Porous materials: The next frontier in energy technologies

Porous Materials: The next frontier in energy technologies

Eliyahu M. Farber, Nicola M. Seraphim, Kesha Tamakuwala, Andreas Stein, Maja Rücker, David Eisenberg*

BACKGROUND: Porous materials, with pores ranging from angstroms to centimeters, consist of two phases—void and matter. These phases allow the transfer of multiple energy vectors, such as mass, charge, heat, radiation, and pressure. The high-area interface between the phases allows for these energy vectors to meet and interconvert by various processes, ranging from desired catalytic conversions between light, heat, electricity, and chemical streams to undesired events, such as cracking, passivation, or quenching of excited states. Thanks to their energy transfer capabilities, porous materials are increasingly adopted in a broad range of energy applications, driving performance breakthroughs in solar, nuclear, electrochemical, thermal, and subsurface energy extraction and conversion.

ADVANCES: By considering energy conversion devices or fuel extraction techniques in terms of energy vectors being simultaneously transferred and interconverted in the solid and void phases of a porous material, it is possible to design better porous components for a variety of applications. Such a view highlights the constraints and reveals new opportunities for optimization, simulation, and cross-disciplinary fertilization. For instance, the simultaneous tuning of mass and charge transfer in porous electrodes where the total volumetric surface area has been maximized leads to higher power density in electrochemical devices, such as supercapacitors, fuel cells, batteries, and electrolyzers. All energy streams are constrained by the geometry (size, shape, and orientation) and spatial distribution (ordering, hierarchy, and directionality) of the pores. Thus, heat storage in pore-embedded phase change materials (such as paraffin in carbons) is boosted by tuning pore sizes and apertures—improving heat conductivity while retaining the active matter. In thermochemically reactive materials that store solar heat at high temperatures, the porous structure can be tuned across multiple length scales, enhancing the simultaneous absorption of light, distribution of heat, and evolution of the reaction front in time and space. Pores can also be used for selective blocking of energy streams: In thermoelectric generators, disconnected pores are introduced to disperse phonons but not electrons, reducing heat conductivity while maintaining the temperature difference and electronic conductivity needed for efficient thermoelectric energy conversion. Porous structures can evolve over time: Pores are formed inside nuclear fuel pellets by the action of evolved gases; by nanometric cracking of Battery particles; or in the soil during unconventional extraction of oil, gas, and geothermal heat from low-porosity rocks (such as hydraulic fracturing).

Porous materials are key components of most energy conversion and extraction technologies. With pores ranging from angstroms to centimeters, porous materials can conduct the transfer of mass, charge, heat, radiation, and pressure, enabling energy conversion across many length-, time-, and energy scales.

OUTLOOK: The ultimate goal in porosity design—a task-specific porous architecture for each application—calls for great advances in analysis, synthesis, and material characterization. Better mathematical and computational models are needed for studying energy transfer processes in porous materials. These, in turn, require the complete three-dimensional visualization of porous structures on all length-scales, using tomographic, spectroscopic, and diffraction techniques. These will guide synthetic advances, leading to fuller control of the distribution of pore sizes, shapes, and connectivity patterns in materials. By taking a broader view of porous materials, commonalities between porosity subfields must be recognized, leading to the exchange of synthetic strategies, analytical tools, and inspiration sources. For example, biomimetically inspired design strategies could tackle challenges such as the simultaneous control of the internal (e.g., hierarchical) porosity of a material and its external morphology (determining textural porosity and roughness) or the synthesis of precise pore architectures without wasteful sacrificial templates. Tomographic and computational methods used for understanding fluid flow in subsurface energy extraction should be embraced even more by researchers in the fields of catalysis or heat storage. Overall, a deeper understanding of energy streams will drive new generations of porous components for our expanding energy landscape. 

Porous materials with pore sizes spanning the range from molecular to macroscopic dimensions (from angstroms to centimeters) are essential in electrochemical, thermoelectric, nuclear, and solar power sources and in the extraction of oil, gas, and geothermal heat. To enable the clean, fast, and efficient conversion of energy, the porous structure must be designed to allow, modulate, or block the flow of energy transfer vectors.

The most important energy streams are mass, charge, heat, radiation, and pressure, and they must be optimized while packing the optimal surface area per device volume. In this Review, we analyze the physical processes that enable energy transfer in porous structures, highlighting recent advances in the design, characterization, modeling, and fundamental understanding of porosity that have enabled breakthroughs across the landscape of energy technologies.

A porous material is composed of two phases—matter and void—and their various interfaces (Fig. 1A). Each phase can transport different energy carriers (molecules, ions, electrons, phonons, or photons), and the large interfacial area allows packing many active sites in a given volume. Porosity—understood broadly to mean the state of being porous, although the term denotes the void fraction (ε)—thus governs energy conversion in devices (such as porous electrodes or light ab- sorbers) and media from which energy carriers are extracted (e.g., oil or hot fluid from porous rocks) (1). The connectivity of the void phase is defined by the pore diameters (d_pore) and their relative distances (d_inter), as depicted by the “connectivity diamond” (Fig. 1B). In some applications, open pores are needed to enhance mass transfer, whereas closed pores are preferred in others for blocking unwanted heat carriers. Different classes of porous structures can range from textural (formed naturally by the packing of solid particles) to designed struc- tures (Fig. 1C), differing in the pore periodicity, directionality, and size distribution (from angstroms to centimeters; Fig. 1D). In this Review, we analyze the fundamental energy transport processes (Fig. 1E) that drive the adoption of porous materials in most energy conversion and extraction technologies, from oil recovery to thermoelectric propul- sion, from solar fuels to nuclear power plants, and from batteries to fuel cells. Inspired to seek unity in variety and purpose in progress (2), we first discuss surfaces and interfaces in porous solids and then the transfer and storage of mass, charge, heat, radiation, and pressure. We conclude with brief comments on the future of porosity research in energy technologies.

