自組裝分子吸附於微懸臂梁之第一原理表面應力計算與跨尺度變形分析

First Principles Surface Stress Calculations and Multiscale Deformation Analysis of Self-assembled Monolayers Adsorbed on Microcantilever

石玉清(Yu-Ching Shih)

指導教授 ： 吳光鐘

共同指導教授 ： 陳俊杉(Chuin-Shan (David) Chen)

國立臺灣大學/工學院/應用力學研究所/博士(2013年)

https://doi.org/10.6342/NTU.2013.02731

摘要

奈米力學生物感測器具有快速、無需標的物及高靈敏度等特性，尤其在近年來預防醫學、食品安全及公共衛生意識提頭下逐漸受到重視。奈米力學生物感測器的結構基本上是以微懸臂梁為主，簡單製作流程是先在微懸臂梁上沈積一層金薄膜，然後再沈積一層硫醇自組裝分子，用來感測化學或生物分子。此硫醇自組裝分子或生物分子吸附在金薄膜表面時，會在金薄膜上產生表面應力的現象，然後造成微懸臂梁彎曲變形，透過觀察微懸臂梁的變形而達到感測生物或化學分子的目的。若能瞭解表面應力產生的來源，對於奈米力學生物感測器的設計能力必能提昇很多。尤其是基礎的硫醇自組裝分子所產生的微懸臂梁變形格外重要，因此本論文主要研究硫醇自組裝分子吸附於微懸臂梁生物感測器的表面應力，以及其對微懸臂梁變形與應力應變場的影響。
本研究首先利用第一原理計算探討與分析硫醇分子吸附在金表面的分子結構及吸附能，所用的理論是密度泛函理論，並使用最近發表的凡得瓦耳密度泛函來考慮分子間的作用力，所得到的分子結構及吸附能與實驗觀察到的結果一致。接著探討吸附所造成之微觀表面應力，我們發現硫醇分子吸附在金表面時，因為有金硫鍵結產生化學反應，金表面電子轉移金硫鍵上，使得金表面電子減少而產生表面壓應力。另外，我們也發現硫醇分子結構則因為凡得瓦耳作用力的關係，會產生表面張應力，其分子結構越長，產生的張應力越大。綜合以上兩項的表面應力結果則是異向性的表面應力。
本研究接著對微懸臂梁生物感測器提出一跨尺度計算方法，使用有限元素計算，將微觀異向性的表面應力帶入有限元素分析以求得感測器之巨觀變形及應力分佈。透過此計算方法，我們發現硫醇分子吸附在金表面的覆蓋率越高，微懸臂梁所產生的變形愈大。然而我們也發現硫醇分子結構越長，微懸臂梁所產生的變形愈小。此跨尺度計算方法能準確將微觀分子吸附現象轉換成巨觀微懸臂梁變形，不但適用在微懸臂梁感測器，也能適用於其他利用奈米力學感測器如薄膜型或奈米線等結構形式的感測器。

關鍵字

自組裝分子 ； 表面應力 ； 微懸臂梁 ； 密度泛函理論

並列摘要

Nanomechanical sensors, which are usually cantilever-shaped, have attracted increasing interests in the last decade as a promising tool for real-time and label-free detection of chemical gas and biomolecules. These adsorbates introduce surface stress and additional mass upon the detective layer of the sensors and sequentially transduce to a static displacement or a resonant frequency shift of the nanomechanical system. The induced surface stress is the key element to design the performance of the microcantilever sensors. The surface stress can be compressive or tensile, which will result in opposite deflection at the free end of the microcantilever beam. Understanding the physical phenomena of stress change and knowing how much of the changes are needed to design the nanomechanical sensors.
In this study, first-principles calculations were employed to investigate the adsorption-induced surface stress of self-assembled alkanethiolate monolayers on a sqrt(3)*sqrt(3)R30 Au(111) surface. A recently developed fully nonlocal van der Waals density functional was used to accurately account for the chain-chain interactions. Our results show that surface charge redistribution produces compressive surface stress, while chain-chain interactions produce tensile surface stress. The stress induced by surface charge redistribution is about one order of magnitude greater than that of chain-chain interactions. We observed that the chain-chain interactions play an important role in determining the molecular configuration during adsorptions, and also contribute significantly to the induced anisotropic tensile (positive) surface stress. As the chain length increases the tensile stress increases at a rate of ~0.32 (~0.18) N/m for the direction perpendicular (parallel) to the chain tilt direction.
We also propose a multiscale modeling framework based on density functional theory calculation and finite element method analysis. The framework has been verified with the Stoney formula. The macroscopic surface stress has also derived from local anisotropic surface stresses. The deflection of microcantilever sensors subjected to randomly distributed SAM domains has shown to be similar to that under the macroscopic isotropic surface stress, endorsed this proposed framework. For coverage effect, the average cantilever deflection has a proportional relationship with the coverage of the surface stress. For chain length effect, the deflections due to the adsorption of fully covered alkanethiolate on Au(111) decrease as the chain length increase. This framework can be used not only for alkanethiolates SAMs on Au(111) in microcantilever, but also for other molecular adsorptions on general substrates in nanomechanical sensors.

並列關鍵字

Self-assembled Monolayers ； Surface stress ； micro-cantilever ； Density functional theory

參考文獻

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