Founder of TriboNet, Editor, PhD (Tribology), Tribology Scientist at ASML, The Netherlands. Expertise in lubrication, friction, wear and contact mechanics with emphasis on modeling. Creator of Tribology Simulator.
Molecular Dynamic Simulations and AFM Experiments at Overlapping Speeds
11.04.2016
Atomic Force Microscopy (AFM) is a powerful and convenient experimental measurement device in the field of nano-scale tribology. It was successfully applied to explore superlubricity in a graphene-gold interface and superlubricity due to repulsive van der Waals forces, to grow tribofilms and to address numerous other problems. At the same time, many phenomena cannot be explored experimentally and theoretical calculations must be performed. Molecular dynamic simulation method (MD) is a useful computational tool that is also frequently employed along with AFM experimentation. In principle, it is capable of solving any type of tribological problem without introducing additional assumptions beyond the accuracy of the interatomic potentials. This comes for the price of high computational costs and the conditions employed in the MD and AFM experiments are frequently different, making the quantitative comparison less reliable.
This is particularly true for the study of a stick-slip friction, a fundamental phenomenon in nanotribology, rising for example between AFM tip and clean crystalline substrate. The mechanical constraints and data acquisition systems allow to slide the AFM tip with the speeds 
m/s at fastest. The same stick-slip behavior can be explored by means of MD simulations. However, the typical sliding speed has to be higher than 
m/s in order to consider realistic sliding time. This comes due to the limitation in the integration time step employed in MD, which is typically in the range of femtoseconds.
An international group of researchers from University of Pennsylvania, California Merced, Calgary and University of Akron performed AFM and MD friction experiments with Au (111) and silicon oxide tips with matched conditions and at overlapping speeds. To achieve this, both the AFM and MD set ups were improved. Instead of moving the AFM tip, the samples were moved. The samples were glued on a high-frequency shear piezo to increase the scanning speed up to 580µm/s. Parallel replica dynamics method (PRD) was employed to decrease the sliding speed during the MD simulations down to as low as 25µm/s. Algorithmically simple (yet having a solid theoretical background), RPD allows to increase the rate of time accumulation in the simulation almost 
times faster compared to conventional MD with the aid of parallel processors.
Using this sophisticated method, the gap between AFM and MD was closed and a good agreement was documented. The research team validated MD simulations to be applicable for the interpretation of AFM data.
Further details can be found in the original article Dynamics of Atomic Stick-Slip Friction Examined with Atomic Force Microscopy and Atomistic Simulations at Overlapping Speeds by Xin-Z. Liu, Zhijiang Ye, Yalin Dong, Philip Egberts, Robert W. Carpick, and Ashlie Martini
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I’m sure this will prove to be a silly question, but was there a measurement of the RMS roughness of the Au111 or AFM tips? Further, were there comparison measurements before and after the experimental runs to determine if any “run-in wear” occurred to change the RMS? I have read that Au111 can have radically different surface roughness depending on the method of deposition and the temperature of deposition, to the extent of an order of magnitude difference.
This is what I found in the supplemental material to the paper: “Gold samples were prepared by thermal evaporation of bulk gold (Kurt Lesker Inc., purity 99.99%) onto freshly cleaved mica (SPI Supplies Inc.) under high vacuum conditions. After evaporation, samples were annealed with a hydrogen flame in air and then inserted in the fast entry lock of the UHV system within a few minutes after annealing. Upon insertion into the UHV chamber, samples were annealed at 300°C for 3 hours to desorb water and surface contaminants. After the samples were cooled, large terraces of more than 100 nm2 in lateral dimension were examined. The inset of Figure SI1 demonstrates the high purity Au(111) surfaces that were prepared, as the herringbone surface reconstruction was observed on these large
terraces”. So the samples were atomically smooth. The TEM images of two AFM tips were shown in the paper, with 10 nm scale. Its difficult to say what the exact value of the tip roughness, but I would guess its considered to be atomically smooth with a certain tip radius of curvature. The roughness evolution due to wear was probably neglected here.
I suggest that neglecting the surface wear evolution (especially considering the sampling was done via a high-frequency shear piezo) was a big mistake. This is stick-slip behavior after all, guys. In the presence of non-atomic asperities of any size, we are not looking at true “atomic” stick-slip friction . . . but I’m sure it made the MD simulations more palatable.
Further, the herringbone reconstruction (alternating FCC/HCP atom stacking) of Au111 under STM shows typical differing terrace widths between 3.3 nm to 7.0 nm. Now that might be “atomic” when talking about the surface of engine metal in your car after Phantaslube®, but for AFM on 99.99% pure Au in the lab?
I actually thought the surface is smoother. In the MD simulations they considered the roughening, but as they showed the incresase of it due to wear is below 1 Angstrom.
I think the “smoother” surface is due to a common DFT “approximation” in the MD simulations.
No, wait a second…my bad!
If the indenter is riding on a (comparatively thick) adsorbed water layer, yes, there would be virtually no wear to the underlying Au surface. Yep, was a silly question after all.
My bad twice…
I forgot the samples were annealed again in UHV conditions before the test.
Although, I did read somewhere that no amount of sample prep can get rid of 100% of the ambient humidity.