Thermodynamics of solid surfaces

Since evaporation is done in vacuum the mean free path of the molecules is long and they move practically in straight lines to condense onto the substrate, which is placed at an appropriate position. Typically amorphous or polycrystalline layers of some 10 nm thickness are produced by this technique. To get a crystalline surface the sample is usually annealed during or after evaporation. The film thickness is usually monitored by a quartz crystal microbalance. 

In molecular beam epitaxy (MBE) [317], molecular beams are used to deposit epitaxial layers onto the surface of a heated crystalline substrate (typically at 500-600° C). Epitaxial means that the crystal structure of the grown layer matches the crystal structure of the substrate. This is possible only if the two materials are the same (homoepitaxy) or if the crystalline structure of the two materials is very similar (heteroepitaxy). In MBE, a high purity of the substrates and the ion beams must be ensured. Effusion cells are used as beam sources and fast shutters allow one to quickly disrupt the deposition process and create layers with very sharply defined interfaces. Molecular beam epitaxy is of high technical importance in the production of III-V semiconductor compounds for sophisticated electronic and optoelectronic devices. Overviews are Refs. [318,319], 

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II. BASIC THERMODYNAMICS OF SOLID SURFACES A. The Gibbs-Duhem Equation... 

The year 1970 saw the publication of the second edition of Guggenheim s monograph and of an Annual Review with a section on the thermodynamics of solid surfaces. Halberstadt has made a translation of Munster s Classical Thermodynamics , a book which is not for the beginner but is suitable for the advanced student. The development of the laws is presented classically, after Joule, Clausius, and Carnot, and in an axiomatic manner after Caratheodory. The treatment is concentrated and formal,... 

The manner in which a film is formed on a surface by CVD is still a matter of controversy and several theories have been advanced to describe the phenomena. ] A thermodynamic theory proposes that a solid nucleus is formed from supersaturated vapor as a result of the difference between the surface free energy and the bulk free energy of the nucleus. Another and newer theory is based on atomistic nucle-ation and combines chemical bonding of solid surfaces and statistical mechanics. These theories are certainly valuable in themselves but considered outside the scope of this book. 

Polanyi s scientific work lay most squarely within a physical chemistry that encompassed thermodynamics, X-ray crystallography, the study of reaction rates, and the application of quantum mechanics to the study of molecular forces and transition states. In two particular areas, the investigation of solid-surface adsorption phenomena and X-ray diffraction studies of the properties of solids, Polanyi helped establish new scientific specialities, at the boundaries of physics and chemistry, for studying the solid state. He also turned his research experiences in these fields into a basis for the formulation of a new philosophy of science centered on scientific practice, rather than scientific ideas. [1] It is these themes that I would like to explore, with remarks in my conclusion on Polanyi s influence in solid-state science. 

Thermodynamically, a solid surface is sufficiently characterized by two parameters surface energy (a scalar), with units of energy per area, and surface stress (a second-rank tensor), also with units of energy per area. For a liquid, these two are the same, but they can be very different for solids. We do not discuss the latter in this book, nor shall we distinguish between surface energy and surface tension, which is defined as the reversible work done in creating unit area of new surface. In one-component systems, surface energy and surface tension are numerically equal. 

Surface stress measurement — The understanding of the thermodynamics of solid/liquid interfaces is of im-... 

In all of these systems, certain aspects of the reactions can be uniquely related to the properties of a surface. Surface properties may include those representative of the bulk material, ones unique to the interface because of the abrupt change in density of the material, or properties arising from the two-dimensional nature of the surface. In this article, the structural, thermodynamic, electrical, optical, and dynamic properties of solid surfaces are discussed in instances where properties are different from those of the bulk material. Predominantly, this discussion focuses on metal surfaces and their interaction with gas-phase atoms and molecules. The majority of fundamental knowledge of molecular-level surface properties has been derived from such low surface area systems. The solid-gas interface of high surface area materials has received much attention in the context of separation science, however, will not be discussed in detail here. The solid-liquid interface has primarily been treated from an electrochemical perspective and is discussed elsewhere see Electrochemistry Applications in Inorganic Chemistry). The surface properties of liquids (liquid-gas interface) are largely unexplored on the molecular level experimental techniques for their study have begun only recently to be developed. The information presented here is a summary of concepts a more complete description can be found in one of several texts which discuss surface properties in more detail. ... 

In order to try to clarify the different types of mechanism involving either redox cycles and/or acid-base properties, a study of the surface chemistry of single, doped and mixed oxides is of much interest. The calorimetric technique, by allowing heat transfer measurements, can provide very informative data on the thermodynamics of solid-gas interactions and for the study of the surface and reactivity of these metal oxides. 

