Abstract
By generalizing the fundamental differential equation valid for a single ideal solute, it is usual to define, for a monomer-dimer nonideal mixture, an apparent molecular weight Mw,app = (2RT/[1 - ρV]ω2) (d lnc/dr2); RT has the usual meaning; ρ is the density of the solvent; V is the partial specific volume of the solute, assumed to be the same for the monomer and the dimer; w is the angular velocity of the rotor; c is the solute concentration at the radial position r in the cell. It is shown here that the above equation can be integrated in the case of a monomer-dimer nonideal mixture and that, after integration, we obtain the following relation between c and r: ([1 + 4Kc]1/2 - 1)/([1 + 4Kc0]1/2 - 1]) exp (BMm[c - c0]) = exp ([σm/2] [r2 - r02]); σm = Mm(1 - ρV)ω2/RT (Mm = molecular weight of the monomer); K is the monomer-dimer equilibrium constant; B is the second virial coefficient, assumed to be the same for the monomer and the dimer. As soon as Mm is known, the above equation permits the calculation of K and B, from the experimental curve c(r). Moreover, the reversibility of the monomer-dimer equilibrium can be tested from this equation: it is necessary and sufficient that the values of K corresponding to different loading concentrations in the cell are identical.
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Selected References
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