Reconfigurable multi-component micromachines driven by optoelectronic tweezers

There is great interest in the development of micromotors which can convert energy to motion in sub-millimeter dimensions. Micromachines take the micromotor concept a step further, comprising complex systems in which multiple components work in concert to effectively realize complex mechanical tasks. Here we introduce light-driven micromotors and micromachines that rely on optoelectronic tweezers (OET). Using a circular micro-gear as a unit component, we demonstrate a range of new functionalities, including a touchless micro-feed-roller that allows the programming of precise three-dimensional particle trajectories, multi-component micro-gear trains that serve as torque- or velocity-amplifiers, and micro-rack-and-pinion systems that serve as microfluidic valves. These sophisticated systems suggest great potential for complex micromachines in the future, for application in microrobotics, micromanipulation, microfluidics, and beyond.

shows the measured 3D profile of a standard micro-gear used here, in which the thickness is indicated in a heat map (blue = low, red = high). Supplementary Figure 1b shows the cross-sectional profile of the micro-gear, corresponding to the dashed-white cutline in Supplementary Figure 1a. As indicated, the width and thickness of the standard micro-gear were approximately 200 μm and 60 μm, respectively, and the overall dimensions were similar to those that were designed (Supplementary Figure 3a). These standard microgears were used for most experiments; large and small micro-gears were used in others, described in Suppementary Note 6, below.

Supplementary Note 2: Direct and Indirect Micro-object control
Micro-objects (including micro-gears) were directely controlled by OET by (1) applying a a sine-wave AC bias between the electrodes on the bottom and top plates of OET devices (if not otherwise specified, the magnitude and frequency was 30 Vpp at 10 kHz), and (2) projecting an optical image onto the bottom plate of an OET device. The order of these steps (1 & 2) was varied; objects in the chamber are not affected until both are engaged (with one exception -see the discussion in Supplementary Note 3, below). In the conditions used here the objects to be controlled experience negative DEP force [1] ; thus, the images in (2) were designed to push particles into regions that were not illuminated. The images used in (2) are described in the following: The most common image was an optical ring-spanner paired with an optical axle (e.g., Figure 1d in the main text). The optical ring-spanner was a negative-relief outline of the perimeter of the standard micro-gear, comprising an illuminated hollow circle (or ring) with 8 illuminated optical teeth (isosceles  (v) A doughnut-(or ring-) shaped image with 68 μm inner diameter and 13 μm ring-thickness was used to manipulate polystyrene microbeads [2] (e.g., Supplementary Figure 5a (vi) Images used to control micro-gear-trains (e.g., Figure 5 in the main text and Supplementary Movie 12-14) included three sub-components: optical boundaries, optical axles, and partial optical ring-spanners.
Optical boundaries are illuminated, hollow outlines (with 30 μm thickness) designed to closely circumscribe the outer perimeter of each gear-train, and optical axles are identical to what is described above. Partial optical ring spanners are similar to what is described above (with rotating optical teeth on a hollow ring used to drive the rotation of a micro-gear), but with an opening (that is not illuminated) located at the portion on the micro-gear that engages with its neighbor. Further, the optical ring thickness and diameter, as well as the number and size of optical teeth were scaled appropriately when used to control small and large gears (described in Supplementary Note 6 below).
(vii) Images used to control micro-rack-and-pinion (e.g. Figure 6 in the main text and Supplementary Movie 15) included three sub-components: optical boundaries, optical axles, and partial optical ring-spanners.
Optical boundaries are illuminated straight lines (with 50 μm thickness) designed to circumscribe the outer perimeter of the pinion. Optical axles are identical to what is described above. Partial optical ring spanners are similar to what is described above (with rotating optical teeth on a hollow ring used to drive the rotation of the rack), but with an opening (that is not illuminated) located at the portion on the rack that engages with the pinion.
In addition to direct OET control, micro-objects (including polystyrene microbeads and mammalian cells) were also controlled indirectly by fluid flow driven by micro-gear rotation. Micro-objects were found to revolve around single rotating micro-gears. In such systems, linear velocities of micro-objects were calculated from the revolution time and the approximate travel-path. Micro-objects were found to travel linearly between microgears in touchless micro-feed-rollers, and their Cartesian coordinates and velocities were determined using Tracker (https://physlets.org/tracker/). Micro-objects were made to (indirectly) follow more complex (3D) trajectories using OET-bridged touchless micro-feed-rollers (Supplementary Note 5, below), and the rotation of secondary micro-gears was (indirectly) controlled by direct action of primary micro-gears (suppelementary note 6, below).

