膠體相圖之理論計算

Theoretical studies of colloidal phase diagrams

黃建程(Chien-Cheng Huang)

指導教授 ： 賴山強

國立中央大學/理學院/物理學系/碩士(2007年)

摘要

本文針對膠體系統，進行相圖之理論計算，工作重點著重於對系統相分離之分析，有別於傳統上檢驗相邊界之作法，本文經由視兩分離相為一合成系統，以計算系統在給定熱力學條件下之最低組合自由能，來轉化相圖計算問題為最佳化求相圖區問題。

為了達此目的，我們放寬了傳統計算相圖上，預設固態結構為FCC之局限，首先藉由定義變數群來變數化固態結構，由此而可決定任意固態結構，接著，本文引進密度泛函理論(Fundamental measure theory)，求取各式結構之硬球自由能，並同時引進Rascón et al.之理論近似法，求取任意結構之徑向分布函數，於是，吾人即可透過微擾法(對等效單成份系統而言)或其他方法，而求得任意結構之固態自由能。

最後，我們以基因演算法整合上述理論，而發展出一套僅需給定初始熱力學條件，便能在基因演算法的平行計算下，自動取得膠體相圖與其對應之固態結構的相圖計算工具。

關鍵字

基因演算法 ； 密度泛函理論 ； 三相共存區 ； 膠體相圖

並列摘要

We draw attention to a theoretical means to calculate the colloidal phase diagrams. The proposed method has the salient feature of following closely the experimental spirit since the crystalline structures of the solid phase is assumed unknown given the initial physical conditions. With this theoretical model, the phase-diagram domains which comprise of pure phases, two coexisting phases, three or multiple separated phases can all be crosshatched in addition to yielding their respective volume proportions. The methodology proceeds with treating the coexisting phases as a combined system whose composite free energy density is written as the sum average of the free energy density values which are weighed by their re-spective volume proportions. Under this scheme, the thermodynamic phase transition has reduced to an optimization problem searching the lowest value of the composite free energy for all possible combination of phases, including pure liquid, pure solid, gas-liquid, gas-solid, liquid-solid, etc. For the calculation of the solid free energy in any structure which is needed in the thermodynamic perturbation theory, we applied the fundamental measure theory to obtain the solid hard sphere free energy, and used the Rascon et al.''s [C. Rascon, L. Mederos, and G. Navascues, Phys. Rev. E 54, 1261 (1996)] theoretical approach to calculate the pair distribution function. The genetic algorithm was finally employed to integrate all these in-gredients. As illustrations to demonstrate the usefulness of the present theory, we first tested the idea by studying the charged colloidal system and confirmed that our calculations reproduced satisfactorily our previous results [G.F. Wang and S.K. Lai, Phys. Rev. E 70, 051402-1 (2004)]. Then, we extend the calculation to the colloid-polymer mixtures. In the latter study, we unveiled the mystery of gas-liquid-solid triangular region previously advo-cated by Lekkerkerker et al. [H.N.W. Lekkerkerker, W.C.K. Poon, P.N. Pusey, A. Stroobants, and P.B. Warren, Europhys. Lett. 20, 559 (1992) ].

並列關鍵字

Fundamental measure theory ； gas-liquid-solid triangular region ； genetic algorithm ； colloidal phase diagram

參考文獻

[1] G. F. Wang and S. K. Lai, Phys. Rev. E. 70, 051402 (2004).

[2] D. Gottwald, G. Kahl and C. N. Likos, J. Chem. Phys. 122, 204503 (2005).

Wien, Ph.D. Thesis, (2005)

[4] C. Rascon, L. Mederos and G. Navascues, Phys. Rev. E 54,1261-1264 (1996).

[5] J.A. Niesse and H.R. Mayne, J. Chem. Phys. 105,4700(1996)