Converting Magazine

Eldridge M. Mount

Extrapolation, Comparison and Use of Polymer Melt Viscosity Data using curve fit data
May 7, 2008

The use of polymer processing simulation packages for complex die and extrusion flow problems as well as the calculation of melt pipe pressure drops requires the use of accurate, corrected viscosity data to insure the best results. However, the viscosity data is often times the weakest link in the simulation because the effective use of polymer melt viscosity data is a much more difficult procedure than would be expected. First it is difficult to obtain high quality melt viscosity data covering a desired melt temperature and shear rate range in a timely fashion. Then you may only receive a graph with no tabulated data or easy way to represent the data in the manner which the simulation package requires. In other cases you may want to substitute one resin for another in an existing manufacturing process and it becomes necessary to compare two sets of viscosity date. If the data only exists as graphs this can be very frustrating because oftentimes the data will be on two graphs with different scales requiring the use of a window in a sunny location and some judgment as to how well the two resins match, hopefully your office has a window. 

In order to avoid these difficulties it is necessary to convert all graphical data into numeric values and have them in a file where they can be readily compared as needed such as with an excel graph. While this is time consuming it pays real dividends in the future. If you have the case where you have to compare two materials at a temperature at which no data was obtained then you have to get a new set of data or if the temperature needed is between two temperatures which you already have data for then you can extrapolate, again this can be a tedious procedure. For use in a simulation package the data will have to be entered as a table or as a curve fit relationship which the simulation package uses.

In general the best way to maintain your viscosity data is in the form of a table of coefficients obtained by curve fitting your experimental data. Here again there are many ways to proceed to accurately represent the data. One of the most successful curve fitting equations for normal melt viscosity data is the six constant equation shown in equation 1.

ln(visc)=B1+B2*T+b3*T^2+B4*T*ln(SR)+B5*ln(SR)+B6*ln(SR)^2                     Eqn 1

Equation 1 is parabolic in temperature and ln (shear rate) with a cross term (B4) for temperature and ln (shear rate) and in general it describes the observed melt viscosity data very well (Figure 1) and is easy to accurately curve fit as opposed to other models such as the power law. 




Figure 1.  comparison of data and curve fit to equation 1

The coefficients of equation 1 allows for the compact storage of the data used to generate the coefficients and permits the rapid recall and display of the data or interpolation to other temperatures using a program such as Excel. If multiple sets of coefficients are at hand for a range of resins then the data can be extrapolated to any temperature and shear rate with in the ranges used in the curve fit and the various materials readily compared. Because of the good fit and ease of fitting equation 1 to polymer melt viscosity data, equation 1 has been used in many processing simulation programs with generally good success.  

 Figure 2 shows a comparison of several resins generated from the coefficients of equation 1 which are being used for trouble shooting a coextrusion problem. 


Figure 2:  Various resins plotted using equation 1 curve fit showing parabolic behavior of the function in the newtonian viscosity region

In figure 2 we see several curves which are clearly non-Newtonian over the range where the data was obtained as well as resins which show a well developed Newtonian range. The resins which show distinct Newtonian regions at relatively high shear rates (up to 10 or higher sec^-1) tend to be the newer metallocene polyethylenes and EVOH resins and have highlighted a problem with equation 1 which can appear due to its parabolic nature. 

Equation 1 represents the non Newtonian shear thinning regions very well as it resembles a portion of a parabola which is the mathematical form of the equation. However, for the Newtonian region equation 1 will estimate a maximum (Newtonian) viscosity well but then as the shear rate is decreased the viscosity calculated by equation 1 will begin to decrease rather than remain constant at the lower shear rates.  This is seen in Figure 2 for shear rates below 1 to 2 sec^-1 for the LLDPE and EVOH resins. It is not possible to prevent this due to the functionality of equation 1. This can cause real problems if equation 1 is used in simulations where calculations requiring the viscosity at the shear rates within the Newtonian range of the data are estimated using equation 1 and will lead to the generation of incorrect results for these polymers. 

In conclusion the six constant equation used for curve fitting polymer melt viscosity data is a convenient way to keep and use melt viscosity data. However, with the emergence of new resins some care must be exercised to insure that the curve fitting equation which you use, especially in simulations, gives a true representation of the viscosity data over the entire shear rate range of interest.

Posted by Eldridge M. Mount on May 7, 2008 | Comments (0)