PHYSICAL REVIEW E 84, 041810 (2011) Orientational ordering transitions of semiflexible polymers in thin films: A Monte Carlo simulation V. A. Ivanov, A. S. Rodionova, E. A. An, J. A. Martemyanova, and M. R. Stukan * Faculty of Physics, Moscow State University, Moscow 119991, Russia M. M¨ uller Institut f ¨ ur Theoretische Physik, Georg-August-Universit¨ at, Friedrich-Hund-Platz 1, D-37077 G¨ ottingen, Germany W. Paul Institut f ¨ ur Physik, Martin-Luther-Universit¨ at Halle-Wittenberg, D-06099 Halle (Saale), Germany K. Binder Institut f ¨ ur Physik, Johannes-Gutenberg-Universit¨ at, Staudinger Weg 7, D-55099 Mainz, Germany (Received 31 May 2011; published 28 October 2011) Athermal solutions (from dilute to concentrated) of semiflexible macromolecules confined in a film of thickness D between two hard walls are studied by means of grand-canonical lattice Monte Carlo simulation using the bond fluctuation model. This system exhibits two phase transitions as a function of the thickness of the film and polymer volume fraction. One of them is the bulk isotropic-nematic first-order transition, which ends in a critical point on decreasing the film thickness. The chemical potential at this transition decreases with decreasing film thickness (“capillary nematization”). The other transition is a continuous (or very weakly first-order) transition in the layers adjacent to the hard planar walls from the disordered phase, where the bond vectors of the macromolecules show local ordering (i.e., “preferential orientation” along the x or y axes of the simple cubic lattice, but no long-range orientational order occurs), to a quasi-two-dimensional nematic phase (with the director at each wall being oriented along either the x or y axis), while the bulk of the film is still disordered. When the chemical potential or monomer density increase, respectively, the thickness of these surface-induced nematic layers grows, causing the disappearance of the disordered region in the center of the film. DOI: 10.1103/PhysRevE.84.041810 PACS number(s): 61.41.+e, 61.20.Ja, 64.70.M− I. INTRODUCTION Solutions of semiflexible polymers under good solvent conditions are known to exhibit a phase transition from an isotropic state to a nematic phase when the concentration and/or the polymer chain length sufficiently increase [1–23]. This transition is entropically driven as in standard lyotropic liquid-crystalline systems, which can be modelled as systems of hard rods or hard spherocylinders, for instance [24–26]. While for such standard liquid-crystalline systems the effect of surfaces and confinement on nematic order has already been extensively studied [27–43], the effect of walls on the orientational ordering of semiflexible macromolecules has been much less considered [44–49]. There has been a lot of work on the behavior of flexible polymers under confinement [50], but this is not our focus here. While early Monte Carlo work [44,46] mostly was concerned with investigating the local packing of the polymers near the walls, Chen et al. [45,48] proposed phase diagrams for the formation of nematic wetting layers at hard walls and for “capillary nematization” [32,33], analogously to “capillary condensation” [51,52] of undersaturated vapor in thin slit pores, a solution may exhibit nematic order in a capillary for conditions where it still would be isotropic in the bulk. However, the theory by Chen et al. [45,48] is a simple mean-field theory, inspired by Onsager’s theory [24] for infinitely thin needles, based on the wormlike * Current address: Schlumberger Dhahran Carbonate Research Center, P. O. Box 39011, Al-Khobar 31952, Saudi Arabia. chain model [53–55], and, hence, neglects excluded volume effects [56]. Apart from the fact that mean-field theories in general are often inaccurate descriptions of order-disorder phenomena in particular at low dimensionality [57], for nematic systems there is an interesting complication due to the tensor character of the nematic order parameter [25]: While the order in a bulk of a nematic has uniaxial character, it is biaxial at the surface [58]. As a consequence, when in an isotropic fluid a nanoscopically thin nematic precursor layer forms near a wall (analogous to precursors of fluid wetting layers [57,59–61] of undersaturated vapor in contact with a wall), it has biaxial rather than uniaxial order. In addition, due to long wavelength fluctuations long-range nematic order in d = 2 dimensions should not exist, one expects an algebraic decay of orientational correlation functions and a Kosterlitz-Thouless type transition [62] to the isotropic phase [63–65]. However, the character of the nematic-isotropic transition in d = 2 dimensions is still not fully understood [66]. This d = 2 limit, however, is pertinent to our system when the bulk system is confined between two walls. Moreover, the character of the phase diagram that one expects for simple lattice models for liquid crystals confined in thin film geometry is debated. For the ordinary Lebwohl-Lasher model [67] there is evidence that the nematic-isotropic transition stays first order up to a minimum number n min of lattice planes, while for n<n min there is no transition whatsoever [68]. For a generalized Lebwohl-Lasher model, Fish and Vink [69] found that for some choices of parameters in the Hamiltonian there is a 041810-1 1539-3755/2011/84(4)/041810(15) ©2011 American Physical Society