Fully developed melt temperature

In this section we will describe a method to predict the fully developed melt temperature in screw extruders based on simple analytical expressions. The method is easy to use and leads to quantitative results with a minimum of time expenditure. 

The fully developed melt temperature is reached when the viscous heat generation is balanced by the heat flux away from the polymer melt. The viscous dissipation in the extruder will cause an increase in melt temperature resulting in reduced viscosity, which will result in a reduction in viscous dissipation. The melt temperature will reach a steady state value when the viscous dissipation has reduced to the point that it equals the heat flux from the polymer melt. 

The melt temperature will rise initially and then level off as the viscous dissipation reduces with increasing melt temperature. When a steady state is achieved, the melt temperature no longer changes along the length of the extruder. This is called the fully developed melt temperature or equilibrium melt temperature. This temperature Te can be determined from a simple energy balance equating the viscous dissipation to the conductive heat loss ... 

This equation leads to the following expression for the fully developed melt temperature ... 

This analysis provides a simple and fast method to estimate the fully developed melt temperature in screw extruders. The effect of material properties, processing conditions, and machine design parameters can be determined quantitatively. As a result, the analysis can be used to predict how melt temperature will change when another... 

It should be noted that there are several simplifying assumptions in the analysis. We have assumed that the melt temperatures are uniform across the depth of the channel. In reality this is not the case in fact, large melt temperature changes can occur across the depth of the channel. We can assume that the melt temperature calculated with this analysis corresponds to a bulk average melt temperature. We have also assumed that the fully developed melt temperature is reached before the end of the extruder. This is a reasonable assumption for small diameter extruders however, this may not be a good assumption for large diameter extruders as discussed in the previous section. 

C. Rauwendaal, Estimating Fully Developed Melt Temperature in Extrusion, Conference Proceedings, 581 SPE ANTEC, Orlando, FL, 307-311 (2000)... 

One of the major problem areas with PMR-15 polyimide is the high final cure temperature required (188-320 °C) to fully develop the high temperature properties of the resin. Serafini and coworkers (119) showed that the use of rw-aminostyrene as an endcapper instead of NE lowered the final cure temperature of the PMR polyimide from 320 to 260 °C. However, the (Tg) was lowered to 260 °C and thus limited the use temperature to 260 °C. The use of equimolar amounts of NE and p-aminostyrene in a PMR resin (120) helped to overcome this problem, however the flow properties suffered. The flow problem could again be overcome through the use of JV-phenylnadimide as a reactive diluent (121). The effect increased when the endo-isomer of the JV-phenylnadimide was used, because it melts at a lower temperature than the exo-isomer (122). 

The development of the -modification is controlled by the relative crystallization thermodynamics and kinetics of the stable a-modification and of the smectic phase towards the metastable / -phase. For PP homopolymers, it is generally accepted that under isothermal conditions, the a-phase grows more rapidly at temperatures below 105 and above 140 °C than its counterpart, which in turn is more prone to develop in between these two temperatures in the presence of selective -promoters [52,70,122]. An elegant way to get fully nucleated /3-PP specimens would consist of pressing /3-PP pellets above their melting temperature (ideally more than 250 °C to erase any a-nuclei in the system), cool the melt quickly up to a crystallization temperature in between 100 and 130 °C, let the sample crystallize, and then quench it to room temperature [70]. However, such a processing method is too time-consuming to be of industrial relevance. 

Numerous detailed studies have been devoted to the measurement of temperature profiles in polymer melts flowing through channels. One of the most comprehensive studies on the theoretical and experimental aspects of temperature measurement of polymer melts was carried out by van Leeuwen [15-18]. Other studies on melt temperature measurement are listed in the following references [19-23]. When a polymer melt flows through a channel, a certain temperature profile will establish itself in the polymer melt. The temperature profile in a steady-state process after some time will become constant with respect to time this is the so-called fully developed temperature profile. 

The temperature profile in the melt film is fully developed... 

We will now address the effect of temperature on melt conveying. Eirst, we will analyze fully developed temperature profiles. These conditions exist when the temperatures no longer change in the flow direction the region before is called the region of developing temperatures. We will address Newtonian fluids first and then analyze power law fluids. 

Equations for the fully developed temperature were developed by Rauwendaal [326]. However, Eq. 7.395 yields more accurate results because it takes into account the temperature dependence of the viscosity as well as the shear thinning behavior of the polymer melt. 

For the case shown in Fig. 7.95 the thermal development length becomes longer than the typical metering section of an extruder when the screw speed is greater than about 1 rev/sec (60 rpm). This means that at high screw speeds it cannot be expected that the melt temperatures become fully developed within the length of the extruder. 

The analytical predictions compare well to numerical predictions. This indicates that the analytical equations can be useful in the analysis of melt temperature development in single screw extruders. The results indicate that the melt temperatures can become fully developed if the heat flux through the barrel is substantial and if the screw speed is not too high. When the screw speed is high and the consistency index large it is not likely that the melt temperatures will be fully developed at the discharge end this is particularly true for large diameter extruders. 

We now have a quantitative, anaiyticai expression from which the fully developed temperature can be calculated. If we define the equilibrium melt temperature rise ATg as the difference between the reference temperature and the fully developed temperature, ATg = Tg-To, we can write ... 

An important point in all of the theories developed is that the equilibrium crystal thickness, obtainable by crystallizing the polymer at its equilibrium melting temperature, yields fully extended crystals, as described in Section... 

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