在許多化學工程領域的應用上，純物質與其混合物的蒸氣壓數據往往在程序的設計以及優化是非常重要的。近年來，Peng-Robinson + COSMOSAC狀態方程式的模型已開發並可提供具有可信度的物質熱力學性質相關的預測以及相平衡的預測，例如純物質的臨界性質、蒸氣壓與混合物的氣-液相平衡與液-液相平衡。此熱力學模型是以溶劑化理論與COSMO-SAC模型為基礎，利用量子力學以及COSMO溶劑化的計算結果來求得Peng-Robinson 狀態方程式的能量參數a與體積參數b。因此，此方法在理論上即可預測所有有機化合物的熱力學性質且不會有缺少參數的問題。
本研究中，我們針對 Peng-Robinson + COSMOSAC狀態方程式的帶電溶合自由能中的分散項做了溫度函數的修正來提高模型在預測純物質蒸氣壓的精確度。在無增加任何參數量的情況下，修正後的方法顯示出更好的蒸氣壓預測結果。此方法共使用1125個有機化合物來結果分析，在修正後的方法顯示其完整的壓力取對數的誤差(ALD-P)為0.210，相較於原方法Peng-Robinson+COSMOSAC(2010)之誤差為0.234，從整體結果來看在蒸氣壓預測的精準度得到改善，尤其是對純物質低溫區的預測。特別是當沒有蒸氣壓實驗值的時候，此模型提供一套有效的方法來預測純物質的蒸氣壓。

The information of vapor pressure of pure substances and their mixtures is crucial in the field of chemical engineering because these data are necessary for the design and optimization of chemical engineering processes. Recently, the Peng-Robinson + COSMOSAC equation of state has been developed to provide reliable estimation of thermophysical properties and fluid phase equilibria, such as critical properties and vapor pressures of pure fluids and vapor-liquid and liquid-liquid equilibria of mixtures. This model, based on solvation theory and the COSMO-SAC model, utilizes results from quantum mechanical and COSMO solvation calculations to determine energy parameter and volume parameter in the Peng-Robinson equation of state. Thus, it theoretically can be used to estimate thermodynamic properties for all organic substances without issues of missing parameters.
In this study, the Peng-Robinson + COSMOSAC equation of state is modified to improve its accuracy in predicting the vapor pressure of pure substances. The temperature dependence of the dispersion contribution is revised to provide better vapor pressure prediction without introducing new adjustable parameters, especially at lower temperature region (temperature between the triple point temperature and normal boiling point of a substances). A total of 1125 organic substances are considered in this work. The overall average logarithmic deviation for pressure (ALD-P) is 0.210 from the modified version, which is greatly improved while comparing to that from the original version (ALD-P = 0.234). This model is particularly useful when no experimental data is available in literature.

中文摘要 v
英文摘要 vi
誌謝 vii
目錄 viii
表目錄 x
圖目錄 xi
符號說明 xii
第一章 緒論 1
1-1蒸氣壓的重要性 1
1-2獲得蒸氣壓的方法與文獻回顧 1
1-3研究背景及動機 4
1-3研究架構 5
第二章 理論 6
2-1 Peng-Robinson + COSMOSAC狀態方程式 6
2-2 修正Peng-Robinson + COSMOSAC狀態方程式 13
2-3 蒸氣壓計算 15
2-4 臨界性質計算 15
第三章 計算細節與參數優化 16
3-1 計算細節 17
3-2 參數優化 17
3-2-1考慮原子種類參數 19
3-3-2考慮原子鍵結參數 22
第四章 結果與討論 25
4-1 蒸氣壓的預測 25
4-2 臨界性質的預測 29
第五章 結論 40
參考文獻 41
附錄(一) 優化原子種類參數之化合物 45
附錄(二) 優化原子鍵結參數之化合物 47

