Cd. Han et al., PLASTICATING SINGLE-SCREW EXTRUSION OF AMORPHOUS POLYMERS - DEVELOPMENT OF A MATHEMATICAL-MODEL AND COMPARISON WITH EXPERIMENT, Polymer engineering and science, 36(10), 1996, pp. 1360-1376
A mathematical model was developed for plasticating single-screw extru
sion of amorphous polymers. We considered a standard metering screw de
sign. By introducing a 'critical flow temperature' (T-cf), below which
an amorphous polymer may be regarded as a 'rubber-like' solid, we mod
ified the Lee-Han melting model, which had been developed earlier for
the extrusion of crystalline polymers, to model the flow of an amorpho
us polymer in the screw channel. T-cf is de facto a temperature equiva
lent to the melting point of a crystalline polymer. The introduction o
f T-cf was necessary for defining the interface between the solid bed
and the melt pool, and between the solid bed and thin melt films surro
unding the solid bed. We found from numerical simulations that (1) whe
n the T-cf was assumed to be close to its glass transition temperature
(T-g), the viscosity of the polymer became so high that no numerical
solutions of the system of equations could be obtained, and (2) when t
he value of T-cf was assumed to be much higher than T-g, the extrusion
pressure did not develop inside the screw channel, Thus, an optimum m
odeling value of T-cf appears to exist, enabling us to predict pressur
e profiles along the extruder axis. We found that for both polystyrene
and polycarbonate, T-cf lies about 55 degrees C above their respectiv
e T(g)s. In carrying out the numerical simulation we employed (1) the
WLF equation to describe the temperature dependence of the shear modul
us of the bulk solid bed at temperatures between T-g and T-cf, (2) the
WLF equation to describe the temperature dependence of the viscosity
of molten polymer at temperatures between T-cf and T-g + 100 degrees C
, (3) the Arrhenius relationship to describe tile temperature dependen
ce of the viscosity of molten polymer at temperatures above T-g 100 de
grees C, and (4) the truncated power-law model to describe the shear-r
ate dependence of the viscosity of molten polymer. We have shown that
the T-g of an amorphous polymer cannot be regarded as being equal to t
he T-m of a crystalline polymer, because the viscosities of an amorpho
us polymer at or near its T-g are too large to flow like a crystalline
polymer above its T-m. Also conducted was an experimental study for p
olystyrene and polycarbonate, using both a standard metering screw and
a barrier screw design having a length-to-diameter ratio of 24. For t
he study, nine pressure transducers were mounted on the barrel along t
he 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 th
e barrier screw design gives rise to much more stable pressure signals
, thus minimizing surging, than the metering screw design. The experim
entally measured axial pressure profiles were compared with prediction
.