碳纳米结与柔性电子器件力学性能的数值分析
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摘要
柔性电子器件可以重复拉伸、压缩、折叠、扭转等和应用于复杂曲面,与传统电子器件相比,柔性电子器件在生物医学、显示、成像系统、电子皮肤和太阳能电池板等领域有着广阔的应用前景。提高电子器件的柔性有两种可行的方法：材料引入柔性和结构引入柔性。材料引入柔性是指使用具有优异力学、电学性能的新材料,如碳纳米管等,替代极限应变只有1-2%的硅,使柔性电子器件具有柔性；结构引入柔性是指使用价格便宜、制备工艺成熟的硅,改变电子器件的结构,使之具有柔性。
虽然关于柔性电子器件的研究取得了较大的发展,但在材料引入柔性和结构引入柔性的力学分析上仍然处于探索阶段。本文基于分子动力学、分子结构力学、解析模型和有限元模拟等方法,在材料引入柔性方面研究了纳米结的压缩屈曲和拉伸破坏力学行为；在结构引入柔性方面分析了应变隔绝效应、材料粘弹性引起的速度对界面脱粘的影响和柔性电子器件制备过程的应变水平。本文所取得的研究进展包括：
基于分子动力学方法模拟不同应变率下碳纳米结的压缩屈曲行为,研究结果表明低应变率范围内,碳纳米结发生准静态屈曲变形,应变率对临界压缩应变影响不明显；高应变率范围内,碳纳米结表现出类似波传递的变形模式。分子动力学和分子结构力学方法揭示碳纳米结的临界压缩应变和屈曲模式与其长度、直径和直径差相关。同时,分子动力学方法发现,碳纳米结长度增加时,临界压缩应变呈上升—下降趋势,屈曲模式由壳状屈曲转变为柱状屈曲。碳纳米结临界压缩应变的上升—下降趋势揭示碳纳米结存在最优长度,使碳纳米结屈曲前可以承受最大载荷,即最大屈曲载荷。
采用分子动力学方法研究不同应变率、温度和几何因素下的碳纳米结拉伸失效行为,研究结果表明碳纳米结的屈服应变与对数应变率和温度分别近似成线性关系。同时,基于线性回归的修正转换态理论模型可以系统预测特定应变率和温度条件下的屈服应变,预测数值与分子动力学模拟结果吻合。分子动力学方法揭示受温度和几何因素影响碳纳米结呈现不同的拉伸破坏模式：脆性和韧性断裂。本文还澄清已有工作中直径决定失效模式的结论的局限性,提出长细比是决定碳纳米结的失效模式的几何因素的概念。
本文还研究了柔性电子器件中网格结构、结构性基体和粘附层导致的应变隔绝效应。有限元模拟结果表明基于曲桥、细带的网格结构和结构性基体可以隔绝基体应变,降低电子元件中的应变,从而提高电子器件的柔韧性和可延展性。例如,由结构性基体构成的电子器件承受124%的变形时,电子元件只有0.3%的压缩变形,远小于其极限应变。同时有限元模拟结果揭示结构性基体中深沟的宽高比h/a存在阈值,使电子元件应力最小。基于剪滞假设的解析模型和有限元模拟结果表明,电子元件层与基体层间的粘附层的厚度、柔度和电子元件层的长度决定电子元件应变。可以通过增加粘附层的厚度、降低粘附层的杨氏模量和电子元件层的长度,更有效地隔绝基体应变,降低电子元件应变。
将转印过程中界面脱粘问题简化为裂纹扩展问题,使用Prony系数表征转体材料PDMS的粘弹性属性,研究特定的界面结合能时由于材料粘弹性引起的提起速度对界面脱粘的影响。当裂纹尖端的能量释放率超过界面结合能时,裂纹由闭合状态转变为张开状态,界面发生脱粘。解析模型和有限元模拟结果表明,低速范围内,随着提起速度的增加,临界拉力呈递增走势；当速度达到50um/s时,临界拉力趋于稳定数值。
分析了引入二维预应变的柔性电子器件的制备过程,提出简化解析模型,预测处于平面、半球形和局部压平状态时弹性基体的应变和电子元件的位置分布以及制备过程中电子元件的最大应变。解析模型和有限元模拟结果表明,简化解析模型可以很好地描述不同状态时弹性基体和电子元件应变水平。
本文对柔性电子器件的材料引入柔性和结构引入柔性的研究,可以指导柔性电子器件的设计和应用,将促进柔性电子器件的发展。
Flexible electronic devices can undergo repeated tensile, compressive, folded and twisted deformations, and they are suitable to be applied to complex curvilinear surfaces. Therefore, compared with traditional electronic devices, flexible electronic devices have better application prospects in the fields of bio-medical systems, displaying systems, imaging systems, skin electronics and solar cell circuit board. There are basically two approaches to improve the flexibility of electronic devices:the material-induced flexibility and the structure-induced flexibility. The former is achieved by using new materials (such as carbon nanotube) with extraordinary mechanical and electrical properties instead of silicon, which has only1-2%failure strain. The latter is acquired by changing the structure of electronic device while still using silicon, which has the mature fabrication technology and low price.
