Example - Measuring Alumina Concentration in Polystyrene

 Dielectric
   Analyzers

 Viscometers

 Rheometers

 Company
    Information
 

A system at NIST composed of a Proceptor® dielectric analyzer on a Haake twin screw extruder was operated at 180°C. Measurements of permittivity and conductivity were made in continuously repeating 2.5 minute sweeps including fifteen frequencies between 500 Hz and 100,000 Hz. There was little variation with frequency of the electrical properties during this experiment. The first graph shows permittivity at 30KHz versus time. Initially the sensor was empty and reported a permittivity of one, the correct reading for air. Polystyrene was added, extrusion was started and the reported permittivity increased to 2.5, in agreement with literature and calculated values. The readings remained steady as extrusion was continued. The system was emptied and the permittivity readings returned to near the air value of one. After a short delay, polystyrene containing 12 wt.% alumina, a mineral powder, was added and extrusion was resumed. The permittivity jumped to a steady value higher than that obtained with the pure polystyrene. The extruder was again emptied and filled with polystyrene containing 24 and then 36 wt.% alumina. The measured permittivities stabilized at progressively higher values as the alumina concentration increased.

To compare the experimental data with the mixing equation

e^1/3 = f_Ae_A^1/3 + f_Be_B^1/3

the second graph shows the cube roots of the measured permittivities plotted against volume fraction of additive. The line through the points represents the mixing equation with appropriate numerical values for the permittivities of polystyrene and alumina. Clearly the agreement is good and the mixing equation can be used to report concentrations of alumina in polystyrene. When this is done, the standard deviation of volume fraction determinations is 0.004, i.e. 0.4%.