# Hydrothermal Preparation of Faceted Vesicles Made of Span 40 and Tween
## 4 Discussion
A conventional formation mechanism of spherical vesicles results from the bending induced in the lamellar structure with open ends (a flake-like membrane [29; 30] or bicell [31; 32; 33]). It was clarified that this curvature correlated with the (1/P)\({}_{\text{DPH}}\) value from the studies using giant vesicles [34; 35]. Therefore, the membrane of the Span 40-rich region with low (1/P)\({}_{\text{DPH}}\) (Figure 6b) could not be bent, which is consistent with the observation (Figure 5b,c). Thus, the facets formed by Span 40 and the rim formation by Tween 40 led to the faceted vesicles. In other words, it could be concluded that the SCW/SD method gave the faceted vesicles of Span 40/Tween 40 (80/20). As shown in Figure 5, the faceted vesicles contained Types A and B. Why Type A rather than Type B vesicles were more likely to be formed is discussed. Type B vesicles have more rims than Type A vesicles (see Figure 5e,f). Type A vesicles, having major and minor axes, possess the side with large curvature corresponding to the minor axis. Tween 40 could then be gathered at the side, which is advantageous for Tween 40 which has a large headgroup relative to Span 40. In contrast, Type B vesicles required more rims than Type A vesicles. This would be entropically unfavorable if Tween 40 molecules gathered at the side of Type A vesicles and were reorientated into new rims on Type B vesicles (i.e., the transition of Type A to Type B vesicles), although the energetical study should be examined. However, it has been shown that faceted structures can be low energy configurations of elastic spherical vesicles [23; 36; 37; 38]. If so, the faceted vesicles closer to the spherical vesicle (Type B) might be more stable than Type A vesicles. This might result from the larger and more steric headgroup of Tween 40 than other surfactants such as catanionic amphiphiles [12], diamidophospholipids [11; 14], and fatty acid/fluorinated fatty acid systems [16; 17]. As long as the Span 40/Tween 40 system is non-ionic, it is, therefore, considered that Type A rather than Type B vesicles were observed in the present experiment. Finally, we discuss why the calcein leakage occurred at the gel state (Figure 6d). Generally, the lipid membranes at a gel state indicate there is low permeability to calcein [39; 40; 41]. It is therefore the bent region, rather than Span 40-rich planes at the gel state, that is responsible for calcein leakage. This is related to the restriction of a free volume in lipid membranes [41] and to an ordered structure of acyl chain at the gel state [42]. The bending of vesicle membrane associated with the localization of Tween 40 would increase the free volume and reduce the ordered structure of the acyl chain. In addition, vesicles made of Span 40 (GP\({}_{\text{340}}\) = 0.6 \(\pm\) 0.04) indicated a higher GP\({}_{\text{340}}\) value than Span 40/Tween 40 (80/20 wt/wt%) (GP\({}_{\text{340}}\) = 0.1-0.2, see Figure 6c), which is in agreement with the previous report [8]. This suggests that the rim (Tween 40) is more hydrophilic than the facets(Span 40-rich region). From this viewpoint, it could be considered that calcein favored the leakage via the rims where Tween 40 was located.