Molecular Theory of Fluids

Molecules are small and light typical linear dimensions are 10 to ICr m, and typical masses are 10 to kg. Hence the number of molecules in a macroscopic system is enonuous. For example, one mole of matter contains 6.022 x 10 molecules (Avogadro s number). Because of these features— smallness, lightness, and numerical abundance— the proper description of behavior at the molecular level and its extrapolation to a macroscopic scale require the special methods of quairtum mechanics aird statistical mechanics. We pursue neitherof these topics here. Instead, we present material nseful for relating molecular concepts to observed thenrrodynamicproperties. 

By convention, a positive F represents an intermolecular repulsion, and a negative F an intermolecular attraction. Hence (Fig. 16.1) molecules repel each other at small separations, and attract each other at modest-to-large separations. 

An algebraic expressionfor the pair-potentialfunctionU is one of the tools of the trade of the molecular scientist or engineer. The methods of statistical mechanics provide for its relation to both thennodynamicand transport properties. Shown in Fig. 16.1 are specific values for U and r that may appear as species-dependent parameters in a pair-potential function. 

The hard-core diameter 3 is a measure of the center-to-center separation for which U, and hence F, becomes infinite. It is not subject to precise determination, but plays the role of a modeling parameter in some expressions for U. The collision diameter a is defined as the separation for which U = 0. The equilibrium, separation ro is the separation for which U attains its minimum value of —e. At r = vq, the net intemiolecularforce is zero. Quantity e is called the well depth. For a particular class of chemical species (e.g., noble gases, or cyclic alkanes), each of these special quantities increases with increasing molecular size. Typical ranges of values for o and E are a 3 to 8 x 10 ° m and e 0.1 to 1.0 x 10 J. Commonly, 

Scores of expressions have been proposed for W. All are essentially empirical, although their functional forms often have some basis in theory. The most widely used is the Lennard-Jones (LJ) 12/6 pair-potential function  

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H. S. Green, The Molecular Theory of Fluids, North-Holland, Amsterdam, The Netherlands,... 

Besprechung der verschiedenen Theorien vgl. H. Benzler, Z. Elektrochem. 581, 482 (1954) vgl. auch H. S Green, The molecular theory of fluids. Amsterdam North-Holland Publ. Co. 1952. 

Green, H. S. The molecular Theory of fluids. Amsterdam North-Holland Publishing Company 1952. 

Newman, F.H. and Searle, V.H., The General Properties of Matter, Butterworths Scientific, London,1957 Green, H.S., The Molecular Theory of Fluids, Dover Publications, New York, 1970. Leonardo da Vinci, Libri, Histoire des Sciences Mathematiques en Italie, Paris, 3, 54, 1838-1841. Poggendorff, F.,Ann. Phys., 101, 551, 1857. 

Green, H. S, Molecular Theory of Fluids, Interscience, New York-London, 1952. 

Prausnitz, J. M., R. N. Lichtenthaler, and E. G. de Azevedo Molecular Theory of Fluid-Phase Equilibria, Prentice-Hall, Englewood Cliffs, N.J., 1986. 

The reptation model was the first to bring the large parameter N into play. As a result, a molecular theory of fluid polymer dynamics has been developed. All the previous theories of the dynamics of polymeric liquids were basically phenomenological. 

Excluding the introductory chapter, the book is organized into three parts. The first. Chapters 2-4, presents the general molecular theory of fluids and mixtures. Here the notions of molecular distribution functions are developed with special attention to fluids consisting of nonspherical particles. We have included only those theories judged to be potentially useful in the study of aqueous fluids, so this part may not be considered as an introduction to the theory of fluids per se. 

In the above sense the SPT is not a purely molecular theory of fluids. This comment should be borne in mind when the theory is applied to complex fluids. In any real liquid, and certainly for water, we need a few molecular parameters to characterize the molecules, say and a in a Lennard-Jones fluid, or, in general, a set of molecular parameters a, b, c,. . . . Thus, a proper statistical-mechanical theory of water should provide us with the Gibbs energy as a function of T, P, N and the molecular parameters, a, b, c, i.e., a function of the form G(T, P, N a,b,c,... ). Instead the SPT makes use of only one molecular parameter, the diameter a. No provision for incorporating other molecular parameters is offered by the theory. This deficiency in the characterization of the molecules is partially compensated for by the use of the measurable density p as an input parameter. 

Computer simulations also constitute an important basis for the development of the molecular theory of fluids. They could be regarded as quasiexpeiimental procedures to obtain datasets that connect the fluid s microscopic parameters (related mainly to the structure of the system and the molecular interactions) to its macroscopic properties (such as equation of state, dynamic coefficients, etc.). In particular, some of the first historical simulations were performed using two-dimensional fluids to test adaptations of commonly used computer simulation methods [14,22] Monte Carlo (MC) and molecular dynamics (MD). In fact, the first reliable simulation results were obtained by Metropolis et al. [315], who applied the MC method to the study of hard-sphere and hard-disk fluids. 

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