Particle-polymer dispersions are ubiquitous in additive manufacturing (AM), where they are used as inks to create composite materials with applications to wearable sensors, energy storage materials, and actuation elements. It has been observed that directional alignment of the particle phase in the polymer dispersion can imbue the resulting composite material with enhanced mechanical, electrical, thermal or optical properties.
where the operator, Re, is used to find the real component of the Clausius–Mossotti term and ε˜=εεo−iσ/ω is the complex dielectric permittivity of the particle or the medium. In the DC limit, where ω = 0, fcm is dominated by conductivity values, while dielectric constants are important at high frequencies (ω→∞).Dipolar chains also form in response to electric field-induced polarization of the particles in solution. The dipolar chain energy acting on a single pair of particles in an electric field is :
where p=3εmεoVpfcmE is the dipole moment of the particle pair, r is the center-to-center separation distance between particle pairs, P2 is a Legendre polynomial of order two, and θ is the angular orientation of the particle pair with respect to the direction of the applied electric field. The force representation of Equation (4) is :
where er is a unit vector that connects the particle pair and ez is a unit vector that points in the direction of the electric field. In uniform electric fields or electric fields with weak gradients, dipolar chain structures are observed in the resulting composite. These dipolar chains assemble with structures oriented in the primary direction of the applied electric field and, with particle loadings in sufficiently high concentrations, bridge the gap between electrodes, forming a percolated network. Spirulina, a microscopic organism with a spring-like structure, is coated with silver and dispersed in polydimethylsiloxane (PDMS) . The Spirulina structures are used to create microcoils, as shown in Figure 2A. These microcoil particles assemble into chains between electrodes to form a composite with a conductivity of 10 S/m, which is eight orders of magnitude larger than non-aligned Spirulina samples (Figure 2B). Carbon nanocones dispersed in an acrylated urethane form chain structures that improve the electrical conductivity of the polymer from 10−7 to 10−3 S/m .
where χp and χm are the magnetic susceptibilities of the particle and medium, respectively, and μo is the magnetic permeability of free space. The magnetic induction, B, is related to the applied magnetic field, H, by the expression   B=μo(1+χm)H. In addition to magnetophoresis, multiple particles also form dipolar chains in the direction of the magnetic field. The interaction energy between a single pair of particles in a magnetic field is :
where m=(χp−χm)VpB/μo is the magnetic moment of the particle and θ is the angle the pair forms with respect to the direction of the magnetic field. The force representation of Equation (7) is :
where er is a unit vector that connects the particle pair and ez is a unit vector that points in the direction of the magnetic field. The use of magnets as a mechanism for composite fabrication has a long history due to the ease of the process and simplicity of blending para- or ferromagnetic particles with a polymer medium [97,98,99,100,101]. When magnetically sensitive particles are crosslinked in a polymer, the composite forms a magnetoelastomer that deforms in the presence of a magnetic field [102,103]. An alternative method for creating magnetoelastomers was suggested by the authors of this review . In this alternative approach, a sacrificial scaffold was created in PDMS. The scaffold was dissolved, and a magnetorheological fluid was introduced to the evacuated channel, rendering the structure sensitive to magnetic field-induced deflections. Magnetoelastic soft actuators (sometimes referred to as ferrogels) are designed by coupling magnetic properties of filler particles and elasticity of the polymer matrix. Understanding the deformation and mechanical properties of such actuators is crucial for optimizing their performance . The deformation of these composites in the presence of a magnetic field is analogous to muscle constriction , which makes these types of composites ideal for actuation applications such as haptic control surfaces for steering . Magnetite (Fe3O4) is one of the most frequently used filler material due to its high magnetic susceptibility , which makes it easy to pattern structures in polymers using externally directed magnetic fields . Fe3O4 can be adsorbed on cellulose nanocrystals to fabricate magnetic cellulose nanocrystals (MGCNCs). The MGCNCs, shown in Figure 3, then are aligned in different configurations (parallel or perpendicular directions) in the polylactic acid matrix through a tunable magnetic field which result in fabrication of particle-polymer nanocomposite with anisotropic electrical and magnetic properties. The percent elongation improvement of the resulting nanocomposite is in the range of 60% to 240% . This use of magnetic fields to locally pattern magnetite-PDMS composites led to a reduction in local elastic modulus by as much as 50% depending on filler particle concentration. While local elastic properties of the composite may see a reduction due to magnetic field-induced concentration, the bulk storage moduli of a magnetite-based composite are observed to increase by a factor of two depending on the field magnitude used to align particles . Magnetite can also be functionally bound to materials that are not ferromagnetic, such as cellulose  or glass , to create materials with anisotropic mechanical properties or functional structures, like the circuit shown in Figure 4A,B.
where β = 1/ρc2 is the compressibility, ρ is density, c is the speed of sound, Φ is the acoustic contrast factor, λ is the wavelength of the acoustic field, and P is the pressure distribution. The subscripts p and m refer to particle and medium properties, respectively. The pressure distribution for a one-dimensional standing wave is   P=Pocos(2πfx/cm), where Po is the pressure amplitude and f is the applied frequency.
Acoustic nodes are created when the acoustic wave is reflected. The resulting superposition of incident and reflected waves interfere with each other . This phenomena, known as standing acoustic waves (SAW), has long been recognized as a method for separating small particles or drops dispersed in a fluid [135,140,141,142]. The relative difference in particle density and compressibility dictates whether particles migrate towards or away from the acoustic pressure node where the wave interference leads to a local pressure of zero. Particles that are more dense and less compressible than the medium, such as polystyrene  or cells , migrate to acoustic pressure nodes. Particles such as microbubbles   or PDMS   are less dense or more compressible than the medium in which they are dispersed, leading to migration towards the acoustic pressure antinode, where the pressure gradient is highest.
To demonstrate the utility of SAWs as a method for particle-polymer composite fabrication, early studies used polysiloxane as the polymer medium due to its ease of use and low cost . The composite was prepared by blending the polysiloxane with a curing agent at a ratio of 20:1. Ten-micron acrylic spheres were dispersed in the polysiloxane fluid to act as filler particles. The acoustic field frequency was adjusted to create multiple acoustic nodes for filler particle assembly and allowed to set for 8 h. Adjusting the orientation and number of transducers can lead to different internal microstructures, such as lines or lattices . Diffraction experiments showed that acoustic fields were excellent for localizing particles around the acoustic node . Diamond nanoparticles with diameters of 5 nm were successfully arranged in ethanol-diluted epoxy matrix using acoustic standing wave to produce polymer nanocomposite. The radiation force of standing waves in a rectangular chamber was used to pattern clusters of nanoparticles. During the epoxy curing cycle of 5 min, the standing wave was activated and diamond nanoparticles migrated toward the nodes due to acoustic radiation force and formed quasi-parallel planes of particle clusters (Figure 5A) . Complex particle-polymer composite structures can be formed using SAWs if the acoustic signal is first passed through a pattern that acts like a “hologram” for the desired structure (e.g., Figure 5B) [151,152,153].