In some cases it is useful to know the diffusivity of a molecule at a particular region in the simulation box; for instance, to study the mobility of water near a surface, inside a nanotube, or across a membrane. Abstracting this information from the mean-square displacement or velocity autocorrelation function is complicated by the fact that molecules will diffuse in and out the region of interest.
One option is to fix a molecule at the position of interest, and record the force acting on it in time, F(t). The diffusivity can then be obtained from the time correlation of this force (see e.g. [1], [2])
where R is the gas constant, T the temperature, and ΔF the force fluctuation,
This approaches the diffusion coefficient of an unconstrained molecule in the Brownian limit.
Attached is a script to calculate the local diffusivity with Forcite using the method above. The input consists of a 3D periodic structure, with a set named "Probe", containing one molecule at the position (and orientation) of interest. The script will fix the molecule, and run a molecular dynamics simulation outputting a trajectory. Since Forcite does not write out force data of fixed atoms, a copy of the trajectory is made in which the constraint is undone. An additional energy calculation on this trajectory provides the forces. Finally the force is time correlated, and integrated, and the diffusivity is output in a study table, for X, Y, and Z direction separately.
As a test I applied the script to an open-ended (and fixed) nanotube immersed in water. I calculated the diffusivity of water inside and outside the nanotube. Below are some results (in Ų/ps). By comparison, the diffusion coefficient of water from mean square displacement analysis in this system gave 0.195 Ų/ps.
| Structure | Dx | Dy | Dz |
|---|---|---|---|
0.060 | 0.042 | 0.149 | |
0.235 | 0.189 | 0.229 |
Please note the disclaimer: This custom script is compatible with Materials Studio version 6.1. It is provided "as is" and is NOT supported by Accelrys nor is it warranted for any purpose whatsoever. The user assumes responsibility for any malfunctions or bugs.
Hope it is of use to anyone!
Reinier
[1] S.-J. Marrink and H.J.C. Berendsen, Simulation of Water Transport through a Lipid Membrane, J. Phys. Chem. 98, 4155 (1994) (link)
[2] R.L.C. Akkermans and W.J. Briels, Coarse-grained dynamics of one chain in a polymer melt, J. Chem. Phys. 113, 6409 (2000) (link)
