Analysis of equations of state for polymers
Padilha Júnior, Erlí José; Soares, Rafael de Pelegrini; Cardozo, Nilo Sérgio Medeiros
http://dx.doi.org/10.1590/0104-1428.1621
Polímeros: Ciência e Tecnologia, vol.25, n3, p.277-288, 2015
Abstract
In the literature there are several studies comparing the accuracy of various models in describing the PvT behavior of polymers. However, most of these studies do not provide information about the quality of the estimated parameters or the sensitivity of the prediction of thermodynamic properties to the parameters of the equations. Furthermore, there are few studies exploring the prediction of thermal expansion and compression coefficients. Based on these observations, the objective of this study is to deepen the analysis of Tait, HH (Hartmann-Haque), MCM (modified cell model) and SHT (simplified hole theory) equations of state in predicting the PvT behavior of polymers, for both molten and solid states. The results showed that all equations of state provide an adequate description of the PvT behavior in the molten state, with low standard deviations in the estimation of parameters, adequate sensitivity of their parameters and plausible prediction of specific volume, thermal expansion and isothermal compression coefficients. In the solid state the Tait equation exhibited similar performance to the molten state, while HH showed satisfactory results for amorphous polymers and difficulty in adjusting the PvT curve for semicrystalline polymers.
Keywords
equation of state, PvT behavior, polymer.
References
1. Zoller, P. (1989). PVT relationships and equations of state of polymers. In J. Brandrup & E. H. Immergut (Eds.), Polymer handbook (pp. 475-483). New York: John Wiley & Sons.
2. Dee, G. T., & Walsh, D. J. (1988). A modified cell model equation of state for polymer liquids. Macromolecules, 21(3), 815-817. http://dx.doi.org/10.1021/ma00181a044.
3. Rodgers, P. A. (1993). Pressure–volume–temperature relationships for polymeric liquids: A review of equations of state and their characteristic parameters for 56 polymers. Journal of Applied Polymer Science, 48(6), 1061-1080. http://dx.doi.org/10.1002/app.1993.070480613.
4. Sy-Siong-Kiao, R. (1995). Models for the prediction of the pressure-volume-temperature relationship and the diffusion coefficient in polymer melts (Doctoral thesis). Purdue University, West Lafayette.
5. Wang, W., Liu, X., Zhong, C., Twu, C. H., & Coon, J. E. (1997). Simplified hole theory equation of state for liquid polymers and solvents and their solutions. Industrial & Engineering Chemistry Research, 36(6), 2390-2398. http://dx.doi.org/10.1021/ie9604132.
6. Chiew, Y. C., Ting, S. K. H., & Leong, K. K. (2000). A perturbed Lennard–Jones chain equation of state for polymer liquids. Fluid Phase Equilibria, 168(1), 19-29. http://dx.doi.org/10.1016/S0378-3812(99)00329-5.
7. Sato, Y., Hashiguchi, H., Inohara, K., Takishima, S., & Masuoka, H. (2007). PVT properties of polyethylene copolymer melts. Fluid Phase Equilibria, 257(2), 124-130. http://dx.doi.org/10.1016/j.fluid.2007.01.013.
8. Sanchez, I. C., & Lacombe, R. H. (1976). An elementary molecular theory of classical fluids. Pure fluids. Journal of Physical Chemistry, 80(21), 2352-2362. http://dx.doi.org/10.1021/j100562a008.
9. Sanchez, I. C., & Lacombe, R. H. (1978). Statistical thermodynamics of polymer solutions. Macromolecules, 11(6), 1145-1156. http://dx.doi.org/10.1021/ma60066a017.
10. Hartmann, B., & Haque, M. A. (1985). Equation of state for polymer solids. Journal of Applied Physics, 58(8), 2831-2836. http://dx.doi.org/10.1063/1.335881.
