Abstract
Acoustic forces are an attractive pathway to achieve directed assembly for multi-phase materials via additive processes. Programmatic integration of microstructure and structural features during deposition offers opportunities for optimizing printed component performance. We detail recent efforts to integrate acoustic focusing with a direct-ink-write mode of printing to modulate material transport properties (e.g. conductivity). Acoustic field-assisted printing, operating under a multi-node focusing condition, supports deposition of materials with multiple focused lines in a single-pass printed line. Here, we report the demonstration of acoustic focusing in concert with diffusive self-assembly to rapidly assembly and print multiscale, mm-length colloidal solids on a timescale of seconds to minutes. These efforts support the promising capabilities of acoustic field-assisted deposition-based printing to achieve spatial control of printed microstructures with deterministic, long-range ordering across multiple length scales.
Keywords: microfluidics, acoustic fields, nanoparticle assembly, architected materials, additive manufacturing
Graphical Abstract

1. Introduction:
Architected materials offer a significantly expanded set of functional properties over bulk material counterparts as a result of optimizing the composite microstructure for a given application[1]. Such materials garner considerable interest[2–6] on account of enhanced electrical, thermal, and structural properties suitable for use in a wide range of applications including . Typical approaches to fabricating materials with hierarchical microstructures utilize stochastic (e.g. freeze-casting)[7, 8], direct patterning[9–14], or self/directed assembly methods[15–19] to embed aligned particles within a polymer matrix. While capable of producing stochastic, short-range-ordered microstructures, these methods lack the capability to manufacture defect-free materials with deterministic, long-range ordering in a rapid, scalable manner.
The ability to control particle alignment across volume fraction ranges would create new opportunities to print composite materials with engineered isotropic/anisotropic properties. Emerging approaches for achieving such top-down control over material microstructure seek to combine field-assisted assembly with direct deposition[20]. While electrostatic or electromagnetic fields are suitable for a narrow range of ink compositions and particle types, acoustic fields are promising on account of broad applicability to a wide class of colloids, spanning a wide range of composition, particle shape, and size[21].
Acoustic forces created by standing pressure waves are an attractive pathway to increasing the density and alignment of particles[22]. Such forces are active over large distances and relatively material agnostic, lacking the specific requirements in surface functionalization, solution chemistries, or electromagnetic properties specified for other field-assembly methods[23]. For many applications of engineered materials, the included particles are micron-sized or larger[24]. In these cases, the magnitude of easily achieved acoustic forces is much greater than those associated with fluid drag, implying that particles can be transported and assembled over relatively long distances on the order of seconds or less[25]. These benefits create new opportunities[26] to incorporate acoustic excitation in nozzles used for three-dimensional printing (particularly for direct-ink-writing[21, 27–30] (DIW) and stereolithography[31] approaches) to dramatically increase the density and alignment of particles relative to that of the ‘ink’.
This perspective highlights progress in utilizing acoustic field-assisted printing to fabricate functional composite materials. Recent reviews contextualize the utilization of acoustic fields for static assembly[32] (i.e. align then solidify) or examine progress in relationship to other field-assisted approaches[20]. These reviews identify several powerful concepts including integration of acoustic fields into vat polymerization[31], molding/casting[23, 33, 34], and gantry-based laser curing[21, 35, 36] of materials with patterned, aligned particle phases. By contrast, the work described here centers on integration of acoustic fields within an active print nozzle[22, 25–27, 29, 37, 38] for use in a dynamic mode of operation (i.e. during printing). We describe our recent efforts to address some of the fundamental challenges to printing functional composite materials with ordered microstructures across multiple length scales.
2. Acoustic field-assisted printing of functional composite materials
Acoustic field-assisted printing methods integrate piezoelectric actuators typically into either microfabricated microfluidic channels or glass capillaries, which serve as print nozzles for DIW[38]. These acoustic nozzles (Fig. 1a) enable alignment of particles or fibers in a viscoelastic matrix upon the application of an applied acoustic force (generated by the piezoelectric elements). Critically, acoustic focusing enables control of the microstructure of the deposited line by modulating acoustic excitation parameters[25, 26]. By tuning the excitation frequency to induce focusing, particles collapse to the acoustic nodes (tunable from 1 to N, frequency dependent). In an initial demonstration[29] using static assembly (i.e. absence of flow in the nozzle), an acoustic field can focus conductive particles into a patterned composite material that exhibits conductivity at a particle volume fraction below the percolation threshold (Fig. 1a-b, unpatterned composite is insulating). This results from structuring particles into percolated bundles rather than a disconnected stochastic network. In order to achieve conductivity in the absence of patterning, a significantly higher particle loading volume is required (Fig. 1c), resulting in loss of mechanical flexibility. As the patterned structures are a function of the acoustic parameters, modulation of the focusing frequency enables facile control of line pitch. This reported conductivity is 1D, parallel to the focused isolated bundles of fibers. Modulating the focusing wavelength controls the bundle spacing, which in turn controls the number of fibers bridging between bundles resulting in control over conductivity in the perpendicular direction (Fig. 1e-g). Controlling the focused line spacing modulates the electrical conductivity of the patterned composites between anisotropic or nearly isotropic.
Fig 1.