Although the researches on the flexible electronic devices have achieved great development, the mechanical analysis on the material-induced flexibility and the structure-induced flexibility is still at the exploratory stage. Based on the molecular dynamics (MD), the molecular structural mechanics (MSM), the analytical model and the finite element analysis (FEA) approaches, this dissertation studies the compressive buckling and the tensile failure behaviors of carbon nanotube (CNT) junctions in the filed of the material-induced flexibility, and the strain isolation effect, the velocity influence on the interfacial delamination due to the viscoelastic property of PDMS stamp and the strain distribution during the fabrication process of the flexible electronic devices. The accomplished studies are as follows:
Based on the MD simulation, the compressive buckling behavior of CNT junctions has been studied under different strain rates. It is revealed that in the low strain rate range, the junction is prone to quasi-static buckling deformation and the influence of strain rate on the critical compressive strain is not evident; in the high strain rate range, the failure mode of junction is wave propagation. The MD simulation and the MSM approach reveal that the critical compressive strain appears to have an increasing-decreasing trend and the buckling mode transfers from the shell buckling to the column bucking with increase of the length. The increasing-decreasing trend suggests the optimal value of junction length, at which the junction can sustain the biggest load before the onset of buckling, namely the biggest buckling load.
The MD simulations have been carried out to study the tensile failure behavior of the junction with different strain rates, temperatures and geometrical factors. It is found that the yield strain has a linear relationship with the temperature and the logarithmic strain rate, respectively. Meanwhile, based on the linear regression approach, the MTST model is capable of systematically predicting the yield strain at specified strain rate and temperature, and the predicted yield strain agrees well with that obtained by the MD simulation. The MD simulations reveal that with different temperatures and geometrical factors the junction has different failure modes:the brittle or ductile failure. This dissertation clarifies the conclusion that diameter determines the failure mode, and proposes the concept that the aspect ratio is the geometrical factor which determines the failure mode.
This strain isolation effect invoked by the mesh structure, the structural substrate and the adhesive layer is studied. The FEA results show that the mesh structure (based on the bent bridge and the filamentary serpentine) and the structural substrate can isolate the strain from the substrate, lower the strain of the electronic component and improve the flexibility and stretchablity of the electronic devices. For example, when the flexible electronic devices based on the structural substrate undergo a124%deformation, the electronic component only has a0.3%compressive strain, which is much lower than its intrinsic limit strain. To minimize the stress of electronic component, the FEA analysis also suggests the optimal value of h/a ratio of the trench of the structural substrate. The analytical model based on the shear-lag assumption and the FEA results show that the strain of the electronic component is related to the length of the electronic component layer, the thickness and the Young's modulus of the adhesive layer. It is also founded that a relatively thick, complicant adhesive layer is effective to reduce the strain of electronic component, and so is a relatively short electronic component layer.
This dissertation proposed a simplifed analytical model (crack propagtion model) for the interfacial delamination during the transfer printing process. The Prony parameters are used to model the viscoelastic properties of PDMS stamp and the influence of the pick-up velocity on the interfacial delamination due to the viscoelastic properties of PDMS is explored. When the energy release rate of the crack tip exceeds the critical adhesive energy, the status of the crack will be transferred from close to open, resulting in an interfacial delamination. The analytical model and the FEA results reveal that the required pulling-off force increases with the increase of the velocity at a low pick-up velocity; when the velocity reaches50μm/s, the required pulling-off force will be saturated.
This fabrication process of the flexible electronic devices with two-dimensional prestrain is investigated. A simplified analytical model is proposed to obtain the strain of elastic substrate, the profile and the max strain of the electronic component at flat, hemispherical and punched states. The analytical model and the FEA simulations results show that this analytical model can well predict the strain distribution of the elastic substrate and the electronic components.
