基于接触几何的微纳米尺度下的粘着研究
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摘要
随着微纳米装置和仪器的快速发展，微纳米尺度下的粘着变得越来越重要。小尺度的机械系统有较高的表面积-体积比，所以更多地受到表面效应而非惯性效应的影响。粘着力是微机电系统(MEMS)在制造和使用中失效的一个主要原因。MEMS的进一步实用化和微型化，都迫切地需要研究和控制粘着力。本文在接触几何的基础上，建立了单峰接触粘着模型，利用原子力显微镜研究了两表面间的粘着、特殊结构表面的粘着和类金刚石膜的减粘效应。本文的主要研究内容如下：
（1）精确的接触几何对于粘着的量化计算至关重要，为此本文建立了单峰接触粘着模型。在粗糙峰和随机表面光滑性假设的基础上，通过微分几何曲面论获得每一点的主曲率。在曲面当前点的一级近似下，把曲面与粗糙峰的接触等价地转化成一个刚性平面和弹性椭圆抛物面间的接触。这种转化保持了原有的接触区间隙和弹性变形性质。随后，通过连续介质接触力学理论和Hamaker方法，用数值方法来求解曲面上每一点的接触面积和粘着力。最后本文给出了两个算例，说明模型在一定程度上是可行的。
（2）为了研究两平面间的粘着和避免针尖磨损，本文采用针尖直径约为1.7μm的平头探针。实验采用的样品是硅片、石英和蓝宝石。实验分别在潮湿的空气中、高纯干燥氮气中(手套箱中)、蒸馏水中和氯化钾溶液中进行。研究表明，真实接触面积只占表观接触面积的很小一部分。热力学表面自由能并不能预测两表面间粘着力的大小。用原子力显微镜测量粘着力的稳定性和重复性取决于样品特征、测量参数和环境。不同环境下，对粘着力有影响的相互作用和因素有所不同，各相互作用和因素之间相互耦合决定了最终的粘着力。
（3）为了研究温度对粘着的影响，实验采用的接触几何是平面与粗糙表面的接触。实验分别在潮湿的空气中和高纯干燥氮气中进行。样品温度从30°C变化到200°C。结果表明，200°C以内的温度对探针微悬臂的法向弹性系数的影响基本可以忽略。在这个温度范围内，每一温度下的粘着力分布都是正态的。在高纯干燥氮气中，粘着力随着温度的升高而持续下降。但在潮湿的空气环境下，随温度的升高，粘着力先增大，在约100°C时达到最大值，接着开始下降。在下降的过程中，开始较为缓慢，在150°C附近，粘着力急剧下降，并在高温区保持较平稳的状态。
（4）在潮湿的空气中和高纯干燥氮气中，我们研究了尖探针、平头探针和小球探针与周期性绝缘表面接触时的粘着行为。结果表明：粘着行为极大地依赖于接触几何、表面形貌和环境，并且这三个因素是共同作用来决定最终的粘着力的。在同一点的多次测量中，多峰接触时的粘着力都出现了分层的现象。在手套箱中不除静电的情况下和在空气中，粘着力在各层逐渐增加，并有层间跳跃的现象。粘着力的增加起因于静电荷的积累和毛细弯月面半径的增大。静电荷只有在接触-分离之后才增加，并且具有累加效应，当达到饱和后，粘着力将表现得平稳。在手套箱中除静电的情况下，粘着力各层的变化不大。在利用小球探针时，我们还发现粘着来源的不同会导致同一点粘着力在区间段上的波动情况不同。具体情况是：有静电时，波动较小；去静电时，波动最大；空气中，波动最小。
（5）在空气中和高纯干燥氮气中，基于不同的接触几何，我们研究了掺杂金属的类金刚石(DLC)膜的减粘效应。结果发现，在不同的接触几何和环境下，DLC膜都可以有效地减小粘着力和磨损。粘着力的减小原因是表面能的降低和DLC膜对水的接触角的增大。粘着力的减小幅度与接触几何、DLC膜的粗糙度、与DLC膜配对的材料特性和所处的环境都密切相关。并且，这些因素是共同作用来决定最后的粘着力减小幅度的。
With the rapid development of micro-scale/nano-scale devices and instruments, theadhesion in these scales becomes more and more important. The small-scale mechanicalsystems have high surface-area-to-volume ratios. Therefore, these systems are moreinfluenced by surface effects rather than inertia effects. The adhesion force is the chief factorof the failures of micro electro mechanical systems (MEMS) in the manufacture and in use.Meanwhile, in order to further the practicability and miniaturization of MEMS, it is urgent todevelop a sophisticated understanding and control of adhesion between solid-solid surfaces.In this thesis, a single-asperity adhesion model is established based on contact geometry.Meanwhile, the adhesion behaviors between two surfaces, the adhesion of special surfacestructure and the effect of reducing adhesion of diamond-like carbon (DLC) films are studiedby using an atomic force microscopy (AFM).
