# Speeds and rates relative to experiment

When performing an atomistic simulation, it is very easy to end up with velocities or rates (I will just use velocities from now on) which are several orders of magnitude greater than in experiment. A classic example is the speed of a nano-indenter tip or the velocity of fluid flow. The velocity is set by the total time and the characteristic distance involved. The total time which can be covered by an MD simulation, in turn, is limited both by the maximum possible timestep and by the computational cost of each step (these topics are discussed in the book in Sections 6.2 and 13.6). The mismatch in velocities can have a profound effect on the results being generated, and this needs to be considered carefully when analysing and writing up. There is always a trade-off between total simulation time and accuracy of results.

A nanoindenter is a standard piece of characterisation equipment, which drives a hard tip into a sample. It allows measurement of materials properties in a small area, including elastic and hardness parameters. A nice example of velocities generated can be found in a study of nanoindentation of Fe single crystals[1]. The modelling used a tip which moved through 8.8nm in 90ps – which is equivalent to 96 m/s (well in excess of experimental velocities where 5 m/s is considered high). The excess energy generated by the indenter speed had to be removed to avoid affecting the results; in this case, by applying damping to all atoms. The results of the study are in good agreement with experiments presented in the same paper, though the effects of the damping and high speeds need to be considered.

Atomistic simulations of water flow through narrow channels, particularly carbon nanotubes, have become very popular. However, there are many possible pitfalls here. First, velocities, which are around 0.25 m/s experimentally – though this is remarkably high[2], and is the cause of some of the interest in the system. One simulation of water flow through a carbon nanotube[3] used high pressure (200MPa) and non equilibrium MD to achieve high rates of water passing through the nanotube. This is equivalent to a velocity of 15 m/s – significantly above measured rates – but allowed simulations of only 4ns in duration, making a saving in computational time.

A paper in Nature Nanotechnology[4] suggested that it was possible for static charges placed outside a nanotube to induce spontaneous water flow through the nanotube, in a set-up designed to mimic natural nanopores such as aquaporins. The resulting simulations required 115ns using the GROMACS package and TIP3P for water, and saw 337 molecules traverse the nanotube, at a speed around 70 cm/s. While this is a more reasonable velocity, it has been suggested[5] that the spontaneous flow of water was generated by problems with settings in the simulation code. Specifically, charge groups which are used to speed up simulations, cutoffs applied to neighbour lists and the use of a Berendsen thermostat (see this post for more details) were blamed. This is not the only example of approximations causing errors, by any means; a particularly startling example[6] showed that truncating electrostatic interactions, even at a large distance of 2.5nm, causes significant artifacts in simulations of lipid bilayers. Random number generators are another well-known source of artificial correlations and artifacts.

It is very, very easy to create a simulation which appears to be relevant to experiment, without adequately testing or considering consequences. It is vital, as part of learning how to perform atomistic simulations, to understand how parameters affect results.

[1] Phys. Rev. B 67, 245405 (2003) DOI:10.1103/PhysRevB.67.245405

[2] Nature 438, 44 (2005) DOI:10.1038/43844a

[3] Microfluid. Nanofluid. 12, 257 (2012) DOI:10.1007/s10404-011-0869-3

[4] Nature Nano. 2, 709 (2007) DOI:10.1038/nnano.2007.320

[5] Nature Nano. 5, 555 (2010) DOI:10.1038/nnano.2010.152

[6] Biophys. J. 84, 3636 (2003) DOI:10.1016/S0006-3495(03)75094-2

This entry was posted in techniques on 2013/7/17.