The Structure of Liquids

A topic of abiding interest is the issue of characterizing the order in liquids which may be defined as the entropy deficit due to preferential orientations of molecular multipoles relative to random orientations (orientational order) and nonuniformly directed intermolecular forces (positional order). Phenomenologically, two criteria are often claimed to be relevant for deciding whether or not a liquid is to be viewed as ordered the Trouton entropy of vaporization or Trouton quotient and the Kirkwood correlation factor gK. Strictly speaking, however, both are of limited relevance to the issue. 

entropy of depacking hard spheres = entropy of repulsion 

ASo can be separated into the entropy fo(ri) of depacking hard spheres to an ideal gas at the liquid volume V, and the entropy of volume expansion to Vg = RT/P, 

Further, fo(ri) can be derived from the famous Chamahan-Starling equation as  

On the other hand, the gK faetor is, loosely speaking, a measure of the deviation of the relative dielectric constant of the solvent with the same dipole moment and polarizability would have if its dipoles were not correlated by its structure. However, the gK factor is only the average cosine of the angles between the dipole moments of neighboring molecules. There may thus be orientational order in the vicinity of a molecule despite a gx of unity if there are equal head-to-tail and antiparallel alignments. Furthermore, the gK factor is not related to positional order. 

On the other hand, the factor is, loosely speaking, a measure of the deviation of the 

Douglas (Doug) Henderson was born in Calgary, Alberta, Canada in 1934. He grew up 

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Most nonpolar substances have very small water solubilities. Petroleum, a mixture of hydrocarbons, spreads out in a thin film on the surface of a body of water rather than dissolving. The mole fraction of pentane, CsH12, in a saturated water solution is only 0.0001. These low solubilities are readily understood in terms of the structure of liquid water, which you will recall (Chapter 9) is strongly hydrogen-bonded. Dissimilar intermolecular forces between C5H12 (dispersion) and H2O (H bonds) lead to low solubility. 

We have developed a new method of interpretation of the photographs which does not suffer from this disadvantage. This radial distribution method, which is closely related to the method of interpretation of x-ray diffraction data developed by Zemike and Prins3 for the study of the structure of liquids and applied by Warren and Gingrich4 to crystals, consists in the calculation (from... 

Using the first-principles molecular-dynamics simulation, Munejiri, Shimojo and Hoshino studied the structure of liquid sulfur at 400 K, below the polymerization temperature [79]. They found that some of the Ss ring molecules homolytically open up on excitation of one electron from the HOMO to the LUMO. The chain-like diradicals S " thus generated partly recombine intramolecularly with formation of a branched Sy=S species rather than cyclo-Ss- Furthermore, the authors showed that photo-induced polymerization occurs in liquid sulfur when the Ss chains or Sy=S species are close to each other at their end. The mechanism of polymerization of sulfur remains a challenging problem for further theoretical work. 

Molecular mechanics force fields have largely been parameterised using the best available data from the gas phase and (in some cases) from liquid phase or solution data. The question therefore arises as to how applicable molecular mechanics force fields are to predicting structures of molecules in the liquid crystal phase. There is now good evidence from NMR measurements that the structure of liquid crystal molecules change depending on the nature of their... 

It is now well-established that for atomic fluids, far from the critical point, the atomic organisation is dictated by the repulsive forces while the longer range attractive forces serve to maintain the high density [34]. The investigation of systems of hard spheres can therefore be used as simple models for atomic systems they also serve as a basis for a thermodynamic perturbation analysis to introduce the attractive forces in a van der Waals-like approach [35]. In consequence it is to be expected that the anisotropic repulsive forces would be responsible for the structure of liquid crystal phases and numerous simulation studies of hard objects have been undertaken to explore this possibility [36]. 

Considerable progress has been made in the last decade in the development of more analytical methods for studying the structural and thermodynamic properties of liquids. One particularly successful theoretical approach is. based on an Ornstein-Zernike type integral equation for determining the solvent structure of polar liquids as well as the solvation of solutes.Although the theory provides a powerful tool for elucidating the structure of liquids in... 

In this section, rather than give a detailed account of theories of the liquid state, a more qualitative approach is adopted. What follows includes first a description of the structure of ice then from that starting-point, ideas concerning the structure of liquid water are explained. 

Before considering the details of the structure of liquid water, it is important to define precisely what is meant by the term structure as applied to this liquid. If we start from ice I, in which molecules are vibrating about mean positions in a lattice, and apply heat, the molecules vibrate with greater energy. Gradually they become free to move from their original... 

