Disordering to Order: de Vries Behavior from a Landau Theory for Smectic Phases

We show that Landau theory for the isotropic ($I$), nematic ($N$), smectic-$A$, and smectic-$C$ phases generically, but not ubiquitously, implies “de Vries” behavior: i.e., a continuous $A\mathrm{\text{−}}C$ transition can occur with little layer contraction while the birefringence increases significantly once the system moves into the $C$ phase. Our theory shows that 1st order $A\mathrm{\text{−}}C$ transitions are also possible. These transitions can be de Vries-like, but in general need not be. Generally, de Vries behavior occurs in models with unusually small orientational order and is preceded by a first order $I\mathrm{\text{−}}A$ transition. These results correspond well with experimental work to date.

Figure 1

The phase diagram in $t_s\mathrm{\text{−}}{t}_n$ space for the $I$, $N$, $A$, and $C$ phases. 1st and 2nd order phase boundaries are shown as dashed and solid lines, respectively. Three decreasing temperature paths from the $I$ to $C$ phase are shown. Path (i) corresponds to a conventional material that does not exhibit de Vries behavior. Path (ii) corresponds to a material exhibiting de Vries behavior and a 2nd order $A\mathrm{\text{−}}C$ transition. Path (iii) leads to a 1st order $A\mathrm{\text{−}}C$ transition with de Vries behavior. The inset shows a possible temperature dependence of birefringence ($M$) and layer spacing ($d$) for path (ii).