Surface Reconstruction of the Lamellar Morphology in a Symmetric Poly(styrene-<i>block</i>-butadiene-<i>block</i>-methyl methacrylate) Triblock Copolymer:  A Tapping Mode Scanning Force Microscope Study

Boisgard

The Journal of Chemical Physics

1999

151

181

The dynamical properties of an oscillating tip-cantilever system are now widely used in the field of scanning force microscopy. The aim of the present work is to get analytical expressions describing the nonlinear dynamical properties of the oscillator in noncontact and intermittent contact situations in the tapping mode. Three situations are investigated: the pure attractive interaction, the pure repulsive interaction, and a mixing of the two. The analytical solutions obtained allow general trends to be extracted: the noncontact and the intermittent contact show a very discriminate variation of the phase. Therefore the measurement of the phase becomes a simple way to identify whether or not the tip touches the surface during the oscillating period. It is also found that the key parameter governing the structure of the dynamical properties is the product of the quality factor by a reduced stiffness. In the attractive regime, the reduced stiffness is the ratio of an attractive effective stiffness and the cantilever one. In the repulsive regime, the reduced stiffness is the ratio between the contact stiffness and the cantilever one. The quality factor plays an important role. For large values of the quality factor; it is predicted that a pure topography can be obtained whatever the value of the contact stiffness. For a smaller quality factor, the oscillator becomes more sensitive to change of the local mechanical properties. As a direct consequence, varying the quality factor, for example with a vacuum chamber, would be a very interesting way to investigate soft materials either to access topographic information or nanomechanical properties. ͓͔͑͒

Section: Fig 8 Experimental Approach-retract Curvesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamical properties of an oscillating tip–cantilever system in the tapping mode

Boisgard

The Journal of Chemical Physics

1999

151

181

“…Among them, images of copolymers are quite convincing of its great potentiality. [10][11][12][13] However, recording a true topography is far to be achieved, it is often worth discussing image as a function of nanomechanical properties of the sample probed by this mode. Several theoretical approaches have been dedicated to the Tapping, [14][15][16][17][18][19] some of them being numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

Influence of noncontact dissipation in the tapping mode: Attempt to extract quantitative information on the surface properties with the local force probe method

Boisgard

The Journal of Chemical Physics

et al. 2001

In the Tapping mode, a variation of the oscillation amplitude and phase as a function of the tip sample distance is the necessary measurement to access quantitatively to the properties of the surface. In the present work, we give a systematic comparison between experimental data recorded on two surfaces, phase and amplitude, and theoretical curves. With an interaction between the tip and the surface taking into account an attractive and a repulsive term, the analytical approach is unable to properly describe the relationship between the phase variation and the oscillation amplitude variation. When an additional dissipation term is involved, due to the attractive interaction between the tip and the surface, the model gives a good agreement with the recorded data. Particularly, the trends in the phase variations related to the noncontact situations have been found to be amenable to an analysis based upon a simple viscoelastic behavior of the surface. ͓͔

“…The "routine" achievement of the atomic resolution with the NC-AFM [7] is thought of as a real breakthrough in the field of the scanning probe microscopy. Moreover, the use of a high vibrating amplitude of the cantilever (CL) with the NC-AFM and the development of the intermittent contact (the so-called tapping mode) [8][9][10] have boosted theoretical works dedicated to a nonlinear analysis [11][12][13][14].Before going a step further, it is worth discussing general ideas at a qualitative level. Leaving aside the technical point that the use of a high amplitude reduces the influence of the fluctuations in frequency [2], a first, counterintuitive, result is the use of a large vibrating amplitude allowing the atomic resolution to be achieved.…”

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confidence: 99%

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confidence: 99%

Nonlinear Dynamic Behavior of an Oscillating Tip-Microlever System and Contrast at the Atomic Scale

Boisgard²,

et al. 1999

Phys. Rev. Lett.

In this paper the dynamic behavior of an oscillating tip-microlever system at the proximity of a surface is discussed. We show that the nonlinear behavior of the oscillator is able to explain the high sensitivity of the oscillating tip microlever and the observed shifts of the resonance frequency as a function of the tip surface distance without the need of introducing a particular short range force. PUBLISHED IN Phys. Rev. Lett. 82(17), 3388-3391 (1999).PACS numbers: 07.79. Lh, 61.16.Ch, 68.35.Bs A few years ago, the resonant noncontact mode (hereafter noted NC-AFM) was developed to map tip surface interaction as shifts of the resonance frequency [1,2]. Since then, numerous experimental efforts have been performed showing that measurements of shifts were able to produce images at the atomic scale [3][4][5][6][7]. The "routine" achievement of the atomic resolution with the NC-AFM [7] is thought of as a real breakthrough in the field of the scanning probe microscopy. Moreover, the use of a high vibrating amplitude of the cantilever (CL) with the NC-AFM and the development of the intermittent contact (the so-called tapping mode) [8][9][10] have boosted theoretical works dedicated to a nonlinear analysis [11][12][13][14].Before going a step further, it is worth discussing general ideas at a qualitative level. Leaving aside the technical point that the use of a high amplitude reduces the influence of the fluctuations in frequency [2], a first, counterintuitive, result is the use of a large vibrating amplitude allowing the atomic resolution to be achieved. Typically, the amplitudes used are 100 times greater than the vertical motion of the surface required, maintaining a given value of the frequency shift. The most common and shared idea is that to probe an attractive field with an oscillator requires the use of a small amplitude in order to keep the force field nearly constant throughout the vibrating amplitude. The idea is that shifts in resonance frequency are uniquely due to the gradient force variations.An image with the atomic resolution based on a repulsive interaction appears quite easily understandable, but getting the same resolution when the attractive van der Waals forces are involved is very puzzling. The van der Waals atom-atom interaction and the finite size of the interacting objects lead to a tip-sample interaction smoothly varying as a function of the CL-surface distance. For instance, the sphere-plan interaction leads to an attractive force with a d 22 power law. The force gradient dependence, with a power law d 23 , gives a too smooth variation of the resonance frequency and is unable to predict the observed shape of the frequency changes as a function of the tip-sample distance.