WO2008097495A1

WO2008097495A1 - Three-dimensional particles and related methods including interference lithography

Info

Publication number: WO2008097495A1
Application number: PCT/US2008/001428
Authority: WO
Inventors: Edwin L. Thomas; Ji-Hyun Jang; Chaitanya K. Ullal; Steven E. Kooi; Cheong Yang Koh
Original assignee: Massachusetts Institute Of Technology
Priority date: 2007-02-02
Filing date: 2008-02-01
Publication date: 2008-08-14

Abstract

The present invention generally provides compositions comprising particles having various sizes and shapes, as well as methods for production of such particles. Particles of the invention may comprise complex, multi-valent structures. In some cases, the particles may have at least one concave surface. The present invention may advantageously provide facile, high yielding methods for producing complex particle structures. The particles may exhibit novel optical or mechanical properties, making them useful as photonic crystals, phononic crystals, mictrotrusses and microframes, multivalent colloidal particles, delivery agents, or the like.

Description

THREE-DIMENSIONAL PARTICLES AND RELATED METHODS INCLUDING

INTERFERENCE LITHOGRAPHY

Field of the Invention The present invention generally provides particle compositions and related methods.

Background of the Invention Self-assembly of "simple" spherical colloidal particles has applications in chemical sensors, biomaterials, optical components, as well as photonic crystals. The use of anisotropically shaped particles as the constituent building blocks can provide increased possibilities for use in additional applications, not only from inherent material properties of the anisotropically shaped particles, but also from the novel types of particle packing exhibited such particles. In some cases, polymer-based micro- or nano- particles with specific size and shape have been widely used for drug delivery. For example, viruses, one type of biological nanoparticle with specific point group symmetries, and metallic nanoparticles have been suggested as building blocks for supramolecular architectures as nanosensors for rapid detection of clinically relevant viruses. To date, most fabrication methods for nonspherical particles have involved the modification of spherical particles. For example, prolate ellipsoids have been produced by heating and then deforming spherical particles embedded in a matrix, followed by cooling to retain the anisotropic shape. Irradiation of spherical colloids containing azo units by polarized light has also produced particles with an aspect ratio of over 2. Highly ordered polyhedra have been fabricated through compaction-sintering of colloidal spheres. Precise shape control of colloidal particles has been demonstrated by the use of photolithography with 2D masks. However, this control is often restricted to 2D or quasi 2D structures. Interfacial tension between the particle and the solvent during the synthesis of colloidal particles in the liquid phase, such as in microfluidic channels, generally restricts the generation of particles to spheres or modified spheres with rounded edges. Ellipsoidal particles have been recently produced via 2D phase mask interference lithography, but such methods often do not offer sufficient control over rational design to produce complex shapes. Optical lithography has been successful in the ability to create two-dimensional patterns spanning the range often nanometers to several microns and can, in some cases, facilitate the extension of Moore's law and the continued development of computational power. However, the fabrication techniques, including "self-assembly-based" techniques and "construction-based" assembly, for three-dimensional structures on this length scale can present challenges. For example, self-assembly often relies on the use of thermodynamic forces to spontaneously pattern components into stable structures, and construction based techniques typically involve piece-by-piece creation or placement of components into the appropriate structure. While self-assembly may achieve large area coverage in a short time and in an inexpensive fashion, and construction-based approaches may allow for the fabrication of arbitrary structures, they can involve the construction of structures in a serial manner, either point-by-point or layer-by-layer. Such techniques are often time-consuming processes and require attention to registrations and joining of the component parts. Accordingly, improved methods are needed.

Summary of the Invention

The present invention provides methods of forming particles comprising providing a precursor material; effecting differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures optionally interconnected; removing material adjacent the particulate material and separating, if interconnected, particles from each other, wherein at least some of the particles have a surface including at least one concave portion.

The present invention also provides methods of forming particles comprising providing a precursor material; effecting differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures optionally interconnected; removing material adjacent the particulate material and separating, if interconnected, particles from each other, wherein at least some of the particles are not spherical or ellipsoidal.

The present invention also provides methods of forming particles comprising providing a particle precursor material; establishing a standing wave pattern in the precursor material, the standing wave pattern defining a template for a plurality of particles and resulting at least in part from the interaction of energy emitted form at least two sources, under conditions causing differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures optionally interconnected; removing material adjacent the particulate material and separating, if interconnected, particles from each other. The present invention also provides methods of forming particles comprising providing a precursor material; effecting differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures that are interconnected; removing material adjacent the particles and separating the particles from each other.

The present invention also provides methods of forming particles comprising providing a precursor material; differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network, the interconnected network defining a three-dimensional matrix; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures optionally interconnected; removing material adjacent the particulate material and separating, if interconnected, particles from each other. - A -

The present invention also relates to compositions comprising a synthetic particle comprising at least one substantially concave portion and at least three valence points, each valence point being a location at which at least three surface portions of the particle meet, no two of the at least three surface portions being coplanar or defining a common spherical portion, and at least two of the at least three portions being concave, wherein the particle has a particle size of 50 microns or less.

The present invention also relates to compositions comprising an interconnected network of individuated particles, wherein each particle is attached to one or more adjacent particles via at least three valence points, each valence point being a location at which at least three surfaces, or surface portions, of the particle meet.

Brief Description of the Drawings

FIG. IA shows (i) an SEM image of an interconnected structure of "four-valent" particles and (ii) a single, "four-valent" unit cell. FIG. IB shows (i) an SEM image of an interconnected structure of "four-valent" particles after UV/ozonylsis, (ii) a single, "four-valent" particle, and (iii) a theoretical model of a single, "four-valent" particle in lower insets iv and vi, respectively.

FIG. 1 C shows (i) an SEM image of an interconnected structure of "six-valent" particles and (ii) a single, "six-valent" unit cell. FIG. ID shows (i) an SEM image of an interconnected structure of "six-valent" particles after UV/ozonylsis, (ii) a single, "six-valent" particle, and (iii) a theoretical model of a single, "six-valent" particle in lower insets iv and vi, respectively.

FIG. 2 A shows (i) a theoretical model of a 4 x 4, two-dimensional square lattice and (ii) a single unit cell of the square lattice. FIG. 2B shows an SEM image of an experimental two-dimensional square lattice fabricated in SU8.

FIG. 2C shows (i) a theoretical model of a 3 x 3 x 3 3D cubic lattice and (ii) a single unit cell of the cubic lattice.

FIG. 2D shows SEM images of (i) an experimental cubic lattice fabricated in SU8 and (ii) a magnified, tilted SEM image of the cubic lattice viewed along the <11 1> direction. FIG. 3 A shows theoretical models of a single unit cell of an interconnected structure having a square lattice (i) having 40% volume fraction and (ii) having 85% relative light intensity, and (iii) a single particle of the square lattice after isotropic etching by strong solvent. FIG. 3 B shows theoretical models of a single unit cell of an interconnected structure having a cubic lattice (i) having 35% volume fraction and (ii) having 75% relative light intensity, and (iii) a single particle of the cubic lattice after isotropic etching by strong solvent.

FIG. 4 shows a schematic representation of the use of (a) negative resists and (b) positive resists to produce patterned, three dimensional structures.

FIG. 5 A shows a general fabrication process of a conformal phase mask, for use in phase mask lithography.

FIG. 5B shows a lithographic setup for use in phase mask lithography.

FIG. 5 C shows (i) an SEM image of a PDMS phase mask comprising an array of circular holes (280 run in diameter and 600 run high on a 750 nm square lattice) and (ii) an SEM of the resulting three-dimensional structure created from the phase mask, and (iii) a computed theoretical intensity distribution for a 2 x 2 x 2 array of unit cells.

FIG. 6 shows (a) illustrative optical components for multibeam interference lithography, (b) a six-beam lithographic setup comprising a prism, (c) an SEM image of P surface into SU-8 fabricated, and (d) a computed theoretical intensity distribution for a 2 x 2 x 2 array of unit cells.

FIG. 7A shows (i) the chemical composition of an SU-8 negative resist and (ii) a photochemical reaction mechanism of the SU-8 negative resist, according to one embodiment of the invention. FIG. 7B shows (i) the chemical composition of a DNQ novolac positive resist and (ii) a photochemical reaction mechanism of the DNQ novolac positive resist, according to one embodiment of the invention.

FIG 8 shows the UV absorbance spectra for (a) a SU-8 negative resist and (b) DNQ novolac positive resist (i) before exposure to UV light and (ii) after exposure to UV light. FIG. 9 shows the schematic diagram demonstrating surface changes with treatment by HMDS (from R. Dammel, SPIE Optical Engineering Press 1993, TTIl). FIG. 10 shows SEM images of (a) a SU-8 ILT structure with R3m symmetry and (b) an inverse TiO₂ structure after infiltration of the SU-8 ILT structure with TiO₂ and subsequent calcination to remove the SU-8 ILT structure.

FIG 11 shows SEM images of the P surface level set structure for (a) a P surface structure with periodicity of 2.7um in SU-8, (b) a P surface structure with periodicity of 1.2 um in SU-8 fabricated using the same wavelength of light as FIG. 1 IA but with a smaller the angle between pairs of beams, (c) an inverse structure of FIG. 11 Avia TiO₂ infiltration, and (d) the reflectivity data of the TiO₂ inverse structure. FIG. 12 shows (a) an SEM image of elastomeric PDMS 3D network/air structure,

(b) AFM images of the sample (i) before and (ii) after deformation, and (c) a BLS spectrum measured along the [lθ 1 θj direction from J. H. Jang, C. K. Ullal, T. Gorishnyy, V. V. Tsukruk, E. L. Thomas, Nano Lett. 2006, 6, 740.

FIG. 13 shows (a) an SEM image of a plastically deformed polymer microframe structure, including (i) a region having a microframe bridge extending from one side of a crack to the other, and (ii) extensive shear, bending and microplastic deformation of the structure near the left terminus of the bridge, (b) an SEM images of the structure, wherein plastic deformation and fracture of transverse beams or "arms" are shown, with up to several hundred % strain in the vicinity of a fracture, (c) an SEM image of a compressed portion of the structure, (d) a cross section of the plastically deformed region of the structure, and (e) microfibrils formed due to peeling of microframe from substrate.

FIG. 14A shows (i) an SEM image of "4-line valent" polymer particles synthesized by interference lithography, (ii) a magnified SEM image of an individual "4- line valent" particle (scale bar = 300 nm), and (iii) calculated light intensity distributions for a single, 4-line valent particle.

FIG. 14B shows (i) an SEM image of "6-point valent" polymer particles synthesized by interference lithography, (ii) a magnified SEM image of an individual "6- point" particle (scale bar = 300 nm), and (iii) calculated light intensity distributions for a single, 6-point particle. FIG. 15 shows the theoretical structure of 2 x 2 x 2 structures having (a) R3m symmetry of a three term "diamond-like" structure and (b) Pm3m(221) symmetry of a Schwarz P surface. Other aspects, embodiments and features of the invention will become apparent from the following detailed description when considered in conjunction with the accompanying drawings. The accompanying figures are schematic and are not intended to be drawn to scale. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the invention shown where illustration is not necessary to allow those of ordinary skill in the art to understand the invention. All patent applications and patents incorporated herein by reference are incorporated by reference in their entirety. In case of conflict, the present specification, including definitions, will control.

Detailed Description

The present invention generally provides particle compositions and related methods.

In some cases, the present invention provides methods for production of materials including particles having various sizes and shapes. The method may comprise exposing a particle precursor material to a source of external energy to form a three-dimensional structure or pattern within the particle precursor material. The three-dimensional structure may be further processed to form the desired material. The present invention also provides compositions comprising particles (e.g., synthetic particles) having complex, geometrical structures. In some embodiments, the particles may be interconnected to form a network. The present invention may advantageously provide facile, high yielding methods for producing complex particle structures including structures having multiple surface portions (i.e., distinct portions of a surface), multiple points or arms, and/or structures having concave surfaces. The particles may exhibit novel optical or mechanical properties, making them useful as photonic crystals, phononic crystals, mictrotrusses and microframes, multivalent colloidal particles, or the like. In some embodiments, the particles may comprise stimuli-responsive materials, including pH-responsive or temperature-responsive materials, and may be useful in applications including drug delivery. In some cases, the invention provides the ability to readily fabricate a wide variety of complex structures on the nano- and submicron scale. For example, the invention may provide methods wherein a precursor material is exposed to an external source of energy, wherein the external source of energy includes information related to structural characteristics of the desired structure, including symmetries and/or other geometrical elements. Upon application of the external source of energy, the information may be transferred and/or translated to the precursor material to produce the desired structure, for example, via interference lithography. Thus, in some embodiments, the present invention advantageously provides the ability to "dial in" the appropriate parameters (e.g., shape, symmetry, geometry, and other structural characteristics) to produce a desired structure.