(a) Conceptual illustration of acoustic print nozzle. Piezoelectric actuation generates acoustic forces that align fibers/particles during printing. (b-d) Photographs of silver-coated fiber elastomeric composites twisted to demonstrate gains in flexibility and conductivity via acoustic patterning. Adapted with permission from[29]. (e-g) Demonstration of modulation in conductive transport properties due to focusing conditions resulting in either (e) isotropic or (f) anisotropic conductivity in contrast to the absence of conductivity (g) in the unfocused material. Adapted with permission from [29]
Integrating this modulation within a printing mode such as DIW enables printing focused structures with complex patterns to modulate material properties throughout a part. Both the print direction and the nature of the focusing at a given point can be utilized to modulate the finished part’s properties. Focusing can be turned on and off and the number of nodes can be adjusted. Early efforts demonstrate significant promise as shown in Fig. 2a-c. Composites with different conductive pitches can be fabricated utilizing the same channel geometry (3 mm, silicon/glass nozzle) with resulting spacing dependent primarily on the number of nodes within the channel (15 nodes: 200 μm pitch; 44 nodes: 68 μm pitch; 63 nodes: 48 μm pitch). While improved control over within-line ordering is required, the limitation of pitch width depend primarily upon obtainable focusing frequencies (equipment depending) and particle size (must be smaller than between-node spacing). Printing with multi-node focusing enables high throughput creation of periodic structures by eliminating sequential printing of the component lines. Fig. 2d-e shows a multi-node print with multiple focused lines of alumina particles in epoxy both as extruded from a print nozzle (onto a glass substrate) and at the conclusion of the single-pass. This mode of operation is further extensible to the scalable production of simple microstructure configurations composed of linear features in a roll-to-roll process by employing a wide nozzle with a sufficiently high node count.
Fig 2.

(a-c) Photographs of silica spheres in water acoustically focused at 3.3 MHz, 10.7MHz, and 14.99MHz respectively. (d) Multi-node acoustic focusing of flowing slurries of alumina particles in epoxy at a range of particle loadings. (e) Glass nozzle extruding multiple acoustically focused lines and (f) single-pass printed line containing multiple focused lines of alumina particles in epoxy
A key benefit to utilizing acoustic fields is the absence of diminished or restricted performance for material systems with high particle loading. Fig. 2f illustrates this concept by examining acoustic focusing performance of flowing slurries of alumina particles in epoxy across a wide range of particle concentrations. Even at comparatively high particle loadings (50 wt %) the presence of focused lines is readily apparent; however, there is a loss of geometric fidelity. This is a consequence of densifying focused structures such that the feature width increases once the focusing channel fills completely in the vertical direction. For highly viscous material systems, this effect is more pronounced as the increased viscosity increases the total time required for particles to translate to nodal positions. Under flow, this results in the poor focusing of a small fraction of particles if the zone of focusing is not of sufficient length. Optimization of the nozzle geometry, length of focusing zone, and capability for increasing applied acoustic energy can yield improved focusing performance.
These initial efforts suggest acoustic focusing is a highly promising approach to modulating other transport phenomena beyond electrical conductivity. As a relatively material agnostic technique for microstructural control, acoustic focusing-assisted additive manufacturing greatly expands the library of printable multiphase inks and resultant material microstructures. This technology demonstrates a novel approach to modulating material properties via microstructure control to pave the way for 3D printing components with embedded electrical circuits or other spatially modulated properties.
3. Integration of diffusive self-assembly with acoustic field-assisted printing
A central challenge to creating bulk materials with ordered microstructures from nanoparticles control over particle distribution across multiple length-scales[39]. Typical microstructures formed by casting or rolling colloidal suspensions of unmodified nanoparticles are highly variable with broad distributions in void size throughout the bulk domain[40, 41]. Functionalization of the nanoparticle surface offers an elegant mode for controlling particle arrangements yielding colloidal crystals with long-range ordering. The growth of such functionalized particle clusters is limited by diffusion with transport times growing prohibitively as microscale aggregates consume nearby particles[40]. Thus, the development of hierarchical assembly pathways with alternative time and length scales are of intense interest. Critical to any multiscale assembly strategy is the requirement that the underlying mechanisms for each assembly stage must be ‘orthogonal’ to the first. That is, any physical, chemical, electrostatic or magnetic change to the system must not interfere with the functionalization used in other stages.
Recently, our group harnessed the material agnostic nature of acoustic forces to print colloidal materials assembled via acoustic fields to overcome the significant timescale limitations of diffusional assembly for particles larger than 1 μm. Using a material system comprised of streptavidin-functionalized fluorescent polystyrene microspheres (SPM, 2 μm diam.) and biotinylated gold nanorods (AuNR, 25 nm dia. x 75 nm) we report the experimental demonstration of SPM forming, in the presence of excess AuNR, large assemblies O[~250 μm] in 12 s with an applied acoustic field via an acoustic nozzle (Fig. 3a,b). Fig. 3c shows continued excitation for a total of 18 s yields a continuous, unified assembly O[1 mm]. These assemblies are robust enough to remain intact when extruded onto a glass substrate (Fig. 3d). Fig. 3e,f show scanning electron microscope (SEM) micrographs of the microstructure of the assembled SPMs and the nanoscale bridges formed by the AuNRs binding the SPM assemblies. Although demonstrated for polystyrene beads and AuNRs, this approach is suitable for both monodisperse colloidal systems[8, 17, 22, 29], and other multiscale material systems (e.g., DNA/SiO2, Si nanoparticles/block copolymers) and extensible in terms of particle size and shape. By harnessing diffusional self-assembly, particles too small for effective acoustic focusing can be assembled into aggregates large enough for acoustic focusing and combined with larger particles. Rapid, long-range control over micro/nano assemblies enables both novel material synthesis and new sensing platforms (e.g., via sintering, controlled spacing, and/or spatially patterned mesostructure). As a relatively material agnostic technique for microstructural control, acoustic field-assisted printing offers a compelling approach for quickly assembling and depositing large-scale assemblies of micro/nanoparticle systems.
Figure 3.

