The Solute Molecules

In a weak electrolyte (e.g. an aqueous solution of acetic acid) the solute molecules AB are incompletely dissociated into ions and according to the familiar chemical equation... 

McMillan-Mayer theory of solutions [1,2], which essentially seeks to partition the interaction potential into tln-ee parts that due to the interaction between the solvent molecules themselves, that due to die interaction between the solvent and the solute and that due to the interaction between the solute molecules dispersed within the solvent. The main difference from the dilute fluid results presented above is that the potential energy u(r.p is replaced by the potential of mean force W(rp for two particles and, for particles of solute in the solvent, by the expression... 

By applying a pulling force at a portion of the solute molecule in a specific direction (see chapters of Eichinger et al. and Schulten in this volume), conformational transitions can be induced in specific directions. In order to reconstruct information about the underlying potential function governing protein motion, the irreversible work performed on the system by these forces must be discounted ([Balsera et al. 1997]). 

From the standpoint of thermodynamics, the dissolving process is the estabHsh-ment of an equilibrium between the phase of the solute and its saturated aqueous solution. Aqueous solubility is almost exclusively dependent on the intermolecular forces that exist between the solute molecules and the water molecules. The solute-solute, solute-water, and water-water adhesive interactions determine the amount of compound dissolving in water. Additional solute-solute interactions are associated with the lattice energy in the crystalline state. 

The angles ot, p, and x relate to the orientation of the dipole nionient vectors. The geonieti y of interaction between two bonds is given in Fig. 4-16, where r is the distance between the centers of the bonds. It is noteworthy that only the bond moments need be read in for the calculation because all geometr ic features (angles, etc.) can be calculated from the atomic coordinates. A default value of 1.0 for dielectric constant of the medium would normally be expected for calculating str uctures of isolated molecules in a vacuum, but the actual default value has been increased 1.5 to account for some intramolecular dipole moment interaction. A dielectric constant other than the default value can be entered for calculations in which the presence of solvent molecules is assumed, but it is not a simple matter to know what the effective dipole moment of the solvent molecules actually is in the immediate vicinity of the solute molecule. It is probably wrong to assume that the effective dipole moment is the same as it is in the bulk pure solvent. The molecular dipole moment (File 4-3) is the vector sum of the individual dipole moments within the molecule. 

It is reasonable to expect that the effect of a solvent on the solute molecule is, at least in part, dependent on the properties of the solute molecule, such as its size. 

The solvent accessible surface area (SASA) method is built around the assumption that the greatest amount of interaction with the solvent is in the area very close to the solute molecule. This is accounted for by determining a surface area for each atom or group of atoms that is in contact with the solvent. The free energy of solvation AG° is then computed by... 

Caution For ionic reactions in solution, solvent effects can play a significant role. These, of course, are neglected in calculations on a single molecule. You can obtain an indication of solvent effects from semi-empirical calculations by carefully adding water molecules to the solute molecule. 

With this terminology in mind, we can restate the objective of this section as the interpretation of the intrinsic viscosities of solutions of rigid molecules. If the solute molecules are known to be spherical, comparison of Eqs. (9.10) and (9.14) shows that the intrinsic viscosity for such systems is given by... 

If the solute molecule is solvated, then any bound (subscript b) solvent (subscript 1) must be added to the volume of the unsolvated solute (subscript 2) that is. 

This simple model illustrates how the fraction K and, through it, Vj are influenced by the dimensions of both the solute molecules and the pores. For solute particles of other shapes in pores of different geometry, theoretical expressions for K are quantitatively different, but typically involve the ratio of solute to pore dimensions. 

In finite boundary conditions the solute molecule is surrounded by a finite layer of explicit solvent. The missing bulk solvent is modeled by some form of boundary potential at the vacuum/solvent interface. A host of such potentials have been proposed, from the simple spherical half-harmonic potential, which models a hydrophobic container [22], to stochastic boundary conditions [23], which surround the finite system with shells of particles obeying simplified dynamics, and finally to the Beglov and Roux spherical solvent boundary potential [24], which approximates the exact potential of mean force due to the bulk solvent by a superposition of physically motivated tenns. 

If classical Coulombic interactions are assumed among point charges for electrostatic interactions between solute and solvent, and the term for the Cl coefficients (C) is omitted, the solvated Eock operator is reduced to Eq. (6). The significance of this definition of the Eock operator from a variational principle is that it enables us to express the analytical first derivative of the free energy with respect to the nuclear coordinate of the solute molecule R ,... 

In the first example of applications of the theory in this chapter, we made a point with respect to the polarizability of molecules and showed how the problem could have been handled by the RISM-SCF/MCSCF theory. However, the current level of our method has a serious limitation in this respect. The method can handle the polarizability of molecules in neat liquids or that of a single molecule in solution in a reasonable manner. But in order to be able to treat the polarizability of both solute and solvent molecules in solution, considerable generalization of the RISM side of the theory is required. When solvent molecules are situated within the influence of solute molecules, the solvent molecules are polarized differently depending on the distance from the solute molecules, and the solvent can no longer be neat. Therefore, the polarizable model developed for neat liquids is not valid. In such a case, solvent-solvent PCF should be treated under the solute... 

Energy of Interaction of the Solute Molecule with the Stationary Phase... 

Consider a distribution system that consists of a gaseous mobile phase and a liquid stationary phase. As the temperature is raised the energy distribution curve in the gas moves to embrace a higher range of energies. Thus, if the column temperature is increased, an increasing number of the solute molecules in the stationary phase will randomly acquire sufficient energy (Ea) to leave the stationary phase and enter the... 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

The standard free energy can be divided up in two ways to explain the mechanism of retention. First, the portions of free energy can be allotted to specific types of molecular interaction that can occur between the solute molecules and the two phases. This approach will be considered later after the subject of molecular interactions has been discussed. The second requires that the molecule is divided into different parts and each part allotted a portion of the standard free energy. With this approach, the contributions made by different parts of the solvent molecule to retention can often be explained. This concept was suggested by Martin [4] many years ago, and can be used to relate molecular structure to solute retention. Initially, it is necessary to choose a molecular group that would be fairly ubiquitous and that could be used as the first building block to develop the correlation. The methylene group (CH2) is the... 

In contrast to apportioning the standard free energy between different groups in the solute molecule, the standard free energy can also be dispensed between the different types of forces involved in the solute/phase-phase distribution. This approach has been elegantly developed by Martire et al. [13]. In a simplified form, the standard free energy can be divided into portions that result from the different types of interaction, e.g.,... 

There are two ways a solute can interact with a stationary phase surface. The solute molecule can interact with the adsorbed solvent layer and rest on the top of it. This is called sorption interaction and occurs when the molecular forces between the solute and the stationary phase are relatively weak compared with the forces between the solvent molecules and the stationary phase. The second type is where the solute molecules displace the solvent molecules from the surface and interact directly with the stationary phase itself. This is called displacement interaction and occurs when the interactive forces between the solute molecules and the stationary phase surface are much stronger than those between the solvent molecules and the stationary phase surface. An example of sorption interaction is shown in Figure 9. 

It diagramatically represents a silica surface in contact with a low concentration of chloroform in n-heptane where the surface is partly covered with chloroform, the remainder covered with n-heptane. The solute molecules can either rest on the surface of the chloroform layer or on the surface of the layer of adsorbed n-heptane. 

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