MULTIFUNCTIONAL METALLIC NANOLATTICES AND METHODS OF MANUFACTURE

Abstract

Nanolattices exhibit attractive mechanical, energy conversion, and optical properties, but it is challenging to fabricate large nanolattices while maintaining the dense regular nanometre features that enable their properties. In this work, we report a crack-free self-assembly approach for fabricating centimetre-scale nickel nanolattices with a feature size of 100 nm and a grain size of 30 nm. The crack-free areas are 20,000 times larger than prior self-assembled nanolattices and contain 1,000 times the number of unit cells as 3D-printed nanolattices. These nickel nanolattices have a 260 MPa tensile strength, which approaches the theoretical strength limit for porous nickel and is 10 times the strength of prior nanolattices. The self-assembly method and porous metal mechanics reported in this work advances the fabrication and applications of high-strength multifunctional porous materials.

Description

TECHNICAL FIELD

The present disclosure relates to the field of nanolattice materials.

BACKGROUND

Strong and lightweight porous materials are commonly used in industry, but their fabrication methods have limited their mechanical properties because of the difficulties in controlling their physical and chemical structure. Nanolattices are porous materials with nanoscale features that promise to overcome these limitations using size-based effects. 3D printing using two-photon polymerization is the most common nanolattice fabrication method, but even with a record-high printing speed, it would take 64 days to fabricate a 20×20×0.1 mm³ woodpile nanolattice. Self-assembled templates, however, are subject to dense cracks that, when filled with a material, form inverted crack structures that divide the sample into small nanolattice domains⁹, cause stress concentrations, block fluid/gas transport¹⁵, and increase optical scattering¹⁶. Accordingly, a method to eliminate template cracks and precisely control metallic nanostructure across millions of units would realize nanolattices with unprecedented properties and enable applications in sensing, energy conversion, and mechanics. Additionally, there is a need to measure, predict, and optimize nanolattice tensile properties to understand how these materials fracture and respond to complex loading. To truly take advantage of the remarkable properties of nanolattices and further understand their large-scale fracture, it is essential to realize methods for fabricating macroscopic nanolattices and understand how their chemical and physical features affect their tensile properties.

SUMMARY

In meeting the described needs, provided here is a crack-free self-assembly approach to fabricate cm-scale multifunctional metallic nanolattices with 100 nm periodic features and 30 nm grain sizes, which corresponds to a 20,000× increase in crack-free area and 1,000× the number of unit cells in the loaded direction than prior nanolattices. These nanolattices have 257 MPa tensile strengths at 1.12% strain and a density of 2.67 g/cm³, which is 2.6 times the strength of the strongest porous metals with the same relative density at any scale. We eliminated cracks during self-assembly by maintaining a wet template and utilizing electrostatic forces to assist metal electrodeposition through the template. The resulting nickel nanolattices have excellent photonic coloration and approach their macroscopic theoretical tensile strength. The high absolute strength and the low density would allow nickel nanolattices to replace sandwich panel cores with 50% smaller volume than porous titanium, 50% lower mass than porous iron, and, importantly, 10× less volume than other nanolattices.

In one aspect, the present disclosure provides a method, comprising: effecting evaporation of a carrier fluid from a colloid that comprises the carrier fluid and a population of particles, the colloid contacting a substrate, the evaporation of the carrier fluid giving rise to assembly of at least some of the population of particles into a plurality of template layers defined by a periodic arrangement of the at least some of the population of particles, each of the plurality of template layers being substantially free of particles positioned outside of the periodic arrangement, and the plurality of template being substantially free of channeling cracks of width greater than two particle diameters, the spacing of adjacent channeling cracks being greater than 100 μm, the evaporation being performed in the presence of a filler fluid, the filler fluid having a vapor pressure lower than the vapor pressure of the carrier fluid, and the filler fluid entering vacancies between particles resulting from the evaporation of the carrier fluid so as to stabilize the positions of the particles during the evaporation of the carrier fluid.

Also provided are methods, comprising: effecting evaporation of a carrier fluid from a colloid that comprises the carrier fluid and a population of particles, the colloid contacting a substrate, the population of particles being at least about 30 vol % of the colloid, the evaporation of the carrier fluid giving rise to assembly of at least some of the population of particles into a plurality of template layers defined by a periodic arrangement of the at least some of the population of particles, each of the plurality of template layers being substantially free of particles positioned outside of the periodic arrangement, and the evaporation optionally being performed in the presence of a filler fluid, the filler fluid having a vapor pressure lower than the vapor pressure of the carrier fluid, and the filler fluid entering vacancies between particles resulting from the evaporation of the carrier fluid so as to stabilize the positions of the particles during the evaporation of the carrier fluid.

Further disclosed are lattices (which can also be termed nanolattices), comprising: a three-dimensional periodic structure of struts of a metal and/or polymer and of spherical voids, the struts and voids being in a periodic arrangement therein, a void defining a cross-sectional dimension in the range of from about 200 to about 10,000 nm, and the network being substantially free of struts or voids disposed outside of the periodic arrangement.

Also provided is a component, the component including a lattice according to the present disclosure (e.g., according to any one of Aspects 16-21).

Further disclosed is a method, comprising: with a magnetized metallic nanolattice (e.g., a lattice according to the present disclosure, such as according to any one of Aspects 16-21), contacting a sample comprising a species that includes a magnetic tag to the magnetized metallic nanolattice under such conditions that the magnetic tag of the sample is immobilized to the magnetized metallic nanolattice.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

In the drawings, which are not necessarily drawn to scale, like numerals may describe similar components in different views. Like numerals having different letter suffixes may represent different instances of similar components. The drawings illustrate generally, by way of example, but not by way of limitation, various aspects discussed in the present document. In the drawings:

FIGS. 1A-1H provide a comparison of the Wet-Electrostatic method for fabricating inverted-crack-free metal nanolattices with the conventional method. (FIG. 1A) Conventional self-assembly of lattice templates from the evaporation of negatively charged particle colloids on negatively charged surfaces. The inset is a top-view optical image of a cracked template in the dried area above the waterline. Scale bar: 20 μm. (FIG. 1B) Fabrication steps to turn a lattice template into a metallic nanolattice. (FIG. 1C) SEM images of nickel nanolattices with inverted cracks (white arrows) fabricated by the conventional method (FIG. 1D) The Wet-Electrostatic (WE) method for fabricating metallic nanolattices without inverted cracks using positively charged particles and a glycerol additive. The inset is a top-view optical image of a wet opal template without cracks. Scale bar: 20 μm. (FIG. 1E) SEM images of nickel nanolattices without inverted cracks fabricated by WE method. (FIG. 1F.) Ratio of wet opal height to total opal height versus volume concentration of low vapor pressure alcohols added to the evaporating colloidal solution. The insets are images of templates made with pure water: top view of the vial after assembly (left) and top view of the sample (right). Schematics of electrostatic forces on negatively charged (FIG. 1G) and positively charged (FIG. 1H) templates during electrodeposition.

FIGS. 2A-2B provide a physical and optical characterization of inverted-crack-free nickel nanolattices. (FIG. 2A) A cross-section SEM image of an inverted-crack-free and free-standing nickel nanolattice. The blue mark represents the prior thickness limit of inverted-crack-free silica nanolattices, equivalent to 16 particle layers¹⁸. The inset is an image of a large-area nickel nanolattice without inverted cracks. (FIG. 2B) An SEM image of a high-quality inverted-crack-free nickel nanolattice with a (111) surface facet that selectively reflects color based on the relative viewing angle. The left inset is the experimental setup for the spectrum images on the right.

FIG. 3A-3D provide tensile properties of nickel nanolattices. (FIG. 3A) Dogbone samples of inverted-crack-free nickel nanolattices with different internal pore sizes. The colored areas are nickel nanolattices. No false coloring was used. (FIG. 3B) The fracture surface of a nickel nanolattice with a 649±13 nm average pore size. The blue-colored area shows a layer of solid nickel at the bottom of the sample. The majority of the fracture surfaces are {111} crystallographic planes. The insets are a dogbone sample in tensile grips before (left), during (middle, the color was excited by external light), and after fracture (right). (FIG. 3C) Tensile stress versus strain of four typical samples with different pore sizes. (FIG. 3D) Ultimate tensile strength of nickel nanolattice dogbones versus the fraction of solid nickel at the sample bottom, t_Ni/t_total. The back dashed line is the linear fit for all data. Error bars show SD.

FIGS. 4A-4D provide nickel nanolattice properties compared to other porous metals and nanolattices. (FIG. 4A) Ultimate tensile strength versus relative density of porous Ag, Al, Au, Cu, Fe, Ni, and Ti. Dashed lines follow equation (1) with Cσ_b from 0 to 1.8 GPa. The black dashed line denotes the empirical limit of prior fabrication methods, including particle sintering, dealloying, Gasar, slurry foaming, and syntactic foaming. (FIG. 4B) Ultimate tensile strength versus relative density of nanolattices, nanoporous graphene, and aerogels. (FIG. 4C) Characteristic volume (σ_UTS^−1/2) versus characteristic mass (ρ*σ_UTS^−1/2) of a rectangular beam to bear a bending moment for different porous materials. The dashed lines are defined by specific tensile strengths between 0.005 and 0.08 MPa/(kg·m⁻³). (FIG. 4D) Specific tensile strength versus the ratio of sample loaded length to unit cell length of nanolattices.

