Lateral force calibration

SrTiO3(305) surface was annealed for 20h at 1100 C in flowing oxygen as discussed in the literature and used for the lateral force calibration. 

Quantitative measurements of nano-scale frictional properties of pure and mixed SAMs on Au (111) were achieved by in situ normal and lateral force calibration of AFM/FFM. For pure SAMs, the friction coefficients for the same alkanethiol system but with different tips, differ by less than 15%, indicating the reliability of nano-scale frictional and normal force measurements using a scanning force microscope. The friction coefficient increases as the chain length decreases as also found previously by other workers. Tip-based molecular dynamics simulations were carried out to interpret the chain length dependence on frictional properties of alkanethiols. Simulation results show that AFM/FFM tip penetrates deeper into films formed by shorter chain SAMs, causing higher friction. 

Substrate. Cut silicon wafers (001) were used as lateral force calibration standards. The silicon wafers were cleaned via sequential sonication in acetone (15 minutes) and methanol (30 minutes) (HPLC grade from commercial sources), rinsed with ultra-pure water (MilliQ systems), and transferr in the last cloning solvent into an environmental chamber under zero humidity. In the low humidity environment, the silicon friction standard surfaces were heated above 100 C to remove excess water. The sample surfaces provide reproducible lateral force values over a time period of two hours. 

Lateral Force Calibration. The following equation was applied to calibrate the lateral force, Fj, measured from the torque of the cantilever ... 

It is the lateral force signal of the detection scheme and corresponds to the photo diode current taken from the friction loop (47), li =AIt /AFn is attained, with the same cantilever, from lateral force measurements on a silicon calibration sample (c.f, silicon surface treatment in Appendix). Note that there are no cantilever length dimensions necessary for the lateral force calibration. 

Cannara, R. J., Eglin, M. and Carpick, R. W. (2006) Lateral force calibration in atomic force microscopy A new lateral force calibration method and general guidelines for optimization. Rev Sci Ins 77 -. 

The lateral force is obtained directly from the FFM. So the lateral force is needed to be quantitatively calibrated first and then the friction force can be calculated. As shown in Fig. 2, the lateral force can be expressed by... 

First we analyzed the states of a tip scanning along an ascent and descent surface on nanometer scale, and then we calibrated the lateral force obtained by the FFM we modified. It may be helpful to understand how to measure the true lateral force by an FFM. 

Abstract. Quantitative measurements of lateral force required for displacement of SWNTs bundle on the surface of highly oriented pyrolytic graphite with the help of atomic force microscope (AFM) were performed in real time . New method of quantitative calibration of lateral forces was used for interpretation results of lateral force microscopy (LFM). It allows us to receive numerical values of adhesion force of bundle to substrate easy and without specific equipment. 

Atomic force microscopy [6, 7] is one of the most suitable methods for research carbon nanotubes. AFM allows to receive not only a relief of the studied sample, but also distribution of mechanical characteristics, electric, magnetic and other properties on its surface. With the help of AFM, controllable manipulation of individual CNTs and CNTs bundles became possible. In this paper we report our approach to manipulating SWCNTs bundles with lateral force microscopy. LFM gives possibility to study lateral forces that probe acts upon bundles. In spite of good visualization of LFM, its lack is absence of reliable techniques of quantitative interpretation of results. The new way of calibration developed ourselves has allowed to pass from qualitative estimations to quantitative investigations [8], The given calibration technique is much more exact, than others known till now [9, 10], and does not assume simplification. With the help of new technique we may study adhesion of bundles to substrate and adhesion of CNTs in bundle qualitatively in real time more easy way. This result will provide new possibilities for nanotube application. 

To define absolute value of force acted during the experiment we need recalculate DFL and LF signals measured in nA into normal load force and lateral force using natural force units (nN). Method of normal load calibration is well known ... 

Calculation of the critical lateral force is more complicated because traditional LFM does not provide us with easy method to translate current units into force ones. There is no way to define the factor of proportionality until calibration algorithm was developed recently by ourselves [8], The required coefficient depends on design of a microscope, adjustment of the optical system, torsion force constant kL of cantilever and tip height lnp. 

