Abstract
Methods are presented by which the limiting viscosity number [η]Θ and the limiting sedimentation coefficient s0 of a monodisperse linear polymer in its theta solvent as functions of the molecular weight M may be deduced from data taken with a series of polydisperse samples of the polymer. The necessary data are the limiting viscosity numbers and the distribution functions of s0 of the chosen samples in the theta solvent, plus their number-average molecular weights. The methods are applied to unfractionated and fractionated samples of a styrene-butadiene co-polymer rubber (SBR) having 24 weight per cent bound styrene in a theta solvent, 2-pentanone, at 21.0° C. The following relations are deduced for monodisperse unbranched SBR in this theta solvent: [η]Θ=1.73×10−3M21 and s0=0.83×10−15M21, where [η]Θ is expressed in deciliters/gram and s0 in seconds. Besides these, the viscosity—molecular weight relations for this cold rubber in toluene and in cyclohexane, both at 30° C, are established. The new relation for the toluene system does not accord with the French-Ewart relation for “hot” rubber in the same solvent. The integral distribution of molecular weight in an unfractionated SBR is calculated from its distribution function of s0 in 2-pentanone at 21.0° C by using the derived s0 versus M relationship, and is found to coincide well with the mass distribution obtained from fractionation data if the new viscosity—molecular weight relation is used for the molecular weight of each fraction.