FIG. 5 provides a depiction for forming a porous membrane in which particles form an opal template, the template is bridged, Ni (or other metal, e.g., Au, Cu, Fe) is electrodeposited, the particles are etched away so as to give rise to an inverse opal, and NiFe and Au coatings can be applied.

FIG. 6 provides a mathematical description of the tensile strength of porous materials.

FIG. 7 provides (left side) a depiction of an existing approach for forming opals, which existing approach can lead to cracking in the final product. The right side of FIG. 7 provides a depiction of an example drop casting approach according to the present disclosure, which drop casting approach can include applying a suitable colloid to a substrate, followed by evaporation-driven self assembly that results in the desired opal. One can modulate the drying conditions as needed; the drying can be performed at room temperature and ambient humidity, but this is not a requirement.

FIG. 8A provides (left side) a depiction of a drop casting approach according to the present disclosure for forming an opal (template). As shown, one can apply a bridging material to form material bridges between neighboring template particles. Also provided (right side) is a depiction of a dip-coating process according to the present disclosure for forming bridges; as shown, a particle template can be immersed in a resin solution (e.g., a resin-ethanol solution) such that the resin solution is imbibed into the spaces between the particles of the template. The resin can be cured (e.g., following solvent evaporation) to form resin bridges between adjacent particles of the template. By varying the concentration of the resin (e.g., the polymer in the resin), one can control the width of the bridges (which can take the form of rings or necks) between adjacent template particles.

FIG. 8B provides illustrative data of a template comprising resin bridges between adjacent template particles; as shown, increasing the concentration of the resin in the resin solution (i.e., from 3 v/v % to 4 v/v %) gives rise to comparatively wider bridges between adjacent template particles. (After electrodepositing metal through the template and etching away the template and bridges, dark spots in the images shows the inter-connecting holes that are resulted from the bridges; the images show 3 inter-connecting holes between each spherical pore and its neighbors.)

FIG. 9 provides (left side) a depiction of a drop casting approach according to the present disclosure for forming an opal (template). As shown, one can apply a bridging material to form material bridges between neighboring template particles. Also provided (right side) is a depiction of a dip-coating process according to the present disclosure for forming a template; as shown, a particle template can be immersed in a resin solution (e.g., a resin-ethanol solution) such that the resin solution is imbibed into the spaces between the particles of the template. The resin can be cured (e.g., following solvent evaporation) to form resin bridges between adjacent particles of the template. By varying the concentration of the resin (e.g., the polymer in the resin), one can control the width of the bridges (which can take the form of rings or necks) between adjacent template particles. As shown in the middle of the figure, one can deposit a metal (e.g., nickel) onto the template and remove the template so as to leave behind the deposited metal in an inverse opal architecture.

FIG. 10 provides a depiction of forming a layered composite using templates according to the present disclosure. As shown, one can form alternating layers of templates (e.g., inverse opals) and binder (e.g., epoxy), which alternating layers can be combined (e.g., consolidated) to form a composite as shown. The inverse opals can be metallic, but can also be carbonaceous.

FIG. 11 provides further illustration of composites according to the present disclosure. As shown, a composite can exhibit a thickness that is at least several times the thickness of a single layer of inverse opal.

FIG. 12 provides an illustrative image of a metallic nanolattice formed using an opal according to the present disclosure, illustrating the crack-free nature of the metallic nanolattice as well as the strength achieved by a lattice made according to the disclosed approach as compared to the strength achieved by an Al₂O₃ nanolattice and the strength achieved by prior approaches.

FIG. 13 provides a depiction of a use of the disclosed nanolattices in a bioseparations application.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present disclosure may be understood more readily by reference to the following detailed description of desired embodiments and the examples included therein.

Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. In case of conflict, the present document, including definitions, will control. Preferred methods and materials are described below, although methods and materials similar or equivalent to those described herein can be used in practice or testing. All publications, patent applications, patents and other references mentioned herein are incorporated by reference in their entirety. The materials, methods, and examples disclosed herein are illustrative only and not intended to be limiting.

The singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise.

As used in the specification and in the claims, the term “comprising” may include the embodiments “consisting of” and “consisting essentially of.” The terms “comprise(s),” “include(s),” “having,” “has,” “can,” “contain(s),” and variants thereof, as used herein, are intended to be open-ended transitional phrases, terms, or words that require the presence of the named ingredients/steps and permit the presence of other ingredients/steps. However, such description should be construed as also describing compositions or processes as “consisting of” and “consisting essentially of” the enumerated ingredients/steps, which allows the presence of only the named ingredients/steps, along with any impurities that might result therefrom, and excludes other ingredients/steps.

As used herein, the terms “about” and “at or about” mean that the amount or value in question can be the value designated some other value approximately or about the same. It is generally understood, as used herein, that it is the nominal value indicated ±10% variation unless otherwise indicated or inferred. The term is intended to convey that similar values promote equivalent results or effects recited in the claims. That is, it is understood that amounts, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact, but can be approximate and/or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and the like, and other factors known to those of skill in the art. In general, an amount, size, formulation, parameter or other quantity or characteristic is “about” or “approximate” whether or not expressly stated to be such. It is understood that where “about” is used before a quantitative value, the parameter also includes the specific quantitative value itself, unless specifically stated otherwise.

Unless indicated to the contrary, the numerical values should be understood to include numerical values which are the same when reduced to the same number of significant figures and numerical values which differ from the stated value by less than the experimental error of conventional measurement technique of the type described in the present application to determine the value.

All ranges disclosed herein are inclusive of the recited endpoint and independently of the endpoints (e.g., “between 2 grams and 10 grams, and all the intermediate values includes 2 grams, 10 grams, and all intermediate values”). The endpoints of the ranges and any values disclosed herein are not limited to the precise range or value; they are sufficiently imprecise to include values approximating these ranges and/or values. All ranges are combinable.

As used herein, approximating language may be applied to modify any quantitative representation that may vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as “about” and “substantially,” may not be limited to the precise value specified, in some cases. In at least some instances, the approximating language may correspond to the precision of an instrument for measuring the value. The modifier “about” should also be considered as disclosing the range defined by the absolute values of the two endpoints. For example, the expression “from about 2 to about 4” also discloses the range “from 2 to 4.” The term “about” may refer to plus or minus 10% of the indicated number. For example, “about 10%” may indicate a range of 9% to 11%, and “about 1” may mean from 0.9-1.1. Other meanings of “about” may be apparent from the context, such as rounding off, so, for example “about 1” may also mean from 0.5 to 1.4. Further, the term “comprising” should be understood as having its open-ended meaning of “including,” but the term also includes the closed meaning of the term “consisting.” For example, a composition that comprises components A and B may be a composition that includes A, B, and other components, but may also be a composition made of A and B only. Any documents cited herein are incorporated by reference in their entireties for any and all purposes.

Methods

We prepared Amidine functionalized PS particles with positive charges by dispersion polymerization with 2,2′-azobis(2-methylpropionamidine) dihydrochloride (AIBA) and poly(diallyl dimethyl ammonium chloride) (PDDA) as the initiator and the stabilizer. In general, a flask was filled with ethanol, PDDA aqueous, and styrene sequentially. The mixture was deoxygenated for 10 min by bubbling nitrogen gas and heated to 70° C. Deoxygenated AIBA aqueous was then injected into the flask. The final mixture was kept at 70° C. and magnetically stirred for 20 h. The synthesized particles were centrifuged, washed by Milli-Q water, and re-dispersed in water by sonication five times before use. The average particle diameters were characterized by SEM and image processing in MATLAB. Delsa™ Nano C particle analyzer characterized particle zeta potentials. MicroParticles GmbH and Thermofisher supplied negatively charged PS colloid suspensions functionalized with sulfate groups and PS particles functionalized with amine groups.

We functionalized substrates to adjust surface charges before using them for self-assembly. ITO-coated glass slides were sonicated in methanol, acetone, and isopropyl alcohol for 15 min each. After that, soaking the ITO slides into a “base piranha” solution (H₂O₂:NH₄OH:H₂O with the volume ratio of 1:1:5) at 80° C. for 2 hours functionalized the ITO surface with hydroxyl groups. Then, soaking the substrates in 1.0 wt % 3-(trihydroxysilyl) propane-1-sulfonic acid methanol solution, or 1.0 wt % N-[3-(trimethoxysilyl) propyl]-N,N,N-trimethylammonium chloride methanol solution, for 24 h, functionalized the substrates with negative/positive charges. The substrates were rinsed by Milli-Q water thoroughly before being used for growing opals. For fabricating dogbone samples, ITO slides were patterned by a UV laser (IPG Photonics IX-255) before functionalization.