Overall, the main conclusions that are to be drawn concerning the structure of liquid water are as follows. 

The structure of water in its liquid state is very complicated and is still a topic of current research. The structure of liquid water, with its molecules connected together by hydrogen bonds, gives rise to several anomalies when compared with other liquids.6... 

Kuharski, R.A. Rossky, P.J., Quantum mechanical contributions to the structure of liquid water, Chem. Phys. Lett. 1984, 103, 357-362... 

The function U fXj is called the PMF it was first introduced by Kirkwood to describe the structure of liquids [61]. It plays the role of a free energy surface for the solute. Notice that the dynamics of the solute on the free energy surface W(X) do not correspond to the true dynamics. Rather, an MD simulation on 1T(X) should be viewed as a method to sample conformational space and to obtain equilibrium, thermally averaged properties. 

Warren, B.E. (1937). X-ray determination of the structure of liquids and glass. Journal of Applied Physics 8 645-654. 

Transition Region Considerations. The conductance of a binary system can be approached from the values of conductivity of the pure electrolyte one follows the variation of conductance as one adds water or other second component to the pure electrolyte. The same approach is useful for other electrochemical properties as well the e.m. f. and the anodic behaviour of light, active metals, for instance. The structure of water in this "transition region" (TR), and therefore its reactions, can be expected to be quite different from its structure and reactions, in dilute aqueous solutions. (The same is true in relation to other non-conducting solvents.) The molecular structure of any liquid can be assumed to be close to that of the crystals from which it is derived. The narrower is the temperature gap between the liquid and the solidus curve, the closer are the structures of liquid and solid. In the composition regions between the pure water and a eutectic point the structure of the liquid is basically like that of water between eutectic and the pure salt or its hydrates the structure is basically that of these compounds. At the eutectic point, the conductance-isotherm runs through a maximum and the viscosity-isotherm breaks. Examples are shown in (125). 

This ensures that thermochemical (TC) lattice stabilities are firmly anchored to the available experimental evidence. Although the liquid phase might be considered a common denominator, this raises many problems because the structure of liquids is difficult to define it is certainly not as constant as popularly imagined. It is therefore best to anchor the framework for lattice stabilities in the solid state. 

ELLIPSOMETRY The structure of liquid surfaces with monomolecular films can be studied by measuring the light reflected from the surface. The range of thickness that one generally considers to be measured varies from 100 to 1000 A (10-100 nm). However, in monolayers in which the molecules are oriented and the thickness involved is 5-50 A, the methods have been not easily pursued. In a differential method in which two beams of light from the same incandescent lamp were directed... 

Once the structures of liquid and amorphous InP have been generated using MD simulations, various properties of these materials can be explored. To give just one example, the structure of disordered materials is often characterized using the radial distribution function ... 

Figure 1.68 The structure of liquid crystalline polymers (a) nematic, (b) smectic and (c) cholesteric. Reprinted, by permission, from J. L. Fergason, Scientific American, 211(2), pp. 78, 80. Copyright 1964 by Scientific American, Inc.

Some important features regarding the structures of liquid silicates are revealed by recent volumetric studies of both alkali (9) and alkaline earth systems 55). First, the partial molar volume of silica in the alkali silicates is nearly equal to that of pure fused silica and is independent of the cation over wide compositional ranges. Second, at about 10 15 mole-% metal oxides, the thermal expansions show a sudden increase. The results for the alkali silicates are shown in Fig. 5. A similar behavior is found in the system... 

This chapter consists of a description of the structure of liquid water and the nature of ions in aqueous solution. The discussion is largely restricted to the interactions between monatomic ions with liquid water in which they become hydrated by acquiring a hydratiun sphere or shell-Additionally, a few diatomic and polyatomic anions are dealt with, including the important hydroxide ion. The hydration of ions derived from the s- and p-block elements of the Periodic Table, and the derivation of values of their enthalpies and entropies of liydralioii, are described in considerable detail. 

The structure of liquid water was described and compared to that of ice. The importance of hydrogen bonding was indicated. 

Schematic diagram of the structures of liquid and frozen water. Black circles represent oxygen atoms, and smaller gray circles represent hydrogen atoms. As water freezes, the molecules link up with hydrogen bonds (dashed lines) to form an open structure that is less dense than liquid water.

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