# Particle repulsive force

Dear LAMMPS users,

I am simulating dense suspensions with particles. Particle interactions include repulsive force that acts normally and decays with interparticle surface separation h exponentially. I am wondering how to add this repulsive force in LAMMPS. In most pair styles, the energy and force are functions of the distance between the centers of particles rather than the interparticle surface separation.

Best wishes,
Ann

This is not a problem because the effective size of those particles is tied to the atom type and the interaction parameters between each pair of atom types takes than into account. For example, with the well-known Lennard-Jones potential the “sigma” parameter is an effective size, representing the distance between two particles when the potential energy is zero (the minimum is at 2^\frac{1}{6}\cdot\sigma). Or with the Morse potential, the potential energy minimum is part of the potential function.

The repulsive force |Fr|=F0exp(-h/lamda). I don’t know how to realize it in LAMMPS. Could you please give me some suggestions?

Thank you.

Please provide complete information. This is just one term and not explaining any details, e.g. what the variables mean. You are effectively just repeating what you posted originally with a little bit more details, but not at all addressing my request. I cannot provide advice out of context.

Sorry for the incomplete information. This exponential potential can be in other forms, such as potential w(r)=cexp(-r/r0), where c and r0 are adjustable constants. These exponential potentials are commonly used mainly due to their mathematical convenience and they allow for the finite compressibility of atoms.

Since you are not very specific, I cannot respond in a very specific way, either. All available pair styles are listed in the manual, you just need to see, if there is one that matches your needs.

Beyond that, you can use one of then LEPTON package pair styles or pair style table to model custom simple pairwise interactions that can be expressed as a function of the distance and for which no C++ implementation exists. Otherwise, you have to implement your own pair style. There is a whole section of the manual dedicated to how you can modify and extend LAMMPS.

Thank you, Akohlmey. I see the pair styles in the manual carefully and found that the pair_style buck is the closest in form to the particle repulsive force I want to use.
The Buckingham potential: E=Aexp(-r/pho)-C/r^6 r<rc, where pho is an ionic-pair dependent length parameter, and rc is the cutoff on both terms.

In this potential r represents the distance between the centers of two atoms. In my granular system composed of spheres of finite size, the repulsive force is a function of the interparticle surface separation h, not the distance between the centers of particles r. Is it possible to modify r to h?

Isn’t the distance between particle surfaces just the distance between particle centers minus a constant (the sum of radii)? So just rewrite your between-surface force as a function of the between-center distance and you should be all good.

More importantly, what do you want your model to do when the particles overlap (that is, the distance between centres becomes less than the sum of radii)?

If you implement a custom pair style, you can modify it any way you want. Similarly, in pair style lepton/sphere you have access to the individual particle radii and thus implement your potential.

Since you mention describing granular media, it seems unlikely to me that this exponential repulsion is the only interaction required. In that case, you should look into adding to pair style granular, which allows to customize the individual components of interaction. This can be done by adding a granular sub model. @jtclemm can explain in more detail, if desired.

Hi srtee, yes, the distance between particle surfaces is the distance between particle centers minus the sum of radii. If the system contains particles of different sizes, the sum of the radii depends on the type of particles, so I think it is best to define a pair style based on granular pair interaction that consider particle sizes.

The particle interactions in my system include contact interaction, repulsive interaction and lubrication interaction. When the particles overlap, the contact force is activated. Now I am unclear about how to implement the repulsive interaction in LAMMPS.