Imaging high-speed friction at the nanometer scale

Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales[1, 2]. The microscopic origin of friction is poorly understood, due in part to a lack of methods for measuring the force on a nanometer-scale asperity sliding at velocity of the order of cm/s.[3, 4] Despite enormous advance in experimental techniques[5], this combination of small length scale and high velocity remained illusive. Here we present a technique for rapidly measuring the frictional forces on a single asperity (an AFM tip) over a velocity range from zero to several cm/s. At each image pixel we obtain the velocity dependence of both conservative and dissipative forces, revealing the transition from stick-slip to a smooth sliding friction[1, 6]. We explain measurements on graphite using a modified Prandtl-Tomlinson model that takes into account the damped elastic deformation of the asperity. With its greatly improved force sensitivity and very small sliding amplitude, our method enables rapid and detailed surface mapping of the full velocity-dependence of frictional forces with less than 10~nm spatial resolution.Comment: 7 pages, 4 figure

Intermodulation electrostatic force microscopy for imaging surface photo-voltage

We demonstrate an alternative to Kelvin Probe Force Microscopy 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.Comment: 4 pages, 3 figures, peer-reviewed, preprin

On modeling and measuring viscoelasticity with dynamic Atomic Force Microscopy

The interaction between a rapidly oscillating atomic force microscope tip and a soft material surface is described using both elastic and viscous forces with a moving surface model. We derive the simplest form of this model, motivating it as a way to capture the impact dynamics of the tip and sample with an interaction consisting of two components: interfacial or surface force, and bulk or volumetric force. Analytic solutions to the piece-wise linear model identify characteristic time constants, providing a physical explanation of the hysteresis observed in the measured dynamic force quadrature curves. Numerical simulation is used to fit the model to experimental data and excellent agreement is found with a variety of different samples. The model parameters form a dimensionless impact-rheology factor, giving a quantitative physical number to characterize a viscoelastic surface that does not depend on the tip shape or cantilever frequency.Comment: 13 pages, 7 figure

Probing nano-scale viscoelastic response in air and in liquid with dynamic atomic force microscopy

We perform a comparative study of dynamic force measurements using an Atomic Force Microscope (AFM) on the same soft polymer blend samples in both air and liquid environments. Our quantitative analysis starts with calibration of the same cantilever in both environments. Intermodulation AFM (ImAFM) is used to measure dynamic force quadratures on the same sample. We validate the accuracy of the reconstructed dynamic force quadratures by numerical simulation of a realistic model of the cantilever in liquid. In spite of the very low quality factor of this resonance, we find excellent agreement between experiment and simulation. A recently developed moving surface model explains the measured force quadrature curves on the soft polymer, in both air and liquid

Investigating nano-scale viscous and elastic forces withintermodulation : Studies in multifrequency atomic force microscopy

Investigating visco-elastic forces at the nanometer-scale is important to thecharacterization of soft materials. A quantitative force measurement can be ob-tained using an atomic force microscope (AFM) with a calibrated force transducer(the AFM cantilever). In this thesis, we discuss and evaluate simple methods ofcalibration and we use these calibrations to measure dynamic force quadraturecurves for both normal and in-plane tip-surface forces using Intermodulation AFM(ImAFM). ImAFM utilizes the nonlinearity of the tip-surface force by measuring the mix-ing between two or more drive frequencies placed close to a resonance of the AFMcantilever. The intermodulation response at many mixing frequencies provides ad-ditional observables, useful for characterization of materials. We use ImAFM nearthe first flexural resonance to measure visco-elastic materials and we show that sur-face motion plays an important role in the analysis of soft samples. To explain ourmeasurements we derive a simple model where the surface position is described byan exponential relaxation when perturbed from its equilibrium. Through numericalsimulations of this model we explain experiments for many different soft sampleswith varying properties. We further apply the intermodulation technique to softsamples in liquid. ImAFM at the first torsional resonance frequency induces motion of the tip in-plane with the surface, enabling friction measurements between the tip and sample.Due to the high torsional resonance frequency, the tip velocity can reach severalcm/s, many orders of magnitude higher than typical AFM friction measurements.By measuring the amplitude dependence of the dynamic force quadrature curves,we can resolve the transition between the tip sticking to the surface, through stick-slip to free sliding motion.QC 20180522</p

Investigating nano-scale viscous and elastic forces withintermodulation : Studies in multifrequency atomic force microscopy

