Concentration dependence of shape and structure fluctuations of droplet microemulsions investigated by neutron spin echo spectroscopy

We describe dynamic modes that originate from shape and structure fluctuations in a droplet microemulsion system. The modes are decoupled by a contrast variation neutron scattering technique using the relative intermediate form factor method. The strategy of the method is analogous to the relative form factor method, which decouples the form and structure factors from the small-angle neutron scattering intensity [M. Nagao et al., Phys. Rev. E 75, 061401 (2007)]. First, we will briefly explain theoretical and experimental approaches to understanding neutron spin echo (NSE) data from droplet microemulsion systems. Then we will introduce the relative intermediate form factor method, which decouples shape and structure fluctuations. The concentration dependence of the droplet dynamics in a microemulsion system is used to elucidate the strengths of this method. The intermediate form and structure factors are successfully decoupled from an observed intermediate scattering function by NSE. The decay rate of the shape fluctuation modes linearly decreases, while the fluctuation amplitude increases as the droplet concentration increases. The first cumulant of the obtained intermediate structure factor shows a clear de Gennes narrowing behavior at a length scale corresponding to the interdroplet distance. However, in the high-momentum-transfer and longer-time regions, the first cumulant deviates from the intermediate structure factor. This result suggests the existence of other dynamic modes of structure fluctuations rather than the center-of-mass diffusion mode.

Figure 1

(Color online) Observed $I\left(q,t\right)/I\left(q,0\right)$ from (a) the bulk contrast and (b) the film contrast samples in AOT microemulsion with a droplet concentration $\varphi$ of 0.3. The solid lines indicate the fit results according to a single-exponential function. The error bars shown in this text indicate $\pm 1$ standard deviation.

Figure 2

$D_{\text{eff}}\left(q\right)$ and SANS profile from $\varphi =0.3$ for (a) the bulk contrast and (b) the film contrast. SANS data shown here are the same data as the previous publication [19]. Dashed vertical lines are shown to guide the eye.

Figure 3

(Color online) Evaluated $R\left(q,t\right)$ for AOT microemulsion of $\varphi =0.3$. The lines are the fit result according to Eq. (15).

Figure 4

Obtained ${\Gamma }_{\text{rel}}\left(q\right)$ and $R\left(q\right)$. The $q$ values of the peak of $R\left(q\right)$ and the dip of ${\Gamma }_{\text{rel}}\left(q\right)$ are at almost the same $q$. The $R\left(q\right)$ data are the same as used in the previous work [19]. The solid line indicates the fit result of ${\Gamma }_{\text{rel}}\left(q\right)$ according to Eq. (16).

Figure 5

(Color online) Comparisons between the static form factor calculated in Ref. [19] and $D_{\text{def}}\left(q\right)$ for $\varphi =0.3$ of both contrasts. The deformation motion is enhanced at the same $q$ value as the dip position of the SANS profile. This tendency is much more visible in the film contrast data.

Figure 6

(Color online) Obtained $F\left(q,t\right)/F\left(q,0\right)$ for $\varphi =0.3$. Solid symbols are those of bulk contrast and open symbols are of film contrast, respectively. The error bars are not shown in this figure for better visualization. The error bars are dominated by the error of $⟨{\left|a_2\right|}^2⟩$ of about 10%.

Figure 7

(Color online) Obtained $S\left(q,t\right)/S\left(q,0\right)$ for $\varphi =0.3$. Solid symbols are those of bulk contrast and open symbols are of film contrast, respectively. The error bars are not shown in this figure for better visualization. The error bars are dominated by the error of $⟨{\left|a_2\right|}^2⟩$ of about 10%. The solid and dashed lines are fit results according to Eq. (23).

Figure 8

Obtained $q$ dependence of $D\left(q\right)$ and $D^{\prime }\left(q\right)$ for $\varphi =0.3$.

Figure 9

Typical example for the first cumulant analysis for the bulk contrast sample of $\varphi =0.3$ at $q=0.10{\text{Å}}^{-1}$. The solid straight line indicates the linear fitting to the first cumulant. In the longer-time region, a clear deviation from the line is obvious.

Figure 10

(Color online) Concentration dependence of best-fit parameters for the shape fluctuation mode, ${\Gamma }_2^{\text{b}}$ and $⟨{\left|a_2\right|}^2⟩$. The solid and dashed lines are the fit results according to Eq. (24) or (25).

Figure 11

Obtained $\varphi$ dependence of the bending modulus $\kappa$. The solid line is a guide to the eye.

Figure 12

(Color online) Obtained $\varphi$ variation of $D\left(q\right)$ and $D^{\prime }\left(q\right)$. The horizontal straight line is a theoretical value of $D_0$ from the Stokes-Einstein relation.