Lattice energies partitioning

Boublik, T., Fried, V., Hala, E. (1984) The Vapor Pressure of Pure Substances, 2nd revised Edition, Elsevier, Amsterdam, The Netherlands. Bowman, B. T., Sans, W. W. (1983) Determination of octanol-water partitioning coefficient (KqW) of 61 organophosphorus and carbamate insecticides and their relationship to respective water solubility (S) values. J. Environ. Sci. Health B18, 667-683. Bradley, R. S., Cleasby, T. G. (1953) The vapour pressure and lattice energy of some aromatic ring compounds. J. Chem. Soc. 1953, 1690-1692. 

Unfortunately, the algorithms of some of the programs used for lattice energy calculation and minimization do not readily enable the extraction of this partitioned energy. 

In summarizing reversed-phase SPE, both the and the log of the octanol-water partition coefficient of the compound are related to the aqueous solubility of the analyte, although the relationship is not always straightforward because there are other factors that affect solubility of an analyte but that do not affect sorption, such as crystal lattice energy for solids. In spite of this factor, one could theoretically estimate the from the solubility of the analyte and relate this solubility to the capacity of the solute for the reversed-phase sorbent. The ability to use solubility to predict capacity is also addressed... 

Gallego R. and Ortiz M., A Harmonic/Anhamionic Energy Partition Method for Lattice Statics Computations, Modelling Simul. Mater. Sci. Eng. 1, 417 (1993). 

While it is a computationally convenient approximation, the rigid molecule approach is only justified under certain conditions. For discussion, we partition the total lattice energy of a crystal structure into intermolecular and intramolecular components ... 

Nitta et. al. ( 7) extended the group interaction model to thermodynamic properties of pure polar and non-polar liquids and their solutions, including energy of vaporization, pvT relations, excess properties and activity coefficients. The model is based on the cell theory with a cell partition function derived from the Carnahan-Starling equation of state for hard spheres. The lattice energy is made up of group interaction contributions. 

Table 14.9 The partition of Pixel lattice energies (kJ mol for the P2i /c crystal structures of the three substituted corannules...

The choice of the upper limit (a — a) is rather arbitrary. In so far as we are interested in excess properties of solutions, we could as well take (a — constant term to the free energy and disappears in the excess functions (cf., however, Ch. XVIII for the quantum case). As in the Lennard-Jones and Devonshire model, we shall use (7.1.23) for the lattice energy" of our system. The cell partition function W is clearly of the same form as for hard spheres (cf. 7.1.11) and depends only on the density. It may be written in the form... 

Let us now consider the general formulae for the excess functions. The quantities which refer to pure liquids at the same pressure and temperature as the mixture will be noted by a double index. For example Waa is the cell partition function of pure A, and (oja 0)I2 the lattice energy per particle of pure A. With this notation, formula (7.1.3) for the configurational free energy of pure A or B is written in the form... 

Each term has a simple physical interpretation. The excess free energy appears to be due to the change of the lattice energies and the ceil partition functions at mixing. The corresponding formulae for th = excess energy and excess entropy axe... 

The first two terms in (16.5.4) are due to the volume dependence of the cell partition function, while the last term is due to the lattice energy. This equation of state can be written in a reduced form. Let us introduce the reduced variables T and (cf. 2.4.11)... 

Starting with the cell partition function (16.3.17) and the lattice energy (16.4.2) we may easily obtain the explicit expressions for the thermodynamic properties. The main difference is that the cell partition function depends only on the voliune but not on the temperature. The calculations are the same as for the harmonic oscillator model and will not be repeated. Instead of (16.5.4) we obtain the equation of state... 

The partitionfunction of the system contains a Boltzmann lattice-energy factor, a combinatorial factor representing the entropy of segment mixing and empty lattice sites, and a statistical-mechanical free-volume term. From the partition function, the equation of state may be calculated in the form of... 

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