1.Key Laboratory of Novel Materials for Sensor of Zhejiang Province, College of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China 2.School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China 3.CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 91963123), the Ten Thousand Talents Plan of Zhejiang Province, China (Grant No. 2018R52003), and the Fundamental Research Funds for the Provincial University of Zhejiang, China (Grant Nos. GK199900299012-022, GK209907299001-014)
Received Date:28 June 2020
Accepted Date:02 September 2020
Available Online:12 January 2021
Published Online:05 January 2021
Abstract:Controlled surface structures have important applications in the fields of flexible electronics, bionic devices, smart materials and surface engineering. Although various instability modes induced by stresses in homogeneous and heterogeneous film systems have been investigated extensively in the past decades, understanding the stress relief mechanisms of gradient film systems is still a challenge. In this work, periodic thickness-gradient metal silver films on flexible polydimethylsiloxane (PDMS) substrates are prepared by using magnetron sputtering technique and by masking weaved copper grid during deposition. The morphological evolutions and structural characteristics of the gradient films in the uniaxial mechanical compression/tension process are detected by using optical microscopy and atomic force microscopy. It is found that the thickness-gradient film spontaneously forms on the PDMS surface due to the specific three-dimensional structure of the weaved copper grid. The maximum film thickness in the mesh center is about twice larger than the minimum one in the region covered by the copper wire. Under the uniaxial mechanical loading, the silver film surface will form stripe wrinkles and straight cracks, which are aligned perpendicular to each other. The variation of film thickness can well modulate the in-plane strain distribution of the film and thus the stress relief patterns. As the compressive strain increases, the wrinkles first form in the region with smaller film thickness, and then extend into the region with larger thickness. The wrinkle wavelength decreases with compressive strain increasing, which is in consistent with the theoretical prediction of accordion model. The wavelength and amplitude of the wrinkles exhibit periodically oscillatory behaviors across the film surface. As the tensile strain increases, the cracks start to propagate in the region with smaller thickness, and then the crack width and number both increase gradually, leading the multiple crack modes to form finally. The crack width and average spacing both increase with film thickness increasing. The morphologies and evolutions of such wrinkles and cracks in the thickness-gradient films are analyzed in depth based on the stress theory. The wrinkle patterns are further simulated by the finite element method, and the simulation results are in good agreement with the experimental results. This study could promote a better understanding of the strain effects of heterogeneous film systems and find the applications in the field of flexible electronics by the structural design of thickness-gradient films. Keywords:flexible electronics/ film/ thickness-gradient/ strain effect
实验用的柔性基底为聚二甲基硅氧烷(PDMS, Sylgard 184, Dow Corning), 按主剂和固化剂10∶1的重量比混合, 用玻璃棒搅拌均匀后水平静置30 min. 待气泡完全消除后, 将混合溶液倾倒在平整的器皿内, 随后在温度为70 °C的加热台上固化5 h, 使PDMS完全交联成为弹性聚合物材料. 固化后的PDMS厚度约为1.2 mm, 用刀具将其切割成宽为12 mm的矩形片. 使用自制的拉伸装置将PDMS沿长度方向固定, 夹具内的PDMS长度为25 mm, 然后将PDMS预拉伸到30 mm, 即预应变为20%(图1(a)). 在预拉伸的PDMS上覆盖编织铜网, 表面贴紧(图1(b)). 铜网由直径约为52 μm的铜线正交编织而成, 网孔的宽度(即周期)w约为125 μm(图1(c)). 应当指出, 当网孔周期与褶皱波长相当时, 它们之间会存在复杂的竞争[18,21,22]. 而本文采用的网孔周期比褶皱波长大很多, 不需要考虑这种竞争关系. 本文主要通过薄膜的厚度梯度诱导应力的重排, 从而调控褶皱和裂纹的形成与分布. 图 1 PDMS基底上周期性厚度梯度薄膜的制备流程及应变施加过程 (a) PDMS基底预拉伸至20%的预应变; (b)编织铜网覆盖到预拉伸的PDMS表面; (c)编织铜网的光学显微镜照片; (d)银薄膜沉积之后, 移除铜网, 并释放预应变至PDMS的原长; (e)进一步拉伸PDMS至任意长度L Figure1. Schematic illustration of sample preparation and loading sequence of periodic thickness-gradient films on PDMS substrates: (a) The PDMS substrate was stretched to 20% prestrain; (b) a weaved copper grid was placed on the pre-stretched PDMS surface; (c) optical micrograph of the weaved copper grid; (d) after deposition of silver film, the copper grid was removed and the prestrain was released to the original length of PDMS; (e) the PDMS substrate was further stretched to a random length, namely L.
