SPACE FILLING AND FLOW BEHAVIOR

The following extension of the Batschinski equation (yielding the original relation as the first member of a series expansion) is proposed: In [(η/ηs) + 1] = DvB*/(v - vB*); η is the viscosity of the fluid, ηs the unit of η, and v the specific volume; vB*, a hard-core specific volume, and D are system-specific constants. In contrast to the original Batschinski equation this relation can describe the behavior of associating liquids and liquid polymers with the same accuracy as the Doolittle equation, but it needs only two parameters, instead of three. In an earlier paper it was demonstrated that the experimental data for polymers can be better reproduced if the fraction of the free volume in the Doolittle equation is replaced by the fraction of the free interparticle distance. Such a replacement also improves the quality of the extended Batschinski equation. The comparison of the Theological hard-core volumes vB*, with the corresponding thermodynamic hard-core volumes v* (calculated from pvT data according to the reduced equation of state of Flory, Orwoll, and Vrij) demonstrates that vB* is typically some 10-15% larger than v*. This result means that the liquid has to expand its volume with respect to the densest possible packing by the above percentage in order to flow. Within a family of substances vB*/v* normally increases with molecular weight, but the contrary is also observed. The reasons for this behavior are discussed. © 1990 American Chemical Society.