Monte Carlo simulations of phase transitions of systems in nanoscopic confinement Kurt Binder a,∗ , J¨ urgen Horbach a , Andrey Milchev b , Marcus M¨ uller c , Richard Vink d a Institut f¨ ur Physik, Johannes Gutenberg Universit¨at, Mainz, 55099 Mainz, Staudinger Weg 7, Germany b Institut for Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria c Institut f¨ ur Theoretische Physik, Universit¨at G¨ottingen, Friedrich-Hund-Platz 1, 37077 G¨ottingen, Germany d Institut f¨ ur Theoretische Physik II, Universit¨at D¨ usseldorf, Universit¨atsstr. 1, 40225 D¨ usseldorf, Germany Abstract When simple or complex fluids are confined to ultrathin films or channels or other cavities of nanoscopic linear dimensions, the interplay of finite size and surface controls the phase behavior, and may lead to phase transitions rather different from the corresponding phenomena in the bulk. Monte Carlo simulation is a very suitable tool to clarify the complex behavior of such systems, since the boundary conditions providing the confinement can be controlled and arbitrarily varied, and detailed structural information on the inhomogeneous states of the considered systems is available. Examples used to illustrate these concepts include simple Ising models in pores and double-pyramid-shaped cavities with competing surface fields, where novel types of interface localization-delocalization phenomena occur accompanied by “macroscopic” fluctuations, and colloid-polymer mixtures confined in slit pores. Finite size scaling concepts are shown to be a useful tool also for such systems “in between” the dimensionalities. Key words: phase transition; nanoscopic confinement; Monte Carlo simulation 1. Introduction Nanoscopic confinement of fluids and solids has received longstanding attention in condensed mat- ter physics and materials science, and is particu- larly relevant for nanotechnology (“lab on a chip”, etc.). Such “nanosystems” are in between bulk mat- ter and single atoms or molecules. As a consequence, finite size and surface effects are important, all phys- ical properties are often rather inhomogeneous, and strong fluctuations may occur. Analytical theories (typically of the “mean field”- type) are in trouble when dealing with such sys- tems. Computer simulation is the method of choice: ∗ Corresponding author. Email address: kurt.binder@uni-mainz.de (Kurt Binder). one always deals with a nanosystem (containing typ- ically 10 2 to 10 6 particles only); when describing bulk matter one normally needs the (physically ar- tificial) periodic boundary conditions. However, for condensed matter under confinement, the confining walls and the forces they exert are an explicit part of the simulated model. In experiment, these bound- ary conditions due to a wall often are incompletely known, and subject to unwanted “dirt effects”. In a simulation boundary effects can be perfectly con- trolled, forces due to the boundaries can be varied at will. Ideal conditions can be created, that are diffi- cult to realize in experiments. Therefore, simulations are ideal to elucidate the novel physical phenomena, that nanoscopic confinement can cause. The insight thus gained is helpful to interpret the more complex phenomena that occur in the real world. The “leitmotif ” of this paper focuses on novel phe- Preprint submitted to Elsevier 22 January 2007