G. Lévêque

ELECTROSTATIC FORCES ACTING ON THE TIP IN ATOMIC FORCE MICROSCOPY : MODELIZATION AND COMPARISON WITH ANALYTIC EXPRESSIONS

With the model of equivalent charge distribution, we calculated the exact electrostatic force acting on the real (conical) tip of an atomic force microscope. This model applies to a conductive tip in front of a conductive plane. We compared the equivalent charge model with several analytic models used to date to approximate the electrostatic forces and discussed their degree of validity. We estimated the contribution of the cantilever to the total force and showed, on the basis of theoretical calculations and experimental results, that the contribution of cantilever may constitute the essential part of the electrostatic force in the range of distances used in electrostatic force microscopy in the air.

Determination of the nanoscale dielectric constant by means of a double pass method using electrostatic force microscopy

We present a method to determine the local dielectric permittivity of thin insulating layers. The measurement is based on the detection of force gradients in electric force microscopy by means of a double pass method. The proposed experimental protocol is simple to implement and does not need any modification of standard commercial devices. Numerical simulations based on the equivalent charge method make it possible to carry out quantification whatever the thickness of film, the radius of the tip, and the tip-sample distance. This method has been validated on a thin SiO2 sample for which the dielectric permittivity at the nanoscale has been characterized in the literature. We also show how we can quantitatively measure the local dielectric permittivity for ultrathin polymer film of poly(vinyl acetate) and polystyrene.

Vibration of the cantilever in Force Modulation Microscopy analysis by a finite element model

The resonance frequency of the cantilever beam of a Force Modulation Microscope is studied in function of the beam shape, the sample stiffness, and the contact model. We used a one dimensional finite element model for the cantilever beam, which permits the exact vibration of the beam to be treated in the contact mode, whatever its shape (rectangular as well as triangular beams) and excitation mode (by the beam holder, by the sample, by a localized, or distributed force). Based on a classic finite element scheme, it is simple to program and as rapid as the usual analytical models. We demonstrate that the mode of excitation of the beam strongly influences the cantilever’s frequency response in the contact mode. Anti-resonance is observed on the amplitude curves, which may perturb the measurements on some samples. We analyzed the true normal and tangential amplitude, for different beams and tip dimensions, in relation with the apparent amplitude of the vibration, as detected by the system. Experimental resul...

Correction of diffraction effects in sound velocity and absorption measurements

The mean pressure over a receptor placed at a small distance from a circular source is calculated in order to estimate the effect of diffraction when the medium is transparent or slightly absorbing. The deviation relative to the propagation without diffraction is written in the form of a simple integral of the radial wave vector. The source and receiver are considered of the same size, but the expression for different diameters is given. Approximate analytical expressions are derived when the diffraction effect is small, i.e., when the source is much larger than the wavelength. The analytical expressions are used to show that diffraction corrections can easily be performed in a standard pulsed echo experiment.

An acoustic sensor for simultaneous density and viscosity measurements in liquids

We studied theoretically the properties of a vibrating sensor, constituted of a cylindrical tip partly immersed in a liquid. The tip is driven axially by a stepped horn and by a piezoelectric element. Equations of the fluid flow around the tip are solved and show that longitudinal and transverse waves are emitted in the fluid. This allows the device to be sensitive to the density and viscosity of the fluid. It is shown that the properties of the fluid can be deduced by measuring the frequency shift at resonance and the corresponding electric impedance. The precision of the actual device is still low for several reasons, which are discussed. Then our apparatus seems to be more convenient to in situ reaction monitoring rather than for rheological precise measurements.

Measurement of the viscosity of liquids by near-field acoustics

We have studied the relationship between the acoustic properties of a near-field acoustic sensor and the properties of a liquid. An acoustic stepped horn is driven by two piezoelectric elements. The generated acoustic waves cause the solid horn to resonate and an acoustic load at the tip modifies these oscillation modes. This leads to a change in electric impedance at the piezoelectric elements. This sensitivity to acoustic load allows a study of semi-infinite liquids. We found a relation between the resonance frequency and the liquid density and a relation between the electric impedance and the viscosity.

Effects of air damping in noncontact resonant force microscopy

The action of viscous forces on the motion of an atomic force microscope cantilever operating in resonant mode in air is modelized. We demonstrate that for most applications, the vibration of a V shaped cantilever in the air can be approximated to a simple damped oscillator. The damping factor is distance dependent and includes terms issued of the interaction of both cantilever and tip with the sample. Expressions for the various damping forces have been derived and related to the geometry of the tip-cantilever system. They lead to an expression which quantifies the variations in oscillation amplitude versus tip sample distance.

Nanoscale dielectric properties of insulating thin films: From single point measurements to quantitative images

Dielectric relaxation (DR) has shown to be a very useful technique to study dielectric materials like polymers and other glass formers, giving valuable information about the molecular dynamics of the system at different length and time scales. However, the standard DR techniques have a fundamental limitation: they have no spatial resolution. This is of course not a problem when homogeneous and non-structured systems are analyzed but it becomes an important limitation for studying the local properties of heterogeneous and/or nano-structured materials. To overcome this constrain we have developed a novel approach that allows quantitatively measuring the local dielectric permittivity of thin films at the nanoscale by means of Electrostatic Force Microscopy. The proposed experimental method is based on the detection of the local electric force gradient at different values of the tip-sample distance. The value of the dielectric permittivity is then calculated by fitting the experimental points using the Equivalent Charge Method. Even more interesting, we show how this approach can be extended in order to obtain quantitative dielectric images of insulating thin films with an excellent lateral resolution.

Image processing for resonance frequency mapping in atomic force modulation microscopy

It has been demonstrated that the resonance frequency of the cantilever in atomic force modulation microscopy can be used to study local mechanical properties. We developed a numerical method to achieve mapping of the resonance frequency without significant modification of the device. By making the assumption that the resonance spectrum can be approximated by a Lorentzian curve, we established analytical expressions of the resonance frequency and the width of the curve (damping) depending on the real and imaginary parts of the vibration at a single frequency. Then, resonance frequency and damping images were produced from the recording of both the real and imaginary part images of the complex amplitude. The results on a standard high-impact polystyrene sample are shown.

Ultrasonic properties of water/sorbitol solutions.

Ultrasonic longitudinal velocity and attenuation were measured for aqueous solutions of sorbitol at approximately 5 MHz. For pure sorbitol, the ultrasonic velocity reached 3200 m s(-1), consequently leading to a high acoustical impedance (around 5 x 10(6) Rayleigh) and good matching between the ultrasonic transducers and material samples.