Supplementary Note 3: Dielectrophoretic manipulation and failure mode analysis
In an OET system, the micromanipulation force relies on dielectrophoresis (DEP), an electrokinetic phenomenon in which a non-zero force is exerted on a polarizable particle suspended in a medium when it is subjected to a non-uniform electric field. The strength of the DEP force depends on the medium's and the object's electrical Supplementary Information properties, on the object's shape and size, as well as on the frequency and magnitude of the electric field. The most widely used method to calculate the DEP force is the classic dipole approximation [1] in which the force acting on a spherical particle is given by the following, where r is the particle radius, m ε is the permittivity of the medium, E is the amplitude of the root-mean-square (RMS) electric field, and Re[K(ω)] is the real part of Clausius-Mossotti (CM) factor. The latter is defined by the following, where * p ε and * m ε are the complex permittivities of the particle and medium, respectively. When Re[K(ω)] > 0, the DEP force acting on the object is positive (such that it moves into the illuminated regions); when Re[K(ω)] < 0, the DEP force acting on the object is negative (such that it moves away from the illuminated regions, as in the conditions used here). Note that equation (1) is derived from the consideration of a single molecular dipole; it is not appropriate for quantitative predictions of force acting on large structures such as the micro-motors used here.
Thus, the qualitative trends predicted from equation (1)  illuminated by a 50-μm-diamater circular light pattern (in the X-Y plane) using a model reported previously. [2] As shown in Supplementary Figure 2a although it is often ignored in the literature, there is also a large field gradient in Z dimension, [3,4] which can influence the behaviour of particles in Z direction as well. This is fundamentally important for the work in Suppelemtnary Note 5, below.
When a rotating optical ring spanner and axle is projected into an OET device, the electric field gradient in the X-Y dimension (Supplementary Figure 2b) drives a dielectrophoretic force (eq. 1) that causes a micro-gear in the vicinity to rotate, as well, such that the micro-gear remains in the dark regions of the device. This effect is predictable at low angular velocities, but begins to fail at high velocities, such that the micro-gear does not keep up with the projection. Interestingly, one of the failure mechanisms that we observe in these cases, which we call flipping, can occasionally be observed without projecting a light pattern. Supplementary Figure 2d-e illustrates such a case -when voltage is applied (20 Vpp at 10 kHz) without a light projection, the mico-gear flips on its side in the Z-dimension. Similar phenomona have been reported for silver nanowires [5] and carbon nanotubes [6] in OET systems (with no light projected), which were attributed to shaped-induced anisotropic polarization. That is, Supplementary Information while the projection of light is typically used to generate strong electric field gradients in OET devices (Supplementary Figure 2b-c), the simple presence (in the dark) of an asymmetric object wth Re[K(ω)] ≠ 0 can also generate electric field gradients, in a manner similar to insulator-based DEP. [7] This may explain why micro- Other mechanisms that may play a role include light-induced AC electroosmosis [9] (LACE), in which ion- N⋅m by integrating the fluidic viscous stress moment (X-Y plane) over the surface of the micro-gear using the following equation, [10] Body in which ∏ is the fluidic viscous stress and r is the position factor of a point relative to the rotational axis.

