WO2020243428A1

WO2020243428A1 - Hierarchically porous open-cell foams

Info

Publication number: WO2020243428A1
Application number: PCT/US2020/035118
Authority: WO
Inventors: Wolfgang Ruettinger; Joseph T. MUTH; Benito ROMÁN-MANSO; Jennifer A. Lewis
Original assignee: President And Fellows Of Harvard College; Basf Corporation
Priority date: 2019-05-31
Filing date: 2020-05-29
Publication date: 2020-12-03

Abstract

Disclosed herein are sintered open-cell ceramic foams, wet foam compositions, methods of their manufacturing and methods of their use. The sintered open-cell ceramic foams disclosed herein are highly permeable and exhibit mechanical strength.

Description

HIERARCHICALLY POROUS OPEN-CELL FOAMS

RELATED APPLICATIONS

[0001] This application claims priority to United States Provisional Patent Application No. 62/855,408, filed on May 31, 2019, which is herein incorporated by reference in its entirety.

FIELD OF THE INVENTION

[0002] The present invention relates generally to hierarchically porous foam materials having an open-cell nature, a multi-component wet foam starting composition, methods of manufacturing thereof, and methods of use thereof

BACKGROUND OF THE INVENTION

[0003] Existing porous ceramic foams lack either mechanical strength or sufficient permeability to be useful in separation applications. It is advantageous to design porous ceramic foam materials whose properties (e.g., mechanical strength, permeability, porosity, relative density) could be tailored based on the target application.

OBJECTS AND SUMMARY OF THE INVENTION

[0004] It is an object of certain embodiments of the present invention to generate a wet foam composition for the production of porous ceramic foam materials with properties that may be tailored to an application of interest. Particular properties that may advantageously be tailored include, without limitations, mechanical strength, permeability, porosity, and relative density, to name a few.

[0005] The above objects and others may be achieved by the present invention, which in some embodiments is directed to ceramic foam materials having a hierarchically porous open- cell nature; a wet multi-component foam composition; methods of their manufacturing; and methods of their use.

[0006] Certain embodiments disclosed herein may be directed to hierarchically porous ceramic foam materials having an interconnected ceramic network with an open-cell nature. The porosity of the interconnected ceramic network may arise from a first pore population and a second pore population. The first pore population may be derived from bubbles introduced during a colloidal processing step. The second pore population may comprise smaller pores (i.e., pores with diameters smaller than the diameters of the bubbles) connecting adjacent bubbles-derived pores. The second pore population may be derived from the removal of a population of fugitive particles. In some embodiments, the first pore population (i.e., bubble- derived pores) may have an average diameter (Dbubbies) ranging from about 5 pm to about 200pm. In some embodiments, the second pore population (i.e., smaller pores connecting the adjacent bubble-derived pores) have an average diameter (D_pores) ranging from about lOnm to about 5000nm. In some embodiments, the ratio of D_bubbies to D_pores may range from about 2: 1 to about 20,000: 1.

[0007] Certain embodiments disclosed herein may be directed to a hierarchically porous ceramic foam material having an open-cell nature. The material may comprise a first pore population having an average diameter D_bubbies and a second pore population having an average diameter D_pores. Dbubbies may be in the micrometer scale and D_pores may be in the nanometer scale. In some embodiments, the hierarchically porous ceramic foam material may have a permeability (K) ranging from about 5xl0 ¹⁴ m² to about 5xl0 ¹² m². In some embodiments, the hierarchically porous ceramic foam material may have a total porosity ranging from about 60% to about 95% (relative density from about 40% to about 5%).

[0008] Certain embodiments disclosed herein may be directed to a hierarchically porous ceramic foam material having an interconnected ceramic network. The porosity of the interconnected ceramic network may arise from a first pore population and a second pore population. The first pore population may be derived from bubbles introduced during colloidal processing. The second pore populations may be smaller pores (i.e., pores with diameters smaller than the diameters of the bubbles) connecting bigger adjacent bubbles-derived pores. The second pore population may be derived from the removal of a population of fugitive materials. The second pore population may have an average diameter D_p0res. The ceramic network may comprise a plurality of ceramic particles. The plurality of ceramic particles may have an average diameter D_partides· The ratio of D_particies to D_pores may range from about 10: 1 to about 1 : 10.

[0009] Certain embodiments disclosed herein may be directed to hierarchically porous ceramic foam materials having an open-cell nature prepared by generating a wet foam having gas bubbles stabilized with a system of solid stabilizing particles positioned on the solvent-gas bubble interfaces. The system of solid stabilizing particles may comprise a first plurality of particles having a first average diameter and a second plurality of stabilizing particles having a second average diameter. The first plurality of stabilizing particles may be different from the second plurality of stabilizing particles. The ratio of the first average diameter to the second average diameter may range from about 10: 1 to about 1 : 10. The method for preparing the hierarchically porous ceramic foam materials having an open-cell nature may further comprise removing (optionally in-situ) either the first plurality of particles or the second plurality of particles to form a network of pores between adjacent gas bubbles. The gas bubbles-derived pores may have an average diameter Dtmbbies. The pores on the interface between adjacent gas bubbles-derived pores may have an average diameter D_p0res. D_pores may be smaller than Dbubbies.

[0010] Embodiments of the present disclosure may be directed to a wet multi-component porous foam. For instance, in certain embodiments, disclosed herein is a composition comprising a wet foam having gas bubbles stabilized with a system of solid stabilizing particles dispersed in a solvent. The system of solid stabilizing particles may comprise a first plurality of particles having a first average diameter, and a second plurality of particles having a second average diameter. The first plurality of particles may be different from the second plurality of particles. In some embodiments, both the first plurality of particles and the second plurality of particles may exhibit a similar hydrophobicity. In some embodiments, the ratio of the first average diameter to the second average diameter in the wet foam composition may range from about 10: 1 to about 1: 10. In some embodiments, at least a first portion of the first plurality of particles and at least a second portion of the second plurality of particles are positioned at the interfacial regions between the solvent and gas bubbles, thereby stabilizing the gas bubbles in the wet multi-component porous foam.

[0011] Embodiments of the present disclosure may be directed to a method for preparing a hierarchically-porous open-cell ceramic foam. The method may include generating a wet foam having gas bubbles stabilized with a system of solid stabilizing particles positioned on the interfaces of the solvent and the gas bubbles. The system of solid stabilizing particles may comprise a first plurality of particles and a second plurality of stabilizing particles. The first plurality of stabilizing particles may be different from the second plurality of stabilizing particles. The method for preparing the ceramic foam material may further comprise the removing either the first plurality of particles or the second plurality of particles to generate an interconnected network of pores, having an average diameter D_p0res· The method for preparing a hierarchically-porous open-cell ceramic foam may optionally further include sintering of the remaining particles, either the first plurality of particles or the second plurality of particles.

[0012] Embodiments of the present disclosure may be directed to a method for manufacturing a wet foam. The method may include combining gas bubbles and a system of stabilizing particles through colloidal processing to form the wet foam composition. The system of solid stabilizing particles may comprise a first plurality of particles having a first average diameter and a second plurality of stabilizing particles having a second average diameter. The first plurality of stabilizing particles may be different from the second plurality of stabilizing particles. The ratio of the first average diameter to the second average diameter may range from about 10: 1 to about 1 : 10.

[0013] Embodiments of the present disclosure may also be directed to a method for printing a three dimensional pattern by extruding the wet foams disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The above and other features of the present disclosure, their nature, and various advantages will become more apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings, in which:

[0015] FIG. 1A depicts a schematic of one entrained bubble in a binary wet foam where both populations of particles are similarly hydrophobized according to embodiments disclosed herein.

