Eur. Phys. J. B 64, 499–503 (2008) DOI: 10.1140/epjb/e2008-00021-5 T HE EUROPEAN P HYSICAL JOURNAL B Phase transitions and interface fluctuations in double wedges and bi-pyramids with competing surface fields M. M¨ uller 1, a , A. Milchev 2 , K. Binder 3 , and D.P. Landau 4 1 Institut f¨ ur Theoretische Physik, Georg-August Universit¨at, 37073 G¨ ottingen, Germany 2 Institute for Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria 3 Institut f¨ ur Physik, WA 331, Johannes Gutenberg Universit¨at, 55099 Mainz, Germany 4 Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602-2451, USA Received 27 August 2007 / Received in final form 7 November 2007 Published online 18 January 2008 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2008 Abstract. The interplay between surface and interface effects on binary AB mixtures that are confined in unconventional geometries is investigated by Monte Carlo simulations and phenomenological consider- ations. Both double-wedge and bi-pyramid confinements are considered and competing surface fields are applied at the two opposing halves of the system. Below the bulk critical temperature, domains of opposite order parameter are stabilized at the corresponding corners and an interface runs across the middle of the bi-partite geometry. Upon decreasing the temperature further one encounters a phase transition at which the AB symmetry is broken. The interface is localized in one of the two wedges or pyramids, respectively, and the order parameter is finite. In both cases, the transition becomes discontinuous in the thermodynamic limit but it is not a first-order phase transition. In an antisymmetric double wedge geometry the transition is closely related to the wedge-filling transition. Choosing the ratio of the cross-section L × L of the wedge and its length Ly according to Ly /L 3 = const., simulations and phenomenological consideration show that the new type of phase transition is characterized by critical exponents α =3/4, β = 0, and γ =5/4 for the specific heat, order parameter, and susceptibility, respectively. In an antisymmetric bi-pyramid the transition occurs at the cone-filling transition of a single pyramid. The important critical fluctuations are associated with the uniform translation of the interface and they can be described by a Landau-type free energy. Monte Carlo results provide evidence that the coefficients of this Landau-type free energy exhibit a system-size dependence, which gives rise to critical amplitudes that diverge with system size and result in a transition that becomes discontinuous in the thermodynamic limit. PACS. 68.08.Bc Wetting – 05.70.Fh Phase transitions: general studies 1 Introduction Boundaries have an important impact on the phase behav- ior of fluid mixtures [1,2]. Examples include capillary con- densation of a vapor into a liquid in a narrow pore or slit where the phase coexistence is shifted away from the bulk coexistence pressure by an amount Δp. The magnitude of the shift is governed by the Kelvin equation, Δp ∼ 1/L, where L denotes the size of the pore. Renewed interest stems from the fact that micro- and nanofabrication tech- niques can produce cavities with precise dimensions and tailor the chemical properties of confining surfaces which find use in microfluidic devices or reaction chambers. In Figure 1 we illustrate the shift of the phase bound- aries upon confining an AB binary (polymer) mixture in a slit pore and compare the results of the MC simulations with the bulk phase behavior [3]. If the two confining sur- a e-mail: mmueller@theorie.physik.uni-goettingen.de faces preferentially attract one component, capillary con- densation occurs and the critical point is shifted to lower temperature and richer composition of the preferred com- ponent. We also note that the binodal in the vicinity of the critical point is characterized by 2D Ising behavior which gives rise to flatter binodals than in the 3D bulk. If we confine the binary mixture into an anti- symmetric film, i.e., one surface attracts the A-component while the opposite surface attracts the B-component with equal strength, the phase behavior is dramatically altered. One finds two critical points and the critical temperatures are close to the wetting transition temperature of the semi- infinite system [4,5]. At high temperatures enrichment lay- ers of A and B gradually form at the respective surfaces and stabilize an interface that fluctuates around the mid- plane of the film. Upon reducing the temperature further, the system laterally phase separates into domains where this internal AB interface is located close to one or the other surface giving rise to an A-rich or B-rich domain,