Ordered mesoporous metal oxides for electrochemical applications: correlation between structure, electrical properties and device performance

Ordered mesoporous metal oxides with a high specific surface area, tailored porosity and engineered interfaces are promising materials for electrochemical applications. In particular, the method of evaporation-induced self-assembly allows the formation of nanocrystalline films of controlled thickness on polar substrates. In general, mesoporous materials have the advantage of benefiting from a unique combination of structural, chemical and physical properties. This Perspective article addresses the structural characteristics and the electrical (charge-transport) properties of mesoporous metal oxides and how these aﬀect their application in energy storage, catalysis and gas sensing.


Introduction
With the introduction of surfactant-templating methods and the evaporation-induced self-assembly (EISA) process in the 1990s, interest in the preparation of ordered mesoporous materials in powder and thin film form has become widespread. [1][2][3][4][5][6] While initial efforts focused on siliceous materials, soft-templating methods, in general, lend themselves to the formation of mesostructured metal oxides with nanocrystalline walls. [7][8][9][10][11][12][13][14][15][16] The preparation usually relies on the solution-phase co-assembly of either sol-gel precursors or preformed (nanocrystal) building blocks with a surfactant or an amphiphilic polymer structuredirecting agent to achieve different pore symmetries, followed by some post-treatment. [13][14][15][16][17][18][19][20][21][22] Because of their unique structural and compositional diversity, mesoporous materials are currently drawing increasing attention for energy applications (batteries, catalysis, gas storage and sensing, etc.). [23][24][25][26][27] In principle, an open pore-solid architecture provides good accessibility of the material and its internal structure to the surrounding medium (note that gasses or liquids can readily penetrate into the porosity), thereby offering a large number of active surface sites. In addition, it enables effective transport of charge carriers due to short diffusion pathways, among others, and endows the material with mechanical flexibility. Most importantly, because of the small dimensions of the crystallites in the pore walls and the high interface density, defect chemistry and surface spacecharge effects strongly affect the device performance and provide the unique possibility of tailoring the materials properties. In this Perspective, we review and describe the interplay between structure and electrical transport properties of mesoporous metal oxides (mainly as thin films), with a particular focus on applications in electrochemical energy storage, catalysis and gas sensing. Challenges and future prospects are also discussed.

Evaporation-induced self-assembly
The principles of self-assembly for sol-gel-derived mesoporous materials have been described in considerable detail elsewhere and will not be further discussed here. [13][14][15][16][17][28][29][30][31][32] However, in the following, we briefly describe the EISA-based preparation of mesostructured thin films, which affords a high degree of control over the intrinsic (chemistry) and extrinsic (environment) processing parameters. In the past two decades, many important metal oxides, primarily with pores in the size range between 5 and 30 nm, and with different crystalline phases have been produced by EISA and related methods. However, crystallization of the wall structure with retention of the porosity is challenging. This is due, in part, to the lack of broad availability of suitable structure-directing agents.
In general, the processing scheme shown in Fig. 1 can be described as follows: a solution containing the structure-directing found to begin at 450 1C and the nanoscale porosity was retained up to about 700 1C. 11 In a related study, Fattakhova-Rohlfing et al. examined the Li-storage properties of KLE-and Pluronic P123templated mesostructured TiO 2 thin films, which allowed quantifying the fraction of crystalline and amorphous phases in the samples. 54 They showed that the Pluronic P123-derived films display a strong tendency for anatase formation already well below 450 1C (approx. 50% crystallinity at 400 1C) and that full crystallization at temperatures Z600 1C is accompanied by collapse of the pore network. This behavior is in stark contrast to that of the KLE-templated material, as schematically shown in Fig. 2. Brezesinski et al. also synthesized cubic mesoporous TiO 2 thin films by a conventional sol-gel route using KLE and TiCl 4 as polymer structure-directing agent and precursor, respectively, and by a particle-based route, with anatase nanocrystals serving as preformed building blocks. 19 The authors demonstrated that the nanocrystal films can withstand much higher temperatures (up to 900 1C) before losing nanoscale order. In addition, they showed much improved Li-storage properties, especially greater power density due to high levels of pseudocapacitive charge storage.
Hartmann et al. compared the photoelectrochemical water splitting properties of cubic mesoporous TiO 2 thin films produced using the same synthetic routes described by Brezesinski and coworkers. 20 Both materials differed significantly in the pore walls thickness, see scanning electron microscopy (SEM) images in Fig. 3, despite using the same polymer structure-directing agent in the preparation process. Interestingly, the sol-gel material showed a significantly higher efficiency, which the authors explained by insufficient electronic connectivity of the nanocrystal films. Overall, these results indicate that not only the pore accessibility and specific surface area but also the transport properties have a profound effect on the device performance. Fig. 1 Schematic illustration of the fabrication steps for ordered mesoporous thin films using an EISA process. (a) Solution consisting of structure-directing agent and inorganic precursors (shown for ZrCl 4 and YCl 3 ; chemical reactions with the solvent are omitted for clarity), (b) micelle formation, coassembly and condensation of the inorganic reagents, (c) inorganic-organic hybrid thin film formation upon solvent evaporation and (d) thermally-induced crystallization of the inorganic wall structure and combustion of the organic structure-directing agent. Fig. 2 The effect of annealing temperature on the pore structure of Pluronic-and KLE-templated TiO 2 thin films. Adapted from ref. 54 with permission.

Transport properties
As briefly discussed in the previous sections, mesoporous oxides are of interest for a broad range of electrochemical applications. For the functionality of such devices, efficient transport of electrical charge carriers (mobile defects of the ideal crystal structure) is required. As mesoporous materials are typically polycrystalline and made from individual crystallites connected in a 3-dimensional framework, as schematically shown in Fig. 4, they contain a high density of interfaces. Solid/solid (grain boundaries), solid/liquid and solid/gas interfaces may significantly alter the mobility of electronic and ionic charge carriers due to the formation of a space-charge region. In general, the electrical conductivity of a charge carrier is given by: where Z is the valence, e is the elementary charge, m is the mobility and n represents the charge-carrier density contributing to the transport. In the presence of an interface, both the chargecarrier density and mobility may differ from the respective bulk values, making detailed understanding of the effect of interfaces on the electrical transport properties indispensable. Apart from elemental doping, optimization of the electronic properties of mesoporous materials, and therefore of the electrochemical device performance, is feasible by tailoring the interface density, for example, by controlling the pore size, the wall thickness or the size of the crystallites (grains) in the wall structure.
In the following, we will give a short description of both the formation of a space-charge layer at interfaces and the characterization of electronic and ionic conductivity using electrochemical impedance spectroscopy (EIS). The influence of a space-charge layer on the electronic and ionic transport properties has been reported in detail for CeO 2 -and ZrO 2 -based ceramics when the crystallite size becomes comparable to its extension. The findings for these systems will be briefly summarized, followed by reports on the investigation of transport properties in mesoporous materials. Finally, we also discuss the protonic conductivity in nanoscale oxides.

Defect chemistry at interfaces
As indicated by eqn (1), the electrical conductivity of a material depends on the concentration and mobility of charge carriers. While the mobility is determined by the electronic and ionic structure of the crystal, the carrier concentration is related to the electrochemical potential of the corresponding defect A, which is given by the sum of the chemical potential and the electrical potential: 55m In the absence of an electrical field, the electrochemical potential is constant throughout the bulk. However, at an interface, the local symmetry is broken. This means the chemical potential (x = 0) differs from that in the bulk (x = N): To ensure constant electrochemical potential, the mobile charge carriers redistribute, resulting in charging of the interface and local variation of the electrical potential f(x), the so-called space-charge region, which compensates for the difference in chemical potential. The redistribution of charge carriers affects the carrier concentration at the interface, and therefore the corresponding electrical conductivity.