[0016] FIG. IB depicts a schematic of a resulting cell microstructure of a binary wet foam according to embodiments disclosed herein.

[0017] FIG. 1C depicts a micrograph showing the cross-section of a sintered extrudate formed from a dry foam composition according to embodiments disclosed herein.

[0018] FIG. ID depicts a micrograph of an alumina sintered foam illustrating its hierarchically porous open-cell nature.

[0019] FIG. 2A depicts a scanning electron microscope (SEM) micrograph image, at 100 pm scale, of a dried ternary alumina, titania, and carbon foam, prior to subjecting it to a burnout thermal treatment.

[0020] FIG. 2B depicts a SEM micrograph image, at 2 pm scale, of a dried ternary alumina, titania, and carbon foam, prior to subjecting it to a burnout thermal treatment. [0021] FIG. 2C depicts a SEM micrograph image, at 10 pm scale, of an aluminum titanate foam, after sintering.

[0022] FIG. 2D depicts a SEM micrograph image, at 2 pm scale, of an aluminum titanate foam, after sintering.

[0023] FIG. 3 depicts a mercury intrusion porosimetry plot showing the pore size distribution of an alumina open-cell foam extrudate.

[0024] FIG. 4A depicts a micrograph of a dried alumina foam generated with a 50% frothing intensity.

[0025] FIG. 4B depicts a micrograph of a dried alumina foam generated with a 70% frothing intensity.

[0026] FIG. 4C depicts a micrograph of a dried alumina foam generated with an 85% frothing intensity.

[0027] FIG. 4D depicts a micrograph of a dried alumina foam generated with a 100% frothing intensity.

[0028] FIG.4E depicts a plot showing the effect of frothing intensity on the average bubble diameter size and on the bubble volume fraction in an alumina foam.

[0029] FIG. 4F depicts a plot showing the effect of frothing intensity on the specific interfacial area of an alumina foam.

[0030] FIG. 4G illustrates plots depicting the storage moduli as a function of shear stress for alumina wet foams subjected to different frothing intensities.

[0031] FIG. 5A shows three representative stress-strain curves for sintered alumina foams with low, medium and high specific interfacial area, obtained from low, medium and high frothing intensities, respectively.

[0032] FIG. 5B shows the elastic module as a function of relative density for sintered alumina foams with decreasing specific interfacial values. [0033] FIG. 5C depicts the compressive strength (o_c) versus relative density (p_rei) log-log plot for the open-cell sintered alumina foams with decreasing specific interfacial area values

(å).

DEFINITIONS

[0034] As used herein, the singular forms "a," "an," and "the" include plural references unless the context clearly indicates otherwise. Thus, for example, reference to "a surfactant" includes a single surfactant as well as a mixture of two or more identical or different surfactants, and the like.

[0035] As used herein, the term“about” in connection with a measured quantity, refers to the normal variations in that measured quantity, as expected by one of ordinary skill in the art in making the measurement and exercising a level of care commensurate with the objective of measurement and the precision of the measuring equipment. In certain embodiments, the term “about” includes the recited number ±10%, such that“about 10” would include from 9 to 11.

[0036] As used herein,“wet foam” refers to an intermediate in a process for manufacturing a ceramic foam material before the intermediate has been dried (e.g., in air) or subjected to heat (e.g., in a furnace). The wet foam may have a paste-like texture. The wet foam may comprise about 1 wt% to about 80 wt%, about 5 wt% to about 60 wt%, or about 10 wt% to about 40 wt% solvent, based on total weight of the wet foam.

[0037] As used herein,“dry foam” refers to wet foam that has been dried (e.g., in air) before being subjected to heat (e.g., furnace). The dry foam may have a crumbly -like texture. The dry foam may comprise up to about 10 wt%, up to about 8 wt%, up to about 6 wt%, up to about 4 wt%, up to about 2 wt%, up to about 1 wt%, or substantially no water (i.e., about 0 wt%), based on total weight of the dry foam. [0038] As used herein,“sintered foam” refers to dry foam that has been heated (e.g., in a furnace).

[0039] As used herein,“ceramic foam material” encompasses a dry foam and a sintered foam.

[0040] As used herein, the language“wherein . . . one or more of [reciting a list], or mixtures thereof,” refers to an open group that includes any combination of the components recited in the list (i.e., a single component from the list, two components from the list, three components from the list and so on) as well as other components that are not explicitly recited in the list. For example,“wherein the composition comprises one or more of titania, silica, zirconia, or mixtures thereof,” refers to the composition comprising at least one of titania, silica, or zirconia or any combination of two or more of the components in the list (e.g., titania and silica, titania and zirconia, silica and zirconia, or titania and silica and zirconia). This phrase should be interpreted as an open group that may also include components that are not explicitly listed (e.g., alumina).

[0041] Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein.

[0042] All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g.,“such as”) provided herein, is intended merely to illuminate certain materials and methods and does not pose a limitation on scope. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the disclosed materials and methods. DETAILED DESCRIPTION

[0043] Existing porous ceramic foams lack either the mechanical strength or sufficient permeability to be useful in separation applications. Furthermore, the shaping of parts is restricted due to the production processes used. The ceramic foam materials disclosed herein exhibit an open-cell nature and can be shaped by additive manufacturing or standard extrusion methods, providing a great morphological versatility of the resulting foam. The pore structure provides high permeability with good mechanical strength.

[0044] Embodiments disclosed herein include a manufacturing method that utilizes colloidal processing to arrive at a hierarchically-porous ceramic foam material that may be generated with the incorporation of two different pore formers during the colloidal processing of the materials. One pore former may be gaseous (e.g. air) and may be incorporated as bubbles into a ceramic suspension, forming pores with an average diameter Dt_mbbies in the pm range. The other may be a system of solid particles -the nature of which could determine the removal procedure. The system of solid particles may be homogeneously distributed and may generate pores with average diameter D_pores in the nm range. The pores may be arranged to form a continuous network which may eventually enable gases and liquids to penetrate throughout the sintered ceramic foam with high permeability. The amount and size of pores can be tailored by the preparation procedure (gas incorporation protocol, surfactant concentration), and by the selection of the size and nature of pore formers (carbon, polymers, SiCh, etc.). After appropriately drying the foams, the sintering process preserves the pore structure generated during the processing step, giving rise to permeable interconnected ceramic networks with mechanical robustness.

[0045] Embodiments disclosed herein may be directed to a composition having a hierarchically porous open-cell nature (also may be referred to as“sintered foam material”). The phrase“hierarchically porous open-cell nature” refers to a continuous interconnected ceramic network having a plurality of pore populations of differing sizes, or in other words, having a hierarchy in pore sizes (e.g., a first pore population having its characteristic average diameter and a second pore population having its characteristic average diameter). For instance, the network may define a first pore population (e.g., derived from gas bubbles) having an average diameter De_bbies. The material may exhibit additional, smaller pores, thereby defining a second pore population (e.g., derived from the porogen removal) having an average diameter D_pores· The“hierarchically porous” portion of the phrase refers to the differing sizes between the plurality of pore populations (i.e., Dbubbies>D_p0res). The pores created by the gas bubbles form“cells” within the ceramic network, and the smaller pores in the ceramic network (i.e., in the cell walls) may be interconnected between adjacent cells, giving rise to the“open-cell nature” portion of the phrase.