FIGS. 1A, 1B show the conventional nickel nanolattice fabrication process using self-assembly. ITO slides functionalized with negative charges were placed in Nalgene vials filled with 0.5 wt % negatively charged PS colloid suspensions. The vials were then heated to 55° C. to assemble opals for 24-36 hours. After self-assembly, opals were sintered at 95° C. for 3 h to increase the adhesion to the substrate, followed by electrodepositing nickel at −1.5V with nickel as a counter electrode in an Elevate Nickel 5910 RTU bath. After electrodeposition, samples were soaked in toluene for over 12 hours to dissolve the PS templates.

FIGS. 1B, 1D show the Wet-Electrostatic (crack-free) fabrication approach for nickel nanolattices without inverted cracks. The self-assembly process followed the conventional method with some important changes. Instead of negatively charged particles and ITO slides, we used amidine functionalized PS particles and positively charged ITO substrates. The positively charged PS colloid solution was 1 wt % PS with 0.06% v/v of added glycerol. The crack-free self-assembled template could be made as thick as 500 μm. After self-assembly, the wet opals were quickly transferred to the electrodeposition bath to electrodeposit nickel at −1.5 V versus a nickel counter electrode. After electrodeposition, samples were mechanically peeled from their substrates and then soaked in toluene for over 12 hours to dissolve the PS template. For the dogbone sample fabrication, only the dogbone pattern was connected to the power source so that the deposited nickel nanolattice automatically formed the dogbone shape.

A camera (Nikon D7100) mounted on top of a sample measured the structural color while the incident light angle was adjusted from 61° to 71° with respect to the camera. An Instron mechanical tester (68SC-2) performed mechanical testing with side-action tensile grips and flat surface specimen holders (FIG. 3b middle inset). During gripping, the specimen was adjusted several times until there was no visible sample distortion to minimize the effect of misalignment. The initial distance between grips was 16.36 mm. Only dogbone samples where the crack-free nickel nanolattices filled the majority of the area between grips were used for mechanical characterization. Preparation of dogbone samples was carried out with caution to ensure that no inverted cracks appear in the gauge sections. The crosshead speed was 1 μm/s, equivalent to a strain rate of 8×10⁻⁵ s⁻¹. Only the samples that fractured in the gauge section were analyzed and reported. The sample thicknesses were characterized in an SEM to calculate the stress (the sample width was 1.95 mm). The strain was estimated by dividing the grip displacement by 12.62 mm, which was determined by simulation and verified using image processing with time-series sample images. Electrodeposited nickel density and nickel nanolattice relative density were calculated from mass and volume measurements. Rigaku MiniFlex XRD characterized the nickel grain size.

Exemplary Results

Conventional self-assembly approaches for fabricating metallic nanolattices lead to fully dense metal walls (inverted cracks) that surround nanolattice domains. FIG. 1a shows the conventional method for growing face-centered cubic (FCC) lattice templates from spherical nanoparticles (see Methods). As a result of free energy minimization^29,30, water evaporation drives nanoparticles to assemble into FCC lattices (also called opals) 9 on a conductive substrate. During self-assembly, the top of the opal dries and cracks (FIG. 1a, inset), while the region closest to the receding waterline remains wet³¹ and has no cracks. The wet region typically maintains a constant height while the dry, cracked region grows until all the water evaporates³¹. The cracked template is then converted into a nanolattice by sintering the particles, electrodepositing nickel into the voids, and removing the template (FIG. 1b). FIG. 1c shows a resulting nickel nanolattice with inverted cracks that separate nanolattice domains typically less than 0.01 mm² (FIG. 1c). Due to the energetic advantage of cracking in dried opals, our previous model confirmed the inevitable crack formation using the conventional fabrication method⁹.

We found that adding low vapor pressure alcohols to the colloidal solution can prevent assembled opals from drying, and therefore cracking, by concentrating the alcohols in the opal voids as water evaporated (FIG. 1d). We chose glycerol and ethylene glycol to prevent the opals from drying because they are soluble in water, are not volatile compared to water, and only have hydroxyl groups that do not screen the charges on nanoparticles. As the assembled particles aggregated³¹, Van der Waals forces between particles were strong enough to hold the template together to survive subsequent processing (FIG. 1B, 1D, 1E). FIG. 1f shows the wet opal height, h_wet, normalized by the full opal height, h_total, for glycerol and ethylene glycol at 0 to 1% initial volume concentrations. Without the alcohols (inset in FIG. 1f), the wet opal height was typically less than 10 mm (h_wet/h_total=0.45 in FIG. 1f). When 0.06% v/v glycerol was added, h_wet/h_total increased to 1. For ethylene glycol, h_wet/h_total was smaller than samples with glycerol but larger than pure water as glycol has an evaporation rate higher than glycerol but lower than water. At low concentrations, glycerol and ethylene glycol did not impact the self-assembly order, whereas the assembled opal quality deteriorated when their concentrations increased beyond 1% v/v and 2% v/v. At this point, the alcohols' local concentration at the assembly front was too high to densify particles into FCC packing. This experiment showed that 0.06% glycerol in the colloidal solution resulted in fully wet opals with high-quality packing and no cracks (FIG. 1d, inset).

Although keeping the opal wet prevented cracks, nickel could no longer be subsequently electrodeposited through the template due to particles' negative surface charges. Negatively charged particles made from sulfated polystyrene (PS), sulfated polymethyl methacrylate (PMMA), and silica are commonly used because they are relatively easy to synthesize with high surface charge densities compared to positively charged particles¹⁷. During electrodeposition, however, the negatively charged electrode repels the particles' negative charges and delaminated the opal from the substrate (FIG. 1g). The conventional fabrication method used sintering to prevent the delamination, but sintering requires a dry opal and exacerbates crack formation⁹.

We solved the delamination problem using positively charged particles, which reversed the electrostatic forces (FIG. 1h) so that nickel nanolattices without inverted cracks can be deposited (FIG. 1e). The positively charged particles, synthesized by dispersion polymerization (see Methods), had amidine functional groups that fully protonated/ionized in water and created strong surface charges (67 to 82 mV zeta potentials). The strong charges were necessary to self-assemble particles into FCC packings^29,30, whereas other weakly ionized positively charged functional groups, such as amine groups, had low zeta potentials and resulted in random particle packings. During electrodeposition, the strong electric field in the electrode double layer attracts positively charged particles after uncovering the ion cloud surrounding the particles (FIG. 1H)³², which allows nickel to deposit through the wet template without cracks (FIG. 1E). FIGS. 1B, 1D, and 1H summarize the developed method, which we call the Wet-Electrostatic (WE) method.

The WE method extended the available materials for crack-free self-assembled nanolattices from only oxides to metals, while simultaneously increasing the maximum nanolattice thickness by 10×, allowing cm-scale samples, and maintaining excellent optical properties. Prior studies that used co-assembly to fabricate oxide nanolattices were limited to 16 particle-layer thicknesses, beyond which large internal stresses generated by oxide sintering cracked the sample¹⁸. In contrast, electrodeposition does not require a sintering process to transform or densify the solid phase as the as-deposited nickel is fully dense (8.908±0.060 g/cm³), and the resulting nanolattice thickness is only limited by the opal thickness (up to 500 μm). FIG. 2a shows a 90 μm thick crack-free nickel nanolattice, which was 10 times thicker than prior crack-free studies on oxide nanolattices¹⁸. The inset shows a cm-scale crack-free nickel nanolattice (>2 cm²), which is a 20,000 times increase in crack-free area compared to the conventional assembly method (0.01 mm²). Eliminating inverted cracks also decreased the surface roughness significantly, which improved the nanolattice optical functionality. FIG. 2b shows a highly ordered (111) crystal plane on the top of a nickel nanolattice, along with a clear color transition from blue to red as the angle, θ, between a camera and incident light increased (see Methods). The regions having slight color variation in the insets were due to variations in nanolattice grain orientations. The overall excellent color uniformity throughout the sample further confirmed that the resulting nickel nanolattices had well-aligned polycrystalline structures separated by small angle grain boundaries.

The WE method also enabled the macroscopic study of nanolattice tensile mechanical properties, which has been very challenging because of the difficulty in fabricating large (>cm²) samples². Most prior studies measured compressive properties using μm-sized cubic or cylindrical samples^{2,3,5,10,20-24}. Even for self-assembled nanolattices, the nanolattice properties could only be isolated with nanoindentation or nanocompression because of small separation between inverted cracks^{9,10,12,20-24}. Using the WE method on an indium-tin-oxide (ITO) coated substrate with a dogbone pattern, we overcame these prior limits and fabricated free-standing crack-free nickel nanolattice dogbones with 2.4 cm sample length and four different internal pore sizes (determined by particle sizes). FIG. 3a shows the dogbone samples. The colored regions show the selective light reflection from the pure nickel nanolattices. ITO's low adhesion to metals allowed easy peeling of the nanolattices from the substrates to form free-standing samples for tensile testing⁹.

