Elena T. Herruzo

The emergence of multifrequency force microscopy

In atomic force microscopy a cantilever with a sharp tip attached to it is scanned over the surface of a sample, and information about the surface is extracted by measuring how the deflection of the cantilever - which is caused by interactions between the tip and the surface - varies with position. In the most common form of atomic force microscopy, dynamic force microscopy, the cantilever is made to vibrate at a specific frequency, and the deflection of the tip is measured at this frequency. But the motion of the cantilever is highly nonlinear, and in conventional dynamic force microscopy, information about the sample that is encoded in the deflection at frequencies other than the excitation frequency is irreversibly lost. Multifrequency force microscopy involves the excitation and/or detection of the deflection at two or more frequencies, and it has the potential to overcome limitations in the spatial resolution and acquisition times of conventional force microscopes. Here we review the development of five different modes of multifrequency force microscopy and examine its application in studies of proteins, the imaging of vibrating nanostructures, measurements of ion diffusion and subsurface imaging in cells.

Fast nanomechanical spectroscopy of soft matter

A method that combines high spatial resolution, quantitative and non-destructive mapping of surfaces and interfaces is a long standing goal in nanoscale microscopy. The method would facilitate the development of hybrid devices and materials made up of nanostructures of different properties. Here we develop a multifrequency force microscopy method that enables simultaneous mapping of nanomechanical spectra of soft matter surfaces with nanoscale spatial resolution. The properties include the Youngs modulus and the viscous or damping coefficients. In addition, it provides the peak force and the indentation. The method does not limit the data acquisition speed nor the spatial resolution of the force microscope. It is non-invasive and minimizes the influence of the tip radius on the measurements. The same tip is used to measure in air heterogeneous interfaces with near four orders of magnitude variations in the elastic modulus, from 1 MPa to 3 GPa.

Bimodal atomic force microscopy imaging of isolated antibodies in air and liquids

We have developed a dynamic atomic force microscopy (AFM) method based on the simultaneous excitation of the first two flexural modes of the cantilever. The instrument, called a bimodal atomic force microscope, allows us to resolve the structural components of antibodies in both monomer and pentameric forms. The instrument operates in both high and low quality factor environments, i.e., air and liquids. We show that under the same experimental conditions, bimodal AFM is more sensitive to compositional changes than amplitude modulation AFM. By using theoretical and numerical methods, we study the material contrast sensitivity as well as the forces applied on the sample during bimodal AFM operation.

Multiscale Sensing of Antibody - Antigen Interactions by Organic Transistors and Single-Molecule Force Spectroscopy

Antibody-antigen (Ab-Ag) recognition is the primary event at the basis of many biosensing platforms. In label-free biosensors, these events occurring at solid-liquid interfaces are complex and often difficult to control technologically across the smallest length scales down to the molecular scale. Here a molecular-scale technique, such as single-molecule force spectroscopy, is performed across areas of a real electrode functionalized for the immunodetection of an inflammatory cytokine, viz. interleukin-4 (IL4). The statistical analysis of force-distance curves allows us to quantify the probability, the characteristic length scales, the adhesion energy, and the time scales of specific recognition. These results enable us to rationalize the response of an electrolyte-gated organic field-effect transistor (EGOFET) operated as an IL4 immunosensor. Two different strategies for the immobilization of IL4 antibodies on the Au gate electrode have been compared: antibodies are bound to (i) a smooth film of His-tagged protein G (PG)/Au; (ii) a 6-aminohexanethiol (HSC6NH2) self-assembled monolayer on Au through glutaraldehyde. The most sensitive EGOFET (concentration minimum detection level down to 5 nM of IL4) is obtained with the first functionalization strategy. This result is correlated to the highest probability (30%) of specific binding events detected by force spectroscopy on Ab/PG/Au electrodes, compared to 10% probability on electrodes with the second functionalization. Specifically, this demonstrates that Ab/PG/Au yields the largest areal density of oriented antibodies available for recognition. More in general, this work shows that specific recognition events in multiscale biosensors can be assessed, quantified, and optimized by means of a nanoscale technique.

Nanomechanical coupling enables detection and imaging of 5?nm superparamagnetic particles in liquid

We demonstrate that a force microscope operated in a bimodal mode enables the imaging and detection of superparamagnetic particles down to 5 nm. The bimodal method exploits the nanomechanical coupling of the excited modes to enhance the sensitivity of the higher mode to detect changes in material properties. The coupling requires the presence of nonlinear forces. Remarkably, bimodal operation enables us to identify changes of slowly varying forces (quasi-linear) in the presence of a stronger nonlinear force. Thus, unambiguous identification of single apoferritin (non-magnetic) and ferritin (magnetic) molecules in air and liquid is accomplished.

Frequency response of an atomic force microscope in liquids and air: Magnetic versus acoustic excitation

modulation AFM, a sharp probe is excited at a fixed frequency, usually near or at the first flexural resonance frequency while the probe is scanned in a raster fashion across the sample surface. The probe-surface interaction forces lead to a reduction of the amplitude of the oscillation from its free value. In the imaging mode, the amplitude reduction is used as a feedback parameter to map the topography of the surface. Two different cantilever driving methods are currently in use: mechanical also know as acoustic 5‐7 and magnetic. 8‐10

Standardized Nanomechanical Atomic Force Microscopy Procedure (SNAP) for Measuring Soft and Biological Samples

We present a procedure that allows a reliable determination of the elastic (Young’s) modulus of soft samples, including living cells, by atomic force microscopy (AFM). The standardized nanomechanical AFM procedure (SNAP) ensures the precise adjustment of the AFM optical lever system, a prerequisite for all kinds of force spectroscopy methods, to obtain reliable values independent of the instrument, laboratory and operator. Measurements of soft hydrogel samples with a well-defined elastic modulus using different AFMs revealed that the uncertainties in the determination of the deflection sensitivity and subsequently cantilever’s spring constant were the main sources of error. SNAP eliminates those errors by calculating the correct deflection sensitivity based on spring constants determined with a vibrometer. The procedure was validated within a large network of European laboratories by measuring the elastic properties of gels and living cells, showing that its application reduces the variability in elastic moduli of hydrogels down to 1%, and increased the consistency of living cells elasticity measurements by a factor of two. The high reproducibility of elasticity measurements provided by SNAP could improve significantly the applicability of cell mechanics as a quantitative marker to discriminate between cell types and conditions.

Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus

Summary Bimodal atomic force microscopy is a force-microscopy method that requires the simultaneous excitation of two eigenmodes of the cantilever. This method enables the simultaneous recording of several material properties and, at the same time, it also increases the sensitivity of the microscope. Here we apply fractional calculus to express the frequency shift of the second eigenmode in terms of the fractional derivative of the interaction force. We show that this approximation is valid for situations in which the amplitude of the first mode is larger than the length of scale of the force, corresponding to the most common experimental case. We also show that this approximation is valid for very different types of tip–surface forces such as the Lennard-Jones and Derjaguin–Muller–Toporov forces.