[0046] The first pore population may have an average diameter Dbubbies that is in the micrometer scale. For instance, D_bubbies may range from lpm to about 50pm, from about 2pm to about 20pm, from about 5pm to about 200 pm, from about 10 pm to about 180 pm, or from about 25 pm to about 150 pm.

[0047] The second pore population may have an average diameter D_pores that is in the nanometer scale. For instant, D_pores may range from about 10 nm to about 5000 nm, from about 20 nm to about 4500 nm, or from about 30 nm to about 4000 nm.

[0048] The size of the second pore population may be lower than the size of the first pore population. In some embodiments, the ratio of the average diameter of the first pore population Dbubbies to the average diameter of the second pore population D_p0res ranges from about 2: 1 to about 20,000: 1, from about 5: 1 to about 10,000: 1, or from about 10: 1 to about 1,000: 1.

[0049] The interconnected network may be a ceramic network resulting from the sintering of a plurality of ceramic particles, also referred to as a sintered, open-cell foam. Exemplary suitable ceramic particles may include, without limitations, one or more of alumina, titania, silica, zirconia, cordierite, aluminum titanate, silicon carbide, mullite, silicon nitride, zirconium diboride, or mixtures thereof.

[0050] The plurality of ceramic particles may have an average diameter D_partides ranging from about lnm to about 5pm, from about 5nm to about 3pm, from about lOnm to about 1 pm, from about 20nm to about 500nm, or from about lOOnm to about 300nm. The ratio of the average diameter of the plurality of ceramic particles D_partides to the average diameter of the second pore population D_pores may range from about 10: 1 to about 1 : 10, from about 8: 1 to about 1 :8, or from about 5: 1 to about 1 :5. D_partides (and ratios referring thereto) refers to the particles after the interconnected ceramic network has been subjected to sintering (since, during sintering, the ceramic particles change in size).

[0051] The sintered foams disclosed herein may have a permeability (K) ranging from about 5xl0 ¹⁴ m² to about 5xl0 ¹² m², from about 7xl0 ¹⁴ m² to about 3xl0 ¹² m², or from about 9xl0 ¹⁴ m² to about lxlO ¹² m². Lower permeability values may correspond to sintered foams with lower porosity and higher permeability values may correspond to sintered foams with higher porosity. The total porosity of the sintered foams disclosed herein may range from about 95% to about 60%, from about 91% to about 75%, or from about 88% to about 80%.

[0052] Permeability (K) of the sintered ceramic foam material may be measured by passing air at flow rates of 0.5-1 L/min (evaluated using a Brooks mass flow controller) through the sintered ceramic foam material with an area of -960 mm² and thickness of 0.7-1.2 mm, and measuring the pressure drop that the sintered ceramic foam material causes in each case using pressure transducers. The permeability is determined by solving the Darcy’s law equation:

_ kA(p_b-pa)

^V mί,

where A is the geometric area the flow passes through, p the dynamic viscosity of air, p_b and p_a the pressure before and after the material, and L the thickness of the material. [0053] Density of the sintered ceramic foam material may be measured by a geometrical method in which the weight of a parallelepiped foam is divided by its volume, calculated by multiplying the length of its three axes. The relative density is estimated by normalizing the sintered ceramic foam material density to that of the same material in bulk (no porosity). The total porosity of the sintered ceramic foam material is calculated by subtracting the relative density of the sintered ceramic foam material from 100 (i.e., total porosity = 100 - relative density ).

[0054] The average diameter of the pore population derived from bubbles (De_bbies) may be measured on cross-sections of sintered ceramic foam materials by the linear intercept method for two-phase materials (ASTM El 12-13), where bubbles are defined as the dispersed phase and the CB-alumina dried green skeleton is defined as the continuous phase. At least 40 mm of lines are analyzed over 5 mm².

[0055] The average diameter of the pore population derived from the porogen removal (D_pores) may be measured on cross-sections of the sintered ceramic foam materials by image analysis on SEM micrographs.

[0056] The average diameter of the starting ceramic particles (D_ceramic) may be measured by a laser diffraction method after dispersing the particles in a liquid.

[0057] Embodiments disclosed herein may be directed to a method for preparing a wet foam composition, and/or the sintered ceramic foam material, which may include the drying of the solvent, the removal of at least one population of particles to generate pores, and the sintering of at least one population of particles. The method for manufacturing the foams may comprise the generation of a wet foam as described herein below in more detail.

[0058] The generation through colloidal processing of a wet foam having gas bubbles stabilized with a system of solid particles may be done by, for example, homogenously dispersing a system of solid stabilizing particles in a solvent to form a precursor mixture and incorporating gas bubbles into the precursor mixture via mechanical or chemical frothing. Any of the additional optional components mentioned below and/or elsewhere in this disclosure may also be homogeneously dispersed in the solvent along with the system of stabilizing particles when forming the precursor mixture.

[0059] The gas bubbles may be incorporated into the precursor mixture using frothing methods. The frothing step might either be mechanical (using an impeller or a gas nozzle) or chemical (e.g., with a blowing agent such as a peroxide), in gas (e.g., air) or a controlled environment. For example, an automated rotating impeller may be employed for frothing at a suitable rotation speed, such as from 100 rpm to 5,000 rpm, or from 1,000 rpm to 2,000 rpm. The frothing conditions may be controlled to obtain bubbles of a desired size as demonstrated in the examples.

[0060] The system of solid stabilizing particles constructing the wet foam disclosed herein comprises at least two different populations of particles (e.g., a first plurality of particles and a second plurality of particles). FIG. 1 A depicts an entrained bubble in a binary wet foam having two different populations of particles (110 and 120) in the interface between the bubble and the solvent. In some embodiments, the system of solid stabilizing particles may further comprise a third plurality of particles, a fourth plurality of particles, and so on (not shown in FIG. 1A). The various particle populations may be different and comprise distinct materials. For instance, the first plurality of particles may be different from the second plurality of particles. Similarly, if a third plurality of particles is present, it may be different from the first plurality of particles and from the second plurality of particles (for instance, the third plurality of particles may be also be an inorganic ceramic material such as alumina, titania, silica, zirconia, cordierite, aluminum titanate, silicon carbide, silicon nitride, zirconium diboride, other oxides, other carbides, other borides, or mixtures thereof, and the like). The disclosure may be further explained with respect to wet foam compositions comprising only two populations of particles (i.e., a binary wet foam composition), but it should be understood that similar embodiments may be applicable when more than two populations of particles constitute the system of solid stabilizing particles (e.g., ternary wet foam composition, quaternary wet foam composition and so on).

[0061] In the binary wet foam depicted in FIG. 1 A, the first plurality of particles (110) may comprise structural inorganic materials or organic materials that may be modified, as described in more detail below, to have a suitable interfacial energy (e.g., metals and/or ceramics and/or semiconductors and/or polymers). The second plurality of particles (120) may comprise fugitive materials (e.g., pore formers or porogens).

[0062] In one embodiment, the first plurality of particles (110) may comprise structural inorganic materials, such as metals and/or ceramics. Exemplary suitable structural inorganic materials may include, without limitations, one or more of alumina, titania, silica, zirconia, ceria, cordierite, aluminum titanate, silicon carbide, other oxides, other carbides, or mixtures thereof.

[0063] The term“fugitive materials”, as used herein, refers to a material that may be removed from the foam in a burnout process (e.g., by heating the foam to a high temperature and burning out the fugitive material), or in a leaching process (e.g., by treating the foam with an acid and leaching out the fugitive material), or any other removal process which is adequate according to the nature of the fugitive material. Exemplary suitable fugitive materials may include, without limitations, one or more of materials removable by a burnout process (e.g., carbon, polymers) or materials that are leachable with acid or base (e.g., silica, zinc oxide (ZnO), magnesium oxide (MgO), calcium oxide (CaO)).