For an ideal interface, the change in charge-carrier concentration relative to the bulk concentration c N is given by (1-dimensional case): [56][57][58] zðxÞ ¼ cðxÞ where Df(x) = f(x) À f N is the potential relative to the bulk potential f N . The distribution of charge carriers can then be calculated by solving the Poisson-Boltzmann equation. 56 Depending on the mobile charge carriers present in the system, different profiles of the resulting charge-carrier distribution are obtained. The two most prominent cases are Gouy-Chapman and Mott-Schottky, 59 both of which are schematically shown in Fig. 5.
In the Gouy-Chapman case, two charge carriers of opposite sign are mobile and contribute to the surface charging. In the space-charge region, the carrier with the opposite sign to the surface charge accumulates at the interface, while the other is depleted. The width of the space-charge region is then given by the Debye length: 59   with e 0 and e N being the vacuum permittivity and permittivity of the material, respectively. If one of the charge carriers is immobile, that is, its concentration profile is independent of the distance to the boundary, redistribution of mobile charge carriers follows a Mott-Schottky profile. Compared with the Gouy-Chapman case, redistribution results in an extended space-charge region of effective width: 59 As the space-charge profile can only be calculated analytically for two charge carriers of opposite sign, for mixed cases or for low space-charge potentials, approximations are needed. Göbel et al. presented a numerical approach to calculate the concentration profile for these cases, allowing to obtain more precise analytical solutions of the Poisson-Boltzmann equation. 61,62 However, determination of the space-charge profile by solving the Poisson-Boltzmann equation does not account for interactions between the charge carriers, which can become important for high defect concentrations. In 2015, Mebane and De Souza presented a generalized space-charge model (Poisson-Cahn theory) to account for defect-defect interactions at high defect concentrations. 63,64 While in the dilute case, the results of the analytic model described above are well reproduced, the profile of the space charge is modified for higher defect concentration. At the positively charged interface, the oxygen-vacancy concentration increases significantly (segregation of oxygen vacancies at the interface). Interestingly, depletion of oxygen vacancies in the adjacent space-charge region is accompanied by an enrichment of carriers before the bulk value is reached.

Electronic and ionic conductivity
The effect of a space-charge layer on the electronic and ionic transport is reasonably well understood for polycrystalline CeO 2 -and ZrO 2 -based ceramics. In both material systems, grain boundaries exhibit a positively charged core, resulting in depletion of oxygen vacancies in the space-charge region, and therefore in a highly resistive grain boundary. The latter hinders the transport of oxygen ions. To investigate the influence of the internal interfaces on the total resistivity, EIS is the most prominent and commonly used tool, [65][66][67][68][69][70] as this method allows distinguishing to some extent between contributions of the grain and the grain boundary due to differences in the corresponding dielectric relaxation times. 66,68,71 In microcrystalline oxides, the total impedance is typically described using the brick-layer model (BLM), [71][72][73] where a transport path through the bulk, across and along the grain boundaries is considered. In oxides with highly resistive grain boundaries, such as yttria-stabilized zirconia (YSZ), the transport path parallel to the grain boundary can be neglected. 67,74 The resulting impedance spectra exhibit two semicircles, as shown in Fig. 6, and can be described with an equivalent circuit consisting of two resistance-capacitance elements connected in series, representing the transport along the grain and across the grain boundary. Analysis then allows determining the grain boundary thickness d gb : 75,76 where d g denotes the grain size and C gb and C bulk are the capacitance values from EIS for the grain boundary and bulk, respectively. Furthermore, the space-charge potential at the interface can be calculated according to: 74 A detailed analysis of the impedance of microcrystalline ZrO 2 (Mott-Schottky case) using the BLM confirms that the blocking behavior of grain boundaries is caused by the formation of a  space-charge region 74,79,80 and not solely by segregation effects, as previously assumed. 67,81,82 The influence of the space-charge region on the overall impedance becomes even more important when the grain size is comparable to the width of the space-charge region, 83,84 which is typically a few nanometers for oxide ceramics. Then, interface effects are more pronounced and may even dominate the impedance. 57,72 As shown in Fig. 6, the decrease in grain size results in merging of the semicircles representing the bulk and grain boundary transport processes, 56,77,85 making their separation difficult. Furthermore, the accumulated charge carriers may also contribute to the transport through the sample. This is typically observed for the Gouy-Chapman case, 59 but can also occur for the Mott-Schottky case at low doping concentration. 86 For large effects, the electrons result in an additional contribution to the conductivity along the grain boundaries: 26,59 where n 0 and n N denote the electron concentration at the interface and in the bulk, respectively. An overview of the conductivity/ resistivity contributions for different space-charge situations due to accumulation/depletion of charge carriers at the interface is given in ref. 59 and 61.
A prominent example, where transport along the grain boundary becomes important, is nanostructured CeO 2 . 59,85,87 Here, the space-charge region results in accumulation of electrons at the grain boundary (Fig. 7). While in microcrystalline samples the transport is mainly determined by oxygen ions, nanostructured CeO 2 reveals a dominant electronic conductivity. 59 As shown in Fig. 8, Tschöpe et al. were capable of describing the change from ionic to electronic transport with decreasing grain size using the space-charge model. 88,89 Furthermore, their numerical calculations revealed that, due to the space-charge layer and segregation effects at the interface, not only the apparent activation energy of the transport process depends on the grain size ( Fig. 8) but also the characteristic exponent of the p(O 2 )dependence of conductivity. [88][89][90] A decrease of the bulk ionic conductivity with decreasing grain size is found for nanocrystalline YSZ due to depletion of oxygen vacancies in the grain, caused by the increasing impact of the space-charge layer. 79 However, the analytical description of transport properties using the space-charge model is only valid as long as the grain size is four times larger than the Debye length, d g 4 4l D . 55,75,90 If the grain size is further reduced, the space-charge regions of opposite grain boundaries start to overlap (Fig. 7) and the concentration profiles according to eqn (4) are not valid anymore. In CeO 2 and ZrO 2 , this condition is typically fulfilled for grain sizes below approx. 20 nm. If the grain size is further reduced to d g { 4l D , the space charges completely extend throughout the grain, resulting in an almost constant carrier concentration. 91 For small space-charge potential, Maier derived a so-called nano-factor g to describe the resulting enhancement of conductivity: 55 Here, c*(d g ) is the concentration of accumulated charge carriers in the center of the grain, which is given by elliptical integrals depending on the grain size d g , the bulk concentration c bulk and the concentration at the interface c 0 . The influence of the space-charge region on the electrical properties is well reported for nanocrystalline oxides with a high grain-boundary density. In case of mesoporous oxides, not only the grain boundaries act as an interface but also the free surface. Although the same description holds as for grain boundaries, 55 the surface potential, and therefore the extension of the space-charge layer in the crystallites, is more sensitive to variations in the surrounding atmosphere (gas or liquid penetrating into the pores), thereby allowing to tailor the  electrical properties. However, because of their unique architecture, mesoporous thin films may show significant differences compared to nanocrystalline materials.
