Liquid structure theories

Marchi and Eyring have developed a partition function based on significant liquid structure theory proposed by Eyring et al. They assumed two solid-like species, a nonrotating hydrogen-bonded species and a rotating monomer. They further assumed that the monomer is able to rotate in the... 

Shredding plastic waste 1117,1138,1371 Significant Liquid Structures theory 129... 

Essentially, the RISM and extended RISM theories can provide infonnation equivalent to that obtained from simulation techniques, namely, thermodynamic properties, microscopic liquid structure, and so on. But it is noteworthy that the computational cost is dramatically reduced by this analytical treatment, which can be combined with the computationally expensive ab initio MO theory. Another aspect of such treatment is the transparent logic that enables phenomena to be understood in terms of statistical mechanics. Many applications have been based on the RISM and extended RISM theories [10,11]. 

We recently proposed a new method referred to as RISM-SCF/MCSCF based on the ab initio electronic structure theory and the integral equation theory of molecular liquids (RISM). Ten-no et al. [12,13] proposed the original RISM-SCF method in 1993. The basic idea of the method is to replace the reaction field in the continuum models with a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM theory. Exploiting the microscopic reaction field, the Fock operator of a molecule in solution can be expressed by... 

In this chapter, we have reviewed the RISM-SCF/MCSCF method, which combines electronic structure and liquid-state theories to deal with the chemistry of solutions. The ability... 

S. Dietrich. Fluids in contact with structured substrates. In C. Cacamo, ed. Proceedings of the NATO-ASI, New Approaches to Old and New Problems in Liquid State Theory, Messina, 1998. (Dordrecht Kluwer, 1999). 

I have tried to remain true to my original brief, and produce a readable text for the more advanced consumer of molecular structure theory. The companion book Chemical Modelling from Atoms to Liquids (John Wiley Sons Ltd, Chichester, 1999) is more suitable for beginners. 

During recent decades a great amount of knowledge about the properties of atomic nuclei has been gathered. An extensive theory of nucleonic interactions and nuclear structure [liquid-drop theory (7), shell theory (2, 3), unified theory (4), cluster theory (5—7)] has been developed... 

Now calculations of Ta and Tk are plagued by the usual difficulties of liquid state structure theory and the accuracy of approximations, some of which are hard to control. Still, even in the face of such approximations, such microscopic considerations lead us to expect a universal value of y/Tg at Tg as we shall discuss next. 

Theories of electron mobility are intimately related to the state of the electron in the fluid. The latter not only depends on molecular and liquid structure, it is also circumstantially influenced by temperature, density, pressure, and so forth. Moreover, the electron can simultaneously exist in multiple states of quite different quantum character, between which equilibrium transitions are possible. Therefore, there is no unique theory that will explain electron mobilities in different substances under different conditions. Conversely, given a set of experimental parameters, it is usually possible to construct a theoretical model that will be consistent with known experiments. Rather different physical pictures have thus emerged for high-, intermediate- and low-mobility liquids. In this section, we will first describe some general theoretical concepts. Following that, a detailed discussion will be presented in the subsequent subsections of specific theoretical models that have been found to be useful in low- and intermediate-mobility hydrocarbon liquids. 

This chapter is concerned with the application of liquid state methods to the behavior of polymers at surfaces. The focus is on computer simulation and liquid state theories for the structure of continuous-space or off-lattice models of polymers near surfaces. The first computer simulations of off-lattice models of polymers at surfaces appeared in the late 1980s, and the first theory was reported in 1991. Since then there have been many theoretical and simulation studies on a number of polymer models using a variety of techniques. This chapter does not address or discuss the considerable body of literature on the adsorption of a single chain to a surface, the scaling behavior of polymers confined to narrow spaces, or self-consistent field theories and simulations of lattice models of polymers. The interested reader is instead guided to review articles [9-11] and books [12-15] that cover these topics. 

A quantity of central importance in the study of uniform liquids is the pair correlation function, g r), which is the probability (relative to an ideal gas) of finding a particle at position r given that there is a particle at the origin. All other structural and thermodynamic properties can be obtained from a knowledge of g r). The calculation of g r) for various fluids is one of the long-standing problems in liquid state theory, and several accurate approaches exist. These theories can also be used to obtain the density profile of a fluid at a surface. 

In the next sections we will focus on analyzing the dynamics of supercooled liquids in more detail and discuss our findings in terms of the modecoupling theory of the glass transition, which is a liquid state theory that predicts the dynamics from the structural properties of the liquid. 

The discussion of potential energy surfaces thus far has implicitly assumed that gas-phase reactions are in focus. For condensed-phase reaction dynamics, where thermal fluctuations have a significant and intrinsic role, the situation is much more unsettled. The reader is referred to the list of challenges to condensed-phase electronic structure theory recently made by Truhlar, who asks if condensed-phase electronic structure may be "... not only waiting for its Hylleraas, but even waiting for its Schrodinger [112] The development of liquid-phase dynamics will surely continue to be an intense area of research through the foreseeable future. 

