PVT scaling parameters for polymer melts. II. Error in all variables



An algorithm is discussed for determining best-fit scaling parameters in the PVT equation of state of polymer melts from experimental data. The underlying theoretical expressions are those employed in our preceding work. There it was assumed that values of pressure and temperature are known exactly and experimental uncertainty was admitted in the volume solely. This condition is now relaxed to allow for errors in P and T also. The methodology developed involves multiple small nonlinear fitting problems for two or three unknowns at a time. We employ it on the experimental data base in the earlier work, which consists of 11 polymer melts. To these is added ethylene monomer, analyzed earlier by Nies et al. by different methods. The numerical values of the scaling parameters differ by at most a fraction of a percent from those in the earlier computations and enhance the accuracy of fit but slightly. The significant improvement over the consecutive procedure (analysis of atmospheric pressure isobar, followed by isotherms at elevated pressures), seen earlier, continues therefore. The scaling parameters so obtained should represent the ultimate in computational accuracy consistent with a specified experimental accuracy. This may have a bearing ultimately on the issue of modeling molecular characteristics, expressed through the scaling parameters, versus macroscopic properties. Using the parameters determined here, it is shown that the entropy is correlated with the scaling temperature and that the flexibility parameter is related to polymer complexity.