[1] S.S.T. Ting., D.L. Tomasko., N.R. Foster., S.J. Macnaughton., Solubility of naproxen in
supercritical carbon dioxide with and without cosolvents. Industrial & Engineering Chemistry
Research. 32 (1993) 1471-1481.
[2] J.-F. Wang., C.-X. Li., Z.H. Wang., Z.J.Li.,Y.B. Jiang., Vapor pressure measurement for
water, methanol, ethanol, and their binary mixtures in the presence of an ionic liquid
1-ethyl-3-methylimidazolium dimethylphosphate. Fluid Phase Equilibria. 255(2007) 186-192.
[3] C.M. Hsieh., S.T. Lin., Prediction of liquid–liquid equilibrium from the Peng–
Robinson+COSMOSAC equation of state. Chemical Engineering Science. 65(2010)
1955-1963.
[4] C.M. Hsieh., S.T. Lin., Determination of cubic equation of state parameters for pure
fluids from first principle solvation calculations. aiche journal. 54(2008) 2174-2181.
[5] D. Ambrose., The correlation and estimation of vapour pressures, IV. Observations on
Wagner’s method of fitting equations to vapour pressures. The Journal of Chemical
Thermodynamics. 18(1986) 45-51.
[6] L.A. Forero.G., A.V.J. Jorge., Wagner liquid-vapour pressure equation constants from a
simple methodology. The Journal of Chemical Thermodynamics. 43(2011) 1235-1251.
[7] R. Mashallah., M. Azam., S. Saeed., Group contribution method based on UNIFAC
groups for the estimation of vapor pressures of pure hydrocarbon compounds. The Journal of Chemical Thermodynamics. 36(2013) 483-491.
[8] J.G. Emilio., B.B. Susana., A.M. Eugenia., Application of a group contribution
equation of state to model the phase behavior of mixtures containing alkanes and ionic
liquids. Fluid Phase Equilibria. 387(2015) 32-37.
[9] T.Y. Wang., X.Z. Meng., M. Jia., X.C. Song., Predicting the vapor pressure of fatty acid
esters in biodiesel by group contribution method. Fuel Processing Technology 131(2015) 223-
229.
[10] Y. Nannoolal., J. Rarey., D. Ramjugernath., Estimation of pure component properties:
Part 3. Estimation of the vapor pressure of non-electrolyte organic compounds via group
contributions and group interactions. Fluid Phase Equilibrium. 269(2008) 117-133.
[11] B. Moller., J. Rarey., D. Ramjugernath., Estimation of the vapor pressure of non-
electrolyte organic compounds via group contributions and group interactions. Journal of
Molecular Liquids. 143(2008) 52-63.
[12] A. Klamt., V. Jonas., T. Burger., J.C.W. Lohrenz., Refinement and parametrization of COSMO-RS. The Journal of Physical Chemistry. A,102(1998) 5074-5085.
[13] F. Eckert., A. Klamt., Fast solvent screening via quantum chemistry COSMO-RS approach. aiche journal. 48(2002) No. 2.
[14] A. Klamt., V. Jonas., T. Burger., J.C.W. Lohrenz., Refinement and parametrization of COSMO-RS. The Journal of Physical Chemistry. A,102(1998) 5074-5085.
[15] S. Wang and S. I. Sandler., C. C. Chen., Refinement of COSMO-SAC and the
Applications. Industrial & Engineering Chemistry Research. Res. 46(2007) 7275-7288.
[16] L. H. Wang., C.M. Hsieh., S. T. Lin., Improved prediction of vapor pressure for
pure liquids and solids from the PR+COSMOSAC equation of state. Industrial
&Engineering Chemistry Research. 54(2015), 10115−10125.
[17] S.T. Lin., S.I. Sandler., A priori phase equilibrium prediction from a segment contribution solvation model. Industrial & Engineering Chemistry Research. 41(2002) 899-913.
[18] S.T. Lin., C.M. Hsieh., M.T. Lee., Solvation and chemical engineering thermodynamics,
Journal of the Chinese Institute of Chemical Engineers. 38 (2007) 467-476.
[19] C.M. Hsieh., and S.T. Lin., First principle predictions of vapor-liquid equilibria for pure
and mixture fluids from the combined use of cubic equations of state and solvation calculations. Industrial & Engineering Chemistry Research 48(2009a) 3197-3205.
[20] C.M. Hsieh., S.T.Lin., Prediction of 1-octanol-water partition coefficient and infinite dilution activity coefficient in water from the PR+COSMOSAC model. Fluid Phase Equilibria. 285(2009b) 8-14.
[21] G.C. Pimentel., A.L. McClellan., The hydrogen bond. W.H. Freeman and Company, New York, 1960.
[22] E. Mullins., Y.A. Liu., A. Ghaderi., S.D. Fast., Sigma profile database for predicting solid solubility in pure and mixed solvent mixtures for organic pharmacological compounds with COSMO-based thermodynamic methods. Industrial & Engineering Chemistry Research. 47(2008) 1707−1725.
[23] E. Mullins, R. Oldland., Y.A. Liu., S. Wang., S. I. Sandler., C.C. Chen., M. Zwolak, K.C. Seavey., Sigma-profile database for using COSMO-based thermodynamic methods. Industrial & Engineering Chemistry Research. 45(2006) 4389−4415.
[24] Cerius2, Dmol3, Accelrys Inc., San Diego, 2003.
[25] DIPPR, DIPPR801 Thermodynamic properties database. Brigham Young
University, Provo. 2008.