Theory of Solution

Kirkwood J G and Buff F P 1951 Statistical mechanical theory of solutions I J. Chem. Phys. 19 774... 

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... 

Simkin B Ya and Sheikhet I I 1995 Quantum Ohemical and Statistical Theory of Solutions (London Ellis Horwood)... 

Kirkwood J G 1934. Theory of Solutions of Molecules Containing Widely Separated Charges witl Special Application to Zwitterions. Journal of Chemical Physics 2 351-361. 

The logic that leads us to this last result also limits the applicability of the ensuing derivation. Applying the fraction of total lattice sites vacant to the immediate vicinity of the first segment makes the model descriptive of a relatively concentrated solution. This is somewhat novel in itself, since theories of solutions more commonly assume dilute conditions. More to the point, the model is unrealistic for dilute solutions where the site occupancy within the domain of a dissolved polymer coil is greater than that for the solution as a whole. We shall return to a model more appropriate for dilute solutions below. For now we continue with the case of the more concentrated solution, realizing... 

When other elements dissolve in a metal to form a solid solution they make the metal harder. The solute atoms differ in size, stiffness and charge from the solvent atoms. Because of this the randomly distributed solute atoms interact with dislocations and make it harder for them to move. The theory of solution hardening is rather complicated, but it predicts the following result for the yield strength... 

I. Prigogine, The Molecular Theory of Solution, North-Holland Publishing Co., Amsterdam, p. 448 (1957). 

Prigogine, I., Bellemans, A., and Mathot, V., The Molecular Theory of Solutions, North Holland, Interscience, New York, 1957. 

We may therefore sum up the results in the statement that the laws of osmotic pressure of a dilute solution are formally identical with the laws of gas pressure of an ideal gas (van t Hoff s Gaseous Theory of Solution). 

Van t Hoff s boiling-point equation, 295 freezing-point equation, 299 theory of solution, 287 principle of mobile equilibrium, 304, 340... 

Still, the chemical establishment remained opposed to the notion of ions in solution. In an attempt to convince the wild army of lonians of how wrong their ideas were, the British Association scheduled a discussion titled Theories of Solution, and invited van t Hoff, Arrhenius, and Ostwald to present their views. The rest of the discussion was packed with conservative older chemists, the idea being that reason would prevail and the lonians would give up their views. Instead, most of the younger chemists sought out the lonians for spirited exchanges, while the old chemists delivered their lectures to nearly empty rooms. 

Hence the theoretical configurational entropy of mixing AaSm cannot be compared in an unambiguous manner with the experimentally accessible quantity ASm- It should be noted that the various difficulties encountered, aside from those precipitated by the character of dilute polymer solutions, are not peculiar to polymer solutions but are about equally significant in the theory of solutions of simple molecules as well. 

A. R. Miller, The Theory of Solutions of High Polymers (Clarendon Press, Oxford, 1948). 

Between 1865 and 1887, Dmitri 1. Mendeleev developed the chemical theory of solutions. According to this theory, the dissolution process is the chemical interaction between the solutes and the solvent. Upon dissolution of salts, dissolved hydrates are formed in the aqueous solution which are analogous to the solid crystal hydrates. In 1889, Mendeleev criticized Arrhenius s theory of electrolytic dissociation. Arrhenius, in turn, did not accept the idea that hydrates exist in solutions. 

A more general theory of solutions would require detailed notions of solution structure and of all types of interactions between the particles (ions and solvent molecules) in the solution. Numerous experimental and theoretical studies have been carried out, and some progress has been made, but a sufficiently universal theory that could describe all properties in not very dilute electrolyte solutions has not yet been developed. 

Kablukov, I. A., Contemporary Theories of Solutions [in Russian], M. Schepkin, Moscow, 1891. 

The development of the theory of solute diffusion in soils was largely due to the work of Nye and his coworkers in the late sixties and early seventies, culminating in their essential reference work (5). They adapted the Fickian diffusion equations to describe diffusion in a heterogeneous porous medium. Pick s law describes the relationship between the flux of a solute (mass per unit surface area per unit time, Ji) and the concentration gradient driving the flux. In vector terms. 

The first of them occurs in thermodynamic theory of solutions and blends of heteropolymers [3] whereas the second one is the gf of the weight SCD /w(l). it can readily be determined from the simple expression ... 

The first theory of solutions of weak electrolytes was formulated in 1887 by S. Arrhenius (see Section 1.1.4). If the molar conductivity is introduced into the equations following from Arrhenius concepts of weak electrolytes, Eq. (2.4.17) is obtained, known as the Ostwald dilution law this equation... 

Prigogine I (1957) The molecular theory of solution. North-Holland, Amsterdam... 

Our point of view is that the evaluation of the partition function (9.5) can be done by using any available tool, specifically including computer simulation. If that computer simulation evaluated the mechanical pressure, or if it simulated a system under conditions of specified pressure, then /C,x would have been determined at a known value of p. With temperature, composition, and volume also known, (9.2) and (9.1) permit the construction of the full thermodynamic potential. This establishes our first assertion that the potential distribution theorem provides a basis for the general theory of solutions. 

Kirkwood, J., Theory of solutions of molecules containing widely separated charges with special application to zwitterions, J. Chem. Phys. 1934, 2, 351-361... 

Hildebrand, J., and Scott, R. (1962). Regular Solutions. Prentice Hall, Englewood Cliffs, NT. One of the standard reference texts on theory of solutions. 

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