Structure of liquids

Pershan P S 1988 Structure of Liquid Crystal Phases (Singapore World Soientifio)... 

P. Schuster, W. Jakubetz, W. Marius, S. A. Rice, Structure of Liquids Springer-Veiiag, Berlin (1975). 

The function W(X) is called the potential of mean force (PMF). The fundamental concept of the PMF was first introduced by Kirkwood [4] to describe the average structure of liquids. It is a simple matter to show that the gradient of W(X) in Cartesian coordinates is related to the average force. 

Figure 13.4 (a) ITie cri-bridged polymeric structure of liquid SbFs (schematic) show-ing the three sorts of F alom. (b) Structure of the tetrameric molecular unit in crystalline (SbFs)4 show[Pg.562]

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. 

It is clear from the forgoing discussions that the important material properties of liquid crystals are closely related to the details of the structure and bonding of the individual molecules. However, emphasis in computer simulations has focused on refining and implementing intermolecular interactions for condensed phase simulations. It is clear that further work aimed at better understanding of molecular electronic structure of liquid crystal molecules will be a major step forward in the design and application of new materials. In the following section we outline a number of techniques for predictive calculation of molecular properties. 

These two (equivalent) conformations are also found experimentally in the crystal structures of liquid crystals with this molecular fragment [58-60],... 

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]. 

In the previous sections, we have seen how computer simulations have contributed to our understanding of the microscopic structure of liquid crystals. By applying periodic boundary conditions preferably at constant pressure, a bulk fluid can be simulated free from any surface interactions. However, the surface properties of liquid crystals are significant in technological applications such as electro-optic displays. Liquid crystals also show a number of interesting features at surfaces which are not seen in the bulk phase and are of fundamental interest. In this final section, we describe recent simulations designed to study the interfacial properties of liquid crystals at various types of interface. First, however, it is appropriate to introduce some necessary terminology. 

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... 

No experimental technique exists for determining I-structures in either the liquid or the solid state. Techniques do exist for obtaining information on both the V- and D-structures of liquid water the results of applying these techniques are considered next. 

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

The possibility of determination of the difference of surface potentials of solvents, see Scheme 18, among others, has been used for the investigation of Ajx between mutually saturated water and organic solvent namely nitrobenzene [57,58], nitroethane and 1,2-dichloroethane (DCE) [59], and isobutyl methyl ketone (IB) [69]. The results show a very strong influence of the added organic solvent on the surface potential of water, while the presence of water in the nonaqueous phase has practically no effect on its x potential. The information resulting from the surface potential measurements may also be used in the analysis of the interfacial structure of liquid-liquid interfaces and their dipole and zero-charge potentials [3,15,22]. 

The present review intends to cover the work reported on nonlinear optics at liquid-liquid interface since the first report of S. G. Grubb et al. [18]. The theoretical aspects of nonlinear optics are first introduced in Section II. The experimental results covering the molecular structure of liquid interfaces are presented in Section III, followed by a section devoted to the dynamics and the reactivity at these interfaces. Section V focuses on new aspects where spherical interfaces with radii of curvature of the order of the wavelength of light are investigated. Section VI presents the field of SFG. 

HOST COMMON STRUCTURES OF LIQUID CRYSTALLINE STATIONARY PHASES Yi (CiH4) X(C H4) Y2 with n 1 or acre. Y and X are usually para substituents. 

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... 

NMR Self-Diffusion of Desmopressin. The NMR-diffusion technique (3,10) offers a convenient way to measure the translational self-diffusion coefficient of molecules in solution and in isotropic liquid crystalline phases. The technique is nonperturbing, in that it does not require the addition of foreign probe molecules or the creation of a concentration-gradient in the sample it is direct in that it does not involve any model dependent assumptions. Obstruction by objects much smaller than the molecular root-mean-square displacement during A (approx 1 pm), lead to a reduced apparent diffusion coefficient in equation (1) (10). Thus, the NMR-diffusion technique offers a fruitful way to study molecular interactions in liquids (11) and the phase structure of liquid crystalline phases (11,12). 

Wyllie, G., 1965, Evaporation and Surface Structure of Liquid, Proc. Roy. Soc. A197.383. (2) Yadigaroglu, G., 1993, Instabilities in Two-Phase Flow, in Workshop on Multiphase Flow and Heat Transfer Bases, Modeling and Applications, chapter 12, University of California, Santa Barbara, CA. (4)... 

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. 

G. C. Lie and E. Clementi, Study of the structure of molecular complexes XII Structure of liquid water obtained by Monte Carlo simulation with the Hartree-Fock potential corrected by inclusion of dispersion forces, J. Chem. Phys. 62 2195 (1975). 

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

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