11. Ougizawa, T., Dee, G. T., & Walsh, D. J. (1989). PVT properties and equations of state of polystyrene: molecular weight dependence of the characteristic parameters in equation-of-state theories. Polymer, 30(9), 1675-1679. http://dx.doi.org/10.1016/0032-3861(89)90329-7.
12. Huang, S. H., & Radosz, M. (1990). Equation of state for small, large, polydisperse, and associating molecules. Industrial & Engineering Chemistry Research, 29(11), 2284-2294. http://dx.doi.org/10.1021/ie00107a014.
13. Ougizawa, T., Dee, G. T., & Walsh, D. J. (1991). Pressure-volume-temperature properties and equations of state in polymer blends: characteristic parameters in polystyrene/poly(vinyl methyl ether) mixtures. Macromolecules, 24(13), 3834-3837. http://dx.doi.org/10.1021/ma00013a015.
14. Song, Y., Lambert, S. M., & Prausnitz, J. M. (1994). A perturbed hard-sphere-chain equation of state for normal fluids and polymers. Industrial & Engineering Chemistry Research, 33(4), 1047-1057. http://dx.doi.org/10.1021/ie00028a037.
15. Sanchez, I. C., & Cho, J. (1995). A universal equation of state for polymer liquids. Polymer, 36(15), 2929-2939. http://dx.doi.org/10.1016/0032-3861(95)94342-Q.
16. Jeon, K. S., Char, K., Walsh, D. J., & Kim, E. (2000). Thermodynamics of mixing estimated by equation-of-state parameters in miscible blends of polystyrene and tetramethylbisphenol-A polycarbonate. Polymer, 41(8), 2839-2845. http://dx.doi.org/10.1016/S0032-3861(99)00350-X.
17. Gross, J., & Sadowski, G. (2001). Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules. Industrial & Engineering Chemistry Research, 40(4), 1244-1260. http://dx.doi.org/10.1021/ie0003887.
18. Broza, G., Castaño, V. M., Martinez-Barrera, G., Menard, K. P., & Simões, K. P. (2005). P–V–T properties of a polymer liquid crystal subjected to pre-drawing at several temperatures. Physica B: Condensed Matter, 357(3–4), 500-506. http://dx.doi.org/10.1016/j.physb.2004.12.018.
19. Wang, M., Takishima, S., Sato, Y., & Masuoka, H. (2006). Modification of Simha–Somcynsky equation of state for small and large molecules. Fluid Phase Equilibria, 242(1), 10-18. http://dx.doi.org/10.1016/j.fluid.2006.01.003.
20. Simha, R., & Utracki, L. A. (2010). PVT properties of linear and dendritic polymers. Journal of Polymer Science: Part B, Polymer Physics, 48(3), 322-332. http://dx.doi.org/10.1002/polb.21893.
21. Winterbone, D. E. (1997). Advanced thermodynamics for engineers. London: Arnold.
22. Utracki, L. A. (2009). Compressibility and thermal expansion coefficients of nanocomposites with amorphous and crystalline polymer matrix. European Polymer Journal, 45(7), 1891-1903. http://dx.doi.org/10.1016/j.eurpolymj.2009.04.009.
23. Utracki, L. A. (2010). PVT of amorphous and crystalline polymers and their nanocomposites. Polymer Degradation & Stability, 95(3), 411-421. http://dx.doi.org/10.1016/j.polymdegradstab.2009.07.020.
24. Chang, R. Y., Chen, C. H., & Su, K. S. (1996). Modifying the tait equation with cooling-rate effects to predict the pressure–volume–temperature behaviors of amorphous polymers: modeling and experiments. Polymer Engineering and Science, 36(13), 1789-1795. http://dx.doi.org/10.1002/pen.10574.
25. Prigogine, I., Trappeniers, N., & Mathot, V. (1953). Statistical thermodynamics of r-MERS and r-MER solutions. Discussions of the Faraday Society, 15, 93-107. http://dx.doi.org/10.1039/df9531500093.