[0064] The different populations of particles may be present in the wet foam in variable amounts and may be randomly positioned at an interface between the solvent and the gas bubbles, thereby stabilizing the bubbles in the suspension. This suspension may be referred to as a particle-stabilized wet foam. When two different populations of particles are randomly located at the interfaces stabilizing the gas bubbles, the suspension may be referred to as a “binary particle-stabilized wet foam” (e.g., FIG. IB). When three different populations of particles stabilize the wet foam, the suspension may be referred to as a“ternary particle- stabilized wet foam”.

[0065] In some embodiments, the stabilizing particles may be modified (if needed), as described in further detail below and depicted in FIG. 1A, to have an interfacial energy that would allow the stabilizing particles to exhibit a contact angle between each particle and the solvent of from about 15° to about 90°, or from about 20° to about 75°.

[0066] In some embodiments, certain properties of the different particle populations in the system of solid stabilizing particles may be adjusted to ensure that all particle populations are present in the interfacial region between the bubbles and the solvent. For instance, in certain embodiments, the surface of the particle populations (e.g., first plurality of particles, second plurality of particles, third plurality of particles, and so on) may be modified in order to provide particles with suitable hydrophobicity and suitable size as described in detail below.

[0067] Suitable size may be where all particle populations have similar sizes. For instance, if the first plurality of particles has a first average diameter and the second plurality of particles has a second average diameter, the ratio of the first average diameter to the second average diameter may range from about 10: 1 to about 1: 10, from about 8 : 1 to about 1 :8, from about 5 : 1 to about 1:5, from about 3: 1 to about 1:3, or from about 2: 1 to about 1 :2. It is important that all particle populations have a similar size so that all particle populations are present at the interface between the stabilized gas bubbles and the solvent.

[0068] The first diameter, second diameter (third diameter of a third population of particles, fourth diameter of a fourth population of particles and so on) may range from about lnm to about 5 pm, from about 5nm to about 3 pm, from about lOnm to about 1pm, from about 20 nm to about 500nm, or from about lOOnm to about 300 nm. The final application of the sintered foam will determine the starting size of solid stabilizing particles.

[0069] The size of the stabilizing particles may also scale with the size of stabilized gas bubbles. For instance, the average stabilizing particles’ diameter D_partides may be under about 50%, under about 20%, under about 10%, or under about 1%, of the average diameter of the air bubbles De_bbies.

[0070] The particle interfacial energy is related to the particle hydrophobicity of the particle populations. These properties may be tuned by: 1) varying the pH in aqueous suspensions, 2) including one or more surface modifiers (e.g., surfactant), 3) tailoring the interfacial energy of the particles via organic solvent optimization, or any suitable combination of l)-3). Thus, the method for manufacturing a wet foam may optionally include the step of achieving a similar hydrophobicity degree (or a similar interfacial energy or a similar contact angle) for both first plurality of particles and second plurality of particles through addition of a surfactant and/or adjustment of a pH of the precursor mixture and/or solvent optimization and/or average particle size of both particle populations.“Similar hydrophobicity degree”, as used herein, refers to an embodiment where both, the first plurality of particles and the second plurality of particles, may similarly be driven to the solvent-bubble interfaces because particles corresponding to both populations exhibit similar contact angles.“Similar size”, as used herein, refers to an embodiment where the average diameter of the first plurality of particles is within about 15%, within about 10%, or within about 5% of the average diameter of the second plurality of particles.“Similar interfacial energy”, as used herein, refers to an embodiment where the average interfacial energy of the first plurality of particles is within about 15%, within about 10%, or within about 5% of the average interfacial energy of the second plurality of particles.“Similar contact angle,” as used herein, refers to an embodiment where the average contact angle of the first plurality of particles with the solvent is within about 15%, within about 10%, or within about 5% of the average contact angle of the second plurality of particles with the solvent.

[0071] The term“within A%” as used herein refers to the value of the measured parameter ± A%. For instance“the average diameter of the first plurality of particles being within about 10% of the average diameter of the second plurality of particles”, for a scenario where the first average diameter is about 500 nm (i.e., ranges from 450 nm to 550 nm due to the term about), for the second average diameter to be within 10% of the first average diameter, it may range from about 450 nm to about 550 nm (i.e., from 405 nm to 605 nm due to the term about). We note that the term about with reference to“within 10%” also implies that the variation could range from within 9% to within 11%.

[0072] Suitable surfactants for adjusting the hydrophobicity and/or particles’ interfacial energy and/or particles’ contact angle with a solvent may comprise short chain organic molecules such as amines, ammonium salts, fatty acids, sulfonates, and salts thereof. The first three may be used for negatively charged particle populations. The latter two may be advantageous for positively charged particle populations. Exemplary amines may include, without limitations, methyl amino propylamine (MAPA), dimethyl amino propylamine (DAP A), or n-propyl amine. Exemplary fatty acids may include, without limitations, butyric acid, valeric acid, propionic acid, or enanthic acid. Exemplary sulfonates may include, without limitations, sodium salts of 1-butanesulfonate, 1-pentanesulfonate, or 1-heptanesulfonate.

[0073] The content of surfactant can be formulated as a function of the specific surface area of each particle in the plurality of particle populations and the length of the hydrophobic portion of the surfactant. Depending on the size, nature, or absolute surface charge of particles in the suspension, the surfactant concentration may range from about 0.1 pmol/m², about 0.5 pmol/m², about 1 pmol/m², or about 3 pmol/m² to about 10 pmol/m², about 12 pmol/m², about 15 pmol/m². or about 20 mihoΐ/ih². The stabilizing particles’ specific surface area may be determined using Brunauer-Emmett-Teller (BET) measurements.

[0074] For certain stabilizing particles, it might not be necessary to use surfactants, as the interfacial energy of particles can be tailored through solvent optimization. Exemplary solvents that may be used include, without limitations, aqueous and organic solvents such as water, ethanol, acetone, isopropanol, dimethylsulfoxide, n-methyl-2-pyrrolidone, or mixtures thereof. In certain embodiments, the solvent may be water.

[0075] The content of solid stabilizing particles in the wet foam may range from about 10 vol. % to about 50 vol. %, from about 15 vol. % to about 45 vol. %, from about 20 vol. % to about 40 vol. %, or from about 25 vol. % to about 35 vol. %. The portion of the stabilizing particles that are positioned at the interface between the solvent and the gas bubbles may be some fraction greater than 0% and less than 100%. For example, at least about 5%, at least about 10%, at least about 20%, or at least about 30% of the stabilizing particles may be positioned at these interfaces. In some cases, less than about 90%, less than about 80%, less than about 70%, or less than about 60% of the stabilizing particles may be positioned at these interfaces.

[0076] The volume content of stabilized bubbles in the wet foam and/or porosity derived from bubbles in the sintered foam may range from about 40 vol. % to about 80 vol. %. The average diameter of the gas bubbles D_bubbies in the wet foam and/or in the sintered foam may range from about lpm to about 50pm, from about 2mhi to about 20mhi. from about 5 pm to about 200pm, from about 10pm to about 180pm, or from about 25pm to about 150pm. The bubbles may be air bubbles, in one embodiment. In other embodiments, the bubbles may comprise another gas, such as N2, Ar, or He.