Hartmann et al. studied the electrical conductivity of mesoporous ceria-zirconia (Ce x Zr 1Àx O 2Àd ) solid solutions of different composition under varying oxygen partial pressure by means of EIS. 94 Because of the small crystallite size in the range between 4 and 12 nm, only one semicircle was observed experimentally, as discussed above. Consequently, only the total impedance could be determined. Fig. 9 shows the calculated conductivity values for the different materials. Especially for the pure CeO 2 sample, high conductivity was found. This result can be attributed to the electronic conductivity in the space-charge layer both at the surface and at the grain boundaries, as the obtained value is in good agreement with that expected from the model of Tschöpe et al. (Fig. 8). However, it is worth mentioning that the conductivity was calculated assuming dense films. This means the actual conductivity in the pore walls is expected to be even higher. Fig. 9 also shows a comparison of the p(O 2 )-dependence of electrical conductivity at 500 1C for mesoporous Ce 0.8 Zr 0.2 O 2 thin film and single crystals of comparable composition. The latter serve as a kind of reference without the influence of interfaces. Similar to the pure CeO 2 , mesoporous Ce 0.8 Zr 0.2 O 2 showed a significant increase in total conductivity (increased electronic conductivity). The p(O 2 )-dependence of conductivity further supports the assumption of dominant electronic transport, as the slope of À1/4 at high oxygen partial pressure is characteristic of electronic transport according to the standard defect chemical description (if the oxygen vacancy concentration can be assumed constant [extrinsic regime]). 85,95,96 For low oxygen partial pressure, standard defect chemistry predicts a À1/6dependence (intrinsic regime) when the concentration of electrons becomes comparable to the oxygen-vacancy concentration. 85,[95][96][97] The mesoporous thin film showed a maximum in conductivity and a decrease with further decreasing oxygen partial pressure, which can be attributed to a hopping maximum of the electronic transport in the Ce 3+ sublattice. Because the electronic conductivity in CeO 2 is determined by electron hopping from Ce 3+ to Ce 4+ sites, the hopping probability depends on the fraction of Ce 3+ and Ce 4+ ions in the lattice according to: 98,99 with a being the distance between the hopping sites, n 0 the attempt frequency, n Ce the number of cerium lattice sites and DH m the migration enthalpy of the hopping process. The product x Ce 3+(1 À x Ce 3+) takes into account that hopping can only occur from Ce 3+ to Ce 4+ . Hence, at high electron concentration, x Ce 3+ \ 0.5, the hopping probability decreases again due to the reduced number of available Ce 4+ species, leading to a decrease in electronic conductivity, as recently reported for Pr-doped CeO 2 single crystals, where the electrons hop in the Pr-sublattice. 99 The increase in electronic conductivity and the occurrence of a hopping maximum suggest high electron concentration, and therefore significantly higher reducibility of the mesoporous material compared to nanocrystalline (dense) material (due to the higher specific surface area). However, more interesting is the p(O 2 )-dependence of conductivity at lower temperatures. As shown in Fig. 9, the mesoporous Ce 0.8 Zr 0.2 O 2 thin film revealed a much stronger p(O 2 )-dependence, with a characteristic slope of À1/2 at 300 1C, while for both mesoporous Ce 0.6 Zr 0.4 O 2 and Ce 0.4 Zr 0.6 O 2 thin films, a p(O 2 )dependence with an exponent of approx. À1/3 was observed. The unusual p(O 2 )-dependence cannot be explained using the standard defect chemical model. Hartmann et al. proposed that oxygen vacancies with a relative charge lower than +2 are responsible for the behavior. Specifically, two scenarios have been discussed. First, formation of defect associates (due to high electron concentration) may either result in not completely , or defect associates formed by vacancies and Ce 3+ ions. 101,102 Second, O À instead of O 2À ions were suggested to exist at the surface to compensate the Ce 3+ ions. While the origin of the unusual p(O 2 )-dependence still remains largely unclear, the results show that the high surface area of mesoporous materials can significantly alter their electrical properties.

Protonic conductivity
In recent years, especially nanostructured materials are receiving much attention, as significant protonic conductivity may be observed under wet atmospheric conditions for oxides, such as YSZ, 103 [113][114][115] Note that their dense counterparts show no signs of protonic conductivity. The increase in conductivity under wet atmospheric conditions is shown in Fig. 10 for various materials.
In contrast to high-temperature proton conductors with a perovskite structure, 116,117 like Y-doped BaZrO 3 , where the protons are incorporated into the bulk of the material, the protonic conductivity in nanostructured oxide ceramics at low temperatures relies on the adsorption of water molecules at the surface and grain boundaries (interfaces). Because it is directly related to the nanostructure, this offers an additional degree of freedom to tailor the protonic conductivity of mesoporous oxides, rendering them interesting as water sensors, 118-121 as proton exchange membranes [122][123][124] or for applications in energy storage and conversion. 106,125 Although the high interface density is responsible for the increased protonic conductivity, at first glance, it is not obvious if the transport of protons occurs along grain boundaries or the (inner) surface. First studies on nanocrystalline YSZ revealed an increase in protonic conductivity with decreasing grain size, 105,114 suggesting that the transport does occur along the grain boundaries 126 (or at least is related to the grain-boundary density). However, it is now widely accepted that the increased conductivity arises from protons moving in chemisorbed and physisorbed water layers along the pores and surface of nanostructured oxides. 100,104,[127][128][129][130] The strong dependence of the protonic conductivity on relative humidity and temperature is related to the structure of the adsorbed water molecules, as summarized by Stub et al. 131 The structure of the water layer on TiO 2 is schematically shown in Fig. 11.
At high temperature and/or low relative humidity, an ''icelike'' layer is formed on the surface, consisting of chemisorbed and physisorbed molecules. In the former case, the oxide surface chemistry determines the amount of adsorbed water molecules and the type of protonic charge carriers. For instance, for an ideal ZrO 2 surface, hydroxyl groups are formed in the chemisorbed layer, which apparently are stable up to 600 1C. 100,131,133,134 Hydroxyl groups can also be formed due to the presence of surface defects, such as oxygen vacancies, where the water molecule fills the vacancy according to (Kröger-Vink notation): 110,117,135 At higher relative humidity, the number of physisorbed layers increases, resulting in transition from ''ice-like'' to ''liquid-like'' water layer on the surface. The increase in water layer thickness is also accompanied by a change in transport mechanism. While in the ''ice-like'' layer, the protonic charge carriers move via Grotthuss hopping, 131 vehicle-type transport of hydronium ions is found in the physisorbed layers due to the weaker bonding between the water molecules. 100,131,133 Stub et al. probed the protonic conductivity in porous TiO 2 with varying doping levels. 132 High-valent dopants, which are more acidic, are likely to attract electrons, thereby increasing the dissociation of water. This in turn increases the protonic charge-carrier concentration, and consequently also their mobility. Overall, donor-dopants improve the protonic conductivity, while the opposite effect is expected for acceptor-doped oxides. Hence, higher surface acidity results in increased protonic conductivity, as also reported for Cl-doped, mesoporous Al 2 O 3 , for example. 111 The profound effect of pore wall chemistry on the protonic conductivity has also been observed by Vichi et al., who investigated the protonic conductivity of mesoporous TiO 2 pretreated in solutions of different pH and by modifying the surface with phosphate anions. 137 Similar results have been reported by Marschall et al., who studied the influence of sulfonic acid functionalization on the protonic conductivity in mesoporous silica. 138 In 2013, Gregori et al. examined the proton transport in porous CeO 2 . They discussed about the influence of space-charge region on the proton transport at oxide surfaces. 107 Here, the   incorporation of water molecules into the space-charge region according to eqn (12) would result in an increase of hydroxide ions in the water layer at the surface, which may be responsible for the enhanced protonic conductivity at low temperature, too. The importance of space-charge effects has also been addressed by Stub et al. in 2018. 136 EIS measurements conducted on nanocrystalline YSZ revealed two transport processes, one representing the proton transport along the grains (intra-grain transport), the other was attributed to a resistive transport across the grain boundaries. The positive core of the grain boundary (space-charge region of positive electric potential) results in accumulation of hydroxide ions, as schematically shown in Fig. 12, hindering the movement of hydronium ions in the physisorbed water layer.
In porous materials, the adsorption of water not only depends on the surface chemistry but also is strongly determined by the structure. Capillary condensation into the nanoscale pores facilitates water uptake. 107,124,127,130 As discussed by Vichi et al. for mesoporous TiO 2 , the adsorption of water at the interface occurs in two steps. 137 First, water molecules are adsorbed depending on the surface chemistry of the material, while in the second step the pores are filled due to capillary condensation, independent of the surface properties. After filling of the pores with water, the protonic conductivity in mesoporous thin films can be maintained, even when changing the relative humidity. 139 However, complete pore filling can also negatively affect the protonic conductivity. Vichi et al. observed an increase in activation energy of the proton transport in completely filled pores, which they attributed to bridges formed between water molecules of opposite walls. 137 Comparable results were also obtained for mesoporous SiO 2 140-142 and Al 2 O 3 ; 111 the highest protonic conductivities were achieved with 4 and 12 nm pores, respectively. For smaller pore size, the movement of protonic carriers is hindered by geometrical restrictions. For cubic mesoporous YSZ thin films with a pore size of about 24 nm, even a gradual decrease in total conductivity with increasing relative humidity was observed above 200 1C, as shown in Fig. 13. 135 However, porous YSZ thin films may show a significant increase in the same temperature range (Fig. 13). 129 The decrease in total conductivity in case of the mesoporous films was attributed to the annihilation of oxygen vacancies at the surface according to eqn (12), which are the majority charge carriers in YSZ. A decrease in total conductivity under wet atmospheric conditions has also been reported for microcrystalline CeO 2 by Chueh et al. They attributed this result to changes in the space-charge potential of grain boundaries upon hydration. 143 Although the influence of pore size on the protonic conductivity in oxide materials is not yet fully understood, the results clearly demonstrate the considerable effect that the pore structure has in general. In contrast to nanocrystalline oxides with an ill-defined porosity, the regular pore network of ordered mesostructured materials seems beneficial to device applications, as the pore size and structure, as well as the wall thickness, can be tailored to some degree to optimize water uptake (adsorption), and therefore the protonic conductivity.

