We report a high-resolution x-ray study of a model multilayer fluid membrane system in the lyotropic $L_{\alpha }$ phase of a quaternary microemulsion system. The structure factor exhibits power-law behavior characteristic of a Landau-Peierls system. As a function of intermembrane distance $3.8 \mathrm{nm}\le d\le 16.3 \mathrm{nm}$, the exponent $\eta \mathrm{}\left(d\right)\mathrm{}$ which describes the algebraic decay of layer correlations is predicted by the model of Helfrich where entropic steric repulsions dominate intermembrane interactions.

• Received 12 August 1986

DOI:https://doi.org/10.1103/PhysRevLett.57.2718