This dissertation further studies the material-induced flexibility and the structure-induced flexibility of the flexible electronic devices. This study is useful in guiding the design and application of the flexible electronic devices and promoting the development of the flexible electronic devices.
虽然关于柔性电子器件的研究取得了较大的发展,但在材料引入柔性和结构引入柔性的力学分析上仍然处于探索阶段。本文基于分子动力学、分子结构力学、解析模型和有限元模拟等方法,在材料引入柔性方面研究了纳米结的压缩屈曲和拉伸破坏力学行为；在结构引入柔性方面分析了应变隔绝效应、材料粘弹性引起的速度对界面脱粘的影响和柔性电子器件制备过程的应变水平。本文所取得的研究进展包括：
基于分子动力学方法模拟不同应变率下碳纳米结的压缩屈曲行为,研究结果表明低应变率范围内,碳纳米结发生准静态屈曲变形,应变率对临界压缩应变影响不明显；高应变率范围内,碳纳米结表现出类似波传递的变形模式。分子动力学和分子结构力学方法揭示碳纳米结的临界压缩应变和屈曲模式与其长度、直径和直径差相关。同时,分子动力学方法发现,碳纳米结长度增加时,临界压缩应变呈上升—下降趋势,屈曲模式由壳状屈曲转变为柱状屈曲。碳纳米结临界压缩应变的上升—下降趋势揭示碳纳米结存在最优长度,使碳纳米结屈曲前可以承受最大载荷,即最大屈曲载荷。
采用分子动力学方法研究不同应变率、温度和几何因素下的碳纳米结拉伸失效行为,研究结果表明碳纳米结的屈服应变与对数应变率和温度分别近似成线性关系。同时,基于线性回归的修正转换态理论模型可以系统预测特定应变率和温度条件下的屈服应变,预测数值与分子动力学模拟结果吻合。分子动力学方法揭示受温度和几何因素影响碳纳米结呈现不同的拉伸破坏模式：脆性和韧性断裂。本文还澄清已有工作中直径决定失效模式的结论的局限性,提出长细比是决定碳纳米结的失效模式的几何因素的概念。
本文还研究了柔性电子器件中网格结构、结构性基体和粘附层导致的应变隔绝效应。有限元模拟结果表明基于曲桥、细带的网格结构和结构性基体可以隔绝基体应变,降低电子元件中的应变,从而提高电子器件的柔韧性和可延展性。例如,由结构性基体构成的电子器件承受124%的变形时,电子元件只有0.3%的压缩变形,远小于其极限应变。同时有限元模拟结果揭示结构性基体中深沟的宽高比h/a存在阈值,使电子元件应力最小。基于剪滞假设的解析模型和有限元模拟结果表明,电子元件层与基体层间的粘附层的厚度、柔度和电子元件层的长度决定电子元件应变。可以通过增加粘附层的厚度、降低粘附层的杨氏模量和电子元件层的长度,更有效地隔绝基体应变,降低电子元件应变。
将转印过程中界面脱粘问题简化为裂纹扩展问题,使用Prony系数表征转体材料PDMS的粘弹性属性,研究特定的界面结合能时由于材料粘弹性引起的提起速度对界面脱粘的影响。当裂纹尖端的能量释放率超过界面结合能时,裂纹由闭合状态转变为张开状态,界面发生脱粘。解析模型和有限元模拟结果表明,低速范围内,随着提起速度的增加,临界拉力呈递增走势；当速度达到50um/s时,临界拉力趋于稳定数值。
分析了引入二维预应变的柔性电子器件的制备过程,提出简化解析模型,预测处于平面、半球形和局部压平状态时弹性基体的应变和电子元件的位置分布以及制备过程中电子元件的最大应变。解析模型和有限元模拟结果表明,简化解析模型可以很好地描述不同状态时弹性基体和电子元件应变水平。
本文对柔性电子器件的材料引入柔性和结构引入柔性的研究,可以指导柔性电子器件的设计和应用,将促进柔性电子器件的发展。
Flexible electronic devices can undergo repeated tensile, compressive, folded and twisted deformations, and they are suitable to be applied to complex curvilinear surfaces. Therefore, compared with traditional electronic devices, flexible electronic devices have better application prospects in the fields of bio-medical systems, displaying systems, imaging systems, skin electronics and solar cell circuit board. There are basically two approaches to improve the flexibility of electronic devices:the material-induced flexibility and the structure-induced flexibility. The former is achieved by using new materials (such as carbon nanotube) with extraordinary mechanical and electrical properties instead of silicon, which has only1-2%failure strain. The latter is acquired by changing the structure of electronic device while still using silicon, which has the mature fabrication technology and low price.
