Structure and dynamics of reverse micelles containing supercooled water investigated by neutron scattering

We present a detailed neutron scattering study of the structure, shape fluctuations, and translational diffusion of microemulsion droplets at low temperatures. We investigate the ternary microemulsion ${\text{D}}_2\text{O}$, AOT [bis(2-ethyl-hexyl) sulfosuccinate], and toluene-d8 (or heptane-d16) which forms spherical water droplets surrounded by a monolayer of AOT dispersed in oil around room temperature. At $T=290\text{K}$, varying the molar ratio $\omega$ of water to AOT between 3 and 12, we find using small angle neutron scattering water core radii $R_c$ between 7 and $18\text{Å}$, respectively. We characterize the structure at low temperatures down to $T=220\text{K}$. Upon cooling the droplet structure is maintained and $R_c$ stays roughly constant down to temperatures where the confined water is deeply supercooled. At an $\omega$-dependent temperature $T_s$ we observe for all compositions a shrinking of the droplets, which depends on the initial droplet size: the smaller the initial radii, the lower the $T_s$ is. At the lowest investigated temperature $T=220\text{K}$ we find an $\omega$-independent remaining water core corresponding to a number of about 2 water molecules per AOT molecule. Neutron spin-echo spectroscopy is used to monitor shape fluctuations and translational diffusion for one microemulsion ($\omega =8$, $R_w=12\text{Å}$) from $T=300\text{K}$ down to temperatures below the corresponding shrinking temperature $T_s$. Thereby we determine the bending elasticity to be $\kappa =0.3k_{B}T$ over the whole investigated temperature range where the droplets are stable. From these results we cannot establish a link between surfactant membrane elasticity and low temperature structural instability of the droplets. Moreover, our results show that reverse AOT micelles are an excellent tool for the study of soft confined water over a broad range of confining sizes and temperatures down to the supercooled state.

Figure 1

Schematic coherent scattering length density $\rho$ profile of an AOT reverse micelle and a ${\text{D}}_2\text{O}$ swollen AOT reverse micelle in toluene-d8. Core radius $R_c$ and shell thickness $d$ are marked below the drawing.

Figure 2

Scattering from sample 3 (${\text{D}}_2\text{O}$/AOT/toluene-d8, $\varphi =0.2$, $\omega =8$) at three different temperatures. Solid lines are fits to the described form factor plus structure factor model. For clarity curves are shifted vertically by a factor shown close to the right axis. With decreasing temperature the micelles decrease in size (shown by arrow, see text for further explanations). Error bars are smaller than the symbols.

Figure 3

Core radii of water swollen micelles as a function of temperature. Sample names as introduced in Table are written above each curve. Error bars are smaller than the symbols.

Figure 4

(Color online) Supercooling $\Delta T$ as a function of micelle core radius $R_c$. Hollow symbols are results from elastic scans on backscattering [18]; full symbols correspond to SANS. Solid line shows the Gibbs-Thomson dependency [Eq. (10)] with the theoretical constant $K_{\text{GT}}=524\text{K}\text{Å}$.

Figure 5

Scattering from $20\text{vol}\%$ AOT reverse micelles dispersed in toluene-d8 (●, sample 5, $T=278\text{K}$) and decane-d22 (○: sample 6, $T=283\text{K}$, shifted by a factor 2). Error bars are smaller than the symbols. Solid lines are fits to a core-shell form factor combined with structure factor (see Sec. 2B2).

Figure 6

Fitting parameters for AOT reverse micelles dispersed in toluene-d8 (●, sample 5) and decane-d22 (○: sample 6). Core radius $R_c$, polydispersity $p$, shell thickness $d$, and scattering length density ${\rho }_s$ of the shell.

Figure 7

(Color online) Sample 4 (figures in first line) and sample 3 (figures in second line): radius $R_c$, shell thickness $d$, and polydispersity $p$ upon cooling (full symbols) and heating (hollow symbols). Cooling and heating rates: 0.5 K/min. Note the hysteresis: cooling and heating curves are in good agreement only above $T\approx 275\text{K}$.

Figure 8

Normalized intermediate scattering function $S\left(Q,t\right)/S\left(Q\right)$ at $T=265\text{K}$. Scattering vectors $Q$ are indicated next to symbols. Solid lines are fits to a single exponential function.

Figure 9

(Color online) Effective diffusion coefficient $D_{\text{eff}}$ as obtained by fitting the NSE curves to a single exponential [Eq. (11)]. Solid lines are fits to Eq. (12). Note that no maximum around $Q=0.14{\text{Å}}^{-1}$ is observed at the lowest temperature $T=250\text{K}$.

Figure 10

Temperature dependencies of fitting parameters of Eq. (12). (a) Mean droplet radius $R$, (b) dimensionless fluctuation amplitude $⟨{\left|u_2\right|}^2⟩$, (c) translational diffusion coefficient $D_{\text{tr}}$, the line is a fit to Eq. (15), and (d) relaxation rate ${\lambda }_2$ of second order oscillation.

Figure 11

Temperature dependence of bending elasticity $\kappa$ of the AOT shell calculated after Eq. (16). Dotted line shows the average bending elasticity $\kappa =\left(0.31\pm 0.06\right)k_{B}T$.