Hi every researchers
I'm working on ions transport in aqueous solution and aim to derive diffusion coefficient via slope of MSD (mean square displacement) vs. time. But, at the long time, MSD curves takes downward slope, corresponding to negative diffusion coefficient.
Could anybody please explain the physical meaning of that observation?
Is it feasible or my work has flaw?
Many thanks in advance.
I think some points are worth mentioning:
1. At very long simulation times, the fact that you are using periodic boundary conditions and your system size is actually limited can have effects on MSD results.
2. It is important not to just calculate MSD with respect to time t = 0 of the trajectory, but to use a sampling over different time origins (think a sliding time window). I have found this point crucial in getting correct MSD results. When you do this, you can also calculate the standard error of your MSD value. It might be that the decreasing value falls withing the error range; because for longer times, fewer samples are available.
3. The MSD behavior with time can undergo different regimes (ballistic, sub-diffusion, Einstein diffusion). So, you need to study the curve in its entirety.
4. If you are studying confined system (like ions in a channel), the diffusion behavior will deviate from a simple MSD = 6 D t expression. Specifically, the exponent of t can change.
It sounds like the temperature is decreasing, check the total energy of the system to see if the system is truly at equilibrium.
Negative diffusion would mean particles are aggregate which is possible. See the attached paper for a simulation study of this.
Article Negative diffusion coefficient in two-dimensional lattice ga...
I think some points are worth mentioning:
1. At very long simulation times, the fact that you are using periodic boundary conditions and your system size is actually limited can have effects on MSD results.
2. It is important not to just calculate MSD with respect to time t = 0 of the trajectory, but to use a sampling over different time origins (think a sliding time window). I have found this point crucial in getting correct MSD results. When you do this, you can also calculate the standard error of your MSD value. It might be that the decreasing value falls withing the error range; because for longer times, fewer samples are available.
3. The MSD behavior with time can undergo different regimes (ballistic, sub-diffusion, Einstein diffusion). So, you need to study the curve in its entirety.
4. If you are studying confined system (like ions in a channel), the diffusion behavior will deviate from a simple MSD = 6 D t expression. Specifically, the exponent of t can change.
Dear Amir Hossein Saeedi Dehaghani!
I agree with mentioned above answers, especially with Prof. Goodwin noting about equilibrium and with point 1 of Prof. Sadeghi answer, and want to note, that interpretation of the artifacts in numerical analysis depend on algorithm, which you use.
For example, if you use molecular dynamics and solve Cauchy problem for many body system, your solution could be far from reality at the long times due to round-off errors. Or if you use Monte-Carlo simulation, probably, at long times your process not entirely convergence (or you use not "very good random numbers" generator).
So, to answer your question certainly is needed to know what algorithm you use.
Finally, not only negative diffusion coefficient could has physical meaning, as Prof. Goodwin note, but diffusion coefficient could has also complex value (as in Schrödinger equation in quantum mechanics).
Sincerely,
Daniil D. Stupin
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