本篇論文的主要目標為我們使用了一個新方法：最小自由能法，重新描述硬球膠體系統混合棒狀粒子的相圖。傳統上，這樣相圖的計算以系統化學能、壓力、溫度相等之方法畫出不同的相區邊界。然而如此的方法無法完整與實驗比較。主要原因在於實驗上為觀察相圖中的某一個初始態；然後觀察隨時間變化，系統會如何演進。例如來說：最後會分解成兩個或三個不同的均勻之相分離態。由於傳統之方法只可以分別出相圖上不同的相分離區域，因此只能說明實驗上的初始態會不會相分離；以及會分成幾個態。卻不能說明相分離後分離到哪裡，以及在相同的相分離區域中不同的初始點，相分離後，末態值的差別。然而，若我們使用最小自由能方法分析相圖，即可直接說明系統初態與末態的關連性，也可以說明相同的相分離區域中，不同的初始態所產生之分離態的差異。
此外，若使用最小自由能法來描述系統，也可以說明長久以來傳統方法難以說明的相區：三相分解區或稱動力行為分解區(kinetic phase-transition domain )，而我們的方法可以說明在此相區的初始態可能分解的動力學行為方式；並且說明此相區中不同的初始態會有如何的行為差異。然而，由於傳統的方法無法分析此相區的行為，因此大多數研究皆甚少說明此相區的行為；頂多只是說明三相區的初始態最後會分解成三相分離的形式。
因此，相較於傳統的方法，若以我們的方法來分析此類系統的相圖，由於理論與實驗上的模式相同(可同時得到初、末態的資訊)，我們將有更多的物理內容可供深入探論，亦有更多的定性數據可與實驗比較。

The semi-grand ensemble theory [H.N.W. Lekkerkerker, Europhys. Lett. 20, 559 (1992)] in conjunction with the fundamental measure density functional theory [V.B. Warshavsky and Xueyu Song, Phys. Rev. E 69, 061113 (2004)] are used to construct the Helmholtz free energy density for both the solid and liquid phases. Given these free energy density functions, we apply the free energy density minimization method [G.F. Wang, S.K. Lai, Phys. Rev. E 70, 051402 (2004)] to crosshatch the coexistence regions of a mixture of uncharged colloidal hard spheres and colloidal rods. The calculated results show that the triangular area bounded by gas-liquid, gas-solid and liquid-solid coexisting phases which has been called coexistence region of gas-liquid-solid corresponds in fact to sets of two phases in coexistence. The phase boundaries which are delimitations of our calculated coexistence domains compare very well with previous theoretical calculations. The relevance of the phase-diagram domains to three phases in coexistence will be discussed.

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