Tensile testing of the dogbones showed an ultra-high ultimate tensile strength (UTS). FIG. 3b shows a typical fracture surface of a nickel nanolattice after tensile failure. The insets show the full sample before, during, and after testing. As indicated by the white dashed-line polygons in FIG. 3b, tensile fracture mainly occurred at {111} crystal planes. A thin solid nickel layer can be seen at the bottom of the fracture surface (blue region, typically 0-3 μm thick), which formed during the nucleation stage of electrodeposition. Although mechanical milling can remove the solid nickel layer, we tested the dogbones without milling to avoid the potential damage from milling. We treated the samples as laminated composites, and the dogbone UTS is σ_UTS=σ_nanolattice (1-x)+σ_Nix, where σ_nanolattice and σ_Ni are stresses in the nanolattice and in the solid nickel layer at failure. x=t_Ni/t_total is the ratio of the solid nickel layer thickness to the total thickness. FIG. 3c shows four typical strain-stress measurements for samples with different pore sizes. The average fracture strain of the composite samples was 1.12% and no obvious yielding stage was present. A 0.2% offset yield stress analysis indicated that there was very little plastic deformation before 0.9% strain. The strain in the figure was estimated using a simulation, which underestimated the strain at failure by 0.15% on average, and was accurate below 0.9%. As the fracture strain of solid nickel was about 2.5%, it suggests that the nickel nanolattice fractured prior to the failure of the bottom solid nickel layer. Therefore, σ_nanolattice is the UTS of the nickel nanolattice, which can be obtained from a linear fit of composite dogbone UTS measurements with respect to x. FIG. 3d shows the UTS of composite dogbones versus t_Ni/t_total. A larger t_Ni/t_total led to a higher UTS as expected. The data presented here was statistically analyzed (over 50 samples) to prevent inaccuracy caused by sample misalignment during testing.

Linear regression analysis of each dataset in FIG. 3d determined the UTSs to be 247.5±9.3, 261.3±7.8, 256.9±6.7, and 264.9±3.7 MPa for 494±10, 649±13, 754±12, and 844±9 nm pore size samples at a 0.298±0.006 relative density, which corresponded to 0.0935±0.006, 0.0988±0.006, 0.0971±0.005, and 0.100±0.004 MPa/(kg m⁻³) specific strengths. The measured relative density was higher than the ideal value, 0.26²⁰, because of particle size variation and defects in the nanolattices. These effects can also broaden the nano strut size variation and potentially cause weak spots in nanolattices, which could be a reason for the limited pore size dependence in FIG. 3d. Our observations agree with previous compression measurements, which showed no strong size dependence with the struts larger than 60 nm (the smallest strut size here is 76 nm)¹⁰. The linear fit for all the data (black dashed line) gave an overall 257.3±3.9 MPa UTS, and indicated the stress in the solid nickel layer, σ_Ni, at fracture was 781±53 MPa, agreeing with the solid nickel stress at 1.12% strain (732±17 MPa).

The fabricated nickel nanolattices approached their theoretical UTS limit and realized a combination of material properties not yet achieved by porous metals. A well-known formula to predict the porous material UTS, σ_UTS, is

$\begin{array}{cc}{\sigma }_{\mathrm{UTS}}=C{{\sigma }_b\left({\rho }^{*}/\rho \right)}^{1.5},& \left(1\right)\end{array}$

where σ_b and ρ*/ρ are the bulk counterpart UTS and the relative density³³. The constant, C (typically, ≤1), characterizes the porous geometric structure³³. A larger C corresponds to a porous structure allowing a more even stress distribution and smaller internal stress concentrations. FIG. 4a summarizes the UTS of several porous metals (Ni^34-36, Fe^37-40, Ti^39,41, Al⁴², Cu^43,44, Au^45-47, and Ag^48,49) versus relative density with the dashed lines following equation (1) at different Cσ_b values. Prior fabrication techniques, including particle sintering^{37,40,41,48,49}, dealloying^36,45-47, Gasar^38,43,44, slurry foaming^34,39, and syntactic foaming⁴², encountered a Cσ_b limit of 0.6 GPa (black dashed line). This empirical limit has been set due to compromises in porous metal manufacturing. For example, a small Cσ_b can result from poor geometric control of internal pores (small (′) or from the inability to tune the material microstructure (small σ_b). The solid dots in the figure show the nickel nanolattice dogbones in this study. Our nanolattices broke the Cσ_b=0.6 GPa limit by a factor of 2.6, with a Cσ_b of 1.57 GPa (overall σ_UTS=257.3 MPa, and ρ*/ρ=0.298). The high strength was due to the FCC arranged nanostructures with 100 nm periodic features (large (′) and 30 nm average grain size tuned by electrodeposition (large σ_b). We compared this performance to the theoretical limit by substituting the strongest bulk nickel (2 GPa in electrodeposited nickel with 26 nm grain size⁵⁰) into the bulk strength in equation (1). Using σ_b=2 GPa and C=1, equation (1) predicts that the theoretical UTS limit of porous nickel is 325 MPa at a relative density of 0.298, only 26% higher than our nickel nanolattices (257 MPa). When compared to other nanolattices^4,19,27,28, nanoporous graphene^51-53, and aerogels⁵⁴, the nickel nanolattices had an order of magnitude higher UTS (FIG. 4b). This agrees with prior simulations showing that the inverse opal structure can outperform octet- and isotropic-trusses in terms of Young's, bulk, and shear modulus²⁰. Compared to other porous metals' tensile failure strains (0.1-7.3% with 0.16-0.84 relative densities)^{36,39,46,47,49}, our nickel nanolattices' average failure strain (1.12%) did not show a significant drawback. Overall, the presented nanolattice has excellent tensile strength compared to prior porous metals because of the unique combination of pore shape and material microstructure.

Porous materials are often used to reduce the weight of structural materials subjected to bending and buckling, such as sandwich panel cores, and our nickel nanolattice shows excellent promise for bearing bending loads with a low volume and low mass. Previous nanolattice studies emphasized specific strength^2,3, but it is also important to consider the total mass and volume required to resist a load. For example, the strongest 3D-printed nanolattice (UTS=27.4 MPa)²⁸ requires 10 times more cross-sectional area (or volume) than a steel wire (UTS>400 MPa) to hold the same weight. Here, we consider how much volume and mass a material needs to resist failure when being bent. For a rectangular beam with variable height, ρ*σ_UTS^−1/2 and σ_UTS^−1/2 characterize the minimum beam mass and volume needed to resist failure⁵⁵. FIG. 4C shows σ_UTS^−1/2 versus ρ*σ_UTS^−1/2 for different porous metals, nanolattices, and nanoporous materials. The dashed lines denote different specific strengths and show that our nickel nanolattices have the highest specific strength among porous metals. The high UTS and low density allow the nickel nanolattices to resist a bending load with 50% smaller volume than porous titanium, 50% lower mass than porous iron, and, importantly, ten times less volume than nanoporous graphene and other nanolattices.

Moreover, the presented fabrication approach can create much larger nanolattices than prior 3D-printing based approaches. The challenge with nanolattice fabrication is to maintain precise nanoscale dimensions at the unit-cell level, which enable the enhanced properties, while simultaneously connecting millions of unit cells in a reasonable time with minimal defects or imperfections, such as big voids and missing struts, that could significantly decrease the strength. Thus, a technique resulting in fewer such imperfections should produce higher-strength nanolattices at larger scales. Here, we define the fabrication method's scalability as the ratio of a sample's loaded length to unit cell length. FIG. 4D shows the specific strength versus the scalability of nanolattices. For our samples, the loaded length was the equivalent length, while for prior work, we used the total distance between grips. The specific strengths of the nickel nanolattices outperform most other nanolattices, and the self-assembly technique allows a scalability that is three orders of magnitude larger than 3D printing. The large sample size and the high specific strength of the nickel nanolattices show that the self-assembly fabrication approach is capable of minimizing imperfections while maintaining nanoscale features across millions of unit cells.

CONCLUSIONS

In summary, this work presents a crack-free self-assembly approach to fabricate large-area multifunctional metallic nanolattices with an ultra-high 257 MPa tensile strength, which is 2.6 times the strength of prior porous metals at 0.298 relative density. We found that the key to eliminating cracks during self-assembly was to keep the template wet with 0.06% glycerol. Additionally, synthesized positively charged PS particles allowed subsequent electrodeposition through the thick, wet opals due to electrostatic forces. Benefiting from the scalability of this fabrication approach, we grew large-area nickel nanolattices without inverted cracks and measured the tensile properties with macroscopic testing equipment. The resulting nickel nanolattices had excellent photonic coloration, approached the theoretical limit of the upper tensile strength, achieved a previously unrealized combination of strength and relative density for porous metals and nanolattices, and could resist bending fractures with a lower volume and mass than most porous materials. The developed methods and findings in this work will further the design and fabrication of lightweight porous metals with the promising combination of high strength, electrical and thermal conductivity, structural coloration, and high specific surface area, which may enhance the performance of many applications such as high-power-density batteries, efficient heat and mass exchangers, and selective infiltration membranes.