图2(a)和(b)为周期性厚度梯度薄膜在预应变释放过程中的原位形貌演化规律. 由图2可知, 编织铜网的存在使得薄膜表面形成与铜网结构一致的周期性阵列, 样品表面深色部分为铜线覆盖区域, 膜厚较小, 浅色部分为网孔中心区域, 膜厚较大. 由于薄膜的残余应力作用, 制备态的样品($\varepsilon = 0$)自发形成了褶皱结构, 其主要分布在膜厚较小区域. 随着预应变的释放, 膜厚较小处开始形成新的褶皱结构, 并逐渐扩展至网孔中心处. 由于泊松效应, PDMS在载荷方向上的收缩将使其在垂直方向上产生拉伸[11,26]. PDMS的泊松比约为0.48, 因而垂直方向上产生的应变约为机械应变的一半. 在$\varepsilon \approx - 3.3\% $时, 受横向拉伸应变的作用, 薄膜开始在垂直于褶皱的方向上出现裂纹[11,26]. 裂纹的长度和数量随着机械应变的增加而增加, 但都限定在膜厚较小的区域. 图 2 PDMS基底上周期性厚度梯度Ag薄膜受单轴压缩的形貌演化及结构特征 (a)光学显微镜放大50倍的图片, 尺寸均为1042 μm × 1390 μm, 箭头指向代表压缩方向; (b)光学显微镜放大200倍的图片, 尺寸均为261 μm × 348 μm; (c)单个网孔内薄膜表面形貌的原子力显微镜图片; (d)不同位置的剖面线结构 Figure2. Morphological evolutions and structural characteristics of periodic thickness-gradient Ag films on PDMS substrates under uniaxial compression: (a) Optical micrographs with 50× magnification. All the images have the size of 1042 μm × 1390 μm. The arrows represent the direction of compression. (b) Optical micrographs with 200× magnification. All the images have the size of 261 μm × 348 μm. (c) Atomic force microscopy (AFM) image of the film surface within a grid period. (d) Cross-sectional profiles of the film surface at different positions.
图2(c)显示了单个网孔内薄膜表面形貌的原子力显微镜图像, 图2(d)为不同位置的剖面线结构. 由图2可知, 褶皱均沿着垂直于机械载荷的方向排列, 呈条纹型结构, 这是由单轴机械压缩引起的[11,26]. 沿着网孔中心线的褶皱(剖面线1)具有良好的周期性变化规律, 其波长和振幅均呈现振荡行为, 在网孔中心处, 波长和振幅达到最大值, 随后逐渐衰减, 至铜网覆盖处达到最小. 偏离网孔中心线的褶皱(剖面线2)仍显示较好的振荡规律, 但波长和振幅均相应变小. 铜线覆盖处(剖面线3)褶皱的波长和振幅都显著变小, 但仍显示一定的振荡规律. 在原子力显微图的右下角(剖面线3的右侧), 褶皱结构消失, 这是因为该处正好是铜线与PDMS表面的接触点, 薄膜厚度为零. 采用编织铜网作掩模来构筑周期性厚度梯度薄膜, 简单方便, 但接触点导致的薄膜不均匀性(或缺陷)没法避免. 可以采用TEM用的平板铜网, 在沉积过程中抬起一定的高度来解决这一问题, 这也是后续要研究的课题. 为了进一步理解预应变释放过程中薄膜结构的演化规律, 系统测量了褶皱波长、裂纹长度和宽度等信息(图3). 图3(a)为预应变释放完毕后褶皱波长在一个周期范围内的分布规律, 可以发现, 中心区域的褶皱波长最大, 而铜网覆盖处的波长最小, 最大波长和最小波长之比接近于2, 与之前的实验结果一致[25]. 图3(b)为中心区域的褶皱波长(即最大波长)随机械应变的演化规律, 可以发现褶皱波长随着压缩应变的增加而持续减小. 图 3 (a)一个周期内褶皱波长沿着中心线的演化规律; (b)中心区域褶皱的波长与机械压缩应变的关系, 实线为手风琴模型的理论结果; (c)归一化的裂纹长度(裂纹长度与网孔宽度之比)与机械应变的关系, 实线为实验数据的线性拟合; (d)裂纹宽度与机械应变的关系, 插图为不同应变下的裂纹形貌, 尺寸均为70 μm × 16 μm Figure3. (a) Evolution of wrinkle wavelength along the center line within a grid period. (b) dependence of the wrinkle wavelength at the mesh center on the mechanical compressive strain. The solid line represents theoretical prediction of accordion model. (c) dependence of normalized crack length (the ratio of crack length to mesh width) on the mechanical strain. The solid line is a linear fit to the experimental data. (d) dependence of the crack width on the mechanical strain. The insets (both 70 μm × 16 μm) show the crack morphologies under different strains.
