Theory surface-based

Classical laminated plate tlieoiy is used to determine the stiffness of laminated composites. Details of the Kitchoff-Love hypothesis on which the theory is based can be found in standard texts (1,7,51). Essentially, the strains in each ply of the laminate ate represented as middle surface strains plus... 

The original microscopic rate theory is the transition state theory (TST) [10-12]. This theory is based on two fundamental assumptions about the system dynamics. (1) There is a transition state dividing surface that separates the short-time intrastate dynamics from the long-time interstate dynamics. (2) Once the reactant gains sufficient energy in its reaction coordinate and crosses the transition state the system will lose energy and become deactivated product. That is, the reaction dynamics is activated crossing of the barrier, and every activated state will successfully react to fonn product. 

A theory of two-phase laminar flow with a distinct interface has been developed. Although this theory is based on a one-dimensional approximation, it takes into account the major features of the process the inertia, gravity, surface tension and friction forces. Thus this study may be expected to give the physically realistic pattern of a laminar flow in a heated micro-channel. This allows one to use the present theory to study the regimes of flow, as well as optimizing a cooling system of electronic devices with high power densities. 

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. 

The models presented above have also been reviewed in Ref 18. Recently, an expression for the adsorption potential at the free water surface based on a combination of the electrostatic theory of dielectrics and classical thermodynamics has also been proposed." ... 

P. Mitchell (Nobel Prize for Chemistry, 1978) explained these facts by his chemiosmotic theory. This theory is based on the ordering of successive oxidation processes into reaction sequences called loops. Each loop consists of two basic processes, one of which is oriented in the direction away from the matrix surface of the internal membrane into the intracristal space and connected with the transfer of electrons together with protons. The second process is oriented in the opposite direction and is connected with the transfer of electrons alone. Figure 6.27 depicts the first Mitchell loop, whose first step involves reduction of NAD+ (the oxidized form of nicotinamide adenosine dinucleotide) by the carbonaceous substrate, SH2. In this process, two electrons and two protons are transferred from the matrix space. The protons are accumulated in the intracristal space, while electrons are transferred in the opposite direction by the reduction of the oxidized form of the Fe-S protein. This reduces a further component of the electron transport chain on the matrix side of the membrane and the process is repeated. The final process is the reduction of molecular oxygen with the reduced form of cytochrome oxidase. It would appear that this reaction sequence includes not only loops but also a proton pump, i.e. an enzymatic system that can employ the energy of the redox step in the electron transfer chain for translocation of protons from the matrix space into the intracristal space. 

Song L, Gao J (2008) On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory. J Phys Chem A ASAP... 

Smoluchowski, who worked on the rate of coagulation of colloidal particles, was a pioneer in the development of the theory of diffusion-controlled reactions. His theory is based on the assumption that the probability of reaction is equal to 1 when A and B are at the distance of closest approach (Rc) ( absorbing boundary condition ), which corresponds to an infinite value of the intrinsic rate constant kR. The rate constant k for the dissociation of the encounter pair can thus be ignored. As a result of this boundary condition, the concentration of B is equal to zero on the surface of a sphere of radius Rc, and consequently, there is a concentration gradient of B. The rate constant for reaction k (t) can be obtained from the flux of B, in the concentration gradient, through the surface of contact with A. This flux depends on the radial distribution function of B, p(r, t), which is a solution of Fick s equation... 

In 1938, Brunauer, Emmett and Teller(12) and Emmett and de Witt(13) developed what is now known as the BET theory. As in the case in Langmuir s isotherm, the theory is based on the concept of an adsorbed molecule which is not free to move over the surface, and which exerts no lateral forces on adjacent molecules of adsorbate. The BET theory does, however, allow different numbers of adsorbed layers to build up on different parts of the surface, although it assumes that the net amount of surface which is empty or which is associated with a monolayer, bilayer and so on is constant for any particular equilibrium condition. Monolayers are created by adsorption on to empty surface and by desorption from bilayers. Monolayers are lost both through desorption and through the adsorption of additional layers. The rate of adsorption is proportional to the frequency with which molecules strike the surface and the area of that surface. From the kinetic theory of gases, the frequency is proportional to the pressure of the molecules and hence ... 

When a phase transition occurs from a pure single state and in the absence of wettable surfaces the embryogenesis of the new phase is referred to as homogeneous nucleation. What is commonly referred to as classical nucleation theory is based on the following physical picture. Density fluctuations in the pre-transitional state result in local domains with characteristics of the new phases. If these fluctuations produce an embryo which exceeds a critical size then this embryo will not be dissipated but will grow to macroscopic size in an open system. The concept is applied to very diverse phenomena ... 