Electrochemical applications
As discussed above, mesoporous oxides are characterized by a high specific surface area combined with a unique pore structure and nanocrystalline walls. These properties make them interesting for a broad range of electrochemical applications, 14,144-146 for example, as active electrode material in batteries, for (photo-)electrocatalysis and oxygen storage or as gas sensor. It should be noted that the favorable properties are not only a result of the increased surface area. Instead, the major advantage is the  presence of a uniform and continuous pore network, allowing effective transport of electronic and ionic charge carriers and providing good accessibility of the material and its internal structure to the surrounding medium, as gasses or liquids can readily penetrate into the porosity. In the following, we discuss in some more detail the pros and cons of mesoporous metal oxides and which properties are beneficial to the functionality and performance of electrochemical devices.

Mesoporous metal oxides for batteries
The working principle of an insertion-or intercalation-type material for secondary battery applications relies on both the reversible storage of ions (Li + , Na + etc.) during electrochemical cycling and the efficient transport of charge-compensating electrons (Fig. 14). In recent years, mesoporous electrode materials have been shown to possess promising properties, allowing for superior energy storage and high power density, among others. 147 The mesoporous morphology ensures equal distribution of electrolyte in the (bulk) structure, minimizing the fraction of inactive material and allowing fast ion diffusion along the pore system. [147][148][149] Furthermore, the interconnection of nanoscale particles in the pore walls provides short diffusion lengths and efficient transport pathways for both the ions and electrons.
The positive effect of mesoporosity on the charge-storage properties has been proven for a variety of cathode and anode active materials, mainly for lithium-ion battery (LIB) applications, such as LiCoO 2 , 150  The mesoporous material delivered the largest specific discharge capacity and showed the best capacity retention, which was attributed to the unique pore-solid architecture with good connection among adjacent crystallites. 150 Brezesinski et al. came to the same conclusion from studying polymer-templated and nontemplated (nanocrystalline) TiO 2 thin films. 19 These results confirm the beneficial effect of nanoscale porosity on the electrochemical performance. An important parameter when characterizing battery materials is the amount of stored charge. In general, the total amount consists of three contributions, as summarized in Fig. 15, namely, the faradaic contribution from the insertion of ions into the bulk of the material, the faradaic contribution from charge-transfer processes at the solid/liquid interface (pseudocapacitive charge storage) and the nonfaradaic contribution due to formation of a Helmholtz double layer. 19,156,[159][160][161] Analysis of cyclic voltammetry (CV) data obtained at different sweep rates v allows distinguishing between diffusion-and nondiffusion-controlled charge storage. Because ion insertion into the bulk is a semi-infinite diffusion process, the current is proportional to v 1/2 . In contrast, for capacitive processes, the current depends linearly on the sweep rate. Hence, current as a function of sweep rate is given by: 162 where k 1 depends on the surface area A and the capacitance C of the electrode, while k 2 is given by the Randles-Ševčík equation: 163 with F being the Faraday constant, D the diffusion coefficient and n the number of electrons transferred in the redox reaction. Rearranging eqn (13) then allows separating between both contributions: Especially for nanocrystalline materials, capacitive charge storage becomes significant and plays an important role in the performance and for the kinetics. 19,156,159,[164][165][166] Analysis of CV data for mesoporous TiO 2 thin films showed that the capacitive contribution to charge storage is virtually independent of the sweep rate, while the bulk insertion significantly decreases with increasing sweep rate. 19 For mesoporous MoS 2 , Cook et al. found that 80% of the theoretical specific capacity is accessible within 20 s due to pseudocapacitive charge storage. 167 These results indicate that fast kinetics in mesoporous materials also originates from nondiffusion-controlled surface charge-storage processes. Significant pseudocapacitive charge storage has also been observed for mesoporous group V transition-metal oxides, including Nb 2 O 5 and Ta 2 O 5 , and for MoO 3 . 166,168 Direct comparison of crystalline and amorphous thin films showed that the pseudocapacitance achieved with the crystalline samples exceeds that   of the amorphous films by large. The increased pseudocapacitive contribution to charge storage was attributed to the lithium insertion into the interlayer gaps of the layered crystalline materials (referred to as intercalation pseudocapacitance). An aspect that is rarely being considered is that the amount of charge stored at the interface can be much larger than that stored in the bulk due to formation of the space-charge region. [169][170][171][172] This effect may even allow to store, e.g., lithium at the interface between two materials, for which such behavior is not possible in the individual phases. 173 For example, Yue et al. investigated the pseudocapacitive charge storage in mesoporous Nb-doped TiO 2 . 156 Because TiO 2 has a low electronic conductivity, doping with Nb, acting as a donor, can significantly improve the conductivity of the material. 174,175 Apart from the increase in electronic conductivity, the authors found that the pseudocapacitance is also increased up to doping levels of about 5 at%. Higher concentrations led to a decrease in pseudocapacitive charge storage. This behavior was explained by changes in the space-charge layer at the interface, as shown in Fig. 16. For TiO 2 in contact with a Li + -containing electrolyte, the space-charge region results in depletion of electrons at the interface and accumulation of lithium ions due to differences in electrical potential between the surface (interface) and the bulk. 170 For low doping concentration, the space-charge region of opposite sites overlaps, resulting in negligible potential differences, 176,177 and therefore in low surface charge storage. With increasing doping level, the space-charge region decreases. Hence, the potential differences increase and more ions can be stored at the interface, leading to increased pseudocapacitance. However, the width of the space-charge region continues to decrease with further increasing doping concentration. For that reason, the pseudocapacitive contribution to charge storage starts to decrease again at some point.
Although the extension of the space-charge region in oxides is typically less than a few nanometers, this example shows that, in mesoporous materials with crystallites of similar dimensions, the charge storage in the space-charge region can become significant and even dominate the overall behavior.
Another major advantage of mesoporous materials is their mechanical flexibility. The insertion/extraction of ions into/ from the electrode during electrochemical cycling is usually accompanied by volume changes, [178][179][180][181] often resulting in mechanical degradation (fracturing or even pulverization of the active material). [182][183][184][185][186][187][188] In mesoporous materials, such adverse effects can be mitigated, as mechanical strain is accommodated to some degree by pore flexing. 144,189,190 Liu et al. investigated the electrochemical properties and cycling stability of ordered mesoporous NiO produced by hard templating. 158 While NiO as anode in LIBs typically suffers from pulverization and accelerated capacity fading due to volume changes during the conversion reaction, among others, 191,192 the mesoporous material maintained a specific capacity of 680 mA h g À1 at 0.1C rate after 50 cycles. Lee et al. studied ordered mesoporous niobium nitride/N-doped carbon composite as an advanced anode material for application in K-ion batteries. 193 Structural characterization using in situ X-ray diffraction (XRD) showed that the high cycling stability (stable performance for 42000 cycles) is due, in part, to the negligible mechanical strain that the material experiences during cycling.