As noted above, the present invention may advantageously provide compositions comprising particles (e.g., synthetic particles) having complex geometrical shapes including particles having multiple surfaces, or interconnected networks of such particles. The particles, or networks thereof, may have a particular shape, size, and/or valency. In some cases, at least some of the particles are not spherical or ellipsoidal. In some cases, substantially all of the particles are not spherical or ellipsoidal. In some cases, at least some of the particles have a surface including at least one concave portion. In some embodiments, the particles may comprises multiple surface portions, wherein each surface is substantially concave. For example, the particles may comprise multiple valence points and/or concave surface portions to form a complex geometrical shape. FIG. 1 shows examples of structures comprising concave surfaces. For example, FIG. IB shows a particle comprising six surface portions, wherein the six surface portions are each concave. FIG. ID shows a particle comprising eight surface portions, each being concave. It should be understood that other particles comprising any number of surface portions may also be obtained by methods of the invention.

The present invention may also provide particles comprising a particular valency. The term "valency" may be used to refer to the minimal number of valence points in a structure required to define a three-dimensional shape. As used herein, "valency" may also be used to refer to the number of outermost points within a structure, i.e., the number of "arms" or "valence points" in a structure. As used herein, a "valence point" refers to location of a particle at which at least three surface portions of the particle meet, such that no two of the at least three surface portions are coplanar or define a common spherical portion. In some embodiments, at least two of the at least three portions are concave. In some cases, each of the three portions are concave. In cases where individual particles are obtained by separation from an interconnected network of particles, the valency of the individual particle may be determined by the number of interconnecting arms that were broken to separate the particle from the network. For example, the particle in FIG. IB comprises a "four- valent" structure while the particle in FIG. ID comprises a "six-valent" structure. In other embodiments, the structure may have at least 4 arms, at least 6 arms, at least 12 arms, or greater. It should be understood that other particles (e.g., multi-arm particles) comprising any number of valence points may also be obtained by methods of the invention. The particles may also comprise a shape and/or valency corresponding to any crystallographic point group symmetry, including triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, cubic, and the like.

In some embodiments, the compositions may comprise a synthetic particle comprising at least one substantially concave portion and at least three valence points. In some cases, the particle comprises at least four, six, eight valence points, or more. Some embodiments of the invention provide particles comprising at least six surface portions, wherein no two of the at least six surface portions are coplanar or define a common spherical portion, and each of the surface portions is concave. Other embodiments of the invention provide particles comprising at least eight surface portions, wherein no two of the at least eight surface portions are coplanar or define a common spherical portion, and each of the surface portions is concave.

Compositions described herein generally comprise synthetic materials, including synthetic particles. As used herein, a "synthetic" material refers to a material that is synthesized, fabricated, or otherwise manipulated in a laboratory setting. That is, the synthetic material may have a structure (e.g., chemical structure, shape, size, etc.) or may exhibit properties not present in the material or material precursor prior to treatment in a laboratory setting. In some cases, the material may be synthesized in a laboratory setting. In some cases, the material may comprise a naturally-occurring material that is treated, processed, or manipulated to exhibit properties that were not present in the naturally-occurring material, prior to treatment. For example, a three-dimensional structure produced using holographic interference lithography may be a synthetic material. However, a naturally-occurring material that is not somehow manipulated in a laboratory setting, such as a plant allergen, for example, is not a synthetic material. In some cases, the invention provides synthetic particles comprising a polymeric material, glass, ceramic, metal, metal-ceramic composite, semiconductor material, and/or combinations thereof

The present invention may also provide particles comprising a particular particle size. For purposes of this application, "particle size" of a particle (non-agglomerated) is its maximum cross-sectional dimension taken along an x, y, or z-axis. For example, the maximum cross-sectional diameter of a four-point, square particle may be the maximum distance between two valence points of the particle. The "average particle size" of a particle composition is the numeric average of the "particle size" of a representative number of primary particles (non-agglomerated) in the composition. For the values in the description and claims of this application, the particle sizes are determined using microscopy techniques, such as scanning electron microscope (SEM) or atomic force microscopy (AFM) techniques.

In some embodiments, the particle has a particle size of 50 microns or less, 25 microns or less, 10 microns or less, 5 microns or less, 1 micron or less, 500 nm or less, 250 nm or less, 100 nm or less, or, in some cases, 50 nm or less. In some cases, the particles of the invention may have a particle size between about 1 nm and 50 microns. In other embodiments, the particles of the invention may have a particle size between about 25 nm and 10 microns. In other embodiments, the particles of the invention may have an average particle size of between about 50 nm and 2 microns.

Some embodiments of the invention may provide compositions comprising an interconnected network of individuated particles, wherein the particles may have a particle size, shape, valency, and/or other particle characteristics as described herein. In some embodiments, each particle of the interconnected network may be attached to one or more adjacent particles via at least three valence points. In some cases, an individual particle may be attached to one or more adjacent particles, each via a single valence point. For example, within an interconnected network, a particle comprising four valence points may be positioned proximate four adjacent particles, wherein the particle is connected to each of the four, adjacent particles via one valence point of the particle. In some cases, the particle may be connected to one of more adjacent particles via valence points of the particle, and may further comprise valence point(s) not connected to an adjacent particle. The interconnected network may comprise individuated particles attached via a connecter, "branch," "arm," or node of the network, such that the interconnected network defines a continuous material comprising many particles. However, though interconnected to form a continuous material via connecter(s), the particles may still be individuated structures that can be distinguished from an adjacent, individuated structure. In some cases, a connector between two adjacent, connected, individuated particles may include a location having the minimum cross-sectional area of the connector, wherein the location indicates the points at which one individuated particle is distinguished from the adjacent, connected, individuated particle. In some embodiments, the total area of all the minimum cross-sectional areas of each connector of an individuated particle is no more than 10%, no more than 5%, or no more than 1% of the total surface area of the individuated particle.

As noted above, the invention also provides various methods for fabricating compositions described herein. In some cases, the method may comprise effecting a differential reaction within the precursor material to define a pattern or template for particle formation. That is, a first portion of the precursor material may be reacted while another portion of the precursor material may be reacted in a different manner than the first portion or may remain unreacted. In some cases, upon formation of the pattern or template, the precursor material may comprise a first portion which may define the particle and a second portion which may define an area adjacent the first portion. In some cases, removal of either the first portion or the second portion may then produce the particle structures, optionally interconnected. In some cases, the portion of the sample exposed to the source of external energy may be used to form the resulting, solid structure. In other cases, the unexposed portion may be used to provide the resulting, solid structure.

The act of effecting the differential reaction may comprise, for example, exposure to an external source of energy. The external source of energy may an electric, magnetic, optical, acoustic, electromagnetic, or mechanical field. In some embodiments, the external source of energy is electromagnetic radiation. In some cases, differential reaction may comprise, for example, polymerization and/or crosslinking of the precursor material. The reaction may also comprise other methods capable of causing the precursor material to become hardened or insoluble with respect to, for example, a developing solvent. In some embodiments, the template may be formed by establishing a standing wave pattern in the precursor material, wherein the standing wave pattern defines a template for a plurality of particles and results at least in part from the interaction of energy emitted form at least two sources. In some cases, at least two source of electromagnetic radiation may be used to establish the standing wave pattern.

The template may comprise an interconnected network of material solidified relative to material surrounding the interconnected network, and a particulate material may then be formed in a pattern directed by the template. In some cases, the template may require a developing process, for example, by removing the material adjacent the particulate material to produce the desired structure. For example, removal of the material adjacent the particulate material may involve sintering, etching, addition of chemical agents (e.g., solvents), or the like. In some cases, the template may not require a developing process.

As noted above, the particulate material may be formed in the shape of an interconnected network comprising individuated particle structures, optionally interconnected. In cases where the particles are interconnected, the method may further comprise separating the individual structures while maintaining the size and shape of the particles. The particles may be separated using various methods, including exposure to oxygen plasma or UV/ozonolysis conditions, or by application of mechanical forces. In some embodiments, the template may comprise a mold for particle formation.

For example, upon formation of a template interconnected network by effecting the differential reaction, the template may be developed by removing the material surrounding the template interconnected network to define an interconnected void, at least part of which may be filled with auxiliary material. The auxiliary material may then be allowed to at least partially solidify as the particulate material, wherein the template then defines the material adjacent the particles which is removed. In some embodiments, the auxiliary material comprises a polymeric material, glass, ceramic, metal, metal-ceramic composite, semiconductor material, combinations thereof, or precursor thereof. Methods of the invention may utilize holographic interference lithography (HIL), a process which involves the formation of a time independent spatial variation of intensity created by the interference of two or more sources of external energy, to pattern the desired structure within a bulk sample of particle precursor material. That is, a sample material may be exposed to at least two sources of external energy to produce a geometrical structure within the bulk of the sample material at the location(s) where the at least two sources of external energy meet or interfere. The pattern that emerges out of the intensity distribution may be transferred to a light sensitive medium, such as a photoresist, to yield structures. Holographic interference lithography (HIL) may allow for control over the detailed geometry of the structures being fabricated, while it has inherent registration and component joining resulting in the rapid creation of large area single crystal structure. Interference lithography may allow one to create ID, 2D and 3D periodic patterns very simply using coherent beams of light. The inherent periodicity present in the light may be exploited to create structures using this technique. Typically, interference lithography involves the formation of a stationary spatial variation of intensity created by the interference of two or more beams of light. The pattern that emerges out of the intensity distribution is transferred to a light sensitive medium, such as a photoresist, to yield structures.

By selecting the appropriate parameters for the sources of external energy, the geometrical elements and volume fraction of the resulting structures may be controlled. For example, manipulation of the experimental parameters of intensity, polarization, phase and wave vectors of the interfering sources may allow one to target specific space group structures. In some embodiments, the use of a small number of, for example, electromagnetic radiation beams may result in a higher contrast in the electromagnetic radiation intensity distribution with regions of high intensity being concentrated in Wyckoff sites of low multiplicity and high symmetry. The valency of the resultant particles may be determined by the connectivity of these Wyckoff sites and the process by which they become disconnected. In some cases, the structure produced by HIL comprises a network of particles interconnected by thin, connecting arms at the valence points of the structure, as shown in FIG. IA. To obtain individual particles, the network may be disconnected by breaking the connecting arms while maintaining the structural integrity of the individual particles. The thickness and crosslinking density of the connecting arms may be reduced by decreasing the exposure and/or by subsequent strong development. The particles can be separated either by various methods known in the art, such as chemical etching with O₂ plasma, UV/ozonolysis, or by mechanical forces. For example, water may be crystallized in the air regions of the lightly crosslinked structure. After solidification of the water, the volume change on crystallization may induce mechanical disconnection at the thin arms with little or substantially no loss of particle shape. In some cases, supercritical drying CO₂ (e.g., CO₂ drying) may be used to improve the quality of the resultant three-dimensional pattern by avoiding the destructive effects of surface tension. For example, supercritical CO₂ development for the negative type molecular-glass photoresist may alleviate pattern collapse in densely packed, high- aspect-ratio structures. Replacement of water with pentane or hexane, which have lower surface tensions (73.05 mN/m, 13.72 mN/m, and 18.43 mN/m for water, pentane, and hexane respectively at 20 ⁰C) has been proposed as an alternative method. Another approach to reducing or eliminating the surface tension problem is to take advantage of the etch selectivity of oxygen for silicon-containing polymers that can form a protective oxide layer when exposed to an oxygen plasma. It has been reported that a critical threshold concentration of 10-15% silicon in the polymer significantly improves O₂-RIE resistance by formation of SiO₂ layer. A dry developable resist can serve as an alternative resist in which the silicon-containing group is deprotected by an acid catalyzed reaction and subsequently dry developed by an oxygen plasma.

