開發以AFM圖像分析胎面膠中二氧化矽奈米顆粒聚集體尺寸及結構之方法

Abstract

奈米複合材料(nanocomposites)為現今無論是學術研究或工業界中都十分常見的材料強化方式，由於其中填料(filler)之分散性通常與性能息息相關，因此可以觀測到奈米等級填料於基材中之聚集結構的小角度X光散射(SAXS)便成為許多人在進行相關研究時不可或缺的工具。然而由於SAXS的使用權限受限，使用時間及次數也極為有限，因此無論是對一般研究單位或企業來說都屬於無法輕易取得之工具。因此本研究希望開發出以取得門檻較低之原子力顯微鏡(AFM)作為工具，並以含有奈米級二氧化矽填料及橡膠基材之輪胎胎面膠作為研究對象，透過分析AFM圖像，希望能開發出能在定量或定性上達到近似由SAXS之奈米聚集結構與尺寸之分析方法。也因此本研究中將以SAXS圖譜及擬合所得粒徑做為我們的分析方法成功與否之評斷標準。 首先我們以市面上之付費顯微鏡圖像分析軟體SPIP進行二氧化矽聚集體尺寸之分析，並針對其中需設定之參數進行討論。我們比較了兩種設定影像閾值之方法，包括以胎面膠配方計算圖像中二氧化矽之理論覆蓋率，或是以高斯分布對圖像之相位分布圖進行擬合。將以上兩種方法之分析結果與SAXS擬合結果比較後我們發現，兩種方法皆無法完全重現由SAXS數據分析得到之粒徑數值及變化趨勢。我們發現圖像分析軟體在分析上存在無法避免之誤差，一般情況下都會導致聚集體粒徑被高估。因為無法以合適標準訂定圖像分析軟體中之參數下，我們轉而研究以無須人為設定參數的方法對AFM圖進行粒徑分析。 研究第二部份我們仿照分析SAXS之散射圖譜原理，希望能透過對AFM圖像中之二氧化矽分布進行二維傅立葉轉換後再進行數據處理，在不需人為設定參數之情形下，得到帶有結構資訊之圖譜並從中擷取聚集體尺寸等資訊。我們首先以自行繪製之簡單圖形對撰寫之圖像轉換程式進行測試，以確認其能根據不同尺寸與結構的圖像，反映出不同之圖譜特徵。結果證實了我們對單一圓形圖像之轉換能得到與理論相近之圖譜特徵，在圖像中具有多顆圓形時，顆粒之間結構的改變也能從圖譜對應區域中看到不同表現。 在對實驗獲得的AFM圖進行轉換之前，我們嘗試將對應胎面膠中二氧化矽結構之SAXS散射公式降階至二維，並希望以此公式進行擬合以得到定量之分析結果與SAXS比較。然而我們發現樣品內部之三維碎形結構(fractal)在二維AFM圖上會被破壞，導致其實際結構無法以推導出之公式描述，因此我們轉而以圖譜中之轉折位置來估算聚集體尺寸。最終我們透過對圖像進行二維傅立葉轉換並分析所得圖譜中轉折位置之方法，減少一般圖像分析方法中受到人為設定參數的影響，成功自正新輪胎T系列樣品之AFM圖中得到與SAXS相似的聚集體尺寸分析結果。

Nanocomposites are materials filled with nanofillers and they are commonly used in both academic research and industry. Since the dispersion of nanofillers in nanocomposites is always closely related to their performance, small-angle X-ray scattering (SAXS) has become an essential tool to determine the aggregation structure of nanofillers in the nanocomposites. However, because the access to SAXS is very limited, it is not a feasible analytical tool for ordinary industries or researchers. Therefore, a new method that is more accessible than SAXS but able to give comparable results is highly desired. In this study we aim to develop an analytical method using Atomic force microscopy (AFM) to obtain the characteristic size and structure of the fillers in nanocomposites. Tire tread compounds containing silica nanoparticles dispersed in rubbers were employed as the standard samples to test our methods. In the first part of the study, we used SPIP, a commercially available microscope image analysis software, to determine the size of silica cluster in AFM images. We investigated two methods of choosing the threshold values dividing silica and rubber: setting the value either by using a theoretical value estimated from the tread compound formulation recipes or by fitting the phase angle histograms of the AFM image with Gaussian distributions. After comparing the characteristic radius of silica clusters obtained from these two methods with those from SAXS, we found the cluster sizes from AFM images did not coincide with the standards. We concluded that the typical image analysis methods have inherited flaws that easily lead to an overestimation of the cluster size and therefore reliable results cannot be obtained by this method. In the second part of this study, we proposed an entirely different method that analyzes the silica cluster size from the two-dimensional Fourier transform of AFM images. This method is based on the three-dimensional scattering theory of SAXS and needs no preset parameters. To evaluate the feasibility of this method, we used images contain a single circle and assemblies of multiple circles with certain structure to see if the transformed spectrums could reveal the characteristics of the images. Although not in exact agreement with the theoretical prediction, the transferred spectrum changes accordingly with the size and arrangement of the circles in the images. To obtain quantitative analysis results for the transformation spectrum of real AFM images, we also revised the SAXS scattering formula corresponding to the silica structure in the tread compound to a two-dimensional version. However, we found that the fractal structure of silica is not reserved in two-dimensional AFM images. Therefore, the two-dimensional formula we derived does not correspond to the silica distribution in AFM images. Failing to obtain quantitative formula to fit the transferred spectrum, we then estimated the characteristic cluster size from the transition position in the transferred spectrum. With this method, we were able to obtain from AFM images the characteristic cluster sizes very close to those from SAXS without using parameters determined by users.