High-sensitivity mass and position detection of micro-objects adhered to microcantilevers

Abstract

A dynamic method for mass detection, considering attaching positions of micro-objects on microcantilevers, is introduced. Two models based on the RayleighRitz method were developed for analyses of the first flexural and the first torsional modes of a "cantilevermass" system, respectively. Due to one-to-one correspondence between the longitudinal adhering positions of the micro-objects and the flexural resonant frequencies of the "cantilever-mass" system, the first model was employed for high-sensitivity mass detections of multi-object with different attaching positions on the cantilevers. The second model was developed for the analyses of links between the first torsional frequency of the "cantilever-mass" system and the transverse attaching positions of the micro-objects. Uniting these two models, the longitudinal and transverse attaching positions of one micro-object can be determined. Experimental results of polystyrene microspheres and ambrosia pollens attached on the microcantilever in the air validated the setup of the analytical models.

In Situ Gelation-Induced Death of Cancer Cells Based on Proteinosomes

“…The spring constant of the cantilevers was determined using the method proposed by Sader et al with values of 0.006 N/m. The relationship between force and deformation of the AFM probe is in accordance with Hooke’s law . That is, when the cantilever exerted a small force, a suitable deformation could be detected.…”

“…The relationship between force and deformation of the AFM probe is in accordance with Hooke's law. 46 That is, when the cantilever exerted a small force, a suitable deformation could be detected. Meanwhile, the probe stiffness needs to be close to the stiffness of the samples.…”

Serial weighting of micro-objects with resonant microchanneled cantilevers

“…In fact, the correction factor of Eq. 6 is exact only for particles attached along the main axis of the cantilever, but it still holds for small distances, for which the shape of the mode itself is not significantly altered by the addition of the particle [29]. As a matter of fact, a configurations in which the sphere is attached near the edge of the cantilever, such as for particle 3, is strongly altering the cantilever dynamics, and the frequency change cannot be simply recovered, so that this situation must be avoided while using the system as a mass sensor.…”

Tailoring the Sensitivity of Microcantilevers To Monitor the Mass of Single Adherent Living Cells

“…The shift in resonance frequency also depends on the position of the cell along the longitudinal axis of the cantilever beam, as the mass sensitivity is maximized at the free end of the cantilever . The correct mass readout thus requires a correction factor, , which substitutes the cell position x c into the mode shape amplitude equation for rectangular cantilevers beams: ψ ( x c ) = α ( sin false( ξ x c false) − ⁢ sinh false( ξ x c false) + false( sin ( ξ L ) + sinh ( ξ L ) false) false( cosh ( ξ x c ) − nobreak0em0.25em⁢ cos ( ξ x c ) false) cos false( ξ L false) + cosh false( ξ L false) ) where α is a normalizing constant such that ψ false( L false) 2 = 1 and L is the length of the cantilever (Figure a).…”

“…The shift in resonance frequency also depends on the position of the cell along the longitudinal axis of the cantilever beam, as the mass sensitivity is maximized at the free end of the cantilever . The correct mass readout thus requires a correction factor, , which substitutes the cell position into the mode shape amplitude equation for rectangular cantilevers beams: where is a normalizing constant such that and is the length of the cantilever (Figure a).…”