100F TEM operating at 200 kV.
Electrochemical characterization.-Allelectrochemical characterization was performed using BioLogic VSP Potentiostat/ Galvanostat.All IOs were investigated in a half cell configuration against a pure Li counter, using a stainless-steel PAT-cell from EL-Cell in a two-electrode configuration.The electrolyte used was lithium hexafluorophosphate solution, in ethylene carbonate and diethyl carbonate, 1.0 M LiPF 6 in EC/DEC=50/50 (v/v), battery grade from Sigma Aldrich.The separator used was glass microfiber from Whatman Grade GF/A cut to size.The typical loading mass of the samples were between 0.4 mg-0.7 mg.C/TiO 2 electrochemical tests were investigated in a potential window of 3.0 V-0.01 V. Supplementary electrochemical tests for carbon and TiO 2 IOs were investigated in a potential window of 3.0 V-0.01 V unless stated otherwise.Cyclic voltammetry was performed at various scan rates for C/TiO 2 and galvanostatic cycling was performed using various specific currents as mentioned in this report (0.05 mV s −1 -1000 m V s −1 , 75 mA g −1 -450 mA g −1 ).

Results and Discussion
Material characterization.-Thecarbon/TiO 2 inverse opal (IO) samples were prepared by evaporation induced self-assembly (EISA) as described by Colvin et al. with a volume faction of 0.2%. 42The polystyrene sphere opal templates were then infilled with 15 μl of the sucrose solution and 15 μl of the TiO 2 precursor.The samples were then dried at 70 °C for 30 min to evaporate the solvents in the precursor followed by a pre-carbonization step which involved heating the samples to 100 °C in air and held for 5 h.The samples were then placed in a tube furnace and heated to 500 °C under Ar and held for 2 h.The sacrificial sphere template decomposed with the high temperature which allowed the IO structure to form and produce highly ordered porous structures which can be seen in the SEM images in Figs.1a-1d.The thickness of the inverse ECS Advances, 2024 3 010502 opal structure is ∼17 μm thick and contains pores with an average diameter of 363 nm (shown in Supplementary material, Fig. S1).The various layers that form the (111)-oriented inverse of the apparent face centered cubic (fcc) opal template can be seen through the pores of the samples from the SEM images.The atomic ratio of carbon to TiO 2 was found to be between 8:1 and 10:1, the variance in ratio may be due to remnant or adventitious carbon from the polystyrene spheres.
Raman scattering spectroscopy in Fig. 1e detected peaks at 173.8 cm −1 , 427.9 cm −1 , 611.3 cm −1 , 801.3 cm −1 and 316.7 cm −1 for modes B 1g , E g , A 1g , B 2g and second order scattering indicative of rutile TiO 2 .Peaks at 1372.7 cm −1 and 1597.2 cm −1 show the D (disorder) and G (graphitic) bands for carbon, respectively.The G band is due to the in-plane stretching of C sp 2 bonded atoms for both chain and rings, while the D band indicates disorder is present, and its intensity is correlated to the presence of sixfold aromatic rings. 43he I D /I G ratio was found to be 0.71 compared to the I D /I G ratio of 1.00 for the carbon-only IO spectra.This decrease in ratio indicates a reduction in order and may indicate increasing amorphization of the carbon.X-ray diffraction (XRD) measurements of the IO structure suggested that the materials are predominantly amorphous, showing no distinct peaks in the XRD pattern other than those for the stainless-steel substrate.Localized laser-induced heating allowed us to see the crystallized form of both materials, but the as-prepared composite IO is an amorphous material. 44,45Notably the XRD patterns align with the electron diffraction patterns depicted in Fig. 2.