Although the researches on the flexible electronic devices have achieved great development, the mechanical analysis on the material-induced flexibility and the structure-induced flexibility is still at the exploratory stage. Based on the molecular dynamics (MD), the molecular structural mechanics (MSM), the analytical model and the finite element analysis (FEA) approaches, this dissertation studies the compressive buckling and the tensile failure behaviors of carbon nanotube (CNT) junctions in the filed of the material-induced flexibility, and the strain isolation effect, the velocity influence on the interfacial delamination due to the viscoelastic property of PDMS stamp and the strain distribution during the fabrication process of the flexible electronic devices. The accomplished studies are as follows:
Based on the MD simulation, the compressive buckling behavior of CNT junctions has been studied under different strain rates. It is revealed that in the low strain rate range, the junction is prone to quasi-static buckling deformation and the influence of strain rate on the critical compressive strain is not evident; in the high strain rate range, the failure mode of junction is wave propagation. The MD simulation and the MSM approach reveal that the critical compressive strain appears to have an increasing-decreasing trend and the buckling mode transfers from the shell buckling to the column bucking with increase of the length. The increasing-decreasing trend suggests the optimal value of junction length, at which the junction can sustain the biggest load before the onset of buckling, namely the biggest buckling load.
The MD simulations have been carried out to study the tensile failure behavior of the junction with different strain rates, temperatures and geometrical factors. It is found that the yield strain has a linear relationship with the temperature and the logarithmic strain rate, respectively. Meanwhile, based on the linear regression approach, the MTST model is capable of systematically predicting the yield strain at specified strain rate and temperature, and the predicted yield strain agrees well with that obtained by the MD simulation. The MD simulations reveal that with different temperatures and geometrical factors the junction has different failure modes:the brittle or ductile failure. This dissertation clarifies the conclusion that diameter determines the failure mode, and proposes the concept that the aspect ratio is the geometrical factor which determines the failure mode.
This strain isolation effect invoked by the mesh structure, the structural substrate and the adhesive layer is studied. The FEA results show that the mesh structure (based on the bent bridge and the filamentary serpentine) and the structural substrate can isolate the strain from the substrate, lower the strain of the electronic component and improve the flexibility and stretchablity of the electronic devices. For example, when the flexible electronic devices based on the structural substrate undergo a124%deformation, the electronic component only has a0.3%compressive strain, which is much lower than its intrinsic limit strain. To minimize the stress of electronic component, the FEA analysis also suggests the optimal value of h/a ratio of the trench of the structural substrate. The analytical model based on the shear-lag assumption and the FEA results show that the strain of the electronic component is related to the length of the electronic component layer, the thickness and the Young's modulus of the adhesive layer. It is also founded that a relatively thick, complicant adhesive layer is effective to reduce the strain of electronic component, and so is a relatively short electronic component layer.
This dissertation proposed a simplifed analytical model (crack propagtion model) for the interfacial delamination during the transfer printing process. The Prony parameters are used to model the viscoelastic properties of PDMS stamp and the influence of the pick-up velocity on the interfacial delamination due to the viscoelastic properties of PDMS is explored. When the energy release rate of the crack tip exceeds the critical adhesive energy, the status of the crack will be transferred from close to open, resulting in an interfacial delamination. The analytical model and the FEA results reveal that the required pulling-off force increases with the increase of the velocity at a low pick-up velocity; when the velocity reaches50μm/s, the required pulling-off force will be saturated.
This fabrication process of the flexible electronic devices with two-dimensional prestrain is investigated. A simplified analytical model is proposed to obtain the strain of elastic substrate, the profile and the max strain of the electronic component at flat, hemispherical and punched states. The analytical model and the FEA simulations results show that this analytical model can well predict the strain distribution of the elastic substrate and the electronic components.
This dissertation further studies the material-induced flexibility and the structure-induced flexibility of the flexible electronic devices. This study is useful in guiding the design and application of the flexible electronic devices and promoting the development of the flexible electronic devices.
引文
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