力学学报, 2021, 53(6): 1609-1621 DOI: 10.6052/0459-1879-21-091

固体力学

磁场力及膜曲率对磁敏感薄膜-基底界面 黏附性能的影响与调控1)

韩明杰, 彭志龙,2), 姚寅, 张博, 陈少华,3)

*北京理工大学先进结构技术研究院, 北京 100081

北京理工大学轻量化多功能复合材料与结构北京市重点实验室, 北京 100081

INFLUENCE AND REGULATION OF INTERFACIAL ADHESION PROPERTIES OF A MAGNETIC SENSITIVE FILM/SUBSTRATE BY MAGNETIC FORCE AND FILM'S CURVATURE1)

Han Mingjie, Peng Zhilong,2), Yao Yin, Zhang Bo, Chen Shaohua,3)

*Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China

Beijing Key Laboratory of Lightweight Multi-Functional Composite Materials and Structures, Beijing Institute of Technology, Beijing 100081, China

通讯作者: 2)彭志龙, 教授, 主要研究方向: 仿生材料力学、表面/界面力学. E-mail:pengzhilong@bit.edu.cn;3)陈少华, 教授, 主要研究方向: 仿生材料与结构力学、表面/界面力学、微纳米力学. E-mail:shchen@bit.edu.cn

收稿日期: 2021-03-5   接受日期: 2021-04-9   网络出版日期: 2021-06-18

基金资助: 1)国家自然科学基金.  12022211
国家自然科学基金.  11872114
国家自然科学基金.  12032004
北京市自然科学基金.  3212011

Received: 2021-03-5   Accepted: 2021-04-9   Online: 2021-06-18

作者简介 About authors

摘要

界面黏附和脱黏的可调控在攀爬装置、黏附开关、机械抓手等方面具有重要的应用需求. 针对磁敏感薄膜-基底界面, 开展了薄膜初始曲率及外加磁场对界面黏附性能影响机制的研究. 首先实验制备了具有初始曲率的磁敏感薄膜, 分别开展了具有初始曲率的磁敏感薄膜-基底界面撕脱实验及理论研究, 研究了薄膜初始曲率、弯曲刚度和外加磁场强度对界面黏附性能的影响规律. 实验和理论结果一致表明: 具有初始曲率的磁敏感薄膜-基底界面黏附力随薄膜初始曲率的增大而减小, 而外加磁场能够有效提高界面黏附力;相比于初始零曲率薄膜-基底界面稳态撕脱力与薄膜弯曲刚度无关, 薄膜弯曲刚度减弱了具有初始曲率薄膜-基底界面的稳态撕脱力. 进一步从能量角度分析了界面等效黏附性能, 揭示了薄膜弯曲能、磁场势能、界面黏附能的相互竞争机制. 最后, 基于本文的实验及理论结果, 提出了一种磁场和薄膜初始曲率协同调控的简易机械抓手, 可连续实现物体的拾取、搬运和释放功能. 本文结果不仅有助于理解多场调控的界面可逆黏附机制, 对界面黏附可控的功能器件设计亦提供了一种新方法.

关键词: 磁敏感薄膜 ; 初始曲率 ; 磁场强度 ; 可调黏附 ; 机械抓手

Abstract

The controllable interface adhesion of attachment and detachment has important application requirements in climbing devices, adhesion switches and mechanical grippers. In present paper, the influence mechanism of external magnetic field and film's initial curvature on the interfacial adhesion of a magnetic sensitive film/substrate is studied. The peel-test of the magnetic sensitive thin film with initial curvature on a substrate as well as the corresponding theoretical study are respectively carried out. Both the experimental and theoretical results indicate that the interfacial adhesion force of the magnetic sensitive thin film/substrate increases with increasing the initial curvature of the film, and the external magnetic field can enhance the interfacial adhesion force. Compared with the steady-state peel-off force of a flat thin film that is independent on the bending stiffness, the bending stiffness would decrease the steady-state peel-off force of the film with initial curvature. The interface effective adhesion energy is further considered from the energy point of view, which can disclose the comparing mechanisms of the film's bending energy, the potential energy of external magnetic field and the adhesion energy. Lastly, based on the experimental and theoretical results, a simply mechanical gripper controlled by both the magnetic field and film's initial curvature is proposed, which can continuously realize the gripping, transport and release of an object. The results obtained in the present paper can not only be helpful for understanding the interface reversible adhesion mechanism actuated by multi-field, but also provide a novel approach to design functional devices with controllable interface adhesion.

Keywords: magnetic sensitive films ; initial curvature ; magnetic strength ; controllable adhesion ; mechanical gripper

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本文引用格式

韩明杰, 彭志龙, 姚寅, 张博, 陈少华. 磁场力及膜曲率对磁敏感薄膜-基底界面 黏附性能的影响与调控1). 力学学报, 2021, 53(6): 1609-1621 DOI:10.6052/0459-1879-21-091

Han Mingjie, Peng Zhilong, Yao Yin, Zhang Bo, Chen Shaohua. INFLUENCE AND REGULATION OF INTERFACIAL ADHESION PROPERTIES OF A MAGNETIC SENSITIVE FILM/SUBSTRATE BY MAGNETIC FORCE AND FILM'S CURVATURE1). Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1609-1621 DOI:10.6052/0459-1879-21-091

引言

界面普遍存在于各种材料、结构和器件中, 界面的力学性能直接影响着整体机构或装备的服役寿命和性能[1-2]. 界面黏附作为界面力学的前沿领域, 由于在诸多领域的重要应用一直吸引着研究人员的广泛兴趣. 例如, 在军民领域均有迫切需求的新型攀爬装置、微/纳机电系统、柔性电子及生物医学领域等. 界面黏附性能的调控是实现上述领域的关键. 因此, 如何实现界面强黏附和易脱黏交替的可逆黏附功能, 进而设计出具有可逆黏附性质的功能化表面一直是学术界和工业界普遍关注的关键科学问题.