The mechanical flexibility also improved the lithium storage in mesoporous CeO 2 . Specifically, Brezesinski et al. probed the charge-storage behavior of polymer-templated and nontemplated thin films (Fig. 17). As expected, the authors observed a significant increase in pseudocapacitive charge storage in the    165 However, for slow sweep rates or long charging times, that is, if the lithium ions have enough time to diffuse into the lattice, the total amount of stored charge was also increased by a factor of about two compared to the nontemplated material. Using small-angle X-ray scattering (SAXS), they were able to show that the mesoporous CeO 2 thin films have tensile stress imposed by the substrate (note that templated sol-gel films usually undergo unidirectional volume contraction during heating). Upon ion insertion into the lattice, the porous structure expands normal to the substrate, relieving in-plane stress, which in turn facilitates charge storage. The structural stability of ordered mesoporous NiCo 2 O 4 during electrochemical cycling has been examined by Bhaway et al. 194 Using grazing-incidence SAXS (GISAXS) and XRD (GIXD), they were able to correlate structural changes of the anode material with the electrochemical performance. Electrodes with approx. 9 nm pores showed severe capacity fading caused by collapse of the nanostructure during the initial cycles. In contrast, for electrodes with larger pores, the nanostructure was retained, which agrees well with the improved cyclability.
Increased structural stability has also been observed by Krins et al. for mesoporous amorphous NbVO 5 thin films with a wormlike pore structure. 195 The authors found that their ability to accommodate the strain from lithium insertion increases with decreasing pore size from 100 to 15 nm, suggesting that the optimal size is closer to 10 nm.
Mesoporous nanocrystalline architectures offer an additional advantage in terms of ion uptake, as the particle size may have a strong impact on the thermodynamics. 196 For example, lithium insertion into bulk TiO 2 is accompanied by a phase transition from anatase TiO 2 to Li 0.55 TiO 2 . [197][198][199][200] With further insertion of lithium, a second phase transition occurs, resulting in the formation of a blocking LiTiO 2 layer at the particle surface. LiTiO 2 exhibits a low lithium-diffusion coefficient, and therefore prevents complete phase transformation (kinetic limitation). 198 However, as discussed by Wagemaker et al., increasing contribution of surface free energy to the total free enthalpy of the system alters the solubility limit of lithium in TiO 2 and can even suppress phase separation. 198,199 For particles r7 nm in diameter, both phase transitions are suppressed, allowing full lithiation to form LiTiO 2 , 198 which also helps explain the larger specific capacity of nanostructured TiO 2 compared with bulk material. [200][201][202] Similar behavior has been observed for a-Fe 2 O 3 (hematite). While larger particles undergo a phase transition from trigonal a-Fe 2 O 3 to cubic Li x Fe 2 O 3 at x E 0.05, in nanoparticles, this transition is suppressed and lithium can be inserted into the lattice up to x E 1. As the lithium uptake is reversible for a-Li x Fe 2 O 3 , nanoparticles exhibit much improved cyclability. 203,204 Note that increased lithium storage and good cycling stability have also been found for mesoporous hematite and other Fe-based oxide thin films. 205,206

Mesoporous metal oxides in catalysis
Because of their unique structural properties, mesoporous oxides represent a promising class of materials for a variety of catalytic applications, for example, as catalyst or support for CO and NO conversion reactions or for (photo-)catalytic hydrogen production and water splitting. While their high surface area provides a large number of catalytically active sites, the 3-dimensional pore structure ensures good accessibility of the bulk and enables efficient transport of reaction species to/from the material. However, the catalytic properties not only depend on the specific surface area but also the wall structure (grain size, crystallinity etc.).
Ceria-zirconia solid solutions are among the most prominent catalytic materials for CO and NO conversion due to the high redox activity of the Ce 3+ /Ce 4+ couple. 207 Furthermore, because of its smaller ionic radius, the incorporation of Zr 4+ ions into the lattice distorts the cubic fluorite structure, resulting in the formation of defects and higher reducibility. 97,208 Overall, ceria-zirconia solid solutions exhibit favorable catalytic properties as a result of their unique oxygen-storage capacity, despite the fact that Zr 4+ is redox inactive. 207,209 There are several reports on the investigation into catalytic properties of mesoporous Ce x Zr 1Àx O 2Àd . [210][211][212][213][214] For example, Petkovich et al. probed the catalytic activity of ordered macroporous versions of such materials, prepared using two different synthetic routes, for H 2 O splitting and H 2 production. 215 They found increased H 2 production rates compared to commercial CeO 2 powder, which was attributed to the increased specific surface area. However, the reaction rate was not directly related to the surface area, but instead to the composition and homogeneity of the crystallites. The highest rate was observed for materials with a Zr content between 10 and 20%. Furthermore, samples with compositional heterogeneity, that is, the presence of Ce-and Zr-rich phases, offered better performance than the respective homogeneous (single-phase) materials. Mamontov et al. also observed a correlation between heterogeneity and oxygenstorage capacity in nanocrystalline ceria-zirconia powders. 216 Ho et al. reported on mesoporous Pd/ceria-zirconia solid solutions with macrochannels, 217 showing superior activity for CO oxidation over reference samples without macrochannels. The improvement in performance was attributed to two main factors: first, alignment of macrochannels, enabling effective mass transport through the pore system, and second, increased Ce 3+ and oxygen-vacancy concentrations at the surface (preferred reaction sites). 218 In contrast to the report by Petkovich et al., crystal structure homogeneity was found to be advantageous, in agreement with other reports, 209,219 as oxygen vacancies are more readily formed in the cubic phase than in mixed-phase structures. 220 Cui et al. examined the influence of La and Pr doping on the catalytic properties of ceria-zirconia solid solutions. They came to the same conclusion that larger pores allow for more effective gas diffusion. They also observed that an increased fraction of Ce 3+ ions due to doping is beneficial to the catalytic activity and the oxygen-storage capacity. 221 Similar results were obtained for mesoporous CeO 2 -based catalysts used in methanol decomposition. 210,222 The strong correlation between oxygen-storage capacity and catalytic activity has been theoretically studied by Sayle  confirmed that the catalytic activity is strongly affected by its oxygen content, and therefore directly related to the oxygenstorage capacity. Furthermore, they found that the catalytic activity depends on the morphology of the material, such as wall diameter and particle size. In general, oxygen extraction from nanoparticles is more facile. This is in agreement with density-functional theory (DFT) calculations by Migani et al., predicting the least oxygen-vacancy formation energy for nanoscale CeO 2 . 224,225 In 2018, Hao et al. confirmed the considerable effect that the particle size has on the oxygen-storage capacity of CeO 2 . 226 The oxygen-storage capacity of 5 nm particles (approx. 260 mmol g À1 at 250 1C) was shown to be two times larger than that of 12 nm particles (Fig. 18). Using scanning tunneling microscopy (STEM) combined with electron energy loss spectroscopy (EELS), they observed an increase in Ce 3+ concentration at the surface of the nanoparticles or, in other words, the presence of a space-charge layer. The space-charge layer extends over the whole nanoparticles when their size is below 6 nm, resulting in a total Ce 3+ content of more than 50%. The increase of Ce 3+ at the surface is accompanied by an increase of the lattice parameter, leading to a lower formation energy for oxygen vacancies. This helps explain the increase in oxygen-storage capacity with decreasing particle size.
Apart from ceria-zirconia solid solutions, other oxides have also been considered for catalytic applications. Ren et al. studied the CO conversion on ordered mesoporous metal oxides, such as Co 3 O 4 , Cr 2 O 3 and Fe 2 O 3 , to name a few. 227 These materials exhibited increased CO conversion rates compared to their bulk counterparts, as shown in Fig. 19. The improvements were attributed not only to the increased specific surface area but also to the presence of a regular 3-dimensional pore structure, providing well-defined pathways for gas transport and equally accessible internal surfaces. Similar results were obtained by both Sun et al. and Tüysüz et al. for CO oxidation over ordered mesoporous Co 3 O 4 . 228,229 Furthermore, noble-metal nanoparticles as co-catalysts have been shown capable of strongly affecting the activity of oxides by facilitating the conversion reaction (for oxide-supported transition-metal catalysts). The reason is that metallic nanoclusters on the surface increase the oxygen-vacancy concentration and improve the charge transfer. 232,233 Both results in an enhancement of catalytic activity at the metal/oxide interface. 234,235 The beneficial effect of using metallic nanoclusters has been shown for a variety of mesoporous oxides. 210,217,236 However, the reaction rate also depends on the size (smaller particles are usually more active), shape and distribution of nanoparticles inside the mesoporous framework, as demonstrated, for example, by Kapoor et al. 210 Because the mesoporous support can be post-loaded, 236 this allows for presynthesis of tailored nanoparticles. Furthermore, the interaction with the oxide surface prevents the agglomeration of particles.