REFERENCES

The following references are listed for convenience only; the inclusion of a reference in this listing should not be construed as an acknowledgment that the reference is material in any way to the appended claims.

• 1 Zhao, B. et al. A review on metallic porous materials: pore formation, mechanical properties, and their applications. The International Journal of Advanced Manufacturing Technology 95, 2641-2659, doi: 10.1007/s00170-017-1415-6 (2018).
• 2 Bauer, J. et al. Nanolattices: An Emerging Class of Mechanical Metamaterials. Advanced Materials 29, 1701850-n/a, doi: 10.1002/adma.201701850 (2017).
• 3 Zhang, X., Wang, Y., Ding, B. & Li, X. Design, Fabrication, and Mechanics of 3D Micro-/Nanolattices. Small 16, e1902842, doi: 10.1002/smll.201902842 (2020)
• 4 Zheng, X. et al. Multiscale metallic metamaterials. Nature Materials 15, 1100-1106, doi: 10.1038/nmat4694 (2016).
• 5 Vyatskikh, A. et al. Additive manufacturing of 3D nano-architected metals. Nature communications 9, 593-598, doi: 10.1038/s41467-018-03071-9 (2018).
• 6 Geng, Q., Wang, D., Chen, P. & Chen, S.-C. Ultrafast multi-focus 3-D nano-fabrication based on two-photon polymerization. Nature Communications 10, 2179, doi: 10.1038/s41467-019-10249-2 (2019).
• 7 Hsueh, H.-Y. et al. Nanoporous Gyroid Nickel from Block Copolymer Templates via Electroless Plating. Advanced Materials 23, 3041-3046, doi: 10.1002/adma.201100883 (2011).
• 8 Bagal, A. et al. Large-Area Nanolattice Film with Enhanced Modulus, Hardness, and Energy Dissipation. Sci Rep 7, 9145, doi: 10.1038/s41598-017-09521-6 (2017).
• 9 Jiang, Z., Hsain, Z. & Pikul, J. H. Thick Free-Standing Metallic Inverse Opals Enabled by New Insights into the Fracture of Drying Particle Films. Langmuir 36, 7315-7324, doi: 10.1021/acs.langmuir.0c00761 (2020).
• 10 Pikul, J. H. et al. High strength metallic wood from nanostructured nickel inverse opal materials. Sci Rep 9, 719, doi: 10.1038/s41598-018-36901-3 (2019).
• 11 Zhang, C. et al. Enhanced Capillary-Fed Boiling in Copper Inverse Opals via Template Sintering. Advanced Functional Materials 28, 1803689-n/a, doi: 10.1002/adfm.201803689 (2018).
• 12 Zhang, R., Cohen, J., Fan, S. & Braun, P. V. Electrodeposited high strength, thermally stable spectrally selective rhenium nickel inverse opals. Nanoscale 9, 11187-11194, doi: 10.1039/c7nr03567e (2017).
• 13 Pikul, J. H., Zhang, H. G., Cho, J., Braun, P. V. & King, W. P. High-power lithium ion microbatteries from interdigitated three-dimensional bicontinuous nanoporous electrodes. Nature communications 4, 1732 (2013).
• 14 Kränzlin, N. & Niederberger, M. Controlled fabrication of porous metals from the nanometer to the macroscopic scale. Mater Horiz 2, 359-377 (2015).
• 15 Pham, Q. N., Barako, M. T., Tice, J. & Won, Y. Microscale Liquid Transport in Polycrystalline Inverse Opals across Grain Boundaries. Sci Rep 7, 10465, doi: 10.1038/s41598-017-10791-3 (2017).
• 16 Phillips, K. R. et al. Nanocrystalline Precursors for the Co-Assembly of Crack-Free Metal Oxide Inverse Opals. Adv Mater 30, e1706329, doi: 10.1002/adma.201706329 (2018).
• 17 Vogel, N., Retsch, M., Fustin, C.-A., del Campo, A. & Jonas, U. Advances in Colloidal Assembly: The Design of Structure and Hierarchy in Two and Three Dimensions. Chemical Reviews 115, 6265-6311, doi: 10.1021/cr400081d (2015).
• 18 Hatton, B., Mishchenko, L., Davis, S., Sandhage, K. H. & Aizenberg, J. Assembly of large-area, highly ordered, crack-free inverse opal films. Proceedings of the National Academy of Sciences 107, 10354-10359 (2010).
• 19 Montemayor, L. C., Wong, W. H., Zhang, Y. W. & Greer, J. R. Insensitivity to Flaws Leads to Damage Tolerance in Brittle Architected Meta-Materials. Scientific Reports 6, 20570, doi: 10.1038/srep20570 (2016).
• 20 do Rosário, J. J., Berger, J. B., Lilleodden, E. T., McMeeking, R. M. & Schneider, G. A. The stiffness and strength of metamaterials based on the inverse opal architecture. Extreme Mechanics Letters 12, 86-96, doi: 10.1016/j.eml.2016.07.006 (2017).
• 21 Schmalbach, K. M. et al. Temperature-dependent mechanical behavior of three-dimensionally ordered macroporous tungsten. J. Mater. Res. 35, 2556-2566 (2020).
• 22 Ramachandramoorthy, R. et al. Dual-templated electrodeposition and characterization of regular metallic foam based microarchitectures. Appl Mater Today 20, 100667 (2020).
• 23 do Rosário, J. J., Häntsch, Y., Schneider, G. A. & Lilleodden, E. T. A combined compression and indentation study of mechanical metamaterials based on inverse opal coatings. Acta materialia 195, 98-108 (2020).
• 24 do Rosário, J. J. et al. Self-Assembled Ultra High Strength, Ultra Stiff Mechanical Metamaterials Based on Inverse Opals. Advanced Engineering Materials 17, 1420-1424, doi: 10.1002/adem.201500118 (2015).
• 25 Meza, L. R., Das, S. & Greer, J. R. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 345, 1322-1326, doi: 10.1126/science. 1255908 (2014).
• 26 Jang, D., Meza, L. R., Greer, F. & Greer, J. R. Fabrication and deformation of three-dimensional hollow ceramic nanostructures. Nature materials 12, 893-898 (2013).
• 27 Bauer, J., Schroer, A., Schwaiger, R. & Kraft, O. The Impact of Size and Loading Direction on the Strength of Architected Lattice Materials Advanced Engineering Materials 18, 1537-1543, doi: 10.1002/adem.201600235 (2016).
• 28 Mateos, A. J., Huang, W., Zhang, Y.-W. & Greer, J. R. Discrete-Continuum Duality of Architected Materials: Failure, Flaws, and Fracture. Advanced Functional Materials 29, 1806772, doi: 10.1002/adfm.201806772 (2019).
• 29 Manoharan, V. N. Colloidal matter: Packing, geometry, and entropy. Science 349 (2015).
• 30 Li, Q., Jonas, U., Zhao, X. & Kappl, M. The forces at work in colloidal self-assembly: A review on fundamental interactions between colloidal particles. Asia-Pacific Journal of Chemical Engineering 3, 255-268 (2008).
• 31 Goehring, L., Clegg, W. J. & Routh, A. F. Solidification and Ordering during Directional Drying of a Colloidal Dispersion. Langmuir 26, 9269-9275, doi: 10.1021/1a100125v (2010).
• 32 Guglielmi, N. Kinetics of the deposition of inert particles from electrolytic baths. Journal of the Electrochemical Society 119, 1009 (1972).
• 33 Gibson, L. J. & Ashby, M. F. Cellular solids: structure and properties. (Cambridge university press, 1999).
• 34 Aly, M. S. Tensile properties of open-cell nickel foams. Materials & Design 31, 2237-2240, doi: 10.1016/j.matdes.2009.10.018 (2010).
• 35 Lee, K. & Lewandowski, J. J. Effects of microstructural characteristics on mechanical properties of open-cell nickel foams. Materials Science and Technology 21, 1355-1358, doi: 10.1179/174328405X64006 (2005).
• 36 Kashani, H. & Chen, M. W. Flaw-free nanoporous Ni for tensile properties. Acta Materialia 166, 402-412, doi: 10.1016/j.actamat.2018.12.056 (2019).
• 37 Furumoto, T. et al. Permeability and strength of a porous metal structure fabricated by additive manufacturing. J Mater Process Tech 219, 10-16, doi: 10.1016/j.jmatprotec.2014.11.043 (2015).
• 38 Kashihara, M. et al. Fabrication of lotus-type porous carbon steel via continuous zone melting and its mechanical properties. Mat Sci Eng a-Struct 524, 112-118, doi: 10.1016/j.msea.2009.06.009 (2009).
• 39 Kato, K. et al. Cytocompatibility and mechanical properties of novel porous 316 L stainless steel. Mat Sci Eng C-Mater 33, 2736-2743, doi: 10.1016/j.msec.2013.02.038 (2013).
• 40 Falkowska, A., Seweryn, A. & Szusta, J. Predicting the fatigue strength and life of 316 L steel sinters of varying porosity for implants in a uniaxial loading state. Engineering Fracture Mechanics 200, 146-165, doi: 10.1016/j.engfracmech.2018.07.030 (2018).
• 41 Kelly, C. N. et al. Fatigue behavior of As-built selective laser melted titanium scaffolds with sheet-based gyroid microarchitecture for bone tissue engineering. Acta Biomater. 94, 610-626, doi: 10.1016/j.actbio.2019.05.046 (2019).
• 42 Tao, X. F. & Zhao, Y. Y. Compressive failure of Al alloy matrix syntactic foams manufactured by melt infiltration. Mat Sci Eng a-Struct 549, 228-232, doi: 10.1016/j.msea.2012.04.047 (2012).
• 43 Nakajima, H. Fabrication, properties and application of porous metals with directional pores. Progress in Materials Science 52, 1091-1173, doi: 10.1016/j.pmatsci.2006.09.001 (2007).
• 44 Simone, A. E. & Gibson, L. J. The tensile strength of porous copper made by the GASAR process. Acta Materialia 44, 1437-1447, doi: Doi 10.1016/1359-6454 (95) 00278-2 (1996).
• 45 Gwak, E. J., Jeon, H., Song, E. J., Kang, N. R. & Kim, J. Y. Twinned nanoporous gold with enhanced tensile strength. Acta Materialia 155, 253-261, doi: 10.1016/j.actamat.2018.06.009 (2018).
• 46 Xia, R. et al. Microtensile tests of mechanical properties of nanoporous Au thin films. J Mater Sci 44, 4728-4733, doi: 10.1007/s10853-009-3731-1 (2009).
• 47 Badwe, N., Chen, X. Y. & Sieradzki, K. Mechanical properties of nanoporous gold in tension. Acta Materialia 129, 251-258, doi: 10.1016/j.actamat.2017.02.040 (2017).
• 48 Ahmed, H. S. T. & Jankowski, A. F. Stiffening of sub-micro-porous silver membranes under tensile deformation. Mater Sci Eng B-Adv 177, 43-47, doi: 10.1016/j.mseb.2011.09.028 (2012).
• 49 Gadaud, P., Caccuri, V., Bertheau, D., Carr, J. & Milhet, X. Ageing sintered silver: Relationship between tensile behavior, mechanical properties and the nanoporous structure evolution. Materials Science and Engineering: A 669, 379-386, doi: https://doi.org/10.1016/j.msea.2016.05.108 (2016).
• 50 Budrovic, Z., Swygenhoven, H. V., Derlet, P. M., Petegem, S. V. & Schmitt, B. Plastic Deformation with Reversible Peak Broadening in Nanocrystalline Nickel. Science 304, 273-276, doi: 10.1126/science. 1095071 (2004).
• 51 Sun, H., Xu, Z. & Gao, C. Multifunctional, Ultra-Flyweight, Synergistically Assembled Carbon Aerogels. Advanced Materials 25, 2554-2560, doi: 10.1002/adma.201204576 (2013).
• 52 Kashani, H., Ito, Y., Han, J., Liu, P. & Chen, M. Extraordinary tensile strength and ductility of scalable nanoporous graphene. Science Advances 5, eaat6951, doi: 10.1126/sciadv.aat6951 (2019).
• 53 Xu, Z., Zhang, Y., Li, P. & Gao, C. Strong, Conductive, Lightweight, Neat Graphene Aerogel Fibers with Aligned Pores. ACS Nano 6, 7103-7113, doi: 10.1021/nn3021772 (2012).
• 54 Parmenter, K. E. & Milstein, F. Mechanical properties of silica aerogels. Journal of Non-Crystalline Solids 223, 179-189, doi: https://doi.org/10.1016/S0022-3093 (97) 00430-4 (1998).
• 55 Betts, C. Benefits of metal foams and developments in modelling techniques to assess their materials behaviour: a review. Materials Science and Technology 28, 129-143 (2012).

