Formation of printable granular and colloidal chains through capillary effects and dielectrophoresis

Abstract

One-dimensional conductive particle assembly holds promise for a variety of practical applications, in particular for a new generation of electronic devices. However, synthesis of such chains with programmable shapes outside a liquid environment has proven difficult. Here we report a route to simply 'pull' flexible granular and colloidal chains out of a dispersion by combining field-directed assembly and capillary effects. These chains are automatically stabilized by liquid bridges formed between adjacent particles, without the need for continuous energy input or special particle functionalization. They can further be deposited onto any surface and form desired conductive patterns, potentially applicable to the manufacturing of simple electronic circuits. Various aspects of our route, including the role of particle size and the voltages needed, are studied in detail. Looking towards practical applications, we also present the possibility of two-dimensional writing, rapid solidification of chains and methods to scale up chain production.

Figure 1. Schematics of chain formation.

(a) Particles are pulled out of a dispersion to form a ‘pearl necklace', by applying an electric field through a needle-shaped electrode. (b,c) A particle at the air–liquid interface experiences an upward dielectrophoretic force F_e and a downward capillary force F_sp stemming from the sphere–plane liquid bridge. (d) Once the particle is pulled out, it automatically forms a sphere–sphere bridge with the particle below it, and pulls that particle upwards with force F_ss.

Figure 2. Experimental realization.

(a–c) Pulling a conductive chain out of a container filled with a dispersion of Ag-coated hollow silica spheres (radius ∼30 μm, density ∼0.17 g cm⁻³) in silicone oil (viscosity=100 mPa s, density∼0.96 g cm⁻³). The electrode is first dipped into the dispersion and then an AC electric voltage (600 V, f=20 kHz) is applied (t>0 s). When the electrode is raised, a conductive chain is pulled out of the dispersion. (d) A nearly 3-cm-long chain comprising hundreds of particles can be formed within a minute (ruler in centimeters). A similar experiment is presented in Supplementary Movie 1.

Figure 3. Viability for a wide range of particle sizes.

(a) ∼100 nm; (b) ∼15 μm; (c) ∼25 μm; (d) ∼55 μm; (e) ∼100 μm; (f) ∼200 μm. The structure in a is a chain of nanoparticle aggregates rather than individual particles, with a thickness of about 1 μm. (a) Scale bar, 20 μm; (b–f) scale bar, 100 μm. See also Supplementary Movie 2.

Figure 4. DEP forces.

(a) Electric field generated by a spherical electrode at U=100 V and a polarized metal sphere right beneath it. The two spheres (solid circles) have radius a=30 μm and are separated by s=3 μm. Other details are provided in the Methods section. The induced surface charge density σ (on the lower sphere) and the electric potential φ (throughout space) are shown as colour maps. Electric field E and resultant surface forces f=σE are presented as black and white arrows, respectively. (b) Dependence of DEP force on particle surface separation s. Two different voltages are considered, U=100 V (red) and U=600 V (blue), respectively. For each voltage, we compare the result from the finite-element analysis (FEA, dots) and that from the conventional DEP model (solid curves), that is, F_e=2πɛ_oilɛ_oa³κ∇(E²)=8πɛ_oilɛ_oa⁵κU²/(2a+s)⁵. The functional form of the asymptotic solution F_e∝1/[s(ln s)²] as s→0 is plotted as the black curve. The capillary force F_sp≈5.6 μN is also shown (dashed line).

Figure 5. Particle deposition and 2D writing.

(a) Direct deposition of a formed chain at a speed of approximately 0.2 mm s⁻¹. Inset: Top view of a pattern formed by subsequent deposition of two individual chains. Particle size is of ∼55 μm. (b) Example of parallel deposition of chains composed of particles with different sizes, of ∼25, ∼55 and ∼100 μm, from left to right. (c–e) Examples of C-shaped, S-shaped and L-shaped pathways, composed of particles with sizes of ∼25, ∼15 and ∼15 μm, respectively. Scale bar, 100 μm.

Figure 6. Solidification of a formed chain.

Scanning-electron-microscopy images of a particle chain embedded in solidified paraffin wax (a) and in solidified resin (b). Scale bar, 200 μm.

Figure 7. Kinking and curling up of a chain.

Three pearl-necklace chains composed of particles with a≈30 μm and formed in silicone oil (viscosity η=350 mPa s) at pulling speeds (a) 0.01, (b) 0.1 and (c) 1 mm s⁻¹, respectively. (a) At low pulling speed, the chain remains stable after the field is turned off. At higher pulling speeds, it kinks (b) and curls up (c). Generally, the amount of excess liquid dragged with the chain depends on the pulling speed.