[0077] In addition to both populations of stabilizing particles, gas bubbles, surfactant and solvent, the wet foam may contain a humectant / drying retarder, such as starch, glycerol, or cellulose, to prevent premature drying of the wet foam during the shaping process. The wet foam may as well contain a binder to bestow strength to the shaped green body after it dries. The binder may comprise one or more of: oxides (alumina sol, zirconia sol, etc.) and/or polymer dispersions (polyvinyl alcohol (PVA), poly lysine, polyacrylamide, chitosan, acrylate, styrene- acrylate co-polymers, silicones, butadiene containing co-polymers, polyurethanes, polyethylene glycol (PEG), crosslinkers such as furan molecules or aldehydes, acid generator to trigger crosslinking, etc.). Binder concentrations in the wet foam composition may range from about 0.1 wt% to about 20 wt% or from about 1 wt% to about 5 wt% relative to the total solids content in the wet foam.

[0078] The method for manufacturing a sintered foam may further comprise removing either the first plurality of particles or the second plurality of particles (or the third plurality of particles or the fourth plurality of particles and so on) to generate an interconnected network of pores in the walls of the gas bubbles. The particle population that is removed may be the one that corresponds to the fugitive material as described hereinabove. For instance, if only the second plurality of particles comprises fugitive material, then the removal step will be implemented with respect to the second plurality of particles alone. Removing may comprise one or more of: a) heating the foam to bum off the fugitive material, and/or b) treating the foam with acid to leach off the fugitive material.

[0079] Embodiments disclosed herein may also be directed to the application of the wet foam discussed as inks for 3D printing to form hierarchically porous structures that may be used as electrodes for batteries or fuel cells, lightweight foams, filtration media, and/or separation media.

[0080] The ceramic foam materials disclosed herein may be suitable for a variety of applications since their properties (such as mechanical strength, specific surface area, and/or permeability) may be tailored by adjusting their manufacturing conditions (e.g., the type of stabilizing particles, the size of the stabilizing particles, the type of gas forming the gas bubbles, the intensity of the mechanical or chemical frothing, the drying time, the removal conditions for fugitive material, the sintering conditions, and the like). In certain embodiments, the sintered foams disclosed herein may exhibit an elastic modulus (E) ranging from about 10 MPa to about 500 MPa. In certain embodiments, the sintered foams disclosed herein may exhibit a compressive strength ranging from about 0.5 MPa to about 25 MPa.

[0081] In embodiments where the wet foams disclosed herein are used as inks for 3D printing, the ink may be loaded in syringe barrels and extruded through a single deposition nozzle connected to the barrel. In some embodiments, an array of deposition nozzles may be utilized for extruding the ink, either simultaneously in parallel and/or sequentially in series. Each nozzle may have the same or a different ink composition. The extruded filament may be deposited on a substrate in a predetermined pattern. The deposition may be carried out in a controlled environment saturated with a vapor of a solvent. For instance, a mist of the solvent may be continuously sprayed onto the nozzle during deposition.

[0082] After deposition, the pattern may be subjected to heat and/or acid treatment (e.g., for drying, fugitive particle bumout/leaching, sintering, and so on) to arrive at a hierarchically porous ceramic foam material exhibiting an open-cell nature in the predetermined pattern. The heat or acid treatment may occur under varying conditions (i.e., temperature, duration, acid type) depending on the desired final result. For instance, drying may occur over a long or a short period of time ranging from about one hour or less to about one week or more, at a temperature ranging from 10°C to about 50°C. Fugitive particle burnout may occur over a long or a short duration ranging from about an hour or less to about 1 week or more, at a temperature ranging from about 100°C to about 900°C, or from about 200°C to about 700°C. Sintering may occur over a long or a short duration ranging from about an hour or less to about 1 week or more, at a temperature ranging from about 800°C to about 2000°C (for inorganic materials) or at about 200°C to about 400°C (for organic materials).

[0083] To facilitate sequential or serial deposition, the deposition nozzles can be independently controlled in the z-direction. Each nozzle may present an inner diameter of from about 100 pm to about 1.2 mm in size, or from about 200 pm to about 600 pm. The size of the nozzle may be selected depending on the desired continuous filament diameter. Depending on the injection pressure and the nozzle translation speed, the filament may have a diameter ranging from about 50 pm to about 10 mm, or from about 200 pm to about 2 mm. The nozzle may be moved and the continuous filament may be deposited at print speeds as high as about 3 m/s (e.g., from about 1 cm/s to about 3 m/s, from about 1 mm/s to about 500 mm/s, from about 0.1 mm/s to about 100 mm/s, or from about 0.5 mm/s to about 10 mm/s). Alternatively, the wet foam can be extruded through a piston extruder equipped with a regulate extrusion die of any suitable shape.

[0084] The extrusion of the ink composition may take place under an applied or injection pressure of from about 1 psi to about 1000 psi, from about 10 psi to about 500 psi, or from about 20 psi to about 100 psi. The pressure during the extrusion may be constant or varied. A variable pressure may yield extrudates having a diameter that varies along the length of the filament. The extrusion may be carried out at controlled ambient or room temperature conditions.

[0085] During the extrusion and deposition of each continuous filament, the nozzle may be moved with respect to the substrate along a predetermined 2D or 3D pathway (e.g., from (Xi, Y i, Zi) to (X2, Y2, Z2)) with a positional accuracy typically within about ±200pm, within about ±100 pm, within about ±50 microns, within about ±10 pm, or within about ±1 pm. The described extrudates may be the forming units of a larger 3D printed bulk or porous structure containing the wet foams discussed herein. ILLUSTRATIVE EXAMPLES

[0086] The following examples are set forth to assist in understanding the invention and should not, of course, be construed as specifically limiting the invention described and claimed herein. Such variations of the invention, including the substitution of all equivalents now known or later developed, which would be within the purview of those skilled in the art, and changes in formulation or minor changes in experimental design, are to be considered to fall within the scope of the invention incorporated herein.

Example 1: Alumina and carbon-based wet foams generation, extrusion and sintering

[0087] A binary wet foam according to embodiments disclosed herein may be prepared based on alumina and carbon particles, as explained below. First, to achieve a well-dispersed colloidal suspension of a-alumina particles (AKP 30; Sumitomo Chemical; dso=300nm and BET surface area about 7.5 m²/g), an alumina stock suspension was homogenized by ball milling for 1 day with 5 mm diameter yttria-stabilized zirconia milling media. To create 1L of stock suspension, 1787 g of alumina were dispersed in 550 ml deionized (DI) water at pH> 12 (adjusted by adding sodium hydroxide, NaOH) to form a stock suspension. After the ball milling process, carbon-based spherical particles (CB; Thermax N990, Cancarb LTD; dso= 280nm and BET surface area about 9.4 m²/g) were added in a step-wise fashion to the stock suspension, which was mixed for 2 min at 2200 rpm in a planetary mixer (SpeedMixer DAC 600.2; FlackTek, Inc.) after each addition, thus creating a binary suspension and avoiding structural damage to the carbon particles during the milling process. CB particles were added until the alumina:CB volume ratio was 30:70. DI water was added to the suspension to reach 14 vol% solids loading. An amine surfactant (decylamine, 95%; Sigma-Aldrich) was added next, to partially hydrophobize the particles. All components were then homogenized in the planetary mixer. The specific concentration of the decylamine surfactant (obtained per unit of particle surface area) was 0.9 pmol/m². Finally, to form the binary colloidal gel, used as a precursor for the production of the wet foam, the pH was adjusted to a final value (within the 10-10.5 range). By way of example, Table 1 exemplifies illustrative amounts of each component in 60 ml of the described binary colloidal gel.

