First-order phase transition lattice models

In many physically important cases of localized adsorption, each adatom of the compact monolayer covers effectively n > 1 adsorption sites [3.87-3.89, 3.98, 3.122, 3.191, 3.214, 3.261]. Such a multisite or 1/n adsorption can be caused by a crystallographic Me-S misfit, i.e., the adatom diameter exceeds the distance between two neighboring adsorption sites, and/or by a partial charge of adatoms (A < 1 in eq. (3.2)), i.e., a partly ionic character of the Meads-S bond. The theoretical treatment of a /n adsorption differs from the description of the 1/1 adsorption by a simple Ising model. It implies the so-called hard-core lattice gas models with different approximations [3.214, 3.262-3.266]. Generally, these theoretical approaches can only be applied far away from the critical conditions for a first order phase transition. In addition, Monte Carlo simulations are a reliable tool for obtaining valuable information on both the shape of isotherms and the critical conditions of a 1/n adsorption [3.214, 3.265-3.267]. 

In the case of a localized 1/n adsorption, which is observed in many Me UPD systems at relatively high AE or low F (formation of expanded Meads superlattice structures, cf. Section 3.4), the adsorption process can be described by the so-called hard-core lattice gas models using different analytical approximations or Monte Carlo simulations [3.214, 3.262-3.264]. Monte Carlo simulation for 1/2 adsorption on a square lattice is dealt in Section 8.4. Adsorption isotherms become asymmetrical with respect to AE and are affected by the structures of the Meads overlayer and S even in the absence of lateral Meads interactions [3.214, 3.262-3.264]. Furthermore, the critical interaction parameter for a first order phase transition, coc, which is related to the critical temperature, Tc, increases in comparison to the 1/1 adsorption. 

An analogous situation is encountered with the 2D ijr-state Potts model, which exhibits a first-order transition for >3. On the basis of renormalization group studies of the Potts lattice-gas [220-221], the mechanism producing a first-order phase transition for has been... 

In the next section, we review a number of lattice gas models for which the addition of directional interactions not only allows for polyamorphism and two liquid phases but also introduces the possibility of a richer phase diagram, in which a critical line following the liquid-liquid first-order phase transition substitutes the critical point. Even though not explored in the literature, this picture is not inconsistent with known experimental results for water and other tetrahedral liquids [38]. 

De Oliviera and Griffits [235] have studied multilayer adsorption on a homogeneous surface. They have obtained stepwise adsorption, which proved that the sruface films grow in a layer-by-layer mode in the series of the successive first-order phase transitions. A general classification of possible scenarios for the film growth has been presented by Pandit et al. [236] in the framework of a mean field theory for the lattice gas model. 

Fig. 29. Phase diagram of the model Eq. (22) for coadsorption of two kinds of atoms in the temperature-coverage space. Circles indicate a second-order phase transition, while crosses indicate first-order transitions. Point A is believed to be a tricritical point and point B a bicritical point. The dashed curve shows the boundary from the Blume-Capel model on a square lattice with a nearest-neighbor coupling equal to 7 in the present model (for - 0 Eq. (22) reduces to this model), only the ordered phase I then occurs. From Lee and Landau. )...

In addition to the Uquid liquid coexistence curve, the confined fluid exhibits two further, smaller phase coexistence regions at larger wa and lower T. The coexisting phases represent water-rich films of a thickness corresponding to one or two layers, which are distinguishable only at lower temperatures. The existence of such first-order layering transitions may be overestimated by our lattice model on a homogeneous surface and enforced unrealistically... 

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