Phase transitions in adsorbed layers

II. EXPERIMENTAL SITUATION A. Phase Transitions in Adsorbed Layers... 

In this section we review several studies of phase transitions in adsorbed layers. Phase transitions in adsorbed (2D) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo, Gibbs ensemble Monte Carlo (GEMC), and finite size scaling techniques. Phase diagrams of fluids with internal quantum states are analyzed. Adsorbed layers of H2 molecules at a full monolayer coverage in the /3 X /3 structure have a higher transition temperature to the disordered phase compared to the system with the heavier D2 molecules this effect is... 

Phase transitions in adsorbed layers often take place at low temperatures where quantum effects are important. A method suitable for the study of phase transitions in such systems is PIMC (see Sec. IV D). Next we study the gas-liquid transition of a model fluid with internal quantum states. The model [193,293-300] is intended to mimic an adsorbate in the limit of strong binding and small corrugation. No attempt is made to model any real adsorbate realistically. Despite the crudeness of the model, it has been shown by various previous investigations [193,297-300] that it captures the essential features also observed in real adsorbates. For example, the quite complex phase diagram of the model is in qualitative agreement with that of real substances. The Hamiltonian is given by... 

A. Patrykiejew, S. Sokolowski, K. Binder, Phase transitions in adsorbed layers formed on crystals of square and rectangular surface lattice, Surf. Sci. Reports 37, 207 (2000). 

MONTE CARLO CALCULATIONS ON PHASE TRANSITIONS IN ADSORBED LAYERS... 

Monte Carlo Calculations on Phase Transitions in Adsorbed Layers 91... 

In this paper recent results of our in-situ STM studies on the structure of bare and adsorbate-covered electrode surfaces are summarized. In particular, we discuss transitions between different phases on these surfaces, which often proceed via nucleation and growth processes. This includes structural transitions in the electrode surface layer, phase transitions in adsorbate layers, electrodeposition processes, and dynamical fluctuations at the metal-electrolyte interfiice under equilibrium. We show that in-situ STM provides a valuable tool for time-resolved, atomic-scale studies of such processes. For experimental details and for in-depth discussions the reader is referred to the original literature. 

Persson B N J 1992 Ordered structures and phase transitions in adsorbate layers Surf. Sci. Rep. 15 1-135... 

D Phase Transitions in Adsorbed Layers Thermodynamics and Electrified Interfaces, Vol 10 Atomically Controlled Deposition and Dissolution of Metals Thermodynamics and Electrified Interfaces, Vol 10 Molecular Epitaxy in... 

Unfortunately, this approach does not give a deeper insight into a structure of surface films at the molecular level. The theory involves a concept of a certain averaging effects connected with heterogeneity of sohd surfaces. Moreover, molecular interactions are usually described in terms of a mean field approximation. As a consequence, the integral equation approach cannot elucidate many experimental findings. In particular, various phase transitions in adsorbed layers, such as the order-disorder transition, cannot be explained in the fiamework of this theory. 

In modern materials science topics of high interest are surface structures on small (nanometer-length) scales and phase transitions in adsorbed surface layers. Many interesting effects appear at low temperatures, where quantum effects are important, which have to be taken into account in theoretical analyses. In this review a progress report is given on the state of the art of (quantum) simulations of adsorbed molecular layers. 

Many interesting quantum effects appear at low temperatures due to the effect of quantum statistics. Very interesting PIMC studies of such effects have been done for structural phase transitions in adsorbed " He and He layers [90-91] and for the superfluidity of H2 layers [92]. For studies of related systems and additional information see Sec. IV D 2. 

Of the variety of quantum effects which are present at low temperatures we focus here mainly on delocalization effects due to the position-momentum uncertainty principle. Compared to purely classical systems, the quantum delocalization introduces fluctuations in addition to the thermal fluctuations. This may result in a decrease of phase transition temperatures as compared to a purely classical system under otherwise unchanged conditions. The ground state order may decrease as well. From the experimental point of view it is rather difficult to extract the amount of quantumness of the system. The delocahzation can become so pronounced that certain phases are stable in contrast to the case in classical systems. We analyze these effects in Sec. V, in particular the phase transitions in adsorbed N2, H2 and D2 layers. 

The Broekhoff-van Dongen isotherm allows for multilayer adsorption with lateral interactions and predicts the possibility of 2D phase transitions in each layer [17]. The most spectacular evidence for 2D phase transitions concerns the adsorption of heavy noble gases on highly homogeneous non-polar surfaces of low atomic weight (typically, exfoliated graphite obtained by thermal dissociation of its intercalation compound with FeCla). This situation guarantees that the adsorbate-adsorbate interaction prevails on ad-sorbent-adsorbate interaction and makes it possible the observation of phase transitions in each layer. See Ref. [18] for a short overview of this subject. 

In Section 2 the phenomenon of the phase transitions in the layers adsorbed on solid sorbents is also discussed. 

Phase transitions in two-dimensional layers often have very interesting and surprising features. The phase diagram of the multicomponent Widom-Rowhnson model with purely repulsive interactions contains a nontrivial phase where only one of the sublattices is preferentially occupied. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are molecular layers of H2, D2, N2 and CO molecules on graphite substrates. We review the path integral Monte Carlo (PIMC) approach to such phenomena, clarify certain experimentally observed anomalies in H2 and D2 layers, and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are analyzed via PIMC as well. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions where quantum effects play a role. 

In Sec. II we briefly review the experimental situation in surface adsorption phenomena with particular emphasis on quantum effects. In Section III models for the computation of interaction potentials and examples are considered. In Section IV we summarize the basic formulae for path integral Monte Carlo and finite size scahng for critical phenomena. In Section V we consider in detail examples for phase transitions and quantum effects in adsorbed layers. In Section VI we summarize. 

In this review we consider several systems in detail, ranging from idealized models for adsorbates with purely repulsive interactions to the adsorption of spherical particles (noble gases) and/or (nearly) ellipsoidal molecules (N2, CO). Of particular interest are the stable phases in monolayers and the phase transitions between these phases when the coverage and temperature in the system are varied. Most of the phase transitions in these systems occur at fairly low temperatures, and for many aspects of the behavior quantum effects need to be considered. For several other theoretical studies of adsorbed layer phenomena see Refs. 59-89. 

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

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