The complexities of solid surfaces and onr inability to characterize exactly their interactions with adsorbed molecules hmits our understanding of the adsorption process. It does not, however, prevent development of an exact thennodynamic description of adsorption equilibrium, applicable alike to physical adsorption and chemisorption and equally to monolayer and multilayer adsorption. The thermodynamic frame work is independent of any particular theoretical or empirical description of material behavior. However, in application such a description is essential, and meaningful results require appropriate models of behavior. 

Liu J (2000) Scanning transmission electron microscopy of nanoparticles. In Characterization of Nanophase Materials. Wang ZL (ed) p 81-132. Wiley-VCH, Weinheim, FRG Linford RG (1973) Surface thermodynamics of solids. In Green M (ed) Solid State Surface Science 2 p 1-152. Dekker, New York... 

The mixture of starters and catalyst (especially with solid starters, such as sucrose or pentaerythritol) is stirred for 1-2 hours, under nitrogen at 80-100 °C, to obtain a thermodynamic equilibrium (partial solid solubilisation, solvation of solid surfaces and so on). All these preparations can be made in the small reactor simultaneously with the PO polymerisation reaction. After the polymerisation step and after final polyether evacuation, the prepared mixture of starters with catalyst is added to the polymerisation reactor and the polymerisation reaction begins immediately. Of course, the catalyst can be added separately, directly into the reactor, after charging the starter mixture. After the creation of an inert atmosphere of nitrogen and the increase of reaction temperature... 

This commentary on the current status of research on heats of immersion begins where our review written in 1958 concludes [6]. The classification of heats of immersion of solids into liquids as a function of precoverage is expanded to include two new types of curves. Several difficulties in heat of immersion research are discussed. Then, current applications of heats of immersion to determine the average polarity of solid surfaces, heterogeneities on solid surfaces, wetting by surfactants, hydrophilicity of solid surfaces, and thermodynamics of the specific interaction of molecules from solution onto solid surfaces are described. 

Acid-base interactions have found numerous applieations in research dealing with adsorption of molecules of liquids on the surfaees of solids. The main focus of this research is to estimate the thermodynamic work of adhesion, determine mechanism of interactions, analyze the morphology of interfaces and various surfaee coatings, develop surface modifiers, study the aggregation of macromolecular materials, explain the kinetics of swelling and drying, understand the absorption of low molecular weight compounds in polymeric matrices, and determine the properties of solid surfaces. In addition to these, there are many other applieations. 

Pfeifer, P. (1988). Fractals in surface science scattering and thermodynamics of adsorbed films. In Chemistry and Physics of Solid Surfaces, Vanselow, R. and Howe, R. (eds). Springer, Berlin, p. 283. 

Nevertheless, the general rules that have been emphasized throughout this book certainly apply to contact catalysis. Our first concern will be to see how rate functions may be modified by the frequent if not universal occurrence on a given surface of active centers that differ in their thermodynamic and kinetic properties. This is the problem of nonuniformity of solid surfaces. Next, several empirical correlations that have emerged from kinetic studies will be considered briefly as an introduedon to this special field of contact catalysis. 

The difficulty of establishing a unique acidity scale for solid surfaces has been mentioned several times. Even the definition of "acid strength" of solid surface sites is not thermodynamically consistent. It is appropriate to analyze some of the theoretical concepts involved and to address some of the solutions advanced by various authors who tried to solve this problem. 

There are many techniques for probing the chemical and physical properties of a solid surface to predict the tending of organic polymers to solid surfaces. The electronic structure of solid surfaces has been studied by measuring the thermodynamic interaction of the solid surface with simple liquids of known molecular structure. Experimental techniques for measuring the thermocfynamic interaction between solid and liquid include contact angle measurement, calorimetry, and gas chromatography. Some of these techniques are discussed below. Specific techniques related to characterization of carbon fiber surfaces are also discussed. 

This variation on traditional IGC has been developed from the McReynolds approach [24], for characterisation of stationary phases, by McMahon and co-workers [25]. It is particularly suited to rapid comparative screening of families of solid surfaces, for example a range of carbon blacks with differing surface chemistry. However, it does not provide quantitative measures of thermodynamic parameters. The multi-probe set includes those specified by McReynolds together with several w-alkanes. Classified groups of these probes can be injected into the column as mixtures. The temperature of the column is increased at a constant rate and the temperature at which the probe elutes is recorded as the retention temperature (T ). 

The thermodynamics of the surface free energy, y, of solids has been reviewed by Etzler [13-14]. The ideal work of adhesion, Vl, between materials A and B is defined by the following relation. 

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