# shear stresses

Dear All,

I am trying to calculate the viscosity of a rather complicated molecular mixture constisting of a phosphonium ion with hydrocarbon arms and of a borate ion. I have tried to evaluate the Green-Kubo relations and to perform shear flow simulations applying the SLLOD equations of motion.

The Green-Kubo relation for the viscosity is equal to the time integral of the time correlation function of the shear stress or the normal stress differens. In a liquid the time average of these quanitties are exactly zero. However, when I use lammps they are small but different from zero. This means that the Green-Kubo relations do not converge and thus it is not possible to obtain any estimates of the viscosity. They are, however, zero when Gromac is used to evaluate them, so it is possible to calulate the viscosity using this program.

When the SLLOD equations are applied the shear stress should go to zero when the velocity gradient or the shear rate goes to zero. Unfortunately there seems to be a constant contribution to the shear stress that does not go to zero when the shear rate goes to zero, so the ratio of the shear stress an the shear rate goes to infinity in the limit of zero shear rate.Thus it is not possible to calculate the the viscosity by this method either.

Therefore I wonder whether there is someone who has experienced similar problems and knows how to solve them.

Best Regards,

Sten Sarman

Possibly Aidan can comment.

Steve

Dear All,

I am trying to calculate the viscosity of a rather complicated molecular mixture constisting of a phosphonium ion with hydrocarbon arms and of a borate ion. I have tried to evaluate the Green-Kubo relations and to perform shear flow simulations applying the SLLOD equations of motion.

The Green-Kubo relation for the viscosity is equal to the time integral of the time correlation function of the shear stress or the normal stress differens. In a liquid the time average of these quanitties are exactly zero. However, when I use lammps they are small but different from zero. This means that the Green-Kubo relations do not converge and thus it is not possible to obtain any estimates of the viscosity. They are, however, zero when Gromac is used to evaluate them, so it is possible to calulate the viscosity using this program.

Perhaps there is something wrong. But, why would you expect the time-average of fluctuations in a molecular dynamics realization over a finite time interval to produce exactly zero?

When the SLLOD equations are applied the shear stress should go to zero when the velocity gradient or the shear rate goes to zero. Unfortunately there seems to be a constant contribution to the shear stress that does not go to zero when the shear rate goes to zero, so the ratio of the shear stress an the shear rate goes to infinity in the limit of zero shear rate.Thus it is not possible to calculate the the viscosity by this method either.

Therefore I wonder whether there is someone who has experienced similar problems and knows how to solve them.

Both of these problems seem to be due to the time-averaged shear stress being non-zero. You should examine what is causing this to happen. Possible causes are:

1. The system is not liquid
2. The longest shear relaxation times are much longer than the simulated time
3. Their is some sort of numerical error e.g. due to long-range electrostatics

I would start by modifying your simulation (increase temperature, decrease density) to eliminate 1 and 2 and see if the problem persists.

Aidan

Aidan P. Thompson
01444 Multiscale Science
Sandia National Laboratories
PO Box 5800, MS 1322 Phone: 505-844-9702
Albuquerque, NM 87185 Fax : 505-845-7442
E-mail:[email protected] Cell : 505-218-1011