(1) The precise contact geometry is crucial to the quantification of adhesion force. Thesingle-asperity adhesion model is established based on contact geometry. On the basis ofsmoothness assumption of the asperity and surface, the principal curvatures of a point on thesurface are obtained by using the surface theory of differential geometry. By using the firstapproximation of the surface, the contact between a parabolic-shaped asperity andarbitrary-shaped surface patch is transformed into the contact between an elastic ellipticparaboloid and a rigid flat surface. The gaps between the asperity and surface of two kinds ofcontacts are the same when applying normal load, and the elastic properties are not changedafter transformation. By using the theories of continuous medium contact mechanics andHamaker approach, the contact area and adhesion force of each point on the surface areobtained by using numerical methods. At last, two examples are given to show theeffectiveness of the model.
(2) In order to study the adhesion between two solid surfaces and prevent wear, a flat tipwith a diameter~1.7μm is used. The adhesion forces of some surface have been determinedby recording the force-displacement curves with the AFM. The adhesion measurements werecarried out under ambient conditions, in a nitrogen-filled glove box, under distilled water, and under potassium chloride (KCl) solution. The outcome shows that the real contact areawithout the applied load is only a small proportion of the apparent contact area. The adhesionforce between solid surfaces cannot be predicted by the theory of thermodynamic surface freeenergy. The measurement stability and repeatability of adhesion by the AFM depend on thesurface characterization, measurement methods and the environment. Under differentenvironments, there are different interactions and factors affecting the adhesion force, and thedominant interactions and factors may be different too. The various interactions and factorsare mutually coupled to determine the final adhesion force.
(3) In order to study the influence of temperature on the adhesion, the contact geometryof smooth surface and rough surface is selected. The adhesion measurements were carried outunder ambient conditions and in a nitrogen-filled glove box. The substrate temperaturechanges from30°C to200°C. The results show that when the temperature is less than200°C,the influence of temperature on the normal spring constant can be ignored. In this temperaturerange, the adhesion distribution for each temperature exhibits a Gaussian-like distribution. Inthe glove box, the mean adhesion force decreases with increasing temperature. However, inhumid environment, with increasing temperature, the mean adhesion force first increases andreaches the maximum at~100°C, then begin to decline. At about150°C, the mean adhesionforce decreases dramatically, and remains relatively stable in the high temperature state.
(4) Under ambient conditions and in a nitrogen-filled glove box, the adhesion of aninsulating periodic structure is studied by using a sharp tip, a flat tip and a ball tip. Theoutcomes show that the adhesion behaviors are largely dependent on the contact geometry,surface topography and the environment. And these factors are mutually coupled with eachother to determine the final adhesion. When numerous measurements are carried out on thesame location, the adhesion of multi-asperity contact exhibits stratification phenomena. In theglove box (without static charge removal) and under ambient conditions, the adhesion force indifferent layers increases with the increasing measurement number, and jumps betweendifferent layers. The increase of adhesion is attributed to the increase of electrostatic chargesand the increase scale of the capillary meniscus. The electrostatic charges will increase only after contact and separation and have an additive effect. When the charges are saturated, theadhesion behavior becomes stable. In the glove box (with static charge removal), the adhesionforce in different layers changes slightly. By using the ball tip, we found that the difference ofinteraction of adhesion will lead to the different adhesion fluctuation situations on the samespot. That is: when there are some changes, the fluctuation is small; by removing the changes,the fluctuation is the largest; under ambient conditions, the fluctuation is the smallest.
