Theory of liquid state

THE.IO. I. Prigogine, Contribution a la theorie de Petal liquide (Contribution to the theory of liquid state), J. Phys. Radium 5, 16-22 (1944). 

In chemistry it is used in particular in the theory of liquid state. 

Recently, Pak, Ahn, and Change have developed a theory of liquid state and called it transient state theory of significant liquid structure. (Hereafter, it is referred to as the transient state theory.) They have applied transient state theory to various liquids such as argon, nitrogen, benzene, chloroform, and carbon disulfide with success. 

S. A. Adelman and R. Muralidhar,/. Chem. Phys., 95, 2752 (1991). Theory of Liquid-State Activated Barrier Crossing The Instantaneous Potential and the Parabolic Model. 

The other and better known is the absolute rate approach, based on the hole theory of liquid state. Eyring, 1936 (29) assumed that during a chemical reaction there is one step which can be identified with an activated state and that the process is uni-molecular. The reaction rate constant k can be expressed as... 

NMR relaxation and its field dependence are a very important source of experimental information on dynamics of molecular motions. This information is conveyed through spectral density functions, which in turn are related to time-correlation functions (TCFs), fundamental quantities in the theory of liquid state. In most cases, characterizing the molecular dynamics through NMR relaxation studies requires the identification of the relaxation mechanism (for example the dipole-dipole interaction between a pair of spins) and models for the spectral densities/correlation functions." During the period covered by this review, such model development was concerned with both small molecules and large molecules of biological interest, mainly proteins. 

To explain the existence of the LC. ST of such a type, a theory of corresponding states (called the theory of liquid state as well) ha.s received a large d< velopment effort by Prigogine et al. (1953), Prigogine (1957), Flory el al. (196dab), Flory (1965, 1970), Patterson and Delmas (1970),, Siow et al. (1972). This approach is baseil on the theory of r-dimcnsional liquids developed by the Brussels school (Ilia Prigogine el al.)... 

J.A. Barker, Lattice theories of liquid state, Oxford Pergamon Press (1%3). 

Baker A.J. (1963) in The International Encyclopedia of Physical hemistry and Chemical Physics Topic 10, the fluid state, J.S. Rowlinson ed. Vol. I, Lattice Theories of Liquid State, Macmillan, New York. 

Barker J and Henderson D 1967 Perturbation theory and equation of state for a fluids II. A successful theory of liquids J. Chem. Phys. 47 4714... 

Wdom B 1965 Equation of state near the critical point J. Chem. Phys. 43 3898 Neece G A and Wdom B 1969 Theories of liquids Ann. Rev. Phys. Chem. 20 167... 

The theory of liquids is based on statistical mechanics [2-5]. A fundamental result in statistical mechanics is that the probabihty of a state having an energy Ei is given by... 

Our second goal is to introduce these simple phenomena in a statistical mechanical scheme such that the calculations keep a transparent significance at each step. Nowadays, the predictions of theoretical approaches depend on approximations of a high level of technicality in the domain of liquid state theory. These approximations seem to have a mathematical rather than... 

A theoretical analysis of the helium-xenon system was reported by Zandbergen and Beenakker (Zl), who based their calculations on the Prigogine-Scott theory of corresponding states for mixtures (PI 5, S2). We cannot here go into the details of their analysis, but will merely indicate the essential elements. Zandbergen and Beenakker use the three-liquid theory to obtain an expression for the volumes of helium-xenon mixtures as a function of temperature, pressure, and composition. This expression is... 

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. 

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. 

Riedel, L. Chem. Ing. Tech. 26 (1954) 259-264. Liquid density in the saturated state. Extension of the theory of corresponding states. 

The kinetic theory of collisions, which has been so effective in developing the kinetics of vapor-phase reactions, has substantially influenced research on the processes of liquid-phase oxidation and in describing these processes. It has been thought that the lack of laws on which to base liquid-state theory (in contrast to the well-developed kinetic theory of gases) would in principle severely limit the development of a quantitative theory of liquid-phase reactions. At present the characteristics of the liquid state are carefully considered in discussing the mechanism of intermolecular reactions, influence of the medium on reactivity of compounds, etc. 

The spectra of liquids and solids are known to have strong induced components. Liquids and solids are, however, so dense that many-body terms dominate the spectra the binary and ternary spectral components which are the main topic of this work (and which are usually measurable in compressed gases at densities much lower than liquid state) will often resemble the spectra of liquids and solids, but a critical comparison will reveal important qualitative and quantitative differences. Nevertheless, a study of binary spectra will help to illuminate important aspects of the theoretical descriptions of liquid spectra and may be considered a basic input into the theory of liquid interactions with radiation. 

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). 

Generalized Correlations. A simple and reliable method for the prediction of vapor—liquid behavior has been sought for many years to avoid experimentally measuring the thermodynamic and physical properties of every substance involved in a process. Whereas the complexity of fluids makes universal behavior prediction an elusive task, methods based on the theory of corresponding states have proven extremely useful and accurate while still retaining computational simplicity. Methods derived from corresponding states theory are commonly used in process and equipment design. 

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or solid. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (5) the intramolecular vibrations are considered identical for molecules in either the gas or liquid phases, and (4) the potential energy of a collection of molecules is a function of only the various intermolecular distances. 

There is also much interest in applying various types of liquid-state theory, to PDMS in particular.219 220... 

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