摘要或動機

The starting point of this experiment is to study the structure of soap-film. By
changing the height of the triangular prisms, cuboids and pentagonal prisms, I observed
the patterns set by the soap within the frameworks. It is surprised that when the
proportion of prism is in a specific range, the phase in the middle of the structure
will overturn 90 degree and then transmitted into another kind of balance pattern.
I named this process “phase transition”. According to the experiment ,we can conclude
the change of film patterns within variable prisms are all applied to this regular
cycle:：



We know the soap films are forever attempting to minimize their energy. It stands
to reason that surface tension tend to set up the film in its minimal surface. From
the point of Mathematic, each structure should have only one single balance pattern,
which is set up on the base of Fermat point and this pattern should stand to the
minimize of it’s energy. However, we discovered that in some specific cases, one
structure can allowed two kinds of balance films-patterns to exist. In these cases,
any small vibration can cause the happening of “phase transition”. To sum up, I
presume some structures have two different types of balance film-patterns: one of
which stands to the local minimum (in this condition the pattern’s surface area
isn’t the smallest); the other stands to the absolute minimum (in this condition
the pattern’s surface area is the smallest).<Picture one>




There is an energy valley separate local minimum from absolute minimum. The second
pattern (local minimum) will appear when the structure is blocked from attaining
its absolute minimum, but surface intention is not powerful enough to support the
film jumping over the energy valley. In this condition, if we works on the structure
(such as blowing), which would provide the film of energy to cross the valley, and
then phase transition take place. Vice versa, we can also force the film to jump
from absolute minimum to local minimum and phase transition will occur as well.
In a word, phase transition can happen in each two way, which connects the two types
of balance pattern.


<Picture two>

This report lays stress to find out the condition of phase transition. We also analyze
the structure of soap-film by its included angles and surface area in hope to go
deep into the science of soap-film.

我們實驗的出發點在於研究泡膜的立體結構。藉由改變正立方柱的高，觀察其平衡薄膜形式，意外的發現當正立方柱的邊長比在某個範圍時，泡膜結構中央會瞬間90 度翻轉，形成另一種平衡型式，我們將這個過程命名為面轉變(Phase
Transition)。為了進一步了解面轉變發生的相關因素，我們設計了一連串的實驗，針對正三角柱、正四角柱、正五角柱、正六角柱發生面轉變的時機和條件分析討論。此外，我們還分析了泡膜結構中膜與膜夾角的特性、最小表面積和表面能之間的相關性，對於泡膜的立體結構做了一系列深入的探討。