# Repulsive Force for Micro- and Nano-Non-Contact Manipulation
## 5 Model and Experimental Measurements Comparison
### Repulsive Force on Polymer Film  
Equation (4) also predicts that the repulsive force increases with the density charge of the surface or of the sphere. In order to validate the model, the charge density of the surface was modified by changing the molecule deposited on the surface. Previous studies demonstrated that polymer film could build up a large repulsion distance to solutes when immersed in an aqueous solution greater than 200 \(\upmu\)m [16]. To increase the charge density of the deposited molecule and to better localize it, an electropolymerization of a film was performed. The polypyrrole was chosen due to the presence of NH groups and its ability to be deposited locally on electrodes (Figure S7). The electrodeposition was performed by potentiostatic chronoamperommetry on a silicon substrate previously covered by sprayed chrome and gold to enhance its conductivity. Different counter ions (0,1M) were used to determine the impact of each other on the repulsive force. The evolution of the current intensity with time was similar regardless of the supporting salt used (Figure SI-8). However, the charge density values differed from one salt to the other: the highest charge density was obtained with tetrafluoroborate anions when the lowest one was obtained for toluenesulfonate anions, which is consistent with the literature [26]. The PPy/LiClO4 film had a granular structure and covered the whole surface of the substrate (Figure S9) even if it could be seen that the thickness of the film was not entirely uniform due to its surface roughness. The same tendency was observed with the other supporting salts used in this work. Indeed, the counter-ion used during the synthesis of the polymer film plays an important role in the structure, and thus on the film morphology (Figure S10) [25; 26]. Hence, its influence on the repulsive force was studied at pH 2, between a polypyrrole-modified surface and a 10 \(\upmu\)m sphere functionalized by APTES (Figure S11) and summarized in Table 3. In Table 3, a repulsive force was measured with an amplitude between 2.5 and 4.9 \(\upmu\)N and a repulsive distance upper to 33 \(\upmu\)m, which was higher than the previous experiment (Figure 1A (blue curve), and Table 1) with the aminosilane APTES. This increase can be explained by the higher density of the amine groups in polymer films compared to aminosilane-film. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**Experimental**} & \multicolumn{2}{c}{**Modeling**} \\ \hline
**Ionic Strength: NaCl** & **Interaction Force** & **Interaction Distance** & **Interaction Force** & **Interaction Distance** \\
**(M)** & **(\(\upmu\)N)** & **(\(\upmu\)m)** & **(\(\upmu\)N)** & **(\(\upmu\)m)** \\ \hline
0 & 0.7 \(\pm\) 0.15 & 5.7 \(\pm\) 0.7 & 0.6 \(\pm\) 0.1 & 5 \(\pm\) 0.5 \\ \hline
0.01 & 0.2 \(\pm\) 0.1 & 0.5 \(\pm\) 0.43 & 0.3 \(\pm\) 0.045 & 2 \(\pm\) 0.2 \\ \hline
0.1 & 0.05 \(\pm\) 0.01 & 0.2 \(\pm\) 0.1 & 0.09 \(\pm\) 0.02 & 0.7 \(\pm\) 0.07 \\ \hline
1 & 0.03 \(\pm\) 0.01 & 0.1 \(\pm\) 0.06 & 0.03 \(\pm\) 0.005 & 0.2 \(\pm\) 0.02 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of the repulsive force and distance measured or modeled between the silica surface and a 10 \(\upmu\)m borosilicate sphere, both of which are functionalized by APTES for different ionic strengths controlled by the addition of NaCl. The data are collected during three experimental campaigns. For every campaign, new bead and substrate are considered, and force is measured in 10 different locations on a substrate. Regardless of the counter-ions used, the repulsive forces with the polypyrrole were at least four times higher than with APTES-modified surfaces, which confirms that an increase of the charge density increases the force, as predicted by the model. The repulsive force differences can partially be explained by the morphology of the polypyrrole film, depending on the counter-ion used.