  The extended Frank elastic energy density is used to investigate the
existence of a stable periodically modulate structure that appears as a ground
state exhibiting a twist-bend molecular arrangement. For an unbounded sample,
we show that the twist-bend nematic phase $N_{TB}$ is characterized by a
heliconical structure with a pitch in the nano-metric range, in agreement with
experimental results. For a sample of finite thickness, we show that the wave
vector of the stable periodic structure depends not only on the elastic
parameters but also on the anchoring energy, easy axis direction, and the
thickness of the sample.
