acta physica slovaca 

Acta Physica Slovaca 65, No.6, 469533 (2015) (65 pages)
PHASE TRANSITIONS OF FIRST ORDER IN FINITE VOLUMES WITH APPLICATIONS TO UNDERPOTENTIAL DEPOSITION OF METALS Igor Medved^{1,2}, Luboš Podobník^{2} , Dale A. Huckaby^{3} ^{1}Department of Physics, Constantine the Philosopher University, 94974 Nitra, Slovakia ^{2}Department of Materials Engineering and Chemistry, Czech Technical University, 16629 Prague, Czech Republic ^{3}Department of Chemistry, Texas Christian University, Fort Worth, Texas 76129, USA Full text: ::pdf :: (Received 26 February 2016, accepted 10 March 2016) Abstract: This review is focused on the behavior of finite macroscopic systems (as opposed to infinitely large systems) determined from microscopic interactions. The temperature is assumed to be sufficiently below the critical point so that coexistence of two or more phases can occur and the systems can undergo firstorder phase transitions. We summarize the rigorous results on the finitesize behavior for a specific but wide class of models of real systems—the latticegas models of dimension d ≥ 2 with a finite number of ground states for which the free energy density can be expressed via convergent cluster expansion series. The behavior is rather sensitive to the interaction of the system with its surroundings (boundary conditions). In addition to periodic boundary conditions, which is a very popular choice, weak boundary conditions are considered. The latter are much more realistic, although they rule out the presence of large interfaces or droplets (phase separation) in the systems. For boundary conditions so strong that phase separation is possible, the situation is very complex, and we provide rigorous results only for a twodimensional Ising model. The majority of the paper, however, is devoted to an application of these finitesize results to an interesting phenomenon in electrochemistry in which firstorder phase transitions may occur at metal–electrolyte interfaces as a result of the deposition of metals on surfaces of other, more noble metals at electric potentials above the Nernst threshold. This is called underpotential deposition (UPD), and, for example, copper or silver may be so deposited on a surface of gold or platinum. The presence of such transitions is associated with sharp spikes that are observed in the current vs. electric potential plots of UPD processes. The application of the finitesize results to this problem is not straightforward, for it must take into account a polycrystalline structure of the surfaces. In fact, for a single crystalline domain on the surface the theory predicts spikes that are two or more orders of magnitude taller and sharper than those observed in experiments. On the other hand, when the surface is modeled realistically as an ensemble of many crystalline domains whose individual contributions are summed up to produce an overall spike, the agreement with experiment can be rather accurate. This is demonstrated in detail for two experimental spikes associated with UPD of copper on the (111) surface of platinum and gold electrodes. PACS: 05.50.+q, 64.60.De, 75.10.Hk, 82.45.Qr Keywords: Firstorder phase transitions, Finitesize effects, Lattice gas, Electrode electrolyte interface, Underpotential deposition, Voltammogram spikes 
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