Mass and pressure transfer in the porous subsurface

Mass transfer is perhaps the most defining property of porosity, even sharing its name: ποροσ in Greek means “passage,” so “transport” is “passage across” (in this work, we use the term “transfer”). Subsurface mass transfer occurs across many length-scales, from nanometric pores to kilometer-wide caves. The sedimentary rock in conventional reservoirs, such as in the Middle East or the North Sea, contains textural porosity (arising from the packing and transformations of soil and inorganic particles) permeated by alkane-rich hydrocarbons. The porosity ε of fuel-rich sandstones and carbonate rocks is 0.2 to 0.3 and the permeability k is 10⁻⁴ to 10⁻² darcy, whereas dense rock (such as clay, shale, or granite; ε < 0.04, k = 10⁻⁹ darcy) must be fractured to yield the fuel or the geothermal heat.

Fuel extraction from conventional reservoirs involves single- and multiphase flow of fluids, such as hydrocarbons and injected brine (Fig. 2A). The pore structure of the rock determines K, the hydraulic conductivity in the flow direction, as well as the fluid front stability (along with fluid viscosity μ and surface tension), which is crucial for efficient recovery (Fig. 2B). The flow in porous rock is described by Darcy’s law for steady, incompressible Newtonian fluids, q = − K/μ(dP/dx) , where q is the instantaneous flux (volume per cross-sectional area) and dP/dx the pressure gradient. The flow can be described numerically using the Brinkman extension for Darcy’s law, if average permeability is assigned to regions with smaller pores (3). This approach can also account for Knudsen diffusion, where fluid molecules collide with walls more often than with each other (d_pore < ~50 nm), which leads to reduced effective diffusivity and surface-dominated transport.

The pore structure determines both the overall permeability of the rock and the local, complex, and sudden dynamics of fluid pockets (ganglia). The fluxes of both oil and brine are determined by their relative permeabilities through the rock (k_ri = 0 to 1) and their relative volume fractions (saturations) through a phenomenological extension of Darcy's law, q = −k_ri K/μ_i(dP_i /dx −ρ_ig) , where ρ_i is fluid density and g is gravitational acceleration (4). Although this model assumes a stable flow pattern for each fluid, multiphase flow in porous rocks may also change rapidly because flow paths can break and reconnect through a complex interplay between viscous and capillary forces (5–7). The capillary pressure at pore throats (P_c) determines this complex flow, along with fluid properties (composition and saturation history) and rock conditions (pressure, temperature, and surface chemistry). This is described by the Young-Laplace equation, P_c = 4γcosθ/d_throat , where γ is the interfacial tension between the two fluids and θ is the local contact angle, expressing “wettability”—the local interplay between the surface energies of the three phases. The buildup of capillary pressure in pore throats causes sudden events, such as snap-off or coalescence of oil droplets (ganglions), piston-like filling of pores (8), or Haines jumps (9), a cascade of sudden pore-filling events upon pressure release (Fig. 2B) (10). The Young-Laplace equation also describes electrolyte wetting in the microporous electrodes of electrochemical power sources (11).

Recent advances in analytical techniques allow for the estimation of hydraulic conductivity from two-dimensional (2D) and 3D imaging of core sections, using electron microscopy, nano– and micro–computed tomography, magnetic resonance, and atomic force microscopy, and then analyzing the pore structure computationally using pore network models (12–14) (Fig. 2C). The 3D structure of fluids in pores can be analyzed geometrically using the four Minkowski functionals (15)— volume, surface area, mean curvature, and Gaussian curvature (reflecting local pore connectivity) (16, 17). Eventually, macroscopic flow observations can be related to fundamental principles in thermodynamics and statistical mechanics (18, 19).

The energy extracted from the subsurface can be enhanced at least fivefold (20) with enhanced (unconventional) extraction, where unconnected pores are accessed by hydraulic fracturing (“fracking”). The injection of high-pressure fluid props open fracture networks in the rock (21) (Fig. 2B), bridging nanometer-sized pores with meter-scale fractures, raising the porosity by orders of magnitude (ε = 0.1 to 0.4)

Fig. 1. Porous materials are central to energy technologies because both the void and solid phases conduct multiple energy transport processes. (A) A porous material is a two-phase composite of matter and void. The surface area (SA) can be normalized relative to the device or material volume (VSA), its specific mass (SSA), or its projected geometry (GSA). (B) The connectivity diamond: Pore diameters and distances determine the applications. Mass transfer is free in open and interconnected porosity, when 1 < d_inter/d_pore< √3 (in 3D; assuming identical, equally spaced pores). (C) Classes of porous materials. (D) Micrographs or simulations of pores found in energy technologies ranging from supercapacitors to subsurface energy (reproduced with permission from Springer-Nature, RSC, AAAS, Wiley, and ACS). Pore nomenclatures of the International Union of Pure and Applied Chemistry (IUPAC) (167) and geoscience (168) are used. (E) Fundamental transfer phenomena governing energy conversion and extraction in porous materials: Each phase can allow, modulate, or block the transfer of mass, charge, heat, radiation, and pressure.

