Ensemble Effects in Small Systems
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resent some recent advances in the analysis of finite size effects in small hard particle systems. Two different size effects can be identified: explicit size effects that arise due to the consideration of different statistical mechanics ensembles, and implicit size effects related to the use of periodic boundary conditions in computer simulations. These effects can take place both in kinetic and in structural properties of the system.
Introduction The study of systems consisting in a reduced number of particles has been the object of great interest in the last few years. The industrial development and control of new materials that involve very small systems reinforce the study of such systems, and the importance of the practical applications justify the increasing scientific activity in the field. This is the case of materials such as zeolites or porous glasses that act as hosts for a fluid that is absorbed in the pores of the confining solid material. The properties of the confined fluid and sometimes those of the host material are altered in this process so that they become significantly different from those in the bulk phase. In situations where the size of the pore is comparable to the fluid particle size the number of particles in the pore can be very small (N ∼ 10) so that one is dealing with a small system. Computer simulations have become an essential tool for the theoretical understanding of small systems. Of course, a key aspect in the computer simulation of a small system is the reduced size of the system. In this case finite size effects play a major role that must be carefully determined in order to relate the properties of the small system with those of an infinite system in the thermodynamic limit. Two kinds of finite size effect can be identified in a typical computer simulation of a small system. On the one hand, it is well known that, contrary to what happens in the thermodynamic limit, for a small system the different statistical mechanics ensembles are no longer equivalent
Rom´ an, F.L. et al.: Ensemble Effects in Small Systems. Lect. Notes Phys. 753, 343–381 (2008) c Springer-Verlag Berlin Heidelberg 2008 DOI 10.1007/978-3-540-78767-9 8
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F.L. Rom´ an et al.
and this leads to the so-called explicit finite-size effects. This implies that one must carefully determine the influence of the surroundings in order to choose the most appropriate ensemble for the study of the system. On the other hand, the consideration of periodic boundary conditions in the simulations leads to the emergence of implicit finite-size effects. When periodic boundary conditions are considered in a computer simulation, the system can be assumed to consist of an infinite set of replica images of the simulation cell. In this case the pair correlation function becomes anisotropic and the system properties measured through this function can be modified. From a different point of view, one can establish a close relation between small systems and inhomogeneous systems. It is clear that the former can only be found in nature under confinement constraints a
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