事实上, 自然界一类爬行生物超强的黏附爬行能力很早就吸引了研究人员的广泛关注[3], 例如壁虎、蜘蛛、蚂蚁、竹节虫等. 该类生物不仅具有超强的黏附能力, 而且能从墙壁上随意脱黏, 其天然的可逆黏附功能为科研人员研究界面黏附性能的调控提供了绝妙创新灵感. 该类生物超强的黏附能力主要依赖于其精细黏附系统结构, 黏附系统按照与物体表面接触情况可分为两类[4]: 一类是毛发状结构, 例如壁虎、蜘蛛等脚掌具有多分级多纤维状绒毛; 一类为表面光滑结构, 例如蚱蜢、竹节虫等脚掌为光滑表面. 为了揭示壁虎等生物的黏附机理, 研究人员开展了大量的实验[3, 5-7]、理论[8-10]及数值模拟工作[11-13]. 尽管不同生物的黏附系统结构不同, 实验已证实其主要黏附机理为范德华力[3, 5]和毛细力[14-15]. Chen等[16-17]以黏附接触力学为基础, 理论研究了壁虎黏附系统整体表现的各向异性和梯度特性, 从宏观上揭示了壁虎实现可逆黏附的机理. Gao等[18]将壁虎最小黏附单元当做柱状纤维, 理论发现了在微尺度领域与宏观界面断裂不同的缺陷不敏感现象. Artz等[19]和Varenberg等[20]发现将一个大尺寸纤维细分成多个细小纤维, 能明显增强界面黏附性能. Peng等[11, 21-23]注意到壁虎最小铲状黏附纤维的真实形状类似于有限尺寸的纳米薄膜, 系统研究了仿生纳米薄膜的黏附性能及主要影响因素, 进而揭示了壁虎可逆黏附的微观力学机理.

受壁虎类生物黏附机理和黏附系统结构启发, 研究人员仿生制备了多种纤维阵列表面研究其黏附行为. Geim等[24]研究了仿生壁虎足部的毛发结构, 利用电子束微影和氧离子干刻蚀法制备了高弹聚酰亚胺纤维阵列, 每平方厘米面积可负重3 N. Glassmaker 等[25-26]利用多孔硅模板制备PDMS多纤维结构, 并对其进行接触力学实验验证了其理论模型. Peressadko 和Gorb[27]用聚乙烯硅氧烷(polyvinylsiloxane, PVS)制备出仿壁虎脚的多纤维结构, 并比较了该结构与块体材料在光滑玻璃上黏附性能, 结果表明多纤维结构能显著提高界面黏附性能. delCampo等[28]实验比较了不同末端形状纤维的黏附性能, 发现蘑菇型纤维黏附力最强, 其次是铲状纤维. Greiner等[29]利用含有多级孔结构的模板制备出PDMS 二级纤维结构, 首次从实验角度研究了多级纤维结构对黏附的影响. Lee等[30]和Jeong等[31]实验研究了倾斜纤维阵列在基底上的黏附行为, 发现界面切向黏附力具有方向依赖性. Murphy等[32]利用多步制备的方法仿生制备出末端为蘑菇形状的倾斜多级纤维结构. 尽管目前在仿生黏附功能表面实验研究方面已取得了显著进展, 但现有研究多关注于如何增强界面黏附, 对于如何实现界面可逆黏附的问题, 由于受实验技术的限制一直是研究的难点. 尽管如此, 研究人员发现可以通过改变界面实际接触面积来调控界面黏附性能[33], 目前通常采用两种方法改变黏附表面接触面积: 一种制备楔形纤维阵列表面, 在加载过程中(loading-drag-pull), 楔形纤维弯曲大变形增大与基底的实际接触面积可提高界面黏附力. 当外力撤去后楔形纤维恢复初始状态实现界面轻松脱黏[34-36]. 研究人员通过研究楔形纤维阵列的黏附性能期望未来能设计新型攀爬或抓取装置甚至在太空环境中应用[37]. 此外, 研究人员发现通过合理地引入外场(例如温度场[38-39]、电场[40-41]、磁场[42-43]等)能有效改变纤维阵列表面形貌或材料性质, 进而改变界面有效接触面积来调控界面黏附性能. 其中, 由于磁场在实验中易于实现成为研究人员普遍采取的一种方式. Drotlef等[42]和Gillies等[43]实验制备了含磁颗粒的纤维阵列表面, 发现在外磁场作用下纤维能发生较大的弯曲变形, 进而改变与基底表面的界面接触状态, 实现磁场调控纤维阵列表面的界面黏附强度.

尽管仿壁虎多纤维阵列结构相比于平表面能产生更强的黏附力[27], 但是多纤维阵列结构的黏附性能严重依赖于材料和几何性质(纤维尺寸必须为微米甚至纳米尺度、大长细比、较高的面密度等)[44], 制备技术和过程复杂(要求高端精细的微纳制造设备), 成本较高且制备的样品尺寸较小, 严重制约了在实际工程的应用. 与壁虎多纤维黏附系统结构不同, 蚂蚁、竹节虫、蚜虫等生物依靠较为平滑的爪垫同样能在物体表面实现高效的可逆黏附功能[7, 45-46], 该类生物依靠往其囊状中垫内充放液体实现中垫的扩张和收缩进而改变中垫与物体表面的接触形貌实现可逆黏附. 仿生该类生物的平表面黏附结构, Carlson等[47]和Dening等[48]实验制备了球状薄膜结构, 通过往其内部充放气体仿生生物中垫的扩张和收缩, 实现了仿生薄膜界面黏附性能调控. 基于该黏附原理, Li等[49]设计了一种仿生薄膜机械抓手, 通过薄膜内气压的控制实现了不同大小和形状物体的拾取与释放. 受蚜虫黏附中垫启发, Linghu等[50]实验制备了仿生薄膜结构并将其固定于一空腔端部, 通过往薄膜上方堆放磁颗粒, 在磁场作用下薄膜变形为具有一定曲率的结构, 且薄膜变形大小可以通过改变磁场强度任意控制, 实现了薄膜与基底界面黏附性能的磁场调控, 并将其应用于转印. Xie和Xiao[51]利用形状记忆聚合材料制备了具有初始曲率的薄膜结构, 发现外界温度的变化可实现薄膜与基底点接触和面接触等不同的接触状态, 通过界面接触构型的改变来调控界面黏附性能.

