Repulsion Between Inorganic Particles Inserted Within Surfactant Bilayers

We study by synchrotron small-angle x-ray scattering highly aligned lamellar phases of a zwitterionic surfactant, doped with monodisperse and spherical hydrophobic inorganic particles as a function of particle concentration. Analysis of the structure factor of the two-dimensional fluid formed by the particles in the plane of the bilayer gives access to their membrane-mediated interaction, which is repulsive, with a contact value of about $4k_{B}T$ and a range of 14 Å. Systematic application of this technique should lead to a better understanding of the interaction between membrane inclusions.

Figure 1

Structure factors $S(q)$ of the 2D fluid formed by the BuSn12 particles in the plane of the membranes, for different concentrations, from top to bottom: $n=0.217$, 0.231, 0.429, 0.434, 0.451, 0.584, 0.801, 1.102, 1.275, 1.976, 2.147, and $2.304\times {10}^{-3}{\AA }^{-2}$. The curves are shifted vertically in steps of 0.2. Gaps in the curves correspond to the presence of (weak) lamellar peaks, due to occasional alignment defects, mainly taking the form of oily streaks.

Figure 2

The Fourier transform of the interaction potential $\tilde{U}(q)$ (open dots) obtained from the structure factors in Fig. 1 in the RPA approximation (1). The solid line is a Gaussian model. The shaded area is chosen to cover most experimental points and is also delimited by two Gaussians (see text for details). The data points far above and far below the shaded range correspond to $n=0.429$ and $0.584\times {10}^{-3}{\AA }^{-2}$, respectively (third and sixth curve from the top in Fig. 1).

Figure 3

Interaction potential $U(r)$ of the BuSn12 particles within the bilayers, obtained by taking the inverse Fourier transform of the solid line and the shaded area in Fig. 2 (see text for the numerical values). The lower curve is the interaction potential of the particles in ethanol. The solid vertical line marks the hard core interaction with radius 4.5 Å.