In addition to their application in conversion reactions, mesoporous metal oxides also gained great interest in the field of photo(electro-)catalysis for water splitting (hydrogen/oxygen production) or carbon dioxide reduction. The basic principle is based on the generation of an electron-hole pair in a semiconducting material under light irradiation, as shown in Fig. 20    Specifically, the valence band should be more positive than the potential for the O 2 /H 2 O redox reaction, while the conduction band has to be more negative than the potential of H + /H 2 . In photoelectrocatalysis, both reactions are separated by applying an electrical bias (Fig. 20). The catalyst is used as photoelectrode, where only one of the redox reactions occurs. An important aspect for efficient photo(electro-)catalysis is the separation of electron and hole to ensure that both carriers can diffuse to the active surface sites for the redox reactions to occur. High (crystal) quality of the absorber material is advantageous, as defects act as carrier traps, increasing the probability of recombination. Overall, there are many reports on mesoporous semiconducting oxides for photocatalytic applications, including TiO 2 , 20,238-240 Ta 246 Given that the water-splitting reaction takes place at the surface of the photocatalytic material, it is reasonable to assume that a high specific surface area leads to superior activity. Cherevan et al. analyzed around 200 publications regarding the photocatalytic activity of mesoporous semiconductors, aiming at correlating improved performance with surface area. 247 They found that increased specific surface area is not the only reason and may even impede any performance improvements, as a high surface area may also increase the probability of carrier recombination. For example, for Ta 2 O 5 , an increase of the specific surface area by a factor of approx. 100 (mesoporous vs. nonporous material) only resulted in a relatively small activity rise by a factor of 1.5. 248 Instead, the crystallinity, the pore size, the pore connectivity and the wall thickness can significantly affect the performance of the material.
Kirchberg et al. compared the photocurrent density of mesoporous ZnFe 2 O 4 photoanodes prepared using two different polymer templates and calcined at various temperatures. In fact, they observed that differences in pore morphology only have a minor influence on the photocurrent. Samples of high crystallinity showed better performance due to the relatively lower concentration of defects acting as recombination centers for the electron-hole pairs. 243 Increased photocatalytic activity because of improved crystallinity has also been reported for mesoporous Nb 2 O 5 , Mn 2 O 3 and NaTaO 3 . [249][250][251] Tüysüz et al. compared mesoporous nanocrystalline NaTaO 3 and amorphous NaTaO x photoanodes and observed a decrease in photocatalytic activity for the crystalline material. 252 Although the crystallinity should reduce the probability of carrier recombination, crystallization of the amorphous matrix resulted in an increase in particle size and a decrease in specific surface area. As discussed by the authors, smaller particles are considered beneficial to the photocatalytic activity. The reason is that the space-charge regions of opposite surfaces overlap, resulting in complete depletion of the particle and negligible band bending at the surface (flat-band condition), 176,177 as mentioned previously. Both photogenerated charge carriers can then easily diffuse to the active surface sites, leading to improved photocatalytic activity, as schematically shown in Fig. 21. For larger particles/crystallites, increasing  band bending impedes the diffusion of one kind of charge carrier to the surface, resulting in higher recombination rates in the bulk, and therefore in lower efficiency. The opposite holds true when the mesoporous material is used for photoelectrocatalytic applications, where the two redox reactions occur at different electrodes. In this case, the band bending in larger crystallites promotes charge separation, thus preventing undesirable recombination. For example, Hartmann et al. investigated the photoelectrocatalytic activity of mesoporous TiO 2 prepared from preformed nanoparticles and a classical sol-gel route. 20 They observed higher photocurrents and improved quantum efficiency for the sol-gel-derived thin films with thicker pore walls and larger crystallites. The results were explained, in part, by a reduced probability of electrons to react at the surface (Fig. 22). This can be directly related to the existing band bending, preventing the diffusion of electrons to the surface. Furthermore, the thicker wall structure gave rise to better connectivity between individual crystallites, allowing for more efficient transport of electrons in the pore-solid architecture and contributing to the higher efficiency. The positive effect that a 3-dimensional pore structure has on the photocatalytic performance (due to improved transport of electronic charge carriers) has also been discussed by Hossain et al. 253 and Zhou et al. 254 As in case of battery applications, the pore connectivity and pore size are critical parameters affecting the photocatalytic activity, as they determine the transport of reactants and products. For example, Weller et al. investigated the influence of pore size of mesoporous CsTaWO 6 (with Rh as co-catalyst) on the photocatalytic performance for H 2 evolution. 255 An optimized synthesis route allowed varying the pore size and mesoporous morphology without affecting the crystallinity of the material. Analysis of the photocatalytic activity revealed that the H 2 evolution rate strongly depends on the pore size and the pore size distribution. This result was explained by transport limitations, as the water/methanol mixture used as electrolyte was partly confined in the small pores due to capillary forces, blocking the release of gas bubbles. 256 Furthermore, comparison between samples with (large-pore) ordered and disordered mesoporous structures revealed higher H 2 evolution rates for the former material, despite having a lower specific surface area (Fig. 23). The increase in activity was rationalized by better accessibility of the bulk material and improved transport pathways in case of the regular pore structure. Similar results have been reported by Fang et al., for example, who were capable of achieving efficient mass transport by introducing additional macropores. 240 Another interesting aspect is that the regular arrangement of crystallites apparently affects the optical properties. For example, Hossain et al. 253 found that ordered mesoporous anatase TiO 2 with 5 nm thick walls exhibits a smaller band gap than individual 25 nm particles. The decrease in band-gap energy by about 0.2 eV was ascribed to the interconnectivity of nanoparticles, increasing their effective size. 253 Hufnagel et al. also observed a significant improvement in light-absorption properties (light-harvesting efficiency) for nanoscale ZnFe 2 O 4 grown on macroporous antimony-doped tin oxide films compared to nonstructured thin films. 244 This result was attributed to the presence of extended light paths caused by multiple light reflection and scattering in the porous electrode, as also reported by Fang et al. for hierarchically structured TiO 2 microspheres. 240 Taken together, the results indicate that a favorable structure for catalytic applications depends on the interplay between surface area, crystallinity, particle size (often determined by the wall thickness), pore size and pore size distribution. However, the individual parameters can significantly differ among different materials, making it necessary to vary them independently.  For mesoporous oxides, unfortunately, this is only feasible to some degree, as e.g., high crystallinity usually requires high-temperature treatment, which in turn results in grain growth and coarsening, and therefore in lowering of the active surface area.

