Interaction between droplets in a ternary microemulsion evaluated by the relative form factor method

This paper describes the concentration dependence of the interaction between water droplets coated by a surfactant monolayer using the contrast variation small-angle neutron scattering technique. In the first part, we explain the idea of how to extract a relatively model free structure factor from the scattering data, which is called the relative form factor method. In the second part, the experimental results for the shape of the droplets (form factor) are described. In the third part the relatively model free structure factor is shown, and finally the concentration dependence of the interaction potential between droplets is discussed. The result indicates the validity of the relative form factor method, and the importance of the estimation of the model free structure factor to discuss the nature of structure formation in microemulsion systems.

Figure 1

$\varphi$ dependence of the SANS profiles from (a) the bulk contrast and (b) the film contrast. The scattering intensity from $\varphi =0.05$ is shown in absolute units, and the others are shifted as shown in the legend for better visualization. The error bars shown in this text indicate $\pm 1$ standard deviation.

Figure 2

$\varphi$ dependence of $R\left(q\right)$s. $R\left(q\right)$ for $\varphi =0.05$ is shown as it is and the others are shifted as shown in the legend for better visualization.

Figure 3

$\varphi$ dependence of the structural parameters of the droplet shape. $r_0$ and $r_s$ are indicated with the left vertical axis unit, and $p$ with the right vertical axis unit. The vertical dotted line indicates the concentration of ${\varphi }^{*}$. The solid, dotted, and dashed lines are guides for the eyes.

Figure 4

Reproduced $F^b\left(q\right)$ and $F^f\left(q\right)$ as well as the experimentally observed SANS profiles, $I^b\left(q\right)$ and $I^f\left(q\right)$, for $\varphi =0.05$. $F^b\left(q\right)$ and $F^f\left(q\right)$ are multiplied by the number density, $n$, in order to compare with SANS profiles.

Figure 5

$\varphi$ dependence of the evaluated $S_{\mathrm{eff}}^b\left(q\right)$. The error bars are shown only for $\varphi =0.05$.

Figure 6

$\varphi$ dependence of the peak position $q_0$ evaluated from $S_{\mathrm{eff}}^b\left(q\right)$. The solid and dashed lines indicate the calculated peak position assuming the random closed packing of a sphere with its radius of 51 and $60\mathrm{\AA }$, respectively.

Figure 7

$\varphi$ dependence of $S_{\mathrm{eff}}^b\left(0\right)$ of the bulk contrast samples. The dashed line is a guide for the eyes.

Figure 8

Concentration dependence of the binding free energy, $B$, and the depth of the inter-droplet potential, $\Omega$. The vertical axis is shown in units of $k_{B}T$. Below $\varphi \approx 0.4$, both the values of $B$ and $\Omega$ tend to increase with $\varphi$; on the other hand, above $\varphi \approx 0.4\mathrm{\Omega }$ tends to decrease. The lines are guides for the eyes.