在薄膜器件(特别是柔性电子器件)的使用过程中, 其往往受到复杂的载荷作用, 而拉伸应变对器件的力学稳定性和使用寿命影响更大. 因而, 在机械压缩的基础上, 进一步考察了Ag/PDMS体系在单轴拉伸载荷下的结构演化. 图4(a)和(b)为周期性厚度梯度薄膜在拉伸过程中的原位形貌演化规律. 可以发现, 在平行于加载方向上出现褶皱, 而在垂直方向上则出现裂纹, 该结果正好与单轴压缩时相反, 这是由应力的性质(拉伸或压缩)决定的. 与单轴压缩情况相似的是, 褶皱最先在膜厚较小区域产生, 随后逐渐扩展到膜厚较大区域. 图4(d)显示中心处褶皱的最大波长随着机械应变的增加而逐渐减小, 与图3(b)的结果一致. 同样, 褶皱的波长也符合手风琴模型的理论预测(图4(d)中红色实线). 图 4 PDMS基底上周期性厚度梯度Ag薄膜受单轴拉伸的形貌演化及结构特征: (a)光学显微镜放大50倍的图片, 尺寸均为1042 μm × 1390 μm, 箭头指向代表拉伸方向; (b)光学显微镜放大200倍的图片, 尺寸均为261 μm × 348 μm; (c)光学显微镜放大500倍的图片, 尺寸均为104 μm × 139 μm; (d)中心区域的褶皱波长与机械拉伸应变的关系, 实线为手风琴模型的理论结果; (e)沿中心线的裂纹宽度和裂纹数目随应变的演化规律; (f)总的裂纹宽度与机械应变的关系, 实线为实验数据的线性拟合. Figure4. Morphological evolutions and structural characteristics of periodic thickness-gradient Ag films on PDMS substrates under uniaxial tension: (a) Optical micrographs with 50× magnification. All the images have the size of 1042 μm × 1390 μm. The arrows represent the direction of tension. (b) Optical micrographs with 200× magnification. All the images have the size of 261 μm × 348 μm. (c) Optical micrographs with 500× magnification. All the images have the size of 104 μm × 139 μm. (d) Dependence of the wrinkle wavelength at the mesh center on the mechanical tensile strain. The solid line represents theoretical prediction of accordion model. (e) Evolutions of the crack width and crack number along the center line with the tensile strain. (f) Dependence of the total crack width on the tensile strain. The solid line is a linear fit to the experimental data.
其中G为薄膜的能量释放率. 本实验中, 薄膜厚度呈周期性变化, 导致应力(或应变)也并不均匀分布在膜面上. 周期性厚度梯度薄膜的表面形貌($\varepsilon = 0$)和膜厚分布如图5(a)和图5(b)所示. 考虑单个周期的情况, 应力可表示成$\sigma = F/S$, 其中F为薄膜两侧的拉力(或压力), $S = wh$为薄膜的横截面. 力具有传递效应, 因而在不同位置力是相等的, 但薄膜横截面与膜厚呈正比, 也呈周期性变化(图5(c)). 因而应力与薄膜厚度之间存在简单的反比关系, 即$\sigma \propto {h^{ - 1}}$. 显然, 在膜厚较小区域, 应力(或应变)具有较大值, 或者说应力倾向于集中在膜厚较小区域, 并率先超过褶皱的临界应力. 因而, 褶皱总是在铜网覆盖区域率先形成, 并逐渐扩展到网孔中心区域(图2和图4). 图 5 (a)周期性厚度梯度Ag薄膜的表面形貌, $\varepsilon = 0$; (b)沿中心线薄膜厚度分布的示意图; (c)膜厚最小区域和最大区域的薄膜横截面示意图. 注意: 图中薄膜厚度h与网孔周期w并不按比例绘制, 膜厚被极大地放大了, 事实上膜厚在纳米量级(最大约90 nm), 而网孔周期在微米量级(约125 μm), 它们之间相差3个数量级 Figure5. (a) Surface morphology of a periodic thickness-gradient Ag film when $\varepsilon = 0$; (b) schematic diagram of the periodic thickness-gradient film along the center line. Note that the film thickness is greatly exaggerated. In fact, the grid period (w ~ 125 μm) is three orders of magnitude larger than the film thickness (hmax ~ 90 nm).