Mesoporous metal oxides for gas sensors
Most gas sensors rely on the interaction of a specific gas with the surface of the sensing material. There are different kinds of sensing principles, all of which take advantage of changes in the materials properties under varying atmosphere. In capacitive gas sensors, the change of permittivity is measured, while optical gas sensors usually detect changes in photoluminescence, reflection or optical absorption. 119 Because oxides are often used as resistive sensors, we only focus on this type in the following. The basic working principle of most resistive gas sensors is schematically shown in Fig. 24. Gas/oxide interactions induce changes of the surface potential, e.g., due to chemisorption of gas molecules (receptor function). The change of the electronic surface structure then results in changes in conductivity, which are detected as the sensing signal (transducer function). In case of an n-type semiconductor, for example, the adsorption of oxygen species (O À ) typically gives rise to formation of an electron-depleted space-charge layer. In the presence of a gas, such as H 2 , O À species are consumed, resulting in a decrease of the space-charge width, and therefore in a decrease of resistance. [258][259][260] Hence, the working principle of a resistive gas sensor is directly related to the space-charge region at the interfaces (grain boundary or surface) of the oxide material. The largest sensitivity is achieved when the conductivity of the grains is completely determined by the space-charge region, that is, when the grain size is smaller than approx. twice the depletion layer. [261][262][263] The large influence of grain size on the resistance and sensitivity of granular SnO 2 sensors is depicted in Fig. 25. Both the sensitivity and response time depend strongly on the morphology and microstructure of the sensing material. To achieve high sensitivity, high surface area is desirable, while efficient and fast diffusion of gas molecules enables good response characteristics of the sensor to changes in the surrounding atmosphere. Consequently, mesoporous materials with tailorable pore and crystallite sizes are of great interest for sensor applications. 119 Similar to granular materials, the crystallite size strongly affects the sensitivity of mesoporous materials. For example, Aqeel et al. probed the NO 2 detection capabilities of mesoporous SnO 2 calcined at 400 and 500 1C. 264 They found that the material heated at 400 1C shows significantly better sensing properties, as the crystallite size (4-5 nm) was smaller than twice the depletion layer. The material heated at 500 1C had larger crystallites of approx. 8 nm in diameter, and therefore showed worse sensing performance. Conductivity measurements confirmed the complete depletion of electrons in the smaller crystallites, which exhibited a much larger resistance. In addition, the selectivity for NO 2 was much improved in case of the smaller crystallites. Xu et al. obtained similar findings for SnO 2 . 262,263 They noticed an increase in sensitivity and resistance with decreasing grain size (Fig. 25).
Waitz et al. examined the methane sensing properties of mesoporous In 2 O 3 as function of the pore size and wall thickness. 265 The sensitivity scaled linearly with the specific surface area. The authors also found that especially the wall   thickness has a strong effect on sensitivity, confirming that a fully depleted pore wall gives rise to superior performance. However, they pointed out that the structural parameters are coupled to one another, and thus cannot be varied independently, making it difficult to distinguish between the impact of each parameter on sensitivity. Ghom et al. tested mesoporous ceria-zirconia solid solutions as oxygen sensors at 600 1C. 266 In Ce x Zr 1Àx O 2Àd , the change in resistance is not caused by changes of the surface space-charge layer due to adsorbed oxygen species, but instead by the significant increase in conductivity because of the release of oxygen under reducing conditions, as described above. As discussed by the authors, the fast response time of such mesoporous sensors is directly related to the oxygen-storage capacity of the material. 209,219 Both the regular arrangement of pores and the pore size not only affect the sensitivity but are also responsible for fast diffusion of gas through the bulk of the material, the latter of which determines the sensor response time. 267 Li et al. investigated ordered mesoporous WO 3 for H 2 S sensing and observed a fast response of 2 s, with a recovery time of approx. 38 s, which they attributed to the unique (continuous) pore-solid architecture and the resulting fast gas diffusion. 269 The similar response time (1-3 s) of mesoporous a-Fe 2 O 3 for ethanol sensing was also ascribed to the high diffusivity through the pore network. 157 Li et al. synthesized mesoporous-macroporous SnO 2 . 268 Compared with conventional granular SnO 2 sensors, the hierarchical pore structure led to significant improvements in response and recovery times, as shown in Fig. 26, which was attributed to facilitated gas diffusion in the macropores. 268 While the sensitivity and response times are determined by structural properties, the selectivity of a sensor depends strongly on the material type and its surface properties. To control or even tailor the selectivity for various gases, the sensing material can be loaded with catalytically active noble-metal nanoparticles, such as Au, Pd or Pt. 260,270,271 As shown in Fig. 27, electrons move from the active oxide to the metal nanoparticles due to different work functions, leading to the formation of a Schottky barrier at the interface, and therefore to an increased electron depletion (electronic sensitization). However, the metal nanoparticles on the surface not only affect the adsorption and dissociation reactions by activating the gas molecules (chemical sensitization) 257,259 but also facilitate oxygen-vacancy formation. 232,233 Shimizu et al. studied the gas sensing properties of porous thick films of SnO 2 loaded with 1 wt% Pt or Pd. 260,270 While the sensitivity to H 2 and CH 4 at the surface was improved in the presence of noble metals, it deteriorated in the interior. This result was explained by reduced permeation into the bulk due to increased surface reactivity, emphasizing the necessity of optimizing the gas diffusion pathways.
Ma et al. reported on a positive effect of partially oxidized Pt nanoparticles on the sensitivity and selectivity of mesoporous WO 3 for CO sensing. 272 The improvements were attributed to the sensitizing effect of nanoparticles on the WO 3 framework. Using X-ray photoelectron spectroscopy (XPS), they found W 5+ states because of the formation of oxygen vacancies (note that they increase the adsorption of oxygen species at the surface). Furthermore, the good sensitivity was justified by changes in the depletion region at the Pt/WO 3 interface with varying atmosphere. After exposure to air, PtO nanoparticles were detected, leading to the formation of a depletion layer at the interface due to their p-type character. The PtO nanoparticles were reduced back to Pt(0) upon CO exposure, resulting in a vanishing depletion layer and pronounced changes in resistance with varying atmosphere. A positive impact of oxygen vacancies on the NO 2 sensing properties has also been reported for mesoporous WO 3 nanofibers 273 and CeO 2 /graphene heterostructures. 274

Surface modification
Although porous architectures are, without doubt, beneficial to various applications, there are certain constraints in using mesostructured powder and thin film materials. First, they tend to suffer from thermal stability issues. Especially for catalytic applications, elevated temperatures (or high relative humidity) are often required. However, such experimental conditions may result in changes of the pore structure due to phase transitions and/or growth of crystallites (sintering effects) or even complete collapse of the pore network. Second, while some variation in pore size (and wall thickness, pore symmetry etc.) can be achieved,  it is mainly determined by the template used. Nevertheless, small changes in pore size can significantly affect the performance of mesoporous materials, as discussed above. Hence, tailoring of structural features on the nanometer level and precise interfacial engineering are desirable. It has been shown that the properties of mesoporous materials can be altered by coating the surface using atomic layer deposition (ALD). ALD is a variant of the chemical vapor deposition (CVD) technique and is receiving increasing attention in recent years. [275][276][277][278] The reason is that ALD is the only method that is suited to produce uniform and conformal coatings on complex surfaces. This is achieved by sequential pulsing of gaseous reactants with intermediate purging steps. The pulses represent self-limiting gas-solid surface reactions, leading to controlled film growth [2-dimensional layer-by-layer (Frank-van der Merwe) growth] and excellent step coverage, unlike other deposition techniques.
The deposition of thin coatings using ALD finds lots of applications, among others, in protection and functionalization of surfaces or stabilization of porous materials. 279 For instance, in the battery field, ALD is typically used to modify electrode surfaces. [280][281][282][283][284] The coating acts as an artificial interphase between the electrode and the electrolyte to suppress adverse side reactions, which may result in gas evolution and/or formation of an ion-transport-blocking layer (anode/cathode solid-electrolyte interface). However, ALD also lends itself to the preparation of active electrode materials. 285,286 Apart from electrochemical energy-storage applications, ALD is actively used to improve the catalytic performance of materials by either depositing metal nanoparticles onto their top surface 287,288 or (partial) overcoating them with an oxide layer. 278,[289][290][291][292][293] The growth of single nanoparticles on carbon or oxide surfaces is usually achieved at comparably high deposition temperatures, where the precursor tends to agglomerate depending on the presence of surface defects and the atmospheric conditions instead of forming a conformal coating during the initial ALD cycles. [294][295][296] In case of partial overcoating, one takes advantage of differences in surface chemistry of the solid (area-selective deposition, also referred to as AS-ALD). 292,[297][298][299][300] In the following, we focus on some selected examples, where ALD has been used to produce a uniform oxide coating in order to modify the structural and/or electrical properties of mesoporous oxides.