Supplementary Note 5: Micro-object manipulation in three dimensions
A series of permanent micro-structures, including micro-walls, micro-plateaus, and square and circular microcorrals, were formed from SU-8 on OET bottom plates using methods similar to what we reported previously. [11] Supplementary Figure  height was determined as a function of apparent (out-of-focus) bead area using methods similar to those described previously. [4] Briefly, first, the microscope stage was fixed in position such that a 15 µm dia. bead at or near the bottom plate surface was in focus (Z = 0). Then, the stage was raised to Z = 60 µm to collect an image of the (out-of-focus) bead. Then, the stage was raised in 5 µm increments from Z = 60 µm to Z = 160 µm, collecting an image of the (out-of-focus) bead at each step. These data allowed for calibration of apparent (outof-focus) bead area as a function of Z-axis position. Second, in OET-bridged touchless micro-feed-roller experiments, the area of the apparent bead-area (when most out of focus) was compared to the calibration data to estimate the Z-axis position at apogee.

Supplementary Note 6: Micro-gear-trains
Micro-gear-trains were formed from two or more micro-gears positioned such that the teeth in the gears can Supplementary Information engage mechanically with each other (e.g., Figure 5 in the main text). Micro-gear-trains were formed from standard micro-gears (Supplementary Figure 1), but also from small and large micro-gears (Supplementary μm, respectively, and the thicknesses are approximately 30 μm. (The reduced thickness was found to be important for manipulation of large micro-gears.) Note that the small micro-gear has eight teeth (like the standard micro-gear), but no through-hole (and was not used with an optical axle), whilethe large micro-gear has sixteen teeth and a through-hole (and was used with an optical axle).
Micro-gear-trains were positioned such that one or more micro-gears was active, with rotation driven by the rotation of a partial optical ring-spanner, and one or more micro-gears was passive, with rotation driven by mechanical interaction with an adjacent micro-gear (in opposite direction to that of the adjacent micro-gear). In general, for each pair of gears in a gear-train, the velocity v of the point of contact on between them is: where the driving or input micro-gear has radius In r and angular velocity In ω , and the output micro-gear has radius Out r and angular velocity Out ω . The mechanical advantage MA (also known as the torque ratio) is: where Out N is the number of teeth on the output micro-gear, In N is the number of teeth on the intput mico-gear, Out T is the output torque, and In T is the input torque.

Supplementary Note 7: Micro-rack-and-pinion systems
Micro-rack-and-pinion systems were formed from a standard micro-gear (the pinion) and a ~500 μm-long, ~63μm thick L-shaped rack (Supplementary Figure 7a-b). Each arm of the L in the rack is ~35 μm wide, and the portion of the long arm closest to the junction features five teeth with dimensions and pitch designed to match those in a standard micro-gear. Micro-rack-and-pinion systems were positioned such that an active pinion was controlled directly by an optical ring-spanner. Rotation of the pinion caused the passive rack to move in a predictable linear pattern when surrounded by the appropriate optical boundaries ( Figure 6 in the main text).
Micro-rack-and-pinion systems were designed to interface with a permanent butterfly pattern microstructure (Supplementary Figure 7c). The center of each butterfly design (Supplementary Figure 7d) features four parallel SU-8 features which together define the sidewalls of three parallel 50 μm wide microchannels. The three microchannels terminate into a large chamber, but at the junction the assembly is bisected by ~55 μm wide openings. The pattern was designed to interface with two rack-and-pinion-systems -one to the left and one to the right of the microchannel junction. When oriented properly, when the pinions rotate, the long axis of each rack penetrates the perpendicular openings at the junction, where they can choke-off the flow through the microchannels. Supplementary Information Each butterfly design was formed from ~93-μm thick SU-8 (Supplementary Figure 7e) on OET bottom plates using methods similar to what we reported previously. [11] OET devices bearing these structures were similar to the standard devices described in the main text, except that the top plate was modified to include two 1 mm dia.
inlet-and outlet-holes, and the spacer between the top and bottom plates (formed from Adhesive Research product 90178, which is ~88 μm thick) featured a linear chamber with shape and dimension shown in Supplementary Figure 7f, formed by xurography using an automated craft cutter (Graphtec ce6000-60). Upon assembly (Supplementary Figure 7g), each device featured one butterfly SU-8 structure located in the center of the chamber, with the three parallel microchannels parallel to the long axis of the chamber. When compressed together, the two plates and the SU-8 microstructure formed a network of sealed microchannels.