Aspects

The following Aspects are illustrative only and do not limit the scope of the present disclosure or the appended claims.

Aspect 1. A method, comprising: effecting evaporation of a carrier fluid from a colloid that comprises the carrier fluid and a population of particles, the colloid contacting a substrate, the evaporation of the carrier fluid giving rise to assembly of at least some of the population of particles into a plurality of template layers defined by a periodic arrangement of the at least some of the population of particles, each of the plurality of template layers being substantially free of particles positioned outside of the periodic arrangement, and the plurality of template layers optionally being substantially free of channeling cracks of width greater than two particle diameters, the spacing of adjacent channeling cracks being greater than 100 μm, the evaporation optionally being performed in the presence of a filler fluid, the filler fluid having a vapor pressure lower than the vapor pressure of the carrier fluid, and the filler fluid entering vacancies between particles resulting from the evaporation of the carrier fluid so as to stabilize the positions of the particles during the evaporation of the carrier fluid.

A substrate can be essentially any surface or any portion of a surface; the substrate can include a flat region, a curved region, or both. Particles within the carrier fluid can be, e.g., metals, metal oxides, metalloids, polymeric, and the like.

A particle can have a minimum zeta potential of 30 mV (if positive zeta potential); a particle can also have a maximum zeta potential of 300 mV (if positive zeta potential), e.g., a zeta potential of from 30 mV to 300 mV (at pH=7 with 20 mM NaCl). A particle can also have a zeta potential of −30 mV (if negative zeta potential) to −300 mV (if zeta potential), e.g., from −30 mV to −300 mV (at pH=7 with 20 mM NaCl). A particle can thus have a zeta potential (absolute value) of from about 30 to about 300 mV (at pH=7 with 20 mM NaCl), and all intermediate values and subranges.

Aspect 2. A method, comprising: effecting evaporation of a carrier fluid from a colloid that comprises the carrier fluid and a population of particles, the colloid contacting a substrate, the population of particles being at least about 0.1 vol % (e.g., at least about 0.1 vol %, at least about 0.5 vol %, at least about 1 vol %, at least about 10 vol %, at least about 20 vol %, at least about 30 vol %, at least about 40 vol %, at least about 50 vol %) of the colloid, the evaporation of the carrier fluid giving rise to assembly of at least some of the population of particles into a plurality of template layers defined by a periodic arrangement of the at least some of the population of particles, each of the plurality of template layers being substantially free of particles positioned outside of the periodic arrangement, and the evaporation optionally being performed in the presence of a filler fluid, the filler fluid having a vapor pressure lower than the vapor pressure of the carrier fluid, and the filler fluid entering vacancies between particles resulting from the evaporation of the carrier fluid so as to stabilize the positions of the particles during the evaporation of the carrier fluid. It should thus be understood that the filler fluid is not a requirement; i.e., the colloid can comprise the carrier fluid (e.g., water) and the particles and be free of a filler fluid. A substrate can be essentially any surface or any portion of a surface; the substrate can include a flat region, a curved region, or both. The particles can be present at from, e.g., about 10 to about 55 vol % in the carrier fluid, or from about 15 to about 50 vol % in the carrier fluid.

Without being bound to any particular theory, the vol % of particles in a carrier fluid using in a drop casing approach can be, e.g., in the range of from about 50 or 55 vol % in some embodiments. In other embodiments, the particle concentration in the carrier fluid in a drop casting approach can be, e.g., from about 10 to about 60 vol %, from about 15 to about 55 vol %, from about 20 to about 50 vol %, from about 25 to about 45 vol %, from about 30 to about 40 vol %, or even about 35 vol %. An example drop casting approach is shown in FIG. 7 (right side). As shown, the drop casting approach can be performed at room temperature. A drop casting approach can include a carrier fluid and a filler fluid; it is not a requirement that a filler fluid be present.

In such methods, the particles can be present at greater than 0.1% vol. concentration in the colloid. A particle can have a surface charge zeta potential (absolute value) of greater than about 30 mV, in some instances. For example, a particle can have a minimum zeta potential of 30 mV (if positive zeta potential); a particle can also have a maximum zeta potential of 300 mV (if positive zeta potential), e.g., a zeta potential of from 30 mV to 300 mV (absolute value; measured at pH=7 with 20 mM NaCl), from about 40 to about 200 mV, from about 4 to about 150 mV, from about 40 to about 120 mV, or from about 40 to about 90 mV. A particle can also have a zeta potential of −30 mV (if negative zeta potential) to −300 mV (if zeta potential), e.g., from −30 mV to −300 mV (at pH=7 with 20 mM NaCl). As discussed elsewhere herein, particles can self-organize into polycrystalline packings in the colloid.

The particles of the colloid can be selected such that they have less than about 10% dispersity. The disclosed methods can be performed as drop casting; one can also utilize a rotation, a spin coating, a doctor blading, or other smoothing/coating process to perform the disclosed methods. The particles can have a charge that is the same as the charge of the substrate onto which the particles are deposited; the particles can also have a charge that is the same as the charge of functional groups of the substrate onto which the particles are deposited.

