SOUND PROPAGATION AND DAMPING IN THE VICINITY OF THE SMECTIC-A-HEXATIC-B PHASE TRANSITION OF 4-PROPIONYL-4'-N -HEPTANOYLOXYAZOBENZENE

Sound velocity and damping were measured in 4-propionyl-${4}^{\ensuremath{'}}\ensuremath{-}n$-heptanoyloxyazobenzene above its $\mathrm{Sm}\ensuremath{-}A\char21{}\mathrm{Hex}\ensuremath{-}B$ phase transition. The measurements were taken at 1 MHz (velocity) and at 3, 9, 15, and 21 MHz (damping) as a function of the angle \ensuremath{\theta} between the sound propagation direction and the normal to the smectic layers. The velocity presents a marked anomaly for $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{},$ whereas a much smaller anomaly is observed for $\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{},$ indicating that the phase transition occurs essentially within the smectic layers. Analysis of these measurements allows the de Gennes elastic constants $A,$ $B,$ and $C$ to be determined. Like the velocity, the damping presents significant pretransitional effects for $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{},$ reminiscent of those generally observed in the vicinity of second-order or weakly first-order phase transitions. The damping also increases for $\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}$ when $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{A\ensuremath{-}\mathrm{Hex}},$ but the behavior observed does not resemble the usual critical behavior. It is shown that this pseudocritical behavior stems essentially from a contribution of the anharmonic effects. The anisotropy of the critical effects on velocity and damping can be explained by the theory elaborated by Andereck and Swift for the $\mathrm{Sm}\ensuremath{-}A\char21{}\mathrm{Sm}\ensuremath{-}C$ transition and transposed to the $\mathrm{Sm}\ensuremath{-}A\char21{}\mathrm{Hex}\ensuremath{-}B$ transition. Analysis of the velocity measurements indicates that the specific-heat exponent is of the order of 0.6. This value, which is far from that associated with the three-dimensional $\mathrm{XY}$ universality class -0.007 to which this transition should in principle belong, confirms the results obtained by calorimetry. The critical relaxation time is characterized by the dynamic exponent $z\ensuremath{\nu}\ensuremath{\simeq}1,$ which corresponds to conventional critical slowing down.