摘要
磁性流體為一具有磁矩的液體，在外加磁場的影響下，其中的磁性粒子會開始聚集且延著磁場方向排列。在平行於薄膜的磁場(平行磁場)作用下，其磁性粒子會聚集且能夠形成沿著磁場方向排列成一度空間的週期性長鍊狀。在垂直於薄膜的磁場(垂直磁場)作用下，薄膜中的磁性粒子會聚集而在低磁場呈現出一些不規則的磁性微粒圓柱體。隨著磁場的增加，磁性微粒圓柱體會排列成一有序的六角型晶格結構，之後經由過渡狀態最後到達第二重的六角型有序晶格結構。在過渡狀態中，可見到磁性微粒圓柱體從一分為二的分裂現象，此現象為磁性粒子在圓柱體內合磁偶矩間的排斥力所造成。而在較高的磁場改變率下，則無第二重的六角型有序晶格結構之形成。
薄膜的溫度T對六角型晶格結構的效應則顯示T的增加使得磁性流體微粒的受到熱能的影響，因而造成微粒圓柱體間的距離d增加。實驗中所使用的磁性流體在T26oC呈過飽和狀態，使得 d 值在19.4 oCT28.5oC達一平衡值。之後當T28.5oC時，d值隨T的增加而快速增加。
而過飽和磁性流體薄膜內所析出的圓型柱狀粒子團，在外加垂直磁場的作用下將產生變形。變形原因亦為磁性粒子在圓柱體內合磁偶矩間的排斥力所造成。隨著磁場的增加，於低磁場增率下，圓型的柱狀變形成為啞鈴狀，進一步成為彎曲的條狀，而後變成迷宮態；於高增率下，圓型的柱狀變形成為樹枝狀，隨後亦形成迷宮態。最後，變成啞鈴狀或樹枝狀的圓型的柱狀會斷裂，而在薄膜中形成六角型晶格有序結構。圓型的柱狀的截面大小則因表面張力的不同，使得在同一磁場增率下，較小的圓型的柱狀在外加垂直磁場的作用傾向於形成啞鈴狀，其截面大小大到某一臨界值時，會形成樹枝狀。

Abstract
Magnetic fluids are fluids consisting of particles with magnetic dipoles. Under the influence of externally applied magnetic fields, the magnetic particles in the fluid start to agglomerate and align with the direction of the field. When a magnetic fluid thin film is subjected to a magnetic field parallel to the plane of thin film (parallel magnetic field), the magnetic particles, inside magnetic fluid thin films, agglomerate and form a one-dimensional periodic long chain structure. Contrarily, under the action of magnetic fields perpendicular to the plane of thin film (perpendicular field), the particles in the film agglomerate and form particle columns. With the increasing H at a lower sweep rate, the columns evolved from a disordered column phase to a first-level hexagonal structure pattern and finally reached a second-level hexagonal structure pattern through a phase transition. During the transition phase, each column was observed to split into two columns. The split of a column was attributed to the dipolar repulsive force in each column. However, there was only one level of hexagonal structure pattern for a high sweep rate within the range of the magnetic field used here.
The effect of the temperature T to the hexagonal structure of the film revealed that the increase of the distance d between particle columns of hexagonal structures was caused by the thermal agitation of the particles in the film as T was increased. The magnetic fluid in this work became over-saturated at T  26oC, and a plateau was found for the d-T curve when T was within the range from 19.4 oC to 28.5 oC. As T  28.5oC, the d was increased rapidly as T increased.
The pattern forming system of magnetic fluid drops have also been investigated. The original cylindrical drops, which were formed by the condensation of magnetic particles in an over-saturated magnetic fluid film, evolved to a dumbbell phase or a branched structure under the influence of perpendicular magnetic fields. The cause of the pattern formation is believed to be mainly due to the competition between surface tension and the magnetic dipolar interactions between particles in each column. As the field strength increase, the pattern changes to a labyrinthine structure and finally to an equilibrium hexagonal structure. In this work, a critical diameter of the original cylindrical drops, which separated these two types of evolution processes, exists in the pattern formation for a given sweep rate. A dumbbell phase occurred when the diameter is below this value; otherwise, a branched structure formed.

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