In some cases, particles having both anisotropic geometry and anisotropic chemical properties may be formed. The particles may be fabricated to comprise different regions having different chemical properties, such as hydrophobicity, hydrophilicity, or the like. For example, a particle may have a substantially hydrophobic body, with hydrophilic portions at the ends of the valence points. In another example, deposition of a particle, or network of particles, onto the surface of the crosslinked polymer lattice followed by disconnection may introduce a different chemical functionality at the vertices of the particles. In some cases, particles responsive to pH or temperature may be produced from, for example, hydrogels or other materials responsive to external stimuli. Additional types of particles, or interconnected networks of particles, from other materials can be made by, for example, infiltration of the parent polymer template (via, for example, electrodposition, chemical vapor deposition, sol-gel deposition, etc.) with, for example, a sol-gel to create polymer-ceramic composites, and after a suitable removal of the polymer and etch, interesting complex particles such as silica and Fe₂O₃, etc., can be made. Other examples of non-organic materials that may be used in this method include, but are not limited to, CdSe, TiO₂, CaCO₃, as well as other non-organic materials described herein.

In addition to being able to control shape and symmetry of the particles obtained, the methods described herein may provide control over the dispersity and yield of the particles. In some cases, large surface area 3D structures (e.g., several mm²) with submicron features have been demonstrated. In one illustrative embodiment, for a 6-inch wafer and 10 micron thick film containing 10 unit cells along the thickness direction, approximately 10⁹ particles may be obtained using the methods described herein. Since the periodicity of the parent structure, and hence size of particles, may be selected or fixed by the wavelength of and the angle between the interfering beams, an extremely narrow size distribution of particles may be readily achieved.

Some embodiments of the invention also provide methods for modulating dispersity in the volume fraction distribution of the particles. Volume fraction of the individual particles may depend on the volume fraction variation across the parent structure (e.g., interconnected network of particles), depending on the local intensity dose during the exposure of the photoresist. In some cases, the use of a flat top beam profile or expanded interfering beams may allow for a high yield of complex colloids with a tight distribution both from a size and volume fraction perspective. Alternatively, by deliberate application of a spatially varying intensity profile, a tailored volume fraction distribution of particles may be obtained. In some cases, changing the exposing wavelength and/or varying the angle between the beams can vary the size of the colloidal particles obtained. In some cases, such as the 6 connected P surface particles, control over the volume fraction may be greater as the parent structure is continuously size scalable with the interference lithography setup configuration. In thicker films volume fraction variation may also be introduced by chirp in the parent structure due to absorption in the photoresist film. This can be mitigated by using thinner films or photosensitizer dyes.

The particle precursor material can be reacted via one of the many techniques known in the art. For example, the reaction may comprise exposure to an external source of energy, such as an electric, magnetic, optical, acoustic, electromagnetic, or mechanical field. In some cases, the external source of energy may be a source of electromagnetic radiation, including visible, ultraviolet, X-ray, and infrared radiation. In some embodiments, the external source of energy comprises ultraviolet radiation. In some embodiments, at least two beams of electromagnetic radiation may be used to establish a standing wave pattern. As used herein, a "standing wave" refers to a wave that remains in a substantially constant position, which may be formed by the interference between at least two waves traveling in opposite directions.

Compositions (e.g., particles, interconnected networks, etc.) and methods of the invention may be useful in various applications. The ability to fabricate three- dimensional, porous, bicontinuous large area, single crystalline micro and nanostructures with control over the geometry and volume fraction with access to other materials platforms has important implications for a number of fields.

In some cases, the invention may be useful in the fabrication of photonic crystals. Photonic crystals can be described as dielectric composites with periodically varying refractive indices, which allow for the control of the interaction of light and matter. This functionality depends both on the materials parameters as well as the geometry of the system employed. The idea, first proposed by Yablonovitch, centers around the concept that full three dimensional spatial periodicity of λ/2 in the refractive index can result in a range of frequencies in the electromagnetic spectrum near the wavelength λ not being able to propagate, irrespective of direction. This is an extension of the principle behind Fabry-Perot resonators into three dimensions. Such photonic crystals hold the promise of numerous applications in integrated optical circuits such as control of the spontaneous emission of light, bending of light around sharp corners for waveguides, and all on-chip optical transistors.

The use of interference lithography to create photonic crystal structures utilizes the inherent periodicity of light to create periodic structures that, in turn, may interact in interesting ways with electromagnetic waves. Strong physical insight into the existence of band gaps can be obtained by viewing these low order Fourier term structures as having sinusoidal modulations along principal directions of the Bravais Lattice. When the gaps associated with each of these sinusoidal modulations overlap, one can obtain a structure with complete photonic band gap, that is, a structure which for a given band of frequencies has no propagating modes regardless of the polarization and propagating direction of the light. The P structure is of particular interest since it is easily size-scalable without resorting to a multiple exposure technique and the associated problem of registration between gratings. This is possible since the three gratings that make up the P structure are perpendicular to each other. FIG 11 shows SEM images of the P surface level set structure for (a) a P surface structure with periodicity of 2.7um in SU-8, (b) a P surface structure with periodicity of 1.2 urn in SU-8 fabricated using the same wavelength of light as FIG. 1 IA but with a smaller the angle between pairs of beams, (c) an inverse structure of FIG. 11 Avia TiO₂ infiltration, and (d) the reflectivity data of the TiO₂ inverse structure. Realizations of the P structure with different spacings via the single exposure of multiple laser beams of 532 nm are shown in FIGS. 1 IA-B, where periodicity is controlled by simply varying the angle between pairs of beams from 7.2° (FIG. 11 A) to 16.3° (FIG. HB).

To produce a structure with strong photonic effects, the refractive-index contrast may be enhanced by exchanging the polymeric ILT with a material with a higher index of refraction. The sol-gel method for infiltration used is as previously described. Since the P surface is a self-complementary structure, the inverse P from the infiltration of TiO₂ into the SU-8 ILT is also a member of the P surface family. FIG. 11C is the SEM image of a TiO₂ inverse P and associated reflectance spectrum. P structures have only a partial photonic bandgap at the dielectric contrast of 5.3:1 which corresponds to that of TiO₂/air. The reflectivity peak of FIG. 11C measured for the (100) plane is shown in FIG. HD.

In some embodiments, the invention may be useful in the fabrication of phononic crystals, which are the acoustic counterpart of photonic crystals. Phononic crystals allow for control over propagation of mechanical (acoustic and elastic waves) by forming gaps in a phononic dispersion relation of a medium. As a result, mechanical waves with frequencies within the gap are completely forbidden from propagation. Phononic crystals have potential for many interesting applications. For example, by creating band gaps in sonic frequency range (20 Hz - 20 kHz) one can make sound and noise isolation structures. This feature may be of interest, for example, for structural and architectural acoustics. Higher frequency ultrasonic waves (100 kHz- 100 MHz) are widely employed in ultrasonic imaging and medical diagnostics. Ultrasonic phononic crystals may be useful as acoustic superlenses that operate based on negative refraction effect. Such lenses can dramatically improve resolution and efficiency of the current acoustic imaging technology. Finally, at very high hypersonic frequencies (IGHz - 1 THz), phononic crystals may influence electronic, optical and thermal properties of materials.

To fabricate phononic crystals one must create structures with mechanical properties (e.g., density and elastic constants) that vary periodically in space. In some cases, interference lithography may be suited for such fabrication. Currently phononic structures have been fabricated via interference lithography to operate at frequencies ranging from 500 MHz to 5 GHz which is ideal for high resolution acoustic imaging. Interference lithography fabricated structures may consist of two bicontinuous networks, one of which may be a solid material (most often polymer resist) while the other may be air. In contrast with photonic crystals, mechanical contrast between polymers and air is very large (p_epoxy/p_air~10³). As a result, complete phononic band gaps can be opened directly in polymer-air structures, without need for additional pattern transfer to a different (e.g. inorganic) material system. Another advantage of interference lithography polymers may be their optical transparency, which allows for the use of optical techniques to characterize the phononic dispersion relation of a structure. In particular, Brillouin light scattering (BLS) has been used to directly measure phononic band diagrams of a number of polymer phononic crystals. It may be desirable to tune the band diagram of phononic (and photonic) crystals after their fabrication. Such tuning may allow, for example, the creation of a lense with a focal distance that can be modified dynamically during operation. In addition, such tuning may also be used to create filters and resonators with adjustable frequencies of operation. Interference lithography may also be used to generate 3D patterns in elastomeric materials, such as PDMS. These materials can then be deformed reversibly and repeatedly leading to mechanical tuning of their dispersion relation. FIG. 12 shows (a) an SEM image of elastomeric PDMS 3D network/air structure, (b) AFM images of the sample (i) before and (ii) after deformation, and (c) a BLS spectrum measured along the [lOToJdirection from J. H. Jang, C. K. Ullal, T. Gorishnyy, V. V. Tsukruk, E. L. Thomas, Nano Lett. 2006, 6, 740. The deformation is observed to result in distortion of Brillouin zone and leads to a shift in the band diagram. In addition, one of the modes that is present in the unstrained sample disappears after the deformation. This is likely the result of the change in symmetry of the lattice.

Compositions and methods of the invention may also be useful in the fabrication of various structures having advantageous mechanical properties, including microtrusses and microframes. For example, the mechanical response of truss-and frame-like arrangements can be affected by the shape and topology of the material, as well as the type of material. Given the length scales over which structures may be created, one might expect to encounter length scale dependent mechanical behavior. Interference lithography can afford control over the geometry of the structures, and may provide the ability to make bicontinuous structures. This means that in addition to carrying loads, the structure can be used to impart additional functionalities. For example, if one of the phases is air, the construct could be used for cooling depending on the size scale of the connected pore space.

The ability to control the topology of the structures may assist in making truss and frame-like structures via interference lithography. Just as at larger length scales, suitable geometries depend on the particular application. For example, topologies that are stiff, strong and bicontinuous may be desired. In some embodiments, stretch dominated structures may be desired, in which all the members of the structure are in tension/compression, as opposed to structures that are bending dominated. It has been demonstrated that such properties can be achieved in lattice structured materials consisting of rods with node connectivities of 12. Further, it has been demonstrated by FEM that the elastic mechanical response of air holes on the basic cubic lattices are superior to their rod connected counterparts. Depending on the set of mechanical properties targeted, once a particular geometry is identified, approximations to these structures can be achieved by interference lithography. Compositions and methods of the invention may also be useful in the fabrication of multivalent colloidal particles. Many structured materials made via self-assembly are based on simple spherical colloids (e.g. magnetic materials, photonic crystals, microlenses, and templates). A particular need in nanotechnology may be to create individual particles with controlled shapes and to have a scalable process that allows fabrication of useful quantities of such particles. The use of more sophisticated shaped 3D particles as the constituent building blocks offers increased functionality in a self- assembled device not only due to the constituent materials, but also from variety in packing. As described herein, interference lithography may afford control over geometry by filling and connecting high symmetry Wyckoff sites in the lattices that it creates. This suggests the possibility of creating particles with targeted 'valencies' if these Wyckoff sites are 'disconnected' in the appropriate 2D and 3D structures. In addition to being able to control shape and symmetry in the particles obtained, this technique has the potential to provide tight control over size and yield.

In an illustrative embodiment, various 3D intensity patterns were designed that would create such particles. Beam parameters and process conditions were used such that the intensity along the arms between nodes would be so low as to not be able to create a stable polymer region, whereupon washing/harvesting of the structure, only the node regions would be solid particles. As a first step to disconnect the structure, a low cross- linked region volume fraction was achieved by lowering the light intensity and by subsequent removal of the low crosslinked regions using a strong development. The particles became separated at the lightly-connected thin arms by either chemical etching with UV/ozonolysis or by mechanical forces, for example, from the expansion due to the freezing of water in the continuous matrix region. FIG. 14 shows particles synthesized using this process.

