奈米顆粒為直徑數十奈米至數百奈米的微小顆粒，如將奈米顆粒加入至潤滑劑中作為添加物時，可有效地提高產能與器械的耐久性，因此奈米顆粒的磨潤性質以及奈米顆粒何以能夠帶來如此優異的潤滑效益，向來是學者們不斷探討的議題。其中，層狀結構的類富勒烯奈米顆粒(inorganic fullerene-like nanoparticle，IF-NP)在低接觸應力如有產生側向位移，可以觀察到滑動與滾動等不同的機制。但在奈米尺度下，滾動行為是否能為摩擦介面帶來優異的潤滑效果，直至今日仍缺乏有力的證據。同時，當顆粒在黏著接觸下，黏著遲滯效應扮演著重要的角色，但此部分在奈米尺度下對奈米顆粒的影響尚未釐清。

故本研究的目的有二，第一為利用分子動力學模擬，探討二硫化鉬(MoS2)類富勒烯奈米顆粒於微觀尺度下的摩擦機制，以闡明在奈米尺度下的滾動機制實為重要的潤滑機制之一，同時探討影響其滾動的微觀機制，希冀能藉此提供一設計準則，作為未來設計具有高度潤滑效果的奈米顆粒的基礎；第二為指出黏著遲滯效應在奈米顆粒處於臨界滾動狀態時的影響，並將分子動力學模擬的結果與連體理論比較。

到目前為止，鮮少有能完整描述Mo-S系統之勢能函數的分子動力學模擬軟體，故本研究將一描述Mo-S之共價鍵系統的經驗勢能函數實作於分子動力模擬軟體(LAMMPS)中。因LAMMPS為目前世界上普遍使用之分子動力學模擬軟體，故本研究之實作將有利於後續學者們在Mo-S系統上的研究。本研究的模擬結果證實了奈米顆粒的滾動行為能夠帶來高達30%的磨潤效益，此結果證明了奈米顆粒的滾動行為確實為提升介面潤滑重要的因素之一。此外，本研究發現其奈米顆粒的微觀滾動機制有一定程度的重複性，故將其機制歸類為兩組不同的滾動模式(Patterns)。

黏著遲滯(adhesion hysteresis)效應是影響奈米顆粒於微觀尺度下滾動機制的重要因素。故本研究延伸連體理論的觀點，在原子尺度下解釋黏著遲滯效應對奈米顆粒滾動行為的影響。本研究參考荷蘭學者Krijt所提出的滾動摩擦理論，計算奈米顆粒欲滾動的瞬間所造成的能量釋放率差值變化，此差值即為黏著遲滯效應。結果指出，能量釋放率差值會在欲滾動的瞬間出現高峰，亦與理論所預測的趨勢相同。因此，本研究指出此臨界的能量釋放率差值為奈米顆粒臨界滾動狀態下的材料性質，並且可以利用此性質作為判斷奈米顆粒是否容易滾動的依據。

本研究利用分子動力學模擬探討奈米顆粒的微觀磨潤機制，並將Mo-S系統之勢能函數於分子動力模擬軟體(LAMMPS)中實作。本研究證實了奈米顆粒滾動行為確實為重要之潤滑機制之一，並且發現其一致的微觀滾動機制。本研究亦發現黏著遲滯的效應如何體現在奈米顆粒的臨界滾動行為中。

Nanoparticle (NP) is a nano-scale material with diameters ranging from tens to hundreds of nanometer. Treating this nanoparticle as lubricant additives can further improve mechanical performance and durability. Hence the tribological properties of nanoparticle have gained much attention and the lubrication mechanisms of nanoparticle have been considered as an important issue. The single inorganic fullerene-like nanoparticle (IF-NP) would display rolling and sliding behavior when nanoparticle is subjected to lateral displacement under low contact stress. However, it has not been revealed that whether the rolling behavior of IF-NP is one of the significant lubrication mechanisms. Meanwhile, under contact stress, adhesion hysteresis play an important role in the rolling mechanism. However, it is not clear whether such effect influence NP rolling mechanism.

