Bernhard Reischl

Free Energy Approaches for Modeling Atomic Force Microscopy in Liquids

High resolution atomic force microscopy (AFM) in liquids offers atomic scale insight into the structure at water/solid interfaces and is perhaps the only tool capable of resolving the nature of formed hydration layers. However, convolution between the imaging signal and the tip/surface interactions and hydration layers means that interpretation is far from straightforward. Modeling the complex imaging mechanism of atomic force microscopy in liquids requires calculation of the free energy profile as a function of the distance between AFM tip and surface. Its derivative is the best approximation for the force acting on the AFM tip, including entropic contributions from interactions with water molecules in hydration layers over the surface and around the tip apex. In order to establish a reliable approach for these simulations, we compare two methods of calculating free energy profiles from atomistic molecular dynamics simulations, umbrella sampling and free energy perturbation, on two model surfaces, calcium fluoride and calcium carbonate. Our results demonstrate that both methods effectively provide equivalent free energy profiles but offer different possibilities in terms of efficiency, constraints, and analysis of the free energy components.

A simple approximation for forces exerted on an AFM tip in liquid

The critical quantity in understanding imaging using an atomic force microscope is the force the sample exerts on the tip. We put forward a simple one-to-one force to water density relationship, explain exactly how it occurs, and in which circumstances it holds. We argue that two wide classes of atomic force microscope (AFM) tip should lead to at least qualitative agreement with our model and represent a significant fraction of AFM tips as currently prepared. This connection between the short-range force and the unperturbed equilibrium water density removes the need to perform simulations for each tip location, conservatively speeding up simulations by around three orders of magnitude compared to current methods that explicitly calculate the force on a tip model at each point in space.

Ab initio Kinetic Monte Carlo simulations of dissolution at the NaCl–water interface

We have used ab initio molecular dynamics (AIMD) simulations to study the interaction of water with the NaCl surface. As expected, we find that water forms several ordered hydration layers, with the first hydration layer having water molecules aligned so that oxygen atoms are on average situated above Na sites. In an attempt to understand the dissolution of NaCl in water, we have then combined AIMD with constrained barrier searches, to calculate the dissolution energetics of Na(+) and Cl(-) ions from terraces, steps, corners and kinks of the (100) surface. We find that the barrier heights show a systematic reduction from the most stable flat terrace sites, through steps to the smallest barriers for corner and kink sites. Generally, the barriers for removal of Na(+) ions are slightly lower than for Cl(-) ions. Finally, we use our calculated barriers in a Kinetic Monte Carlo as a first order model of the dissolution process.

Understanding 2D atomic resolution imaging of the calcite surface in water by frequency modulation atomic force microscopy

Frequency modulation atomic force microscopy (FM-AFM) experiments were performed on the calcite (10[Formula: see text]4) surface in pure water, and a detailed analysis was made of the 2D images at a variety of frequency setpoints. We observed eight different contrast patterns that reproducibly appeared in different experiments and with different measurement parameters. We then performed systematic free energy calculations of the same system using atomistic molecular dynamics to obtain an effective force field for the tip-surface interaction. By using this force field in a virtual AFM simulation we found that each experimental contrast could be reproduced in our simulations by changing the setpoint, regardless of the experimental parameters. This approach offers a generic method for understanding the wide variety of contrast patterns seen on the calcite surface in water, and is generally applicable to AFM imaging in liquids.

Atomistic simulation of the measurement of mechanical properties of gold nanorods by AFM

Mechanical properties of nanoscale objects can be measured with an atomic force microscope (AFM) tip. However, the continuum models typically used to relate the force measured at a certain indentation depth to quantities such as the elastic modulus, may not be valid at such small scales, where the details of atomistic processes need to be taken into account. On the other hand, molecular dynamics (MD) simulations of nanoindentation, which can offer understanding at an atomistic level, are often performed on systems much smaller than the ones studied experimentally. Here, we present large scale MD simulations of the nanoindentation of single crystal and penta-twinned gold nanorod samples on a silicon substrate, with a spherical diamond AFM tip apex. Both the sample and tip sizes and geometries match commercially available products, potentially linking simulation and experiment. Different deformation mechanisms, involving the creation, migration and annihilation of dislocations are observed depending on the nanorod crystallographic structure and orientation. Using the Oliver-Pharr method, the Young’s moduli of the (100) terminated and (110) terminated single crystal nanorods, and the penta-twinned nanorod, have been determined to be 103 ± 2, 140 ± 4 and 108 ± 2 GPa, respectively, which is in good agreement with bending experiments performed on nanowires.

Nanoindentation of gold nanorods with an atomic force microscope

The atomic force microscope (AFM) can be used to measure mechanical properties of nanoscale objects, which are too small to be studied using a conventional nanoindenter. The contact mechanics at such small scales, in proximity of free surfaces, deviate substantially from simple continuum models. We present results from atomistic computer simulations of the indentation of gold nanorods using a diamond AFM tip and give insight in the atomic scale processes, involving creation and migration of dislocations, leading to the plastic deformation of the sample under load, and explain the force–distance curves observed for different tip apex radii of curvature, as well as different crystallographic structure and orientation of the gold nanorod samples.

Atomic force microscope adhesion measurements and atomistic molecular dynamics simulations at different humidities

Due to their operation principle atomic force microscopes (AFMs) are sensitive to all factors affecting the detected force between the probe and the sample. Relative humidity is an important and often neglected—both in experiments and simulations—factor in the interaction force between AFM probe and sample in air. This paper describes the humidity control system designed and built for the interferometrically traceable metrology AFM (IT-MAFM) at VTT MIKES. The humidity control is based on circulating the air of the AFM enclosure via dryer and humidifier paths with adjustable flow and mixing ratio of dry and humid air. The design humidity range of the system is 20–60 %rh. Force–distance adhesion studies at humidity levels between 25 %rh and 53 %rh are presented and compared to an atomistic molecular dynamics (MD) simulation. The uncertainty level of the thermal noise method implementation used for force constant calibration of the AFM cantilevers is 10 %, being the dominant component of the interaction force measurement uncertainty. Comparing the simulation and the experiment, the primary uncertainties are related to the nominally 7 nm radius and shape of measurement probe apex, possible wear and contamination, and the atomistic simulation technique details. The interaction forces are of the same order of magnitude in simulation and measurement (5 nN). An elongation of a few nanometres of the water meniscus between probe tip and sample, before its rupture, is seen in simulation upon retraction of the tip in higher humidity. This behaviour is also supported by the presented experimental measurement data but the data is insufficient to conclusively verify the quantitative meniscus elongation.

Simulating solid-liquid interfaces in atomic force microscopy

In this chapter, we will cover the main approaches taken to model AFM in liquids in a variety of different systems, discussing the advantages and problems of different methods, outlining the main issues to take into account in general, while also attempting to build a perspective for the future of the field. We hope this will provide a fundamental platform of understanding for future Atomic Force Microscopy studies of solid-liquid interfaces at the nanoscale.