FIG. 14A shows (i) an SEM image of "4-line valent" polymer particles synthesized by interference lithography, (ii) a magnified SEM image of an individual "4- line valent" particle (scale bar = 300 nm), and (iii) calculated light intensity distributions for a single, 4-line valent particle. FIG. 14B shows (i) an SEM image of "6-point valent" polymer particles synthesized by interference lithography, (ii) a magnified SEM image of an individual "6-point" particle (scale bar = 300 nm), and (iii) calculated light intensity distributions for a single, 6-point particle. The materials may also be constructed to be responsive to an external stimulus

(e.g., pH, temperature or magnetic fields, other sources of external energy) and loading them with an agent, such as a therapeutic or diagnostic agent (e.g., functionalized quantum dots). Alternatively, if a diamond network were employed instead, the node regions would be 4-functional and after pinch off, and 43m point group objects with tetrahedral symmetry could be harvested. Deposition of materials onto the surface of the crosslinked polymer lattice followed by the disconnection may introduce a different chemical functionality at the vertices of the particles, thereby providing the possibility of having particles with both anisotropic geometry and chemistry.

Interference lithography is a fast and relatively easy technique capable for fabricating finite complex 3D structures. The fabrication may result in defect-free, high fidelity single crystalline structures that cover a large area. Phase mask lithography using 2D masks may allow for the fabrication of very large area 3D nanostructures in a simple way. Other applications of the present invention may involve producing photonic crystals with complete band gaps via double inversion method and the mechanical properties of the inverse ceramic microtruss structures. Also, 3D hydrogel structures useful in biological applications such as cell patterning or drug release may be obtained. Additionally, the particles may be re-assembled by the introduction of proper functional groups at tips of the particles.

A wide variety of materials may be used as particle precursor materials, as described herein. The particle precursor material may be any material that is capable of reacting upon exposure to an external source of energy such as one or more beams of electromagnetic radiation. In some cases, the particle precursor material may comprise a group that, upon exposure to electromagnetic radiation, may react to form a polymer or cross-linked polymer. Those of ordinary skill in the art would be able to select the appropriate materials for the formation of particles as described herein. For example, in cases where electromagnetic radiation is employed to form the structure, the particle precursor material may be selected to be optically transparent at the wavelength of the electromagnetic radiation. In some cases, the strong absorption of photoactive compounds in particle precursor materials can prevent the electromagnetic radiation from reaching the bottom of the resist film, leading to variations in volume fraction of the developed structure in the direction of the thickness of the film. Also, in some cases, strong absorption of the particle precursor material may result in diminished photoresist sensitivity. The transparency of the resist at the wavelength of exposure may allow for the fabrication of a uniform structure through the thickness of a resist film.

In some cases, the particle precursor material may be selected to have good adhesion to a substrate, high contrast, refractive index, thermal stability, mechanical stability, and the like, as described more fully below. For example, in some cases, the particle precursor material may be selected to be sufficiently basic (e.g., via addition of an appropriate amount of base) to neutralize photoacids generated during photoinitiated cationic polymerization of the material, thereby reducing or eliminating the DC offset and hence enhancing the contrast. In some cases, the particle precursor material may be selected to withstand standard process conditions such as exposure to high temperature. In some cases, the particle precursor material may have sufficient mechanical strength to maintain its structure when treated to form a particle, while also allowing facile removal of the un-treated portion of the particle precursor material.

A simple screening test for determining if a material would be suitable for use in the invention may involve exposing a small sample of a material to a single source of external energy, such as electromagnetic radiation, and observing whether or not the material reacts to form a hardened material. This would indicate that the material, if exposed to multiple sources of external energy in a three-dimensional sample as described herein, would react in the desired manner to form a particle of the invention. The materials described herein may be useful as particle precursor materials to form particles or networks of particles as described herein, as well as infiltration materials, i.e., materials which may be used to fill in the void space of a template structure or network to form a structure having the shape of the void space. In some cases, the template structure may then be removed. For example, in an "inversion" method, particles or a network of interconnected particles may be formed as described herein, and the material adjacent to the formed structure may be removed to produce a void space. In a "double inversion" method, the void space may be filled with a material (e.g., an infiltration material), wherein the particles or a network of interconnected particles and/or space act as a template for the infiltration material. Subsequent removal of the particles or network of interconnected particles template may yield the desired structure comprising the infiltration material. In some embodiments, the particle precursor material may be a photoresist material, including negative resists and positive resists. FIG. 4 shows a schematic representation of the use of (a) negative resists and (b) positive resists to produce patterned, three dimensional structures.

In some cases, the photoresist material may be a negative resist, wherein the portion of the material that is exposed to electromagnetic radiation may become insoluble to the developer (e.g., reacts to form a solid structure) and the unexposed portion of the material may be removed. (FIG. 4A) This insolubility can be achieved by an increase in molecular weight, photochemical rearrangement to form new insoluble products, for example. To increase molecular weight, photo-initiators may be used to generate free radicals, or strong acids may be used to facilitate polymeric cross-linking or the photopolymerization of monomeric or oligomeric species. In some embodiments, the use of a negative photoresist results in a high crosslink density of insoluble polymer in the exposed regions. In some embodiments, negative patterns can be achieved by the photochemical formation of hydrophobic or hydrophilic groups which provide differential solubility between the exposed and unexposed regions of the resist film. In some cases, the negative photoresist pattern may be achieved with minimal or essentially no increase in molecular weight of the material.

One example of a negative photoresist for interference lithography may be SU-8, an epoxy based monomer that may undergo cationic photopolymerization. It has many advantages, such as chemical amplification, which increases the sensitivity; mechanical robustness, which may allow access to high aspect ratio structures; and wide processing latitude with respect to radiation wavelengths. For many optical and mechanical applications it may be desirable to infiltrate interference lithography patterned polymeric structures with other materials (for example, high refractive index materials for photonic crystals) and then to remove the original polymer structure.

In some embodiments, the particle precursor material may be a positive resist, wherein regions exposed to electromagnetic radiation (e.g., UV radiation) become soluble to the developer, while unexposed regions remain insoluble. (FIG. 4B) That is, the portion of the material that is not exposed to electromagnetic radiation reacts to form a solid structure and the unexposed portion of the material may be removed. Examples of positive photoresists suitable for use in the invention include I-line photoresists (e.g., 365 nm) and Gline photoresists (e.g., 436 run). In one embodiment, the positive resist comprises diazonaphthoquinone (DNQ) and novolac resin (a phenol formaldehyde resin), wherein DNQ may act as both photosensitizer and dissolution inhibitor. Upon exposure, DNQ may undergo molecular rearrangement generating a carboxylic acid, and the exposed area may become soluble in basic developers, resulting in a positive image in regions of high electromagnetic radiation intensity. In some cases, the use of positive resists may advantageously reduce or prevent shrinkage from cross-linking and can be easily removed after an infiltration step by, for example, flood illumination of the composite and dissolution in a subsequent developer treatment.

FIG. 7 shows illustrative embodiments of photoresists, as well as reaction mechanisms by which a portion of the photoresist forms a solid structure. FIG. 7A shows (i) the chemical composition of an SU-8 negative resist and (ii) a photochemical reaction mechanism of the SU-8 negative resist, according to one embodiment of the invention. FIG. 7B shows (i) the chemical composition of a DNQ novolac positive resist and (ii) a photochemical reaction mechanism of the DNQ novolac positive resist, according to one embodiment of the invention. Various factors may be considered in selecting photoresists for interference lithography. For example, the photoresist may be select to exhibit transparency at the exposure wavelength. The strong absorption of photoactive compounds (PACs) in photoresist formulations can prevent the light from reaching the bottom of the resist film, leading to variations in volume fraction of the developed structure in the direction of the thickness of the film. The transparency of the resist at the wavelength of exposure may affect the ability to achieve a uniform structure through the thickness of a resist film and may determine the practical exposable thickness of the resist. Strong absorption may also result in diminished photoresist sensitivity.

SU-8 is an example of a chemically amplified resist (C AR), in which a single incident photon can catalyze many chemical events leading to very high resist sensitivity. Therefore, in some cases, only a small amount of highly absorbing photoinitiator or sensitizer may be needed. FIG 8. shows the UV absorbance spectra for (a) a SU-8 negative resist and (b) DNQ novolac positive resist (i) before exposure to UV light and (ii) after exposure to UV light. The commercial SU-8 resist (Microchem Chemicals) comprises derivatives of the eight epoxy bisphenol-A-novolac base resin with triaryl sulfonium salt as the photoacid generator (PAG). Since SU-8 is transparent in the near- UV and visible regions of the electromagnetic spectrum but highly opaque in the deep- UV region, the use of SU-8 photoresist for thicker films than 5 μm in lithographic technologies utilizing < 350 nm light may be hampered by the absorbance of the resist itself.

Many positive resists based on novolac and DNQ for I-line and G-line exposure may be non-CARs. The amount of DNQ present in the photoresist resin may be about 30%. An important feature of the DNQ systems may be that, with increasing exposure to radiation, the absorption bands of these molecules disappear as the compounds are converted to indene-carboxylic acid photoproducts. This decrease in absorbance during exposure is referred to as "bleaching" and allows light to propagate to the bottom of thick and strongly absorbing resist films as the exposure proceeds (FIG. 8B). Many DNQ derivatives have high absorbance and may be poorly photobleached in the wavelength region longer than 480 nm. For example in the case of the photoresist AZ5214E, the thickness of the film successfully used was 3 microns at 532 nm exposure. Polysilane polymers, which possess a backbone consisting of silicon atoms, are a promising class of positive photoresists. Upon exposure to ultraviolet (UV) radiation in air, photoinsertion of oxygen takes place. The resultant introduction of Si-O-Si and Si- OH bonds induces changes in some properties of the polysilane films, such as solubility and wettability. It has been proposed that the photodecomposition of the organosilane backbone leads to its photobleaching by UV irradiation and is attributed to the shortening of α-conjugation of the Si backbone due to the Si-Si bond scission or Si-O bond formation.

The photoresist may also be selected to exhibit good adhesion to an underlying substrate. For example, the surface oxide of many substrates (e.g. silicon wafer or glass) may form extensive hydrogen bonds with water adsorbed from the air. When a resist is spun onto such a surface, it may interact with the water rather than the surface, resulting in poor adhesion. Incorporating some hydrophilic moiety such as a hydroxyl group into hydrophobic resist formulations can increase the adhesion of the polymer to the substrate. In some embodiments, SU-8 may be sufficiently hydrophilic to allow film formation on common substrates by spin coating. However, polarity changes and physical stresses associated with shrinkage after crosslinking. as well as thermal stress created during the fabrication process, may cause delamination of the film during the developing step. To improve the adhesion between the porous film of crosslinked SU-8 and the substrate, a buffer layer can be spun on the substrate first, flood exposed and post-exposure baked. This may be followed by spin coating the imaging layer for the 3D structure, which prevents delamination by inducing chemical grafting of the patterned layer onto the buffer layer.

In another example, Novolac-DNQ phenolic resin may have excellent film forming properties on polar substrates because of the hydroxyl group. Additional treatments utilizing adhesion promoters such as hexamethyldisilazane (HMDS) or trichlorophenylsilane (TCPS) can further increase the adhesion of some relatively hydrophobic resists onto the substrate by forming a more hydrophobic substrate surface. FIG. 9 shows a schematic diagram demonstrating surface changes with treatment by HMDS (from R. Dammel, SPIE Optical Engineering Press 1993, TTl 1). This change may be a consequence of the creation of siloxane linkages (Si-O-Si) between the polar surface and the silane primer. The newly formed termination on the substrate may render the surface more hydrophobic in character and may lead to greater wettability by the photoresist. As a result of the altered characteristics of the surface chemistry, the treated silicon surfaces may become highly compatible with both negative and positive photoresists.

In some cases, the photoresist may be selected to have a high I(r) contrast. In multi-beam interference, an inherent DC offset in the light intensity can result in insufficient contrast which can make it experimentally challenging to find exposure conditions for which the resultant developed structure is bicontinuous. Contrast can be maximized by several different approaches, as known to those of ordinary skill in the art. In one case, beam polarizations may be optimized to minimize the overall intensity while preserving the desired symmetry of the final structure. In another case, an appropriate amount of organic base may be added into the SU-8 photoresist formulation. Since the negative photoresist platform is a photoinitiated cationic polymerization system, the base may neutralize a controlled amount of the photoacids generated during exposure in spatially homogeneous manner, thereby reducing or eliminating the DC offset and hence enhancing the contrast. The photoresist may also be selected to have a particular refractive index. In some embodiments, a change in refractive index of the photoresist during the exposure in continuous wave (cw) mode may not be desirable since this can result in perturbation of the incident light and cause deviations from the desired interference pattern. SU-8 generally does not exhibit any detectable change in refractive index, even after the hard- baking process (n=l .59 for crosslinked and uncrosslinked films at 633 nm). The refractive index of the DNQ/novolac resists is n=l .66 at 532nm and is also not changed detectably during exposure. Pulsed laser systems may allow access to a wider window of materials because the duration of the exposure (~ 8 ns) may be much shorter than the duration of exposure for PAG generation via diffusion.

