物理

本研究從大自然中之「蓮花效應」引發學習興趣與研究動機，在蒐集相關資訊與文獻後，發現疏水功能不只是防水，還關係著日常生活品質之許多材料特性，包括防水、撥水、防潮、防銹、防蝕、抗菌防污、自清潔…等。而影響固體表面疏水性之兩大特性，包括物理之表面粗糙度與化學之超低表面能，本研究針對物理之表面粗糙度與疏水性之關係做探討，以相同之化學特性來比較不同號數之工業用砂紙之疏水行為，並就廣泛被引用之兩種模擬表面粗糙度與疏水性關係之模式：Wenzel and Cassie model，比較現有文獻對兩種模式之特性，選擇Cassie model 來進一步實驗驗證，以量測之平均接觸角 Θ 推算Cassie model 之表面粗糙係數Φ 值，並簡化不同砂紙顆粒模型為相同粒徑之球狀，以簡化之方程式來求得水珠與砂紙顆粒之實際接觸面積與球心夾角 θ，以提供高中學校能在經費與設備之限制下，仍能有效應用與印證Cassie model，獲得砂紙顆粒直徑與球心夾角 θ 自然對數值之關係。並就疏水性之生活應用，建立接觸角與 Φ 之關係曲線，驗證實驗之方程式，與延續過去之科展成果，以實驗成果提出可行性應用之建議。The interest and motivation of the present work was introduced from “lotus effect” in nature. After we collected related literature and information, we found that the function of the so-called “superhydrophobicity” behaves not only water repellency, but also a variety of real-life applications, including anti-fog, anti-corrosion, anti-bacteria, anti-fouling, self-cleaning, and so on. Pervious studies have pointed out that two criteria affecting the performance of hydrophobic surfaces are physical (roughness) and chemistry (surface tension) properties. This study focused on influence of physically surface roughness on hydrohyphobicity. Based on an identical surface chemistry, we employed different types of industrial sandpapers to mimic the lotus leaf, and investigated the relationship between roughness and hydrophobicity by using two famous models: Wenzel and Cassie models. Comparing with their basic assumptions to our study, we applied Cassie model to confirm our experimental results, in where one Cassie parameter (?) was proposed to simplify the Cassie equation. This superhydrophobic behavior can be well predicted by the Cassie model. This study continues previous achievement and offers some practical utilization according to our\r experimental results.

This experiment mainly aims at three kinds of solution - Dextrose, Saccharose, and Fructose. By changing its temperature, density, length of tube, as well as different wave length factor of polarized light, we observe the influence of the direction of polarization by those factors. The experimental result showed as follow. The Dextrose and the Saccharose can cause the polarized light with the rotary direction of clockwise, so both are ‘dextrorotatory’. The Fructose can cause the polarized light with the direction of counterclockwise, so it is the ‘laevorotatory’. For the Dextrose, when the\r temperature is lower than 20℃, the direction of polarization has changed observably, but doesn’t have any rule. When the temperature is higher than 20℃, the direction of polarization increase slowly. For those three kinds of solution, when\r density increased, the polarization increased observably. When the polarized light passed through the solution with longer path, the direction of polarization has more change. When the wave length of the polarized light changed, the direction of polarization has been changed observably. When the wave length of the polarized light is shorter, the direction of polarization change increased.本實驗主要針對葡萄糖、蔗糖、及果糖等三種旋光性溶液，改變其溫度、濃度、容器管長、以及不同波長的偏振光等因子，觀察這些因素對偏振方向所造成的影響。實驗結果顯示：葡萄糖與蔗糖會使得偏振光的偏振方向以順時針旋轉，屬右旋性之光學異構物；果糖會使得偏振光的偏振方向以逆時針旋轉，屬左旋性之光學異構物。若溶液為葡萄糖，當溫度低於20℃時，偏振光的偏振方向會有明顯的改變，但無規則可尋；當溫度大於20℃時，偏振方向旋轉角位移則以非常緩慢的方式增加。當此三種溶液之濃度增加時，偏振光的偏振方向有明顯遞增的現象。此外，當容器長度越長（即偏振光在介質中的行程越長）時，偏振方向的改變亦越明顯。當偏振光的波長改變時，偏振光的偏振方向有明顯的變化，且當偏振光的波長越短，偏振方向的改變越大，似乎與波長呈反比，但此結果與理論值（即旋光度與波長平方成反比）仍有一些差距。

