## 3 Results
### Analysis of Limitations of 5 CB and HTAB for Homeotropic Alignment  
Despite the different design considerations between RF applications and LCDs, no prior research has evaluated the importance of the cell gap condition. Therefore, we analyzed the effectiveness of HTAB as a surface-active agent with 5 CB at different cell gaps. We studied how the vertical self-assembly of 5 CB LC molecules was affected by [HTAB] and by the cell gap (Figure 4). We plotted the evaluation of the effectiveness of the HTAB for each case. In the fully-homeotropic aligned state (Figure 4, blue circle), every part of the sample looked black between the crossed-polarizers, and OT was \(<\) -0.83%. The partially homeotropically aligned state (Figure 4, green triangle) was caused by insufficient [HTAB], and a non-aligned state was caused by a large cell gap condition (Figure 4, red cross); these regions looked bright under the cross-polarized configuration and had high OT (Figure S1, Supporting information).  
In this work, we proposed a reference for the minimum [HTAB] for fully VA to 20 \(\upmu\)m. In this range of the cell gap, we found that for the higher cell gap, more [HTAB] is needed for a fully aligned state. For the cell gap = 2.5 \(\upmu\)m and 5 \(\upmu\)m, [HTAB] = 0.05 wt% is enough. However, at the cell gap = 10 \(\upmu\)m and 20 \(\upmu\)m, [HTAB] must be \(\geq\) 1 wt%. This is because for a larger cell gap, stronger anchoring strength for a fully aligned state is necessary, which is related to the [HTAB]. This surfactant's concentration dependency can be found in other studies [23; 36]. The anchoring strength is related to the concentration of ions at the ITO glass surface [37]. If [HTAB] is too low in the solution, the molecules cannot orient well. There are some references to [HTAB] and the cell gap condition, using HTAB for VA (Table 1).  
At the cell gap \(\geq\) 50 \(\upmu\)m, HTAB could not form a homeotropic alignment (Figure S1, Supporting Information), because HTAB has a weak anchoring force. Although [HTAB] in 5 CB was high enough and a sufficient number of layers formed to the ITO glass surface, when the cell gap was too large, the fluidity and interaction forces among the molecules  
\begin{table}
\begin{tabular}{c c c c} \hline
**Ref.** & **Liquid Crystals** & **Cell Gap [\(\upmu\)m]** & **HTAB Concentration [wt\%]** \\ \hline
[8] & 8 CB (Achiral Nematic LC) & 20 & 0.1 \\
[10] & 8 CB (Achiral Nematic LC) & 10 & 0.94 \\
[23] & 5 CB (Nematic LC) & 3.25 & 0.05 \\
[38] & Unknown (Positive Nematic LC) & 3 & 0.1 \\ \hline \end{tabular}
\end{table}
Table 1: The references about the homeotropic alignment using HTAB.  
Figure 4: Diagram of alignment states vs. cell gap and surface-active agent concentration. _times_: no alignment, \(\Delta\): non-uniform homeotropic alignment caused by insufficient [HTAB], \(\circ\): fully-homeotropic alignment across the entire cell.  
disturbed the homeotropic alignment, so it was not maintained throughout the LC medium. This limitation imposed by the cell gap means that when HTAB is used as a surface-active agent for homeotropic alignment in RF structures, they must be designed to have the cell gap \(<\) 20 \(\upmu\)m, perhaps by adjusting design parameters such as electrode conditions or using the RF technique such as loaded line design for a lower cell gap [25].