Study of entanglement of polymers in solution by viscosity measurements

A study has been made of the flow behavior of solutions of a single sample of polystyrene in five different solvents in both the Newtonian and non-Newtonian regions. The concentration range covered was approximately 0-20% by weight, and the temperatures were 20, 30, 40, and 50°C. By application of the Ree-Eyring theory it was found possible to represent the observed data in terms of two flow units, and to obtain from the parameters of the Ree-Eyring equation the effective hydrodynamic volume occupied by the polymer in solution, ev, where v is the volume fraction of polymer and e an effective volume factor. For any given solvent e varies from [η]/2 at v = 0 to e = ca. 4 at v∞, the volume fraction at which ev = 1 and the viscosity becomes infinite; and, except in very dilute solutions, e is essentially independent of the temperature. Again, for any given value of v, e is a function of the nature of the solvent only between v = 0 and v = 0.04. Above the latter concentration e is completely independent of the solvent in which the polystyrene is dissolved, and becomes merely a function of the solution concentration. These results indicate that chain entanglement in solution, if it does occur, can take place only below a concentration of v = 0.04. Above v = 0.04 no entanglement can be present, and the configuration of the polymer chain, as reflected in the effective volume they occupy, is governed only by the nonspecific factor of the space available for occupancy by each molecule. As this space decreases with increase in concentration, the polymer molecule is forced to reduce its effective volume by coiling into a tighter mass. This process continues until ev becomes equal to unity, at which point the state of tightest coiling is reached without change in the nature of the flow. In the latter state the polymer molecule is shown to occupy a volume 2 to 3 times, and to have a cross section 1.26 to 1.44 times, that of the polymer in bulk.