Relationship of Fractional Free Volumes Derived from the Equations of State (EOS) and the Doolittle Equation

Abstract

This research investigates the relationships of the pressure–volume–temperature (PVT) and the zero-shear viscosity of polymer melts through their correlations with the fractional free volume. Polystyrene (PS) has been used as a case example in this study. First, the fractional free volume is determined from the Simha–Somcynsky (SS) equation of state (EOS) or the Sanchez–Lacombe (SL) EOS using the PVT data of a polymer melt. Then the fractional free volume is also determined from the Doolittle equation (with respect to the occupied volume) using the zero-shear viscosity and PVT data. These two fractional free volumes are compared to check if the EOS and the Doolittle equation consistently describe the PVT behaviors and the zero-shear viscosity through the fractional free volume. Before comparison, the fractional free volume based on the Doolittle equation is recalculated with respect to the total volume to be consistent with other fractional free volumes defined with respect to the total volume.

Keywords

free volume equation of state (EOS)Doolittle equation

Get full access to this article

View all access options for this article.

References

Zoller, P. and Walsh, D.J. (1995). Standard Pressure-Volume-Temperature for Polymers, Technomic Publishing Co., Lancaster, PA .

Sato, Y. , Yamasaki, Y. , Takishima, S. and Masuoka, H. (1997). Precise Measurement of the PVT of Polypropylene and Polycarbonate up to 330°C and 200 MPa , J. Appl. Polym. Sci., 66: 141-141 .

Rodgers, P.A. (1993). Pressure-volume-temperature Relationships for Polymeric Liquids: A Review of Equations of State and Their Characteristic Parameters for 56 Polymers , J. Appl. Polym. Sci., 48: 1061-1061 .

Park, J. and Kim, H. (1998). A New Equation of State Based on Hole Theory , Fluid Phase Equilibria, 144: 77-77 .

Doolittle, A.K. (1951). Studies in Newtonian Flow. II. The Dependence of the Viscosity of Liquids on Free-Space , J. Appl. Phys., 22(12): 929-929 .

Doolittle A.K. and Doolittle, D.B. (1957). Studies in Newtonian Flow. V. Further Verification of the Free-Space Viscosity Equation , J. Appl. Phys., 28(8): 901-901 .

Utracki, L.A. (1985). A Method of Computation of the Pressure Effect on Melt Viscosity , Polym. Eng. Sci., 25(11): 655-655 .

Lee, M. , Park, C.B. and Tzogonakis, C. (1999). Measurements and Modeling of PS/Supercritical CO2 Solution Viscosities , Polym. Eng. Sci., 39: 99-99 .

Lee, M. , Tzogonakis, C. and Park, C.B. (1998). Extrusion of PE/PS Blends with Supercritical Carbon Dioxide , Polym. Eng. Sci., 38: 1112-1112 .

10.

Simon, G.P. (1997). The Use of Positron Annihilation Lifetime Spectroscopy in Probing Free Volume of Multicomponent Polymeric Systems , Trip, 5(12): 394-394 .

11.

Simha, R. and Somcynsky, T. (1969). On the Statistical Thermodynamics of Spherical and Chain Molecule Fluids , Macromolecules, 2(4): 342-342 .

12.

Sanchez, I.C. and Lacombe, R.H. (1976). An Elementary Molecular Theory of Classical Fluids. Pure Fluids , J. Phys. Chem., 80: 2352-2352 .

13.

Utracki, L.A. and Simha, R. (2001). Free Volume and Viscosity of Polymer-compressed Gas Mixtures During Extrusion Foaming , J. Polym. Sci. B: Polym. Phys., 39: 342-342 .

14.

Sanchez, I.C. and Lacombe, R.H. (1978). Statistial Thermodynamics of Polymer Solutions , Macromolecules, 11: 1145-1145 .

15.

Guo, Q. (2002). Study of the Relationships between PVT and Viscosity of Polymers and Predicting Viscosity of Polymer/Gas Systems, Master Thesis, University of Toronto.

16.

Macosko, C.W. (1994). Rheology Principles, Measurements, and Applications, VCH, New York, NY .