As but one example (by reference to FIG. 1D), the opal particles and the substrate can both be positively charged. Alternatively, both the opal particles and the substrate can both be negatively charged. Without being bound to any particular theory, this charge matching can prevent the particles from attaching to the substrate. Positively-charged particles (and a positively charged substrate) can be useful when the user desires to electrodeposit a metal onto the particles (via reduction), as shown in FIG. 1H. Negatively-charged particles (and a negatively charged substrate) can be useful when the user desires to deposit a material (e.g., an oxide) onto the particles via oxidation. One can, e.g., deposit MnO onto particles by placing a template into a bath of water and a Mn salt. One can also deposit LiCoO in a similar manner; one can also deposit PEDOT (or other conductive polymers) onto an opal according to the present disclosure.

In a drop casting approach, the colloid (and any filler fluid that may be present; a filler fluid is not a requirement in a drop casting approach) and/or environmental conditions can be selected such that evaporation of solvent results in colloid particles being a continuous film. One can perform the drop casting in a system that allows for control of the evaporation rate; one can modulate evaporation rate by adjusting temperature and humidity. Without being bound by any particular theory or embodiment, one can effect an evaporation rate that is less than about 0.4 cm/min, e.g., less than about 0.4 cm/min, less than about 0.3 cm/min, less than about 0.2 cm/min, or even less than about 0.1 cm/min. A particle of the colloid can be positively charged; a particle of the colloid can also be negatively charged. Similarly, the substrate can be positively charged, but the substrate can also be negatively charged in some embodiments.

Aspect 3. The method of any one of Aspects 1-2, further comprising, with a resin, joining neighboring particles within the plurality of template layers to one another. This can be accomplished by, e.g., first dissolving the resin in a solvent, which solvent is later cured and removed; removal can be performed before deposition of metal onto the template layers. Without being bound to any particular theory or embodiment, the resin can act as a bridge between adjacent particles and can even be used to expand or increase the spacing between adjacent particles.

An example resin bridging is shown in FIG. 8A. As shown, one can use a resin (e.g., a resin and solvent, such as a UV-curable resin with ethanol) solution to bridge adjacent template particles. The process can be performed such that the resin solution does not completely fill all spaces between adjacent template particles. In this way, when the resin is cured, one can form cured bridges (or necks) between adjacent particles; such bridges can be ring-shaped in form. The width of a given bridge can be proportional to the concentration of resin in the resin solution. One can carbonize the particles and bridges to form a carbonaceous opal. Alternatively, one can coat the opal with a coating (e.g. a polymer, such as a polymer that is electrodeposited or otherwise placed onto the opal), remove the opal, and carbonize the coating so as to form a carbonaceous inverse opal, which inverse opal can have the form of a nanolattice. The inverse opal can then be consolidated with a binder (e.g., as shown in FIG. 10) to form a composite structure. A nanolattice can be used as an electrode (e.g., in a battery) and also in catalysis applications. As but one example, a nanolattice can have catalyst material disposed thereon or therein.

In some embodiments, one can substantially completely or completely filled with a curable material (e.g., UV-curable monomer; crosslinker can also be present). The curable material can then be cured/polymerized, thereby filling in the spaces between the particles of the opal. The opal particles can be removed and the curable material can (e.g., when the curable material is a polymer) then be carbonized so as to leave behind a carbonaceous lattice in the form of an inverse opal.

Also as shown in FIG. 8A, drop casting can be used to form a template, and dip coating can then be performed to strengthen the template via cured resin bridges. Drop casting can be performed in a batch manner, but can also be performed in a roll-to-roll manner as well. Dip coating approach can be performed in a batch manner, but can also be performed in a roll-to-roll fashion in which template is continuously run through a bath of resin solution. As shown in FIG. 9, metal electrodeposition can then be performed and the underlying template (and the resinous inter-particle bridges) can be removed, leaving behind a metallic nanolattice.

Aspect 4. The method of Aspect 3, further comprising selectively removing the resin. It should be understood that the addition and inclusion of resin can be accomplished without sintering the particles and/or without calcining the resin. The resin can be cured (e.g., via UV illumination or other modality) without calcining, although this is not a requirement. In this way, resin can be used to join polymer particles, which polymer particles can be comparatively heat-sensitive. One can also select a solvent for the resin that does not swell the polymer particles.

Aspect 5. The method of any one of Aspects 1-4, further comprising depositing any one or more of metal, an oxide, or a polymer (including a conductive polymer, such as PEDOT) onto the plurality of template layers. The deposition can be, e.g., electroplating or other methods. Deposition can be performed so as to place the metal within the voids of the template layers. The particle and substrate charge can be the opposite of the working electrode in the electrodeposition process. By using positive particles, one can allow for subsequent electrodeposition of metal.

Aspect 6. The method of Aspect 5, wherein the metal, oxide, or polymer is deposited in a direction from the substrate through a thickness of the plurality of template layers.

Aspect 7. The method of Aspect 5, further comprising selectively removing the plurality of template layers so as to leave behind a metallic, oxide, or polymeric nanolattice. The removing can be accomplished by dissolving the particles of the affected template layer(s); the removing can also include removal of any bridges (e.g., polymeric bridges) between particles of a template layer.

Aspect 8. The method of any one of Aspects 1-7, wherein a particle defines a cross-sectional dimension in the range of from about 50 nm to about 50,000 nm, e.g., from about 200 nm to about 10,000 nm, from about 500 nm to about 7500 nm, from about 1000 nm to about 5000 nm, and all intermediate values.

Aspect 9. The method of any one of Aspects 1-8, wherein the filler fluid comprises an alcohol. Without being bound to any particular theory, an alcohol can be present at from about 0.06 to about 40 wt % of the colloid, e.g., about 0.06 to about 40 wt %, about 0.075 to about 25 wt %, about 0.08 to about 10 wt %, about 0.1 to about 5 wt %, and all intermediate values. It should be understood, however, that the filler fluid need not be an alcohol, as a filler fluid can be a fluid that has a vapor pressure that is lower than the vapor pressure of the carrier fluid. Glycols and polyols (e.g., diols, triols) are considered suitable filler fluids, as well as other fluids that have a lower vapor pressure than the carrier fluid (e.g., water). A filler fluid can be one that does not disrupt (or minimally disrupts) the charges of the particles used to form the template; water-miscible filler fluids are considered particularly suitable.

Aspect 10. The method of Aspect 9, wherein the alcohol is glycerol or ethylene glycol.

Aspect 11. The method of any one of Aspects 1-10, wherein the filler fluid is present in the colloid at from about 0.01 vol % to about 40 vol %. The filler fluid can be present at, e.g., from about 0.1 to about 40 vol %, or from about 1 to about 30 vol %, or from about 2 to about 25 vol %, or from about 5 to about 20 vol %, or from about 7 to about 17 vol %, or from about 10 to about 14 vol %.

Aspect 12. The method of any one of Aspects 1-11, wherein the particles define a positive charge. Without being bound to any particular theory, using a filler fluid can avoid the formation of cracks or non-period structures in the template layers, and the use of charged particles can facilitate metal deposition such that metallic nanolattices that are free of inverted cracks (e.g., regions of dense or solid metal) can be formed. The particles can also, however, define a negative charge.

Aspect 13. The method of any one of Aspects 1-12, wherein the method is performed in a continuous manner.

Aspect 14. The method of any one of Aspects 1-13, wherein the plurality of template layers defines a thickness in the range of from about 1 to about 5,000 μm. The plurality of layers can define a thickness of, e.g., from about 1 to about 5000 μm, or from about 10 to about 1000 μm, or from about 20 to about 500 μm, or even from about 50 to about 100 μm.

Aspect 15. The method of any one of claims 1-14, further comprising removing carrier fluid.

Aspect 16. A lattice, comprising: a three-dimensional periodic structure of (i) struts of a metal and/or polymer and (ii) of spherical (or of substantially spherical) voids, the struts and voids being in a periodic arrangement therein, a void defining a cross-sectional dimension in the range of from about 200 to about 10,000 nm, and the network being substantially free of struts or voids disposed outside of the periodic arrangement. A void can have a cross-sectional dimension of from about 50 to about 50,000 nm, or from about 500 to about 5,000 nm, or from about 1000 to about 2500 nm.

Metals used in the disclosed lattices can be, e.g., gold, silver, tin, zinc, iron, copper, cadmium, chromium, nickel, platinum, lead, and the like. Any metal that can be electroplated or otherwise electrodeposited is suitable for use in the disclosed technology.

Aspect 17. The lattice of Aspect 16, wherein the lattice defines a thickness therethrough of from about 1 to about 5,000 μm, e.g., from about 1 to about 5000 μm, from about 5 to about 2500 μm, from about 10 to about 1500 μm, or even from about 50 to about 1000 μm.

Aspect 18. The lattice of any one of Aspects 16-17, wherein the lattice defines a tensile strength of from about 30% to about 100% of the theoretical tensile strength of the metal in porous form, defined as the highest bulk metal tensile strength multiplied by the porous metal's relative density to the second power.

Aspect 19. The lattice of any one of Aspects 16-18, wherein the lattice defines a relative density of from about 15 to about 40.

