On Search for a Generalized Constant of Polymer Melts

A linear multivariable power function P = f (M, MWD, LCB), representing the dependence of a polymer property P on the polymer molecular characteristics, where M is the molecular weight, MWD - the molecular weight distribution, and LCB - the long chain branching, has recently been applied for investigation of polymer melts, cf. Dobkowski (1982, 1988, 1994, 1998). If the polymer fluidity difference between the Newtonian and non-Newtonian conditions is taken as the polymer property, then the master line can be obtained for polymer melts in reduced log-log coordinates. Thus, the multivariable power function (MVP) for the dependence of η₀ and Δϕ on M, MWD and LCB can be written as log where η₀ is the zero shear rate melt viscosity, ω is the frequency, Δϕ is the fluidity difference between the Newtonian and non-Newtonian conditions where, in turn, ϕ = 1/η is the fluidity and Δϕ = 1/η - 1/η₀ . It should be noted that the frequency can be replaced by the shear rate according to the Cox-Merz rule, cf. Cox and Merz (1958), Dobkowski (1998). The exponents b₁, b₂ and b₃ can be found from respective regression equations using the experimental data from rheological measurements. In particular, the exponent b₁ of the MVP function enables distinguishing linear and branched polymer structures, cf Dobkowski (1982).