Models of simple liquids

In the gas-like model of a liquid an attempt is made to extrapolate the structure of a gas to temperatures below the critical temperature Tq, The simplest model of a gas assumes that the molecules can be treated as point masses that interact with each other and with the walls of the container only during colhsions and then in a crude contact sense. This implies that the attractive forces between the molecules are negligible and that the repulsive forces are of vanishingly short range. This model readily gives the equation of state for the ideal gas  

Attempts to improve on this model try to allow for the nonzero, but short-range, attractive forces, and also for the finite range of the repulsive force, which, essentially, gives a molecule its size. One well-known attempt to improve on the simple model is that of van der Waals, who wrote the equation of state for a real gas in the form  

Despite these difficulties this type of model has been used in certain situations. In particular, the negative pressure regions have been interpreted as denoting the liquid phase under tension, and the maximum value of this tension, for a particular temperature, is interpreted as the tensile strength of the liquid phase at that 

A typical model in which a simple liquid is treated as a broken-up solid is the cell model. 

The results described in section 4.7 indicate that the general reduction in bulk density that occurs when a solid changes to a liquid arises from the decrease in coordination number, rather than from a uniform increase in the distance between neighbouring molecules. In the cell model a liquid is treated as a collection of molecules that spend most of their time in small clusters that fit together in a rather loose manner. Each cluster can be treated as a cell, the walls of which are formed by molecules and inside which one molecule is trapped. Any particular molecule can be pictured as a wall molecule of one cell or as a molecule trapped in another cell. This does not affect the analysis and, in any case, the cells are constantly breaking up and reforming. 

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Equations of state derived from statisticai thermodynamics arise from proper con-figurationai partition functions formuiated in the spirit of moiecuiar modeis. A comprehensive review of equations of state, inciuding the historicai aspects, is provided in Chapter 6. Therefore, we touch briefly in oniy a few points. Lennard-Jones and Devonshire [1937] developed the cell model of simple liquids, Prigogine et al. [1957] generalized it to polymer fluids, and Simha and Somcynsky [1969] modified Pri-gogine s cell model, allowing for more disorder in the system by lattice imperfections or holes. Their equations of state have been compared successfully with PVT data on polymers [Rodgers, 1993]. 

This chapter continues by looking at some of the macroscopic properties of simple liquids, particularly the tensile strength and flow properties. A brief discussion is then given of some molecular models of simple liquids and, finally, the unusual behaviour of liquid helium is described. 

Since the temperature coefficients of the sound velocity, the speciBc volume, and the specific heat are related to the thermal conductivity, a step of the temperamie coefHcient, K dXnXl dT, of the thermal conductivity is suggested. Measurements of the thermal conductivity in the melt of n-tetracosane have been performed by Gustafsson et al. resulting in a step-like behavior of K with AK = K (T ) - K (r ). The measured values of 2 x lO /K < AAT < 5 x 10" /K compare quite well to the calculated value of 7 x lO /K. This calculation is based on the harmonic oscillate model of simple liquids of Hotrocks and McLaughlin. ... 

Wood W W 1968 Monte Carlo studies of simple liquid models Physics of Simple Liquids ed H N V Temperley, J S Rowlinson and G S Rushbrooke (Amsterdam North Holland) chapter 5, pp 115-230... 

Hiwatari Y. The applicability of the soft core model of fluids to dynamical properties of simple liquids, Progr. Theor. Phys. 53, 915-28 (1975). 

These results have been initially considered as evidence for specific ion adsorption at ITIES [71,72]. Its origin was ascribed to extensive ion pair formation between ions in the aqueous phase and ions in the organic phase [71] [cf. Eq. (20)], or to a penetration into the interfacial region [72]. The former model, which has been considered in this context earlier [60], allows one to interpret the enhanced capacity in terms of Eq. (22). Pereira et al. (74) presented more experimental data demonstrating the effect of electrolytes and proposed a simple model, which is based on the lattice-gas model of the liquid liquid interface [23]. Theoretical calculations showed that ion pairing can lead to an increase in the stored... 