由以上研究可以看出, 无论对于仿生多纤维阵列表面还是仿生无初始曲率的薄膜结构均可以通过改变接触构型实现界面强黏附和易脱黏的调控. 目前对于仿生多纤维阵列表面已有系统研究, 但由于微尺度纤维阵列表面制备工艺复杂限制了在实际工程的应用. 仿生无初始曲率的薄膜结构在实验中易于制备, 但对于其界面附性能调控的研究目前仅局限于通过不同方法发现了相关实验现象. 外场尤其是磁场作为一种调控仿生薄膜与基底界面接触形貌的简单方法目前还鲜有研究[50-51], 而且磁场调控仿生薄膜界面可逆黏附的机理仍不清楚.

针对以上问题, 本文提出了一种磁场调控仿生薄膜界面黏附性能的方法, 通过引入磁感应薄膜的初始曲率, 当薄膜与基底完全接触时, 无磁场作用下薄膜内储存的弯曲应变能将克服界面能, 甚至使薄膜发生自发脱黏;当施加磁场时, 作用在磁感应薄膜上的磁场力能阻止薄膜初始变形的恢复, 抑制储存在其内部弯曲能的释放, 实现界面强黏附. 进一步基于能量原理, 理论揭示了磁场和薄膜初始构型调控界面黏附性能的机理, 并基于该机理设计了一种简易的黏附机械装置. 本文结果不仅提供了一种实现调控薄膜界面黏附性能的方法, 而且对设计新型可逆黏附的功能表面提供了理论基础.

1 实验样品制备及界面黏附性能测试

本文采用聚二甲基硅氧烷聚合物(PDMS, Sylgard 184, 美国道康宁公司)制备磁感应薄膜, 首先将PDMS基液与固化剂以质量比10: 1进行充分混合后置于真空箱中30 min去除其中的气泡. 然后将平均直径为50 $\mu$m的羰基铁粉(CIP, 河北乐伯金属材料科技有限公司)以1: 2的质量比添加到PDMS预聚液中, 随后将Fe/PDMS混合液放置于行星式离心真空搅拌机(Thinky Planetary Vacuum MixerARV-310)中以1000 r/min的速度搅拌6 min, 使羰基铁粉在PDMS液体中均匀分布并将混合液中的多余气泡充分排出. 利用刮膜器进行磁感应平薄膜制备, 设置薄膜厚度为1.5 mm, 宽度为17.5 mm, 并将其置于真空干燥箱中(45 $^{\circ}$C)保持8 h使Fe/PDMS混合液完全固化. 为了得到含有初始曲率的磁敏感薄膜, 将制备的含有铁粉的PDMS薄膜与预先准备的具有不同等曲率的聚氯乙烯(PVC)薄膜利用压敏胶黏结在一起. 为了增强薄膜与基底表面的界面黏附力, PVC薄膜与玻璃基底接触的一面同样涂了一层压敏胶, 如图1所示.

图1

图1   (a) 具有初始曲率的磁敏感薄膜示意图; (b) 实验制备的含有初始曲率的磁敏感薄膜

Fig.1   (a) Schematic of magnetic sensitive film with initial curvature; (b) Magnetic sensitive film with initial curvature fabricated in experiment


目前研究人员已发展多种方法表征薄膜/基底系统的界面黏附性能, 其中撕脱法(peel-test)由于操作简单实验中易于实现成为被广泛采用的一种方法[52-53]. 本文同样采用薄膜撕脱实验(撕脱角为90$^\circ$)来表征界面黏附性能, 使用专门配备撕脱夹具的材料试验机(Instron 2367)进行撕脱实验(见图2), 采用位移加载模式, 加载速率为0.2 mm/s, 传感器量程为5 N (美国TransducerTechniques, GSO-500, 精度为5 mN). 基底采用光滑的玻璃表面. 为了研究磁场对磁敏感薄膜界面黏附性能的影响, 使用长方形永磁体(10 cm$\times$10 cm$\times$4 cm)引入磁场作用, 将永磁体置于玻璃基底下方, 薄膜处的磁场强度可以通过调节永磁体与玻璃基底的距离改变[54], 由于永磁体尺寸远大于薄膜尺寸, 薄膜距离永磁体相同高度处磁场强度可近似认为均匀分布.

图2

图2   磁场作用下薄膜撕脱实验装置

Fig.2   Experimental set-up of peel-test with the action of magnetic field


2 实验结果与讨论

2.1 初始曲率对薄膜界面黏附性能的影响

为了研究薄膜初始曲率对界面黏附性能的影响, 制备了厚度相同曲率分别为$\rho =1/60$ mm$^{-1}$, 1/45 mm$^{-1}$, 1/20 mm$^{-1}$及无曲率($\rho =0$)的磁感应薄膜, 首先通过相同的预压力使具有不同初始曲率的磁敏感薄膜与基底完全接触, 分别在有磁场(永磁体与玻璃基底距离为零)和无磁场作用下开展薄膜撕脱实验. 图3(a)所示为典型的薄膜撕脱力-位移曲线, 每条曲线测量3次取平均值. 由图3(a)可以看出, 当撕脱位移较小时, 撕脱力随撕脱位移的增大而增大, 当撕脱位移增大到一定临界值时, 撕脱力达到最大值并保持不变, 此时薄膜进入稳态撕脱阶段. 本实验采用稳态撕脱力表征薄膜与基底的界面黏附强度. 无论有磁场作用还是无磁场作用下, 薄膜与基底的稳态撕脱力均随着薄膜初始曲率的增大而减小; 当薄膜曲率一定时, 磁场作用下界面黏附强度明显大于无磁场作用时界面黏附强度, 如图3(b)所示. 这是因为与平薄膜相比, 具有一定初始曲率的薄膜在预压力作用下与基底完全接触时, 薄膜内储存一定的弯曲应变能, 当薄膜与基底脱黏时, 薄膜内弯曲应变能的释放将克服界面黏附能, 使界面更易脱黏. 随着曲率的增大, 薄膜内储存的弯曲能增大, 因此界面黏附力随之减小. 当薄膜曲率一定时, 磁场的作用提供了额外磁场力作用于磁敏感薄膜, 磁场力与撕脱力方向相反. 因此, 磁场作用下薄膜撕脱力始终大于无磁场作用时的撕脱力.

