Solares Santiago D, Matsuda Yuki, Goddard William A
Materials and Process Simulation Center, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
J Phys Chem B. 2005 Sep 8;109(35):16658-64. doi: 10.1021/jp052758g.
Previous studies have shown that when using carbon nanotubes (CNTs) as tapping-mode AFM probes, their tilt angle with respect to vertical (denoted phi) must be close to 0 degrees to obtain high-quality images and that very poor images are obtained for phi > 30 degrees . Here we present a quantitative theoretical investigation of the effect of phi on tapping-mode AFM imaging for single-wall and multiwall nanotube (SWNT and MWNT, respectively) probes of diameters 3.4-5.5 nm and aspect ratio 7.5, which have been found ideal for imaging via TEM. Using molecular and classical dynamics, we investigate the effect of phi on CNT probe stiffness (quantified through the maximum gradient of the tip-sample interaction force) and show that it decreases linearly with increasing phi, becoming negligible at around phi approximately 40 degrees , thus confirming the conclusions of previous studies. We find that MWNT probe stiffness is proportional to the number of walls, but that the difference in stiffness between SWNTs and MWNTs also decreases linearly with increasing phi and becomes negligible at around phi approximately 40 degrees . The simulated cross-sectional scans of a sample SWNT using two different values of phi show that the image can be distorted and shifted laterally when phi is large, in some cases giving measured heights appreciably greater than the sample dimensions. We show analytically that the tip-sample forces that occur during imaging can be significantly lower when CNT probes are used instead of conventional probes, even in the absence of buckling, and that they can be further reduced by increasing phi. On the basis of this result, we propose the design of free-standing kinked probes for the characterization of sensitive samples, whereby the probe approaches the sample at a vertical orientation and possesses a tilted section that regulates the tip-sample interaction forces.
先前的研究表明，当使用碳纳米管（CNT）作为轻敲模式原子力显微镜（AFM）探针时，其相对于垂直方向的倾斜角（记为φ）必须接近0度才能获得高质量图像，而当φ>30度时，图像质量会非常差。在此，我们对直径为3.4 - 5.5 nm且长径比为7.5的单壁和多壁纳米管（分别为SWNT和MWNT）探针在轻敲模式AFM成像中φ的影响进行了定量理论研究，这些纳米管已被发现是通过透射电子显微镜（TEM）成像的理想选择。利用分子动力学和经典动力学，我们研究了φ对CNT探针刚度（通过尖端 - 样品相互作用力的最大梯度来量化）的影响，并表明其随φ的增加呈线性下降，在φ约为40度左右时可忽略不计，从而证实了先前研究的结论。我们发现MWNT探针刚度与壁数成正比，但SWNTs和MWNTs之间的刚度差异也随φ的增加呈线性下降，在φ约为40度左右时可忽略不计。使用两个不同φ值对样品SWNT进行模拟横截面扫描表明，当φ较大时，图像可能会发生扭曲并横向偏移，在某些情况下，测量的高度明显大于样品尺寸。我们通过分析表明，即使在没有屈曲的情况下，使用CNT探针代替传统探针时，成像过程中发生的尖端 - 样品力也可能显著更低，并且通过增加φ可以进一步降低这些力。基于这一结果，我们提出了用于表征敏感样品的独立扭结探针的设计，即探针以垂直方向接近样品，并具有一个倾斜部分来调节尖端 - 样品相互作用力。