Fig. 2. Energy extraction from porous subsurface reservoirs. (A) Extraction of oil, gas, or geothermal heat, with or without hydraulic fracturing of the rock. (B) Modes of mass transfer: Stable viscous flow of injected and extracted fluids (such as brine and oil or cold and hot water in geothermal extraction), in parallel with complex dynamics of fluid pockets (ganglions) inside the pores, including corner flow due to capillary forces, Haines jump leading to ganglion coalescence, or piston-like flooding. MT, mass transfer; PT, pressure transfer. (C) Focused ion beam–scanning electron microscopy (FIB-SEM) imaging and 3D reconstruction of a shale core, allowing for pore network analysis and permeability simulations (169). (D) Micro–computed tomography imaging of ganglion dynamics in multiphase flow (170). and increasing the effective drainage volume of the well. The optimal fracture network is hierarchical to hasten the fuel release (d_crack =10⁻⁶ to 10⁻³ m). Fracking is also useful for geothermal heat extraction, distributing the cold water in the hot underground rock (22).

The change in fluid pressure may induce local seismicity by trigger- ing instabilities in prestressed faults or activate aseismic slip, outpac- ing the fluid migration (Fig. 2B). To understand pressure transfer in porous media (23, 24), multiscale approaches join to describe multi- phase fluid flow, the geomechanics of propagating fractures (25), ther- mal conductivity (in geothermal heat), electrical conductivity (for soil diagnostics), and even biochemistry (for pore clogging by soil mi- crobes). Fluid pressure also causes pore deformation, coalescence, and cracking (26) in electrochemical (27) and thermal devices (28). Thus, models relating microscopic and heterogeneous features with the formation and propagations of large-scale transfer events are also promising for understanding electrochemical devices, such as fuel cells and electrolyzers, where pressure, heat, and charge transfer are combined with complex fluid flow and confinement dynamics (29, 30).

Surfaces and interfaces in electrochemical devices

Supercapacitors, or electrochemical double-layer capacitors, store electrical energy by electrostatic adsorption of ions at the electrode surface with a given area (A), delivering high power with high fidelity (>10⁶ cycles) at voltages (U) up to 4 V (31, 32). During operation, electrons (flowing through the solid) and oppositely charged ions (flowing through the pores) meet at the interface, converting their kinetic electrical energies to potential electrical energy (E), which scales with the cell capacitance (C_cell), E = 1/2C_cellU ². C_cell, in turn, depends on the capacitance of each porous electrode, derived from its surface area, Celec = ϵA ∕ d (where is the relative dielectric permittivity, A is the area of the interface, and d is the separation between charges). In typical electrodes, porous carbons are filled with aqueous, organic, or ionic liquid electrolytes (33). Micropores (<2 nm) contribute to high specific surface areas (up to 3000 m²/g) and 2- to 4-nm mesopores boost mass transfer in an electronically conductive and chemically tunable matrix (34). Ultramicropores (d_pore < 1 nm), formerly considered closed for ion adsorption, may boost the capacitance with similarly sized electrolyte ions (35, 36). This has sparked a debate about capacitance mechanisms, including on the meaning and measurement of surface area in a solid capable of intercalation between its layers (37). Thus, adjusting the pore size for optimal ion confinement while maximizing volumetric surface area can increase capacitance (Fig. 3B) (38). Such ion confinement also affects yield and selectivity in catalysis by prolonging the retention time of intermediates in catalyst pores. Similarly, the entropy loss arising from anion confinement in metal-organic frameworks (MOFs) boosts energy storage in a redox flow battery (39).

Supercapacitor electrodes can also store energy in the continuum between fast redox reactions and intercalation (“pseudocapacitance”) (40), boosting the energy density by 10- to 100-fold at the expense of power density (41). Although pseudocapacitance is possible in carbons by surface functionalization (42), it is most pronounced in metal oxides(43) and sulfides (43). In MXenes, layered transition metal carbides, or carbonitrides (44), porosity is tuned by foaming (45), varying interlayer spacing (46), or introducing in-plane pores (47). MOFs offer huge surface areas (up to 6000 to 8000 m²/g), precisely tunable pores by ligand tailoring, and rich surface reactivity (48), which leads to extraordinary volumetric capacitances (>700 F/cm³; Fig. 3C) (49). Yet in both MXenes and MOFs, the high surface area accelerates degradation, and the narrow pore throats limit mass transfer (50). High surface area may promote undesired reactivity in energy devices, such as corrosion, passivation, crack initiation, and energy dissipation, which stresses the need for finetuning surface area versus other energy transfer vectors.

Fig. 3. Electrochemical energy conversion by porous materials in supercapacitors, fuel cells, and Li-ion batteries. (A to C) Supercapacitors. (D to F) Fuel cells.