图3

图3   初始曲率对薄膜在无磁场和有磁场作用下界面黏附性能的影响

Fig.3   Effect of the initial curvature on the interfacial adhesion with and without magnetic field


图3可知, 对于无初始曲率的薄膜与玻璃基底接触时, 尽管磁场作用能进一步增强界面黏附作用, 但当无磁场作用时, 平薄膜界面依然具有较强的黏附力(约为0.45 N). 因此, 对于无初始曲率的薄膜, 仅通过磁场力的变化难以实现界面可逆黏附功能. 当薄膜引入初始曲率后, 薄膜与基底完全接触时, 薄膜内储存的弯曲应变能将克服界面能, 使界面黏附作用减弱, 例如, 当薄膜曲率$\rho ={1/{20 }}$ mm$^{-1}$时, 无磁场作用下界面黏附力为0.04 N, 为平薄膜黏附力的1/11.如果薄膜曲率进一步增大, 使薄膜内储存的弯曲应变能大于界面能, 此时薄膜将从基底上自发脱黏. 当施加外界磁场(永磁体与玻璃基底距离为零)后, 磁场将对磁感应薄膜产生额外的磁场力, 磁场力将抑制薄膜内弯曲应变能的释放, 使界面依然保持较强的黏附力, 例如, 薄膜曲率$\rho ={1/{20}}$ mm$^{-1}$时, 在上述磁场作用下界面黏附力为0.3 N, 与无磁场作用时无初始曲率的薄膜黏附力相当. 由以上结果可知, 可以通过外界磁场和薄膜初始曲率的协同作用实现界面黏附性能的调控, 以及界面的黏附可逆.

2.2 弯曲刚度对薄膜界面黏附性能的影响

对于宽度相同的薄膜, 弯曲刚度依赖于薄膜杨氏模量和厚度, 本实验通过增大薄膜厚度来改变其弯曲刚度. 分别制备了厚度为1.6 mm, 1.7 mm和1.8 mm的无初始曲率的薄膜和具有初始曲率($\rho =1/60$ mm$^{-1}$)薄膜, 并测量了有磁场和无磁场作用下的薄膜的界面黏附性能, 如图4所示. 结果表明, 与无初始曲率的薄膜不同, 具有初始曲率薄膜的稳态撕脱力无论在有磁场作用还是无磁场作用下均随薄膜厚度的增大而减小. 这是由于随着薄膜厚度的增大薄膜弯曲刚度增大, 当薄膜与基底完全接触时, 薄膜内储存的弯曲应变能也随着薄膜厚度的增大而增大, 因此更易克服界面作用使薄膜脱黏. 而对于无初始曲率的薄膜, 无论有磁场作用还是无磁场作用下, 薄膜稳态阶段的撕脱力随着薄膜弯曲刚度(厚度)的增大基本保持不变, 这是因为当薄膜进入稳态撕脱阶段, 薄膜构型保持不变, 在90$^\circ$撕脱角下, 撕脱力做功基本完全用于克服界面能, 此时稳态撕脱力大小等于界面黏附能[55]. 对于不同弯曲刚度的薄膜, 界面作用完全相同, 因此稳态撕脱力基本保持不变.

图4

图4   弯曲刚度对平薄膜和具有初始曲率薄膜在无磁场和有磁场作用下界面黏附性能的影响. 本实验通过变化薄膜厚度改变其弯曲刚度

Fig.4   Effects of bending stiffness on the interfacial adhesion with and without magnetic field. Various bending stiffness is achieved by changing the film's thickness in the present experiment


2.3 磁场强度对薄膜界面黏附性能的影响

薄膜处磁场强度的变化可以通过改变永磁体与玻璃基底的距离(距离越大磁场越弱)实现[54]. 图5所示为当薄膜厚度(1.7 mm)和初始曲率($\rho =1/60$ mm$^{-1}$)一定时, 界面黏附力随着磁场强度的变化关系. 由图5可以看出, 薄膜的界面黏附力随着磁场强度的增大而增大. 磁场强度越大, 意味着施加在磁感应薄膜上的额外磁场力越强, 由于磁场力与撕脱力方向相反, 因此界面黏附力随着磁场强度的增强而增大.

