Units of temperature and length

[Remya Ann]

Hello everyone,

I use the expanded mie potential to simulate 2 different systems.

The epsilon and sigma values are different.

The values of m and n are the same.

The diameter of the particle is the same in both systems, but I understand that the sigma effects would control the effective diameter of the particle.

But, I guess the length unit in the simulation is set with the set particle diameter, which is the same in both cases. So would the length unit be the same in both systems?

Also, is the actual temperature in the system dependent on the epsilon value of the potential?

My precise question would be, since the epsilon values are different, will both systems be at the same temperature if the kT value in the integrator is the same in both systems?

Any suggestions would be really helpful !

Kind regards,

Remya

[antoni...@googlemail.com]

Dear Remya,

The sigma parameter in the Mie potential is the diameter of your particle and can be used to set your base unit of length. See the hoomd documentation on units for more discussion. I also recommend Allen & Tildesley, Computer Simulations of Liquids, for a discussion of reduced units. 

If you give the same kT value, your temperature in the simulation will be the same. The system will behave differently due to the different epsilons (which sets your energy scale). It is most likely possible to map your systems by rescaling by size/sigma and energy/epsilon. I highly recommend reading  Allen & Tildesley, Computer Simulations of Liquids for more background on reduced units before running any simulations. 

Best,

Antonia

[Joshua Anderson]

Reduced units are useful to understand single particle type simulations. Once you have multiple types, it gets confusing very quickly.

For example, if you have 2 particle types then your Mie potential has 3 sigma and 3 epsilon parameters (AA, AB, BB). All 3 sigmas are lengths in the same base unit of length. Note that the particles are *points* and have no intrinsic diameter. You might choose to interpret sigma_AA as the effective diameter of the A particle - but whether the system behaves like a diameter with respect to B depends on the value of sigma_BB and sigma_AB. Also, while the effective diameter of A clearly scales with sigma_AA, the coefficient out front may depend on the system temperature and the shape of the potential. There have been many papers over the years that have attempted to assign appropriate effective diameters to potentials that are equivalent to a hard particle simulation. Depending on your project, you may or may not need this level of detail.

------

Joshua A. Anderson, Ph.D.

Research Area Specialist, Chemical Engineering, University of Michigan

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[Remya Ann]

Dear Antonia and Dr. Anderson,

Thank you for your email. 

I'm sorry I wasn't very clear earlier. I do understand the basics of reduced units.

I work on a system that undergoes cis-to-trans transition within the same simulation.

All the particles have the same name and defined diameter to start with (I understand that the effective diameter would actually based on the sigma value of the potential once the simulation starts. I define the diameter just to initialise the system and I was hoping that this would be taken as the unit of length.)

In the cis condition the sigma and epsilon values are say S1 and E1. After a particular simulation time, I shift to the trans condition which has sigma and epsilon parameters say S2 and E2.

I do not change the kT value in the integrator, or the box value as part of the transition.

My question is will the effective density and temperature I am working with change, because of the transition that I do from cis to trans (and will this change be based on the sigma and epsilon values in each case)

If it does change, then obviously I would have to calculate the reduced density and  temperature based on cis and trans conditions to account for the same real conditions and use the corresponding box and kT values in each case. Is this correct?

To answer the above 2 questions I need to know whether the length and temperature units are scaled with respect to the sigma and epsilon of the mie potential.

Hope I am a bit more clear now.

Please let me know your thoughts. If attaching my script would help, please let me know and I shall do so.

Kind regards,

Remya