In selecting a photoresist platform, the thermal stability of the photoresist may also be considered. For example, methods of the invention may comprise one or more bake steps during the lithographic process, including prebake, post exposure bake (PEB), and hard bake. The recommended temperature and time of each step may depend on the photoresist and the properties of the resist resulting from the bake step. Generally, prebake may be a low temperature bake step after deposition of photoresist on the substrate. This may be done to evaporate the solvent from the spun-on resist, improve the adhesion of the resist to the wafer, and/or anneal out the stresses introduced during the spin-coating. PEB may be done to drive diffusion of the photoproduct and/or drive the acid-catalyzed reaction that alters the solubility of the polymer in many CARs. Hard bake is an annealing step performed after resist developing, in some cases, to strengthen and stabilize the patterned structure. In some embodiments, photoresists having high degradation temperature may be desirable in order to ensure that the photoresist be able to withstand standard process conditions such as prebake and PEB. Further, a relatively high glass transition temperature of the photoresist may be needed in CAR to minimize, for example, the acid diffusion during the exposure step. The glass transition temperature of uncrosslinked SU-8 may be approximately 50 °C which minimizes acid diffusion during the room- temperature exposure, allowing for subsequent accelerated acid diffusion during the PEB (75 °C). As a consequence of its aromatic functionality and highly cross-linked matrix, the final SU-8 structure may be thermally and chemically stable. Fully crosslinked SU-8 may be thermally stable and exhibits no flow up to 220 ⁰C. In another embodiment, the novolac resin in novolac/DNQ positive resist systems may provide the physical properties desired in the photoresist, such as etch resistance and thermal stability (150- 19O⁰C for multifunctional and orthocresol novolac). In general materials including DNQs may be modified to alter their thermal stability so they do not break down during prebake or PEB. Photoresists may also be selected to exhibit good mechanical stability.

Mechanical stability of the final structure may be needed to make thick samples with high aspect ratio patterns and low overall polymer volume fraction, which may be advantageous for many optical, acoustical and mechanical applications. The elastic modulus of fully crosslinked SU-8 film is around 4 GPa with the ultimate strain reaching 8% and can be modulated by changing the exposure or post-exposure bake time. The fully crosslinked SU-8 may be, like most thermosets, a rather brittle material. However, both the submicron framework and an intermediate crosslink density could push the strain-to-break value up to 300%, demonstrating that high plastic deformation can be achieved in an otherwise rather brittle material by suitable microframe structures. This suggests an interesting new pathway for making ultralight, mechanically dissipative structures. Photoresists having good mechanical stability may also aid in reducing or preventing collapse of the resulting, solidified material. For example, pattern collapse due to high surface tension after wet developing (e.g. PGMEA for SU-8 and basic solution in water for novolac/DNQ) during the drying process is another important issue in the fabrication of high quality 3D structures. Supercritical (sc) CO₂ drying of SU-8 is a well known technique to improve quality of the resultant 3D pattern by avoiding the destructive effects of surface tension. Sc CO₂ development for the negative type molecular-glass photoresist has been suggested as a new process step to alleviate pattern collapse in densely packed, high-aspect-ratio structures. However, supercritical drying of some positive photoresists resulted in the formation of cracks. Replacement of water with pentane or hexane, which have a lower surface tension (73.05 mN/m, 13.72 mN/m, and 18.43 mN/m for water, pentane, and hexane respectively at 20 ⁰C) has been proposed as an alternative method. Another approach to eliminate the surface tension problem is to take advantage of the etch selectivity of oxygen for silicon-containing polymers that can form a protective oxide layer when exposed to an oxygen plasma. It has been reported that a critical threshold concentration of above 10-15% silicon in the polymer significantly improves O₂-RIE resistance by formation of a SiO₂ layer. A dry developable resist can be an alternative resist system in which silicon-containing group is deprotected by acid catalyzed reaction and subsequently dry developed by an oxygen plasma. In some cases, it may be advantageous to select a precursor material, wherein, upon formation of the template, at least a portion of the template (e.g., solidified material) and/or the material adjacent the template (e.g., the un-solidified material) may be easily removed during the fabrication process. In some cases, upon formation of the template, the material adjacent the template may be removed to produce a three- dimensional structure comprising void space. As noted above, the three-dimensional structures formed may also be useful as molds or templates (e.g., interference lithographic templates or ILTs) in the fabricate of other structures. In some cases, void spaces within the template may be filled or infiltrated with other, auxiliary materials, and at least a portion of the template may be subsequently removed (e.g., inversion method).

In some cases, a polymeric precursor material may be selected such that the material may be readily removed at temperatures above, for example, 150-200 ⁰C. Various steps of the fabrication process, such as effecting the differential reaction, developing, infiltration, etc, may be performed at temperatures below, for example, 150- 200 ⁰C, such that subsequent removal of the polymeric material to obtain geometrical complementary, three-dimensional structure with superior, for example, mechanical or optical properties than the original polymer template. In some embodiments, positive photoresist platforms may be useful as an ILT for infiltration with a PDMS precursor to create an elastomeric three dimensional structure. The positive resist could be readily removed via a water-based basic solution which circumvented PDMS swelling or pattern collapse during the ILT removal process. In some cases, the resultant structure may have a mechanically tunable phononic dispersion relation, as described more fully below. In addition to easy removal of the precursor material and/or template in order to facilitate an exchange of materials, the ILT may be selected to retain its integrity during the exchange process. For example, SU-8 also can be used as an ILT using a high temperature removal process. Methods of the invention may also comprise additional steps to produce the solid particles from the photoresist materials, including exposure to solvents (e.g., N-methyl-2-pyrrolidone, alkaline solutions) or other developing methods known in the art. Examples of polymers that may be useful as photoresist materials include, but are not limited to, acrylate polymers, styrenes, and the like.

In some embodiments, the particle precursor material may be capable of forming a gel. As used herein, the term "gel" is given its ordinary meaning in the art and refers to polymer chains that may be crosslinked to form a network, wherein the network may be able to trap and contain fluids. Depending on the level of crosslinking, various properties of a particular gel can be tailored. For example, a highly crosslinked gel may generally be structurally strong and may resist releasing fluid under pressure, but may exhibit slow transition times, while a lightly crosslinked gel may be weak structurally, but may react quickly during its phase transition. In the design of gels for a particular application, the degree of crosslinking may be adjusted to achieve the desired compromise between speed of absorption and level of structural integrity. Those of ordinary skill in the art would be able to identify methods for modulating the degree of crosslinking in such gels.

In some embodiments, the gel may be a hydrogel, including a crosslinkable hydrogel. The term "hydrogel" refers to water-soluble polymer chains that are crosslinked in the presence of water to form a network. Examples of polymers capable of forming hydrogels include, silicon-containing polymers, polyacrylamides, crosslinked polymers (e.g., polyethylene oxide, polyAMPS and polyvinylpyrrolidone), polyvinyl alcohol, acrylate polymers (e.g., sodium polyacrylate), and copolymers with an abundance of hydrophilic groups. In some embodiments, the gel may be a sol-gel. A "sol-gel" refers to a colloidal suspension capable of being gelled to form a solid. In some cases, the sol-gel may be formed from a mixture of solid particles (e.g., inorganic salts) suspended in a liquid, wherein a series of reactions including hydrolysis and polymerization reactions may be performed to form a colloidal suspension. The particles may condense in a new phase, the gel, in which a solid macromolecule is immersed in a solvent.

Certain types of polymers are known to form crosslinking bonds under appropriate conditions. Non-limiting examples of crosslinkable polymers include: polyvinyl alcohol, polyvinylbutryl, polyvinylpyridyl, polyvinyl pyrrolidone, polyvinyl acetate, acrylonitrile butadiene styrene (ABS), ethylene-propylene rubbers (EPDM), EPR, chlorinated polyethylene (CPE), ethelynebisacrylamide (EBA), acrylates (e.g., alkyl acrylates, glycol acrylates, polyglycol acrylates, ethylene ethyl acrylate (EEA)), hydrogenated nitrile butadiene rubber (HNBR), natural rubber, nitrile butadiene rubber (NBR), certain fluoropolymers, silicone rubber, polyisoprene, ethylene vinyl acetate (EVA), chlorosulfonyl rubber, flourinated poly(arylene ether) (FPAE), polyether ketones, polysulfones, polyether imides, diepoxides, diisocyanates, diisothiocyanates, formaldehyde resins, amino resins, polyurethanes, unsaturated polyethers, polyglycol vinyl ethers, polyglycol divinyl ethers, copolymers thereof, and those described in U.S. Patent No. 6,183,901. Those of ordinary skill in the art can choose appropriate polymers that can be crosslinked, as well as suitable methods of crosslinking, based upon general knowledge of the art in combination with the description herein.

Examples of polymers that may be suitable for use in as a particle precursor material (either crosslinked or non-crosslinked) include, but are not limited to, polyamines (e.g., poly(ethylene imine) and polypropylene imine (PPI)); polyamides (e.g., polyamide (Nylon), poly(e-caprolactam) (Nylon 6), poly(hexamethylene adipamide) (Nylon 66)), polyimides (e.g., polyimide, polynitrile, and poly(pyromellitimide-l,4-diphenyl ether) (Kapton)); vinyl polymers and acrylate polymers (e.g., polyacrylamide, poly(2-vinyl pyridine), poly(N-vinylpyrrolidone), poly(methylcyanoacrylate), poly(ethylcyanoacrylate), poly(butylcyanoacrylate), poly(isobutylcyanoacrylate), poly( vinyl acetate), poly (vinyl alcohol), poly( vinyl chloride), poly( vinyl fluoride), poly(2-vinyl pyridine), polychlorotrifluoro ethylene, poly(isohexylcynaoacrylate), polyisobutylene, poly(methyl styrene), poly(methylmethacrylate) (PMMA), poly(ethylene glycol) diacrylate, polyethylacrylate, polymethylmethacrylate, and polyethylmethacrylate); polyacetals; polyolefins (e.g., poly(butene-l), poly(n-pentene-2), polypropylene, polytetrafluoroethylene); polyesters (e.g., polycarbonate, polybutylene terephthalate, polyhydroxybutyrate); polyethers (poly(ethylene oxide) (PEO), poly(propylene oxide) (PPO), poly(tetramethylene oxide) (PTMO)); polyaramides (e.g., poly(imino-l,3-phenylene iminoisophthaloyl) and poly(imino-l,4-phenylene iminoterephthaloyl)); polyheteroaromatic compounds (e.g., polybenzimidazole (PBI), polybenzobisoxazole (PBO) and polybenzobisthiazole (PBT)); polyheterocyclic compounds (e.g., polypyrrole); polyurethanes; phenolic polymers (e.g., phenol-formaldehyde); polyalkynes (e.g., polyacetylene); polydienes (e.g., 1,2- polybutadiene, cis or trans- 1 ,4-polybutadiene); polysiloxanes (e.g., poly(dimethylsiloxane) (PDMS), poly(diethylsiloxane) (PDES), polydiphenylsiloxane (PDPS), and polymethylphenylsiloxane (PMPS)); and inorganic polymers (e.g., polyphosphazene, polyphosphonate, polysilanes, polysilazanes). The mechanical and physical properties (e.g., conductivity, resistivity) of these polymers are known. Accordingly, those of ordinary skill in the art can choose suitable polymers for use as particle materials or particle precursor materials, e.g., based on their mechanical and/or electronic properties, etc., by, for example, tailoring the amounts of components of polymer blends, adjusting the degree of cross-linking (if any), etc.