In our daily life, objects and the contacts between objects they will have mutually affect each other, some initially chaotic systems after a sufficient amount of time will mutually correct each other, and finally achieve synchronization (example: the speed of bird and fish migration, market prices, infantry…), although some are unable to achieve this. We will illustrate and explain the synchronization system, its process and discover the conditions for synchronization. Using linking concepts, we will integrate the coupled map lattices with global coupling and coupled map lattices with intermediate-range models into a synchronization mode in order to simulate a synchronization system. We first used a small system of n≦50 to obtain results that will demonstrate the linking concepts: 1. The more chaotic a system, a longer period of time is required for synchronization. 2. An increase in the number of individual objects requires an increase in the range of concepts and the amount of time in order to achieve an in depth synchronization. 3. Initial concept values which randomly effect synchronization critical point conditions are not obvious in a mathematically incorrect graph. In a closer look, when we increased the synchronization to n≦400 and the number of times to t-->100,000 we discovered:1. Using the function G(x) we hoped the results from the graph after apply the function and correction able to overlap and test with “Scaling and Universality in Transition to Synchronous Chaos with Local-Global Interactions”, but the part which overlapped the measurements was not identical: 2. We can use the significance of the critical point and the Interactive Process to find the approximate value of the critical value up to 4 digits following the decimal point. 3. We can also use the approximate value to find out the range for the simultaneous conditions and the various points on the system itself, as well as obtain a negative correlation between them, and then it can be similarly expressed with using a curve. A computer can calculate values with this kind of enumerating method, even without any special resolution capabilities to quickly obtain large amounts of approximate values of simultaneous conditions, this is especially true when calculating unfamiliar systems. 日常生活中，物件與物件的接觸，彼此會互相影響，有些原本雜亂的系統再經過充裕時間的互相修正後，最後竟能達成同步(例如：鳥群、魚群遷徙的速度、市場價格、行軍步伐…)，有些則不能。因此，我們試著利用描述同步系統的模型，觀察系統同步的過程，並且找出同步的條件。由連結的觀點，我們將Coupled map lattices with global coupling 和Coupled map lattices with intermediate-range 模型的優點整合成Synchronization mode 去模擬同步系統。我們先用小系統(n≦50)得到能印證連結觀點的結果：(一)、系統越雜亂，就需要稍長的時間同步；(二)、個體數越多時，各點需要更大範圍的點數去影響於每單位時間內以及更深的影響才能同步；(三)、起始值隨機影響同步臨界條件並不明顯，在誤差範圍內。更進一步，我們將系統推向n≦400 點,t→100,000 次，我們發現：(一)、在”G(x)”我們希望能將圖形經過函數修正之後能疊和，驗證”Scaling and Universality In Transition to Synchronous Chaos with Local-Global Interactions ”中的結果，但只有部分疊和，尺度不相同；(二)、可以直接利用臨界點的意義用十分逼近法求出臨界值的近似值到小數後四位；(三)、我們用近似值也能發現同步條件與系統各點本身可跳躍的數值範圍是負相關，可用曲線去近似。這種窮舉方式，交由電腦運算，不需要特別的解析能力就能夠快速且大量求得同步條件的近似值，尤其在運算不熟悉的系統時。

