(88c) Sanchez-Lacombe Parameters for Silicone Alkoxides

Physico-chemical properties such as density, kinematic viscosity, and gas-liquid equilibrium are indispensable information for the chemical process design. Measurements on the pure and mixed hydrocarbons were intensely conducted in the field of petroleum engineering. However, as the measurements need specialized equipment and a long measurement period, the experimental data are always insufficient. To solve the problem, the equation of state (EoS) is a powerful tool for the estimation and/or correlation of the physico-chemical properties. Unfortunately, data of the pure substances are necessary for the calculation of the mixtures with using the EoS. Recent advances in the development of new materials made the situation more complex because such materials need new substances whose physico-chemical properties are not reported.

In this study, silicon alkoxides, which are expected as raw materials of a new polymer/silane composite insulation materials, were chosen as the target material because there are a few reports on thermodynamic properties of these materials. At the same time, among many EoS, Sanchez-Lacombe Equation of State¹⁾ (SL EoS) based on lattice fluid theory was selected as the EoS due to its applicability to systems including polymers. In SL EoS, the parameters representing the characteristics of a compounds are called as characteristic parameters and can be determined from the PVT relationship of the materials. Further, these parameters could be estimated from the molecular structure of the component by means of so called the group contribution (GC) method. However, as the base data is not sufficient, the accuracy of GC parameters for silicon-containing components is not guaranteed.

In this work, the characteristic parameters for the silicon alkoxides were determined by two methods, fitting the measured PVT data (Parameter I) and GC method (Parameter II). In addition, with using the experimental phase equilibrium data and the density data of CO₂ / silicon alkoxide binary systems, effectiveness of the newly determined characteristic parameters as well as the GC method were examined.

Experimental

In this study, the PVT relationship was measured by the experimental apparatus based on a general variable method. First, liquid sample of known weight was introduced into a variable volume piston type high pressure cell (ca. 7 cm³). Temperature was stabilized to a predetermined temperature, and the position of the piston at the time of pressurization was measured. Then, PVT relationship was obtained by calculating density from the volume change of the sample. Experiments were performed at temperatures from 303 to 363 K and pressures up to 160 MPa. Measurements were repeated at least three times. The silicon alkoxides used were methyltrimethoxysilane (MTMS, CH₃(CH₃O)₃Si) and tetramethoxysilane (TMOS, (CH₃O)₄Si). Obtained data were correlated by the SL EoS to determine the characteristic parameters (characteristic temperature, characteristic pressure, characteristic density).

Results and discussion

According to the Guide to the Expression of Uncertainty in Measurement (GUM), the uncertainty of PVT measurement was calculated to be 0.1% to 0.7% for all measurements.

The measured PVT relationship of MTMS and TMOS was correlated with the SL EoS. In the course of the correlation, it became clear that the SL EoS could not correlate the high pressure range PVT accurately. Thus, new characteristic parameters, Parameter I, were determined with using the PVT data from 10 to 80 MPa. The average absolute relation deviations (AARDs) between the experimental and correlated value were 0.13 % for MTMS and 0.069 % for TMOS, respectively. The fact that the experimental results in the high pressure region could not be correlated by the SL EoS seems to represents the limit of the model.

The characteristic parameters of MTMS and TMOS were estimated using the group contribution method reported by Nannoolal^{2, 3)} (Parameter II). With Parameter II, the PVT relationship was calculated by the SL EoS, and the AARD were 5.1 % and 6.4 % for MTMS and TMOS, respectively. There is no wonder that the Parameter I gave the good results than Parameter II.

Furthermore, to confirm the necessity of the more precise parameters, phase behavior, or the vapor liquid equilibrium, of the CO₂ / silicon alkoxide binary system were correlated with the Parameter I and II. Surprisingly, there observed no difference between the correlations with these parameter sets. It is presumably due to the fact that to calculate the mixed system, interaction parameters must be introduced to correct the differences of the components. Error of the pure components must be incorporated in the interaction parameters.

The density of homogeneous CO₂ / silicon alkoxide binary mixtures was also estimated by the SL EoS. Differ from the phase behavior, the estimation accuracy is strongly affected by the values of the pure component characteristic parameters. The estimated error was 2.5 % with parameter I, while 6.4% with parameter II in the CO₂ / MTMS binary system. It was found that the error of the pure component cannot be completely compensated by the interaction parameters.

Considering the fact that the PVT relationship is the basis for the calculation of various thermodynamic properties, the errors by GC approach could not be described as “small”. The cause of the errors was found to be derived from the characteristic density.

Therefore, to improve the accuracy of estimation with as few information as possible, a new attempt was made to improve the estimation accuracy: characteristic temperature and characteristic pressure were determined from the GC approach, and the characteristic density was determined from the standard density which is easy to measure (Parameter III). With the Parameter III, the PVT of the silicon alkoxides was estimated. The AARD was 1.8 % and 1.5 % for MTMS and TMOS, respectively, which is the quite improvement of the accuracy compared with the GC method by Nannoolal. It was confirmed that along with the improvement of the accuracies for the pure components, that of the estimation of the density CO₂ / MTMS binary system were improved (AARD of 6.4 % to 3.4 %).

Conclusion

The PVT relationship of the MTMS and TMOS were measured, and the characteristic parameters for the SL EoS were determined (Parameter I). The average absolute relative deviations (AARDs) between the experimental and correlated value were 0.13 % and 0.069 % for MTMS and TMOS, respectively. Characteristic parameters of SL EoS of MTMS and TMOS were determined using Nannoolal group contribution method separately (Parameter II). The PVT relationship was calculated by the SL EoS, and the AARD were 5.1 % and 6.4 % for MTMS and TMOS, respectively. Differ from the pure component PVT data, there were no difference between the correlation of the CO₂ / silicone alkoxide systems with these two parameters. This is presumable due to the introduction of interaction parameters which taken in the difference of the parameters. On the other hand, also differ from the phase equilibrium data, difference between to parameters strongly affects the correlation of the density of the mixture.

To improve the GC approach, new method which determines the characteristic temperature and characteristic pressure from the GC approach and the characteristic density from the standard density was proposed. With using the new method, the estimation accuracy of the PVT relationship could be improved. As the number of the GC parameters are still limited, accumulation of experimental data should be continued.

Reference

1) Isaac C. Sanchez et al., J. Phys. Chem., 80 (1976) 2352-2362

2) Y. Nannoolal, J. Rarey, D. Ramjugernath, W. Cordes, Fluid Phase Equilib, 226 (2004) 45-63

3) Y. Nannoolal, J. Rarey, D. Ramjugernath, Fluid Phase Equilib, 252 (2007) 1-27