A general expression for the correlation of the simple shear （tanφ） to the molecular parameters and the shear rate （·↑γ） was deduced. It shows that the simple shear （tanφ） may be resolved into free recoil （recoverable strain） and viscous heating （unrecoverable strain）. The magnitudes of the simple shears for recoil （tanφE） and （tanφv） for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable （1--↑W·↑γ） and unrecoverable （-↑W·↑γ） conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears （tanφE） for recoil and （tanφv） for viscous heating are, respectively, expressed as the partition function to the （1--↑W·↑γ）th power and the partition function to the （-↑W·↑γ）th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [n′, α, η0, GN^0 and （1--↑W·↑γ）] and the operational variables （·↑γ, （L/D） and tr） were deduced respectively, which show that at very different shear rates （0≤·↑γ≤∞） the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=（L/D）], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [n′, α, η0, GN^0 and （1--↑W·↑γ）] and the operational variables （·↑γ, （L/D） and tr） were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene （HDPE） which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.
The structural model of the multiple-transient networks and the mechanism of the multiple-reptation entangled chains due to the dynamic reorganization in the entangled sites were extensively applied on the die swell of polymeric liquids in the steady simple shear flow. The total （recoverable and unrecoverable） viscoelastic free energy of deformation and flow, the constitutive equation and the expression of the simple shear （tanψ） were deduced from the conformational probability distribution function of the entangled polymer chains. It found that： （1） the magnitudes of simple shear （tanψ） depended not only on the free recoil （or recoverable strain） but also on the viscous heating （or unrecoverable strain）; （2） the total recoil may be resolved into the instantaneous and delayed recoil. Based on these facts, the functions of the partition and two experiential fractions of the recoverable （1-Wγ） and the unrecoverable （Wγ） conformations for the recoil and viscous heating of polymeric liquids were defined correspondingly. Then the correlation of the instantaneously and ultimately （or total） recoverable strains to the （N1/T12）w and the fraction of trans-form conformation was obtained. After introducing the condition of uniform two-dimensional extension （αx=αy=α, αz=α^-2） and the swell ratio （B=α）, two sets of equations on the instantaneous and ultimate swelling ratios （BE, BEVT） were obtained, and a method to determine the fraction of the recoverable transform conformation were proposed, The equations of BE and BE5 were verified by the experimental data of HDPE （high denisity polyethylene） at two different high temperatures. It shows that the molecular theory of die swell can be used to predict the correlation of the swelling to the （NI/TI2）w and the fraction of trans-form conformation.
Mingshi SONG Guixian HU Zhihong YANG Qiang xu Sizhu WU