Methods of AFM, by means of a new method of calibration of lateral forces, allow to quantitavely investigate various mechanical characteristics of nanotubes. We have demonstrated one of applications of this method and determined critical lateral force that displace bundle of nanotubes over HOPG surface. The advantage of the work is possibility of real time observation of moment of nanotubes displacement, so relatively exact value of the lateral force caused such event can be estimated. 

It can be shown that relations between measured lateral forces (half width of friction loop W = (Mu-Md)/2) and the friction loop offsets (A (Mu + Md)/2) for sloped and flat surfaces at a given load (2.7-2.10) can be used to calculate the friction force calibration factor a [nN/V]. M denotes the torsion moment involved, the subscripts u and d denote uphill and downhill scan directions, and the subscripts. v and/denote sloped and flat surfaces, respectively. 

The nano-friction force, measured in torsion mode, is directly proportional to the TMR value (trace minus retrace, in volts), which is given as the difference between the lateral forces scanning left-to-right and right-to-left. Absolute adhesion and friction forces can be obtained with calibration methods but such techniques... 

Figure 3. lateral force versus appUed load for pH 4 and pH 9. The solid curves are the best fit JIQt m el. Note that althoi the lateral force signal is not calibrated in our experiment, the adhesion energy can he determined from this fit, if the radius of the tip is known. The same entity can be obtained fi-om the pull-off forces fi om loading—unloading cycles and the values are in exellent agreement. 

Since our lateral force signal is not calibrated, the experimental data can only be modeled qualitatively. For low and constant potentials and a flat-flat geometry, the electrostatic component of the pressure between tip and surface is given by [12,25]... 

From our results, we can exclude any large hydrostatic pressure effects induced by contact mechanical SPM approaches such as lateral force or shear modulation methods. The lateral force method has strong potential for heterogeneous surfaces. On homogeneous surfaces, however, the shear modulation mode is much more reliable without die difficulties of calibrating the load and scan velocity dependence. In figure 4, tip response vs. tenq>erature measurements on thick (476 nm) PS (M 90 k) films are presented for various loads. As the temperature is increased, we see a distinct increase in the ancqplitude response. We identify Tc as the intersection between the two line fits. The precision of the value is estimated to 2 K. At an applied load of... 

We present a quantitative study of frictional properties of pure self-assembled monolayers (SAMs) of alkanethiols as a function of chain length and mixed SAMs of dodecanethiol and 11-mercapto-l-undecanol as a function of surface composition on Au (111) using atomic force/friction force microscopy (AFM/FFM). The lateral and normal forces were calibrated in situ using a combined two-slope and added-mass method. Molecular dynamics simulations were also carried out to interpret the chain length dependence of frictional properties of alkanethiols. We then extended the in situ force calibration method to the mixed SAMs and investigated the effects of chemical nature and relative humidity on the frictional properties. Friction coefficients were plotted as a function of surface composition with different relative humidity. Such a plot could serve as a reference in determining surface composition in a nanoscale domain by measuring its friction coefficient. 

Instrumentation. Commercial atomic force microscopes Explorer from Topometrix Inc., Nanoscope Illa Digital Instruments Co. Ltd.) which are based on the laser beam deflection detection scheme were used in conjunction with digital oscilloscopes of very stable low frequency (1-20 Hz) trigger system for lateral force (friction) measurements, and dual-phase lock-in amplifiers and function generators for force modulation measurements. Various triangular silicon nitride cantilevers were used. The lateral spring constants were determined with the "blind torsional calibration method discussed in more detail in the Appendix. 

Scanning Force Microscopy / Lateral Force Microscopy. The SFM experiments were performed on a NanoScope III (Digital Instruments, (DI) Santa Barbara, CA) using triangular shaped cantilevers (Dl) with a nominal spring constant of 0.12 N/m and 0.38 N/m, respectively. The torsional spring constant was calibrated as described in reference 20). In addition to unmodified tips, chemically modified tips were also used. The procedure for self-assembled monolayer deposition for the chemical modification of the tips is described in reference 20). 

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