Scaling relations for elongational flow of polystyrene melts and concentrated solutions of polystyrene in oligomeric styrene

A consistent model of the rheology of polymer melts and concentrated solutions is presented, based on the idea that the pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic (Doi and Edwards. The Theory of Polymer Dynamics, Oxford University Press, 1986). In a tube model with variable tube diameter, chain stretch and tube diameter reduction are related, and at deformation rates larger than the inverse Rouse time τ _R, the chain is stretched and its confining tube becomes increasingly anisotropic. Tube diameter reduction leads to an interchain pressure in the lateral direction of the tube (Marrucci and Ianniruberto. Macromolecules 37:3934-3942, 2004). Chain stretch is balanced by interchain tube pressure in the lateral direction, which is proportional to the third power of stretch, and by a spring force in the longitudinal direction of the tube, which is linear in stretch. Analyzing elongational viscosity data of Huang et al. (Macromolecules 46:5026-5035, 2013a; ACS Macro Letters 2:741-744, 2013b) shows that dilution of polystyrene by oligomeric styrene does not change the relative interchain tube pressure. Based on this extended interchain pressure concept, scaling relations for linear viscoelasticity and elongational viscosity of polystyrene melts and concentrated solutions of polystyrene in oligomeric styrene are presented based exclusively on the relaxation modulus of a reference polymer melt, the volume fraction of polymer in the solution, and the time-molar-mass shift as well as the time-temperature shift caused by the reduction of the glass transition temperature T _g of the polymer in a solution relative to T _g of the melt.