Aspect 20. The lattice of any one of Aspects 16-19, wherein the lattice defines at least one area of about 0.1 mm² that is free of fully dense metal wider than twice the diameter of single particle. Such a diameter can correspond to the diameter of a particle used to form a template on which the lattice is formed. A single particle diameter can be in the range of from about 200 to about 10,000 nm.

Aspect 21. The lattice of any one of Aspects 16-20, wherein the lattice is characterized as having a Cσ_b value of from about 0.6 MPa and about 2 MPa as applied in the following equation:

${\sigma }_{\mathrm{UTS}}=C{{\sigma }_b\left({\rho }^{*}/\rho \right)}^{1.5}$

Aspect 22. The method of Aspect 7, further comprising converting the polymer to a carbonaceous material. This can be accomplished by, e.g., heat treatment and/or chemical treatment.

Aspect 23. A component, the component including a lattice according to any one of Aspects 16-21. A component can be, e.g., a filter. The lattice of a component can also be used to, e.g., heat a fluid (gas, liquid) disposed in the voids of the lattice.

Aspect 24. A method, comprising: with a magnetized metallic nanolattice (e.g., a metallic ferromagnetic nanolattice according to the present disclosure), contacting a sample comprising a species that includes a magnetic tag to the magnetized metallic nanolattice under such conditions that the magnetic tag of the sample is immobilized to the magnetized metallic nanolattice.

The species can be, e.g., a biomolecule. Example biomolecules include, e.g., cells, vesicles (e.g., exosomes), and the like. The magnetized metallic nanolattice can be demagnetized (e.g., by removing a magnet nearby to the magnetized metallic nanolattice or by eliminating a magnetic field applied to the magnetized metallic nanolattice. This can in turn release the species (which is tagged with the magnetic tag) from the magnetized metallic nanolattice for further analysis and processing. A magnetic tag can be, e.g., a magnetic nanoparticle, a ferromagnetic particle, and the like.

The disclosed technology can also be applied to separations applications, such as bioseparations. One such application is shown in FIG. 13, which depicts an immunomagnetic separations approach. Immunomagnetic separation is a technique of using magnetic materials to capture biomaterials that are tagged with magnetic nanoparticles, e.g., via an antibody reaction between the nanoparticle and the biomaterial of interest.

As shown in the upper left of FIG. 13, one can form an opal template according to the present disclosure and then form bridges (e.g., polymeric bridges) between neighboring particles. One can then deposit a metal (e.g., Ni) onto the bridged template, with the metal filling in the spaces between particles. The opal particles and bridges can be removed (e.g., via dissolving), thereby leaving behind a metallic nanolattice in the form of an inverse opal. One can apply a further coating, which coating can be ferromagnetic. As shown in FIG. 13, such a further coating can be NiFe, as both Ni and NiFe are ferromagnetic. In this way, when the inverse opal is placed in a magnetic field, the ferromagnetic metals will be magnetized. An additional coating (e.g. Au) can be applied, with the additional coating being a material that is non-reactive with the biomaterial of interest.

As shown in the middle panel of FIG. 13, an exemplary device can include an Au coating atop a NiFe coating, which NiFe coating conforms to an inverse opal nanolattice. A targeted biomaterial (e.g., a cancer exosome of interest) can be tagged with magnetic nanoparticles that bind specifically to the target biomaterial, thereby specifically tagging the biomaterial of interest and not tagging biomaterials that are not of interest. A sample that includes the tagged biomaterial of interest is flowed through the exemplary device while the device is magnetized, and the tagged biomaterial of interest is held against the surface of the device while untagged biomaterial flows through the device. The magnetic field can then be reduced or turned off, thereby releasing the tagged biomaterial for collection and further processing. Exemplary data are provided in the right panels of FIG. 13, which exemplary data provide enrichment versus flow rate when inverse opal was magnetized by a magnet (top right) and was non-magnetized, i.e., magnet was removed (bottom right). The enrichment is defined as captured magnetic particles divided by flow-through magnetic particles. As shown, the disclosed technology allows for appreciable sample enrichment, which enrichment can vary by flow rate.

As an alternative, one can coat a nanolattice with a capture molecule (e.g., an antibody, a receptor, a ligand) that is complementary to a biomaterial of interest. A user can then contact a sample that comprises (or is believed to comprise) the biomaterial of interest to the nanolattice, and the capture molecule can capture the biomaterial of interest from the sample. The captured biomaterial can be released and/or further analyzed.

It should be understood that one can deposit (e.g., via electric deposition) polymer onto a lattice so as to at least partially fill and/or coat a lattice or template according to the present disclosure. Similarly, one can use monomer/or other polymer precursors to fill the template or lattice and then solidify the monomers/precursors. The resulting polymer lattice can be further carbonized (e.g., via application of heat) to form a carbon nanolattice.

Claims

1. A method, comprising: effecting evaporation of a carrier fluid from a colloid that comprises the carrier fluid and a population of particles,the colloid contacting a substrate,the evaporation of the carrier fluid giving rise to assembly of at least some of the population of particles into a plurality of template layers defined by a periodic arrangement of the at least some of the population of particles,each of the plurality of template layers being substantially free of particles positioned outside of the periodic arrangement, andthe plurality of template optionally being substantially free of channeling cracks of width greater than two particle diameters,the spacing of adjacent channeling cracks being greater than 100 μm,the evaporation optionally being performed in the presence of a filler fluid,the filler fluid having a vapor pressure lower than the vapor pressure of the carrier fluid, andthe filler fluid entering vacancies between particles resulting from the evaporation of the carrier fluid so as to stabilize the positions of the particles during the evaporation of the carrier fluid.

2. A method, comprising: effecting evaporation of a carrier fluid from a colloid that comprises the carrier fluid and a population of particles,the colloid contacting a substrate,the population of particles being at least about 10 vol % of the colloid,the evaporation of the carrier fluid giving rise to assembly of at least some of the population of particles into a plurality of template layers defined by a periodic arrangement of the at least some of the population of particles,each of the plurality of template layers being substantially free of particles positioned outside of the periodic arrangement, andthe evaporation optionally being performed in the presence of a filler fluid,the filler fluid having a vapor pressure lower than the vapor pressure of the carrier fluid, andthe filler fluid entering vacancies between particles resulting from the evaporation of the carrier fluid so as to stabilize the positions of the particles during the evaporation of the carrier fluid.

3. The method of claim 1, further comprising, with a resin, joining neighboring particles within the plurality of template layers to one another.

4. The method of claim 3, further comprising selectively removing the resin.

5. The method of claim 1, further comprising depositing any one or more of a metal, an oxide, or a polymer onto the plurality of template layers.

6. The method of claim 5, wherein the metal, oxide, or polymer is deposited in a direction from the substrate through a thickness of the plurality of template layers.

7. The method of claim 5, further comprising selectively removing at least some of the plurality of template layers so as to leave behind a metallic, polymeric, or oxide nanolattice, the selectively removing optionally comprising dissolving.

8. The method of claim 1, wherein a particle defines a cross-sectional dimension in the range of from about 200 nm to about 10,000 nm.

9. The method of claim 1, wherein the filler fluid comprises an alcohol.

10. The method of claim 9, wherein the alcohol is glycerol or ethylene glycol.

11. The method of claim 9, wherein the filler fluid is present in the colloid at from about 0.1 vol % to about 40 vol %.

12. The method of claim 1, wherein the particles define a positive charge.

13. The method of claim 1, wherein the method is performed in a continuous manner.

14. The method of claim 1, wherein the plurality of template layers defines a thickness in the range of from about 1 to about 5,000 μm.

15. The method of claim 1, further comprising removing carrier fluid

16. A lattice, comprising: a three-dimensional periodic structure of struts of (i) a metal, a polymeric material, or a carbonaceous material and (ii) spherical voids, the struts and voids being in a periodic arrangement therein,a void defining a cross-sectional dimension in the range of from about 200 to about 10,000 nm.

17. The lattice of claim 15, wherein the lattice defines a thickness therethrough of from about 1 to about 5,000 μm, and

18. The lattice of claim 16, wherein the lattice defines a tensile strength of from about 30% to about 100% of the theoretical tensile strength of the metal in porous form, defined as the highest bulk metal tensile strength multiplied by the porous metal's relative density to the second power.

19. The lattice of claim 16, wherein the lattice defines a relative density of from about 15 to about 40.

20. The lattice of claim 16, wherein the lattice defines at least one area of about 0.1 mm2 that is free of fully dense metal wider than a twice the diameter of single particle.

21. The lattice of claim 16, wherein the lattice is characterized as having a Cσb value of from about 0.6 MPa and about 2 MPa as applied in the following equation:

22. The method of claim 6, further comprising converting the polymer to a carbonaceous material.

23. A component, the component including a lattice according to claim 16.

24. A method, comprising: with a magnetized metallic nanolattice, contacting a sample comprising a species that includes a magnetic tag to the magnetized metallic nanolattice under such conditions that the magnetic tag of the sample is immobilized to the magnetized metallic nanolattice.

25. The method of claim 24, further comprising releasing the magnetic tag of the sample from the magnetized metallic nanolattice.