The theory is based on the autotrophic metabolism of low-molecular-weight constituents in an environment of iron sulfide and hot vents. Figure 2.4 gives an illustration of one reaction pathway. It is worthwhile to consider that the metabolism is a surface metabolism, namely with a two-dimensional order, based on negatively charged constituents on a positively charged mineral surface. Actually Wachtershauser sees this as an interesting part of a broader philosophical view (Huber and Wachtershauser, 1997). 

An important aspect of semiconductor films in general with regard to electronic properties is the effect of intrabandgap states, and particularly surface states, on these properties. Surface states are electronic states in the forbidden gap that exist because the perfect periodicity of the semiconductor crystal, on which band theory is based, is broken at the surface. Change of chemistry due to bonding of various adsorbates at the surface is often an important factor in this respect. For CD semiconductor films, which are usually nanocrystalline, the surface-to-volume ratio may be very high (several tens of percent of all the atoms may be situated at the surface for 5 mn crystals), and the effects of such surface states are expected to be particularly high. Some aspects of surface states probed by photoluminescence studies are discussed in the previous section. 

In theory, spatially resolved measurements of concentrations of atmospheric trace substances could be made by remote sensing from either surface-based or satellite platforms, but remote sensing capabilities have not yet been developed for many species. Furthermore, both surface- and satellite-based remote sensing methods have distinct limitations in resolving... 

There is a difference between experimentalists and theoreticians experimentalists observe the minima and maxima in free energy profiles—the experimental entities of intermediates and transition states—whereas theoreticians wish to calculate the entire energy surface of a reaction. Experimentalists talk about pathways, theoreticians about energy landscapes. Experiment and theory touch base around the ground and transition states that provide the milestones in the energy landscapes for the theoreticians to benchmark their calculations. The two views are reconciled in section G. 

Rice et al. [99] developed a global potential energy surface based on the Mowrey et al. [103] results and performed extensive classical trajectory calculations to study the dynamics of the CH2NN02 dissociation reactions. They calculated rates for reactions (III) and (IV) with classical barriers of 35 and 37 kcal/mol, respectively. They found that N-N bond fission dominates at low energy but that HONO elimination is competitive. Chakraborty and Lin [104] predict the opposite on the basis of their ab initio barriers and RRKM theory calculations. The two dissociations channels are closely competitive and it is not clear that ab initio methods are sufficiently reliable to distinguish between two reactions that have such similar energy requirements. Also, the Zhao et al. results [33] are not in accord with the theoretical predictions. 

While the period of the interference curve does not depend on the properties of a metal surface, the magnitude of effect, that is the amplitude of the interference curve, can reveal a strong dependence of such a kind. Indeed, Kadomtsev s theory is based on the assumption, that the atom interacts with quasi-free electrons in the thin surface layer. Therefore, the state of such electrons must be tightly connected with the properties of such a layer-for instance its temperature and crystal structure. 

Since DFT calculations are in principle only applicable for the electronic ground state, they cannot be used in order to describe electronic excitations. Still it is possible to treat electronic exciations from first principles by either using quantum chemistry methods [114] or time-dependent density-functional theory (TDDFT) [115,116], First attempts have been done in order to calculate the chemicurrent created by an atom incident on a metal surface based on time-dependent density functional theory [117, 118]. In this approach, three independent steps are preformed. First, a conventional Kohn-Sham DFT calculation is performed in order to evaluate the ground state potential energy surface. Then, the resulting Kohn-Sham states are used in the framework of time-dependent DFT in order to obtain a position dependent friction coefficient. Finally, this friction coefficient is used in a forced oscillator model in which the probability density of electron-hole pair excitations caused by the classical motion of the incident atom is estimated. 

Semiconductors are considered to be catalytic particles that contributed to the development of primitive metabolism. According to Wahtershauser life could have developed on the surface of iron sulphide minerals (eg mackinawite or pyrrhotite [FeS] or pyrite [FeS2]) [8], The chemoautotrophy theory is based on the reaction between iron sulphide and hydrogen sulphide, which acts as a reducing agent, whereas iron sulphide provides adsorption sites for substrates and acts as a catalyst (equation 10.1) ... 

One of the most interesting is the theory of surface metabolism, an approach that was proposed, in different forms, by John Bernal in 1951, by Graham Cairns-Smith in 1982 and by Gunter Wachters-hauser in 1998. The central idea of this theory is based on solid thermodynamic arguments. The formation of a peptide bond is not favoured in solution because it increases the entropy of the system, but on a surface the same process takes place with a decrease of entropy, and is therefore favoured. And this is true not only for peptide bonding but for many other types of polymerisation. A great number of enzymatic reactions require a collision of three molecules, an event which is highly unlikely in space but much more probable on a surface. 

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