Vlachová Jana, König Rebekka, Johannsmann Diethelm
Clausthal University of Technology, Institute of Physical Chemistry, Arnold-Sommerfeld-Straße 4, 38678 Clausthal-Zellerfeld, Germany.
Beilstein J Nanotechnol. 2015 Mar 30;6:845-56. doi: 10.3762/bjnano.6.87. eCollection 2015.
The stiffness of micron-sized sphere-plate contacts was studied by employing high frequency, tangential excitation of variable amplitude (0-20 nm). The contacts were established between glass spheres and the surface of a quartz crystal microbalance (QCM), where the resonator surface had been coated with either sputtered SiO2 or a spin-cast layer of poly(methyl methacrylate) (PMMA). The results from experiments undertaken in the dry state and in water are compared. Building on the shifts in the resonance frequency and resonance bandwidth, the instrument determines the real and the imaginary part of the contact stiffness, where the imaginary part quantifies dissipative processes. The method is closely analogous to related procedures in AFM-based metrology. The real part of the contact stiffness as a function of normal load can be fitted with the Johnson-Kendall-Roberts (JKR) model. The contact stiffness was found to increase in the presence of liquid water. This finding is tentatively explained by the rocking motion of the spheres, which couples to a squeeze flow of the water close to the contact. The loss tangent of the contact stiffness is on the order of 0.1, where the energy losses are associated with interfacial processes. At high amplitudes partial slip was found to occur. The apparent contact stiffness at large amplitude depends linearly on the amplitude, as predicted by the Cattaneo-Mindlin model. This finding is remarkable insofar, as the Cattaneo-Mindlin model assumes Coulomb friction inside the sliding region. Coulomb friction is typically viewed as a macroscopic concept, related to surface roughness. An alternative model (formulated by Savkoor), which assumes a constant frictional stress in the sliding zone independent of the normal pressure, is inconsistent with the experimental data. The apparent friction coefficients slightly increase with normal force, which can be explained by nanoroughness. In other words, contact splitting (i.e., a transport of shear stress across many small contacts, rather than a few large ones) can be exploited to reduce partial slip.
通过采用可变幅度（0 - 20纳米）的高频切向激励，研究了微米级球体 - 平板接触的刚度。接触是在玻璃球体与石英晶体微天平（QCM）的表面之间建立的，其中谐振器表面已涂覆有溅射的SiO₂或聚甲基丙烯酸甲酯（PMMA）的旋铸层。比较了在干燥状态和水中进行的实验结果。基于共振频率和共振带宽的变化，该仪器确定接触刚度的实部和虚部，其中虚部量化了耗散过程。该方法与基于原子力显微镜（AFM）的计量学中的相关程序非常相似。接触刚度的实部作为法向载荷的函数可以用约翰逊 - 肯德尔 - 罗伯茨（JKR）模型拟合。发现接触刚度在液态水存在时会增加。这一发现初步解释为球体的摇摆运动，它与靠近接触处水的挤压流动相互耦合。接触刚度的损耗角正切约为0.1，其中能量损失与界面过程相关。在高振幅下发现会发生部分滑动。如卡塔内奥 - 明德林模型所预测的，大振幅下的表观接触刚度与振幅呈线性关系。这一发现很显著，因为卡塔内奥 - 明德林模型假设滑动区域内存在库仑摩擦。库仑摩擦通常被视为一个宏观概念，与表面粗糙度有关。一个替代模型（由萨夫库尔提出）假设滑动区内的摩擦应力恒定，与法向压力无关，但与实验数据不一致。表观摩擦系数随法向力略有增加，这可以用纳米粗糙度来解释。换句话说，可以利用接触分裂（即剪切应力通过许多小接触而非少数大接触的传递）来减少部分滑动。