(a) Schematic illustration of a two-stage acoustic field-assisted deposition nozzle using diffusive self-assembly and focusing to assembly mm-length multiscale structures. (b) Fluorescent microscope images illustrate the absence of large-scale structure formation from the material system via diffusive self-assembly alone. Utilization of acoustic fields facilitates assembly of colloidal structures on the order of minutes in the absence of flow. (c) Under applied flow, large scale structures can be fabricated on the order of seconds (18 s for structure here). (d) Colloidal structures exhibit sufficient robustness to support extrusion from the acoustic nozzle and subsequent imaging via SEM. (e-f) SEM images show the multiscale microstructure comprising gold nanoparticles and polystyrene microspheres
4. Expanding theoretical models of acoustic field-assisted printing
Most studies examining acoustophoretic-induced particle motion and the resultant structures that form employ low particle concentration material systems to avoid direct contact between particles[22, 26, 42–46]. The minimization of particle-to-particle interactions within such systems enables the detailed study of system physics; however, the production of functional materials with programmed properties requires material systems with higher particle concentrations. This concentration increase introduces new questions regarding particle interactions during focusing and the nature of the resultant structures. Recently, we reported[37] molecular dynamics simulations that model interactions between high concentrations of particles and yield insight into the geometry of the aggregate structure. As Fig. 4 highlights, these simulations closely mimic the particle behavior observed experimentally, both in terms of particle transit paths and structure formation. These simulations also yield insight into influence of acoustic focusing parameters on structure geometry. Fig. 4c shows that increasing the applied acoustic pressure results in the densification of the banded particle structures (increased height, decreased width). Models such as the one described here and those developed by others offer substantial promise for enabling prediction of the final structure of acoustically focused composite materials. Coupling these efforts into multiphysics simulations may provide a pathway not only for predictive insight into printed structure but also for optimizing focusing conditions to generate materials with specific, programmed material properties.
Figure 4.

(a) Sequential images from a simulation of focusing silica spheres in water. (b) Sequential images from experiment of focusing silica spheres in water at the same volume fraction and pressure as used in the simulation. (c) Simulated focused line cross section profiles for a range of acoustic pressures. (c) is adapted with permission from [37]
5. Opportunities and Outlook
Existing additive manufacturing technologies have demonstrated exciting capabilities for fabricating complex geometries unobtainable via traditional methods. Current printing methods are primarily limited to monolithic materials (metals, ceramics, and soft materials) and lack programmatic control over the printed microstructure. Emerging techniques for printing multiphase materials using hydrodynamics with particle-laden inks or voxelated print nozzles offer expanded capabilities; however, such methods remain restricted in ability to achieve high particle densities and/or long-range ordering. Integration of field-assisted spatial control, particularly in the form of colloidal assembly, with direct deposition printing techniques represents a promising approach for achieving top-down control over the microstructure during fabrication. While electrostatic or electromagnetic fields are promising for a narrow range of ink compositions and particle types, acoustic fields are broadly applicable to a wide class of colloids, spanning a range of composition, particle shape, and size. Efforts by our groups and others have established the promise of acoustic focusing for hierarchical material assembly[20]. Further advances are required to identify the key relationships between particle properties, external field parameters, and processing conditions yield defect-free bulk materials in a scalable mode of operation. Realization of a such a fabrication pathway is vital to unlocking the unparalleled potential offered by the coupling of electromagnetic, transport, mechanical phenomena in materials with custom-tailored properties.
Footnotes
CRediT Statement:
K.J.: Writing- Original draft preparation, Writing- Reviewing and Editing, D.M., M.B., D.S.G.: Writing- Reviewing and Editing, T.R.R.: Conceptualization, Writing- Original draft preparation, Writing- Reviewing and Editing
Conflict of Interest:
D.M., M.B., D.S.G., and T.R.R. declare that patent applications based on this work have been submitted to the University of California, Santa Barbara. All authors declare no additional conflicts of interest.
Data Availability:
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
