A new molecular weight distribution technique for polystyrene. I. Theory

Abstract

AbstractThis paper is concerned with the description of a simple technique for determining the molecular weight distribution curve of polystyrene (and presumably any other soluble polymer consisting of a polymer‐homologous series). The general theory of the method as well as preliminary experimental results will be covered. The method is characterized by: (1) simple technique and equipment; (2) no need to isolate and measure fractions; and (3) a general basis in thermodynamic theory of polymer solutions, although a double calibration is needed to determine numerical parameters. The method consists in adding increasing quantities of nonsolvent to a dilute solution of polystyrene in a good solvent and observing the cumulative volume of precipitate as a function of nonsolvent content. The settled gel must re‐equilibrate (hence deswell) with the new solvent after each alcohol addition. The swelling ratio, S (cc. of swollen gel per gram of dry polymer), of the swollen precipitate is approximately independent of the molecular weight and depends mainly on the volume percent of nonsolvent, γ according to where α, σ, and s are constants. Likewise, the molecular weight, M, of the species precipitated at any nonsolvent content is given by the Schulz precipitability equation: where α, β, and m are constants. For the system polystyrene–benzene–methanol, we find s = 4/3 while Schulz had already noted that m = 2/3. Elimination of γ and α leads to the prediction of a linear relation between M and S2. A two‐fold calibration to obtain the constants in equations (1) and (2) is necessary to convert the observed data to an absolute cumulative weight versus molecular weight curve. However, even the simple plot of cc. of precipitate versus percent nonsolvent is informative. The relationship of these results to the thermodynamic theories of polymer solutions of Flory, Huggins, Gee, and Scott is outlined. The plot of cumulative volume of precipitate against percent nonsolvent has two characteristic features: an inflection point and a maximum. If the original polymer has a weight distribution function of the Schulz type, i.e., MkM × (1 − k)2, where k is related to the number‐average molecular weight, M̄n, through M̄n = M0(1 − k)−1, then it can be shown that the maximum occurs at M̄n while the inflection point occurs at 2.15 M̄n.