Force calibration

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. 

Calibration of TA instrumentation and development of standards for calibration continue to be administered by ICTAC in conjunction with ASTM. The standardization Committee of ICTAC has certified a range of materials for temperature calibration of TA systems, and in addition, standards for calibration of mass (known as Class M Standards ) are available for this purpose. A range of certified reference materials are available for enthalpy calibration in DSC. Temperature calibration for TMA and dynamic mechanical analysis (DMA) is effected by using disks of pure metals (silver, aluminum, and tin) separated by alumina disks. Load or force calibration for DMA is a complex process involving the use of calibrated weights. Temperature calibration for DETA is effected by measuring the melting transition of benzoic acid and dielectric calibration is... 

Elastic modulus and hardness can be also evaluated by analysis of the force-displacement curve, using AFM nanoindentation. The important factors in this technique are the force calibration and the depth (or so-called displacement). The force constant of a cantilever, the shape of the tip, and other mechanical properties such as tip glue determine the total force exerted onto a sample. 

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. 

Dodecanethiol and 11-mercapto-l-undecanol were purchased from Aldrich Chemical Company, Inc. (Milwaukee, WI) and used as received. Glassware for the preparation of SAMs was cleaned with chromic acid cleaning solution (Fisher Scientific). Gold shots (99.99%) were purchased from D.F. Goldsmith. Glass beads (10-30 pm) from Polyscience were used for the normal force calibration. The faceted... 

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. 

Before performing a force calibration, the weight of the probe itself must be tared. Then, the force motor used to apply the static force on the sample is calibrated using a weight standard (such as a 50 or 100 g gram-force calibration standard weight). Force loads as small as 1 mN (0.1 g-force) and as high as ION (1 kg g-force) can be applied with a resolution of 0.001 N. 

B AFM Key Issues. In both cases, several parameters are not accurately known, making quantitative measurements difficult to achieve. In this section is given a short list of these parameters. The key issues are force calibration, tip characterization with estimation of the contact area between the tip and the sample, and effects of the experimental environments. The behavior of the contact area, either stationary or fluctuating, is a key parameter to have at least robust, reproducible experimental data. We arbitrarily focus on the attempts to design in situ experiments that allow the measurements to be more quantitative. Most of these key issues are far from being resolved or standardized. They still appear to be very dependent of the scale at which the required signal has to be obtained. The experimental constraints will not be the... 

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. 

Inertia is the QCM experimenter s best friend. In many wa, QCM experiments come down to the measurement of an (oscillatory) force. One may even spell out "QCM" as "quartz crystal micro- (force) balance." In contrast to AFM, force calibration is close to trivial in... 

ISO 4965 1979 Axial load fatigue testing machines—Dynamic force calibration—Strain gauge technique... 

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 -. 

Force calibration is commonly not directly done, but trap stiffness is determined. Then, the force is calculated by multiplying trap stiffness by particle displacement from the trap center. The first method involves again measuring the power spectrum of thermal motion of a bead in the harmonic potential, which is described by a Lorentzian as given by Eq. (3.20). By fitting the power spectrum and using the relation... 

Here, the asymptotic value AqP//2kt can be used to estimate trap stiffness. This method does not require high detection bandwidth and allows mapping of the linear range of the trap where kt is constant. Recently, Tolic-Norrelykke et al. [329] used a combination of sinusoidal drag force and power spectrum to obtain both distance and force calibration without the need of independent information on the hydrodynamic drag coefficient. A similar approach has been introduced to allow calibration in viscoelastic media such as the cytoplasm, where the viscoelastic properties of the medium are not known a priori [330]. 

The pressure in the chamber was determined by the chamber-pressure/ press-force calibration curves. The calibration curves for each pair of anvils were plotted by the changes of electrical resistance at polymorphic transformations in reference metals Bi (7.7 GPa), Sn (9.5 GPa), Ba (12.5 GPa), Pb (13 GPa), and ZnS (15 GPa) at room temperature (Figure 16.1b). 

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