利用粗格化分子動力學以及相場法模擬柔版印刷製程的油墨行為

Abstract

導電油墨柔印製程是以具導電性質的懸浮溶液快速印製出電路之技術。此油墨印刷製程之關鍵在於油墨液體於網輥與版輥間的傳遞正確模擬。其需考慮多重物理機制，例如：油墨分散品質、流體力學及液氣兩相介面的問題，對此我們使用相場法計算多物理耦合的油墨液滴在印刷時的轉移過程。另外，單壁奈米碳管因其具有特殊的導電性質，也常被當作柔印製程裡的油墨材料。單壁奈米碳管在水溶液中的分散穩定性一直以來都是相當重要的議題。在本研究中，我們使用粗格化分子動力學 (Coarse-grained Molecular Dynamics) 與Derjaguin−Landau− Verwey−Overbeek (DLVO) 理論來預測碳管於水溶液中的穩定性。 分子動力學的模擬中，我們添加不同濃度的十二烷基硫酸鈉 (SDS) 活性劑 與三種不同管徑的碳管，分別是 (6, 6)、(12, 12)、(18, 18) SWCNTs 。利用 Langmuir isotherm 來描述 SDS 吸附於碳管上與懸浮在溶液中的數量關係。隨著吸附物 SDS 吸附量的增加，可防止碳管聚集的電雙層斥力會跟著上升。接著使用 DLVO 理論計算不同管徑的碳管在不同 SDS 活性劑濃度下的能量障壁，藉此預測碳管於溶液中的分散行為。由結果發現在活性劑濃度略大於臨界微胞濃度時，碳管會有最佳的分散效果，此結果與實驗的趨勢相符合。此外，本研究亦估算半徑為 0.35~0.7 nm的碳管，隨活性劑濃度碳管變化的 zeta potential (ζ-potential)。模擬與實驗結果於 SDS 濃度約為 30~80 mM 時， ζ-potential 的值相當接近。 柔印製程的解析度還會受到接觸角、滾輪半徑、油墨黏度等物理現象的影響，因此我們建立一個多物理耦合的平板對滾輪 (plate-to-roll) 的模型。運用 Navier–Stokes equations 來分析水珠流動的力學行為，並配合相場法模擬液氣介面演進，進而預測油墨在不同黏滯度與網輥帶墨速度下的轉移率。在油墨轉移的模擬結果發現，當接觸角愈小，油墨愈傾向於附著。而滾輪半徑愈大，油墨轉移量也會增大。但半徑大到某一程度時，對油墨液滴形同一平板，油墨轉移量上升的程度會趨緩，達一最大值。另外，當接觸角上升，油墨黏度對轉移率的影響會有反轉的現象。這些模擬結果亦和過去文獻做比較，也有相符的結果。故可藉此找出柔印滾輪幾何、油墨材料配比等設計之參考。

The resolution of flexographic printing process determines the quality of the printed electronic devices. The fundamental issues are to determine the quantity of the transferred ink and to produce the colloidal stabilized conductive ink. A commonly used ink material, the single-walled carbon nanotubes (SWCNTs), was chosen to be investigated. Therefore, a computational framework combining the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory with the coarse-grained molecular dynamics (CG-MD) simulations is developed to predict the stability of the SWCNTs in aqueous solutions. The dispersion of SWCNTs in aqueous solutions is an important issue. However, it is a challenging task since it requires the understanding of both macroscopic properties of the solution and the colloidal mechanism at the molecular level. The various concentration of surfactant, sodium dodecyl sulfate (SDS), is considered to each size of the SWCNTs, including (6, 6), (12, 12) and (18, 18). The Langmuir isotherm model is used to find the relationship between the amount of the adsorbed SDS and the bulk SDS concentration. With the increasing number of the SDS covered on SWCNTs, the surface charge density is also enhanced, and thus, greater electrical double layer repulsion is achieved to prevent the aggregation of the SWCNTs. The potential energy barrier as a function of the radius of the SWCNT and the SDS concentration can then be obtained by using DLVO theory so that the dispersion of the SWCNTs in the solution can be predicted. The results suggest an optimal surfactant concentration which can stabilize the SWCNTs in the solution. Also, we calculate the zeta potential for SWCNTs with the radius of 0.35~0.7 nm which has a good agreement with the experimental results when the concentration of SDS is within 30~80 mM. The current framework is expected to provide the guidance for the design of the concentration of SDS surfactants and the radius of SWCNTs in dispersion experiments. Furthermore, to study another issue of flexographic printing processes, it is necessary to consider multi-physics mechanics such as fluid mechanics and the interface evolution between liquid and air. In the current work, a multi-physics model was developed by coupling Navier–Stokes equations and phase field method to analyze the behavior of the droplets and to model the air-liquid interface. We proposed a plate-to-roll model to calculate the ink transfer ratio by changing the contact angle, the radius of the roller, and the viscosity of the ink, which affect the flexographic printing. We simulated the effects of these different parameters and compared the results with the literature. Modeling and simulations proposed herein should be useful to improve designs of the geometry of roller, properties of the ink, and printing accuracy.