In some cases, methods of the invention employ the use of a crosslinking agent. As used herein, a "crosslinking agent" is an atom or molecule with a reactive portion(s) designed to interact with functional groups on the polymer chains in a manner that will form a crosslinking bond between one or more polymer chains. Examples of crosslinking agents that can crosslink materials described herein include, but are not limited to: metal ions (e.g., bivalent or other multivalent ions), organometallic complexes, polyamide-epichlorohydrin (polycup 172); glyoxal; aldehydes (e.g., dialdehydes, glutaraldehyde, acetaldehyde, hydroxyadipaldehyde, formaldehyde, urea- formaldehyde, and hydroxyadipaldehyde); acrylates (e.g., ethylene glycol diacrylate, di(ethylene glycol) diacrylate, tetra(ethylene glycol) diacrylate, methacrylates, ethelyne glycol dimethacrylate, di(ethylene glycol) dimethacrylate, tri(ethylene glycol) dimethacrylate); amides (e.g., N,N'-methylenebisacrylamide, N,N'- methylenebisacrylamide, N,N'-(l,2-dihydroxyethylene)bisacrylamide, N-(l-hydroxy- 2,2-dimethoxyethyl)acrylamide); silanes (e.g.,methyltrimethoxysilane, methyltriethoxysilane, tetramethoxysilane (TMOS), tetraethosxysilane (TEOS), tetrapropoxysilane, methyltris(methylethyldetoxime)silane, methyltris(acetoxime)silane, methyltris(methylisobutylketoxime)silane, dimethyldi(methylethyldetoxime)silane, trimethyl(methylethylketoxime)silane, vinyltris(methylethylketoxime)silane, methylvinyldi(mtheylethylketoxime)silane, methylvinyldi(cyclohexaneoneoxxime)silane, vinyltris(mtehylisobutylketoxime)silane, methyltriacetoxysilane, tetraacetoxysilane, and phenyltris(methylethylketoxime)silane); divinylbenzene; peroxides; melamine; zirconium ammonium carbonate; dicyclohexylcarbodiirnide/dimethylaminopyridine (DCC/DMAP); 2-chloropyridinium ion; 1-hydroxycyclohexylphenyl ketone; acetophenon dimethylketal; benzoylmethyl ether; aryl triflourovinyl ethers; benzocyclobutenes; phenolic resins (e.g., condensates of phenol with formaldehyde and lower alcohols, such as methanol, ethanol, butanol, and isobutanol), epoxides; melamine resins (e.g., condensates of melamine with formaldehyde and lower alcohols, such as methanol, ethanol, butanol, and isobutanol); polyisocyanates; dialdehydes; and other crosslinking agents known to those of ordinary skill in the art. In some cases, stimuli-responsive materials (e.g., polymers) may also be employed in the context of the invention. For example, materials which can undergo a change in a physical property such as size, shape, volume, or the like, upon exposure one or more stimuli such as temperature, pH, light, a fluid, ionic strength, change in concentration of a species, and electric or magnetic fields, may be used. Those of ordinary skill in the art would be able to select such stimuli-responsive materials. For example, materials comprising polymethacrylic acid may be responsive to changes in pH while materials comprising poly(N-isopropylacrylamide) may be responsive to changes in temperature. Other examples of particle precursor materials include, for example, photoetchable glasses. Photoetchable glasses generally comprise inorganic materials, and may further comprise metal ions as dopants. One example of a photoetchable glass may be lithium-aluminum-silicate glass containing silver and germanium ions. The particle precursor material may also be a ceramic precursor composition. As used herein, the term "ceramic precursor composition" refers to compositions that, when appropriately treated (e.g., sintered), can form a full density ceramic structure or ceramic-containing structure. A ceramic precursor composition can have one or more different ceramic components. In some embodiments, the ceramic component may be in the form of particles. For example, the ceramic precursor composition may comprise at least one type of ceramic particle. In some cases, the ceramic precursor composition may comprise at least two types of ceramic particles. In some embodiments, the ceramic component may be in the form of a liquid precursor, including pre-ceramic polymers, suspensions and/or solutions (e.g., a solvent comprising dissolved matter, non-particulate liquids). It is also possible for one or more ceramic components to contain a metal, such that the resulting ceramic body may be a metal-ceramic composite (or cermet). In some cases, the metal may be a metal particulate.

The ceramic-forming compositions may comprise at least one ceramic or ceramic-forming powder which can be any material that, when appropriately treated (e.g., sintered), can form a full density ceramic structure. Examples of such materials include cordierite, mullite, talc, clay, zircon, zirconia, spinel, aluminas, silicas, silicates, aluminates, lithium aluminosilicates, feldspar, titania, fused silica, nitrides, carbides, borides, precursors thereof, and/or mixtures thereof. The ceramic-forming composition may also comprise a liquid precursor. Examples include, but are not limited to, solutions of sodium silicate and polycarbosilazane precursors to silicon carbide.

In some cases, the particles precursor material may be a metal, such as a semiconductor material, or precursor thereof. Examples of semiconductor materials include, but are not limited to, metals, metal alloys, intermetallic compounds, metal nitrides, metal sulfides, metal carbides, metal oxides, etc. For example, metals may be formed of Group II- VI compounds or elements such as semiconductors. Suitable elements from Group II of the Periodic Table may include zinc, cadmium, or mercury. Suitable elements from Group III may include, for example, gallium or indium. Elements from Group IV that may be used in semiconductor materials may include, for example, silicon, germanium, or lead. Suitable elements from Group V that may be used in semiconductor materials may include, for example, nitrogen, phosphorous, arsenic, or antimony. Appropriate elements from Group VI may include, for example, sulfur, selenium, or tellurium. Some examples of semiconductor materials include silicon, germanium, gallium arsenide, silicon carbide, indium compounds (e.g., indium arsenide, indium antimonide, and indium phosphide) selenium sulfide, and the like.

Some specific examples of materials suitable for use as semiconductor materials include, but are not limited to, MgO, MgS, MgSe, MgTe, CaS, CaSe, CaTe, SrS, SrSe, SrTe, BaS, BaSe, BaTe, ZnO, ZnS, ZnSe, ZnTe, CdO, CdS, CdSe, CdTe, HgO, HgS, HgSe, HgTe, AlN, AlP, AlAs, AlSb, Al₂S₃, Al₂Se₃, Al₂Te₃, Ga₂S₃, Ga₂Se₃, GaTe, In₂S₃, In₂Se₃, InTe, SnS, SnSe, SnTe, PbS, PbSe, PbTe, AlP, AlAs, AlSb, GaN, GaP, GaAs, GaSb, InN, InP, InAs, InSb, TiN, TiP, TiAs, TiSb, BP, Si, SiC, and Ge, and ternary and quaternary mixtures, compounds, alloys, mixtures, and solid solutions thereof. The semiconductor material may include alloys or mixtures of these materials, or different Groups may be combined together as in, for example, AlGaAs, InGaAs, InGaP, AlGaAs, AlGaAsP, InGaAlP, or InGaAsP.

In an illustrative embodiment, a network of particles may be formed as described herein using a photoresist material as the particle precursor material, and the structure may be treated to remove the portion of the photoresist material adjacent the network, resulting in a void space. The void space may be filled with, for example, a semiconductor material or precursor thereof, such that the network/void space acts as a template for the semiconductor material. The semiconductor material may be further processed to produce the desired structure. In some cases, the network of particles may be removed to leave the semiconductor structure and a void space (e.g., via a double inversion method).

EXAMPLES

Example 1

The following example includes a discussion of various factors that may be considered in the use of interference lithography to produce particles and networks as described herein, having dimensions and/or properties to suit a particular application. The electric field associated with a monochromatic plane wave can be described mathematically as:

where m is the index identifying the particular beam, E₀ is the wave amplitude and direction of polarization, k is the wave vector, ω is the angular frequency, and φ is the phase. The intensity distribution created by a set of beams is proportional to the square of the magnitude of the resultant vector sum. Since the polarization associated with an electromagnetic wave need not necessarily be linear, but can be circular or elliptical as well, the intensity may be arrived at by the inner product of the electric field with its complex conjugate. From this equation, it can be observed that the interference pattern has only a spatial variation and no temporal variation.

Note that l(r ) is simply the sum of sinusoidal terms. Thus, in order to understand the extent to which interference lithography allows control of the geometry and the nature of the resultant patterns it is useful to view the intensity equation as a discrete Fourier sum. The intensity distribution may have its translational periodicity determined by the difference between the wave vectors Jc₁ - k_m of the interfering beams while the polarizations, represented by a set of complex electric field vectors, to determine the pattern or motif placed within the unit cell. The combination of the motif and the translational periodicity may determine the full set of symmetries associated with, and hence the space group, of the resultant structure. Any arbitrary structure can be expressed as a sum of Fourier terms each of which could correspond to a grating arising from the interference of two beams. For each grating, the magnitude of the relative phase amplitudes may fix the position of the origin along the direction of its periodicity. One of the current primary challenges in interference lithography is to simply and reproducibly achieve registration between independent gratings. Examples of approaches to tackle this registration problem include restricting the number of beams used so that registration is assured, or, using a , phase mask to generate the set of beams and, if necessary, employ multiple exposures. In general, the interference of two, three and four beams of coherent light may result in one, two and three dimensionally periodic patterns. A change in phase of one of the interfering beams may result in a shift in the pattern commensurate with the dimensionality of the pattern. Since the use of five beams in general may create a pattern that is periodic in four-space, a shift in phase may result in a translation in four-space, and create a completely new pattern in three dimensions. Thus if registration between beams is not ensured through any other means, one may be restricted to the use of four beams of light. The interference of four beams of light with arbitrary directions, amplitudes and phases may result in a maximum of thirteen terms (the four terms along the diagonal are all fixed constants and, therefore, can be combined as a single constant) of which there are six terms along distinct directions (some terms only differ from each other by π/2 in phase). The set of thirteen terms may restrict the sort of structures one can form through a four-beam approach, making it useful to develop a crystallographic approach that allows one to target particular symmetries and space groups.

One approach may be to consider the translational periodicity associated with these structures. As with all translationally periodic structures, the minimum set of vectors that need to be considered may be the set of basis vectors, since the remaining vectors can be achieved by linear combinations. In two dimensions there are five lattice nets, while in three dimensions there are fourteen Bravais lattices. Thus in order to obtain a desired translational periodicity it may be necessary to equate the difference between the wave vectors with basis vectors associated with that translational periodicity. One way to do this is to set the first wave vector, Jc₀ to the reciprocal lattice vector that is equidistant from the origin and the basis vectors b_m . The remaining wave vectors may then be simply given by k_m = b_m + k₀. Since there are an infinite number of choices of basis vectors for a particular type of translational symmetry, the size of the unit cell can be varied simply by changing the angle between the beams. The control of the lattice size may be limited by the span of the mutual angles between the beams and may not continuous. A list of wave vectors for the translational periodicities associated with the fourteen Bravais lattices can be found in L. Z. Cai, X. L. Yang, Y. R. Wang, Opt. Lett. 2002, 27, 900, the contents of which are incorporated herein by reference.

To achieve a particular space group, suitable values for k and E may be selected to impose the set of symmetry operators for that space group, as listed in the International Tables of Crystallography. The generalized intensity equation can be taken and the symmetry operations corresponding to the generators (the minimum subset of symmetry operators) imposed on it to yield a set of conditions for a final target equation: This target equation may then be examined to verify that it belongs to the desired space group and does not possess additional symmetry elements that could place it in another super group. This target equation may then be compared to the generalized intensity equation and the resultant set of simultaneous equations solved, to yield the beam parameters that are required to obtain a structure with the desired space group.

Another method for obtaining the target equation to which the intensity equation can be compared may be to consider the Fourier transforms of the space group in consideration. As such, target equations may be found in the diffraction patterns associated with these groups. Such a 'level-set' approach may use the structure factor of the chosen space group to obtain candidate functions that possess the requisite symmetries. The structure factor may describe the amplitudes and phases of the three- dimensional diffraction pattern due to the scattering of incident radiation from the planes (hkl) of atoms in the crystalline structure. Such an approach also has an important physical insight, as the addition of higher order structure factor terms may fill Wyckoff sites of greater multiplicity and decreasing symmetry and may lead to structures of increasing topological complexity.

