For moderately thin cells, in which the tendency to form a helical
structure can be
ignored[1], the liquid crystal molecules in the absence of an applied
electric field form an anti-parallel sequence 
.
When an
applied electric field reaches the value 
, the
ferroelectrically
aligned state is reduced in energy below the antiferroelectric one.
We shall see from the calculation below that the transition from
the antiferroelectric into the ferroelectric state
will not instantaneously occur at an electric field exactly equal
to 
unless nucleated at a defect or a boundary. The transition in a
homogeneous system contained in a thin cell (i.e. one having a small d)
may not occur until fields considerably in excess of are reached. In
thick cells, on the other hand, the transition may begin at fields lower than
, but not become complete until fields greater than are
reached.
In the rest of this section the stability requirements for the antiferroelectric state subject to an electric field will be analyzed in two different model approaches. In the first calculation, which closely follows Ref. [1], molecular rotations in the odd layers of the AFLC, which contain molecules initially aligned in the direction of the electric field, will be neglected. Correspondingly, the motion of only the even layers will be considered. In the second model calculation the cooperative motion of all layers will be taken into account.