(G to I) Li-ion batteries. The operational principles point to the transport phenomena occurring in each application, including mass transfer (MT), charge transfer (CT), and heat transfer (HT). (B) Capacitance is increased by packing more surface area per volume and matching pore size to ion size for optimal confinement (38). (C) Tuning a 2D MOF allows packing more pores per volume, and the metal node provides pseudocapacitive energy storage (49). (E) A thickness-tuned MPL switches the O₂ flow mode from capillary fingering to viscous fingering (171). (F) X-ray tomography reveals preferential mass transfer channels in inhomogeneous gas transport layers (56). (H) Fast Li⁺ transfer through nanometric pores in a lithium titanate anode, coupled with fast solid-state transfer through the boundary-free single-crystalline matrix, preserves battery capacity even at high discharge rates (79). (J) Zn dendrites are prevented in inverse opal porous electrodes due to confined Zn deposition and a homogeneous electric field (81).

Mass transfer in fuel cells and electrolyzers

High power is a key objective in electrochemical power sources, such as fuel cells, electrolyzers, and batteries. This calls for optimizing the pore structure for fast mass transport of reactants and products to and from a high volumetric surface area while maintaining electronic and heat conduction through the solid and across the solid-solution interface. Most mass transfer occurs by bulk and Knudsen diffusion inside pores and cracks, driven by the concentration gradients caused by reactant consumption and product formation. Convection plays a role when pumping (e.g., redox flow batteries), and migration occurs in insulating solids (e.g., lithium-ion batteries).

In proton exchange membrane fuel cells, multisized pores distribute the flow of reactants and products. O₂ gas arriving at the cathode passes through porosity-graded layers (Fig. 3D) (51). The flow is dis- tributed by machined channels in a bipolar plate (width, 0.6 to 1 mm) into a gas diffusion layer (GDL), typically composed of fibrous carbon paper [d_pore, 10 to 50 μm (52)], and then to finer microporous layers (MPLs), whose textural porosity arises from the packing of carbon particles and polymeric binders (d_pore, 20 to 500 nm). When the O₂ reaches a catalyst layer (CL) of platinum nanoparticles on microporous carbon [d_pore, 1 to 50 nm (53)], it is reduced (O₂ + 4H⁺ + 4e⁻ → 2H₂O). Porosity is crucial for exposing the catalyst nanoparticles to reactants (54), protecting them from poisoning by the ionomer (55), and evacuating the produced water backward through the same sequence of layers (lest it condenses and blocks access to incoming O₂). Designed pores can help retain water at the CL-GDL interface, abating membrane dehydration. Natural drainage channels, such as textural porosity and random cracks, may be sufficient or detrimental, depending on operating conditions (Fig. 3E) (56). “Hierarchical” (size-graded) porosity can be introduced to different layers for managing water transport by electrospinning differently spaced fibers (57), deliberate cracking (58), laser grooving (59, 60), or other nanofabrication methods (61, 62). A thickness-tuned MPL can switch the oxygen flow pattern in a polymer electrolyte membrane water electrolyzer from capillary to viscous fingering, improving the electrolyte-electrode contact and exposing active sites (Fig. 3E).

For mass transport, the pores must be large enough for the diffusing species (O₂, H₂O, or ions), open to the external world, and interconnected; however, the introduction of porosity must minimize both the loss of volumetric surface area (VSA_∝1∕d²_pore) and the loss of bulk matter, which conducts charge, heat, and absorbing light(ε∝1∕d³_pore ).

These requirements define the “void triangle,” where mass transfer is possible (Fig. 4A). In electrochemical devices and in oil-rich rocks, the pore dimensions determine the balance between the surface tension and capillary forces wicking the water out (56) or breaking water into pores(11). Because the water pressure for entering a pore scales inversely with d_throat (per Young-Laplace above ), the layer hydrophobicity can be enhanced (and O₂ delivery improved) by engineering the pore curvature(11). Paradoxically, limiting mass transfer may enhance the yield of multistep electrochemical reactions—for example, O₂ (63) or CO₂ (64) reduction intermediates are retained in mesopores (30 to 50 nm) to react fully.

The porosity of electrodes that consume or produce gases, such as water electrolyzers (65), electrosynthetic reactors (66), or direct liquid fuel cells (67), must be tuned to balance the multiphase fluid transfer. High-temperature devices, such as phosphoric acid fuel cells, face specific challenges on shutoff, when condensation leads to pore blocking(68). Beyond pore size, fast gas diffusion in a porous electrode (D_eff) calls for minimal tortuosity (τ, ratio between the shortest possible pathway and the Euclidean distance between points), Deff = D ⋅ ε∕τ (where D is the species diffusivity). Tortuosity is estimated as τ = ε^−0.5 by the Bruggeman model for mass transport around randomly distributed spheres; yet, this is a poor approximation for fibrous and ionomer-embedded GDLs (69). The water distribution in electrodes is visualized and modeled on multiple length-scales by microscopic, spectroscopic, and tomographic techniques (65, 70), some of which borrowed directly from geoscience. X-ray tomographic microscopy of commercial MPL-GDL composites reveal the spatial distribution of heterogeneities, such as cracks, holes, and variations in thickness and density (Fig. 3F) (56), leading to preferential pathways for reactant flow (71). Visualization methods can be coupled with measurements of wetting angle distributions (70) or flow pathways (72) and analyzed computationally (73, 74), a strategy inspired by the geosciences.