图5

图5   磁场强度对薄膜界面黏附性能的影响

Fig.5   Effect of the magnetic strength on the interfacial adhesion


3 理论分析

3.1 理论模型

由以上实验可知, 具有初始曲率的磁感应薄膜与基底完全接触时, 由于薄膜内弯曲应变能的存在将减弱界面相互作用, 而通过施加外界磁场又能增强界面黏附. 因此, 可以通过合理控制外界磁场和薄膜初始构型, 实现薄膜界面黏附性能的调控. 但目前对于磁场和薄膜初始构型如何调控界面黏附性能仍缺乏相应的理论研究. 本文基于能量原理, 对外界磁场和薄膜初始曲率的共同作用如何调控界面黏附性能的机理进行了系统理论分析. 如图6(a)所示, 具有初始等曲率$\rho $的磁感应薄膜, 长度为$L$, 厚度为$h$, 杨氏模量为$E$. 首先通过一定的预压力使薄膜与基底完全接触(图6(b)), 撤去预压力, 在薄膜右端施加竖直方向的撕脱力$F$, 磁场作用下薄膜受到的磁场力用分布载荷$q$表示, 如图6(c)所示, 由于实验中永磁体尺寸远大于薄膜尺寸, 假设薄膜与永磁体距离不变时磁场强度均匀分布, 磁场力$q$仅随薄膜与永磁体距离的变化而改变. 随着撕脱力$F$的增大, 薄膜逐渐从基底上脱黏. 分别引入直角坐标系($x$, $ y$)和曲线坐标系$(s, \theta )$, 并使它们的原点$o$重合位于薄膜最左端, 如图6(d)所示, 两个坐标系的关系满足${{dx}/{ds=\cos \theta }}$, ${{dy}/{ds=\sin \theta }}$. $s$为弧长, $\theta $为薄膜中性层任意点处切线与$x$轴的夹角. 假设薄膜长度$L$足够长, 使薄膜始终能进入稳态撕脱阶段. 已有研究表明, 对于薄膜在90$^\circ$撕脱时, 薄膜的拉伸变形可以忽略[55-56], 因此本理论仅考虑了薄膜撕脱过程中的弯曲变形. 在薄膜撕脱过程中任意时刻, 系统总势能为

$\begin{align} E=\int_0^L \frac{1}{2}D\theta^{'2}(s)ds +\int_0^L V_eff (y)ds+ \\ \int_0^L \left[ {\int_0^y {q(y)dy} } \right] ds-Fy(L) + \\ \int_0^L {\lambda_{1} (x'-\cos \theta )ds} + \int_0^L {\lambda_{2} (y'-\sin \theta )ds} \end{align}$

图6

图6   磁场作用下磁敏感薄膜与刚性基底黏附的撕脱理论模型

Fig.6   Theoretical model of a magnetic sensitive film peeling from a rigid substrate under the action the magnetic field


式(1)右侧第一项表示薄膜弯曲应变能, $D={{Eh^{3}}/{12}}$为薄膜弯曲刚度;第二项为等效的界面相互作用势, 对于平薄膜与基底间的相互作用势, Needleman[57]提出了指数型函数形式

$V(y)=\Delta \gamma \left[ {1-\left( {1+\frac{T_c y}{\Delta \gamma }}\right)} \right]e^{-\frac{T_c y}{\Delta \gamma }}$

其中, $\Delta \gamma $为平薄膜的界面黏附能, $T_c $为界面最大黏附强度. 对于具有初始曲率的薄膜与基底完全黏附时, 薄膜内储存的弯曲能(${{D\rho ^{2}}/2})$将能克服界面黏附能. 引入等效黏附能概念[22], $\Delta \gamma_eff =\Delta \gamma -{{D\rho ^{2}}/2}$, 表征具有初始曲率的弯曲薄膜与基底的黏附作用. 因此, 式(2)可变形为

$V_eff (y)=\Delta \gamma_eff \left[ {1-\left( {1+\frac{T_c y}{\Delta \gamma_eff }} \right)} \right]e^{-\frac{T_c y}{\Delta \gamma_eff }}$

第三项表示磁场力势, 对于永磁体在任意位置产生的磁场强度可表示为[58-59], $H(y)={{A_{1} }/{(d+y)^{3}}}$, 其中$A_{1}$表示磁场强度的常数, $d$为永磁体与基底的距离. 假设磁颗粒在薄膜内均匀分布, 薄膜受到磁场力可表示为[60]

$q(y)=-B_r \int_y^{y+h} {\frac{\partial H(y)}{\partial y}} dy= \\ A\left[ {\frac{1}{(d+y)^{3}}-\frac{1}{(d+y+h)^{3}}} \right]$

其中, $A=A_{1} B_r $, $B_r $为薄膜内磁颗粒的剩磁. 第四项为外力势;最后两项为由于$x$和$y$与$s$和$\theta $的几何关系额外引入项, $\lambda_{1}$和$\lambda_{2} $为拉格朗日乘子.

通过系统的总势能对$\theta $一阶变分等于零, 使系统总势能最小, 可得

$\begin{align} \Delta E=-\int_0^L \left( {D\theta^{"}-\lambda_{1} \sin \theta +\lambda _{2} \cos \theta } \right) \Delta \theta ds- \\ \int_0^L {\lambda_{1}' } \Delta x ds-\int_0^L {\left( {\lambda_{2}' -q(y)-\frac{T_c^{2} y}{\Delta \gamma_eff }e^{-\frac{T_c y}{\Delta \gamma_eff }}} \right)} \Delta yds + \\ \int_0^L {\left( {x'-\cos \theta } \right)} \Delta \lambda_{1} ds+\int_0^L {\left( {y'-\sin \theta } \right)} \Delta \lambda_{2} ds + \\ D\theta'\left. {\Delta \theta } \right|_{0}^{L} +\lambda _{1} \left. {\Delta x} \right|_{0}^{L} +\lambda_{2} \left. {\Delta y} \right|_{0}^{L} -F\Delta y(L)=0 \end{align}$

结合相应的边界条件$\theta (0)=0$, $\theta '(0)=0$, $\theta '(L)=0$, 得到

$\left. {\begin{array}{l} D\theta^{"}-\lambda_{1} \sin \theta +\lambda_{2} \cos \theta =0 \\ \lambda_{1}' =0, \ \ \lambda_{2}' =q(y)+\dfrac{T_c^{2} y}{\Delta \gamma_eff }e^{-\frac{T_c y}{\Delta \gamma_eff }} \\ x'=\cos \theta, \ \ y'=\sin \theta \\ \end{array}} \right\}$
$\theta (0)=0, \theta '(0)=0, \theta '(L)=0, \lambda_{1} (L)=0, \lambda_{2} (L)=F \\$

式(6)为在外界撕脱力作用下薄膜达到平衡的控制方程, 式(7)为边界条件. 上述方程组属于典型的非线性常微分方程的边值问题, 可以通过数值方法(例如打靶法)求解.

