# Repulsive Force for Micro- and Nano-Non-Contact Manipulation
## 6 Applications  
The repulsive force generated between the surface and the object could be used for micromanipulation tasks. Indeed, if we compare the repulsive force generated by the interaction between a microsphere and a surface in pH 2 (4.9 uN, Table 3) with the weight of the microsphere of borosilicate (11 pN), it appears that it would be easy to place it easily in levitation up to a substrate. This may be interesting for the non-contact micromanipulation to guarantee that a manipulated object will never come into contact with the substrate.  
We may also imagine other ways to exploit this high density of charges on micro-objects in non-contact micromanipulation. Indeed, the chemical functionalization generates an important charge density on the sphere, which may induce a high electrophoresis force when located in the electric field. These properties can be used to control the trajectory of the object by electrophoresis. As an example, we consider a sphere functionalized with APTES located in an electric field controlled with an electric voltage located on micro-electrodes. We consider a working space made up of four square electrodes of 100 um each in aqueous medium, and a voltage applied to each of the electrodes one after the other every 2 s, clockwise. As it is impossible to apply larger tensions when the point of water electrolysis is at 2 V (electrolysis bubbles would perturb object manipulation), we thus consider a voltage of 1.8 V. The results of the simulation presented in Figure 4A show the trajectory of the microsphere. The travel speed increases exponentially between each position (electrode) from 80 um.s\({}^{-1}\) at the beginning of the movement to 170 um.s\({}^{-1}\) at the end of the trajectory (Figure S12). As the electrophoresis and the drag forces are surface forces, the behavior of the microsphere, and thus its speed, will be the same regardless of the microsphere radius. If we compare these results with the dielectrophoresis, which generates a volume force [5], the manipulation speed varies from 25 um.s\({}^{-1}\) to 1000 um.s\({}^{-1}\) for an object diameter from 2 um to 80 um, respectively. Thus, the electrophoresis combined  
\begin{table}
\begin{tabular}{c c c} \hline
**Salt** & **Interaction Force (\(\mu\)N)** & **Interaction Distance (\(\mu\)m)** \\ \hline LiClO\({}_{4}\) & 4.9 \(\pm\) 0.2 & 47 \(\pm\) 4 \\ \hline PTS & 2.5 \(\pm\) 0.1 & 33 \(\pm\) 3 \\ \hline NaNO\({}_{3}\) & 3.6 \(\pm\) 0.1 & 38 \(\pm\) 4 \\ \hline NaBF\({}_{4}\) & 4.1 \(\pm\) 0.2 & 45 \(\pm\) 5 \\ \hline \end{tabular}
\end{table}
Table 3: Repulsive force and distance measured at pH 2 for different counter-ions used during the pyrrole electrodeposition.  
with surface functionalization appears to be an interesting alternative to dielectrophoresis when the object size is lower than 10 \(\upmu\)m.  
Moreover, several different chemical functions may be placed on different locations on a micro-object to generate more advanced behaviors. Concretely, the orientation of the object may also be controlled by the combination of localized surface functionalization and an electric field. As an example, considering an object having both oxide surfaces and conductive surfaces, a polymer electrodeposition (APTES) can be localized on a conductive surface (Figure S7), whereas the silane molecules could be grafted on oxide surfaces. If the object is grafted with localized amine and carboxylic groups on each side, it generates a high electric dipole (Figure S13). The object will behave as a dipole in an electric field and experiences a high torque which enables it to control its rotation. We demonstrated through simulations that the total rotation of a microsphere may be realized in 6 s with the electrodes defined previously and by applying to the opposite electrodes +0.9 V and -0.9 V simultaneously, every 1.5 s to maximize the speed (Figure 4B).