Fig. 4. Mapping transfer processes in porous structures. (A) The void triangle: A map of mass transfer regimes and conditions. The diagonal limit is set by the size of the moving species (unsolvated ion, molecule, or photon; d_photon∼5/π λ ) relative to the pore diameter. The vertical limit marks the disappearance of matter. Mass transfer regimes include flow (by bulk diffusion, convection, or migration), Knudsen (surface) diffusion for pores smaller than the MFP, and confinement. These processes occur in most applications discussed in this Review, from geology to electro-, thermo-, and photochemistry. (B) The matter triangle: A map of solid-state heat, charge, radiation, and mass transfer regimes and conditions. The diagonal limit is set by the size of the moving species relative to interpore distance (d_neck), but it is less strict than in (A) because some species (e.g., photons, phonons, excitons, and electrons) can diffract around the pores. The vertical limit marks the disappearance of pores. In the nano-regime, the matter dimensions give rise to energy quantization. Both triangles assume a random distribution of spherical pores (connected and disconnected, respectively); the maps would look different under other assumptions.

Mass and charge transfer inside battery electrodes

In batteries, deployed from portable to grid energy storage, pores throughout the electrodes can be filled with electrolyte to facilitate ion transport across an enhanced electrode surface. Batteries have higher energy density than supercapacitors (because ions fill the solid volume too) but lower power density because of slower mass transfer (Fig. 3G) (75). Battery porosity is typically textural (ε = 0.3 to 0.4), depending on the sizes and shapes of the packed particles. Templating the pores allows tuning both the sizes of pores and their wall thickness: Thinner walls shorten ion diffusion lengths in the solid and improve high-rate capabilities (76). To achieve “extreme fast charging,” electrode particles are downsized to shorten intraparticle diffusion lengths of intercalating ions (e.g., Li⁺); yet, this increases the tortuosity, slowing diffusion through interparticle voids (77). Textural porosity can be tweaked to improve both electronic and ionic conductivity of lithium titanate—a safe alternative to graphite in Li-ion batteries—by nanometric sculpting of the particles (78), and a similar approach is taken in fuel cell electrodes. Alternatively, porous single crystals were designed to reduce energy loss at particle boundaries, providing thin walls for fast Li⁺ diffusion and a porous network (formed by removing ~5-nm octahedra) to speed electrolyte diffusion (Fig. 3H) (79). Electronic conductivity can also be enhanced by tuning the ligand structure of MOF electrodes (80).

Well-ordered porosity (e.g., in inverse opals and carbon frameworks) helps homogenize the electric field in metalair batteries, enhancing mass transfer and mitigating the growth of dendrites that short the device (Fig. 3I) (81). However, such high porosity lowers the volumetric surface area and promotes unwanted formation of electrode-blocking interphases. In contrast to such devices, where the porosity of the metal electrode changes during operation, metal sulfur batteries store the active sulfur inside the fixed and tunable pores of a carbon matrix. In this case, pore throats must be tuned to minimize leaching of lithiated polysulfide chains (Li_XS_y) (76, 82), to protect the sulfur from pulverization during cyclic volume changes (83) and to enable sufficient electrical conductivity to the carbon (84). Overall, d_pore determines the amount of stored active material (energy density), and d_throat determines the mass transfer rate (power density) as well as loading and leaching efficiency (which contribute to energy density). Active materials are also encapsulated in porous heat storage reactors, which calls for an exchange of matrix materials and porosity engineering methods between the fields.

The “matter triangle” (Fig. 4B), describing the limits and conditions for heat, charge, radiation, and mass transfer in the solid matrix, is a conceptual mirror of the void triangle (Fig. 4A), which shows mass and radiation transfer in the pores. As seen in batteries and thermochemical applications (see “Thermal heat storage” section), charge and heat carriers move more easily at larger interpore distances (d_neck) but at the expense of slower diffusion between the pores and the solid [t ∝ D ∕ d²_neck , or less if defects block diffusion channels (85)]. In both the matter and void triangles, the porous nature of the material is destroyed by an excess of matter or voids, respectively (the right vertical). All transfer processes become limited when carriers are larger than throats (d_neck or d_pore, respectively; the diagonal), although solid-state energy carriers, such as phonons and electrons, can diffract around pores. Below d_neck < 100 nm, quantum confinement in the solid creates a distinct nano-regime, somewhat mirroring intermediate confinement in supercapacitors (40), electrocatalysts (86), or subsurface oil (29). In this regime, higher strains created by nano-pores improve the miscibility of Li⁺ in battery materials (85) while enhancing resistance to cracking upon volume expansion (27).

