Sedimentation-Diffusion Equilibrium of Monomer-Dimer Mixtures, Studied in the Analytical Ultracentrifuge

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 M_w,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 (BM_mc - c₀]) = exp (σ_m/2] r² - r₀²]); σ_m = M_m(1 - ρV)ω²/RT (M_m = 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 M_m 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.