耦合系統與高分子系統相平衡預測

Prediction of Phase Equilibria of Associating and Polymeric Systems

許展嘉(Chan-Chia Hsu)

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(2013年)

https://doi.org/10.6342/NTU.2013.00886

摘要

本研究致力於改進複雜系統相行為的熱力學模型預測。眾多液體模型中，COSMO-SAC液體模型從量子化學的計算取得有關分子的資料，因此可以成功的在沒有任何實驗數據迴歸下預測液體的非理想熱力學性質。於是，本研究的目標是提升該模型對大型分子（如高分子）及強作用力流體（如含氫鍵分子的流體甚至產生化學反應）的相行為表現。首先，從配位數的角度可以更詳細的了解液體模型的基本原理。本研究提出一個推導液體模型的標準作法，此作法可以保證推導得出的液體模型的配位數必定滿足兩個重要的物理原則：（1）任何濃度及溫度下，任何液體裡的任意分子旁邊接觸到的總分子數必須維持定值; ( 2 ) 任意兩種分子在液體中的配對數目必須守恆，換言之，從A分子旁邊找到的接觸到的B分子總數必須和B分子旁邊找到的接觸到的A分子總數相等。本研究據此推導出之COSMO-SAC模型之配位數同時滿足此二重要物理原則，於是，配位數能夠定性上幫助對該模型局部流體結構的理解，進而改進該模型對複雜流體的相行為預測。
針對COSMO-SAC模型在大型如高分子的相行為預測，首先必須減少大型分子量子化學計算的計算時間。本研究開發一個有效率的新方法，使用只有三個單體的高分子（tri-mer）量子化學屏蔽電荷計算結果來預測具有任何聚合度的同種高分子相行為。在21種不同的高分子與35種不同溶劑並跨越從274.15K到477.15K溫度範圍的汽液二元相平衡測試中，此新方法和實驗取得的溶劑活度對數總誤差(log deviation)約為0.08，然而，高分子溶液中COSMO-SAC模型的配位數計算顯示出高分子的構型會顯著的被溶劑的極性影響。
含有複雜作用力如包含氫鍵的分子在系統中常常會產生複雜的雙分子聚合或甚至多分子聚合結構，因此使得相平衡難以得到準確的預測。本研究指出，透過反應平衡直接的考慮這些分子間的聚合體[如乙酸的雙分子聚合體(cyclic dimmer)及鏈狀碎片(chain fragment)]，可進而改進預測模型如PR+COSMOSAC氣體狀態方程式的局部流體結構，大幅改進乙酸混合物中因為氫鍵發生強烈耦合行為的相行為預測。在本研究中，測試了15種不同含有乙酸的混合系統相平衡並與實驗值(共388 實驗點，溫度範圍跨越293.15 到 373.2K)比較，在平衡壓力的誤差約為7.10% (AARD-P%)，而在平衡濃度方面只有2.38% (AAD-y%)，此準確度已經非常接近使用大量參數回歸的mod-UNIFAC+HOC equation of state (Hayden-O’Connell 氣體狀態方程式)模型的預測結果（5.14% 和 1.85%.）。
透過化學反應改進耦合系統的局部流體結構，使得COSMO-SAC模型在強作用力的複雜系統取得顯著的進步，本研究更進一步開發針對有機酸系統預測的Reactive COSMO-SAC模型。在該模型中，原本的模型的氫鍵表面可以經過化學反應在不同電性的表面之間形成化學鍵結，這樣的表面鍵結亦可改進耦合系統的局部流體結構，此新模型在與前述相同的乙酸測試系統中取得5.33% (AARD-P%)以及4.32% (AAD-y%)的平衡壓力以及平衡濃度的誤差。不同於前述模型，此新模型同時不需要任何來自實驗的耦合係數，在所有的有機酸測試系統中（25種不同有機酸混合流體共859個實驗點跨越293.15K到502.9K的溫度範圍），取得14.74%(AARD-P%)以及6.06%(AAD-y%)的平衡壓力、平衡濃度誤差的準確預測結果，此結果相較於原本的COSMO-SAC模型（18.12% and 7.07%）有大幅度的進步。除此之外，新開發的Reactive COSMO-SAC模型在液液相平衡取得準確的預測結果。在5種含乙酸雙組成液液平衡的測試系統中（51個實驗點，溫度範圍跨越289.15K到337K），從原本的COSMO-SAC模型的49%（AAD-x%）平衡濃度誤差，大幅度改進至7.3%。

