我們希望可以推廣自由能密度最佳化方法來研究相變的課題‧自由能密度最佳化方法是一個非常直覺的數值工具可以用來研究盤狀粒子、膠體的相變行為‧基本想法就是把總混合自由能密度定義成各別共存相自由能的相加，用其所佔據的體積和總體積的比例常數當作對總自由能密度的貢獻權重‧要使用此方法前，首先，必須先透過半巨正則系綜理論來建構盤狀粒子、膠體混合系統的自由能‧藉著自由體積理論和定標粒子理論，可以得到各共存相所佔據的體積比例‧而在做最佳化的過程，我們必須先求得固體和液體的自由能函式‧這部分可以透過Fundamental measurement theory(FMT)來求得‧自由能最佳化的方法和傳統上求壓力和化學能的方法不同的地方在於前者提供了理解三項共存相相的背後物理機制‧此方法能夠產生相圖單相和混合相的區域而非僅止於相的邊界‧我們的方法所得到的共存相的區域和膠體實驗上量測到的結果非常吻合‧此外，文獻上有名的三相共存三角形區域其實是透過不同的共存相,在動態上的合併所得到的結果‧如果初始密度值落在此三角形區域中，系統會經過兩階段過程來達到三項共存平衡態‧落在三角區域中的各相(固、液、氣)總是落在三角形的頂點位置，但其所佔據的體積會因為初始密度不同而有所變化‧這個動態達到平衡的過程和近期文獻上巨分子-膠體的實驗所觀察到的結果非常一致‧如果實驗上可以將此巨分子-膠體系統換成盤狀粒子-膠體系統‧可驗證我們使用的理論和預測的結果是否正確‧We draw attention to the free energy density minimization method as an insightful means to study the phase equilibrium behaviors of the platelet-colloid mixture. The basic idea of the method hinges on treating phases in coexistence as a composite free energy density which is defined by the sum of the free energy density of respective coexisting phases weighted by their respective volume proportions. To implement this method, the semi-grand canonical ensemble theory was first applied to construct a Helmholtz free energy function of a platelet-colloid mixture. Augmented by the free volume approximation and with the help of the scaled particle theory, we derived the free volume fraction that appears in the free energy function. Formulas of the Helmholtz free energy in liquid and solid phases are needed in effecting the free energy density minimization and these quantities are obtained in the context of the fundamental measure density functional theory. That the free energy density minimization method was preferred instead of the usual way of computing pressure and chemical potential is because of the insight it provides in understanding the origin of the triple coexistence. The method yields the phase-diagram domains (rather than the phase boundaries) of homogeneous single phases as well as their coexisting phases. For the coexistence domains, they are in the same pattern as one often encounters in colloidal laboratory experiments. Our calculated platelet-colloid phase diagram displays the well-known triangular area of gas-liquid-solid coexisting three phases, but it has to be realized as some kind of a kinetic phase transition coalescence of sets of two coexisting phases. A remarkable scenario in our phase-diagram domains is that, for any set of initial concentrations of colloids and platelets that fall inside this triangular area, the system proceeds in two stages to reach the triple coexisting phases. In this triangular domain, the three coexisting phases (gas, liquid and solid) always assume the vertices of the triangle, but depending on location of initial concentrations the spatial volume of each phase is different generally. This kinetic phase transition process is reminiscent of several recently reported experiments in polymer-colloid mixtures. It would thus be interesting if colloidal laboratory experiments at the same quantitative level as these reported papers for the colloid-polymer mixture can be carried out to confirm our theoretical predictions.