The structure of a simple mixture is dominated by the repulsive forces between the molecules [15]. Any model of a liquid mixture and, a fortiori of a polymer solution, should therefore take proper account of the configurational entropy of the mixture [16-18]. In the standard lattice model of a polymer solution, it is assumed that polymers live on a regular lattice of n sites with coordination number q. If there are n2 polymer chains, each occupying r consecutive sites, then the remaining m single sites are occupied by the solvent. The total volume of the incompressible solution is n = m + m2. In the case r = 1, the combinatorial contribution of two kinds of molecules to the partition function is... 

Following the early studies on the pure interface, chemical and electrochemical processes at the interface between two immiscible liquids have been studied using the molecular dynamics method. The most important processes for electrochemical research involve charge transfer reactions. Molecular dynamics computer simulations have been used to study the rate and the mechanism of ion transfer across the water/1,2-dichloroethane interface and of ion transfer across a simple model of a liquid/liquid interface, where a direct comparison of the rate with the prediction of simple diffusion models has been made. ° ° Charge transfer of several types has also been studied, including the calculations of free energy curves for electron transfer reactions at a model liquid/liquid... 

Guenza M, Freed KF (1996) Extended rotational isomeric model for describing the long time dynamics of polymers. J Chem Phys 105(9) 3823-3837 Hansen JP, McDonald JR (1986) Theory of simple liquids, 2nd edn. Academic Press, London... 

Ej Term of simple liquid enthalpy model in the inside-out methods,... 

Wood WW (1968) Monte Carlo studies of simple liquid models. In Temperley HNV, Rowlinson JS, Rushbrooke GS (eds) The physics of simple liquids, Amsterdam, North Holland, ppl15-230... 

Water is not only the most abundant of all liquids on this planet but also one of the most complex (see Section 2.4). The dielectric constant (permittivity) at frequencies below about lO is about 78 at room temperature, and this is about one whole order of magnitude higher than the dielectric constant of simple liquids such as carbon tetrachloride. Kirkwood was the first to develop a model to explain why the dielectric constant of water is so high. He pictured groups of HjO s coupled together by means of H bonding. His idea was that the dielectric constant of water consists of three parts. 

The category of simple liquids is sometimes used to establish the complementary category of complex liquids (Barrat and Hansen, 2003). Another and a broad view of complex liquids is that they are colloid, polymer, and liquid crystalline solutions featuring a wide range of spatial length scales - sometimes called soft matter (de Gennes, 1992). Planting ourselves at an atomic spatial resolution, the models analyzed for those complex liquids are typically less detailed and less realistic on an atomic scale than models of atomic liquids. 

Sestak, J., Zitny, R., and Houska, M. 1983. Simple rheological models of food liquids for process design and quality assessment. J. Food Eng. 2 35-49. 

Hence, one may conclude that in the limit k —> 0 the dynamics of the charge fluctuations is completely determined by relaxation processes with the finite (nonzero) relaxation time. In this sense we can speak about the fast kinetic-like behavior of the charge fluctuations in the model considered. This results in the effective independence of the other hydrodynamic Eqs. (44), (46), and (47), from the time evolution of fast charge subsystem, so that the hydrodynamics of a binary mixture of charge particles becomes rather similar to the case of simple liquids. However, we have to remember that in the hydrodynamic limit the additional (comparing with simple liquids) well-defined transport coefficients, namely the mutual D and />r thermal diffusion coefficients, exist in the system that play a crucial role in the electric and the thermoelectric properties, respectively. 

Our simulations use a lattiee-spin model of a liquid erystal, of the t5q)e pioneered by Lebwohl and Lasher. We use a simple Lebwohl-Lasher pairwise interaetion among rod-like lattiee spins S,. The nature of the energy means that, as with all liquid erystal systems, there is never a distinction between S and - S. This ean simulate either a thermotropie or a lyotropic LC. The sites are arranged in a ri-dimensional eubie lattiee, of length L lattice constants, with total number of sites (i.e. partieles) N = lf, subjeet to periodic boundary conditions. In all subsequent work, distanees are scaled with respect to the lattiee eonstant. 

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