預測溶質於超臨界二氧化碳及有機高分子之溶解度

Prediction of Solubility in Supercritical Carbon Dioxide and Organic Polymeric Materials

王立行(Li-Hsin Wang)

指導教授 ： 林祥泰

國立臺灣大學/工學院/化學工程學研究所/博士(2017年)

https://doi.org/10.6342/NTU201703333

摘要

本研究致力開發針對溶解度性質具有預測性的熱力學模型。在理論模型方面，我們選擇改良COSMOSAC液相模型(liquid model)及PR+COSMOSAC狀態方程(equation of state)，因其參數皆可從量子計算所得到，即不需預先得知任何的實驗值。我們相信此研究所改良的純預測模型，對於實驗甚至工業應用上能夠提供有用的資訊，例如分析實驗操作的最佳溫壓條件、分析化合物的分離效率…等等。
在本研究的第一部分，我們利用PR+COSMOSAC 狀態方程式預測藥物於超臨界二氧化碳的溶解度。在計算上，針對藥物我們唯一需要的參數為藥物的融解溫度(melting temperature)及融解焓(melting enthalpy)。藉由修正針對環狀結構的分散力貢獻(ring dispersion contribution)，預測的精準度能得到大幅提升。另外，我們亦藉由藥物與二氧化碳的固液氣三相平衡的計算來討論模型中所得到之溶解度的合理性(stability)。在研究中我們發現藥物溶解度預測的精準度與分子的分散力描述息息相關，因此我們更進一步而修正了PR+COSMOSAC狀態方程式中分子間分散力(dispersion force)與溫度的關係。其改良過後的PR+COSMOSAC狀態方程式，除了能提供更精確的溶解度預測外，對於純物質的飽和蒸汽壓(saturated pressure)預測精準度更有大幅度的提升。
本研究的第二部分則利用PR+COMOSAC 狀態方程結合COSMO-SAC建立一個針對氣體在有機高分子的溶解度模型。針對此分子大小極端非對稱性的系統(asymmetric system)，我們採用SCMR (self-consistent mixing rule)取代一般常用的MHV1 (modified Huran-Vidal) 及WS (Wong-Sandler) 作為結合狀態方程式與液相模型的混和相律。由於高分子的結構過於龐大，無法在有限時間藉由量子計算得到其所需的模型參數，為了能實現高分子系統的預測，我們建立了一個計算策略。此策略藉由計算高分子單體(monomer)、二聚體(dimer)及三聚體(trimer)，來推估高分子的量子性質。針對氣體於有機高分子的溶解度，此研究所建立的模型，比目前文獻中亦具備純預測性的COSMO-RS能有更高的精準度，並且藉由狀態方程式的輔助，我們不須額外針對高溫氣體進行蒸氣壓外插(extrapolation)的假設。
最後，我們發現針對高度非對稱性的系統，相較於一般的混和律如MHV1，SCMR保留了純液相模型針對液體相行為預測的精準度，並且藉由PR+COSMOSAC狀態方程式的輔助及此研究所建立的方法，我們相信對於一般複雜的系統於極端溫壓條件下之相行為，皆能提供合理及有用的預測。

關鍵字

溶解度 ； 理論預測 ； 有機高分子 ； 超臨界二氧化碳 ； 飽和蒸氣壓 ； PR+COSMOSAC EOS狀態方程式 ； COSMOSAC液相模型

並列摘要

Developing predictive models to provide useful information for the phase behaviors, especially for the properties of solubility in complex systems, is the main goal of this research. The drug solubility in the supercritical carbon dioxide and the gas solubility in the organic polymer membrane are considered in this study since the application of these novel technologies reduces the energy use and the pollution generated. In the past, to our best knowledge, fewer studies focus on developing “predictive models” that require no experimental inputs for making the predictions. As a result, COSMO-based methods which only require the quantum properties of molecules are chosen, and modifications are introduced in order to provide better prediction accuracy.
In the first part of this research, the drug solubility in supercritical carbon dioxide is predicted from Peng-Robison plus COSMOSAC equation of state (PR+COSMOSAC EOS). The melting temperature, Tm and enthalpy of melting, Hm, of the solid drug and the critical properties (Tc,Pc) and acentric factor for fluid are the only properties required. The average logrithmetic deviations (ALD-x) in predicted solubility of 46 drugs in subcritical and supercritical carbon dioxide (T= 293.15 K~473K, P= 8.5MPa~50MPa, and 1150 solubility data ranging from 10-7~10-2) is found to be 1.14(8145.04%). The prediction inaccuracy can be significantly reduced to 0.81(3689.35%) when introducing an additional correction to the dispersion energy for aromatic and ring structures. Solid-vapor-liquid equilibrium for the drug-solvent pair is also determined in order to examine the stability of the predicted solubility.
From the first part of this research, we found the deficiency of the PR+COSMOSAC EOS for the prediction of saturated pressure at low temperatures. In order to improve the prediction quality systematically, we introduce two modifications in PR+COSMOSAC EOS. In particular, the accuracy for the vapor pressure near triple point shows major improvement, with the ALD-P reduced from 0.391(4747.67%) to 0.321(3029.12%). The sublimation pressure can also be estimated providing that the melting temperature and enthalpy of fusion are available. The ALD-P in sublimation pressure from the modified PR+COSMOSAC EOS for 1140 substances is 0.71(412.9%), which is only 1/3 of that from the original model (1.13(1249%)). This model is capable of providing both the vapor pressure and sublimation pressure over a wide range of conditions (from the critical point to below the triple point). It is particularly useful when no experimental data is available.
In the last part of this research, A predictive approach based on the combination of PR+COSMOSAC equation of state (EOS) and COSMO-SAC liquid model through self-consistent mixing rule (SCMR) is proposed for the prediction of gas solubility in polymers. We have validated this approach using 84 binary systems consisting of 9 gas molecules and 21 polymers with temperature ranging from 283.15 K to 498 K. The root mean square error (RMSE) in the predicted log_10 k_H is 0.33(86.71%), which is significantly more accurate than those from other predictive approaches. We believe this new method may provide useful assistants to the development of polymer membrane-based gas separation processes especially when experimental information is not available.

並列關鍵字

solubility ； prediction ； polymer ； supercritical carbon dioxide ； saturated pressure ； PR+COSMOSAC EOS

參考文獻

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