Study of surfaces

Just as an equation of the first degree between two variables represents a straight line of the first order, so does an equation of the first degree between three variables represent a surface of the first order. Such an equation in its most general form is Ax + By + Cz + D = 0, the equation to a plane. 

An equation of the second degree between three variables represents a surface of the second order. The most general equation of the second degree between three variables is 

All plane sections of surfaces of the second order are either circular, parabolic, hyperbolic, or elliptical, and are comprised under the generic word conicoids, of which spheroids, paraboloids, hyperboloids and ellipsoids are special cases. 

Since any section cut perpendicular to the T- or 0-axis is a rectangular hyperbola, the surface is a hyperboloid. The isothermals T, T2, Ts . . . (Fig. 29, page 111) may be looked upon as plane sections cut perpendicular to the 0-axis at points corresponding to Tlt T2,. . ., and then projected upon the pv-plane. In Fig. 176, the curves corresponding to pv and ab have been so projected. 

As a general rule, the surface generated by three variables is not so simple as the one represented by a gas obeying the simple laws of Boyle and Charles. 

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The physical chemist is very interested in kinetics—in the mechanisms of chemical reactions, the rates of adsorption, dissolution or evaporation, and generally, in time as a variable. As may be imagined, there is a wide spectrum of rate phenomena and in the sophistication achieved in dealing wifli them. In some cases changes in area or in amounts of phases are involved, as in rates of evaporation, condensation, dissolution, precipitation, flocculation, and adsorption and desorption. In other cases surface composition is changing as with reaction in monolayers. The field of catalysis is focused largely on the study of surface reaction mechanisms. Thus, throughout this book, the kinetic aspects of interfacial phenomena are discussed in concert with the associated thermodynamic properties. 

A modification of the foregoing procedure is to suspend the plate so that it is partly immersed and to determine from the dry and immersed weights the meniscus weight. The procedure is especially useful in the study of surface adsorption or of monolayers, where a change in surface tension is to be measured. This application is discussed in some detail by Gaines [57]. Equation 11-28 also applies to a wire or fiber [58]. 

The field emission microscope (FEM), invented in 1936 by Muller [59, 60], has provided major advances in the structural study of surfaces. The subject is highly developed and has been reviewed by several groups [2, 61, 62], and only a selective, introductory presentation is given here. Some aspects related to chemisorption are discussed in Chapter XVII. 

Friction can now be probed at the atomic scale by means of atomic force microscopy (AFM) (see Section VIII-2) and the surface forces apparatus (see Section VI-4) these approaches are leading to new interpretations of friction [1,1 a,lb]. The subject of friction and its related aspects are known as tribology, the study of surfaces in relative motion, from the Greek root tribos meaning mbbing. 

Studies of surfaces and surface properties can be traced to the early 1800s [1]. Processes that involved surfaces and surface chemistry, such as heterogeneous catalysis and Daguerre photography, were first discovered at that time. Since then, there has been a continual interest in catalysis, corrosion and other chemical reactions that involve surfaces. The modem era of surface science began in the late 1950s, when instmmentation that could be used to investigate surface processes on the molecular level started to become available. 

Plummer E W and Eberhardt W 1982 Angle-resolved photoemission as a tool for the study of surfaces Adv. Chem. Rhys. 49 533... 

Shen Y R 1994 Nonlinear optical studies of surfaces Appi. Rhys. A 59 541... 

Kneipp K, Kneipp H and Seifert F 1994 Near-infrared excitation profile study of surface-enhanced hyper-Raman scattering and surface-enhanced Raman scattering by means of tunable mode-locked... 

The dynamics of fast processes such as electron and energy transfers and vibrational and electronic deexcitations can be probed by using short-pulsed lasers. The experimental developments that have made possible the direct probing of molecular dissociation steps and other ultrafast processes in real time (in the femtosecond time range) have, in a few cases, been extended to the study of surface phenomena. For instance, two-photon photoemission has been used to study the dynamics of electrons at interfaces [ ]. Vibrational relaxation times have also been measured for a number of modes such as the 0-Fl stretching m silica and the C-0 stretching in carbon monoxide adsorbed on transition metals [ ]. Pump-probe laser experiments such as these are difficult, but the field is still in its infancy, and much is expected in this direction m the near fiitiire. 