Table 1 - composition of a binary alumina and carbon wet foam

[0088] Five wet foams were obtained from five colloidal gels by mechanical frothing. 60 ml of each of the different colloidal gels were mechanically frothed in 240 ml glass jars to entrain air with a four-bladed impeller attached to an overhead mixer at 600, 900, 1300, 1500 and 1800 rpm for 300 seconds each, where each of these mixing levels encompass all of the lower intensity mixing levels.

[0089] These wet foams were used as inks for the production of extrudates through nozzles. To do so, the ink was loaded in syringe barrels and extruded through a single deposition nozzle connected to the barrel. An array of deposition nozzles could also be utilized, either simultaneously in parallel, or sequentially in series, or both. The nozzles could be independently controlled in the z-direction. The extruded wet foams were slowly dried and underwent a burnout process at 700 °C for 3 hours in an air atmosphere to remove carbon based fugitive particles. Then, the foams underwent sintering at 1500 °C for 2 hours. Micrographs depicting the cross-section of a sintered extrudate, at a 500pm scale and at a 20pm scale, are shown in FIG. 1C and FIG. ID, respectively.

Example 2: Ternary wet foam generation and sintering for the production of aluminum titanate porous materials

[0090] Similarly to example 1, a ternary colloidal gel was prepared based on alumina, titania and carbon particles, as explained below. Two well-dispersed stock suspensions were created for the ceramic particles: a-alumina (AKP 30; Sumitomo Chemical; dso= 300nm and BET surface area ~7.5 m²/g), and titania (T1O2, rutile phase, US-nano; dso= 300 nm and BET surface area— 16.5 m²/g). Both stock suspensions were homogenized by ball milling for 1 day with 5 mm diameter yttria-stabilized zirconia milling media. To create 1L of these stock suspensions, 1787 g of alumina were dispersed in 550 ml deionized (DI) water, and 1904 g of titania were also dispersed in 550 ml deionized (DI) water. Both stock suspensions were at a pH> 12 (adjusted by adding sodium hydroxide, NaOH).

[0091] After the ball milling process, the suspensions were mixed in a 1 : 1 molar proportion (i.e., the mass ratio of the alumina to the titania stocks was 56.42:43.58). Carbon-based spherical particles (CB; Thermax N990, Cancarb LTD; dso=280 nm and BET surface area ~9.4 m²/g) were added to the alumina and titania mixture in a step-wise fashion. The alumina, titania, and carbon mixture was mixed for 2 min at 2200 rpm in a planetary mixer (SpeedMixer DAC 600.2; FlackTek, Inc.) after each addition, thus creating a ternary suspension and avoiding structural damage to the carbon particles during the milling process. The CB particles were added until the ceramic (alumina+titania) to CB volume ratio was 30:70.

[0092] Subsequently, DI water was added to reach a 15 vol% loading. Additionally, an amine surfactant (decylamine, 95%; Sigma- Aldrich) was added to partially hydrophobize the three types of colloidal particles. The ceramic, carbon, and surfactant mixture was then homogenized in the planetary mixer. The specific concentration of the decylamine surfactant, obtained per unit of colloids surface area, was 0.9 pmol/m². Finally, to form the colloidal gels, which are used as precursors for the production of the wet foams, the pH was adjusted to a final value (within the 10-10.5 range). By way of example, Table 2 exemplifies illustrative amounts of each component in 60 ml of the described ternary colloidal gel.

Table 2 - composition of a ternary alumina, titania, and carbon wet foam

[0093] Five ternary wet foams were obtained from five colloidal gels by mechanical frothing, similarly to example 1. 60 ml of each of the different colloidal gels were mechanically frothed in 240 ml glass jars to entrain air with a four-bladed impeller attached to an overhead mixer at 600, 900, 1300, 1500 and 1800 rpm for 300 seconds each, where each of these mixing levels encompass all of the lower intensity mixing levels.

[0094] The ternary wet foams were then slowly dried. FIG. 2A depicts a SEM micrograph, at 100 pm scale, of the dried ternary foam of alumina, titania, and carbon particles. FIG. 2B depicts a SEM micrograph of the dried ternary foam of alumina, titania, and carbon particles. [0095] The dried alumina, titania, and carbon dried foam was then subj ected to two thermal treatments. The first one was performed for the carbon to bum out (also referred to as“porogen burnout step” or“fugitive particle burnout step”) by subjecting the dried foam to 700 °C for 3 hours in an air atmosphere. The second thermal treatment for sintering by subjecting the calcined foam to 1425 °C for 2 hours. The thermal treatment temperatures (for both heating and cooling) were reached at a rate of 2 °C/min. During the sintering step, alumina and titania particles reacted to form aluminum titanate grains. FIGs. 2C and 2D depict SEM micrographs, at a 10 pm and at a 2 pm scale, respectively, of the sintered foam, which was shown by x-ray diffraction analysis to have converted into aluminum titanate.

Example 3: pore structure determination

[0096] The pore structure of samples from example 1 was determined using mercury intrusion porosimetry. The porosity comprised approximately spherical (i.e., having a sphericalness value of about 0.8 or greater, about 0.9 or greater, or about 1) voids derived from the gas bubbles, and smaller pores in the ceramic structure derived from the fugitive material removal. The plurality of pore populations (gas bubbles and the smaller pores) created an interconnected network of pores.

[0097] Samples were analyzed using a Micromeritics AutoPore series mercury porosimeter. The samples were heat treated at 350°C for 1 hour before analysis to remove any volatile material. Samples were analyzed using a fixed pressure table (from 1.5 psi to 60,000 psi) and equilibration for 10 seconds at each of those pressures. Samples were run using an advancing and receding contact angle of 140° and the surface tension of mercury set at 480 dynes/cm (0.48 N/m). A blank analysis run was subtracted from the data. Data was calculated using the Washburn equation: D = - - - , where D = diameter, P = pressure, g = surface tension of mercury, q = contact angle.

[0098] FIG. 3 depicts a mercury intrusion porosimetry plot showing the pore size distribution of an alumina open-cell foam extrudate.

Example 4: Impact of frothing intensity on the bubble size and elasticity of wet foams

[0099] Properties of the sintered foams may be controlled through the processing conditions of the wet foams, as well as through the sintering process. This example explored the impact of frothing intensity on the bubble microstructure of the wet foam. The frothing intensity was modified by adjusting the mechanical energy that was introduced into the system with the rotational impeller. The mixing energy was adjusted by varying the frothing speed and frothing time of the rotational impeller.

[00100] In the below description, the maximum frothing speed was set as 1800 rpm and will be referred to herein as 100%. All other test frothing speeds were normalized based on this maximum speed. Therefore, a frothing speed of 900 rpm will be denoted as 50%, a frothing speed of 1300 rpm will be denoted as 70%, a frothing speed of 1500 rpm will be denoted as 85%. Each frothing speed encompasses all lower frothing speeds as summarized in Table 3 below (e.g., a frothing speed of 1500 rpm would encompass a frothing speed of 1300 rpm and 900 rpm but not 1800 rpm).

Table 3 - frothing protocol (frothing speed and time) for the production of binary wet foams

[00101] A reference composition (surfactant concentration = 0.9 pmol/m², pH = 10.25, J C = 0.14) was used to assess the impact of the frothing intensity (based on the frothing protocols summarized in Table 3 above) on the structure and elasticity of this representative wet foam. The alumina to carbon volume ratio in the wet foam compositions that were tested was kept constant at 30:70. A sequential increase in the frothing speed from 50% to 100% performed in the precursor gel illustrated a gradual refinement of the bubble microstructure of the as- generated foam, as shown in FIGs. 4A, 4B, 4C, and 4D.

