Type-I and type-II smectic-C^{*} systems: A twist on the electroclinic critical point.

We conduct an in-depth analysis of the electroclinic effect in chiral, ferroelectric liquid crystal systems that have a first-order smectic-A^{*}-smectic-C^{*} (Sm-A^{*}-Sm-C^{*}) transition, and show that such systems can be either type I or type II. In temperature-field parameter space type-I systems exhibit a macroscopically achiral (in which the Sm-C_{M}^{*} helical superstructure is expelled) low-tilt (LT) Sm-C_{U}^{*}-high-tilt (HT) Sm-C_{U}^{*} critical point, which terminates a LT Sm-C_{U}^{*}-HT Sm-^{*}C_{U} first-order boundary. Notationally, Sm-C_{M}^{*} or Sm-C_{U}^{*} denotes the Sm-C^{*} phase with or without a modulated superstructure.