Calibration of the torsional and lateral spring constants of cantilever sensors

Abstract

A method suitable for the calibration of the spring constants of all torsional and lateral eigenmodes of micro-and nanocantilever sensors is described. Such sensors enable nanomechanical measurements and the characterization of nanomaterials, for example with atomic force microscopy.The method presented involves the interaction of a flow of fluid from a microchannel with the cantilever beam. Forces imparted by the flow cause the cantilever to bend and induce a measurable change of the torsional and lateral resonance frequencies. From the frequency shifts the cantilever spring constants can be determined. The method does not involve physical contact between the cantilever or its tip and a hard surface. As such it is noninvasive and does not risk damage to the cantilever.Experimental data is presented for two rectangular microcantilevers with fundamental flexural spring constants of 0.046 and 0.154 N/m. The experimentally determined torsional stiffness values are compared with those obtained by the Sader method. We demonstrate that the torsional spring constants can be readily calibrated using the method with an accuracy of around 15%.Calibration of the torsional and lateral spring constants of cantilever sensors 2

An analytic model for accurate spring constant calibration of rectangular atomic force microscope cantilevers

“…Although the spring constant measurement is not a simple task, several widely used static or dynamic experimental calibration methods have been developed such as the static mass hanging method 6 , reference cantilever/spring method 7 8 9 , dynamic mass attachment method 10 , resonant frequency method 11 , and thermal noise method 12 . Very recently, some variants of the above-mentioned calibration methods have been proposed such as the Sader method for surface modified cantilevers 13 , direct thermal noise method for colloidal probe cantilevers 14 , calibration structures-based method 15 and microchannel-aided method 16 . Some closely related topics also attract attention such as the nanoscale-resolved elasticity 17 and the effect of surface stress on the stiffness of micro/nano cantilever 18 , which helps to gain insight into the measurement interpretation.…”

Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

“…In addition to the determination of the static flexural spring constant, the presented setup can also be employed to obtain other useful information: knowledge of the static spring constant and the applied force allows the cantilever deflection to be determined, which in turn can be exploited to extract the torsional and lateral spring constants from the same measurement if the corresponding resonant frequencies are recorded [ 30 ]. Furthermore, the setup also allows the linear range of the force constants to be systematically tested for all kinds of cantilever sensors and other micro- and nanomechanical structures.…”

“…Experiments were performed with a commercial Bruker Dimension FastScan AFM system (Bruker, Santa Barbara, CA, USA). In our setup, a custom-built, smooth parallel plate microchannel of height ≈100 μm and length 4.5 mm was used [ 27 , 29 – 30 ]. An accurate value of the channel height was obtained by contacting the free end of a cantilever on the bottom surface of the channel with the channel aligned parallel to the cantilever length and measuring the distance to the top of the channel by lifting the cantilever with the AFM microstepper motor until it contacted the top surface of the channel.…”

“…The forces applied to the cantilever by the fluid flow cause a static flexural bending [ 30 ]. The bending of the cantilever as a function of fluid velocity was recorded by reading out the photodiode signal of the AFM with a self-coded LabVIEW routine via a signal access module (SAM-V, Bruker, CA, USA) and an external interface (USB-6251, National Instruments).…”

“…It is therefore desirable to have a universal force tool that can exert well-defined forces on all types of cantilever sensors independent from their physical and chemical properties. A microfluidic flow tool has been previously employed in connection with cantilever spring constant determination [ 27 – 30 ], and it was shown that forces due to the flow from a microfluidic channel can be exploited to determine the dynamic flexural spring constants [ 29 ] as well as the torsional and lateral spring constants [ 30 ]. In the following, we describe a method to determine the static flexural spring constant for cantilevers of any geometric shape.…”