Towards Holonomic Control of Janus Particles in Optomagnetic Traps

Janus particles generally refer to a class of colloids with two dissimilar faces having unique material properties. The spherical asymmetry associated with Janus particles is the key to realizing many commercial applications, including electrophoretic displays, nanosviscometers, and self-propelling micromachines. These diverse functionalities were accomplished by using an external electric or magnetic field to control the particle orientation, and in the process, modulate its reflectivity, hydrodynamic mobility, or direction of motion, respectively. However, these same asymmetries can interfere with optical trapping techniques that are used to control the translational degrees of freedom of a particle. Optical fields present an effective method for controlling the three translational degrees of freedom for particles ranging from tens of nanometers to micrometers in size. Previously, optical fields have been used in combination with magnetic fields to control four degrees of freedom of an asymmetric particle or particle aggregate. To achieve five or more degrees of freedom, magnetic Janus particles can theoretically be used; however, none so far have been stable in an optical trap. Controlling all six degrees of freedom of Janus particles, including three translational and three rotational, would open up new applications not only in biophysical force and torsion measurements, but also in microfluidics and material selfassembly. Here we report on a new type of spherical Janus that can be manipulated by a combination of optical and magnetic fields. We demonstrate the ability to directly control five degrees of freedom of the particle’s motion (three translational and two orientational) while constraining the final sixth degree of freedom. Ultimately, this demonstration represents the most control ever achieved over freely suspended spherical colloidal particles and opens up many exciting applications; the most obvious being the exertion of torsional and linear forces on biomolecules. The main achievement reported here was to develop a method of synthesizing magnetically anisotropic Janus particles that are also compatible with conventional optical trapping systems. We developed a novel lithographic technique for forming so-called ‘‘dot’’ Janus particles, which have a metallic coating covering <20% of their surface area. The advantage of this approach is that the dot Janus particles behave more like normal dielectric particles in an optical trap, while also responding to magnetic forces and torques produced by an external magnetic field. Purely dielectric and metallic Mie and Rayleigh particles have been optically trappedusing a variety of techniques. Bothdielectric microparticles and nanoparticles can be trapped in three dimensions with a high degree of spatial control. Metallic nanoparticles can also be trapped in three dimensions because scattering frommetallic and dielectric particles are similar in this size regime. However, metallic microparticles can only be controlled in two dimensions, due to considerations previously documented by others. For anisotropic Janus particles, such as dielectric particles that are partially covered by metal, the trapping stability in a focused optical beam depends to a great extent on the degree of metal coverage of the particle surface. Here we propose a general explanation for why optical trapping is more easily accomplished with dot Janus particles than with half-coated Janus particles. In the Mie size regime, where the particle diameter is large compared with the trapping wavelength, l, the momentum imparted by a focused optical beam can be described using geometric ray optics following Ashkin’s line of reasoning. In brief, each light ray refracts and reflects at the particle/fluid interface according to Snell’s law, and the momentum change between the incident ray and the refracted/reflected ray is summed over all incident rays to determine the net force on the particle. Typically, the net force is artificially divided into a gradient force, arising from refraction through the particle, and a scattering force, arising from reflection at the particle surface. The gradient force tends to pull the particle towards the beam focus, whereas the scattering force tends to push the particle away from the emission source. Figure 1 illustrates the incident light rays a and b refracted through the particle and the gradient forces ~Fa and ~Fb imparted on the particle due to each light ray. The ray optics approach reveals the importance of the symmetry of conjugate light rays in an optical trap. As long as the gradient force balances the scattering force, ~Fs, the trap will remain stable. For particles partially coated by reflective metal, the symmetry of this process may be broken, leading to unbalanced torques and forces that will depend on the position and orientation of the particle. As illustrated in Figure 1b, the metal coating inhibits light