Braumann, T. Determination of hydrophobic parameters by reversed-phase liquid chromatography theory, experimental techniques, and application in studies on quantitative structure-activity relationships, J. Chromatogr., 373 191-225, 1986. 

Transient Nucleation If a liquid is cooled continuously, the liquid structure at a given temperature may not be the equilibrium structure at the temperature. Hence, the cluster distribution may not be the steady-state distribution. Depending on the cooling rate, a liquid cooled rapidly from 2000 to 1000 K may have a liquid structure that corresponds to that at 1200 K and would only slowly relax to the structure at 1000 K. Therefore, Equation 4-9 would not be applicable and the transient effect must be taken into account. Nonetheless, in light of the fact that even the steady-state nucleation theory is still inaccurate by many orders of magnitude, transient nucleation is not discussed further. 

A further criticism of the BET theory is the assumption that the heat of adsorption of the second and higher layers is equal to the heat of liquefaction. It seems reasonable to expect that polarization forces would induce a higher heat of adsorption in the second layer than in the third, and so forth. Only after several layers are adsorbed should the heat of adsorption equal the heat of liquefaction. It is, therefore, difficult to resolve a model of molecules adsorbed in stacks while postulating that all layers above the first are thermodynamically a true liquid structure. The apparent validity of these criticisms contributes to the failure of the BET equation at high relative pressures (P/Pq > 0.35). However, in the range of relative pressure leading to coverage near W/ = 1, the BET C values... 

Fig. 6.77. Calculations done using the statistical mechanical theory of electrolyte solutions. Probability density p(6,r) for molecular orientations of water molecules (tetrahedral symmetry) as a function of distance rfrom a neutral surface (distances are given in units of solvent diameter d = 0.28 nm) (a) 60H OH bond orientation and (b) dipolar orientation, (c) Ice-like arrangement found to dominate the liquid structure of water models at uncharged surfaces. The arrows point from oxygen to hydrogen of the same molecule. The peaks at 180 and 70° in p(0OH,r) for the contact layer correspond to the one hydrogen bond directed into the surface and the three directed to the adjacent solvent layer, respectively, in (c). (Reprinted from G. M. Tome and G. N. Patey, ElectrocNm. Acta 36 1677, copyright 1991, Figs. 1 and 2, with permission from Elsevier Science.

The papers in the second section deal primarily with the liquid phase itself rather than with its equilibrium vapor. They cover effects of electrolytes on mixed solvents with respect to solubilities, solvation and liquid structure, distribution coefficients, chemical potentials, activity coefficients, work functions, heat capacities, heats of solution, volumes of transfer, free energies of transfer, electrical potentials, conductances, ionization constants, electrostatic theory, osmotic coefficients, acidity functions, viscosities, and related properties and behavior. 

Finally, an important if tentative conclusion emerges concerning the symmetry of distribution functions, which could be relevant to the general theory of polarization and to current ideas about liquid structure. Theoretical analysis in terms of radially symmetric models does not necessarily tell us about the structure of a system, because the short-range forces, by their very nature, have a directional character which is not lost in any averaging process. Is it this averaged directional force which is responsible for structure in liquids and solutions ... 

Significant Structure Theory and Eucken s Polymer Model. If we drop the restriction that the bulky species represent only Ice-I-like structures and reserve the term ice-like for water molecules which have merely the same spatial arrangement as ice (i.e., tetrahedrally hydrogen-bonded), we may include in this two-state theory (in which we have a bulky and a dense species) the treatment by Marchi and Eyring (107). This is a special case of the significant structure theory of liquids and introduces, as a specific element, fluidized vacancies in addition to the individual monomers (which, in turn, are assumed capable of free rotation). 

Cluster Theories. Historically, the most important study of water structure based on the existence of clusters was Stewart s x-ray diffraction work (142). In his theory, clusters ( cybotactic swarms ) were postulated to exist, each containing on the order of 10,000 water molecules. Although this constituted an apparently reasonable theory at the time, this view has now yielded to the concept of clusters of considerably smaller sizes. It is interesting to note that without much critical analysis, Frenkel (57) viewed Stewart s theory of water as essentially correct. In fact, Frenkel apparently expected that further work on liquid structures in general would be along the lines Stewart advocated. Luck has discussed this in some detail (100). Subsequent to Stewart s papers, Nomoto (113) discussed a water model, based on ultrasonic studies, involving clusters of several thousand water molecules. 

B. M. Ladanyi, Computer simulation studies of solvation dynamics in mixtures, in J. Samios and V. A. Durov (eds), Novel Approaches to the Structure and Dynamics of Liquids Experiments, Theories and Simulations, Kluwer, Dordrecht, 2004, NATO Sci. Ser. II, Vol. 133, p. 560. 

A Combination of Electronic Structure and Liquid-state Theory RISM-SCF/MCSCF Method... 

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