PHYSICAL REVIEW E VOLUME 51, NUMBER 5 MAY 1995 Smectic-A surface order in a nematic-substrate system A. Poniewierski and A. Samborski Institute of Physical Chemistry, Polish Academy of Sciences, Department III, Kasprzaka 44/52, 01 224-Warsaw, Poland (Received 7 December 1994) Nematic liquid crystals in contact with a Aat substrate are studied by means of the Landau — de Gennes formalism. It is assumed that the substrate provides homogeneous boundary conditions and that the nematic phase undergoes a first-order transition to the smectic-A phase in the bulk. Above the bulk transition temperature, a smectic-A film with layers perpendicular to the substrate can form if the sur- face field is sufficiently strong. This surface phase transition is found to be continuous in the mean-field approximation. Apart from the symmetry-breaking transition, an ordinary prewetting transition may occur. The e6'ect of smectic layer fluctuations on the stability of the smectic film is discussed. It is sug- gested that the continuous surface transition can be a Kosterlitz-Thouless transition, where the defects are edge dislocations. PACS number(s): 61. 30. Gd, 64.70. Md, 68. 45.Gd I. INTRODUCTION The ordering of liquid crystals (LC's) by surfaces still attracts a great deal of experimental and theoretical at- tention [1]. This is because of the practical importance of LC devices and a potential wealth of surface phenomena that can occur at LC interfaces. Apart from wetting transitions, observed also in sim. pie fluids, there exists a possibility of surface transitions in which the LC close to the surface has different symmetry than in the bulk [2]. So far the most studied surface effects have concerned nematic order in nematogen-substrate systems [1, 3]. Rel- atively less work has been devoted to the onset of smectic order near a limiting surface. It is known that smectic order can appear at the free surface of the isotropic phase or at the interface between the isotropic phase and a solid substrate, for some systems exhibiting a direct isotropic — smectic-A transition [4]. Theoretical models [5 — 7] confirm to some extent experimental observations. In both cases the onset of smectic order is compatible with the geometry of the system, i.e. , smectic layers are parallel to the limiting surface. In this paper we consider another possibility, when LC molecules prefer to lie on the substrate. Then smectic-A layers have to be perpendicular to it. We assume that the system undergoes a first-order nematic — smectic- A transi- tion and that the substrate enhances the surface nematic order. It is interesting to see whether the increased nematic order at the surface can result in smectic-A sur- face ordering above the bulk nematic — smectic-A transi- tion temperature. As far as we know this phenomenon has not yet been observed in real systems. However, very recent experimental studies of a bulk LC in an external electric field [8] show that it is possible to induce the nematic — smectic-A transition by changing the intensity of the field. The field couples directly to the nematic or- der parameter and the influence on the smectic order is indirect, through the coupling of the nematic and smectic order parameters [9]. We expect that a similar mecha- nism could be responsible for formation of smectic-A lay- ers in the direction perpendicular to the substrate. In the next section we define the model and present our results. In the last section we discuss the effect of Auctua- tions on the stability of the surface smectic-A phase and also the relation of the surface phase transition to the Kosterlitz-Thouless transition. Some details of the calcu- lations are presented in the Appendix. II. THEORY AND RESULTS We study the problem outlined in the Introduction us- ing a Landau — de Gennes formalism. It is assumed that the free-energy density of the bulk system depends on the nematic order parameter Q, which is a traceless sym- metric tensor, and the smectic order parameter f as fol- lows [10]: F= Af +BP +C TrQ +D TrQ +E(TrQ ) +g [FTrQ +G(k Qk. )+H(k Q k) +L(Q k) ], where k is normal to the smectic layers. The nematic and smectic-3 phases are uniaxial and there is only one in- dependent component of Q, which measures the degree of orientational order with respect to the nematic direction n. Moreover, in the smectic-A phase, k~~n. It is con- venient to rescale the order parameters and the free ener- gy to reduce the number of independent coupling con- stants. After rescaling we have F=(t+1)ri — 2g +ri +(ao+a, ri+azri )g +g where g is the nematic order parameter, t measures the temperature, and for simplicity we have used the same symbols for the rescaled free-energy density and the smectic order parameter. All quantities appearing in Eq. (2) are dimensionless. As the smectic order cannot ap- pear without the nematic order, ao must be positive. When the temperature is lowered the nematic order pa- rameter increases, and this should favor smectic ordering; 1063-651X/95/51(5)/4574(6)/$06. 00 51 4574 1995 The American Physical Society