The ability to create structures using an arbitrary number of beams may be a particularly useful tool. If multiple gratings, each with a different periodicity can be reproducibly registered with respect to one another in space, then any arbitrary structure can potentially be accessed by writing it out as a sum of its Fourier terms. The ability to control the relative phases of a large number of beams may be useful in this context. A first approach may be to control the phase of each individual beam using a setup such as a delay stage or a phase retarder that does not introduce a change in polarization. Such a scheme can be used to ensure that all the gratings share the same origin. Alternatively, if the phase of each of the individual gratings is known, a stage can be used to move the sample around to achieve the appropriate registration.

Another approach may be to use a phase mask. A phase mask is a surface relief diffraction grating from which a set of outgoing beams (at specific angles related to the geometry of the mask) may be created from a single incident beam (plane wave). It has favorable process conditions for integrated optics platforms since the beams all come from the same half space. Also, the phase difference between the different beams as they leave the grating may be determined by the grating.

In an illustrative embodiment, two structures were fabricated using the beam conditions summarized in Table 2. FIG. 15A shows the theoretical structure of 2 x 2 x 2 structures having (a) R3m symmetry of a three term "diamond-like" structure and (b) Pm3m(221) symmetry of a Schwarz P surface.

Table 2. Beam parameters for 3D interference lithography structures.

Example 2

In the following example, a 3D polymer microframe was fabricated and mechanically tested by using interference lithography to pattern SU-8. A four-functional network was fabricated, having a basic unit comprised of a thick vertical post supporting three thinner beams and has the space group R3m as shown in Table 2 below. In some cases, the bulk, crosslinked SU-8 was brittle. A peeling test was performed to make a preliminary assessment of the deformation behavior of the microframe film. Since peeling involved a complex interplay of forces, the mechanical response of the microframe structure in a wide variety of deformational modes was observed. Thus, the effects of tension, bending, compression, and shearing are seen and reveal a host of interesting morphologies. FIG. 13 shows (a) an SEM image of a plastically deformed polymer microframe structure, including (i) a region having a microframe bridge extending from one side of a crack to the other, and (ii) extensive shear, bending and microplastic deformation of the structure near the left terminus of the bridge, (b) an SEM images of the structure, wherein plastic deformation and fracture of transverse beams or "arms" are shown, with up to several hundred % strain in the vicinity of a fracture, (c) an SEM image of a compressed portion of the structure, (d) a cross section of the plastically deformed region of the structure, and (e) microfibrils formed due to peeling of microframe from substrate. Some unusual structures were observed including portions of microframe bridging across wide cracks (FIG. 13A), highly stretched members could be seen in front of arrested cracks (FIG. 13B), and crushed and densifϊed areas in regions of compression (FIG. 13C). The diameter of the most highly stretched members decreases dramatically. By comparing the strut length in unperturbed unit cells with those in deformed regions, member strain was estimated to be upwards of 300 % (see elongated members in FIG. 13B). The strain to failure of these features was about an order of magnitude higher than that observed for uncured (ε_f ~ 30 %) and for fully crosslinked bulk novolac resins (ε_f ~ 8-10 %). The plasticity of the fine scale structure was further evidenced in the formation of microfibrils in regions of extension, due to pull out and alignment of the struts (FIG. 13D).

Example 3 The following example describes an embodiment wherein phase mask interference lithography is employed to achieve beam configurations that can yield three- dimensional interference patterns, for use in the context of the invention.

One implementation of the phase mask approach may be to use a conformable elastomeric phase mask, which may ensure that the beams travel a repeatable optical path for different exposures. It may have favorable process conditions for integrated optics platforms compared to multibeam interference lithography in that the beams all come from the same half space. The elastomeric phase mask may be placed in contact with a film of photoresist and light is incident on the phase mask. The diffracted beams may then interfere within the volume of the photoresist to create the structure. FIG. 5 A shows a general fabrication process of elastomeric conformal phase masks and FIG. 5B shows a schematic diagram of the lithographic setup showing the three-dimensional interference pattern generated when a beam is incident on the phase mask. In an illustrative embodiment, phase mask interference lithography was used to fabricate a three-dimensional structure using a PDMS phase mask. FIG. 5C shows (i) an SEM image of the PDMS phase mask comprising an array of circular holes (280 run in diameter and 600 nm high on a 750 nm square lattice) and (ii) an SEM of the resulting three-dimensional structure created from the phase mask, and (iii) a computed theoretical intensity distribution for a 2 x 2 x 2 array of unit cells. Example 4

The following example describes an embodiment wherein multi-beam interference lithography is employed to achieve beam configurations that can yield three- dimensional interference patterns, for use in the context of the invention.

In multi-beam interference lithography (e.g., free space interference lithography), the required interference pattern may be created by first assembling collimated, coherent laser beams with beam parameters appropriate for the desired targeted structure and then interfering them within the volume of a photoresist. In such a setup one laser beam may be typically divided into multiple beams using a beam-splitter. The beams may then be recombined by mirrors to obtain the desired geometry. The polarization and intensity of the beams may be controlled by wave plates and polarizers. In some cases, the configurations employed may be restricted to four beams or less. An overview of the optical components for the multibeam interference lithography setup, experimental setup with prism and the realization into SU-8 are shown in FIG. 6. FIG. 6 shows (a) illustrative optical components for multibeam interference lithography, (b) a six-beam lithographic setup comprising a prism, (c) an SEM image of P surface into SU-8 fabricated, and (d) a computed theoretical intensity distribution for a 2 x 2 x 2 array of unit cells.

The preservation of beam directions and polarizations may be an important consideration in the experimental setup. Upon entering the photoresist the beams can be refracted and the polarization can change due to variations in the reflectivity of the TE and TM components that make up the incoming wave. The utilization of an appropriately shaped refractive index matched prism with surfaces normal to the incoming beams can circumvent this issue in some cases. A similar consideration may be the back reflection of the exposing light from the substrate, which, in some cases, can be eliminated by using a transparent refractive index matched substrate. In the case that the substrate is opaque, an anti-reflection coating can be utilized to minimize the back reflection. Since it may not be necessary to configure the beams such that the angles of incidence between the beams and the substrate are equal, it might be necessary in some cases to optimize the anti-reflection coating, and/or use an absorbing layer to minimize back reflections. In addition, when using an opaque substrate, it may be required that all the beams come from the same half-space. In order to be able to fabricate structures (e.g., a diamond structure), beams with k vectors that do not come from the same half space may be used. In some cases, structures may be accessed that retain most of the Fourier terms and properties of the desired structure, which at the same time can be achieved by beams which are launched from the same half-space. For example, if the sinusoidal term along the <111> direction is dropped from the equation of the diamond structure, the resultant structure may still retain its band gap. The beams used to make this structure by single exposure now may all come from the same half space as described in Table 1 as the 3 term "Diamond-like" structure.

Utilization of both continuous and pulsed lasers have been demonstrated to be effective in multi-beam interference lithography. Continuous wave systems may be useful in setups where the matching of path lengths are not guaranteed, including systems in which a phase plate is used. However, the fabrication of thicker samples with a continuous wave system may, in some cases, require the use of a photoresist platform that does not undergo a refractive index change during the relatively long exposure time (e.g. 5 min). Thus, in some embodiments, a sufficiently short pulse width, high-intensity laser would potentially allow access to a wider variety of materials systems.

Some laser systems have Gaussian beam profiles, which can lead to a significant variation in the light intensity between the center and the periphery of the beam. This intensity variation may cause a spatial variation in the volume fraction of the resultant structure. Examples of approaches for reducing this risk include expanding the beam sufficiently such that the variation in volume fraction is within the desired limits, and/or converting the Gaussian profile into a top hat function via, for example, a refractive beam shaper.

Example 5

The fabrication of two types of concave multivalent polymer particles, 4-valent particles from a parent simple square lattice and 6-valent particles from a parent simple cubic structure via interference lithography, are described below. As described herein, the parameters selected for the external source of energy to be applied to the particle precursor structure may determine the size, shape, etc, of the resultant structure. Listed below are the parameters for fabrication of a 4-valent particle (simple square lattice) and 6-valent particle (simple cubic structure). The light intensity distribution may depend on the relative directions and polarizations of the interfering beams. The final directions and polarizations of the beams inside the photoresist are respectively given by:

Simple Square Lattice

Jc₀ = 2π/λ [0 0.316 0.949] E₀ = [I O O]

Jc_x = 2π/ λ [0 -0.316 0.949] £, = [1 0 0]

Simple cubic structure [Co-ordinate system is oriented with each orthonormal axis parallel with each pair of coplanar beams]

Jt₀ = 2π/λ [-0.970 -0.243 0] E₀ = [0 0 1]

Jt₁ = 2π/ λ [-0.970 0.243 0] E₁ = [0 0 1] Jc₂ = 2π/ λ [0 -0.970 0.243] E₂ = [I O O]

Jc₃ = 2π/ λ [0 -0.970 -0.243] E₃ = [1 0 0] k₄ = 2π/λ [-0.243 0 -0.970] E₄ = [0 1 0] k₅ = 2π/ λ [0.243 0 -0.970] E₅ = [0 1 0]

Where Jc₁ and E₁ are the wave vector and polarizations of the I^th beam respectively, and λ is the propagating wavelength of the beam in the photoresist. Perspective views of the targeted 2D square and the 3D simple cubic bicontinuous parent structures are shown in FIG. 1 (scale bars are 300 nm). FIG. IA shows (i) an SΕM image of an interconnected structure of "four-valent" particles and (ii) a single, "four-valent" unit cell. The interconnected structure is shown after dissolution of the lightly crosslinked and uncrosslinked regions in the photoresist material by wet development in N-methyl-2- pyrrolidone (NMP), followed by supercritical CO₂ drying. The 2D periodic square structure has plane group p4mm symmetry, the high crosslink density nodes occupy Wyckoff site Ia and are 4-connected along the <10> directions. Similar procedures were followed to obtain an interconnected structure of "six-valent" particles. FIG. 1C shows (i) an SΕM image of the interconnected structure of "six-valent" particles and (ii) a single, "six-valent" unit cell. The 3D periodic simple cubic structure is a member of the Schwarz P surface level set family (space group Pm3>m ). The high crosslink density nodes occupy Wyckoff site Ia and are 6-connected along the <100> directions. The motif occupying the high symmetry Wyckoff sites in each structure is shown in the single unit cells. The interconnected network of particles described above were disconnected at the thinnest part of the arms between neighboring nodes to obtain the discrete multivalent colloidal particles. O₂ plasma or UV-assisted ozonolysis can remove organic polymer selectively and isotropically in 3D structures. Since the overall network may have very thin connections, O₂ plasma or UV/ozonolysis may not affect the final shape of the particle, and may only decrease the size of the polymer particle by 2-3 %. Further, since this is a dry process, surface tension forces may not distort shape of the particles.

FIGS. IB and ID show SΕM images of the particles after treatment to obtain individual particles. FIG. IB shows (i) an SΕM image of an interconnected structure of "four-valent" particles after UV/ozonylsis, (ii) a single, "four-valent" particle, and (iii) a theoretical model of a single, "four-valent" particle in lower insets iv and vi, respectively. FIG. ID shows (i) an SΕM image of an interconnected structure of "six- valent" particles after UV/ozonylsis, (ii) a single, "six-valent" particle, and (iii) a theoretical model of a single, "six-valent" particle in lower insets iv and vi, respectively.

In this Example, the fabricated polymer particles closely resemble the theoretically computed structures, confirming that the transfer of the light intensity pattern into the photoresist and the separation into discrete particles occurred with high fidelity. Due to the manner in which the particles disconnect, the resultant colloidal particles have a line "valency" of 4 for the square lattice and a point "valency" of 6 for the simple cubic structure.

Example 6 In the following example, various interconnected networks were fabricated using methods described herein, and the resulting structures were compared to the theoretical structures. FIG. 2A shows (i) a theoretical model of a 4 x 4, two-dimensional square lattice and (ii) a single unit cell of the square lattice, and FIG. 2B shows an SEM image of the experimental two-dimensional square lattice fabricated in SU8. FIG. 2C shows (i) a theoretical model of a 3 x 3 x 3 3D cubic lattice and (ii) a single unit cell of the cubic lattice, and FIG. 2D shows SEM images of (i) the experimental cubic lattice fabricated in SU8 and (ii) a magnified, tilted SEM image of the cubic lattice viewed along the <11 1> direction. The fabricated interconnected networks closely resembled the theoretically computed structures, confirming transfer of the light intensity pattern into precursor material with high fidelity.

