No abstract

Knowledge of surface forces is the key to understanding a large number of processes in fields ranging from physics to material science and biology. The most common method to study surfaces is dynamic atomic force microscopy (AFM). Dynamic AFM has been enormously successful in imaging surface topography, even to atomic resolution, but the force between the AFM tip and the surface remains unknown during imaging. Here we present a new approach that combines high-accuracy force measurements and high-resolution scanning. The method, called amplitude-dependence force spectroscopy (ADFS), is based on the amplitude dependence of the cantilever's response near resonance and allows for separate determination of both conservative and dissipative tip-surface interactions. We use ADFS to quantitatively study and map the nano-mechanical interaction between the AFM tip and heterogeneous polymer surfaces. ADFS is compatible with commercial atomic force microscopes and we anticipate its widespread use in taking AFM toward quantitative microscopy.

Atomic force microscopy has recently been extented to bimodal operation, where increased image contrast is achieved through excitation and measurement of two cantilever eigenmodes. This enhanced material contrast is advantageous in analysis of complex heterogeneous materials with phase separation on the micro or nanometre scale. Here we show that much greater image contrast results from analysis of nonlinear response to the bimodal drive, at harmonics and mixing frequencies. The amplitude and phase of up to 17 frequencies are simultaneously measured in a single scan. Using a machine-learning algorithm we demonstrate almost threefold improvement in the ability to separate material components of a polymer blend when including this nonlinear response. Beyond the statistical analysis performed here, analysis of nonlinear response could be used to obtain quantitative material properties at high speeds and with enhanced resolution.

We demonstrate an alternative to Kelvin Probe Force Microscopy (KPFM) for imaging surface potential. The open-loop, single-pass technique applies a low-frequency AC voltage to the atomic force microscopy tip while driving the cantilever near its resonance frequency. Frequency mixing due to the nonlinear capacitance gives intermodulation products of the two drive frequencies near the cantilever resonance, where they are measured with high signal to noise ratio. Analysis of this intermodulation response allows for quantitative reconstruction of the contact potential difference. We derive the theory of the method, validate it with numerical simulation and a control experiment, and we demonstrate its utility for fast imaging of the surface photo-voltage on an organic photo-voltaic material.One of the most popular and useful methods of Electrostatic Force Microscopy (EFM) is Kelvin Probe Force Microscopy (KPFM)1 which provides a measurement of the contact potential difference V CPD (sometimes referred to as the surface potential). KPFM is widely used for advanced imaging of composite polymeric materials 2 and for imaging of the local work function on the surface of organic photo-voltaic materials 3 . Although KPFM is a useful technique to investigate electric properties of surfaces at the nanoscale, the signal-to-noise ratio, accuracy and speed are limited by the additional feed-back loops commonly used in its implementations 4 . To overcome these limitations, an open-loop technique was first proposed by Takeuchi et al.5 to image the contact potential difference in vacuum. Later the technique was used to measure the potential of nanoparticles in liquid 6 and to characterise ferroelectric thin films 7 . In this paper we propose and demonstrate an openloop technique that exploits the intermodulation (frequency mixing) of an electrostatic drive force and a mechanical drive force, to up-convert the electrostatic frequency to the first flexural resonance where the high quality factor allows for a more sensitive measurement. The contact potential difference can be imaged in a singlepass, allowing for imaging times shorter than 5 min with 256 × 256 pixel resolution.The electrostatic energy stored in a system of two perfect conductors is E EL = 1 2 CV 2 , where C is the capacitance and V the electrostatic potential difference between the two. The attractive electrostatic force is therefore;where z is the distance between the two conductors. In EFM the two conductors are the conductive tip and the a) Electronic mail: borgani@kth.se b) Electronic mail: haviland@kth.se sample substrate, which can be approximated as an axially symmetric electrode and an infinite conducting plane respectively. The resulting capacitance gradient varies as a non-linear function of z that depends on the tip geometry 8 . Intermodulation EFM (ImEFM) excites the cantilever with a shaker piezo at frequency ω D close to resonance ω 0 , while at the same time an AC voltage is applied to the cantilever at frequency ω E ≪ ω D . The total potential between t...

We study the interaction between an AFM tip and a soft viscoelastic surface. Using a multifrequency method we measure the amplitude-dependence of the cantilever dynamic force quadratures, which clearly show the effect of finite relaxation time of the viscoelastic surface. A model is introduced which treats the tip and surface as a two-body dynamic problem with a nonlinear interaction depending on their separation. We find good agreement between simulations of this model and experimental data on polymer blend samples for a variety of materials and measurement conditions.