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The other term in Eq. , the standard state chemical potential. Evidently in this case it is equal to μί at the particular concentration for which dj = 1 (since In 1 = 0, implying /Xj = μ°). , 1 g/ml or 1 M), μ,? is simply a reference state from which changes in μ{ due to, for instance, concentration changes can be predicted. Now, as is seen from its definition, Eq. (9), the chemical potential represents the small change in the free energy of mixing of a solution associated with slightly changing the amount of species i present.

The basic assumption behind this technique is that at the isoelectric point of a protein (or particle), the partition is not determined by any electrostatic effects such as the potential difference, ionic strength, or electrostatically induced conformation changes. Thus a plot of the partition coefficient as a function of the pH, or the net 2. Theoretical Aspects of Partitioning 37 charge, in two systems containing salts that give different potential differences should cross at the isoelectric point.

For instance, for a mixture of two polymers in a single solvent the free energy of mixing is given by: AGm = kT[na In φ1 + n2 In φ2 + n 3 In φ3 + (na + n2P2 + η3Ρ3)(Φιφ2χι2 + Φιφ3χι3 + Φ2Φ3Χ23)] f . where component 1 is the solvent and components 2 and 3 are the two polymer species characterized by molecular weight parameters (actually their relative molecular volumes) P2 and P 3 , respectively. The other parameters are defined by: , ψι = njPi ηα + n 2 P 2 + n 3 P 3 where n, is the number of molecules of component i on the lattice, i = 1, 2, or 3; χί;· = z Awj/kT, i = 1, 2, or 3; and AWJ,· = wi;· - i[wn + ιν;·,·), i, j = 1, 2, or 3.

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