ASSOCIATED LIQUID BY THE METHOD OF INTEGRAL EQUATIONS. E. So Yakub. UDC 532.74. The possibilities provided by the approximate solution of the ...
CALCULATION OF THE STRUCTURE AND PROPERTIES OF AN ASSOCIATED LIQUID BY THE METHOD OF INTEGRAL EQUATIONS E. So Yakub
UDC 532.74
The possibilities provided by the approximate solution of the system of integral equations for the correlation functions of an associated liquid, proposed eariier~ have been analyzed, and it has been shown that on this basis it is possible to construct a systematic statistical theory of the structure and thermodynamic properties of a liquid of this kind.
INTRODUCTION The structure of the short-range order in monatomic and simple molecular liquids is determined chiefly by short-range forces of intermolecular repulsion [i]. In associated liquids, on the other hand, an important role in the production of the structures is played by the forces of attraction between the molecules, arising as a result of the formation of hydrogen bonds. Unlike other forms of intermolecular attraction, these forces show two characteristic features. Firstly, they can be saturated. Each molecule can form not more than a definite number of bonds of this kind, which we shall call ~. Thus for the HF molecule, v = 2; for the H20 molecule, ~ = 4; etc. Secondly, the energy of the hydrogen bond is much greater than both the energy of attraction due to other interactions and the average energy of thermal motion of the molecules. These characteristic features make the hydrogen bond similar to a chemical bond, and the term "weak chemical bond" is even applied to it. At the same time, the physical nature of the saturation of a hydrogen bond is significantly different from, for example, that of a covalent bond. Here, we cannot speak of the pairing of valence electrons, but only of steric hindrance, which allows the formation of the bond only for definite relative orientations of the molecules. By itself, the high value of the energy of the hydrogen bond does not exclude the application, to associated liquids, of the same approach (for example, thermodynamic perturbation theory [2]) as that applied to nonassociated liquids. The principal contribution to the energy of the interaction usually related to the energy of the hydrogen bond is made by the purely electrostatic, primarily dipole-dipole, interaction of ~the molecules [3]. These interactions are successfully taken into account in the present-day statistical theory of polar fluids [5]. An obstacle to the application of statistical theory to polar associated liquids is provided by the nonelectrostatic short-range contribution to the interaction leading to hydrogen bond formation. This contribution is determined by the mutual polarization of the electron clouds and by so-called "charge transfer" [3]. It corresponds to forces of attraction which are localized in an extremely narrow range of intermolecular distances and which therefore have a significant influence on the force constants on the elongation and other deformations of the bond. Since there have been no effective methods of taking account of the influence of interactions of this type on the structure of a liquid until recently the statistical theory of associated l i q u i d s h a s developed chiefly in two directions: i) the development of model theories in which the structure of the liquid is postulated beforehand (see for example [6, 7]), and 2) the development of computer experiments by the Monte Carlo method [8, 9] or the methods of molecular dynamics [i0, ii]. The aim of the present work was to try to evaluate the possibility of applying a systematic statistical approach to the calculation of the structure and thermodynamic properties of associated liquids on the basis of the system of integral equations for their correlation Odessa Institute of the National Economy. Translated from Zhurnal Strukturnoi Khimii, Vol. 25, No. 3, pp. 54-60, May-June, 1984. Original article submitted March 21, 1983.
0022-4766/84/2503-0389508.50
9 1984 Plenum Publishing Corporation
389
functions proposed in [12]o MODEL OF INTERMOLECULAR INTERACTION It is subsequently assumed that two types of force act between molecules: i) pairedadditive "nonchemical" forces, which have the same physical components [4] (exchange, electrostatic, dispersion, etc.) as in the case of molecules which show no tendency to associate; and 2) "chemical" forces which can be saturated, and which are produced as a result of hydrogen bond formation. The latter are assumed to be localized only in a narrow range of intermolecular distances (and orientations), where they may reach high values. Thus the energy of interaction of a system of N molecules is written in the form [12]:
u~ =
E E
l~in(v--l)>>n(v--2)...;
n=
~
(14)
n(k)~n(v).
O~k~v
We introduce the functions Yts(12), related to y(kl[12) by the following expressions
Z
g(k/ll2)=
k!l! s!(k--s)!t!(l--t)! Yr.(f2).
Z
(15)
o..