本實驗主要是探討磁色效應，光通過狹縫會產生繞涉現象產生繞涉圖形，為了要了解繞涉現象，要先瞭解光柵的結構。要探討光柵，就要先探討探討磁流體的結構結構，磁流體乃是將一般磁性物質製成小粒子，再使其懸浮於非磁性液體中，根據統計力學，只要粒子夠小，就可經由布朗運動均勻散佈在溶液中。而散佈在溶液中的磁性粒子會因為磁力及凡得瓦力而聚集，所以一般都會在小粒子周圍覆蓋一層介面活性劑，防止發生『沈澱』的聚集現象。磁流體具有磁性特徵及流體特徵，磁性特徵是磁流體的居禮溫度和一般鐵磁固體相當，而且在外加磁場時磁性顆粒會連接成磁柱，而流體特徵則表現在其具有各式各樣的、流動性、黏滯性、揮發性、飽和性及導熱性。我分別將磁流體薄膜在加入不同磁增率的磁場、不同大小的電場、混入液晶等的狀態下，做各種的光柵樣本。接著再打入平行光，觀察繞涉圖形，其中加入磁場的，磁性顆粒會連接成磁柱，縱切面會形成點狀的六角行有序結構，非常適合做光柵，繞涉圖形是一七彩圓環。加入電場的，並沒有規則的排列，沒有如加上磁場般有規律的變化，但是觀察到很多磁性顆粒的擾動和聚集，還有電極邊界的一些變化。而加入液晶混和均勻之後，為一個比原本顏色更深黑的流體，磁流體的粒子即固定不動，成黑色團塊混合乳白色的液晶，對電場磁場都沒有反應。就實驗觀察到的，我們發現了，最是合作光柵的是在磁場下的磁流體，而電場對磁流體的結構也有一定的影響，在探討光柵的實驗中，也觀察到了很多磁流體的特殊現象。

隨著社會漸漸的現代化，我們需要愈來愈多的電力，然而在享用電力時，更伴隨著汗染的到來。所以討論如何有效的利用能源及探討無汗染能源，是本實驗研究的主要課題，以下即是我們的介紹。

掃描式穿隧顯微鏡(Scanning Tunneling Microscope)，是在奈米尺度下觀察物體表面的一大利器。但一台精密的STM，造價動輒數百萬元新台幣，本研究嘗試利用簡單、便宜的材料，製作一台簡易的掃描式穿隧顯微鏡。眾所皆知：掃描式穿隧顯微鏡的關鍵，就是量子力學中的穿隧效應原理，及壓電材料的應用，所以這些主題都是本實驗涉及的內容。除此之外，我們也運用簡單的物理原理，取代價格高昂的儀器，例如：利用彈簧代替昂貴的避震系統等。此研究利用穿隧效應的原理，並進而利用電腦得知樣品表面的結構，以達顯微鏡觀察分析物體之功用。 ;The major purpose of our project is to assemble a simple scanning tunneling microscopy with cheap and available materials for ordinary senior high school students. For example, we use springs for damping instead of electromotive force device. Weweld all the electronic circuit boards for ourselves in order to not only lower the cost but also inspect the inner structure more clearly and precisely. After the microscopy is assembled, we will use it as an appliance to observe the samples of nano-particles. We must repeat this procedure several times so as to make sure that the images we’ve gained is true, not just some disturbances produced by the environment. Finally, the microscopy can be applied to research fields as well as academic courses.

