We have studied the theology of bicontinuous ternary cubic phases form
ed by the system didode-cyldimethylammonium bromide (DDAB)/D2O/octane.
The cubic samples have the appearance and texture of optically clear,
isotropic, highly viscous gels. The microstructure of these cubic pha
ses is such that the surfactant bilayer containing the paraffinic tail
s and the oil may be visualized as decorating a minimal surface so tha
t the latter constitutes the mid-surface bisecting the bilayer. Linear
theology confirms that the dissipation becomes low at high acoustic f
requencies and is consistent with the phenomenon of ''ringing'' in whi
ch underdamped shear modes in the gel couple to sound via the gel surf
ace. The frequency-dependent theology also reveals a universal scaling
form bt the melting transition of the cubic phase, with the dynamical
scaling observed at this point reminiscent of a percolation transitio
n. Nonlinear theological response is consistent with the formation of
dislocation or slip-planes in the cubic structure, parallel to the dir
ection of shear. The experimental observations are related to the dyna
mics of the water/surfactant/oil interface, and theoretical ideas are
presented to account for the observed behavior. Our results suggest th
at frequency dependent theology is a useful structural probe of the dy
namics of ternary cubic phases;