3.2 理论结果与讨论

通过求解式(6), 可以得到具有不同初始曲率的薄膜在有磁场($A/(L^{2}\Delta \gamma )=15$)和无磁场($A=0$)作用下的典型撕脱力-位移曲线, 其他参数取值为$L/h=250$, $Eh/\Delta \gamma =5000$, $T_ch/\Delta \gamma=3/50$, 如图7(a)所示. 可以看出理论结果与本文实验现象定性一致, 在薄膜撕脱的初始阶段, 撕脱力随着撕脱位移的增大逐渐增大;当薄膜进入稳态撕脱阶段后, 撕脱力保持不变. 薄膜稳态阶段的撕脱力随薄膜初始曲率的变化关系如图7(b)所示. 结果表明, 无论在有磁场还是无磁场时薄膜稳态阶段的撕脱力均随着薄膜初始曲率的增大而减小. 当初始曲率一定时, 磁场作用下的界面黏附力始终大于无磁场时的黏附力, 与实验结论一致. 特别地, 在无磁场作用下当薄膜初始曲率增大到一临界尺寸时, 界面黏附力趋于零, 说明此时薄膜将能从基底上发生自发脱黏. 薄膜发生自发脱黏的临界曲率可以通过薄膜内储存的弯曲应变能等于界面黏附能, 即$\Delta \gamma_eff =\Delta \gamma -{{D\rho _cr^{2} }/2}=0$, 得到$\rho _cr =\sqrt {{{2\Delta \gamma }/D}} $. 当$\rho >\sqrt {{{2\Delta \gamma}/D}} $时, 说明薄膜与基底完全接触时储存在薄膜内部的弯曲应变能始终大于界面黏附能, 此时不需要施加外界撕脱力薄膜将从基底上自发脱黏;当$\rho <\sqrt {{{2\Delta \gamma }/D}} $时, 虽然薄膜内储存的弯曲能不能完全克服界面能, 与无初始曲率的平薄膜相比仍能一定程度地减弱界面作用, 通过施加较小的撕脱力就能使界面脱黏. 当施加外界磁场后, 尽管界面黏附力也随着薄膜初始曲率的增大而减弱, 但磁场作用能抑制薄膜内弯曲应变能的释放. 由图7(b)可知, 当薄膜初始曲率增大到使薄膜在无磁场时自发脱黏的临界尺寸时, 磁场作用下的界面黏附力依然和无磁场平薄膜的界面黏附力相当, 表明此时界面依然具有较强的黏附作用. 理论结果同样说明依靠外界磁场和薄膜初始构型的共同作用可以调控界面的黏附性能, 甚至实现薄膜的界面可逆黏附.

图7

图7   具有不同初始曲率的薄膜在无磁场和有磁场作用下撕脱性能的理论结果

Fig.7   Theoretical results of the peeling performance of a film with initial curvature with and without the magnetic field


图8表示薄膜弯曲刚度在有磁场($A/(L^{2}\Delta \gamma)=15$)和无磁场($A=0$)时对界面黏附性能的影响, 其他参数取值为$L/h=250$, $\rho h = 2/45$, $T_c h /\Delta \gamma =3/50$. 结果表明, 对于具有初始曲率($\rho h={2/{45}}$)的薄膜弯曲刚度对撕脱力的影响与薄膜初始曲率的影响类似, 稳态阶段的撕脱力随着弯曲刚度的增大而减小. 这是因为当薄膜与基底完全接触时, 其内部储存的弯曲应变能正比于薄膜弯曲刚度和曲率的平方, 弯曲刚度越大, 储存的弯曲应变能越大, 界面更易脱黏. 同样当弯曲刚度增大到某一临界值($D_cr={{2\Delta \gamma }/{\rho ^{2}}}$)时, 无磁场时的撕脱力趋于零, 薄膜将发生自发脱黏, 但此时磁场作用下的界面黏附力依然显著. 然而对于无曲率的平薄膜, 弯曲刚度仅影响薄膜初始脱黏阶段的界面黏附力, 当薄膜达到稳态撕脱阶段后, 界面黏附力不随薄膜弯曲刚度的变化而改变, 与上述实验及已有理论结果一致[55]. 当薄膜其他参数一定时, 磁场强度对界面黏附力的影响规律如图9所示. 随着磁场强度的增大界面黏附力基本成线性增大. 由式(4)可知, 磁场强度越大, 施加在磁感应薄膜上的额外磁场力$q$也越大, 相当于增强了界面作用, 因此界面撕脱力也随之增大, 与相应的实验结果一致.

图8

图8   弯曲刚度对薄膜在无磁场和有磁场作用时撕脱性能影响的理论结果

Fig.8   Theoretical results of the effect of bending stiffness on the peeling behavior of a film with and without magnetic field


图9

图9   磁场强度影响薄膜撕脱力的理论结果

Fig.9   Theoretical results of the effect of magnetic strength on the peeling force


