仿生粘附结构的方向性粘附机理研究
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摘要
壁虎等动物的微纳分级粘附系统为具有仿生粘附结构的干粘附材料的研发提供了仿生学原型。这种仿生粘附材料在爬壁机器人,微操纵,微纳转印工艺,生物医学胶带等领域具有广泛的应用前景。生物和仿生粘附力学,仿生粘附结构的加工方法和测试技术的研究可为高性能仿生粘附材料的研发奠定理论和技术基础,并己成为国内外的研究热点。然而对实际可应用的具有方向性粘附特性的仿生粘附结构的分析和优化设计工作亟待深入探索。
本文以揭示典型仿生粘附结构的方向性粘附机理为目标,系统研究了几种典型仿生粘附结构在刚性平面的粘附问题,进而探讨了粘附结构在正弦表面和粗糙表面上的方向性粘附规律,分析了粘附结构阵列的优化设计问题,并探索了仿生粘附结构的飞秒激光双光子加工方法和基于原子力显微镜(AFM)平台的方向性粘附特性的测试技术。
在粘附力学分析方面,首先基于不可拉伸欧拉弹性杆理论和表面能概念,利用变分法和数学分析推导出不可拉伸直纤维结构在刚性平面上粘附的侧面接触模型(ISCM, Inextensible Side Contact Model)。这一模型可用于预测这种粘附结构的脱附模式和粘附规律。研究结果表明,增加剪切力,纤维倾角和纤维的弯曲柔性都能够有效地增加法向拔出力。而且利用能量最小化原理证明所有粘附平衡状态都是稳定的。
其次,通过将轴向变形能计入系统的能量泛函,将ISCM模型推广到可拉伸直纤维结构的情况,建立了可拉伸侧面接触模型(ESCM, Extensible Side Contact Model)。而且对ESCM模型作简单的修正,可将它用于分析纤维粘附部分的预张力对粘附行为的影响。研究结果表明：由于纤维的可拉伸变形,当施加最优的剪切力时纤维存在最大法向拔出力,且在弯曲刚度不变的情况下,最大法向拔出力随轴向刚度的增大而增强。而对预应力效应的研究表明：施加一个最优的预张力能够使最大法向拔出力极大化。
接着,还将ESCM模型推广到两级纤维结构在刚性平面上粘附的情况。结果表明,对于典型的两级纤维结构,存在一个依赖于结构参数的临界剪切力。当剪切力低于这个临界值时,弯曲变形起主导作用,粘附力随着剪切力几乎线性地增加,且可以通过改变纤维的结构参数来调控其粘附规律；而当剪切力超过这个值,轴向变形起主导作用,且粘附规律与经典的Kendall模型所预测的结果一致。从定性的角度看,模型所预测的粘附规律与文献报道的对生物和仿生多级粘附结构的实验结果比较一致。
最后,也将侧面接触模型推广到直纤维在刚性曲面,尤其是正弦表面上粘附的情况。研究表明：当纤维在正弦表面上粘附时,存在最有利的位置使法向拔出力最大化。当沿着纤维的倾斜方向施加适度的剪切力时,纤维在曲面上的法向拔出力会随着剪切力的增加而增强(即所谓的“方向性粘附特性”)；而当剪切力超过临界值时,纤维会沿着表面滑移,这有利于实现纤维与表面之间的位置匹配,从而能在一定程度上增强纤维的粘附力。基于这些研究和进一步的分析,可对壁虎脚掌在不同粗糙表面上粘附时所表现出的粗糙度尺度效应进行定性地解释。
在粘附纤维结构阵列的优化设计方面,基于推导出来的单根粘附结构的粘附规律,分别对单级和两级纤维结构阵列的优化设计问题进行了系统的研究。对于每一种纤维结构阵列,定义了纤维阵列的结构参数,推导了相邻纤维不发生聚集的条件(抗聚集条件)和纤维阵列的粗糙表面适应性条件,进而对优化问题进行了深入的分析和讨论。由此获得的知识和优化方法能够帮助仿生纤维阵列的优化设计。
在实验研究方面,用飞秒激光双光子聚合加工技术加工了仿生粘附结构及其阵列,并提出了将端头带微柱子的微悬臂梁集成到AFM的两轴力测试平台上,对单根仿生粘附结构的方向性粘附特性进行测试的方法,还通过结构设计和微加工工艺初步研制出这种特殊的微悬臂梁。
基于以上研究,本论文在以下方面做出了创新：1)为不可拉伸和可拉伸直纤维结构在刚性平面上粘附问题建立了不可拉伸侧面接触模型(ISCM)和可拉伸侧面接触模型(ESCM)。这些模型可直接用于预测相应粘附结构在刚性平面上的脱附模式和方向性粘附规律。2)将侧面接触模型推广到两级直纤维结构在刚性平面上粘附和单级直纤维结构在刚性曲面上粘附的情况。这些模型可对相应的粘附规律进行理论预测,从而能够为相应的实验结果提供理论解释。3)提出将端头带微柱子的微悬臂梁作为传感元件,集成到AFM平台上对单根仿生粘附结构的方向性粘附特性进行测试的方法。
The hierarchical micro/nano adhesive system of geckos provides a biomimetic model for the researches and developments of dry adhesives with biomimetic structures. This kind of biomimetic adhesives has wide applications in the vast fields of adhesion based climbing robots, micromanipulations, micro/nano transfer printing techniques and biomedical adhesives, etc. Researches on adhesion mechanics, micro/nano fabrication methods and test techniques of biomimetic adhesive structures will form the basis for the developments of high-performance biomimetic adhesive materials and have become a hot research field at home and abroad. However, very few jobs on analysis and optimization have been done with respect to practically applicable biomimetic fibrillar adhesive structures with directional adhesion property.