(5) Under ambient conditions and in a nitrogen-filled glove box, the effect of reducingadhesion of metal-doped diamond-like carbon (DLC) films is studied based on differentcontact geometries. The outcome shows that the DLC film can effectively reduce adhesionand wear for different contact geometries under different environments. The reduction ofadhesion is attributed to the decrease of surface energy and the increase of the contact angle towater. The reduction ratio is closely related to contact geometry, the roughness of DLC film,material characteristics paired to DLC film and the environment. And these factors aremutually coupled to determine the final reduction ratio.
（1）精确的接触几何对于粘着的量化计算至关重要，为此本文建立了单峰接触粘着模型。在粗糙峰和随机表面光滑性假设的基础上，通过微分几何曲面论获得每一点的主曲率。在曲面当前点的一级近似下，把曲面与粗糙峰的接触等价地转化成一个刚性平面和弹性椭圆抛物面间的接触。这种转化保持了原有的接触区间隙和弹性变形性质。随后，通过连续介质接触力学理论和Hamaker方法，用数值方法来求解曲面上每一点的接触面积和粘着力。最后本文给出了两个算例，说明模型在一定程度上是可行的。
（2）为了研究两平面间的粘着和避免针尖磨损，本文采用针尖直径约为1.7μm的平头探针。实验采用的样品是硅片、石英和蓝宝石。实验分别在潮湿的空气中、高纯干燥氮气中(手套箱中)、蒸馏水中和氯化钾溶液中进行。研究表明，真实接触面积只占表观接触面积的很小一部分。热力学表面自由能并不能预测两表面间粘着力的大小。用原子力显微镜测量粘着力的稳定性和重复性取决于样品特征、测量参数和环境。不同环境下，对粘着力有影响的相互作用和因素有所不同，各相互作用和因素之间相互耦合决定了最终的粘着力。
（3）为了研究温度对粘着的影响，实验采用的接触几何是平面与粗糙表面的接触。实验分别在潮湿的空气中和高纯干燥氮气中进行。样品温度从30°C变化到200°C。结果表明，200°C以内的温度对探针微悬臂的法向弹性系数的影响基本可以忽略。在这个温度范围内，每一温度下的粘着力分布都是正态的。在高纯干燥氮气中，粘着力随着温度的升高而持续下降。但在潮湿的空气环境下，随温度的升高，粘着力先增大，在约100°C时达到最大值，接着开始下降。在下降的过程中，开始较为缓慢，在150°C附近，粘着力急剧下降，并在高温区保持较平稳的状态。
（4）在潮湿的空气中和高纯干燥氮气中，我们研究了尖探针、平头探针和小球探针与周期性绝缘表面接触时的粘着行为。结果表明：粘着行为极大地依赖于接触几何、表面形貌和环境，并且这三个因素是共同作用来决定最终的粘着力的。在同一点的多次测量中，多峰接触时的粘着力都出现了分层的现象。在手套箱中不除静电的情况下和在空气中，粘着力在各层逐渐增加，并有层间跳跃的现象。粘着力的增加起因于静电荷的积累和毛细弯月面半径的增大。静电荷只有在接触-分离之后才增加，并且具有累加效应，当达到饱和后，粘着力将表现得平稳。在手套箱中除静电的情况下，粘着力各层的变化不大。在利用小球探针时，我们还发现粘着来源的不同会导致同一点粘着力在区间段上的波动情况不同。具体情况是：有静电时，波动较小；去静电时，波动最大；空气中，波动最小。
（5）在空气中和高纯干燥氮气中，基于不同的接触几何，我们研究了掺杂金属的类金刚石(DLC)膜的减粘效应。结果发现，在不同的接触几何和环境下，DLC膜都可以有效地减小粘着力和磨损。粘着力的减小原因是表面能的降低和DLC膜对水的接触角的增大。粘着力的减小幅度与接触几何、DLC膜的粗糙度、与DLC膜配对的材料特性和所处的环境都密切相关。并且，这些因素是共同作用来决定最后的粘着力减小幅度的。
With the rapid development of micro-scale/nano-scale devices and instruments, theadhesion in these scales becomes more and more important. The small-scale mechanicalsystems have high surface-area-to-volume ratios. Therefore, these systems are moreinfluenced by surface effects rather than inertia effects. The adhesion force is the chief factorof the failures of micro electro mechanical systems (MEMS) in the manufacture and in use.Meanwhile, in order to further the practicability and miniaturization of MEMS, it is urgent todevelop a sophisticated understanding and control of adhesion between solid-solid surfaces.In this thesis, a single-asperity adhesion model is established based on contact geometry.Meanwhile, the adhesion behaviors between two surfaces, the adhesion of special surfacestructure and the effect of reducing adhesion of diamond-like carbon (DLC) films are studiedby using an atomic force microscopy (AFM).