Transmission electron microscopy (TEM) analysis was employed to gain further insight into the porous structure of the C/TiO 2 composites.In Figs.2a, 2b, TEM images of the C/TiO 2 composite at different magnifications reveal a hierarchical porous structure characterized by macroscopic pores.The wall diameters were measured to be ∼30 nm on average, compared to ∼26 nm for carbon IOs and ∼12 nm for TiO 2 IOs (shown in Supplementary material, Fig. S2).The high-resolution TEM (HRTEM) image in Fig. 2c has no discernible lattice fringes indicating the amorphous nature, which is confirmed by the selected area electron diffraction (SAED) pattern in Fig. 2d.By comparison, pure TiO 2 -only IOs are crystalline in the anatase phase, and pure carbon-only IOs are amorphous.Further HRTEM details on the crystalline TiO 2 -only IOs are shown in Supplementary material, Fig. S3.The dark-field TEM image and the corresponding EDS elemental mapping images can be seen in Figs.2e-2h, revealing a notably uniform dispersion of carbon (C), oxygen (O), and titanium (Ti) species.Figure 2i show an SEM images of the C/TiO 2 IO material and the resulting EDS line scan, revealing a generally homogenous and consistent dispersion of carbon (C), oxygen (O), and titanium (Ti) species across the trace line.
Electrochemical characterization.-Theelectrochemical behavior of the material was characterized in a half cell system against a Li metal counter electrode.Figure 3a shows the cyclic voltammetry (CV) curves at a scan rate of 0.05 mV s −1 in the potential window 3 V-0.015V. Four regions of interest in the cathodic scan include the peaks at 1.4 V, 1.28 V, 0.73 V and the sloping region from 0.49 V-0.015 V.These peaks correlate to major lithiation reactions with C/TiO 2 .The cathodic reduction peak at 1.4 V and the anodic oxidation peak at 1.86 V are associated with the lithiation/ delithiation of TiO 2 , which follows the Eq.1: Evidence of SEI layer formation is found at 1.3 V as this peak is only visible for the first cycle.The peak centered at 0.73 V suggests lithium insertion into the carbon material and is observed in CVs for carbon only IOs (Fig. 3b).The sloping region from 0.49 V to 0.015 V correlates to the lithiation of carbon, which follows the reaction Eq.2: The anodic peak at 1.16 V is attributed to the delithiation of carbon, and the delithiation of TiO 2 is shown by the peak at 1.86 V.While TiO 2 is described as an intercalation mode material, hard carbons react with lithium by capacitive ionization/deionization and adsorption/desorption processes.C/TiO 2 IOs were compared to carbon IOs that were cycled between 2 V-0.01 V in Fig. 3b, highlighting the increased current density arising from the addition of TiO 2 .To investigate charge storage properties for C/TiO 2 , CVs were taken at various scan rates from 0.1 mV s −1 to 1000 mV s −1 in the voltage range of 0.015 V to 3 V as shown in Fig. 3c.The total stored charge can be separated into faradaic and non-faradaic processes, faradaic processes involve a transfer of charge at the electrode-electrolyte interface, such as intercalation and/or alloying, while non-faradaic processes [46][47][48][49][50] involve electrostatic interactions without significant chemical changes. 51apacitive effects can be characterized by analyzing the CV at various scan rates according to 52 where i is the current (mA), v is the scan rate (mV/s) and a, b are adjustable values.The b-values can be obtained by setting a log on both sides of Eq. 3, and finding the slope (Figs.3e, 3f).When b = 0.5, the process is considered diffusion limited and when the b-value approaches 1.0, capacitive behavior is dominant. 53In Fig. 3e we show the plot of log (i) vs log (v) for the 3 cathodic peaks observed in the CV, and for a range of currents from the CVs in Fig. 3f.All 3 voltage points show a b-value below 0.5, indicating that the current response is primarily due to intercalation reactions rather than capacitive.The total current (i) at a specific potential (V) is the sum of both the diffusion-controlled and capacitive reactions according to: where k v 1 and k v 2 1 2 correspond to the current attributed to capacitive and diffusion-controlled process respectively.By rearranging this equation to we can find k 1 and k 2 through the linear fit It is then possible to distinguish between currents arising from Li + insertion and those occurring from capacitive-like processes. 54,55Figure 4 shows the voltage profiles for the intercalation (red) and capacitive (green) currents compared to the measured current (grey) for scan rates 0.1 mV s −1 -1000 mV s −1 .Diffusion processes account for ∼99.5% of the current measured for the 0.1 mV s scan as per Figs.4a, 4f, this decreases slightly to ∼98% for the 1 mV s −1 scan showing little contribution from capacitive processes.This is in excellent agreement with the b-values calculated for the cathodic peaks which were on or below 0.50.Once a scan rate of 100 mV s −1 is reached (Figs. 4d, 4f) we observe pseudocapacitive behavior at the surface, with ∼21% of the current arising from capacitive-like processes.Intercalation is a slower process than capacitive charge compensation at the surface, 53 which could explain the drop in specific capacity under fast voltage scanning conditions to 9.8 mAh g −1 as shown in Supplementary material, Fig. S4.Specific capacity for the cell was found using the following equation, ECS Advances, 2024 3 010502 where V c and V a are the cathodic and anodic voltage limits respectively, m is the mass loading of the electrode and v is the scan rate.At 1000 mV s −1 we find almost 50:50 contribution from capacitive and diffusion reactions.The presence of capacitance contributions occurring with an opposite polarity of current (or beyond the region covered by the measured current in grey), results from the deconvolution process applied to the measured current.The sum total of the inferred intercalation and capacitive contributions at each given potential corresponds to the observed current (grey).