The objectives of this study are twofold, first to study the friction coefficients and tribological mechanisms of a single molybdenum disulfide (MoS2) IF-NP using molecular dynamics simulation. It has been interpreted in this work that the rolling behavior is indeed a remarkable lubrication mechanism. Through these results, we can provide a guideline which will enable the design of NP with high performance of lubrication. The second objective is to address the effect of adhesion hysteresis on the onset of the rolling of nanoparticles. The results from the atomistic studies are compared with analysis from the elasticity theory.

Until now, there are few appropriate molecular dynamics simulator which can describe the Mo-S covalent bond system. In the present study, a covalent bond potential describing the interaction between molybdenum and sulfur atoms has been implemented in LAMMPS. This implementation will benefit researchers to undertake the future studies in Mo-S system. It has been reported that rolling behavior could result in significant lubricant effects. From our results, the rolling behavior could reduce the friction for about 30%, which demonstrates that the rolling behavior is a significant lubricant mechanism for MoS2 nanoparticle. In addition, we observed the repeating behaviors when nanoparticle is rolling and categorized these behaviors into two rolling patterns.

The adhesion hysteresis plays an important role in the rolling mechanism. We therefore extended the continuum theory to atomic scale for interpreting the influence of adhesion hysteresis within rolling behavior. Present study indicates that the adhesion hysteresis represented by a difference of energy release rates, is apparent at the onset of rolling. The peak value of difference of energy release rates occurs when nanoparticle starts to roll. This result has agreed well with the rolling friction theory proposed by Krijt. Therefore, we conclude that the critical difference of energy release rates is a material property for the onset of rolling. This property can be used to determine whether a given nanoparticle is easy to roll.

From our study, the tribological mechanisms have been investigated using molecular dynamics simulation. A Mo-S system bond-order potential has been implemented in LAMMPS. We conclude that the rolling behavior is certainly an important lubricant mechanism, which has been demonstrated in present study. We also observe repeating behaviors when MoS2 nanoparticle is rolling. Moreover, how the adhesion hysteresis influences the onset of rolling of nanoparticle has been revealed as well.

致謝 I
中文摘要 II
ABSTRACT IV
目錄 VI
圖目錄 IX
表目錄 XII
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 8
1.3 論文架構 9
第二章 類富勒烯奈米顆粒的微觀磨潤機制 10
2.1 勢能函數 10
2.1.1 用來描述Mo-S系統的Reactive Many-body Bond-order Potential 10
2.1.2 勢能函數的驗證 14
2.2 定義與計算正向力與摩擦力 17
2.3 摩擦係數與滾動指數計算 18
2.4 模擬系統設置 20
2.4.1 模型設置 20
2.4.2 系統控溫 21
2.4.3 模擬步驟 21
2.5 模擬實作 22
2.5.1 模擬實作軟體 22
2.5.2 環境參數設置 23
2.5.3 模擬流程的實作 24
2.6 結果與討論 27
2.6.1 模擬結果 27
2.6.2 二硫化鉬奈米顆粒的磨潤機制與整體性質 32
2.6.3 因滾動機制帶來的潤滑效益 33
2.6.4 奈米顆粒的滾滑行為與接觸面積的關係 36
2.6.5 奈米顆粒的stick-slip行為 41
2.7 結語 44
第三章 以黏著遲滯解釋奈米顆粒臨界滾動行為的探討 47
3.1 黏著接觸下的滾動摩擦預測理論 47
3.2 能量釋放率在離散系統下的計算方法 49
3.3 勢能函數 51
3.4 模擬系統設置 53
3.4.1 模型設置以及系統控溫 53
3.4.2 模擬步驟 53
3.5 結果與討論 55
3.5.1 奈米顆粒臨界滾動狀態下的黏著遲滯效應 55
3.5.2 半徑以及滾動摩擦與滾動位移的關係 59
3.6 結語 60
第四章 結論與未來研究方向 61
4.1 結論 61
4.2 未來研究方向 62
參考文獻 64

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