4 一种简易机械抓手的设计

本文通过实验发现了外界磁场和薄膜初始曲率的共同作用能实现对界面黏附性能的调控, 并理论揭示了磁场和薄膜初始曲率影响界面黏附性能的机理. 界面黏附性能的调控对制备新型智能黏附材料[24]、转印[50]及设计黏附抓取装置实现物体的拾取和释放[49]具有重要意义. 基于上述机理, 本文进一步设计了一种简易机械抓手, 采用上述实验同样方法制备了初始曲率为1/15 mm$^{-1}$的磁感应薄膜, 尺寸为弧长3.5 cm, 宽度1.2 cm, 在薄膜凹面一侧中心处连接一杆件方便施加外力(图10(a)), 被抓取的物体选用直径3英寸 (1英寸 = 2.54 cm)的硅片(质量5.6 g). 当没有磁场作用时, 通过一定的预压力使该薄膜与硅片完全接触(图10(b)), 撤去预压力后, 薄膜内储存的弯曲弹性能释放能完全克服界面能, 薄膜从硅片表面自发脱黏, 如图10(c)所示. 当将硅片放置于永磁体上时, 使该薄膜从上方逐渐与硅片靠近, 随着薄膜与硅片距离的减小, 薄膜处的磁场强度逐渐增强, 作用在薄膜上的磁场力也随之增大. 因此在薄膜靠近硅片过程中, 其曲率逐渐减小, 当薄膜与硅片接触时, 薄膜基本趋于平薄膜状态, 如图10(d) $\sim\!$图10(f)所示, 表明此时作用在薄膜上的磁场力基本能完全抵抗薄膜内弯曲应变能的释放, 使其黏附性能类似于无初始曲率的薄膜的黏附. 磁场作用下, 当薄膜与硅片接触时, 同样施加相同的预压力使界面充分接触, 然后撤去预压力. 通过连杆向反方向提升薄膜, 发现硅片从永磁体上被拾取与薄膜黏结在一起(图10(g)). 随着薄膜提升距离(与永磁体的距离)的增大, 薄膜处的磁场强度逐渐减弱, 作用在薄膜上磁场力减小, 当磁场力不足以抑制薄膜内弯曲应变能的释放时, 薄膜与硅片间界面开始脱黏(图10(h)), 随着薄膜提升距离的进一步增大, 硅片与薄膜间的界面黏附力不足以克服硅片自身重力, 此时硅片完全从薄膜上脱落(图10(i)).

图10

图10   (a)黏附机械抓手; (b)通过预压力使薄膜与硅片完全接触; (c)撤去预压力后无磁场时薄膜从硅片基底上自发脱黏; (d) $\sim$ (f)磁场作用下薄膜靠近硅片过程中曲率逐渐减小; (g)硅片被拾取; (h)薄膜与硅片界面开始脱黏; (i)硅片从薄膜上完全释放

Fig.10   (a) Adhesively mechanical gripper; (b) film completely contact with the silicon substrate through a preload; (c) film detaches from the substrate spontaneously without the action of magnetic field after removing the preload; (d) $\sim$ (f) curvature of the film decreases with decreasing the separation between the film and substrate with the action of magnetic field; (g) gripping the silicon substrate; (h) initial detachment of the interface; (i) complete detachment of the silicon from the film


该部分设计并制备了一种简易的黏附机械抓手, 通过外加磁场和薄膜初始曲率的共同作用, 能够实现磁场作用下物体的拾取, 当磁场减弱或无磁场时能够在特定的位置释放该物体. 因此可以通过调控磁场变化连续实现物体的抓取、搬运和释放等功能. 根据本文的实验和理论结果, 界面等效黏附性能依赖于薄膜的初始构型、几何性质、材料性质和外界磁场强度等因素的影响, 后续工作可进一步研究不同质量、不同形状、不同尺寸物体的黏附抓取装置设计.

值得注意的是, 本文实现的是对宏观物体的操控. 当被操控物体尺寸减小到微米尺度, 特别是纳米尺度时, 物体的质量基本可以忽略. 由接触力学可知, 即使无外界磁场作用时, 具有初始曲率的薄膜与物体接触时, 由于分子间相互作用, 界面仍然会产生一定的接触面积, 具有相当的界面黏附力使两物体吸引在一起. 因此, 对于微纳尺度物体可能难以通过本文方法进行操控.

5 结论

本文提出了一种外加磁场和初始薄膜曲率协同调控界面黏附性能的方法. 首先实验制备了具有初始等曲率的磁敏感薄膜, 通过撕脱实验研究了薄膜初始曲率、弯曲刚度和外界磁场强度等因素对界面黏附性能的影响. 实验结果发现: 无论有无磁场作用, 薄膜-基底界面黏附力均随薄膜初始曲率的增大而减小; 当薄膜初始曲率一定时, 磁场作用下的界面黏附力始终大于无磁场时的黏附力, 并且界面黏附力随着磁场强度的增大而增大. 与零曲率平薄膜的情况不同, 具有初始膜曲率的界面稳态撕脱力随膜弯曲刚度的增大而减小, 而零曲率薄膜的稳态撕脱力与膜弯曲刚度无关. 进一步建立了磁场作用下初始曲率薄膜-基底界面撕脱理论模型, 基于势能最小原理, 揭示了磁场和薄膜初始曲率对界面黏附性能的影响机制, 主要是薄膜弯曲能、磁场势能、界面黏附能相互竞争的结果. 理论预测与实验结果一致且表明: 可通过合理设计薄膜初始曲率实现磁场作用下界面黏附性能的调控. 最终设计了一种磁场与薄膜初始曲率协同作用的简易抓取装置, 能实现物体的连续拾取、搬运和释放功能.

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[本文引用: 1]

Krahn J, Menon C.

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Langmuir, 2012, 28(12): 5438-5443

DOI      URL     [本文引用: 1]

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Acs Applied Materials & Interfaces, 2014, 6(11): 8702-8707

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Advanced Functional Materials, 2013, 23(26): 3256-3261

DOI      URL     [本文引用: 2]

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Gecko-inspired surfaces: A path to strong and reversible dry adhesives

Advanced Materials, 22(19): 2125-2137

DOI      URL     [本文引用: 1]

Drechsler P, Federle W.

Biomechanics of smooth adhesive pads in insects: Influence of tarsal secretion on attachment performance

Journal of Comparative Physiology A-Neuroethology Sensory Neural And Behavioral Physiology, 2006, 192: 1213-1222

PMID      [本文引用: 1]

Many insects possess smooth adhesive pads on their legs, which adhere by thin films of a two-phasic secretion. To understand the function of such fluid-based adhesive systems, we simultaneously measured adhesion, friction and contact area in single pads of stick insects (Carausius morosus). Shear stress was largely independent of normal force and increased with velocity, seemingly consistent with the viscosity-effect of a continuous fluid film. However, measurements of the remaining force 2 min after a sliding movement show that adhesive pads can sustain considerable static friction. Repeated sliding movements and multiple consecutive pull-offs to deplete adhesive secretion showed that on a smooth surface, friction and adhesion strongly increased with decreasing amount of fluid. In contrast, pull-off forces significantly decreased on a rough substrate. Thus, the secretion does not generally increase attachment but does so only on rough substrates, where it helps to maximize contact area. When slides were repeated at one position so that secretion could accumulate, sliding shear stress decreased but static friction remained clearly present. This suggests that static friction which is biologically important to prevent sliding is based on non-Newtonian properties of the adhesive emulsion rather than on a direct contact between the cuticle and the substrate.