We report an investigation on the synthesis, characterization, and application of photonic crystal. In the study of the synthesis of SiO? nanoparticles for the building blocks of photonic crystal, it is found that by changing the concentration of NH3 solution, we are able to control the size of SiO? nanoparticles. After trying several different methods, we discover that the vertical substrate method is the best way to arrange nanoparticles into a periodic structure. From scanning electron microscope, we confirm that SiO? nanoparticles can form a three dimensional hexagonal photonic crystal. From transmission experiment, we find that the wavelength of the minimum transmission is proportional to the size of nanoparticles. This result implies that using photonic crystals we can control the behavior of electromagnetic wave. Finally, we fabricate CdS nanoparticles on the top of photonic crystals with different diameter of SiO? nanoparticles. Using photoluminescence measurements, we show that by controlling the lattice constant of a photonic crystal the luminescent efficiency of CdS nanoparticles can be substantially enhanced. Out results, therefore demonstrate that photonic crystals are very important for the application of light emitting devices. 本研究主要是著重於探討光子晶體合成、特性分析及其應用。在有關合成光子晶體之奈米二氧化矽顆粒方面， 發現在合成過程中利用氨水的溶量可以控制顆粒的大小。在將奈米顆粒排列成光子晶體的研究中， 嘗試了多種方法後， 發現垂直基座法為最快速有效的方法。從掃瞄電子顯微鏡的觀測， 證實奈米顆粒是以六角對稱排列成整齊的光子晶體。在光子晶體的特性分析中， 利用光穿透實驗， 發現電磁波穿透率最小的波長與奈米顆粒成正比關係， 這顯示出可以利用光子晶體來控制光的行為。最後，本研究將光子晶體與硫化鎘奈米顆粒結合，經由光激螢光譜， 證明光子晶體確實可以增進物體之發光效率,這對發光元件的應用， 將有很大的幫助， 可以節省大量的能源

在綠色能源中太陽能的利用充滿了無限的機會，其中利用太陽熱能發電的太陽能煙囪觀念有很大的潛力。在本研究中，我們以實驗的方法討論煙囪高度、入風口大小、管型等因素對solar chimney 效益的影響，發現就原先的觀念設計中，有相當大的改進空間。整體實驗而言，所改變的各項變數中，以管型之改變有最大的改進效益。就同長度直管與漸擴管而言，漸擴管在風速上有明顯改進效果，且以流速與截面積換算成效率，較原直管設計之效率高出約20 倍，因此推測漸擴管應用在現行之solar chimney 以改進效能是極有可行性的。研究中也發現煙囪管壁的熱傳導也會影響氣體的總體流動，使效率降低。相信此實驗之數據對日後嘗試對solar chimney 進行改進的研究者有相當之參考價值。Solar energy has a great market potential among many clean energies. The new solar chimney concept using solar thermal power in power generation may have a bright future. Experimental work was performed to study the energy conversion characteristics of a solar chimney. The air moving capability and the influences of chimney height, the shape of chimney and air entrance dimension were studied. It was found that there is a great room to improve the current solar chimney design and thus the efficiency. Overall speaking, the chimney pipe geometry may have the most significant impact on the improvement of performance. A diverged pipe configuration can induce nearly 20 times more flow than a traditional straight pipe. Another finding is the heat transfer effect on the chimney pipe may have the effect in reducing the flow. It is believed that the present study0 is valuable for those people in designing a future solar chimney.

