Step response measurement of AFM cantilever for analysis of frequency-resolved viscoelasticity

Microrheology of growing Escherichia coli biofilms investigated by using magnetic force modulation atomic force microscopy

Microrheology of growing biofilms provides insightful information about its structural evolution and properties. In this study, the authors have investigated the microrheology of Escherichia coli (strain HCB1) biofilms at different indentation depth (δ) by using magnetic force modulation atomic force microscopy as a function of disturbing frequency (f). As δ increases, the dynamic stiffness (k_s) for the biofilms in the early stage significantly increases. However, it levels off when the biofilms are matured. The facts indicate that the biofilms change from inhomogeneous to homogeneous in structure. Moreover, k_s is scaled to f, which coincides with the rheology of soft glasses. The exponent increases with the incubation time, indicating the fluidization of biofilms. In contrast, the upper layer of the matured biofilms is solidlike in that the storage modulus is always larger than the loss modulus, and its viscoelasticity is slightly influenced by the shear stress.

Sensitivity analysis of rectangular atomic force microscope cantilevers immersed in liquids based on the modified couple stress theory

The modified couple stress theory is adopted to study the sensitivity of a rectangular atomic force microscope (AFM) cantilever immersed in acetone, water, carbon tetrachloride (CCl4), and 1-butanol. The theory contains a material length scale parameter and considers the size effect in the analysis. However, this parameter is difficult to obtain via experimental measurements. In this study, a conjugate gradient method for the parameter estimation of the frequency equation is presented. The optimal method provides a quantitative approach for estimating the material length scale parameter based on the modified couple stress theory. The results show that the material length scale parameter of the AFM cantilever immersed in acetone, CCl4, water, and 1-butanol is 0, 25, 116.3, and 471 nm, respectively. In addition, the vibration sensitivities of the AFM cantilever immersed in these liquids are investigated. The results are useful for the design of AFM cantilevers immersed in liquids.

Microrheology of cells with magnetic force modulation atomic force microscopy

We propose a magnetic force modulation method to measure the stiffness and viscosity of living cells using a modified AFM apparatus. An oscillating magnetic field makes a magnetic cantilever oscillate in contact with the sample, producing a small AC indentation. By comparing the amplitude of the free cantilever motion (A0) with the motion of the cantilever in contact with the sample (A1), we determine the sample stiffness and viscosity. To test the method, the frequency-dependent stiffness of 3T3 fibroblasts was determined as a power law k(s)(f) = α + β(f/f¯)(γ) (α = 7.6 × 10(-4) N m(-1), β = 1.0 × 10(-4) N m(-1), f¯ = 1 Hz, γ = 0.6), where the coefficient γ = 0.6 is in good agreement with rheological data of actin solutions with concentrations similar to those in cells. The method also allows estimation of the internal friction of the cells. In particular we found an average damping coefficient of 75.1 μN s m(-1) for indentation depths ranging between 1.0 μm and 2.0 μm.

Pulse-response measurement of frequency-resolved water dynamics on a hydrophilic surface using a Q-damped atomic force microscopy cantilever

The frequency-resolved viscoelasticity of a hydration layer on a mica surface was studied by pulse-response measurement of a magnetically driven atomic force microscopy cantilever. Resonant ringing of the cantilever due to its 1st and 2nd resonance modes was suppressed by means of the Q-control technique. The Fourier-Laplace transform of the deflection signal of the cantilever gave the frequency-resolved complex compliance of the cantilever-sample system. The significant viscoelasticity spectrum of the hydration layer was successfully derived in a frequency range below 100 kHz by comparison of data obtained at a distance of 300 nm from the substrate with those taken in the proximity of the substrate. A positive value of the real part of the stiffness was determined and is attributed to the reported solidification of the hydration layers.

Dynamic response of a cracked atomic force microscope cantilever used for nanomachining

The vibration behavior of an atomic force microscope [AFM] cantilever with a crack during the nanomachining process is studied. The cantilever is divided into two segments by the crack, and a rotational spring is used to simulate the crack. The two individual governing equations of transverse vibration for the cracked cantilever can be expressed. However, the corresponding boundary conditions are coupled because of the crack interaction. Analytical expressions for the vibration displacement and natural frequency of the cracked cantilever are obtained. In addition, the effects of crack flexibility, crack location, and tip length on the vibration displacement of the cantilever are analyzed. Results show that the crack occurs in the AFM cantilever that can significantly affect its vibration response.PACS: 07.79.Lh; 62.20.mt; 62.25.Jk.