One interesting new field in the area of optical spectroscopy is near-field scaiming optical microscopy, a teclmique that allows for the imaging of surfaces down to sub-micron resolution and for the detection and characterization of single molecules [, M]- Wlien applied to the study of surfaces, this approach is capable of identifying individual adsorbates, as in the case of oxazine molecules dispersed on a polymer film, illustrated in figure Bl.22,11 [82], Absorption and emission spectra of individual molecules can be obtamed with this teclmique as well, and time-dependent measurements can be used to follow the dynamics of surface processes. 

NMR has developed into a powerfiil analytical teclmique in the past decades, and has been used extensively in the characterization of a great number of chemical systems. Its extension to the study of surfaces, however, has been hampered by the need of large samples because of its poor sensitivity. On the otiier hand, the development of magic-angle-spiiming NMR (MAS-NMR) and the extension of NMR to many nuclei besides... 

Fleiiweii E J, Casassa M P, Cavanagh R R and Stephenson J C 1989 Picosecond vibrationai energy transfer studies of surface adsorbates Ann. Rev. Rhys. Chem. 40 143-71... 

Engel T and Rieder K H 1982 Structural studies of surfaces with atomic and molecular beam diffraction Structural Studies of Surfaces With Atomic and Molecular Beam Scattering (Springer Tracts in Modern Physics vol 91) (Berlin Springer) pp 55-180... 

Pisani C 1993 Embedded-cluster techniques for the quantum-mechanical study of surface reactivity J. Mol. Catal. 82 229... 

Whitten J L 1993 Theoretical studies of surface reactions embedded cluster theory Chem. Phys. 177 387-97... 

For practical reasons, the application of the adsorption method to the study of surface area and porosity has to be limited to bodies which are either very finely divided or possess an extensive pore system. It is helpful to consider the case of finely divided bodies first. 

Table 1 provides an overview of many of the techniques available for the characterization of surfaces and interfaces. These techniques are categorized on the basis of the nature of the exciting and detected species (or force). As can be seen by Table 1, a tremendous number of approaches are available for the study of surfaces. In fact, multiple methods capable of answering all of the three questions posed above have been developed over the past thirty years. 

Optical Techniques. The most important tool in a museum laboratory is the low power stereomicroscope. This instmment, usually used at magnifications of 3—50 x, has enough depth of field to be useful for the study of surface phenomena on many types of objects without the need for removal and preparation of a sample. The information thus obtained can relate to toohnarks and manufacturing techniques, wear patterns, the stmcture of corrosion, artificial patination techniques, the stmcture of paint layers, or previous restorations. Any art object coming into a museum laboratory is examined by this microscope (see Microscopy Surface and interface analysis). 

In 1954 the surface fluorination of polyethylene sheets by using a soHd CO2 cooled heat sink was patented (44). Later patents covered the fluorination of PVC (45) and polyethylene bottles (46). Studies of surface fluorination of polymer films have been reported (47). The fluorination of polyethylene powder was described (48) as a fiery intense reaction, which was finally controlled by dilution with an inert gas at reduced pressures. Direct fluorination of polymers was achieved in 1970 (8,49). More recently, surface fluorinations of poly(vinyl fluoride), polycarbonates, polystyrene, and poly(methyl methacrylate), and the surface fluorination of containers have been described (50,51). Partially fluorinated poly(ethylene terephthalate) and polyamides such as nylon have excellent soil release properties as well as high wettabiUty (52,53). The most advanced direct fluorination technology in the area of single-compound synthesis and synthesis of high performance fluids is currently practiced by 3M Co. of St. Paul, Minnesota, and by Exfluor Research Corp. of Austin, Texas. 

Chemical appHcations of Mn ssbauer spectroscopy are broad (291—293) determination of electron configurations and assignment of oxidation states in stmctural chemistry polymer properties studies of surface chemistry, corrosion, and catalysis and metal-atom bonding in biochemical systems. There are also important appHcations to materials science and metallurgy (294,295) (see Surface and interface analysis). 

VARIABLE TEMPERATURE FTIR SPECTROSCOPY IN THE STUDIES OF SURFACE PHENOMENA... 

