Membrane flexibility in a dilute lamellar phase : a multinuclear magnetic resonance study

We demonstrate that the bending rigidity, $\kappa$, of amphiphilic bilayers can be accurately determined from the quadrupole splitting in the NMR spectrum. We study the lamellar phase in the system water/SDS/pentanol/dodecane at layer volume fractions in the range 0.1-1, measuring the quadrupole splittings of water ($^2$H ), counterions ($^{23}$Na), and $\alpha$-deuteriated SDS ($^2$H). The splittings are governed by the layer director fluctuation $\langle n^2_{\perp}\rangle$, which we calculate self-consistently (allowing for the finite thickness of the bilayer) from the continuum elasticity theory for a sterically stabilized lamellar phase. Analysis of the data yields the same result, $\kappa = 2.2 \pm 0.2~k_{\rm B}$ $T$, for all three nuclei. Since $\langle n^2_{\perp}\rangle$ is determined by short-wavelength layer fluctuation modes, this value should be close to the bare (intrinsic) rigidity of the bilayer. In contrast, the crumpling renormalized rigidity previously deduced from light scattering studies of the layer undulation dynamics in the same system is considerably smaller. Our $\kappa$ value is also much larger than the value recently deduced from the dilution behaviour of the X-ray Bragg spacing. We argue that this discrepancy is due to an inconsistency in the data rather than to a deficiency in the theory