# A Review on Optoelectrokinetics-Based Manipulation and Fabrication of Micro/Nanomaterials
## 3 OEK-Based Manipulation of Micro/Nanomaterials  
### Separation and Assembly of Micro-Scaled Particles  
The OEK chip has been commonly used to perform manipulations such as separation, concentration and assembly on micro/nanoparticles, with the aid of an ODEP and/or ACEO mechanism. The OEK chip permits the assembly of 2D colloidal microparticles by using the electrohydrodynamic flows [54; 55; 56] and the manipulation of droplets [57; 58; 59]. Differently sized polystyrene beads serve various functions in material science and biomedical research. Hence, finding a rapid and automatic method to manipulate and separate them is critical in investigating the performance of targets of interest. The conductivity of polystyrene beads is size-dependent and expressed as \(\sigma=2K_{S}/R\), where \(K_{S}\) is the surface conductivity of polystyrene beads [42]. The relationship between the crossover frequency (Re [\(K(\omega)\)] = 0) of the ODEP force and the size of the polystyrene beads can be further derived as [42]  
\[f_{\text{{\tiny crossover}}}=\frac{1}{2\pi}\sqrt{\frac{(\sigma_{m}R-2K_{S})(2K _{S}+2\sigma_{m}R)}{R^{2}\Big{(}\varepsilon_{p}-\varepsilon_{m}\Big{)}( \varepsilon_{p}+2\varepsilon_{m})}}. \tag{3}\]  
The size-dependent crossover frequency as a function of the liquid conductivity, i.e., Equation (3), is illustrated in Figure 4[42]. Then, separation of 1 \(\upmu\)m and 10 \(\upmu\)m polystyrene beads was successfully demonstrated by using ODEP forces in different directions, i.e., a positive ODEP force exerted onto the 1 \(\upmu\)m polystyrene beads and a negative one onto the 10 \(\upmu\)m ones, as shown in Figure 5[42]. Figure 4: Crossover frequency vs. liquid conductivity of three differently sized polystyrene beads (reproduced from Ref. [42]). Figure 3: Structure of T\({}_{i}\)OP\({}_{c}\)-based OEK chip and simulation of the electric field (reproduced from Ref. [50]). Moreover, polystyrene beads with three different diameters, i.e., 500 nm, 1 \(\upmu\)m, and 10 \(\upmu\)m, were separated simultaneously. Figure 6 shows the detailed experimental process [42]. A negative ODEP force would be exerted onto the 10 \(\upmu\)m diameter polystyrene beads, while a positive ODEP force would be exerted onto both the 500 nm and 1 \(\upmu\)m ones. However, the 1 \(\upmu\)m polystyrene beads would experience a much higher magnitude of ODEP force than the 500 nm ones because the magnitude of the ODEP force is proportional to the third power of the particle radius. Manipulation and assembly of metallic microspheres into patterns were proposed [60]. It was observed that conductive silver-coated poly(methyl methacrylate) (PMMA) microspheres (50 \(\upmu\)m diameter) could move in an OEK chip at a maximum velocity of 3200 \(\upmu\)m/s, much quicker than  
Figure 5: Separation of 10 \(\upmu\)m and 1 \(\upmu\)m polystyrene beads. (**a**) Initially, polystyrene beads were suspended in the liquid solution; (**b**) the OEK chip was illuminated by the optical ring pattern, with the AC bias potential switched on simultaneously; (**c**) 10 \(\upmu\)m polystyrene beads were pushed towards the central area of the ring under the action of a negative ODEP force, while the 1 \(\upmu\)m ones were attracted into the ring under the action of a positive ODEP force as the ring size decreased; (**d**,**e**) are captured images showing the positions of the polystyrene beads with two different diameters as the ring size decreased dynamically; (**f**) shows the final positions of the 10 \(\upmu\)m and 1 \(\upmu\)m polystyrene beads (reproduced from Ref. [42]). Figure 6: Simultaneous separation of polystyrene beads with diameters of 500 nm, 1 \(\upmu\)m, and 10 \(\upmu\)m. (**a**) When the OEK chip was illuminated by the optical rectangle pattern under the action of an external AC bias potential, both the 500 nm and 1 \(\upmu\)m polystyrene beads were attracted to the illuminated area.