26. Simha, R., & Somcynsky, T. (1969). On the statistical thermodynamics of spherical and chain molecule fluids. Macromolecules, 2(4), 342-350. http://dx.doi.org/10.1021/ma60010a005.
27. Zhong, C., Wang, W., & Lu, H. (1993). Simplified hole theory equation of state for polymer liquids. Fluid Phase Equilibria, 86(1), 137-146. http://dx.doi.org/10.1016/0378-3812(93)87172-W.
28. Utracki, L. A. (2007). Pressure–volume–temperature of molten and glassy polymers. Journal of Polymer Science: Part B, Polymer Physics, 45(3), 270-285. http://dx.doi.org/10.1002/polb.21031.
29. Sato, Y., Yoshiteru, Y., Takishima, S., & Masuoka, H. (1997). Precise measurement of the PVT of polypropylene and polycarbonate up to 330°C and 200 MPa. Journal of Applied Polymer Science, 66(1), 141-150. http://dx.doi.org/10.1002/(SICI)1097-4628(19971003)66:1<141::AID-APP17>3.0.CO;2-4.
30. Olabisi, O., & Simha, R. (1975). Pressure-volume-temperature studies of amorphous and crystallizable polymers. I. Experimental. Macromolecules, 8(2), 206-210. http://dx.doi.org/10.1021/ma60044a022.
31. Quach, A., & Simha, R. (1971). Pressure‐volume‐temperature properties and transitions of amorphous polymers; polystyrene and poly (orthomethylstyrene). Journal of Applied Physics, 42(12), 4592-4606. http://dx.doi.org/10.1063/1.1659828.
32. Sato, Y., Inohara, K., Takishima, S., Masuoka, H., Imaizumi, M., Yamamoto, H., & Takasugi, M. (2000). Pressure-volume-temperature behavior of polylactide, poly(butylene succinate), and poly(butylene succinate-co-adipate). Polymer Engineering and Science, 40(12), 2602-2609. http://dx.doi.org/10.1002/pen.11390.
33. Wang, J., Xie, P., Yang, W., & Ding, Y. (2010). Online pressure–volume–temperature measurements of polypropylene using a testing mold to simulate the injection-molding process. Journal of Applied Polymer Science, 118(1), 200-208. http://dx.doi.org/10.1002/app.32070.
34. Himmelblau, D. M. (1970). Process analysis by statistical. New York: John Wiley & Sons.
35. van Krevelen, D. W., & te Nijenhuis, K. (2009). Properties of polymers. Amsterdam: Elsevier Science.
36. van der Vegt, A. K. (2002). From polymers to plastics. Delft: DUP Blue Print.
2. Dee, G. T., & Walsh, D. J. (1988). A modified cell model equation of state for polymer liquids. Macromolecules, 21(3), 815-817. http://dx.doi.org/10.1021/ma00181a044.
3. Rodgers, P. A. (1993). Pressure–volume–temperature relationships for polymeric liquids: A review of equations of state and their characteristic parameters for 56 polymers. Journal of Applied Polymer Science, 48(6), 1061-1080. http://dx.doi.org/10.1002/app.1993.070480613.
4. Sy-Siong-Kiao, R. (1995). Models for the prediction of the pressure-volume-temperature relationship and the diffusion coefficient in polymer melts (Doctoral thesis). Purdue University, West Lafayette.
5. Wang, W., Liu, X., Zhong, C., Twu, C. H., & Coon, J. E. (1997). Simplified hole theory equation of state for liquid polymers and solvents and their solutions. Industrial & Engineering Chemistry Research, 36(6), 2390-2398. http://dx.doi.org/10.1021/ie9604132.
6. Chiew, Y. C., Ting, S. K. H., & Leong, K. K. (2000). A perturbed Lennard–Jones chain equation of state for polymer liquids. Fluid Phase Equilibria, 168(1), 19-29. http://dx.doi.org/10.1016/S0378-3812(99)00329-5.
