Water partition function for

In a different approach, Bottinga (1969a) evaluated the nonclassical rotational partition function for water vapor, molecular hydrogen, and methane through the asymptotic expansion of Strip and Kirkwood (1951) ... 

Figure 11.30 Reduced partition function for various minerals calulated by Kieffer (1982) through equation 11.61 plotted against T. Heavy curve labeled H20(l) is reduced partition function of water according to Becker (1971). Dashed curve is a extrapolation of high-r reduced partition curve for quartz. Mineral abbreviations Qtz (quartz), Calc (calcite), Albt (albite), Muse (muscovite), Enst (clinoenstatite), Anor (anorthite). Diop (diopside), Pyrp (pyrope), Gros (grossular), Zron (zircon), Fors (forsterite), Andr (andra-dite), Rutl (rutile). Reprinted with permission from Kieffer (1982), Review of Geophysics and Space Physics, 20, 827-849, copyright 1982 by the American Geophysical Union.

It is mandatory to consider the underlying statistical mechanical formalism in order to systematize the preceding ideas. For this purpose we will examine the partition function for an N-molecule water cluster. The isothermal-isobaric ensemble is appropriate (5) since constant normal stress (denoted below by "pressure" p) seems relevant to most cases of interest. The partition function for this ensemble, Ayv(j3,p),... 

The partition function for liquid water is developed according to the transient state theory of significant liquid structure proposed by Pak, Ahn, and ChangT This theory assumes that the molecules may possess solid-like, transient, and gas-like degrees of freedom in liquid state. 

Pak and Chang have previously developed a partition function for liquid water applying the modified theory of significant liquid structure proposed by Chang et al. There, it is assumed that Ice-I-like, Ice-III-like, and gas-like molecules exist in liquid water and the molecules like Ice I and Ice III, both of which are oscillating torsionally, are in thermodynamic equilibrium. The equilibrium constant has been taken equal to the ratio of the partition functions of the two species. Various thermodynamic properties and the surface tension of liquid water from the partition function were successfully calculated. 

Then, according to the transient state theory, the partition function for liquid water is given as follows ... 

We present a brief derivation of the partition function for the cluster model. It is basically the same as the one derived by Lovett and Ben-Naim (1969), except for the simplification of the pair interactions. In the following, we treat the case of pure water. We shall revert to this model for the study of aqueous solutions in Sec. 3.9. 

The partition function for the system of two-component, water-like and inert solute particles is fairly complicated. Details are provided in Lovett and Ben-Naim (1969). Here, we present the final form of the partition function and the computational procedure to obtain the cluster-size distribution and the solvation quantities in a very dilute solution of HRs in a solvent. 

Here, is the number of waters, fi2 is the chemical potential, and/2 the absolute activity of the nonvolatile solute species (such as a protein) at temperature T and pressure p. The are then partition functions for N2 solutes in the solvent of Af, waters at T and p. From this point of view, the standard thermodynamic derivatives yield the various observables required such as. 

The most fundamental starting point for any theory of water should be the quantum-mechanical partition function for the whole system. However, since at present we cannot solve the Schrodinger equation for such a complex system, we resort to the partially classical partition function, written as... 

In the present study we try to obtain the isotherm equation in the form of a sum of the three terms Langmuir s, Henry s and multilayer adsorption, because it is the most convenient and is easily physically interpreted but, using more a realistic assumption. Namely, we take the partition functions as in the case of the isotherm of d Arcy and Watt [20], but assume that the value of V for the multilayer adsorption appearing in the (5) is equal to the sum of the number of adsorbed water molecules on the Langmuir s and Henry s sites ... 

Figure 5.6 The difference between liposome-water and octanol-water partitioning as a function of the octanol-water partition coefficient for a series of unrelated structures [149,385,386,429]. For example, acyclovir partitions into liposomes over 3000 times more strongly than into octanol, and amiodarone partitions into liposomes 100 times more weakly than into octanol. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]...

Equation (87) and analogous equations for AG , AHm, and for surface tensions apply to molten salt mixtures in which the interaction potential can be classed as conformal. These relations may also be used to test whether the ionic interaction potential in aqueous solutions may be considered as conformal. Thus, as will be shown in one simple example, the limits of usefulness of some interionic interaction potentials may be tested in ranges of concentration of salts in water too high to obtain absolute values for the partition functions. A similar test may be made for associations in salt vapors such as... 

The presence of a residual hydrocarbon phase in soils or sediments has been shown to increase the soil- or sediment-water distribution coefficients of poorly water-soluble organic contaminants [463,464]. Such petroleum-hydrocarbon-based phases have been shown to function as effective partition media for PCB congeners [467]. In general, sorption of contaminants by soils and sediments reduces their bio availability to microorganisms [468,469]. In this fashion, the... 

Figure 3.3-6 The distribution ratios between [BMIMjlPFg] and water (neutral pH) for organic solutes correlate with literature partition functions of the solutes between octanol and water (log P).

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