[00102] FIGs. 4A, 4B, 4C, and 4D depict micrographs of dried alumina foams obtained with the 50%, 70%, 85%, and 100% frothing intensity protocols summarized in Table 3, respectively. FIG. 4E depicts a plot summarizing the average bubble diameter size (d) and bubble volume fraction (fi₃) as a function of frothing intensity (also referred to as“mixing intensity”). As seen in FIGs. 4A-4E, the average bubble diameter size (d) decreases with increasing frothing intensity, from about 135pm diameter at 50% frothing intensity down to about 40pm diameter with 100% frothing intensity. The average bubble volume fraction (fi₃) increases with increasing frothing intensity, from about 0.6 at 50% frothing intensity to about 0.8 at 100% frothing intensity.

[00103] With increasing frothing intensity, the bubble size becomes smaller, more air was entrained in the wet foam, the specific interfacial area (å) increased from about 30 mm²/mm³ for a 50% mixing intensity to about 120 mm²/mm³ for a 100% mixing intensity (as depicted in FIG. 5F), and a larger number of particles contributed to the stabilization of the bubbles and of the wet foam.

[00104] The storage moduli (G’) of the wet foams showed an increase from about 3 x 10⁴ Pa of the precursor gel (i.e. the suspension prior to introduction of any gas), to about 4 x 10⁴ Pa for a lightly frothed foam (50%), and finally to about 8 x 10⁴ Pa for the foam produced with maximum mixing intensity (100%) (as depicted in FIG. 4G). [00105] The adsorption energy of the particles at the interfaces between the gas bubbles and the solvent was measured to be at least 2 orders of magnitude higher than those of the attractive van der Waals bonds for the particles in the bulk gel (about 10³ kT at the interface versus about 1-10 kT in the bulk).

[00106] It is believed, without being limited to this purported description, that the elasticity of the wet foam is a result of interparticle forces between the particles and/or group of particles in the bulk as well as between the particles in the interface between the gas bubbles and the bulk.

Example 5: determination of the mechanical strength of sintered alumina foams

[00107] Sintered alumina foams with increasing densities prepared at different frothing intensities, as shown in examples 1 and 4, were tested under compression using a universal testing machine (Instron 5566) at a displacement rate of 1 pm/s. The top/bottom foam surfaces were ground prior to compression analysis to attain a homogeneous distribution of the load. A stress-strain compression curve was generated for each specimen.

[00108] The elastic modulus (E) of each specimen was estimated from the slope in the linear region of the load/displacement plots, and the compressive strength (o_c) was calculated from the peak load divided by the contact surface.

[00109] FIG. 5A shows three representative stress-strain curves for sintered alumina foams with low, medium and high specific interfacial area (å), obtained from low, medium and high frothing intensities, respectively. The open-cell ceramic foams presented a linear deformation regime under compression, which corresponded to the elastic bending of the ceramic cell walls (e.g., sintered foams with lower specific interfacial area values (å) were able to extend up to about 4% strain). After a certain stress, the linear regime was followed by a nearly flat plateau. [00110] The elastic modulus (E) of the foams can be inferred from the slope of the curves in the linear elastic regime. The elastic modulus (E) was plotted in FIG. 5B as a function of the relative alumina foam density with decreasing specific interfacial area value (å). In a modulus (E) versus relative density (p_rei) log-log plot, elastic moduli were shown to follow approximately a linear trend. The stiffest ceramic foam (having a relative density, p_rei, of about 23%) showed elastic modulus (E) values of about 400 MPa. The most elastic ceramic foam (having a relative density, p_rei, of about 7%) showed elastic modulus (E) values of about 13

MPa.

[00111] Similarly, FIG. 5C depicts the compressive strength (o_c) versus relative density (p_rei) log-log plot for the open-cell alumina foams with decreasing specific interfacial area values (å). For the higher specific interfacial area (å) foams, compressive stress (o_c) values of about 0.7 MPa were registered. The compressive stress (o_c) values increased up to about 24 MPa for foams with relative density values of about 25%. Therefore, it was possible to fit the compressive stress (o_c) and relative density (p_rei) values according to the model:

where, in the case of the present open-cell alumina foams, the empirically determined constant n was about 2.9.

[00112] For simplicity of explanation, the embodiments of the methods of this disclosure are depicted and described as a series of acts. However, acts in accordance with this disclosure can occur in various orders and/or concurrently, and with other acts not presented and described herein. Furthermore, not all illustrated acts may be required to implement the methods in accordance with the disclosed subject matter. In addition, those skilled in the art will understand and appreciate that the methods could alternatively be represented as a series of interrelated states via a state diagram or events. [00113] In the foregoing description, numerous specific details are set forth, such as specific materials, dimensions, processes parameters, etc., to provide a thorough understanding of the present invention. The particular features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments. The words“example” or “exemplary” are used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as“example” or“exemplary” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Rather, use of the words “example” or“exemplary” is intended to present concepts in a concrete fashion. As used in this application, the term“or” is intended to mean an inclusive“or” rather than an exclusive “or”. That is, unless specified otherwise, or clear from context,“X includes A or B” is intended to mean any of the natural inclusive permutations. That is, if X includes A; X includes B; or X includes both A and B, then“X includes A or B” is satisfied under any of the foregoing instances. Reference throughout this specification to “an embodiment”, “certain embodiments”, or“one embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrase“an embodiment”,“certain embodiments”, or“one embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment.

[00114] The present invention has been described with reference to specific exemplary embodiments thereof. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. Various modifications of the invention in addition to those shown and described herein will become apparent to those skilled in the art and are intended to fall within the scope of the appended claims.

[00115] Table 4 below summarizes the various symbols used throughout this disclosure:

Table 4- Symbol Meanings

Claims

CLAIMS What is claimed is:

1. A ceramic foam having hierarchical pores comprising a first pore population and a second pore population, wherein the first pore population has an average diameter D_bubbies ranging from about 5pm to about 200pm, and wherein the second pore population has an average diameter D_pores ranging from about lOnm to about 5000nm.

2. A ceramic foam having a hierarchically porous open-cell nature, the hierarchically porous open-cell nature comprising:

a first pore population having an average diameter Dbubbies, and

a second pore population having an average diameter D_p0res,

wherein Dbubbies is in a micrometer scale and D_pores is in a nanometer scale, and

wherein the ceramic foam has a permeability (K) ranging from about 5x1 O ¹⁴ m² to about 5x10 ¹² m².

3. A ceramic foam having a hierarchically porous open-cell nature, the hierarchically porous open-cell nature comprising:

a first pore population having an average diameter D_bubbies, and

a second pore population having an average diameter D_pores,

wherein Dbubbies is in a micrometer scale and D_p0res is in a nanometer scale, and

wherein the ceramic foam has a total porosity ranging from about 60% to about 95%.

4. A ceramic foam having hierarchical porosity, comprising a first pore population and a second pore population, the second pore population having an average diameter D_pores, wherein the ceramic foam comprises a plurality of ceramic particles having an average diameter D_partides, wherein the ratio of D_partides to D_pores, after the ceramic foam has been subjected to sintering, ranges from about 10: 1 to about 1 : 10.

5. The ceramic foam of claim 4, wherein the plurality of ceramic particles comprise one or more of alumina, titania, silica, cerium oxide, cerium-zirconium oxide, zirconia, cordierite, aluminum titanate, silicon carbide, silicon nitride, zirconium diboride, or other metal oxides, or other carbides, or other borides, or mixtures thereof.

