藉由考慮長距離相關性及分子間交互作用改進晶格模型

Improvement of Lattice Model by Consideration of Long-Range Correlation and Interaction between Molecules

劉德謙(Te-Chien Liu)

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(2021年)

https://doi.org/10.6342/NTU202102060

摘要

這項研究中，我們希望從兩個面向修改COSMO-SAC模型使其能更好的描述耦合流體。此二面向包含研究分子表面如何與其他表面接觸以及接觸表面間的交互作用力。為了求得晶格流體的熱力學性質，我們提出了一個新的方法，Liu-Lin模型。藉由將系統的內能及熵表達成系統組成(bulk composition)及局部組成(local composition)的函數，透過最小化系統的自由能進而求得平衡時的局部組成。在一維二成分且成分間可經由化學變化互相轉換的系統中，我們證明Liu-Lin模型表現與著名的易辛模型(Ising model)相同。這個方法也適用於成分間無法互相轉換的系統，進而能得到其他系統組成下的熱力學資訊。而在無限大的系統中，我們也證明Liu-Lin模型與COSMO-SAC模型完全吻合。
二維系統僅有少數系統有局部組成的確切解(exact solution)，比如Onsager的二維易辛模型確切解。我們發現難以求得一般二維系統中局部組成確切解的主要原因是流體結構中的長距離相關性(long-range correlation)。我們提出將帶狀的二維系統都轉換成多成分的一維系統的方法，可以避免處理長距離相關性，而一維的系統就能用Liu-Lin模型及COSMO-SAC模型來計算。我們發現用轉換後的Liu-Lin模型求得的無論是局部組成、系統內能還是熵都與用蒙地卡羅模擬(Monte Carlo simulation)及王-藍道取樣(Wang-Landau sampling)得到的數值一致。藉由增加帶狀系統的寬度，Liu-Lin模型計算出的熱力學性質可以無限逼近Onsager的二維易辛模型確切解。而這個模型也適用在Onsager的確切解無法適用的系統，例如有外加磁場或是成分間無法互相轉換的系統。然而此方法有一很大的限制，就是轉換後的系統需要耗費大量的時間運算，這也是現在它難以直接應用在COSMO-SAC模型上的原因。
另一放面，我們藉由考慮"不同混合物中分子間的距離應不同"以改良COSMO-SAC模型。我們將化合物分為兩類，第一類是分子中同時擁有氫鍵施體(donor)及受體(acceptor)的化合物，而第二類則是不同時擁有的化合物。我們在COSMO-SAC模型中加入三個作用力參數，用以描述被分類出來的分子的交互作用力。為了驗證這個改良後的COSMO-SAC模型，COSMO-SAC(2021)，我們計算了它在相平衡及熱力學性質上的表現，包含氣液相平衡、液液相平衡、無限稀釋下的活性係數及辛醇-水分配係數。相較於COSMO-SAC(2018)，這個模型在預測氣液相平衡、液液相平衡、無限稀釋下的活性係數及辛醇-水分配係數的表現上分別有約8%、6%、6%及2%的進步。
只要耗時的計算可以被更有效率地處理，Liu-Lin模型便可以做為一個建構適用於更複雜系統的局部組成模型的有用基礎，而將分子分類這項新觀點也是一塊更加精進COSMO-SAC模型的基石。

關鍵字

晶格模型 ； 局部組成 ； 耦合流體 ； 氫鍵 ； COSMO-SAC

並列摘要

In this work, we attempt to revise the COSMO-SAC model and improve its performance on associating fluids from two aspects, inclusion of the correlation between segments and refinement of the interactions between paired segments. To address the segment correlations, we propose a novel approach, called the Liu-Lin model, for obtaining thermodynamic properties of lattice fluids based on local compositions. The equilibrium local composition is determined based on minimization of free energy of the system, and the process is made possible by expressing the potential energy and entropy of a system in terms of a given bulk and local composition. We show that the Liu-Lin model coincides with the well-known Ising model for a binary mixture in one-dimension with an interchangeable chemical reaction. Moreover, it is applicable even when the species are not interchangeable, and therefore the free energy of all possible compositions can be obtained. In the limit of infinitely large lattice, we also show the Liu-Lin model coincides with the COSMO-SAC model.
Exact solution to the local compositions is available for only few cases for 2D lattice fluids, for example, the Onsager’s solution to 2D Ising models. We discover that the long-range correlation in the fluid structure is the main reason for the complication of getting the exact local compositions for general 2D lattice fluids. Nonetheless, we show that for any stripe-like 2D lattices, the long-range correlations can be avoided by transforming the system to a multi-component 1D system, to which the Liu-Lin model and the COSMO-SAC model are applicable. We found that the local compositions, energy and entropy predicted from the Liu-Lin model, modified by the approach we developed for 2D lattices, are in excellent agreement with those obtained from Monte Carlo simulations and Wang-Landau sampling. By increasing the width of the stripe, the thermodynamic properties predicted from the Liu-Lin model approaches the exact Onsager solution for 2D systems to arbitrary precision. This model can also be applied to conditions where the Onsager’s solution is not applicable, such as systems under external magnetic field or with fixed species compositions. The transformation of the 2D problem to 1D comes with a cost of considerable computational resources needed. In fact, it is exactly the difficulty in its application to the COSMO-SAC model now.
As an alternative approach to improve the COSMO-SAC model, we consider the difference in molecular interactions due to different separation distances between molecules in different chemical mixtures. We categorized associating chemicals into 2 types, one is composed of molecules with both hydrogen bonding donor and acceptor and the others. We introduced 3 additional interaction parameters to describe the interactions between different types of chemicals. As the verification of this modified model, referred to as COSMO-SAC(2021), we computed its performance on phase equilibria and thermodynamic properties, including vapor-liquid equilibrium (VLE), liquid-liquid equilibrium (LLE), infinite dilution activity coefficient (IDAC), and octanol−water partition coefficient (Kow). Compared to the COSMO-SAC(2018) the improvement in the performance on VLE, LLE, IDAC, and Kow calculations are 8%, 6%, 6%, and 2%, respectively.
The Liu-Lin model could serve as a valuable basis for development of local composition models for more complicated systems once the time-consuming process can be handled more efficiently. Also, the new perspective of classifying molecules could serve as the foundation for further improvement of the COSMO-SAC model.

並列關鍵字

COSMO-SAC ； lattice model ； local composition ； associating fluids ； Hydrogen-bond

參考文獻

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