We construct a continuum model of a recently discovered ferroelectric smectic-A $\left({\mathrm{SmA}}_{\mathrm{F}}\right)$ liquid crystal that has a layered structure with orientational order and polarization along the layer normal. We take into account the layer order by a complex order parameter $\psi$, and the orientational order by a director $\vec{n}$. Screened electrostatic interaction of induced charges is also introduced. We carry out numerical calculations of the dynamics of phase transition from an isotropic phase directly to ${\mathrm{SmA}}_{\mathrm{F}}$ for a simple case of small screening length. Then the electrostatic interaction is reduced to splay elastic energy and can be incorporated into the variation of the splay elastic constant $\left(K_1\right)$. We show that the enhancement of the effective $K_1$ significantly promotes the coarsening dynamics of the layered structure to a uniform one by suppressing the bending of the layers. We calculated three different characteristic lengths from the correlation of $\vec{n}$, number density of the defects of $\vec{n}$, and the structure factor of $\psi$. All the characteristic lengths for different effective $K_1$ exhibit power-law time evolution whose exponent is close to $1/4$, except for the case when the effective $K_1$ is unrealistically small compared with the bend elastic constant $K_3$. Our model can be exploited to a wide class of problems concerning the structural properties of a ferroelectric ${\mathrm{SmA}}_{\mathrm{F}}$ liquid crystal.

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• Ferroelectric liquid crystals
• Liquid crystals
• Smectic liquid crystals