This dissertation focuses on clarifying the directional adhesion mechanism of typical biomimetic adhesive structures. To be specific, the adhesion problems of several typical fibrillar adhesive structures on a rigid flat surface or on a rigid curved surface, the design and optimization of both single-level and two-level adhesive fiber arrays, and the femtosecond laser two-photon polymerization based fabrication and the atomic force microscopy (AFM) platform based test of fibrillar adhesive structures are systematically investigated in this dissertation.
Firstly, in order to study the directional adhesion behavior of an inextensible straight fiber on a rigid flat surface, an inextensible side contact model (ISCM) is proposed via a variational method based on the inextensible Euler elastica theory and the surface energy concept. The ISCM can be used to directly predict the detachment mode and the adhesion law of the fiber. It is found that increasing the applied shear force, the slanted angle or the bending compliance will effectively enhance the normal pull-off force. Moreover, all the adhesion equilibrium states are found stable by using the stability criterion of energy minimization.
Secondly, by taking the axial deformation energy into account in the energy functional of the system, the ISEM model is generalized to the extensible case, thus forming an extensible side contact model (ESCM) that is applicable to extensible straight fiber. Moreover, the ESCM can be slightly modified so as to be applicable to study the pretension effect on the adhesion behavior. It is found that, due to the extensibility of the fiber, there exists a maximum normal pull-off force (MNPF) when an optimal shear force is applied. The MNPF increases with the fiber's axial stiffness when its bending stiffness is constant. Studies on the pretension effect demonstrate that when an optimal pretension is applied, the MNPF is maximized.
Thirdly, the ESCM is generalized to the case of two-level fibers. The generalized model predicts that for a typical two-level fiber, there exists a structural parameters-dependent critical shear force, below and above which the bending deformation dominates or the axial deformation dominates. In the bending deformation dominated region, the adhesion force increases almost linearly with the applied shear force and the adhesion law can be tuned effectively by varying the structural parameters; while in the axial deformation dominated region, the adhesion law is almost the same with that predicted by the classical Kendall model. Additionally, an optimum structure behaving consistently with geckos'setal arrays is obtained by designing the structural parameters properly, especially the slanted angles.
