Plasticating single‐screw extrusion of amorphous polymers: Development of a mathematical model and comparison with experiment

Abstract

AbstractA mathematical model was developed for plasticating single‐screw extrusion of amorphous polymers. We considered a standard metering screw design. By introducing a ‘critical flow temperature’ (Tcf), below which an amorphous polymer may be regarded as a ‘rubber‐like’ solid, we modified the Lee‐Han melting model, which had been developed earlier for the extrusion of crystalline polymers, to model the flow of an amorphous polymer in the screw channel. Tcf is de facto a temperature equivalent to the melting point of a crystalline polymer. The introduction of Tcf was necessary for defining the interface between the solid bed and the melt pool, and between the solid bed and thin melt films surrounding the solid bed. We found from numerical simulations that (1) when the Tcf was assumed to be close to its glass transition temperature (Tg), the viscosity of the polymer became so high that no numerical solutions of the system of equations could be obtained, and (2) when the value of Tcf was assumed to be much higher than Tg, the extrusion pressure did not develop inside the screw channel. Thus, an optimum modeling value of Tcf appears to exist, enabling us to predict pressure profiles along the extruder axis. We found that for both polystyrene and polycarbonate, Tcf lies about 55°C above their respective Tgs. In carrying out the numerical simulation we employed (1) the WLF equation to describe the temperature dependence of the shear modulus of the bulk solid bed at temperatures between Tg and Tcf, (2) the WLF equation to describe the temperature dependence of the viscosity of molten polymer at temperatures between Tcf and Tg + 100°C, (3) the Arrhenius relationship to describe the temperature dependence of the viscosity of molten polymer at temperatures above Tg + 100°C, and (4) the truncated power‐law model to describe the shear‐rate dependence of the viscosity of molten polymer. We have shown that the Tg of an amorphous polymer cannot be regarded as being equal to the Tm of a crystalline polymer, because the viscosities of an amorphous polymer at or near its Tg are too large to flow like a crystalline polymer above its Tm. Also conducted was an experimental study for polystyrene and polycarbonate, using both a standard metering screw and a barrier screw design having a length‐to‐diameter ratio of 24. For the study, nine pressure transducers were mounted on the barrel along the extruder axis, and the pressure signal patterns and axial pressure profiles were measured at various screw speeds, throughputs, and head pressures. In addition to significantly higher rates, we found that the barrier screw design gives rise to much more stable pressure signals, thus minimizing surging, than the metering screw design. The experimentally measured axial pressure profiles were compared with prediction.