Figure 5a shows the discharge/charge voltage profile of the C/TiO 2 composites at a current density of 150 mA g −1 in a potential window of 0.014-3 V.All capacities were calculated based on the mass loading of the C/TiO 2 active material.Galvanostatic cycling shows initial capacities of 869 mAh g −1 and 472 mAh g −1 for the discharge and charge, respectively, with an initial coulombic efficiency (ICE) of 54.3%.This discharge capacity exceeds the theoretical capacity of both TiO 2 (336 mAh g −1 for LiTiO 2 ) and for carbon (372 mAh g −1 for LiC 6 ).The higher capacities observed mainly stem from the presence of defects formed during calcination which serve as additional charge compensation sites for lithium.A weak plateau was observed during the initial charge, from 1.50--1.15V, followed a sloping region from 1.00 V-0.45 V, and another sloping region extending to the lower potential limit, which is in close agreement with the cathodic peaks observed in the CV.The low coulombic efficiency is limited to the first cycle and caused by irreversible side reactions such as the SEI layer formation.In comparison, for carbon only and TiO 2 inverse opal electrodes tested under the same conditions, the initial discharge (charge) capacities for carbon IOs were 835 mAh g −1 (299 mAh g −1 ), with an ICE of 36% and TiO 2 IOs showed 648 mAh g −1 (312 mAh g −1 ), with an ICE of 48%.The C/TiO 2 IOs show good capacity retention with a discharge capacity of 420 mAh g −1 after 100 cycles, reaching 471 mAh g −1 on the 250th cycle.This slight increase in capacity may be attributed to the retention of electrolyte decomposition byproducts ECS Advances, 2024 3 010502 within the walls of the macroporous structure. 56While initial coulombic efficiency was 54.3%, this increased to 97% by the 10th cycle and had an average of 99.6% for the 250 cycles.This is an improvement on the average 98.5% coulombic efficiency recorded  for the carbon only IOs and the 96.4% CE recorded for the TiO 2 IOs.The capacity values achieved surpass previous research reported for nanocomposite carbon and TiO 2 materials prepared under comparable temperature conditions (see Supplementary material, table S1). 57,58This improved reversibility may be due to the porous nature of our inverse opal structures which alleviates volumetric stress arising from the swelling and contracting of the material during cycling under galvanostatic conditions where the reactions are diffusion-limited intercalation.
