Surface theories

B. H. Lengsfield and D. R. Yarkony, Nonadiabatic Interactions Between Potential Energy Surfaces Theory and Applications, in State-Selected and State to State Ion-Molecule Reaction Dynamics Part 2 Theory, M. Baer and C.-Y. Ng, eds., John Wiley Sons, Inc., New York, 1992, Vol, 82, pp. 1-71. 

OM Becker, M Karplus. The topology of multidimensional potential energy surfaces Theory and application to peptide stiaicture and kinetics. I Chem Phys 106 1495-1517, 1997. 

V. N. Kusovkov, O. Kortluke, W. von Niessen. Kinetic oscillations in the catalytic CO oxidation on Pt single crystal surfaces Theory and simulation. J Chem Phys 705 5571-5580, 1998. 

The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. 

Wu, S. and Mills, D. L. (2002) STM-induced enhancement of dynamic dipole moments on crystal surfaces theory of the lateral resolution. Rhys. Rev. B, 65, 205420-1-205420-7. 

Wright, B.M. (1950). Freshly fractured surface theory of silicosis. Nature 166, 538-540. 

Lengsfield BH, Yarkony DR (1992) Nonadiabatic interactions between potential energy surfaces theory and applications. In Baer M, Ng CY (eds) State-selected and state-to-state ion-molecule reaction dynamics part 2 theory, Vol. 82 of Advances in Chemical Physics, John Wiley and Sons, New York, p 1-71. 

In an effort to understand the mechanisms involved in formation of complex orientational structures of adsorbed molecules and to describe orientational, vibrational, and electronic excitations in systems of this kind, a new approach to solid surface theory has been developed which treats the properties of two-dimensional dipole systems.61,109,121 In adsorbed layers, dipole forces are the main contributors to lateral interactions both of dynamic dipole moments of vibrational or electronic molecular excitations and of static dipole moments (for polar molecules). In the previous chapter, we demonstrated that all the information on lateral interactions within a system is carried by the Fourier components of the dipole-dipole interaction tensors. In this chapter, we consider basic spectral parameters for two-dimensional lattice systems in which the unit cells contain several inequivalent molecules. As seen from Sec. 2.1, such structures are intrinsic in many systems of adsorbed molecules. For the Fourier components in question, the lattice-sublattice relations will be derived which enable, in particular, various parameters of orientational structures on a complex lattice to be expressed in terms of known characteristics of its Bravais sublattices. In the framework of such a treatment, the ground state of the system concerned as well as the infrared-active spectral frequencies of valence dipole vibrations will be elucidated. 

The book has been written as an introductory text, not as an exhaustive review. It is meant for students at the start of their Ph.D. projects and for anyone else who needs a concise introduction to catalyst characterization. Each chapter describes the physical background and principles of a technique, a few recent applications to illustrate the type of information that can be obtained, and an evaluation of possibilities and limitations. A chapter on case studies highlights a few important catalyst systems and illustrates how powerful combinations of techniques are. The appendix on the surface theory of metals and on chemical bonding at surfaces is included to provide better insight in the results of photoemission, vibrational spectroscopy and thermal desorption. 

Vanghan, D. J., Becker, U., Wright, K., 1997. Sulphide mineral surfaces theory and experiment. Inter. J. Miner. Process, 51 1-4... 

Flowers, M. C., Jonathan, N. . H., Yong, L. and Morris, A. Temperature programmed desorption of molecular hydrogen from a Si(100)-2 x 1 surface theory and experiment. Journal of Chemical Physics 99, 7038 (1993). 

A wide variety of homogeneous and hetrogeneous systems are effective for polymerizing various monomers to isotactic structures. Therefore the question must be raised as to whether macro-surface theories have any required validity for steric control but whether some other factor is important. Fig. 10 summarizes the monomers polymerized to isotactic polymers and shows that all propagate with an asymmetric center at the end of the chain. 

A review of Muraour s work was given by Sc nmidt(Ref 15). All surface theories lead to the conclusion that the fate of burning depends upon the gas temp near the solid and that the rate is proportional to pressure except at high pressures... 

Surface Theories. A review of the earlier theories on combustion is presented by Comer(Ref 6). Theories in which the rate -determining step occurs at the surface of a burning proplnt were proposed by Muraour (cited in Ref 6) and Daniel s( Ref 1 and cited in Refs 7 9). The theory proposed by Muraour is based on the burning race law r= a+ bP... 

Combination Theory of Rice Ginell and Parr Crawford This theory combines the surface theory of Daniels and the gas phase theory of Boys Corner. The essential feature of the theory is the determination of the surface temp (Tg) of a burning proplnt and its dependency on the gas phase reactions. 

Roger Smith, Atomic and Ion Collisions in Solids and at Surfaces Theory, Simulation and Applications, Cambridge University Press, Cambridge, UK, 1997. 

Diffusion of vacancies in metal surfaces theory and experiment... 

Ultimately one wants to understand the catalytic reactivity of metal surfaces. What we have learned experimentally is that reactivity depends in interesting ways on the metal, on the surface exposed, on the impurities or coadsorbates on that surface, on defects, and on the coverage of the surface. Theory is quite far behind in making sense of these determining factors of surface reactivity, but some pieces of understanding emerge. One such factor is the role of the Fermi level. 

Bohnenkamp and Engell (3) measured the capacity of a germanium electrode in KOH as a function of potential with respect to a reversible half-cell using a counter electrode to bias the germanium surface. Theory predicted that this capacity should go through a minimum and also how this minimum should depend on equilibrium electron hole density in the germanium. They measured how the electrolytic potential for the capacity minimum depended on electron-hole ratio. In this case the capacity is a function of frequency so the interpretation is not as simple as in the case of Dewald s results. The conclusion was that this potential behaved within experimental error as expected. 

Two of the leading mathematicians of the nineteenth century, Riemann and Weierstrass, played crucial roles in the further development of minimal surface theory. Their most important result, for which Weierstrass is accredited, is the triplet of integrals known as the Weierstrass equations. These equations offer a useful route to periodic minimal surfaces. A summary of the theory follows. 

P. Tangney and S. Scandolo (2002) How well do Car-Parrinello simulations reproduce the Born-Oppenheimer surface Theory and examples. J. Chem. Phys. 116, p. 14... 

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