When you draw a wet finger around the edge of a half filled wine glass, a sweet musical sound comes forth. The pitch of this sound is directly correlated to the amount of liquid in the glass- the higher the height of the liquid is, the lower the frequency is. It means that the shorter the air column in the glass is, the lower the frequency is. This phenomenon differs from the variance in pitch in a wind instrument. In a wind instrument such as a flute, the shorter the air column in its chamber is, the higher the resulting pitches are. In order to study the wine glass phenomenon, we used a piezoelectric crystal loudspeaker connected to an oscilloscope. We recorded the resulting data by using a digital video recorder to capture the images of the waveform of sound, and than analyzed the waveform by using the computer. Our conclusions are as follows: 1. The frequency of sound thus produced was the same whether we draw our finger around the rim, or we strike the glass rim. The higher the height of the liquid is, the lower the frequency is. But the frequencies vary when we strike the glass and when we blow on the edge. 2. When we used a glass without liquid in it, the frequency emitted when we drew our finger around the edge, this frequency varied inversely as the cube root of their weights. 3. In a glass with liquid, the emitted frequency did not have any correlation to the weight of the contents. By taking two identically filled glasses and placing in each a solid object of the same size but different weight, we were able to see that there was no change in the frequency emitted between the two glasses as long as the height of the liquid remained constant. 4. According to “The Flying Circus of Physics”, if we tap the side of a glass of beer, because of the air bubbles in the beer, the frequency emitted will be lower than that from a glass of pure water. This is according to the book, because the speed of sound is lower in air than in water, therefore the speed of sound in an air-water mixture would be lower than in pure water. The resonant frequencies of the mixture will also be lower. However, in our experiment, we discovered that\r when the glass contained air bubbles, the frequency emitted higher. Our explanation is that the sound emitted since the rim of the glass oscillated transversely, the frequency depends only on the retard of the rim and that the frequency is independent of the speed of sound. The intention of this research is to clarify the many misconceptions of this interesting phenomenon.以溼的手指在玻璃酒杯邊緣摩擦，會有悅耳的聲音，而且頻率會隨著內裝液體減少（空氣柱變長）而變高，這種變化與管樂器隨空氣柱的變長而音調變低不同，為了研究它的原因，我們利用壓電晶片喇叭連接到示波器上，並且利用數位錄影機錄下示波器上的訊號，再以電腦分析出瞬間的頻率，結果發現：一、摩玻璃杯與敲玻璃杯，杯所發出之頻率相同，都是所裝液體愈多發出之頻率愈低。但敲玻璃管與吹玻璃管所發出之頻率不同。二、不裝液體之高腳杯，摩擦時所發出之頻率與重量之立方根成反比。（與鐘相同）\r 三、裝液體之高腳杯發出之頻率，不再與總重量有關，而是與液體之高度有關，保持液體高度不變，即使在杯子中央加入不同重量之固體，杯子振動頻率還是不變。若改裝不同密度之液體，則密度愈大頻率愈低。四、在“The Flying Circus of Physics”書中提到輕敲裝有啤酒之杯時，會因杯中含有氣泡而聽到較低之音調，書中解釋是”空氣中之音速低於水中之音速，混有空氣之水中音速變低，其共振頻率也會降低。”但我們的實驗結果是有氣泡時頻率反而高。我們的解釋是杯子所發出之聲音是由於杯面之振動也就是杯壁的橫向振盪，振盪頻率與液體對杯壁之阻尼有關，但與液中聲速無關，密度愈大之液體阻尼愈大。有氣泡時接觸杯壁之液體變少，阻尼較少所以頻率高。希望本研究能使大多數人對這有趣之現象不再有誤解。

本研究目的在探索不同大小之氣泡在不同黏滯性液體中運動情形。實驗結果發現大氣泡向上運動的速度較大，其下方會漸漸向內凹。並且觀察到氣泡間結合時的相互作用：氣泡在相同黏滯性膠水中上升時，若下方氣泡體積較大，其較快的速率會使距離縮短。此時小氣泡的下半向內凹，大氣泡的下半則向外呈現流線型尖端並且在接近小氣泡時速率增加，最後與小氣泡結合。若上方氣泡體積很小，與下方大氣泡的距離縮短至相互貼合，小氣泡會先停留在大氣泡的上半表面，再沿大氣泡表面下滑至大氣泡的下半才與大氣泡結合。This research traces the motions of bubble with different volume in viscid liquid. The experimental results show that the bigger bubble rises at faster speed. The shape of the small bubble is round. As the volume of the bubble increases, it turns hamburger-like. And if the bubble is big enough, its underside would be concaved. In viscid liquid, the speed of the bubble is not smooth but waved. The smaller the bubble is, the more the variation in speed is. The interaction of two bubbles is also studied. There are two types of the combination of two bubbles. While the big one closes to the small one, it is accelerated. The underside of the small one becomes concave. And the big one becomes streamline shape. If the difference in volume between two bubbles is significant, the small one slides along the surface of the big one, and goes into the concave beneath it, then combines with it.