Thermodynamics and materials modelling

Published in Chemical Thermodynamics of Materials by Svein Stdlen and Tor Grande 2004 John Wiley Sons, Ltd ISBN 0 471 492320 2 

We start in this chapter with potential-based methods, the computationally cheapest approach, which can be applied to large assemblies of molecules. We then move on to the use of quantum mechanical techniques, as used for problems involving smaller numbers of atoms. The aim is to give a brief overview of the subject and its applications, and to show what type of information can be obtained from the different methods. The reader is referred to specialist texts for fuller details. 

2-body potential 3-body potential 4-body potential 

1 Einstein s comments on quantum mechanics include his belief that God does not play dice. 

Extension to a molecule with more than four atoms or to a solid is straightforward. Usually the two-body terms are much larger than the three-body terms, which in turn are greater than the four-body. For ionic solids, for example, the three-body and four-body terms are often neglected. In contrast, for metals and semiconductors including only two-body terms leads to very poor results (see Sutton (Further reading)). 

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Advanced adhesives are composite liquids that can be used, for example, to join aircraft parts, thus avoiding the use of some 30,000 rivets that are heavy, are labor-intensive to install, and pose quality-control problems. Adhesives research has not involved many chemical engineers, but the generic problems include surface science, polymer rheology and thermodynamics, and molecular modeling of materials... 

The symbols are P for profit, / for equality constraints, g for inequality constraints, x for optimization variables, y for dependent variables, and / (constant) for updated parameters. The objective function is a scalar measure of plant profit it is usually the instantaneous profit ( /hr), because the optimization variables do not involve the time value of money. Typical equality constraints include material and energy balances, heat and mass transfer relationships, and thermodynamic and kinetic models, and typical inequality constraints include equipment limitations limit compressor horsepower, and distillation tray hydraulics. The optimization variables are flow rates, pressures, temperatures, and other variables that can be manipulated directly. The dependent variables involve intermediate values required for the detailed models for example, all distillation tray compositions, flow rates, and temperatures. Because of the fundamental models often used in RTO, the number of dependent variables can be quite large, on the order of hundreds of thousands. 

Considering oxidations employing air or molecular oxygen as the oxidizing reagent, the reactivity of different chemical groups in carbohydrates can be predicted on the basis of thermodynamic and kinetic models. Under ambient conditions, monomeric molecules can be more easily oxidized than polymeric materials but, in any case, the kinetics are very slow, and most of the processes require catalysis. On the basis of reaction models underpinned by experimental data, the reactivity of carbohydrates is more predictable in the case of chemical catalysis than in the case of enzymatic catalysis. 

In addition to thermodynamic and macroscopic models, the behavior of amorphous systems can be viewed in terms of microscopic and molecular arguments. While these are equivalent in theory, each view provides different insights and advantages for explaining certain behaviors. In particular, the microscopic viewpoint allows a fundamental interpretation in terms of molecular interactions and packing, while thermodynamics allows material-independent equations to be developed based on macroscopic energy content arguments. 

The use of the computer in the design of chemical processes requires a framework for depiction and computation completely different from that of traditional CAD/CAM appHcations. Eor this reason, most practitioners use computer-aided process design to designate those approaches that are used to model the performance of individual unit operations, to compute heat and material balances, and to perform thermodynamic and transport analyses. Typical process simulators have, at their core, techniques for the management of massive arrays of data, computational engines to solve sparse matrices, and unit-operation-specific computational subroutines. 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

Finally, it must be recalled that the transport properties of any material are strongly dependent on the molecular or ionic interactions, and that the dynamics of each entity are narrowly correlated with the neighboring particles. This is the main reason why the theoretical treatment of these processes often shows similarities with models used for thermodynamic properties. The most classical example is the treatment of dilute electrolyte solutions by the Debye-Hiickel equation for thermodynamics and by the Debye-Onsager equation for conductivity. 

The theoretical solar conversion efficiency of a regenerative photovoltaic cell with a semiconductor photoelectrode therefore depends on the model used to describe the thermodynamic and kinetic energy losses. The CE values, which consider all the mentioned losses can generally only be estimated the full line in Fig. 5.65 represents such an approximation. Unfortunately, the materials possessing nearly the optimum absorption properties (Si, InP, and GaAs) are handicapped by their photocorrosion sensitivity and high price. 

A kinetic model based on the Flory principle is referred to as the ideal model. Up to now this model by virtue of its simplicity, has been widely used to treat experimental data and to carry out engineering calculations when designing advanced polymer materials. However, strong experimental evidence for the violation of the Flory principle is currently available from the study of a number of processes of the synthesis and chemical modification of polymers. Possible reasons for such a violation may be connected with either chemical or physical factors. The first has been scrutinized both theoretically and experimentally, but this is not the case for the second among which are thermodynamic and diffusion factors. In this review we by no means pretend to cover all theoretical works in which these factors have been taken into account at the stage of formulating physicochemical models of the process... 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

However, it has turned out that the most accurate way of fixing these parameters is through matching of simulated phase equilibria to those derived from experiment.33 As a final step, the potential, regardless of its source, should be validated through extensive comparison with available experimental data for structural, thermodynamic, and dynamic properties obtained from simulations of the material of interest, closely related materials, and model compounds used in the parameterization. The importance of potential function validation in simulation of real materials cannot be overemphasized. 

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