Investigation of the effect of bilayer membrane structures and fluctuation amplitudes on SANS/SAXS profile for short membrane wavelength.

The effect of bilayer membrane structures and fluctuation amplitudes on small angle neutron scattering (SANS) and small angle X-ray scattering (SAXS) profile is investigated based on harmonic motions of the surfactant bilayers with bending as well as thickness fluctuation motions. In this study we consider the case in which the wavelength of the bilayer membrane is shorter than the thickness of the membrane. We find that the thickness of the surfactant bilayer membrane, d(m), affects both q(dip) and q(peak) of I(q,0) profile, and that the fluctuation amplitude, a, of the membrane changes the peak of I(q,0). A simple formula is derived to estimate the thickness of the bilayer based on the q(dip) of the profile obtained from the simulation. The resulting estimates of the thickness of the bilayer with harmonic motion showed accuracy within 1%. Moreover, the bilayer thicknesses estimated from the proposed formula show an excellent agreement with the SANS and SAXS experimental results available in the literatures. We also propose a curve fit model, which describes the relationship between the fluctuation amplitude and the normalized q(peak) ratio. The present results show the feasibility of the simple formula to estimate the fluctuation amplitude based on the SANS and SAXS profiles.