Polar order and tilt in achiral smectic phases Damian Pociecha, 1 Ewa Gorecka, 1 Mojca Čepič, 2,3 Nataša Vaupotič, 2,4 and Wolfgang Weissflog 5 1 Department of Chemistry, Warsaw University, aleya Zwirki i Wigury 101, 02-089 Warsaw, Poland 2 Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia 3 Faculty of Education, University of Ljubljana, Kardeljeva pl 16, 1000 Ljubljana, Slovenia 4 Faculty of Education, University of Maribor, Koroška 160, 2000 Maribor, Slovenia 5 Institute of Physical Chemistry, Department of Chemistry, Martin-Luther Universität Halle-Wittenberg, Halle, Germany Received 21 April 2006; published 7 August 2006 Material with the phase sequence SmA-SmAP-SmCP is studied as an example of a system in which the spontaneous electric polarization and the molecular tilt develop independently at the SmA-SmAP and the SmAP-SmCP phase transition, respectively. The temperature dependence of the spontaneous electric polariza- tion clearly shows a strong coupling between the polarization and tilt. The system exhibits also very strong precritical polarization and tilt fluctuations. Experimental observations are explained within the theoretical model. DOI: 10.1103/PhysRevE.74.021702 PACS numbers: 61.30.Cz, 64.70.Md, 77.84.Nh, 77.22.Gm I. INTRODUCTION In the chiral smectic phases made of rodlike molecules the polarization is an improper order parameter and as such it can appear only if the phase is tilted 1. On the other hand, in the bent-core molecular systems 2 both the polarization and the tilt are proper order parameters and they can appear in the system independently. The appearance of the sponta- neous electric polarization without the molecular tilt, i.e., the phase transition from the paraelectric to the orthogonal polar phase, has already been reported in some materials 3–6. In general, materials exhibiting such a phase transition are rare since the vast majority of the bent-core liquid crys- tals tend to form polar tilted phases. In Ref. 6 we reported on the critical freezing of molecular rotation, which led to polar ordering through the second order paraelectric- antiferroelectric phase transition in the achiral liquid crystal formed by the bent-core molecules. The system was studied both experimentally and theoretically. To study the development of polarization and tilt, a mate- rial with the phase sequence: orthogonal paraelectric— orthogonal polar—tilted polar phase is needed. Any material with such a phase sequence can be considered as a model system in which the spontaneous electric polarization and the molecular tilt appear independently at the paraelectric- orthogonal polar and the orthogonal-tilted phase transition, respectively. In the present paper we report on experimental and theoretical studies of a liquid crystal formed by the bent- core molecules exhibiting the phase sequence smectic ASmA-smectic AP A SmAP A -smectic CP A SmCP A . II. EXPERIMENTAL RESULTS In order to examine the polarization and tilt development in an achiral smectic phase formed by bent-core molecules, the material named 1g in Ref. 7 with a phase sequence: Iso 142 °C SmA 96 °C SmAP A 90 °C SmCP A has been chosen Fig. 1. Texture observations revealed the interlayer tilt structure of the SmCP A phase, which shows a strong memory effect. In the freshly cooled samples the ground state is synclinic, SmC S P A . The application of the electric field switches the sample to the ferroelectric state, however the synclinic interlayer tilt structure is preserved. The syn- clinic ferroelectric state transforms into the anticlinic antifer- roelectric structure after the field is switched off, and even several hours later the sample does not relax completely to the initial synclinic state. The temperature dependence of the tilt Fig. 2 was deduced from the x-ray measurements of the smectic layer spacing. The measurements were performed with the modi- fied DRON diffractometer Cu K line in the reflection mode using one surface free sample. The temperature stabil- ity was controlled with the accuracy 0.1 K. The results show continuous SmAP A -SmCP A phase transitions with the tilt temperature dependence as T - T c  0.4 , where T c is the transition temperature to the tilted phase. The polar and optical properties of the materials were studied in 3–5 m thick glass cells, having ITO transparent electrodes and surfactant layers for planar orientation. The cells were placed into Mettler FP82HT hot stage for temperature control with the accuracy 0.1 K. In both polar phases, SmAP A and SmCP A , the switching of the electric polarization upon the reversal of the applied electric field is accompanied by the double current peak. This unambiguously confirms the antiferroelectric nature of the phases. The spontaneous polarization P s , was determined by integrating the current peaks obtained upon the electric field reversal. It is about 300 nC cm -2 in the SmAP A phase and FIG. 1. Chemical formulas for the studied compounds. PHYSICAL REVIEW E 74, 021702 2006 1539-3755/2006/742/0217026 ©2006 The American Physical Society 021702-1