Mesoporous oxides are metastable, that is, accelerated grain growth occurs at elevated temperatures, leading to collapse of the pore structure. The deposition of a thin coating using ALD may help to enhance the thermal stability of mesoporous materials. For example, Kraffert et al. synthesized mesoporous ferrihydrite, 301 showing a phase transition to hematite at 400 1C. By depositing silica onto the pore walls of the mesostructured thin films using a single ALD cycle, the stability of the ferrihydrite phase could be increased to 600 1C. Similar results were achieved for alumina-coated samples. In addition, the onset temperature for sintering, and therefore the thermal stability of the mesoporous thin films, was found to be significantly increased by ALD coating (up to 800 1C for silica). Differences in the stabilizing effect were attributed to different interaction strengths of the coating materials with the mesoporous substrate. Significant improvement in thermal stability of mesoporous Rh 2 O 3 thin films by ALD coating (by 4300 1C compared to uncoated material) has also been observed by Dubraja et al. 246 Pagán-Torres et al. reversed the strategy to stabilize mesoporous materials for applications under harsh conditions. They deposited catalytically active niobia onto the pore walls of mesoporous silica. 302 The hybrid material revealed improved hydrothermal stability, with catalytic activity superior to that of commercial niobia. 303 Optimizing the pore size to achieve a high active surface area while providing efficient mass transport through the material and/or efficient charge-transport pathways in the walls is crucial for many applications. Unfortunately, arbitrary variation of pore size on the nanometer level is experimentally not possible. However, ALD can be used to reduce the pore size of pre-synthesized materials in a systematic fashion. 304 Dendooven et al. investigated the decrease in pore size in mesoporous TiO 2 thin films with ink-bottle shaped pores upon deposition of HfO 2 using ALD. Achieving a conformal coating in such films is challenging, as there are only small channels within the walls that connect the mesopores and may lead to pore clogging during deposition. Using X-ray fluorescence (XRF) measurements, the authors confirmed that the inner surfaces are uniformly coated until the pore necks are closed, preventing further diffusion of molecular precursor into the architecture, as schematically shown in Fig. 28. Additional ALD cycles then only result in growth of a top (sealing) layer. 304   Dendooven et al. also reported on the implementation of ellipsometric porosimetry onto an ALD reactor, allowing to determine the pore size, the film thickness and the mechanical properties in situ during ALD. 307 In another work, the authors monitored the pore shrinkage by means of in situ GISAXS, also confirming uniform and conformal coating of the inner surfaces. 308 Note that for sub-nm control of the coating thickness, the process parameters must be tailored. 309 Too long exposure and/or insufficient purging result in precursor condensation (at the bottom of the pores) and pore plugging, whereas insufficient doses prevent full coverage of the inner surfaces. Especially for materials with a complex porosity, precursor diffusion limitations can lead to anisotropic ALD profiles, as reported for example by Pulinthanathu Sree et al. 310 Spatial control of deposition has been achieved using plasma-assisted ALD. Here, ALD precursors are employed that need to be activated through plasma irradiation. As shown by Jiang et al., this method allows sealing the pores of mesoporous materials at the immediate surface, as the plasma cannot penetrate into the inner structure. 311 These and other examples demonstrate that conformal surface coating of mesoporous materials can be achieved using ALD. [313][314][315][316] However, in order to tailor the surface properties to a certain application, it is necessary to control the crystallinity of the deposited material (note that the lattice structure determines the electrical or catalytic properties, among others). Mitchell et al. characterized ALD-derived TiO 2 thin films on silicon substrates. 317 They found that native-oxide-free silicon promotes the growth of crystalline TiO 2 islands. In contrast, an initially amorphous TiO 2 film is formed on silicon with an amorphous interfacial SiO x layer. Nevertheless, after exceeding a critical thickness, the amorphous TiO 2 crystallizes. Zscherp et al. also examined the nanostructure of an ALD oxide coating, namely, 9-20 nm ceria deposited onto porous YSZ thin films. 312 TEM investigations revealed epitaxial growth of ceria with a columnar structure and excellent conformality (Fig. 29). An amorphous-to-crystalline phase transition with increasing layer thickness has also been reported by Celik et al. 129 They coated porous YSZ thin films by ALD of TiO 2 . While the deposition of 6 nm TiO 2 resulted in the formation of amorphous material, a crystalline coating (anatase TiO 2 ) was found for a thickness of approx. 18 nm using the same deposition conditions (150 1C substrate temperature). Furthermore, the authors studied the influence of crystallinity on the surface protonic conductivity. The amorphous TiO 2 coating led to a lower protonic conductivity compared with bare YSZ thin films. However, it increased again for the sample with the crystalline surface shell (accompanied by a decrease in proton mobility at high relative humidity, as the reduced pore size resulted in complete filling with water).
Cop et al. further probed the electrical properties of mesoporous ZrO 2 thin films coated with ceria using different numbers of ALD cycles. 318 Characterization via ellipsometry confirmed the homogeneity of coating in the pores up to 100 ALD cycles, after which pore plugging occurred. XPS measurements revealed a large Ce 3+ fraction in the coating because of the space-charge layer at the surface, which decreased with increasing thickness, as shown in Fig. 30. In addition, the total conductivity of the composite thin films was found to be strongly affected by the coating and its thickness due to the non-stoichiometry of the ceria layer. High Ce 3+ concentration resulted in dominant electronic conductivity because of small polaron hopping of electrons between the Ce 3+ and Ce 4+ ions.
Collectively, these studies demonstrate the profound effect that the coating thickness has on the structural and electrical properties. Because the thickness can be controlled precisely, post ALD treatment allows for rational materials design.

Conclusions
Herein, developments in the field of ordered mesoporous metal oxides for electrochemical applications are reviewed. Advantages and disadvantages arising from the unique architecture, consisting of open r50 nm pores surrounded by interconnected crystallites, are discussed. In the last decades, much research has been carried out into assessing the potential of mesoporous metal oxides for energy applications, ranging from batteries and catalysis to sensors. The presence of an ordered 3-dimensional pore network is advantageous, as it offers a large number of active surface sites and facilitates the accessibility of the material and its internal structure to the surrounding medium. For instance, high-surface-area metal  View Article Online oxide electrodes may increase the charge-storage capacity of batteries due to pseudocapacitive redox reactions, while the porosity is capable of somewhat mediating the transport of reaction species in catalysis. It also endows the materials with a certain degree of mechanical flexibility, which helps accommodate volume changes during electrochemical cycling, among others. However, the favorable properties cannot only be attributed to the increased surface area and uniform pore size distribution, but also to the interconnectivity of crystallites in the wall structure, giving rise to short diffusion pathways for electron and ion transport. An important aspect affecting the properties of mesoporous metal oxides is the existence of a space-charge region at the surface, which has been shown to exert a profound effect on the charge transport. Resistive oxide sensors are based on this working principle. Considering the surface space-charge region is also critical when evaluating the performance of mesoporous battery electrodes, as it directly affects the interfacial charge storage. In case of catalytic applications, the space-charge potential facilitates the separation of photogenerated charge carriers. This is beneficial for photoelectrocatalytic devices, but counterproductive in photocatalysis, where both redox reactions occur at the surface of the catalyst. However, the structural features of mesoporous metal oxides come at a price. For instance, the high surface area may lead to severe corrosion and adverse side reactions with liquid electrolytes or reactive gases. Furthermore, the nanoscale porosity negatively affects the thermal stability of the material, which in turn limits the temperature range for operation, especially in catalysis. In general, there is a complex interplay between the structural parameters, which makes it difficult to vary them independently (note that this is one of the major drawbacks of mesoporous materials).
Finally, this review article also summarizes recent work on post-surface modification of mesoporous metal oxides using atomic layer deposition (ALD). Because ALD allows conformal coating of complex substrates, it represents a promising technique to tackle the above-mentioned problems. Recent results confirm that surface coating helps to improve the thermal and structural stability. The thickness of the deposited material can also be controlled on the atomic level, since the ALD process relies on self-limiting surface reactions. Hence, the pore size can be adjusted without altering other structural parameters. In addition, the surface potential/chemistry can be manipulated via interfacial engineering, thus directly affecting the space-charge region and offering the possibility to tailor the electrical and electrochemical properties of mesoporous metal oxides for future device applications.

Conflicts of interest
There are no conflicts to declare.