A comparison of equations for the effect of pressure on the viscosity of amorphous polymers

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Abstract
Several equations which are used to predict the pressure coefficient of viscosity for amorphous polymers have been examined on the basis of type of information required and equation reliability. These equations can be useful in accounting for pressure effects observed in tubular flow and in other shear geometries. The correlations of Penwell and Porter and of Miller are evaluated and in the perspective of expressions by Matheson and by Eyring. Data on linear amorphous polystyrene (PS), polyisobutylene, poly(vinyl acetate), poly(methyl methacrylate) (PMMA), natural rubber, and polycarbonate are examined and presented. Predictions from the Penwell‐Porter and Miller equations are compared with experimental coefficients at one atmosphere for all data available. For PS and PMMA, it was found that Miller's equation tends to predict values somewhat higher than experiments but is closer to the data on PS and on a high molecular weight PMMA. The Penwell‐Porter equation, on the other hand, tends to predict values somewhat lower than experiments and does a slightly better job for lower molecular weight PMMA. Both equations require WLF or Vogel coefficients and Tg‐pressure‐molecular weight data. Miller's equation also requires compressibilities at Tg and at the temperature of interest, although an alternate method can be used which only requires average “K” values without Tg‐pressure or compressibilities at Tg.