Problem 13.2 The shear-rate dependent viscosity of an LDPE (Rexene 143) may be described by Eq. (6.10) with 0=1.06104Pas,1=0.62s, and n=0.224 at 160C. Note that the shear-rate dependent viscosity () of LDPE/(FC-114) mixtures at any temperature for a specified blowing agent (FC-114) concentration can be estimated once the viscosity () of Rexene 143 is known because plots of / given in Figure 13.11 are independent of shear rate and temperature. Calculate, with the aid of Eq. (13.6), the known because plots of / given in from 102 to 103s1 and prepare plots of ()/0 versus 1 for the mixture. (,T)=K(T)n1 where n1 represents the slope of the log versus log plot at >0, and K and n are empirical constants characteristic of a given polymer structure. Experimental studies suggest that K varies with temperature T, while n is virtually independent of temperature. Since the values of given in Figure 6.1 were calculated using the definition =/, from Eq. (6.1) we have (,T)=K(T)n Figure 13.11 Plots of aRF versus moles of FC blowing agent /kg of polymer in (O) Rexene 143/(FC-12) mixtures, (O) Rexene 143/(FC-114) mixtures, and () Styron 678/(FC12) mixtures. (Based on Han and Ma 1983a and 1983b.) What is common in Figures 13.513.8 is that the viscosity of a neat polymer, LDPE or PS, is decreased considerably by the solubilization of an FC blowing agent. It would be of practical interest to determine the extent of viscosity reduction of a molten polymer by a solubilized gaseous component. For this, let us define a viscosity reduction factor aRF by (Han and Ma 1983a, 1983b) aRF=(,T,c)/(,T)