Heat and charge transfer in thermoelectric generators

In thermoelectric generators, two dissimilar materials (e.g., a p-type and an n-type semiconductor) produce a voltage by the Seebeck effect when subjected to a temperature difference (Fig. 5A). The dimensionless figure of merit for thermoelectric conversion is ZT = S²Tσ/κ_phon,sol +κ_e−,sol +κ_MT,por +κ_cond,por +κ_RT,por ,where S is the Seebeck coefficient, σ is electrical conductivity, and κ is thermal conductivity caried in the solid (by phonons, κ_phon,sol, and electrons, κ_e−,sol) or in the pores (by convection, κ_MT,por, and conduction, κ_cond,por, by pore-filling fluids, or by radiation in the pores, κRT,por). This equation reveals a built-in contradiction of designing thermoelectric solids: Low thermal conductivity is needed for improving the heat gradient, whereas high electrical conductivity is required for increasing power; unfortunately, the same charge carrier (electrons) can conduct both heat and electricity (87).

Porosity emerges as a detour around this conundrum (88). Because heat-conducting electrons and phonons (lattice vibrations) differ in mean free path (MFP) (~1 to 10 and ~10 to 100 nm, respectively), pores can be tuned in size to scatter phonons while letting electrons through(89). Fine-tuning the pore fraction in Si nanowires lowered κ without compromising σ too much, overall boosting ZT (Fig. 5B) (90). The carrier depletion that porosity introduces can be modeled by x_por = x_bulk 1−ε/1+ε, where x is either κ or σ (91); this is also a useful first approximation for mass transport in electrochemical devices. More complex models, taking into account pore size, shape, orientation, and spatial distribution, predict a drop in phononic heat conductivity when ε > 0.75 (92). The heat transport in a porous matrix also depends on phonon size [κ_solid∝ MFP_phonon(1 −ε)] and on convection (κ_MT ∝1/dⁿ_pore) and conduction(κ_fluid∝d_pore/MFP_fluid)by any pore-trapped fluids. Thus, introducing closed pores (93) or pores smaller than the MFP of air (~70 nm), helps reduce κ.

Nanoporous thermoelectric materials, from Bi₂Te₃ alloys to lead chalcogenides, display lower κ and higher ZT values (94, 95) because smaller pores mean a shorter MFP_phonon and a sharper decline in κ(96). Pores oriented perpendicularly to the heat transport direction can block more phonons, as do interconnected pores (at the expense of stronger electrical isolation) (97). Periodic porosity blocks phonons while allowing the electrons to travel in a straight line (96). Although low-density MOFs are ideal for thermal insulation, their thermoelectric performance still lags behind (98). A Zr-based MOF with both tetrahedral and octahedral pores (0.8 and 1.1 nm, respectively) was used to host pyrrole monomers selectively in the larger pores, yielding, upon polymerization, a network of conductive polypyrrole wires through the material (Fig. 5C). This increased σ a million-fold while mostly retaining the low κ thanks to the porosity of the smaller voids (99).

Thermal heat storage

Latent heat storage uses phase change materials (PCMs) hosted in porous matrices (100), whereas thermochemistry converts heat by reversible endothermic reactions of porous or pore-encapsulated materials (101). The heat stored is Q = X ⋅ n ⋅ ΔH_r, where X is the reaction conversion (1 for phase change, less for thermochemistry), n is the number of moles, and ΔH_r is the molar reaction enthalpy.

PCMs are best suited for waste heat and concentrated solar storage, typically storing 20 to 500 kJ/kg at temperatures of 50° to 600°C (Fig. 5D) (102). To improve the heat conductivity through a packed bed reactor of thermally insulating PCM particles, the material (such as paraffin wax) can be stored inside porous aerogels (103), sponges (104), or microporous polymers (105). As in metal sulfur batteries, the infiltration of a PCM into the porous matrix requires open porosity, leading to leaching during operation (106). Alternatively, cosynthesis of nanoparticles (e.g., Sn or Pb) in a mesoporous carbon is achieved by pyrolysis, yielding well-dispersed and stably anchored PCMs and fast heat transfer across the large solid-solid interfacial area (107). The mesopores confine the volume expansion, decreasing mechanical stresses and interfering with their crystallization (lowering the melting temperature ). Such supercooling can tweak the operating temperature to the temperature of a home or a factory (108) at the expense of some latent heat (109). In the Pb/C system, suited for higher temperatures, the melting point could be tweaked by tuning the metal particle sizes, thus varying the metal surface: volume ratio and the metal-carbon interface area (Fig. 5E) (107). A porosity-within-porosity concept was implemented in solar walls, absorbing sunlight at daytime and releasing heat at night, where 10-mm carbon fibers were impregnated with 10-μm polymer-encapsulated paraffin wax (110). Heat and mass transfer were optimized numerically to minimize the day-to-night difference ΔT (Fig. 5F). Larger throat diameters (>100 nm) are desired for better heat conductivity, giving porous carbons an advantage over MOFs as thermochemical hosts. Both fields of PCMs and electrochemistry use carbons, offering better pore tuneability than brittle and hard inorganic oxides or carbonates. Moreover, pore-collapsing sintering of most thermochemical inorganic oxides begins in the 400° to 800°C range, whereas the micropores of a thermoset carbon only start shrinking around 800° to 1200°C (111).