Investigating visco-elastic forces at the nanometer-scale is important to thecharacterization of soft materials. A quantitative force measurement can be ob-tained using an atomic force microscope (AFM) with a calibrated force transducer(the AFM cantilever). In this thesis, we discuss and evaluate simple methods ofcalibration and we use these calibrations to measure dynamic force quadraturecurves for both normal and in-plane tip-surface forces using Intermodulation AFM(ImAFM). ImAFM utilizes the nonlinearity of the tip-surface force by measuring the mix-ing between two or more drive frequencies placed close to a resonance of the AFMcantilever. The intermodulation response at many mixing frequencies provides ad-ditional observables, useful for characterization of materials. We use ImAFM nearthe first flexural resonance to measure visco-elastic materials and we show that sur-face motion plays an important role in the analysis of soft samples. To explain ourmeasurements we derive a simple model where the surface position is described byan exponential relaxation when perturbed from its equilibrium. Through numericalsimulations of this model we explain experiments for many different soft sampleswith varying properties. We further apply the intermodulation technique to softsamples in liquid. ImAFM at the first torsional resonance frequency induces motion of the tip in-plane with the surface, enabling friction measurements between the tip and sample.Due to the high torsional resonance frequency, the tip velocity can reach severalcm/s, many orders of magnitude higher than typical AFM friction measurements.By measuring the amplitude dependence of the dynamic force quadrature curves,we can resolve the transition between the tip sticking to the surface, through stick-slip to free sliding motion.QC 20180522</p

Investigating nano-scale viscous and elastic forces withintermodulation : Studies in multifrequency atomic force microscopy

Investigating visco-elastic forces at the nanometer-scale is important to thecharacterization of soft materials. A quantitative force measurement can be ob-tained using an atomic force microscope (AFM) with a calibrated force transducer(the AFM cantilever). In this thesis, we discuss and evaluate simple methods ofcalibration and we use these calibrations to measure dynamic force quadraturecurves for both normal and in-plane tip-surface forces using Intermodulation AFM(ImAFM). ImAFM utilizes the nonlinearity of the tip-surface force by measuring the mix-ing between two or more drive frequencies placed close to a resonance of the AFMcantilever. The intermodulation response at many mixing frequencies provides ad-ditional observables, useful for characterization of materials. We use ImAFM nearthe first flexural resonance to measure visco-elastic materials and we show that sur-face motion plays an important role in the analysis of soft samples. To explain ourmeasurements we derive a simple model where the surface position is described byan exponential relaxation when perturbed from its equilibrium. Through numericalsimulations of this model we explain experiments for many different soft sampleswith varying properties. We further apply the intermodulation technique to softsamples in liquid. ImAFM at the first torsional resonance frequency induces motion of the tip in-plane with the surface, enabling friction measurements between the tip and sample.Due to the high torsional resonance frequency, the tip velocity can reach severalcm/s, many orders of magnitude higher than typical AFM friction measurements.By measuring the amplitude dependence of the dynamic force quadrature curves,we can resolve the transition between the tip sticking to the surface, through stick-slip to free sliding motion.QC 20180522</p

Year 2 Student Possibilities of Work Individualization and Differentiation of the Learning Processes of Latvian Language

Diplomdarba „Skolēnu darba individualizācijas un diferenciācijas iespējas latviešu valodas mācību procesā 2.klasē” mērķis ir pētīt un analizēt skolēna darba individualizēšanas un diferencēšanas iespējas latviešu valodas mācību procesā 2.klasē. Pētījuma aktualitāte izriet no tā, ka mācību procesam skolā jānodrošina katra skolēna izaugsme. Individualizēts un diferencēts mācību process ir veids, kā ievērot katra skolēna individuālās iezīmes un nodrošināt mācību procesu atbilstoši tām. Pētījuma rezultāti liecina, ka sākumskolas latviešu valodas mācību procesā ir diferencējams mācību saturs un tā apguves metodika.The aim of the thesis „Year 2 student possibilities of work individualization and differentiation of the learning processes of Latvian language” is to research and analyse the individualizing and differentiation options of the student during the learning processes in grade 2. The relevancy of the topic can be noted in the fact that the learning process in school has to assure development of each and every student. Individualized and differentiated learning process is a way to notice the individual characteristics of each student, and to provide the learning process accordingly. The results of the research show that in the learning process of the Latvian language classes, there is presence of differentiated content of learning and the method of practice