Many important industrial applications, as well as insight into the phenomena of nature, rely crucially on knowledge about fluid phase behavior. In space and other high-temperature industries, as well as in combustion processes, the properties of gases manifesting various types of reaction, including dissociation and ionization, are required. In chemical and environmental science and technology, phase and reaction equilibria of multicomponent mixtures form the basis of understanding the phenomena and designing synthesis, separation, and purification processes. Biotechnological downstream processing relies on the distribution properties of biomolecules in different phases of aqueous and organic solutions. Even in standard mechanical engineering equipment technology, such as refrigerator design, lack of data for new environmentally friendly refrigerants has proved to be a severe obstacle to technological progress. In all these cases, and many others, fluid phase properties form the basis of modern technological processes and detailed and quantitative knowledge of their properties is the premise of innovation. Experimental studies alone, although indispensible in the field of fluid system science, cannot serve these needs. The project of studying the fluid phase behavior of a multicomponent system experimentally is hopeless in view of the large number of data that would be needed. Instead, molecular models, which can be evaluated on a computer and make use of the limited data available to predict the fluid phase behavior in the full range of interest, are needed. Due to the broad availability of high-speed computers, such models can be quite ambitious, including use of quantum-chemical and molecular simulation computer codes.

When fluid phase behavior over a large region of states is considered, excess function models are no longer appropriate. They are designed to address mixing effects at constant density or pressure. Effects of varying density are most conveniently treated in terms of an equation of state. The thermodynamic relations for computing fluid phase behavior from an equation of state in combination with ideal gas properties are well established; cf. Section 2.1. Although they are more demanding computationally than excess function models, there are now many well-tested computer codes available that allow the computation of fluid phase behavior from an equation of state. Basically, this approach is free from any of the restrictions associated with the use of excess function models. In principle, an equation of state model is generally applicable, including simple and complicated molecules, and, in particular, mixtures of small and large molecules, as in polymer solutions. In practice, different equation of state models are used for different applications and no general model suitable for all applications has yet emerged. The generality of the equation of state approach requires full generality of the potential energy model. A formulation in terms of contact energies, adequate for excess function models, is unsufficient. Rather, the potential energy will in principle depend on the distances between the molecular centers, on the orientations of the molecules, and, in the most general case, also on their internal coordinates. In this book we shall concentrate on equation of state models for systems composed of small molecules, such as those typically encountered in the gas industries.

The book deals with the prediction of the macroscopic behavior of fluids from the properties of their molecular constituents. The basis of such prediction is the availability of molecular models. Designing molecular models for fluids has an interdisciplinary background of foundations. Their thorough understanding is the basis for developing new models and appreciating the promise as well as the limitations of those that are established.

Molecular models are formulated in terms of the energy of a system of three-dimensional flexible bodies, i.e., the molecules. This molecular energy depends on the geometrical structures of the molecules and the force field they are moving in. The relation between the geometrical structure of a body and its energy is defined in mechanical terms. The force field results from the electrical properties of the molecules. On this level the models are thus based on classical mechanics and electrostatics. Classical theory, although most powerful even on the molecular scale, is, however, incomplete in the sense that it does not provide information on the geometry of the molecules or on their charge distributions as the origin of the electrical force field. This gap is closed by quantum mechanics, which also gives important corrections to the classical results in order to make them ultimately applicable to molecules. The link between the molecular energy of a system and its macroscopic thermodynamic functions is provided by statistical mechanics and by computer simulation. By using this link the molecular model leads to numerical data for the thermodynamic functions, from which the macroscopic behavior of a fluid can be calculated by the laws of classical thermodynamics.

Our society relies on the use of energy and matter in a plenitude of different forms. They are produced from natural resources by technical processes of energy and matter conversion that have to be designed in an economically and ecologically optimum way. In these processes it is the fluid state of matter that dominates the relevant phenomena. In particular, the properties of fluid systems in equilibrium enter into the fundamental process equations and control the feasibility of the various process steps. Models for fluids in equilibrium are thus a prerequisite for any scientific process analysis. Although fluid models can be constructed entirely within the framework of a macroscopic theory on the basis of experimental data, it is clear that this approach is limited to those few systems for which enough data can be obtained. Typical examples are the working fluids of the standard power generation and refrigeration processes. The vast majority of technically relevant processes are, however, concerned with complex fluid systems that cannot be analyzed experimentally in sufficient detail with a reasonable effort. In such cases one must turn to the microscopic basis of matter and design a theory based on the molecular properties of a fluid that requires only few data or is even fully predictive. In this introductory chapter we present an overview of the challenges of this approach by presenting a review of macroscopic fluid phase behavior in equilibrium, along with the problems associated with obtaining the necessary information from data. We also give a first introduction to the primary concepts of the microscopic world, including a brief glance at the properties of real molecules and the philosophy behind formulating molecular models.

To derive an expression for the relative probability Pi of a microstate i we first consider a canonical ensemble, i.e., a collection of systems, each with fixed values of N, V, and T; cf. Figure A 3.1. The ensemble as a whole is isolated adiabatically so that the total energy of the canonical ensemble has a fixed value, Uc. Each of the πc systems of the canonical ensemble finds itself in a large heat bath at temperature T provided by the other systems.

Many different microstates or quantum states are associated with each fixed macrostate of the canonical ensemble. Different quantum states of a canonical ensemble may be represented by different distributions of its systems over the many possible energy states of the single system.We denote by {Ei} the various possible energy values of a system in the canonical ensemble. In principle, the spectrum of energy values of the system follows from its Schrödinger equation. We assume in the following that the spectrum of energy values is known. It is identical for each system of the canonical ensemble, because the values of V and {Nα} are identical. Thus {Ei} is available as a set of values (E1, E2, E3, …, Ej), if we assume a total of j quantum states for each system. At each moment of time each system of the canonical ensemble will be found in one of these energy states, whose number j is extremely large.

The fluid phase behavior of dense fluids, e.g., liquids, is not described adequately by the ideal gas molecular model. Thus, our interest now turns to configurational properties, i.e., those that are determined by the intermolecular potential energy. It is this potential energy that controls the most important aspects of fluid phase behavior, such as phase equilibria, and reaction equilibria in solutions.

A particularly simple approach to fluid phase behavior of dense fluids is offered by excess function models. The thermodynamic relations for computing phase and reaction equilibria as well as heat effects from excess functions are well established; cf. Section 2.1. They are basically rather straightforward and even allow evaluation by hand in many simple applications. The excess function approach is particularly suited to liquid mixtures made up of large molecules. The fluid phase behavior of such fluids tends to be interesting only over a narrow liquid density range at normal pressure, such that it may be formulated in terms of constant density and constant pressure mixing effects. Such effects are adequately formulated in terms of excess functions. Restriction to excess functions for liquid mixtures implies two important simplifications in the molecular models. First, we will not need explicit potential models over a large range of intermolecular distances and orientations. Because the molecules in liquids can be considered to be densely packed, the interactions between them can be modeled by contact energies of nearest neighbors. In this sense the potential model adequate for excess functions is the strict opposite to that of an ideal gas, where the distance between interacting molecules was assumed to be infinite.