Fig. 5. Thermal energy conversion by porous materials in thermoelectric generators, latent heat storage PCMs, and thermochemical reactors. (A to C) Thermoelectric generators. (D to F) Latent heat storage PCMs. (G to I) Thermochemical reactors. The operational principles point to the transport phenomena occurring in each application, including mass transfer (MT), charge transfer (CT), and heat transfer (HT). (B) High-temperature thermoelectricity in Si nanowires is enhanced by tuning porosity to lower thermal conductivity without degrading electrical conductivity (90). (C) A bicontinuous MOF enables ultralow thermal conductivity, and partial filling of pores with a conductive polypyrrole polymer enhances the electronic conductivity a million-fold (99). (E) Lead nanoparticles PCM form inside a mesoporous carbon without postsynthetic impregnation, and their melting point can be tweaked by varying the nanoparticle size (107). (F) Multilevel simulations of heat transfer inside a hierarchically porous solar wall are crucial for optimizing this passive house heating technology (110). (H) Cycling in the Mg(OH)₂/MgO couple can be enhanced and stabilized if the material is prepared as high–surface area flower-shaped particles (121). (I) Porosity designed by partial sintering of nanostructured materials increases and steadies the thermochemical reoxidation rates (123).

In thermochemical cycling, an inorganic material may store heat by partial decomposition to produce a gas (e.g., H₂O, CO₂, or O₂) and release the heat by reacting with the gas again (Fig. 5G). High energy densities (<0.9 MJ/kg) (112) are achieved at high operating temperatures (<1500°C) (102). The active material is either porous itself or encapsulated in a porous matrix (113) to enable fast mass transfer of reactive gases to a high surface area (114). Many thermochemical loops use abundant and naturally porous alkaline earth minerals (115). The cycle CaCO₃(s) ⇌ CaO(s)+CO₂(g) (ΔH° = 178 kJ/mol), where both calcination (energy storage ) and carbonation (energy release ) proceed best at high temperatures (700° to 900°C), is ideal for storing solar thermal radiation (116). Understanding the reaction fronts and pore dynamics in thermochemical materials is both important and challenging because all transfer processes are coupled (Fig. 4B) (117). Ca-based materials lose porosity rapidly during operation by pore sintering (118) or by particle attrition due to cyclic mechanical stresses (119). This leads to complex reaction fronts within the porous reactive media (116). Powders can be stabilized against attrition by shaping into porous forms (120), but typically up to 50% of the volumetric energy density is lost within 20 to 30 cycles (116). In both heat-driven and electrochemical applications, a desire for high reactive surface area must be balanced against chemo-mechanical degradation and tortuosity. Solutions such as hierarchical porosity of MgO flowers prevent mechanical stresses during the Mg(OH)₂(s) ⇌ MgO(s)+H₂O(g) cycle (ΔH° = 81 kJ/mol,400°C), thanks to expansion buffering by the interwall gaps, thinner MgO walls, and improved conductivity (Fig. 5H) (121).

Cobalt oxide thermochemistry uses O₂, obviating the need for separate gas storage: Co3O4(s) ⇌ 3CoO(s)+1∕2O2(g) (ΔH° = 196 kJ/mol), with high energy density (844 kJ/kg), fast reaction kinetics, and high conversion (122). Carefully designed porosity enhances reactivity and mass transfer (123) and can even stabilize against pore collapse (123). For example, cube-shaped Co₃O₄ particles undergo partial sintering, forming a stable porous structure that keeps breathing O₂, whereas commercial Co₃O₄ powder collapses (Fig. 5I). The porosity of cobalt oxides can be enhanced by doping (124) or by coating on a foam-shaped cordi- erite mineral, which operates for 100 cycles (125), whereas Co₃O₄ pellets crack within 10 cycles.

Radiation transfer in solar cells and reactors

Solar radiation can be harvested by photovoltaic panels or thermochemical converters. Conversion of photons to voltage or heat occurs in the solid phase, but porosity governs light harvesting and scattering (including diffraction, reflection, and refraction). Light harvesting in solar cells may be improved by reflectors or absorbers made of porous silicon, which enhance light scattering (126). Metamaterials based on pore arrays have been shown to confine photons, improving harvesting and scattering behavior. Periodically porous light-trapping layers, such as inverse opal TiO₂, reduce the group velocity of photons at stop band edges (127), suppressing electron-hole recombination and boosting light conversion efficiency compared with a disordered macroporous film (128). The control of radiation transfer by porous structures is also exploited in photoelectrocatalysis (129). Simulations show that the pore sizes (130) and total porosity (131) determine refractive indices as well as the light absorption peaks (value, intensity, and shape), creating a photonic crystal that can capture and guide light to the device (132).

In dye-sensitized solar cells, mesopores formed between packed TiO₂ nanocrystals in the electron transport layers allow the passage of electrolyte redox couples (133). In perovskite-based solar cells, porous transport layers host the perovskite crystals [affecting their size, crystallinity, and thus optical properties (134)], and their roughness improves contact to the perovskite layer, shortening the charge conduction pathways (135). Small pores improve the charge extraction from the perovskite layer by tightening the contact to the trans- port layers and can also scatter incoming light, lengthening its path in the material and boosting overall light harvesting efficiency (136). MOFs also serve as the electron- or hole-transport layer or are embedded in either. To address the pressing issue of stability, Pb²⁺ ions leaching from the perovskite layer were caught in thiol-lined pores of a Zr-MOF embedded in the electron transport layer (Fig. 6, B and C) (137), whereas pyridyl-lined pores in an In-MOF captured leaching Li⁺ (138). When the perovskite material is hosted in MOF pores, charge transfer through the scaffold is enhanced, and the growth of 

the perovskite crystals is moderated, boosting the cell efficiency of the solar cell (139). Alternatively, a MPL of Zn-MOF can store and release reactive salts gradually during perovskite growth, compensating for vacancy defects (140). The storage abilities of MOFs could be exploited for storing active materials in batteries (141) and heat storage devices (142).

