Thermal fluctuations of fluid membranes in multilamellar systems have been extensively studied during the past decade by means of nuclear spin relaxation. Such data have generally been analyzed in terms of an effectively two-dimensional membrane model, which does not properly incorporate the mutual coupling of the individual membranes. Here we present a comprehensive theory of spin relaxation induced by small-amplitude, long-wavelength elastic distortions in a multilamellar stack of fluid membranes. In contrast to previous theoretical treatments, we find that membrane coupling can profoundly affect the spin relaxation behavior via its effect on the amplitudes and rates of membrane distortion modes. A physical basis for the resulting, rather intricate, spin relaxation behavior is provided by analyzing the spatial correlation function for the local membrane orientation. We find that the decay of this function involves two correlation lengths: one is related to interactions with the two adjacent membranes, and the other reflects the coherent fluctuation modes in the entire membrane stack. This analysis explains why the time correlation function has the asymptotic form $1/{\tau }^2$ rather than $1/\tau ,$ as expected for a two-dimensional system. A reinterpretation of existing low-frequency spin relaxation data from multilamellar phospholipid-water dispersions in terms of our theory should provide valuable insights into the nature of intermembrane forces.

• Received 10 July 1996

DOI:https://doi.org/10.1103/PhysRevE.56.690