7. Sato, Y., Hashiguchi, H., Inohara, K., Takishima, S., & Masuoka, H. (2007). PVT properties of polyethylene copolymer melts. Fluid Phase Equilibria, 257(2), 124-130. http://dx.doi.org/10.1016/j.fluid.2007.01.013.
8. Sanchez, I. C., & Lacombe, R. H. (1976). An elementary molecular theory of classical fluids. Pure fluids. Journal of Physical Chemistry, 80(21), 2352-2362. http://dx.doi.org/10.1021/j100562a008.
9. Sanchez, I. C., & Lacombe, R. H. (1978). Statistical thermodynamics of polymer solutions. Macromolecules, 11(6), 1145-1156. http://dx.doi.org/10.1021/ma60066a017.
10. Hartmann, B., & Haque, M. A. (1985). Equation of state for polymer solids. Journal of Applied Physics, 58(8), 2831-2836. http://dx.doi.org/10.1063/1.335881.
11. Ougizawa, T., Dee, G. T., & Walsh, D. J. (1989). PVT properties and equations of state of polystyrene: molecular weight dependence of the characteristic parameters in equation-of-state theories. Polymer, 30(9), 1675-1679. http://dx.doi.org/10.1016/0032-3861(89)90329-7.
12. Huang, S. H., & Radosz, M. (1990). Equation of state for small, large, polydisperse, and associating molecules. Industrial & Engineering Chemistry Research, 29(11), 2284-2294. http://dx.doi.org/10.1021/ie00107a014.
13. Ougizawa, T., Dee, G. T., & Walsh, D. J. (1991). Pressure-volume-temperature properties and equations of state in polymer blends: characteristic parameters in polystyrene/poly(vinyl methyl ether) mixtures. Macromolecules, 24(13), 3834-3837. http://dx.doi.org/10.1021/ma00013a015.
14. Song, Y., Lambert, S. M., & Prausnitz, J. M. (1994). A perturbed hard-sphere-chain equation of state for normal fluids and polymers. Industrial & Engineering Chemistry Research, 33(4), 1047-1057. http://dx.doi.org/10.1021/ie00028a037.
15. Sanchez, I. C., & Cho, J. (1995). A universal equation of state for polymer liquids. Polymer, 36(15), 2929-2939. http://dx.doi.org/10.1016/0032-3861(95)94342-Q.
16. Jeon, K. S., Char, K., Walsh, D. J., & Kim, E. (2000). Thermodynamics of mixing estimated by equation-of-state parameters in miscible blends of polystyrene and tetramethylbisphenol-A polycarbonate. Polymer, 41(8), 2839-2845. http://dx.doi.org/10.1016/S0032-3861(99)00350-X.
17. Gross, J., & Sadowski, G. (2001). Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules. Industrial & Engineering Chemistry Research, 40(4), 1244-1260. http://dx.doi.org/10.1021/ie0003887.
18. Broza, G., Castaño, V. M., Martinez-Barrera, G., Menard, K. P., & Simões, K. P. (2005). P–V–T properties of a polymer liquid crystal subjected to pre-drawing at several temperatures. Physica B: Condensed Matter, 357(3–4), 500-506. http://dx.doi.org/10.1016/j.physb.2004.12.018.
19. Wang, M., Takishima, S., Sato, Y., & Masuoka, H. (2006). Modification of Simha–Somcynsky equation of state for small and large molecules. Fluid Phase Equilibria, 242(1), 10-18. http://dx.doi.org/10.1016/j.fluid.2006.01.003.
20. Simha, R., & Utracki, L. A. (2010). PVT properties of linear and dendritic polymers. Journal of Polymer Science: Part B, Polymer Physics, 48(3), 322-332. http://dx.doi.org/10.1002/polb.21893.