The galvanostatic discharge and charge curves for the composite C/TiO 2 IOs at a high current density of 700 mA g −1 in a voltage window of 0.014 V-3 V are shown in Fig. 5c.Initial discharge capacity was 615 mAh g −1 with a charge capacity of 274 mAh g −1 resulting in an ICE of 44.6%.The capacity decreases to ∼230 mAh g −1 by the 10th cycle, and experiences a steady decrease, falling to ∼103 mAh g −1 by the 250th cycle.Our composite material shows higher overall capacity as well as capacity retention when compared to TiO 2 IOs and carbon IOs shown in Fig. 5d.The TiO 2 IO had an initial discharge and charge capacity of 343 and 162 mAh g −1 respectively, falling to 60.45 and 49.7 mAh g −1 for the final discharge and charge.While the carbon IOs showed 364 mAh g −1 for the first discharge with an ICE of 18%, falling to 65 mAh g −1 by the 10th cycle and failing before the 100th cycle.The C/TiO 2 material experienced a capacity loss of 68% from the 2nd to 250th cycle, excluding the first cycle because of SEI layer formation, while TiO 2 experienced 72% loss.This better performance at high rates may be due to the conductivity of carbon in our C/TiO 2 material. 59hile we do see relatively low coulombic efficiency for both materials, our C/TiO 2 possesses an average CE of 87.3% over the 250 cycles while the TiO 2 had an average CE was 80.7%.
The rate performances of C/TiO 2 , TiO 2 and carbon inverse opals at the current rates of 0.2 − 1.5C are compared in Fig. 6a.The C rates were calculated from the theoretical capacity of the composite material arising from the weight percentages, which equates to ∼70.4 wt% of C/TiO 2 IO displayed good stability at high rates however, greater capacity loss than its individual C and TiO 2 counterparts.Our composite material achieved average capacities of 461, 377, 325, 309, and 286 mAh g −1 for the 0.2, 0.5, 0.8, 1, and 1.5C rates, respectively.This performance at high current density demonstrates that the incorporation of carbon enhances both cycling stability and high-rate performance when compared to TiO 2 IOs, under galvanostatic conditions.The TiO 2 IOs showed capacities of 244, 158, 131, 119 and 99 mAh g −1 for the same current densities, while carbon IOs achieved 393, 339, 274, 252, and 209 mAh g −1 , respectively.The reversible capacity of C/TiO 2 IOs recovered to 403 mAh g −1 when the current density was reverted to 70 mA g −1 .This equates to a 12.8% loss in capacity after the specific current was returned to 0.2 C.This is similar, if not better, to rate performances observed in other C/TiO 2 macroporous structures, where capacity losses of 12% 31 and 27% 57 were documented after rate tests.In comparison to the pure samples, TiO 2 IOs and carbon IOs lost 6.7% and 9.7% of their initial capacity, respectively, after the specific current was returned to the lower rate.
While the composite material exhibits lower capacity retention during the rate test compared to the individual carbon and TiO 2 IOs, an analysis of the charge/discharge curves at each specific current as shown in Fig. 6b, reveals that the composite material maintains a coulombic efficiency of ∼99% when the current is returned to 0.2 C. Extended cycling at 70 mA g −1 for the C/TiO 2 IOs can be found in Fig. S5, along with the associated coulombic efficiencies.
Post-cycling structural characterization.-Afterelectrochemical testing, the cells were disassembled for structural analysis using SEM to identify any changes resulting from cycling. Figure 7 shows line-scan profiles acquired from grey-scale SEM images of C/TiO 2 IO materials before and after cycling at current densities of 150 mA g −1 and 700 mA g −1 .These profiles clearly reveal the periodicity of the materials and illustrate the minimal volume expansion observed in the IO material post cycling.Specifically, after 250 cycles at 150 mA g −1 (Fig. 7a) there was a negligible change (<1% increase) in wall diameter.
Even at the higher rate of 700 mA g −1 , the samples retained their structural integrity, experiencing only a 19% volume expansion, with a pore diameter of ∼500 nm for the pristine material to ∼405 nm diameter for the same material after cycling.Several factors likely contribute to these outcomes.Firstly, the C/TiO 2 IO materials feature a substantial specific surface area and a network of interconnected pore structures.Consequently, the lithiation/delithiation process occurs within the porous channels as well as uniformly on the material surface, promoting the formation of stable SEI layers. 60,61Secondly, the honeycomb-like IO skeleton reduces the Li + transport resistance between the electrode and electrolyte. 56astly, the carbon addition enhances the overall conductivity of TiO 2, allowing the IO structure to serve as a continuous carrier for electron transport at higher rates under galvanostatic conditions where the voltage change is slow.ECS Advances, 2024 3 010502

Conclusions
Highly ordered, porous inverse opal structures can be made as C/TiO 2 nanocomposites using a facile method that involves a colloidal templating approach and sucrose as the carbon precursor.Material characterization showed amorphous TiO 2 at the atomic scale with 3D architecture at the macro scale.EDS shows uniform distribution of C, Ti and O elements.