The side contact model is also generalized to the case of a straight fiber in side contact with a curved surface, especially a sinusoidal surface. Detailed studies show that, for fibers adhered on a sinusoidal surface, there exists a benefit position so that the normal pull-off force is maximized. More importantly, if a proper shear force is applied, the normal pull-off force increases with the shear force; however, if the shear force exceeds a critical value, the fiber will slide along the surface, which would benefit for matching the position between the fiber and the curved surface, thus promoting the fiber's adhesion force to a certain degree. Based on these studies and further analysis, the size effect of roughness found in the geckos' adhesion on surfaces with different roughness is qualitatively explained.
Based on the derived adhesion law of a single straight fiber, the design and optimization of both single-level and two-level adhesive fiber arrays are systematically studied. For each kind of fiber array, the structural parameters are defined, the condition that adjacent fibers do not adhere with each other (anti-bunching condition) and the rough surface adaptable condition are analyzed, and the adhesion strength is formulated. On these bases, the optimization problem is analyzed and discussed. The derived knowledge and analysis method should contribute to rational design of biomimetic adhesive fiber arrays.
On the aspect of experiment, the femtosecond laser two-photon polymerization technique is adopted to fabricate a single fibrillar adhesive structure. The adhesive fiber array is also fabricated parallelly with the aid of computed hologram loaded spatial light modulator (SLM). In order to test the directional adhesion property of the fabricated adhesive structure, a micro cantilever with a micro pillar at its free end is designed and fabricated. It can be used as a sensing element and is integratable to the AFM measurement platform so as to measure the two axial forces, the normal adhesion force and the shear force of the adhesive structure.
It's concluded from the above researches that the following contributions have been made to the fields of biomimetic adhesion:1) Two models (ISCM and ESCM) are proposed to predict the directional adhesion laws for inextensible and extensible straight fibers adhered on a rigid flat surface respectively;2) The ESCM model is generalized to the case of two-level fibers adhered on a rigid flat surface and the case of single-level fibers adhered on a rigid curved surface;3) A method for characterizing the directional adhesion property of a single biomimetic adhesive structure is proposed by using a specially designed micro-cantilever as the sensing element and integrating it into the two-axial force measurement platform of AFM.
本文以揭示典型仿生粘附结构的方向性粘附机理为目标,系统研究了几种典型仿生粘附结构在刚性平面的粘附问题,进而探讨了粘附结构在正弦表面和粗糙表面上的方向性粘附规律,分析了粘附结构阵列的优化设计问题,并探索了仿生粘附结构的飞秒激光双光子加工方法和基于原子力显微镜(AFM)平台的方向性粘附特性的测试技术。
