Abstract
中文摘要 碳黑及矽膠等次毫米級填充物填充之橡膠系統，其動態機械性質隨填充量不同會有極大差異，當填充物含量低於臨界含量，填充物會因為粒子表面作用力影響而相互糾集成一次凝聚體分散於橡膠基材中，當填充物含量超過臨界含量，一次凝聚體會相互連接形成連續的二次凝聚體網狀結構，在動態變形時，隨變形量不同，二次凝聚體會產生不同程度的破壞造成非線性現象，不能採用傳統線性黏彈性理論來加以解釋。本研究利用碎形理論及浸透理論來探討上述非線性現象，以L-N-B模型將二次凝聚體簡化為單鍵鏈及團體相互連接而成的網狀結構。 重要的物理參數包含(1)單鍵鏈數目密度分佈函數，(2)對應於橡膠相非線性行為的密度分佈函數及(3)顯降伏應變振幅。單鍵鏈受外力變形的特性相當於角變形元件和張力變形元件串聯而成的機械元件。其中，角變形元件受填充物周圍的固著橡膠物性影響而張力元件則決定於填充物間的凡得瓦作用力。利用此一模型成功地解釋在小應變條件下（應變量約在0.1%至100%之間）填充橡膠之巨觀動態非線性特性與微觀之填充材料及橡膠基材物性間的相互關係。在填充橡膠二次凝聚體於動態變形過程中的破壞及再結合機構方面，分別採用零應變再結合模型及應變極限點再結合模型進行模擬分析，與實驗結果比較顯示應變極限點再結合模型和填充橡膠的實際動態行為一致，意即二次凝聚體的破壞及再結合位置接近應變極限點而非應變平衡點。在貯存模數方面，經過標準化後，滿足唯一函數特性。對各種碳黑填充的填充橡膠系統，唯一函數的參數近乎為一常數，同時在L-N-B模型中團體和單鍵鏈的分佈情形也都相似。溫度對動態機械模數的影響方面，有關凡得瓦力論及固著橡膠論之間的爭議，在本研究中獲致圓滿結論。當溫度低至固著橡膠的玻璃轉化溫度以下時填充物周圍橡膠的彈性係數趨近於填充物的彈性係數，此時填充橡膠的動態機械特性不再適用L-N-B模型。在填充物種類的影響方面，研究結果顯示顯降伏應變振幅可以使用凡得瓦力模型來解釋，顯降伏應變振幅正比於填充物間的作用力常數而反比於單鍵鏈上單鍵的長度。由P1型矽膠和N330型碳黑填充的橡膠系統分析結果確認前者的顯降伏應變振幅值約為後者的20倍，和矽膠粒子間作用力大於碳黑間作用力有直接關係。在基材的影響方面，填充物在填充油系統中和在填充橡膠系統中的碎形結構分佈情形並不相同，前者碎形結構較為鬆散而後者較為緻密，造成前者顯降伏應變振幅約比後者小一個數量級。在混練時間影響方面，隨混練時間增加，唯一函數的參數之絕對值逐漸增加並趨近常數值，也代表L-N-B鏈上單鏈數目隨混練時間增加而降低並趨近常數值。 在L-N-B模型的應用限制方面，除了溫度必須高於固著橡膠的玻璃轉化溫度之外，當應變量低至接近顯降伏應變振幅時或是在非常高溫的條件下，團體內部的變形諸如基本粒子間的滑動磨擦和封閉橡膠的變形對填充橡膠動態機械特性的影響都必需加以考慮。AbstractA model for strain-dependent dynamic properties of filler loadedrubber systems ( Payne effect ) has been derived based on theLinks-Nodes-Blobs (L-N-B) model of percolation theory. It isthe first time that a L-N-B model is applied in the study ofdynamic properties of filled rubbers. A blob in the L-N-B modelcan be a primary aggregate or a cluster formed by coagulation ofprimary aggregates, occluded rubber and bound rubber. The linkscorrespond to tenuous filler bondings between dense filleraggregates. The chains made of links and blobs are called as L-N-B chains. The connected points among L-N-B chains are callednodes. During deformation, the blobs are assumed entirely rigidso that they are not deformed. However, the links deform undertension, bending and/or torsion. The links even tend to breakoff when some failure strain is attained.Important parameters in the model include (1) the average forceconstant of a L-N-B chain, (2) the apparent yield strainamplitude, (3) the storage modulus at large strain and the lossmodulus at large strain, (4) the critical length of the L-N-Bmodel, (5) the density distribution function of the number ofsingly connected bonds, and (6) the density distributionfunction that accounts for the break-down of secondaryaggregate attributed to non-linear rubber phase deformation.The average force constant corresponds to the angulardeformation element ( primarily attributed to bound rubber) inseries with the tension element (controlled by van der Waalsforce between fillers ).Simulation results indicate that the apparent yield strainamplitude and the density distribution function control thebreak-down and recombination of the filler network. Tworecombination mechanisms are adopted in this study. Result ofsimulations from the extreme ends recombination mechanismmatches the experimental data better than that from the zerostrain recombination mechanism. With the combination of van derWaals force model, these parameters can be described in terms ofbasic physical material properties of filler and rubber matrix.The temperature dependence of dynamic properties of filledrubbers is successfully described in terms of the seriescombination of the angular deformation element in series withthe tension element. Moreover, normalized storage modulus canbe expressed as a master curve. The parameter of the mastercurve is almost a constant for different carbon black filledsystems. The distributions of blob and link in a L-N-B modelare similar for carbon black filled rubber systems. Besides theeffect of fillers (carbon black vs. silica), the effect ofmatrix ( filler-in-oil vs. filler-in-rubber) and the effect ofmixing time are discussed too. The limitationof L-N-B model is also discussed. The result of simulationssuggests that, at very small strain region, deformation insideof aggregates such as slippage between primary particle surfaceand deformation of occluded rubber contribute some degree ofhysteresis loss.