Lees AD, Hardie J.

The organs of adhesion in the aphid megoura viciae

Journal of Experimental Biology, 1988, 136: 209-228

DOI      URL     [本文引用: 1]

Carlson A, Wang SD, Elvikis P, et al.

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Advanced Functional Materials, 2012, 22: 4476-4484

DOI      URL     [本文引用: 1]

Dening K, Heepe L, Afferrante L, et al.

Adhesion control by inflation: Implications from biology to artificial attachment device

Applied Physics A, 2014, 116: 567-573

DOI      URL     [本文引用: 1]

Li LZ, Liu ZY, Zhou M, et al.

Flexible adhesion control by modulating backing stiffness based on jamming of granular materials

Smart Materials & Structures, 2019, 28: 115023

DOI      URL     [本文引用: 2]

Linghu CH, Wang CJ, Cen N, et al.

Rapidly tunable and highly reversible bio-inspired dry adhesion for transfer printing in air and a vacuum

Soft Matter, 2019, 15: 30-37

DOI      URL     [本文引用: 3]

Xie T, Xiao XC.

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Chemistry of Materials, 2008, 20: 2866-2868

DOI      URL     [本文引用: 2]

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Aircraft Engineering and Aerospace Technology, 1953, 25(3): 64-70

DOI      URL     [本文引用: 1]

李炳奇, 张振宇, 李斌 .

基于内聚力模型的高速水流聚脲基涂层剥离破坏模型研究

力学学报, 2020, 52(5): 1538-1546

DOI      [本文引用: 1]

冲磨和空蚀破坏是水利水电设施最为常见的病害之一,严重影响水利水电设施的安全运行和效益发挥. 泄洪建筑物通常喷涂聚脲基涂层来提高抗冲耐磨性能,但在泄洪高速水流速度作用下抗冲磨聚脲基涂层的剥离破坏机理的研究尚属空白. 本文基于高速水流的流态形式,提出了高速水流对泄洪建筑物的力学作用模型,水流作用对泄洪建筑物的载荷主要包括拖曳力、冲击力、脉动力和上浮力;采用内聚力模型表征聚脲基涂层与泄洪建筑物防护体界面的剥离破坏过程,建立了高速水流聚脲涂层的剥离破坏模型, 给出了模型的有限元形式方程、本构关系以及损伤起始原则、演化原则和接触碰撞模型. 通过聚脲涂层与混凝土基底的剥离破坏试验,分析了不同剥离倾角下界面剥离破坏的拉应力与倾角之间的变化规律,得到了聚脲涂层剥离破坏过程中应力-$\!$-位移变化关系. 根据剥离破坏试验计算了界面剥离破坏断裂模型参数,采用数值方法对模型进行了验证,试验结果与模型计算结果吻合良好,为泄洪建筑物的抗冲耐磨设计提供理论依据.

(Li Bingqi, Zhang Zhenyu, Li Bin, et al.

Study on debonding failure model of polyurea-based coating with high velocity water flow based on cohesive zone model

Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1538-1546 (in Chinese))

[本文引用: 1]

Chai Z, Liu M, Chen L, et al.

Controllable directional deformation of micro-pillars actuated by a magnetic field

Soft Matter, 2019, 15: 8879-8885

DOI      PMID      [本文引用: 2]

It is well known that special surface functions can be designed by varying the topography of micro-structured surfaces. In the present paper, a simple but effective method to control the directional deformation of micro-pillar arrays is proposed through a rotating magnetic field. The large deformation of each micro-pillar can be tuned by the magnetic field strength and direction. When the magnetic field strength is fixed, the deformation direction of micro-pillars is controlled by the direction of magnetic field. When the direction of magnetic field is determined, the deflection of micro-pillars increases with the increase of magnetic field strength. Based on the principle of minimum potential energy, a theoretical model is further established to disclose such a large deformation mechanism of micro-pillars. The theoretically predicted morphology of deformed pillars is well consistent with the experimental results. The present experimental technique and theoretical results should be useful for the design and preparation of typical functional surfaces such as reversible adhesion, controllable wettability and directional surface transport.

Peng ZL, Chen SH.

Effect of bending stiffness on the peeling behavior of an elastic thin film on a rigid substrate

Physical Review E, 2015, 91(4): 042401

DOI      URL     [本文引用: 3]

Kendall K.

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Journal of Physics D-Applied Physics, 1975, 8(13): 1449-1452

DOI      URL     [本文引用: 1]

Needleman A.

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International Journal of Fracture, 1990, 42(1): 21-40

DOI      URL     [本文引用: 1]

Kamiyama H, Takaki H.

A possible distribution of ion density in the iono-exosphere with a dipole magnetic field

Journal of Geomagnetism and Geoelectricity, 1966, 18: 1-11

DOI      URL     [本文引用: 1]

王明勇, 郎志坚, 李国军.

方形磁体的空间磁场分布

磁性材料及器件, 2001, 32: 17-20

[本文引用: 1]

(Wang Mingyong, Lang Zhijian, Li Guojun.

The spacial magnetic field distribution of square magnet

Journal of Magnetic Materials and Devies, 2001, 32: 17-20 (in Chinese))

[本文引用: 1]

Said MM, Yunas J, Pawinanto RE, et al.

PDMS based electromagnetic actuator membrane with embedded magnetic particles in polymer composite

Sensors and Actuators A-Physical, 2016, 245: 85-96

DOI      URL     [本文引用: 1]

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