在粘附力学分析方面,首先基于不可拉伸欧拉弹性杆理论和表面能概念,利用变分法和数学分析推导出不可拉伸直纤维结构在刚性平面上粘附的侧面接触模型(ISCM, Inextensible Side Contact Model)。这一模型可用于预测这种粘附结构的脱附模式和粘附规律。研究结果表明,增加剪切力,纤维倾角和纤维的弯曲柔性都能够有效地增加法向拔出力。而且利用能量最小化原理证明所有粘附平衡状态都是稳定的。
其次,通过将轴向变形能计入系统的能量泛函,将ISCM模型推广到可拉伸直纤维结构的情况,建立了可拉伸侧面接触模型(ESCM, Extensible Side Contact Model)。而且对ESCM模型作简单的修正,可将它用于分析纤维粘附部分的预张力对粘附行为的影响。研究结果表明：由于纤维的可拉伸变形,当施加最优的剪切力时纤维存在最大法向拔出力,且在弯曲刚度不变的情况下,最大法向拔出力随轴向刚度的增大而增强。而对预应力效应的研究表明：施加一个最优的预张力能够使最大法向拔出力极大化。
接着,还将ESCM模型推广到两级纤维结构在刚性平面上粘附的情况。结果表明,对于典型的两级纤维结构,存在一个依赖于结构参数的临界剪切力。当剪切力低于这个临界值时,弯曲变形起主导作用,粘附力随着剪切力几乎线性地增加,且可以通过改变纤维的结构参数来调控其粘附规律；而当剪切力超过这个值,轴向变形起主导作用,且粘附规律与经典的Kendall模型所预测的结果一致。从定性的角度看,模型所预测的粘附规律与文献报道的对生物和仿生多级粘附结构的实验结果比较一致。
最后,也将侧面接触模型推广到直纤维在刚性曲面,尤其是正弦表面上粘附的情况。研究表明：当纤维在正弦表面上粘附时,存在最有利的位置使法向拔出力最大化。当沿着纤维的倾斜方向施加适度的剪切力时,纤维在曲面上的法向拔出力会随着剪切力的增加而增强(即所谓的“方向性粘附特性”)；而当剪切力超过临界值时,纤维会沿着表面滑移,这有利于实现纤维与表面之间的位置匹配,从而能在一定程度上增强纤维的粘附力。基于这些研究和进一步的分析,可对壁虎脚掌在不同粗糙表面上粘附时所表现出的粗糙度尺度效应进行定性地解释。
在粘附纤维结构阵列的优化设计方面,基于推导出来的单根粘附结构的粘附规律,分别对单级和两级纤维结构阵列的优化设计问题进行了系统的研究。对于每一种纤维结构阵列,定义了纤维阵列的结构参数,推导了相邻纤维不发生聚集的条件(抗聚集条件)和纤维阵列的粗糙表面适应性条件,进而对优化问题进行了深入的分析和讨论。由此获得的知识和优化方法能够帮助仿生纤维阵列的优化设计。
在实验研究方面,用飞秒激光双光子聚合加工技术加工了仿生粘附结构及其阵列,并提出了将端头带微柱子的微悬臂梁集成到AFM的两轴力测试平台上,对单根仿生粘附结构的方向性粘附特性进行测试的方法,还通过结构设计和微加工工艺初步研制出这种特殊的微悬臂梁。
基于以上研究,本论文在以下方面做出了创新：1)为不可拉伸和可拉伸直纤维结构在刚性平面上粘附问题建立了不可拉伸侧面接触模型(ISCM)和可拉伸侧面接触模型(ESCM)。这些模型可直接用于预测相应粘附结构在刚性平面上的脱附模式和方向性粘附规律。2)将侧面接触模型推广到两级直纤维结构在刚性平面上粘附和单级直纤维结构在刚性曲面上粘附的情况。这些模型可对相应的粘附规律进行理论预测,从而能够为相应的实验结果提供理论解释。3)提出将端头带微柱子的微悬臂梁作为传感元件,集成到AFM平台上对单根仿生粘附结构的方向性粘附特性进行测试的方法。
The hierarchical micro/nano adhesive system of geckos provides a biomimetic model for the researches and developments of dry adhesives with biomimetic structures. This kind of biomimetic adhesives has wide applications in the vast fields of adhesion based climbing robots, micromanipulations, micro/nano transfer printing techniques and biomedical adhesives, etc. Researches on adhesion mechanics, micro/nano fabrication methods and test techniques of biomimetic adhesive structures will form the basis for the developments of high-performance biomimetic adhesive materials and have become a hot research field at home and abroad. However, very few jobs on analysis and optimization have been done with respect to practically applicable biomimetic fibrillar adhesive structures with directional adhesion property.
This dissertation focuses on clarifying the directional adhesion mechanism of typical biomimetic adhesive structures. To be specific, the adhesion problems of several typical fibrillar adhesive structures on a rigid flat surface or on a rigid curved surface, the design and optimization of both single-level and two-level adhesive fiber arrays, and the femtosecond laser two-photon polymerization based fabrication and the atomic force microscopy (AFM) platform based test of fibrillar adhesive structures are systematically investigated in this dissertation.
