And generalized molecular distribution

Relations between thermodynamic quantities and generalized molecular distribution functions... 

We start with detailed definitions of the singlet and the pair distribution functions. We then introduce the pair correlation function, a function which is the cornerstone in any molecular theory of liquids. Some of the salient features of these functions are illustrated both for one- and for multicomponent systems. Also, we introduce the concepts of the generalized molecular distribution functions. These were found useful in the application of the mixture model approach to liquid water and aqueous solutions. 

In section 2.7, we introduced the generalized molecular distribution functions GMDFs. Of particular importance are the singlet GMDF, which may be re-interpreted as the quasi-component distribution function (QCDF). These functions were deemed very useful in the study of liquid water. They provided a firm basis for the so-called mixture model approach to liquids in general, and for liquid water in particular (see Ben-Naim 1972a, 1973a, 1974). 

In all of these models, the hydrogen bonds, or the structure of liquid water, were traditionally emphasized as the main molecular reasons for the anomalous behavior exhibited by liquid water. However, underlying this relatively ill-defined concept of structure (which was much later defined in statistical mechanical terms see Sec. 2.7) lies a more fundamental principle which can be defined in molecular terms, and which does not explicitly mention the concept of structure yet is responsible for the unusual properties of liquid water. This principle was first formulated in terms of generalized molecular distribution functions in 1973. It states that there exists a range of temperatures and pressures at which the water-water interactions produce a unique correlation between high local density and a weak binding energy. Clearly, this principle does not mention structure. As will be demonstrated in this section, it is this principle, not the structure per se, which is responsible for the unique properties of water as well as of aqueous solutions. ... 

Generalized Molecular Distribution Functions and the Mixture-Model Approach to Liquids... 

We do not have a simple relation between the difference in the enthalpies Hi — Hu and the generalized molecular distribution functions. Therefore, the conclusion drawn here is basically intuitive. Furthermore, from the behavior of the function K)... 

A system of nonspherical particles in two dimensions is, from the computational point of view, an intermediate case between spherical particles (in either two or three dimensions) and nonspherical particles in three dimensions. The pair potential in this case depends on three coordinates (see below), compared with six in the three-dimensional case. Some very useful information on the numerical procedure, on the problem of convergence, and so forth, can thus be gained in a system which is relatively simpler than the three-dimensional case. We shall also present some results on the generalized molecular distribution function, which thus far are available only in two dimensions, yet are of relevance to the case of real liquid water. 

Another feature of the mode of packing of waterlike particles akin to the behavior of liquid water is demonstrated by the joint singlet generalized molecular distribution function, constructed by combining the binding energy and coordination number (Fig. 6.28). The values of K) Av... 

In this section we generalize the concept of molecular distribution to include properties other than the locations and orientations of the particles. We shall mainly focus on the singlet generalized molecular distribution function (MDF), which provides a firm basis for the so-called mixture model approach to liquids. The latter has been used extensively for complex liquids such as water and aqueous solutions. 

Born M and Green H S 1946 A general kinetic theory of liquids I. The molecular distribution functions Proc. R. Soc. A 188 10... 

Synthetic, nonionic polymers generally elute with little or no adsorption on TSK-PW columns. Characterization of these polymers has been demonstrated successfully using four types of on-line detectors. These include differential refractive index (DRI), differential viscometry (DV), FALLS, and MALLS detection (4-8). Absolute molecular weight, root mean square (RMS) radius of gyration, conformational coefficients, and intrinsic viscosity distributions have... 

The Born-Oppenheimer approximation is the first of several approximations used to simplify the solution of the Schradinger equation. It simplifies the general molecular problem by separating nuclear and electronic motions. This approximation is reasonable since the mass of a typical nucleus is thousands of times greater than that of an electron. The nuclei move very slowly with respect to the electrons, and the electrons react essentially instantaneously to changes in nuclear position. Thus, the electron distribution within a molecular system depends on the positions of the nuclei, and not on their velocities. Put another way, the nuclei look fixed to the electrons, and electronic motion can be described as occurring in a field of fixed nuclei. 

The synthesis of well defined block copolymers exhibiting controlled molecular weight, low compositional heterogeneity and narrow molecular weight distribution is a major success of anionic polymerization techniques 6,7,14-111,112,113). Blocks of unlike chemical nature have a general tendency to undergo microphase separation, thereby producing mesomorphic phases. Block copolymers therefore exhibit unique properties, that prompted numerous studies and applications (e.g. thermoplastic elastomers). 

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