The C/TiO 2 inverse opal electrodes exhibited high initial discharge and charge capacities of ∼870 mAh g −1 and 472 mAh g −1 , exceeding theoretical limits for TiO 2 and carbon.This enhanced performance could potentially be linked to defects formed during calcination, which provide additional charge compensation sites for lithium.The porous structure contributed to remarkable capacity retention and improved coulombic efficiency (99.6% after 250 cycles), outperforming the individual carbon and TiO 2 materials.Despite a 68% loss in capacity from the 2nd to 250th cycle at a high current density of 700 mA g −1 , C/TiO 2 maintained an average Coulombic efficiency of 87.3%, surpassing that of pure TiO 2 IO at ∼81%.Rate testing further revealed our C/TiO 2 IO material's specific capacities when compared to both TiO 2 and carbon IOs at various specific currents.Despite experiencing greater capacity loss than the individual counterparts, C/TiO 2 maintained stable CE at all currents.
Post-mortem analysis shows our C/TiO 2 IOs maintain a highquality inverse opal architecture after cycling, indicating minimal expansion (1% and 19%) after 250 cycles at 150 mA g −1 and 700 mA g −1 , respectively.The electrochemical and physical properties of C/TiO 2 IOs are attributed to the ordered interconnected macroporous structure that can help with electrolyte wetting, increased surface area, interconnected pores which accommodate for volume expansion and reduce Li + transport resistance.While capacitive effects from the composite are seen under voltammetric conditions at higher rates, slower scan rates and all galvanostatic measurements are primarily diffusion-limited and promote intercalation reactions.The data highlights some benefits of tailoring porous material and their compositions to improve capacity and ratebehavior.

Figure 1 .
Figure 1.(a)-(c) SEM images of C/TiO 2 inverse opals at various magnifications.(d) EDX mapping of key elements overlayed onto an SEM image.(e) Raman spectra of C/TiO 2 IO and carbon only IO, showing rutile TiO 2 and D and G bands for carbon.(f) XRD pattern depicting amorphous C/TiO 2 , peaks labelled * correspond to the stainless-steel substrate.

Figure 2 .
Figure 2. (a), (b) Bright and dark-field TEM images of C/TiO 2 IO material showing the interconnected structure and a local pore.(c) HRTEM image of C/TiO 2 material showing no distinct lattice fringes and (d) resulting SAED indicating dominant amorphous nature.(e) Dark field TEM of C/TiO 2 IO and resulting EDS mapping showing distribution of (f) titanium, (g) carbon, and (h) oxygen.(i) SEM image and corresponding EDS line scan (yellow line shows the line scan trace) showing atomic ratios of carbon (blue), oxygen (grey) and titanium (red).

Figure 3 .
Figure 3. (a) CV of C/TiO 2 IO for the first five scan at scan rate 0.05 mV s −1 .(b) CV of C/TiO 2 IO compared to carbon only at 0.1 mV s −1 .(c) CV of C/TiO 2 IO at various scan rates from 0.1-1000 mV s −1 , (d) is magnified (c) to show curves at 0.1 and 1 mV s −1 .(e) b-values for log (i) as a function of log (v) for C/TiO 2 IOs at key insertion voltages (f) calculated b-values for C/TiO 2 IO overlaid on the first cathodic scan at a scan rate of 0.1 mV s −1 .

6 .
(a) Rate capability test for C/TiO 2, pure TiO 2 and carbon inverse opals with various specific currents ranging from 70-540 mA g −1 .(b) Charge/ Discharge curves for the 5th cycle of C/TiO 2 IOs at each current density in the rate test.