即能量释放率与薄膜厚度呈反比. 因而膜厚较小区域具有较大的能量释放率, 同时薄膜的断裂韧性为一常量. 随着拉伸应变的增加, 膜厚较小区域的能量释放率将率先超过薄膜的断裂韧性, 裂纹开始萌生. 该裂纹将有效释放附近的拉伸应力, 使周围薄膜的能量释放率低于临界值, 从而抑制了其它裂纹的萌生. 此时拉伸应变主要通过单条裂纹的长度和宽度的增加得以释放. 当该裂纹的宽度达到饱和之后, 将不能再有效地释放应变能, 此后周围薄膜的能量释放率快速增加, 并超过薄膜的断裂韧性, 从而形成多重裂纹模态. 实验显示, 多重裂纹基本都限定在膜厚较小的区域, 至少在20%的拉伸应变作用下, 网孔中心区域的薄膜仍保持完好(图4(b)). 为了进一步研究拉伸应变作用下厚度梯度薄膜的形态分布, 考察$\varepsilon = 20\% $时单个周期的结构特征(图6(a)). 方便起见, 选取如图所示的坐标系, 膜厚最小处为原点, 加载方向为x轴, 垂直方向为y轴. 样品在x和y两个方向上都具有厚度梯度, 因而褶皱波长随着x的增加而增加, 随着y的增加而减小, 如图6(b)所示, 这一结果与压缩应变诱导的褶皱类似. 另一方面, 在y方向上, 裂纹的形态和数目有显著变化. 随着y的增加, 裂纹的数目增加, 宽度变小, 同时裂纹的平均间距也变小(图6(c)). 根据材料的断裂理论, 薄膜裂纹的平均间距可以表示为[26,31] 图 6 (a)$\varepsilon = 20\% $时单个周期的典型结构特征; (b)在x和y方向上, 褶皱波长随距离的演化规律; (c)裂纹数目和裂纹平均间距随距离y的变化规律; (d)在y方向上, 裂纹平均间距和褶皱波长的依赖关系, 实线为实验数据的线性拟合 Figure6. (a) Typical surface morphology of Ag film within a grid period under $\varepsilon = 20\% $; (b) evolutions of the wrinkle wavelength with the distance both in x and y directions; (c) evolutions of the crack number and average crack spacing with the distance y; (d) dependence of the average crack spacing on the wrinkle wavelength in the y direction and the solid line is a linear fit to the experimental data.
由于薄膜厚度梯度的存在, 当面内压应力未达到临界应力时, 面内应变的分布不均匀, 且与膜厚成反比, 薄膜两端厚度最小处的压应变最大, 而薄膜中间处的压应变最小(图8(a)). 最大应变与最小应变之比约为2∶1, 与上文通过力的传递效应推导的结果一致. 这就导致膜厚最小处率先达到临界应变, 首先发生屈曲, 通过面外褶皱释放应变, 并逐步向膜厚处扩展. 薄膜褶皱幅值与面内压应变关系曲线如图8(b)所示, 在薄膜屈曲褶皱的演化过程中, 模拟所得的临界屈曲应变为0.047%, 与通过(1)式所得理论值0.052%接近, 说明模拟结果可信. 图 8 有限元模拟结果 (a)一个周期内薄膜面内压应变的分布图; (b)褶皱幅值随薄膜面内压应变的演化规律; (c)一个周期内褶皱形貌的模拟图; (d)褶皱波长在一个周期的变化规律 Figure8. Finite element simulation results: (a) Distribution of the in-plane compressive strain within a period; (b) evolution of the wrinkle amplitude with the in-plane compressive strain; (c) simulated wrinkle morphology within a period; (d) distribution of the wrinkle wavelength within a period.