## 3 Results
### Oil in Water Emulsion in the Presence of HNT  
We explored the possibility of driving the oil droplet inclusion into the HNT lumen by electrostatic interactions. On this basis, an anion surfactant (SDS) was selected because it drives interactions with the positive charges of the HNT's inner surface.  
Figure 2 displays the autocorrelation function, g(\(\tau\)), obtained for the prepared suspensions with various HNT amounts in the microemulsion. A double exponential decay is observed and is correlated to the presence of two particle populations namely, oil in water droplets and HNTs. In particular, the initial decay is associated with fast particles (microemulsion) and as time progresses, the decay is associated with slow particles (HNTs). Typically, the particle volume is the parameter that most affects DLS behavior. We also observed an increase in g(\(\tau\)) intensity for the second decay as the HNT content increased.  
The hydrodynamic radii, calculated from the field-time autocorrelation functions, were reported as a function of % HNT content (Figure 3a). The increase of HNT content in the investigated suspensions appears to have a negligible effect on the Rh of the two particle populations, indicating a type of interaction that does not involve a significant change in particle size. These findings may be correlated to an electrostatic adsorption of negative oil droplets into the positively charged HNT lumen. Furthermore, the g(\(\tau\)) function provides information about the concentration of the dispersed particles (B and C parameters in Equation (1)). Figure 3b shows the concentration percentage of the two populations as the HNT content increases. The microemulsion decreases, and the content of nanotubes increases, with a non-linear trend. This behavior suggests that the oil droplets have been partially driven into the halloysite nanocontainer lumen.  
The oil droplet inclusion into the HNT lumen is shown in Figure 4 and represents the B/C ratio as a function of the SDS/HNT ratio. We observe a linear increase if the interaction between particles, ideally, does not involve any changes in their concentration. On the contrary, it was found that for \(\mathrm{R_{SDS/HNT}}\leq 915\), as SDS content increases, the B factor increases at a lower rate. This can be explained by considering a possible interaction involving an adsorption of microemulsion into the HNT lumen. In this case, the loaded oil droplets do not scatter, resulting in a slower increase to the B/C ratio.  
In particular, for \(\mathrm{R_{SDS/HNT}}\leq 1000\) (0.02% of HNT), it is possible to hypothesize the instauration of an equilibrium between micelles dispersed in solution and loaded into the nanotubes. The value of \(\mathrm{R_{SDS/HNT}}=1000\) can be considered as a parameter for the estimation of the saturation limit. In fact, with a higher amount of SDS, the B/C rises linearly as in absence of any interaction.  
Figure 4: B/C ratio as a function of sodium dodecyl sulphate (SDS)/HNT ratio for the HNT-microemulsion prepared and their schematic representation.  
Figure 3: (**a**) Hydrodynamic radius of HNT (red circles) and microemulsion (black squares). (**b**) % of particles from DLS intensity for microemulsion (black squares) and HNT (red circles) particles.