It is generally recognized that an increase in the molecular weight of a polymer leads to better physical properties while the ease of fabrication decreases with increasing molecular weight. Work reported in the literature indicates interesting effects of molecular weight distribution on the physical property-fabrication relationship. Merz, Nielsen, and Buchdahl' have reported that most of the physical properties obtained on films of fractionated and unfractionated polystyrene follow the number-average molecular weight, an, according to the relationship developed by Flory :2where a and b are constants. On the other hand, the melt viscosity of polystyrene has been reported by Fox and Flory3 to vary with the weightaverage molecular weight, am, according to the relationship :Spencer and Dillon415 iound that the melt viscosity relates to the weightaverage molecular weight over a much wider molecular weight range by the equation:where q is between three and four. Since a narrowing of the molecular weight distribution causes the number-average molecular weight to approach the weight-average molecular weight, according to the work just quoted, this narrowing of the distribution should lead to higher physical properties in relation to the melt viscosity or ease of fabrication.More complete studies on the effect of molecular weight distribution upon the physical properties of polymers have been rather difficult to perform, since the fractionation processes required to obtain sufficient quantities of narrow distribution polymer are quite tremendous. Advent of the anionic polymerization process as elucidated by Szwarc, Levy, and Milkovichc has overcome this objectional feature of the study by making it possible to produce reasonably large quantities of a narrow distribution polymer by direct polymerizatjon. The present work reports the physical 87
The problem of how the distribution of molecular weight affects the properties of a polymer has led to the need for a rapid and accurate method for determining molecular weight distributions. Most of the commonly employed methods for determining how the mass is distributed over different molecular weights are either very time-consuming or give inferior results. Recent a d v a n c e~l -~ in the analysis of the progressive boundary spreading in sedimentation velocity experiments indicate that the velocity ultracentrifuge can be used to obtain such rapid and accurate determinations of molecular weight distribution. The present work will report on the use of such sedimentation velocity experiments to determine the molecular weight distribution of polystyrene.
EXPERIMENTAL
MaterialsPolystyrene samples of narrow molecular weight distribution were prepared by anionic polymerization of styrene as described by the method of S~w a r c .~ A styrene solution in tetrahydrofuran was added slowly to a sodium naphthalene complex in tetrahydrofuran under a nitrogen atmosphere at OOC. The molecular weight of the polymer was established by the ratio of monomer to complex. The polymer formed was precipitated from solution in methanol and dried in a vacuum oven.Polystyrene A having a broad distribution was commercial material produced by thermal polymerization over a varying temperature range. Polystyrene B having a somewhat narrower distribution was produced by thermal polymerization under isothermal conditions.
Methods
Sedimentation Velocity. A Spinco Model E ultracentrifuge with thePhilpot-Svensson optical system utilizing a phase plate was used for sedimentation velocity experiments. Runs were made a t 35OC. in a 0 solvent, cyclohexane, a t polymer concentrations between 0.1 and 0.75 g./100 ml. All runs were made a t a speed of 59,780 r.p.m. A cell having a double-341
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