# Help to clarify chemcial potential

1. Nov 10, 2014

### KFC

Hi there,
The first time I heard about chemical potential is statistical mechanics but I didn't understand that so well due to the misleading term "chemical". Recently, I am reading some introduction articles on optical lattices for bosons and it again mentions there a chemical potential for each lattice site for bosons sitting on that site. I wonder what's chemical potential is really about? What happens if it increases or decreases? What's difference for big chemical potential and small one? Thanks.

2. Nov 10, 2014

### Staff: Mentor

The chemical potential is the energy necessary to add a particle to a system. In the example you cite, it is the energy necessary to add a boson at a particular lattice site.

When two systems can exchange particles, the chemical potential acts pretty much in the same way as temperature does for energy. Particles will move from the system with a higher chemical potential to the one with the lower chemical potential, until equilibrium is reached, i.e., when the chemical potential in both systems is equal. This idea can be extended to different species in chemical equlibrium, where the "chemical" adjective takes on its full meaning.

3. Nov 12, 2014

### zhanhai

"The chemical potential is the energy necessary to add a particle to a system."

I would doubt this. A crystal has its chemical potential, say Ef. If an electron at an energy (Ef-V) in the crystal is taken away from the crystal, can a new electron with energy (Ef-V) be added to the crystal?

4. Nov 13, 2014

### DrDu

It is the change of internal energy with particle number $\mu=\partial U(S,V,N)/\partial N=\partial G(T,p,N)/\partial N$.

5. Nov 13, 2014

### Matterwave

On should specify; however, that T and P are required to be constant in the above definitions of chemical potential. So the Chemical potential is the energy needed to add a particle to a system at constant temperature and pressure.

6. Nov 13, 2014

### DrDu

No, from the formulas I gave, you can see that T and P have to be held constant when considering the Gibbs free energy, while for the change of ordinary energy U, S and V have to be held constant.

7. Nov 13, 2014

### Matterwave

Of course, you are right. :)