Pratt-Chandler theory

An elegant theory to go beyond the hard-sphere cavity was presented by Pratt and Chandler [17], where the attractive part of the solute-water interaction was treated perturbatively (in the spirit of the Weeks-Chandler-Andersen (WCA) theory [18]). The central quantities in the Pratt-Chandler theory are two radial distribution functions, gAw f) that give, respectively, the... 

The Pratt-Chandler theory provides an expression for the modification in the chemical potential of the non-polar solute due to non-hard-sphere interaction... 

UAw, r) = UHs r) +u r). In the Pratt-Chandler theory, UAw r) considers the interaction between the oxygen atom of water and the non-polar solute. 

In the Pratt-Chandler theory, the distortion of the liquid structure and the work done when two neutral hard-sphere solutes are brought from infinity to a certain distance gives a measure of the hydrophobic effect. 

The Pratt-Chandler theory has been extended to consider complex molecules. For example, the hard-sphere model of -butane may have an excluded volume Av(f, X), which is a function of the torsion angle (j) and depends on the exclusion radius X of the methylene spheres. Then the part of the PMF (the potential of mean force) arising from the solute-solvent interaction can be related to the reversible work required to create a cavity with the shape and excluded volume Av((/>, X) of the -butane molecule. 

The eelebrated Pratt-Chandler (PC) theory is usually the starting point of any diseussion on the hydrophobie effeet. This theory ean be regarded as an application of the Weeks-Chandler-Andersen (WCA) perturbative theory of liquids to the solvation of one and a pair of non-polar solute moleeules. While Stillinger discussed the ehemieal potential involved in ereating a hard-sphere cavity in water using the scaled partiele theory, the Pratt-Chandler theory used an integral equation deserip-tion and showed how to properly discuss the effect within a general statistieal mechanical theory. 

Equation (15.A.11) can be solved with the help of the closure relations (15.A.13) and (15.A.14) - this is the main idea behind the Pratt-Chandler theory. 

Pt = —(l/V )(9V /9p)r the isothermal compressibility ITM = information theory model PC = Pratt-Chandler theory RSPM = revised scaled particle model SPM = scaled particle model. 

In this section, we give a short summary of some of these theories and their applications, with an emphasis on contrasting the Pratt-Chandler, Cummings -Stell, and Wertheim approaches. The interested reader can find more technical details in the references. 

Equilibrium theories of classical fluids are often formulated as integral equations for the distribution functions, e.g., AA(r) giving the probability distribution of AA pairs at a specified separation in water. The Pratt-Chandler (PC) theory was the first theory of hydrophobic effects largely built on that conventional basis. A less conventional feature was that the PC theory avoided calculating separately the structure of water in the absence of hydrophobic solutes, much in the spirit of the scaled particle models. Instead, the measured goo(r) was used as input to the theoretical calculation of gAA(r). The idea was to use what is known about pure water to make predictions about hydrophobic effects. The ITM makes this heuristic point of view explicit. Moreover, the success of the simplest two-moment ITM provides important support for... 

Analytical perturbation theories led to a host of important, nontrivial predictions, which were subsequently probed by and confirmed in numerical simulations. The elegant theory devised by Lawrence Pratt and David Chandler [15] to explain the hydrophobic effect constitutes a noteworthy example of such predictions. 

Pratt, L. R. and Chandler, D., Theory of the hydrophobic effect. J. Chem. Phys. 67,... 

Chandler and Pratt have developed a theory for describing... 

There is, however, no strong inducement for a small number of small hydrophobic groups to associate in water. It is more likely that water can separate such species rather than drive them together. Small-length-scale hydrophobic interaction can be understood in terms of Stillinger s scaled particle theory and the integral equation theory of Pratt and Chandler. Of course, association/coagulation of non-polar solutes occurs when concentration of the solute is increased beyond a critical concentration. The critical micellar concentration is an example of such an association. 

As can be seen from Fig. 4.44, there are considerable discrepancies between results obtained by different simulations and by theoretical calculations. At present, it is difficult to claim that one simulated result is better than another. This is also true for any theoretical calculations based on a specific pair potential for water. It is a fortiori true if the theory uses as an input the orientational averaged pair correlation function of water, as was done by Pratt and Chandler (1977). In my opinion, using such an input into the theory will inevitably fail to reproduce any property of water and aqueous solutions that is sensitive to the angular dependence of the pair potential — or, equivalently, that depends on the principle. For further details, see Ben-Naim (1989), Guarino and Madden (1982), and Tani (1984). 

Chandler and Pratt developed a similar approach based on graph theory to study systems undergoing chemical reaction. The formal theory is quite complex, but the application to a simple bimolecular reaction, e.g. the chemical equilibrium between nitrogen dioxide and di-nitrogen tetroxide (N204 2N02), illustrates the results obtained. For this reaction. Chandler and Pratt illustrated their results by calculating the solvent effect on the chemical equilibrium constant. 

Their results show a qualitative similarity to ours, but they do not give a quantitative result for the potential of mean force. Our work supports the theory of Pratt and Chandler (2) on the hydrophobic effect. Previous Monte Carlo work (3) along similar lines displayed no oscillation in , although in that study the authors explored values of r smaller than T.Oa. 

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