(1) The precise contact geometry is crucial to the quantification of adhesion force. Thesingle-asperity adhesion model is established based on contact geometry. On the basis ofsmoothness assumption of the asperity and surface, the principal curvatures of a point on thesurface are obtained by using the surface theory of differential geometry. By using the firstapproximation of the surface, the contact between a parabolic-shaped asperity andarbitrary-shaped surface patch is transformed into the contact between an elastic ellipticparaboloid and a rigid flat surface. The gaps between the asperity and surface of two kinds ofcontacts are the same when applying normal load, and the elastic properties are not changedafter transformation. By using the theories of continuous medium contact mechanics andHamaker approach, the contact area and adhesion force of each point on the surface areobtained by using numerical methods. At last, two examples are given to show theeffectiveness of the model.
(2) In order to study the adhesion between two solid surfaces and prevent wear, a flat tipwith a diameter~1.7μm is used. The adhesion forces of some surface have been determinedby recording the force-displacement curves with the AFM. The adhesion measurements werecarried out under ambient conditions, in a nitrogen-filled glove box, under distilled water, and under potassium chloride (KCl) solution. The outcome shows that the real contact areawithout the applied load is only a small proportion of the apparent contact area. The adhesionforce between solid surfaces cannot be predicted by the theory of thermodynamic surface freeenergy. The measurement stability and repeatability of adhesion by the AFM depend on thesurface characterization, measurement methods and the environment. Under differentenvironments, there are different interactions and factors affecting the adhesion force, and thedominant interactions and factors may be different too. The various interactions and factorsare mutually coupled to determine the final adhesion force.
(3) In order to study the influence of temperature on the adhesion, the contact geometryof smooth surface and rough surface is selected. The adhesion measurements were carried outunder ambient conditions and in a nitrogen-filled glove box. The substrate temperaturechanges from30°C to200°C. The results show that when the temperature is less than200°C,the influence of temperature on the normal spring constant can be ignored. In this temperaturerange, the adhesion distribution for each temperature exhibits a Gaussian-like distribution. Inthe glove box, the mean adhesion force decreases with increasing temperature. However, inhumid environment, with increasing temperature, the mean adhesion force first increases andreaches the maximum at~100°C, then begin to decline. At about150°C, the mean adhesionforce decreases dramatically, and remains relatively stable in the high temperature state.
(4) Under ambient conditions and in a nitrogen-filled glove box, the adhesion of aninsulating periodic structure is studied by using a sharp tip, a flat tip and a ball tip. Theoutcomes show that the adhesion behaviors are largely dependent on the contact geometry,surface topography and the environment. And these factors are mutually coupled with eachother to determine the final adhesion. When numerous measurements are carried out on thesame location, the adhesion of multi-asperity contact exhibits stratification phenomena. In theglove box (without static charge removal) and under ambient conditions, the adhesion force indifferent layers increases with the increasing measurement number, and jumps betweendifferent layers. The increase of adhesion is attributed to the increase of electrostatic chargesand the increase scale of the capillary meniscus. The electrostatic charges will increase only after contact and separation and have an additive effect. When the charges are saturated, theadhesion behavior becomes stable. In the glove box (with static charge removal), the adhesionforce in different layers changes slightly. By using the ball tip, we found that the difference ofinteraction of adhesion will lead to the different adhesion fluctuation situations on the samespot. That is: when there are some changes, the fluctuation is small; by removing the changes,the fluctuation is the largest; under ambient conditions, the fluctuation is the smallest.
(5) Under ambient conditions and in a nitrogen-filled glove box, the effect of reducingadhesion of metal-doped diamond-like carbon (DLC) films is studied based on differentcontact geometries. The outcome shows that the DLC film can effectively reduce adhesionand wear for different contact geometries under different environments. The reduction ofadhesion is attributed to the decrease of surface energy and the increase of the contact angle towater. The reduction ratio is closely related to contact geometry, the roughness of DLC film,material characteristics paired to DLC film and the environment. And these factors aremutually coupled to determine the final reduction ratio.
引文
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