21. Winterbone, D. E. (1997). Advanced thermodynamics for engineers. London: Arnold.
22. Utracki, L. A. (2009). Compressibility and thermal expansion coefficients of nanocomposites with amorphous and crystalline polymer matrix. European Polymer Journal, 45(7), 1891-1903. http://dx.doi.org/10.1016/j.eurpolymj.2009.04.009.
23. Utracki, L. A. (2010). PVT of amorphous and crystalline polymers and their nanocomposites. Polymer Degradation & Stability, 95(3), 411-421. http://dx.doi.org/10.1016/j.polymdegradstab.2009.07.020.
24. Chang, R. Y., Chen, C. H., & Su, K. S. (1996). Modifying the tait equation with cooling-rate effects to predict the pressure–volume–temperature behaviors of amorphous polymers: modeling and experiments. Polymer Engineering and Science, 36(13), 1789-1795. http://dx.doi.org/10.1002/pen.10574.
25. Prigogine, I., Trappeniers, N., & Mathot, V. (1953). Statistical thermodynamics of r-MERS and r-MER solutions. Discussions of the Faraday Society, 15, 93-107. http://dx.doi.org/10.1039/df9531500093.
26. Simha, R., & Somcynsky, T. (1969). On the statistical thermodynamics of spherical and chain molecule fluids. Macromolecules, 2(4), 342-350. http://dx.doi.org/10.1021/ma60010a005.
27. Zhong, C., Wang, W., & Lu, H. (1993). Simplified hole theory equation of state for polymer liquids. Fluid Phase Equilibria, 86(1), 137-146. http://dx.doi.org/10.1016/0378-3812(93)87172-W.
28. Utracki, L. A. (2007). Pressure–volume–temperature of molten and glassy polymers. Journal of Polymer Science: Part B, Polymer Physics, 45(3), 270-285. http://dx.doi.org/10.1002/polb.21031.
29. Sato, Y., Yoshiteru, Y., Takishima, S., & Masuoka, H. (1997). Precise measurement of the PVT of polypropylene and polycarbonate up to 330°C and 200 MPa. Journal of Applied Polymer Science, 66(1), 141-150. http://dx.doi.org/10.1002/(SICI)1097-4628(19971003)66:1<141::AID-APP17>3.0.CO;2-4.
30. Olabisi, O., & Simha, R. (1975). Pressure-volume-temperature studies of amorphous and crystallizable polymers. I. Experimental. Macromolecules, 8(2), 206-210. http://dx.doi.org/10.1021/ma60044a022.
31. Quach, A., & Simha, R. (1971). Pressure‐volume‐temperature properties and transitions of amorphous polymers; polystyrene and poly (orthomethylstyrene). Journal of Applied Physics, 42(12), 4592-4606. http://dx.doi.org/10.1063/1.1659828.
32. Sato, Y., Inohara, K., Takishima, S., Masuoka, H., Imaizumi, M., Yamamoto, H., & Takasugi, M. (2000). Pressure-volume-temperature behavior of polylactide, poly(butylene succinate), and poly(butylene succinate-co-adipate). Polymer Engineering and Science, 40(12), 2602-2609. http://dx.doi.org/10.1002/pen.11390.
33. Wang, J., Xie, P., Yang, W., & Ding, Y. (2010). Online pressure–volume–temperature measurements of polypropylene using a testing mold to simulate the injection-molding process. Journal of Applied Polymer Science, 118(1), 200-208. http://dx.doi.org/10.1002/app.32070.
34. Himmelblau, D. M. (1970). Process analysis by statistical. New York: John Wiley & Sons.
35. van Krevelen, D. W., & te Nijenhuis, K. (2009). Properties of polymers. Amsterdam: Elsevier Science.
36. van der Vegt, A. K. (2002). From polymers to plastics. Delft: DUP Blue Print.
Facebook
Google+
Twitter
LinkedIn
Mendeley
StumbleUpon
CiteULike
Reddit
Email