According to Gatos, the needs of solid-state electronics, not least in connection with various compound semiconductors, were a prime catalyst for the evolution of the techniques needed for a detailed study of surface structure, an evolution which gathered pace in the late 1950s and early 1960s. This analysis is confirmed by the fact that Gatos, who had become a semiconductor specialist in the materials science and engineering department at was invited in 1962 to edit a new journal to be... 

The scientific study of surfaces, and the full recognition of how much a surface differs from a bulk structure, awaited a drastic improvement in vacuum technique. The next Section is devoted to a brief account of the history of vacuum. 

The many papers in this proceedings are partitioned into very abstruse theoretical analyses of structure and stability of quasicrystals on the one hand, and practical studies of surface structures, mechanical properties and potential applications. The subject shows signs of becoming as deeply divided between theorists and practical investigators, out of touch with each other, as magnetism became in the preceding century. 

A laboratory study of surface-treatment tanks by Braconnier et al." showed the effects of cross-drafts and obstructions to airflow on capture efficiency. They found that, without obstructions, capture efficiency decreased with increasing cnrss-draft velocity but the importance of this effect depended on freeboard height. In their study, cross-draft direction was always perpendicular to the hood face and directed opposite to the hood suction flow. Follow cro.ss-draft velocities (less than 0.2 m s ), efficiency remained close to 1.0 for the three freeboard heights studied. With higher cross-draft velocities, efficiency decreased as freeboard height decreased. For example, when the crossdraft velocity was 0.55 m s , efficiency decreased from 0.90 to 0.86 to 0.67 as freeboard height decreased from 0.3 m to 0.15 m to 0.1 m, respectively. 

The computer simulation of models for condensed matter systems has become an important investigative tool in both fundamental and engineering research [149-153] for reviews on MC studies of surface phenomena see Refs. 154, 155. For the reahstic modeling of real materials at low temperatures it is essential to take quantum degrees of freedom into account. Although much progress has been achieved on this topic [156-166], computer simulation of quantum systems still lags behind the development in the field of classical systems. This holds particularly for the determination of dynamical information, which was not possible until recently [167-176]. 

According to the aim of the present chapter, let us focus our attention on the academic-theoretical approach. It should be mentioned that in the study of surface reaction processes one frequently has to deal with fairly complex systems. Since the handling of such systems imposes severe problems, the standard procedure is to rationalize their study. The academic approach starts from simplified systems and a reduced number of plausible assumptions, and the goal is to achieve a general solution. The knowledge and understanding of these solutions allows us to undertake specific topics and more complex problems. 

The study of surface chemical reaction processes using computer simulation techniques is quite an active field of research. Within this context the Monte Carlo method emerges as a powerful tool which contributes to the... 

Due to the interesting technological applications, challenging phenomena, and continuous output of experimental information, it is expected that the study of surface chemical reactions will continue to attract increasing activity in the future. 

J. H. Block, M. Ehsasi, V. Gorodetskii. Dynamic studies of surface reactions with microscopic techniques. Prog Surf Sci 42.-143-168, 1993. 

In this review we put less emphasis on the physics and chemistry of surface processes, for which we refer the reader to recent reviews of adsorption-desorption kinetics which are contained in two books [2,3] with chapters by the present authors where further references to earher work can be found. These articles also discuss relevant experimental techniques employed in the study of surface kinetics and appropriate methods of data analysis. Here we give details of how to set up models under basically two different kinetic conditions, namely (/) when the adsorbate remains in quasi-equihbrium during the relevant processes, in which case nonequilibrium thermodynamics provides the needed framework, and (n) when surface nonequilibrium effects become important and nonequilibrium statistical mechanics becomes the appropriate vehicle. For both approaches we will restrict ourselves to systems for which appropriate lattice gas models can be set up. Further associated theoretical reviews are by Lombardo and Bell [4] with emphasis on Monte Carlo simulations, by Brivio and Grimley [5] on dynamics, and by Persson [6] on the lattice gas model. 

D. P. Landau, K. Binder. Monte Carlo study of surface phase transitions in the three-dimensional Ising model. Phys Rev B 47 4633-4645, 1980. 

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