Firstly, in order to study the directional adhesion behavior of an inextensible straight fiber on a rigid flat surface, an inextensible side contact model (ISCM) is proposed via a variational method based on the inextensible Euler elastica theory and the surface energy concept. The ISCM can be used to directly predict the detachment mode and the adhesion law of the fiber. It is found that increasing the applied shear force, the slanted angle or the bending compliance will effectively enhance the normal pull-off force. Moreover, all the adhesion equilibrium states are found stable by using the stability criterion of energy minimization.
Secondly, by taking the axial deformation energy into account in the energy functional of the system, the ISEM model is generalized to the extensible case, thus forming an extensible side contact model (ESCM) that is applicable to extensible straight fiber. Moreover, the ESCM can be slightly modified so as to be applicable to study the pretension effect on the adhesion behavior. It is found that, due to the extensibility of the fiber, there exists a maximum normal pull-off force (MNPF) when an optimal shear force is applied. The MNPF increases with the fiber's axial stiffness when its bending stiffness is constant. Studies on the pretension effect demonstrate that when an optimal pretension is applied, the MNPF is maximized.
Thirdly, the ESCM is generalized to the case of two-level fibers. The generalized model predicts that for a typical two-level fiber, there exists a structural parameters-dependent critical shear force, below and above which the bending deformation dominates or the axial deformation dominates. In the bending deformation dominated region, the adhesion force increases almost linearly with the applied shear force and the adhesion law can be tuned effectively by varying the structural parameters; while in the axial deformation dominated region, the adhesion law is almost the same with that predicted by the classical Kendall model. Additionally, an optimum structure behaving consistently with geckos'setal arrays is obtained by designing the structural parameters properly, especially the slanted angles.
The side contact model is also generalized to the case of a straight fiber in side contact with a curved surface, especially a sinusoidal surface. Detailed studies show that, for fibers adhered on a sinusoidal surface, there exists a benefit position so that the normal pull-off force is maximized. More importantly, if a proper shear force is applied, the normal pull-off force increases with the shear force; however, if the shear force exceeds a critical value, the fiber will slide along the surface, which would benefit for matching the position between the fiber and the curved surface, thus promoting the fiber's adhesion force to a certain degree. Based on these studies and further analysis, the size effect of roughness found in the geckos' adhesion on surfaces with different roughness is qualitatively explained.
Based on the derived adhesion law of a single straight fiber, the design and optimization of both single-level and two-level adhesive fiber arrays are systematically studied. For each kind of fiber array, the structural parameters are defined, the condition that adjacent fibers do not adhere with each other (anti-bunching condition) and the rough surface adaptable condition are analyzed, and the adhesion strength is formulated. On these bases, the optimization problem is analyzed and discussed. The derived knowledge and analysis method should contribute to rational design of biomimetic adhesive fiber arrays.
On the aspect of experiment, the femtosecond laser two-photon polymerization technique is adopted to fabricate a single fibrillar adhesive structure. The adhesive fiber array is also fabricated parallelly with the aid of computed hologram loaded spatial light modulator (SLM). In order to test the directional adhesion property of the fabricated adhesive structure, a micro cantilever with a micro pillar at its free end is designed and fabricated. It can be used as a sensing element and is integratable to the AFM measurement platform so as to measure the two axial forces, the normal adhesion force and the shear force of the adhesive structure.
It's concluded from the above researches that the following contributions have been made to the fields of biomimetic adhesion:1) Two models (ISCM and ESCM) are proposed to predict the directional adhesion laws for inextensible and extensible straight fibers adhered on a rigid flat surface respectively;2) The ESCM model is generalized to the case of two-level fibers adhered on a rigid flat surface and the case of single-level fibers adhered on a rigid curved surface;3) A method for characterizing the directional adhesion property of a single biomimetic adhesive structure is proposed by using a specially designed micro-cantilever as the sensing element and integrating it into the two-axial force measurement platform of AFM.
引文
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