Solar thermal converters use porous ceramics as receivers to store solar heat radiation in chemical bonds at high temperatures (>1000°C; Fig. 6D). For example, macroporous ceria (CeO₂) can be endothermically reduced at ~1600°C and then catalytically reoxidized by incoming H₂O or CO₂ at ~1100°C. Theory predicts a thermochemical solar-to-fuel efficiency of 35%, but experimental reactors rarely reach 10% (143). At these temperatures, radiation through the pores dominates heat trans- fer, improving at higher porosity (ε < 0.9) and boosting fuel yield at the expense of active material loading; the optimum for overall productivity is ε = 0.6 to 0.75 (143). High incident radiation requires large pores and high porosity to homogenize the temperature. Grading the pores by size (Fig. 6E) may enhance photon influx and reduce radiation loss at the back side (Fig. 6F) (144), although reactor design may prove porosity grading unnecessary (145) or even detrimental (146).

Fig. 6. Solar energy conversion by porous materials in perovskite photovoltaics, and solar thermochemical reactors. (A to C) Perovskite photovoltaics. (D to F) Solar thermochemical reactors. The operational principles point to the transport phenomena occurring in each application, including mass transfer (MT), charge transfer (CT), heat transfer (HT), and radiation transfer (RT). (B) The thiol-lined pores of a Zr-MOF embedded in the electron transfer layer can catch Pb²⁺ ions leaching from the perovskite layer (137), leading to (C) better Pb retention. (E) Optimal pore gradients were identified by experiment and simultaneous optimization of light penetration and heat and mass transfer, leading to (F) improved solar fuel production (143).

Approaches are being developed to understand the simultaneous transfer of radiation, heat, and mass at such high illumination intensities. Beyond treating a porous material as a lower-density nonporous one, the radiation transport in pores can be analyzed by geometrical optics, valid when pores are large enough relative to the photon wavelength, roughly πd_pore > 5λ (147). Although such models neglect scattering, they yield the effective transfer properties by semiempirical combinations of real porous geometries (from 3D tomographic imaging) with numerical simulations (by Monte Carlo or ray tracing methods) (148). The fullest, and computationally heaviest, descriptions of radiation transport come from pore scale models that solve the Maxwell equations explicitly. This approach captures the effects of light trapping in the regime when λ ~ d_pore (149). Such modeling methods can also help solve local hotspots in fuel cell electrodes caused by inhomogeneous reactivity or current distribution, which degrade the material and complicate device operation (150).

Radiation-induced porosity occurs in nuclear reactors, where incoming neutron irradiation produces gaseous nuclear fission products (Xe and Kr) in the nuclear fuel pellet (²³⁵UO₂) (151). To release these bubbles, lest they block heat removal and further neutron propagation, the pellet must have interconnected porosity. Thus, the choice of fuel composition and crystallinity, along with radiation intensity, determines the evolving porosity and, in turn, the radiation, heat, and mass transfer in the material (152). This situation is somewhat analogous to the spontaneous (and often undesired) porosity that forms upon metal deposition in batteries (153).

The future of porosity research in energy technologies

The ultimate goal in porosity research is to predict an optimal pore structure for each energy application. This calls for multiscale computational models (154) and mathematical tools (155) to describe and predict coupled energy transfer processes. New ideas for synthetic regulation of porosity, such as controlled twisting of packed polymer chains (156) or zeolite exfoliation (157), require multiscale characterization techniques, including extending computerized tomography (158) or nuclear magnetic resonance cryoporometry (159) to the nanoscale. Such cross-fertilization of imaging methods is already affecting thermal catalysis (160) and electrocatalysis (70) and could benefit from more biomimetic inspirations (161). Porous materials could be shared more between different applications—e.g., carbon electrocatalysts as PCM matrices or oxide photoelectrodes as thermochemical reactants. Other energy transfer processes can be considered, such as magnetocaloric cooling in oxide foams (162), piezoelectricity and triboelectricity in porous energy harvesters (163), or directional mass transfer in water-purifying membranes (164). Porous materials can find new energy applications, such as mechanical energy absorption in titanium bone implants with gradient porosity (165) or integrated circuits with reduced power consumption using porous low-dielectric polymers (166). Ultimately, when porous structures can be precisely designed, fully described, and modeled on all length- and timescales, their potential for energy devices will be truly realized.

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ACKNOWLEDGMENTS

We thank M. K. Mudunuru, S. Mondal, I. Salton, T. Burshtein, Y. Amouyal, Y. Edery, E. T. C. Vogt, and the members of the Structures of Strength Centre, NL, for advice and T. Hartman for graphic design. Funding: This work received funding from Israel Ministry of Energy grant 218-11-024, NWO Veni 19121, and NWO DEEP.NL.2019.006. Competing interests: The authors declare that they have no competing interests. License information: Copyright © 2025 the authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original US government works. https://www.science.org/about/science-licenses-journal-article-reuse