Thermal Fluctuations and Positional Correlations in Oriented Lipid Membranes

We have determined the positional correlation functions in aligned stacks of fully hydrated phospholipid bilayers from the thermal diffuse scattering measured by nonspecular x-ray reflectivity. While fair agreement can be obtained between experiment and linear smectic theory at length scales above 120 Å, significant deviations occur at small $r$, which are tentatively attributed to collective protrusion modes.

Figure 1

Sketch of the setup with the typical intensity pattern on the 2D detector.

Figure 2

(a) Horizontal cut through the 2D intensity array, yielding the structure factor $S(n,q_r)$ of an average bilayer along with power-law fits (solid lines), and (b) the corresponding correlation function (open circles) along with $g(r)$ according to Eq. (2) (solid line), as well as an asymptotic power law (dotted line).

Figure 3

(a) Cuts through the $n=1$ diffuse Bragg sheet along $q_z$ at different $q_y$, showing a characteristic broadening of the $q_z$ width (FWHM), quantified in (b) as a function of $q_r$, along with a parabolic fit (solid line).

Figure 4

$T$ dependence of the elasticity coefficients and fluctuation amplitude: (a) $\lambda (T)$, (b) ${\sigma }_s^2(T)$ or equivalently $\eta (T)$ (right axis), and (c) $\kappa (T)$ (full circles, left axis) and $B(T)$ (open squares, right axis).