關鍵字

COSMO-SAC模型 ； 配位數 ； 高分子混合物 ； 局部流體結構 ； PR+COSMOSAC 氣體狀態方程式 ； reactive COSMO-SAC 模型

並列摘要

Efforts are made to improve the prediction capability for the phase behaviors of complex systems, such as polymers and associating fluids. The COSMO-SAC model, based on quantum mechanical calculation of molecular information, is a powerful model to predict the liquid phase nonidealities without any experimental data. Our goal is to improve the method for systems with increasing conformation complexity (from small molecules to polymers) and/or increasing interaction complexity (hydrogen-bonding and reactive systems).
A general approach for developing liquid activity coefficient models is proposed that ensures at least two important physical conditions: (1) the total number of neighboring molecules around one molecule of species A must be a constant at any temperature for all possible mixture compositions, and (2) the number of pairs between any two species A-B determined from the local composition of B around A must be the same the that of A around B. Our results show that while most existing liquid models satisfy condition (1), only COSMO-SAC model satisfies both two conditions. Furthermore, the local composition of COSMO-SAC model is derived. The local compositions provide a means of qualitative analysis and understanding the local fluid structure.
For the large molecules with increasing conformation complexity, a new method is developed here to efficiently determine the screening charge distribution of polymers for use in the COSMO-SAC model. The vapor-liquid equilibrium of 21 different polymers with 35 different solvents is tested by COSMO-SAC without any further modification in this work. The overall average error of solvent activity is 0.08 with temperature range from 274.15K to 477.15K. The local composition of the polymer systems suggests the conformation of polymers indeed depends on the polarity of the solvents.
For systems with increasing interaction complexity (e.g. hydrogen bonds), specific fluid structures, such as the dimers and/or hydrogen bonding network, may occur and affect the phase behavior. By explicit inclusion of the specific local fluid structures, the phase behaviors of fluid containing acetic acid can be accurately predicted via the PR+COMOSAC equation of state (EOS). The prediction accuracy in describing the vapor-liquid equilibrium of 15 binary mixtures (388 data points, temperature range from 293.15 to 373.2) is 7.10% (AARD-P%) in pressure and 2.38% (AAD-y%) in vapor composition, which is similar to those from the mod-UNIFAC+HOC (Hayden-O’Connell EOS) 5.14% and 1.85%. The root-mean square error in predicting liquid composition in liquid-liquid equilibrium of 5 binary systems (51 data points, temperature range from 289.15K to 337K) is found to be 0.096, which is more accurate than that from mod-UNIFAC, 0.173.
The finding of specific local fluid structures leads to the development of a reactive COSMO-SAC model for strongly associating fluids. In this model, hydrogen-bonding surfaces are allowed to react with each other and form chemical bonds. The advantage is that no experimental association constant is needed. The prediction accuracy in describing the vapor-liquid equilibrium of 15 binary mixtures (the same as the last paragraph) is 5.33% (AARD-P%) in pressure and 4.32% (AAD-y%) in vapor composition, which is similar to PR+COSMOSAC equation of state with explicit consideration of cyclic-dimmer and chain-fragment. For total 25 binary mixtures (859 data points, temperature range from 293.15 to 502.9) is 14.74% (AARD-P%) in pressure and 6.06% (AAD-y%) in vapor composition, which is significantly reduced from COSMO-SAC model 18.12% and 7.07%. The root-mean square error in predicting liquid composition in liquid-liquid equilibrium of 5 binary systems (51 data points, temperature range from 289.15K to 337K) is found to be 0.073, which is also more accurate than that from original COSMOSAC model (0.439) and PR+COSMOSAC equation of state (0.096).

並列關鍵字

COSMO-SAC model ； local composition ； VLE of polymer mixtures ； specific fluid structures ； PR+COSMOSAC EOS ； reactive COSMO-SAC model

參考文獻

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