第一部份我們利用平均場的近似方法來計算非均勻電解質的自由能，與之前的理論相比，我們得到對自由能有重要貢獻的另外兩項：其一，當電解質密度有緩慢變化時會比均勻的時候額外貢獻一微分項。其二，當離子被侷限於交界面的一邊時，會貢獻另一邊界效應項。 這兩項會使得空氣跟鹽水交界面附近的離子被排開量變多而所得表面張力也比之前的理論所得到的要大。我們也用這理論來計算純水-鹽水交界面和鹽水-鹽水交界面附近的電解質分佈。另外，也計算了兩個不帶電的大球在電解質中的相互作用力。 第二部分我們分別從理論跟實驗上以二維系統來研究單一方向的偶極子所形成的柱狀結構。考慮偶極子之間的作用，在理論計算得到柱狀結構的寬度與長度成正比，而比值在偶極子所佔體積比很小時趨近0.17，且隨著體積比增加而增加。實驗上，我們在磁性流體薄層外加 一平行磁場，觀察得到週期性的柱狀結構。發現這些柱狀結構的寬度跟間距與所用的薄層厚度無關。其間距幾乎與其長度相等且其寬度如同理論所預測與長度成正比，不過所得到的比值比二維理論所得為高。 In the first part, we calculate the free energy density for inhomogeneous electrolytes based on the mean field Debye-H¨uckel theory. Derived are the contributions of (1) the differential term for the electrolyte density being slow-varying in one direction and (2) the boundary term for an electrolyte confined to one side of a planar interface. These contributions are shown to cause the electrolyte depletion near the air-water interfaces, which makes the surface tension to increase, to be significantly larger than those predicted by previous theories. Non-uniform electrolyte densities are also computed near the water-electrolyte and electrolyte-electrolyte interfaces. Finally we remark on the interaction of two uncharged macro-spheres due to the electrolyte depletion. In the second part, we study the columnar structure of the uniaxial dipoles in two dimension both theoretically and experimentally. The columnar width is theoretically computed to be proportional to its length by the consideration of the dipole-dipole interaction. The ratio is obtained to be 0.17 in the case of low volume fraction and becomes larger at a larger volume fraction. In experimental study, we apply an external magnetic field parallel to the magnetic fluid film to study the structure in equilibrium. The columnar width and spacing are shown to be independent of the height. The spacing is observed to almost equal to the columnar length. The columnar width is proportional to its length but with a larger ratio than the theoretical results.