Example 7

The HIL technique may allow for easy control of volume fraction along iso- intensity surfaces through several experimental parameters i.e. laser intensity, time of exposure, and chemistry of the photoresist platform. FIG. 3 shows the variation in particle shape as a function of volume fraction assuming various iso-intensity contours and the effect of an isotropic etch on the 2D square and 3D simple cubic structures, respectively. The iso intensity contour may determine the threshold which separates the highly crosslinked insoluble and low crosslinked soluble material. FIG. 3 A shows theoretical models of a single unit cell of an interconnected structure having a square lattice (i) having 40% volume fraction and (ii) having 85% relative light intensity, and (iii) a single particle of the square lattice after isotropic etching by strong solvent. FIG. 3B shows theoretical models of a single unit cell of an interconnected structure having a cubic lattice (i) having 35% volume fraction and (ii) having 75% relative light intensity, and (iii) a single particle of the cubic lattice after isotropic etching by strong solvent.

FIGS. 3A and 3B show particles obtained by lowering the light intensity and subsequently removing solvent from the low crosslinked regions. Continuously decreasing the volume fraction of the network structure via lowering the exposure may eventually pinch off the thin areas and yield disconnected particles. However, simply decreasing light intensity along isointensities may result in a less pronounced effect of the "valency" and less concave shapes in the final particles. In order to retain the pronounced nature of the "valency" and a strongly concave particle shape, an isotropic etch using a stronger solvent followed by supercritical CO₂ drying to prevent distortion of the structure due to high surface tension forces can be performed.

Example 8 The following example describes the formation of a three-dimensional structure and its subsequent use as an interference lithography template (ILT), as described herein. Titania was deposited into a SU-8 ILT from titanium propoxide (IV) under atmospheric pressure at room temperature. The ILT was removed during calcination at 500 ⁰C. SEM images of the initial polymeric ILT and the final TiO₂ inverse structure are shown in FIG. 10. X-ray diffraction measurements confirmed the phase of the annealed TiO₂ as rutile. Because of shrinkage from the sol-gel reaction, the period of the structure was reduced about 15% from 980 nm to 830 run. The bicontinuous TiO₂ structure can be used as a photonic crystal as well as a dye-sensitized solar cell with a large internal surface area for the adsorption of light-harvesting dye molecules. FIG. 10 shows SEM images of (a) a SU-8 ILT structure with R3m symmetry and (b) an inverse TiO₂ structure after infiltration of the SU-8 ILT structure with TiO₂ and subsequent calcination to remove the SU-8 ILT structure.

While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the functions and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the teachings of the present invention is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the scope of the present invention. The indefinite articles "a" and "an," as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean "at least one."

The phrase "and/or," as used herein in the specification and in the claims, should be understood to mean "either or both" of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Other elements may optionally be present other than the elements specifically identified by the "and/or" clause, whether related or unrelated to those elements specifically identified unless clearly indicated to the contrary. Thus, as a non-limiting example, a reference to "A and/or B," when used in conjunction with open-ended language such as "comprising" can refer, in one embodiment, to A without B (optionally including elements other than B); in another embodiment, to B without A (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc. As used herein in the specification and in the claims, "or" should be understood to have the same meaning as "and/or" as defined above. For example, when separating items in a list, "or" or "and/or" shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as "only one of or "exactly one of," or, when used in the claims, "consisting of," will refer to the inclusion of exactly one element of a number or list of elements. In general, the term "or" as used herein shall only be interpreted as indicating exclusive alternatives (i.e. "one or the other but not both") when preceded by terms of exclusivity, such as "either," "one of," "only one of," or "exactly one of." "Consisting essentially of," when used in the claims, shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase "at least one," in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase "at least one" refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, "at least one of A and B" (or, equivalently, "at least one of A or B," or, equivalently "at least one of A and/or B") can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitional phrases such as "comprising," "including," "carrying," "having," "containing," "involving," "holding," and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases "consisting of and "consisting essentially of shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

What is claimed:

Claims

1. A method of forming particles, comprising: providing a precursor material; effecting differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures optionally interconnected; and removing material adjacent the particulate material and separating, if interconnected, particles from each other, wherein at least some of the particles have a surface including at least one concave portion.

2. A method as in claim 1 , the method not requiring the developing process, wherein the template interconnected network is the particulate material individuated structures, interconnected.

3. A method as in claim 1 , wherein the template comprises a mold for particle formation, the method comprising developing the template by removing material surrounding the template interconnected network to define an interconnected void, the method further comprising: filling at least part of the interconnected void with auxiliary material; and allowing the auxiliary material to at least partially solidify as the particulate material, wherein the template then defines the material adjacent the particulate material which is removed.

4. A method as in claim 3, wherein the auxiliary material comprises a polymeric material, glass, ceramic, metal, metal-ceramic composite, semiconductor material, or combinations thereof.

5. A method as in claim 1 , wherein the particles are substantially non-spherical.

6. A method as in claim 1, wherein the particles comprise at least one concave surface.

7. A method as in claim 1, wherein the particles are synthetic particles comprising at least one substantially concave portion and at least three valence points, each valence point being a location at which at least three surface portions of the particle meet, no two of the at least three surface portions being coplanar or defining a common spherical portion, and at least two of the at least three portions being concave.

8. A method as in claim 1 , wherein the particles comprise at least four valence points.

9. A method as in claim 1 , wherein the particles comprise at least six valence points.

10. A method as in claim 1, wherein the particles comprise at least eight valence points.

11. A method as in claim 1, wherein the particles comprise at least six surface portions, no two of the at least six surface portions being coplanar or defining a common spherical portion, and each of the surface portions being concave.

12. A method as in claim 1, wherein the particles comprise at least eight surface portions, no two of the at least eight surface portions being coplanar or defining a common spherical portion, and each of the surface portions being concave.

13. A method as in claim 1 , wherein the act of effecting comprises exposure to an external source of energy.

14. A method as in claim 13, wherein the external source of energy is an electric, magnetic, optical, acoustic, electromagnetic, or mechanical field.

15. A method as in claim 13, wherein the external source of energy is electromagnetic radiation.

16. A method as in claim 1, wherein the precursor material comprises a polymeric material.

17. A method as in claiml , wherein the polymeric material is a gel or hydrogel.

18. A method as in claim 1 , wherein the precursor material further comprises a crosslinking agent.

19. A method as in claim 1, wherein the act of removing comprises sintering the material adjacent the particulate material.

20. A method as in claim 1, wherein the act of removing comprises etching the material adjacent the particulate material.

21. A method as in claim 1, wherein the act of removing comprises contacting the material adjacent the particulate material with a solvent.

22. A method as in claim 1, wherein the act of separating comprises exposure to oxygen plasma.

23. A method as in claim 1 , wherein the act of separating comprises exposure to UV/ozonolysis conditions.

24. A method as in claim 1 , wherein the act of separating comprises application of mechanical forces.

25. A method of forming particles, comprising: providing a precursor material; effecting differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures optionally interconnected; and removing material adjacent the particulate material and separating, if interconnected, particles from each other, wherein at least some of the particles are not spherical or ellipsoidal.

26. A method of forming particles, comprising: providing a particle precursor material; establishing a standing wave pattern in the precursor material, the standing wave pattern defining a template for a plurality of particles and resulting at least in part from the interaction of energy emitted form at least two sources, under conditions causing differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures optionally interconnected; and removing material adjacent the particulate material and separating, if interconnected, particles from each other.

27. A method of forming particles, comprising: providing a precursor material; effecting differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures that are interconnected; and removing material adjacent the particles and separating the particles from each other.

28. A method of forming particles, comprising : providing a precursor material; differential reaction, within the precursor material, to define a template for particle formation, the template comprising an interconnected network of material solidified relative to material surrounding the interconnected network, the interconnected network defining a three-dimensional matrix; optionally developing the template; forming particulate material, in a pattern directed by the template, as individuated structures optionally interconnected; and removing material adjacent the particulate material and separating, if interconnected, particles from each other.

29. A composition, comprising: a synthetic particle comprising at least one substantially concave portion and at least three valence points, each valence point being a location at which at least three surface portions of the particle meet, no two of the at least three surface portions being. coplanar or defining a common spherical portion, and at least two of the at least three portions being concave, wherein the particle has a particle size of 50 microns or less.

30. A composition as in claim 29, wherein the particle has a particle size of 25 microns or less.

31. A composition as in claim 29, wherein the particle has a particle size of 10 microns or less.

32. A composition as in claim 29, wherein the particle has a particle size of 5 microns or less.

33. A composition as in claim 29, wherein the particle has a particle size of 1 micron or less.

34. A composition as in claim 29, wherein the particle has a particle size of 500 nm or less.

35. A composition as in claim 29, wherein the particle has a particle size of 250 nm or less.

36. A composition as in claim 29, wherein the particle has a particle size of 100 nm or less.

37. A composition as in claim 29, wherein the particle has a particle size of 50 nm or less.

38. A composition as in claim 29, wherein the particle is substantially non-spherical.

39. A composition as in claim 29, wherein the particle comprises at least four valence points.

40. A composition as in claim 29, wherein the particle comprises at least six valence points.

41. A composition as in claim 29, wherein the particle comprises at least eight valence points.

42. A composition as in claim 29, wherein the particle comprises at least six surface portions, no two of the at least six surface portions being coplanar or defining a common spherical portion, and each of the surface portions being concave.

43. A composition as in claim 29, wherein the particle comprises at least eight surface portions, no two of the at least eight surface portions being coplanar or defining a common spherical portion, and each of the surface portions being concave.

44. A composition as in claim 29, wherein each surface portion of the particle is a substantially concave surface portion.

45. A composition as in claim 29, wherein the particle comprises a polymeric material, glass, ceramic, metal, metal-ceramic composite, semiconductor material, or combinations thereof.

46. A composition as in claim 29, wherein the particle comprises a stimuli- responsive material.

47. A composition as in claim 29, wherein the particle comprises a gel or hydrogel.

48. A composition, comprising: an interconnected network of individuated particles, wherein each particle is attached to one or more adjacent particles via at least three valence points, each valence point being a location at which at least three surfaces, or surface portions, of the particle meet.

49. A composition as in claim 48, wherein the particle has a particle size of 50 microns or less.

50. A composition as in claim 48, wherein the particle has a particle size of 25 microns or less.

51. A composition as in claim 48, wherein the particle has a particle size of 10 microns or less.

52. A composition as in claim 48, wherein the particle has a particle size of 5 microns or less.

53. A composition as in claim 48, wherein the particle has a particle size of 1 micron or less.

54. A composition as in claim 48, wherein the particle has a particle size of 500 nm or less.

55. A composition as in claim 48, wherein the particle has a particle size of 250 nm or less.

56. A composition as in claim 48, wherein the particle has a particle size of 100 nm or less.

57. A composition as in claim 48, wherein the particle has a particle size of 50 nm or less.

58. A composition as in claim 48, wherein the particle is substantially non-spherical.

59. A composition as in claim 48, wherein the particle comprises at least four valence points.

60. A composition as in claim 48, wherein the particle comprises at least six valence points.

61. A composition as in claim 48, wherein the particle comprises at least eight valence points.

62. A composition as in claim 48, wherein the particle comprises at least six surface portions, no two of the at least six surface portions being coplanar or defining a common spherical portion, and each of the surface portions being concave.

63. A composition as in claim 48, wherein the particle comprises at least six surface portions, no two of the at least six surface portions being coplanar or defining a common spherical portion, and each of the surface portions being concave.

64. A composition as in claim 48, wherein the particle comprises at least eight surface portions, no two of the at least eight surface portions being coplanar or defining a common spherical portion, and each of the surface portions being concave.

65. A composition as in claim 48, wherein each surface portion of the particle is a substantially concave surface portion.

66. A composition as in claim 48, wherein the particle comprises a polymeric material, glass, ceramic, metal, metal-ceramic composite, semiconductor material, or combinations thereof.

67. A composition as in claim 48, wherein the particle comprises a stimuli- responsive material.

68. A composition as in claim 48, wherein the particle comprises a gel or hydrogel.