6. A ceramic foam having hierarchical porosity, comprising a first pore population and a second pore population, wherein the first pore population has an average diameter Dtmbbies, the second pore population having an average diameter D_p0res, wherein the ratio of Dbubbies to D_Pores ranges from about 2: 1 to about 20,000: 1.

7. A ceramic foam having a hierarchically porous open-cell nature formed by:

generating a wet foam having gas bubbles stabilized with a system of solid stabilizing particles positioned on interfaces of the gas bubbles and a solvent, the system of solid stabilizing particles comprising:

a first plurality of particles having a first average diameter, and a second plurality of particles having a second average diameter, wherein the first plurality of particles is different from the second plurality of particles, and

wherein the ratio of the first average diameter to the second average diameter ranges from about 10: 1 to about 1: 10; and removing either the first plurality of particles or the second plurality of particles to form a network of pores, having an average diameter D_p0res, between adjacent gas bubbles, having a diameter Dbubbies, wherein D_pores is smaller than Dbubbies-

8. The ceramic foam of any one of claims 1 and 3-7, having a permeability (K) ranging from about 5xl0 ¹⁴ m² to about 5xl0 ¹² m².

9. The ceramic foam of any one of claims 1-2 and 4-7, having a total porosity ranging from about 60% to about 95%.

10. The ceramic foam of any one of the preceding claims, having an elastic modulus ranging from about 10 MPa to about 5 GPa.

11. The ceramic foams of any one of the preceding claims, having a compressive strength ranging from about 0.5 MPa to about 1 GPa.

12. The ceramic foam of any one of claims 1-6 and 8-11, wherein the first pore population is derived from bubbles introduced during a colloidal processing step, and wherein the second pore population is derived from a removal of a population of fugitive particles.

13. A composition comprising a wet foam having gas bubbles stabilized with a system of solid stabilizing particles, the system of solid stabilizing particles comprises:

a first plurality of particles having a first average diameter, and a second plurality of particles having a second average diameter, wherein the first plurality of particles is different from the second plurality of particles, and wherein both the first plurality of particles and the second plurality of particles exhibit a similar hydrophobicity.

14. A composition comprising a wet foam having gas bubbles stabilized with a system of solid stabilizing particles, the system of solid stabilizing particles comprises:

wherein the ratio of the first average diameter to the second average diameter ranges from about 10: 1 to about 1: 10.

15. The composition of any one of claims 7 and 13-14, wherein the first plurality of particles comprises an inorganic material and the second plurality of particles comprises fugitive materials.

16. The composition of claim 15, wherein the inorganic material comprises alumina, titania, silica, zirconia, cordierite, mullite, aluminum titanate, silicon carbide, silicon carbide, zirconium diboride, or other oxides, or other carbides, or other borides, or mixtures thereof.

17. The composition of any one of claims 15-16, wherein the fugitive material comprises carbon, one or more polymers, silica, zinc oxide, magnesium oxide, calcium oxide, or mixtures thereof.

18. The composition of any one of claims 7 and 13-17, further comprising a stabilizing particle surface modifier.

19. The composition of claim 18, wherein the stabilizing particle surface modifier comprises a surfactant selected from the group consisting of amines, ammonium salts, fatty acids, sulfonates, salts thereof, and combinations thereof.

20. The composition of any one of claims 7 and 13-19, wherein both the first plurality of particles and the second plurality of particles exhibit a positive charge or wherein both the first plurality of particles and the second plurality of particles exhibit a negative charge.

21. The composition of any one of claims 7 and 13-20, wherein the ratio of the first diameter to the second diameter ranges from about 8: 1 to about 1 :8, from about 5:1 to about 1:5, from about 3: 1 to about 1:3, or from about 2: 1 to about 1 :2.

22. The composition of any one of claims 7 and 13-21, further comprising a humectant.

23. The composition of any one of claims 7 and 13-22, further comprising a binder.

24. The composition of any one of claims 7 and 13-23, wherein the system of stabilizing particles further comprises one or more additional plurality of particles that are different from the first plurality of particles and from the second plurality of particles.

25. The composition of claim 24, wherein the one or more additional plurality of particles comprises an inorganic material comprising alumina, titania, silica, zirconia, cordierite, aluminum titanate, silicon carbide, silicon carbide, zirconium diboride, or other oxides, or other carbides, or other borides, or mixtures thereof.

26. The composition of any one of claims 13-23, wherein the composition is a binary wet ceramic foam.

27. The composition of any one of claims 24-25, wherein the composition is a ternary wet ceramic foam.

28. The composition of any one of claims 13-27, wherein the system of solid stabilizing particles is present in the composition at from about 10 vol.% to about 50 vol.%, from about 15 vol% to about 45 vol%, from about 20 vol% to about 40 vol%, or from about 25 vol% to about 35 vol%.

29. A method for manufacturing a composition according to any one of claims 1 to 6 and 8-11, the method comprising:

generating a wet foam having gas bubbles stabilized with a system of solid stabilizing particles positioned on interfaces of the gas bubbles and a solvent, the system of solid stabilizing particles comprises:

a first plurality of particles, and

a second plurality of particles; and removing either the first plurality of particles or the second plurality of particles to form a network of pores, having an average diameter D_p0res, between adjacent gas bubbles, having an average diameter Debbies, wherein D_pores is smaller than Dbubbies-

30. The method of claim 29, wherein generating a wet foam comprises:

a) homogenously dispersing the system of stabilizing particles in the solvent to form a precursor mixture;

b) optionally, achieving a similar hydrophobicity degree for both first plurality of particles and second plurality of particles through addition of a surfactant and/or adjustment of a pH of the precursor mixture; and

c) incorporating the gas bubbles into the precursor mixture via mechanical or chemical frothing.

31. The method of claim 29, wherein the removing comprises one or more of:

a) heating the wet foam to bum out one of the first plurality of particles or the second plurality of particles, and/or

b) treating the wet foam with acid to leach off one of the first plurality of particles or the second plurality of particles.

32. A method for manufacturing a wet foam, the method comprising:

combining gas bubbles and a system of stabilizing particles through colloidal processing to form the wet foam, the system of solid stabilizing particles comprises:

33. The method of claim 32, wherein the combining comprises:

homogenously dispersing the system of stabilizing particles in a solvent to form a precursor mixture.

34. The method of claim 33, wherein combining further comprises:

achieving a similar hydrophobicity degree for both first plurality of particles and second plurality of particles through addition of a surfactant and/or adjustment of a pH of the precursor mixture.

35. The method of any one of claims 32-34, wherein the combining further comprises:

incorporating the gas bubbles into the precursor mixture via mechanical or chemical frothing.

36. The method of claim 30, wherein the incorporating of the gas bubbles into the precursor mixture is done via mechanical frothing, and wherein the wet foam’s permeability, after sintering, may be controlled by adjusting an intensity of the mechanical frothing.

37. A wet foam comprising:

gas bubbles and a system of solid stabilizing particles dispersed in a solvent, the system of solid stabilizing particles comprises: a first plurality of particles, and

a second plurality of particles,

wherein the first plurality of particles is different from the second plurality of particles,

wherein at least a first portion of the first plurality of particles and at least a second portion of the second plurality of particles are positioned at interfacial regions between the solvent and the gas bubbles, thereby stabilizing the gas bubbles in the wet foam.

38. A method of printing a hierarchically porous structure, the method comprising extruding the composition of any one of claims 12-28 or 37 through a nozzle.