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 - rhoV]omega(2)) (d lnc/dr(2)); RT has the usual meaning; rho 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 + 4Kc(0)](1/2) - 1]) exp (BM(m)[c - c(0)]) = exp ([sigma(m)/2] [r(2) - r(0) (2)]); sigma(m) = M(m)(1 - rhoV)omega(2)/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.