Ultracentrifuge study of critically branched polycondensates III. Sedimentation equilibrium

Abstract

Sedimentation-equilibrium experiments were performed on 2-butanone solutions of standard polystyrene (one sample) and polycondensates (five samples) obtained near the gel point of decamethylene glycol and benzene 1,3,5-triacetic acid stabilized afterwards by modification of the unreacted groups with diazomethane and ketene. The materials are known to deviate very little from the classical theory of polycondensation. The ordinary theory of plotting the reciprocal of apparent molecular mass M app against the average concentration c was successful for the standard polystyrene, because it had a narrow distribution with respect to molecular mass. For the polycondensates, however,the apparent molecular mass depends too strongly on rotor speed to extrapolate it reliably to infinite dilution. Two complementary ways for eliminating the dependence of ipp on rotor speed are proposed. Method (i): a plot of ( M app ) -1 against the generalized speed parameter A, and method (ii): M app p against Ac 2 /2(c 0 ) 2 , where A c is the difference in concentration between the ends of a solution column and c 0 stands for the initial concentration. Both are successful for the polycondensates, giving the same results within experimental error. Method (i) is based on the theory of the asymptotic case X M i > 1 (where M i is the molecular mass of component i) which is derived with adequate rigour for dilute solutions of critically branched poly condensates, and it may be applicable more widely.