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These two examples show that an electrical potential and a chemical potential can both give the same result: A redistribution of the chemical species. Therefore, it makes sense to combine them into a single "potential", the electrochemical potential , which can directly give the net redistribution taking both into account.
The phrase "chemical potential" sometimes means "total chemical potential", but that is not universal. [13] In some fields, in particular electrochemistry, semiconductor physics, and solid-state physics, the term "chemical potential" means internal chemical potential, while the term electrochemical potential is used to mean total chemical ...
[2] [3] Other theoretical concepts that use electron affinity include electronic chemical potential and chemical hardness. Another example, a molecule or atom that has a more positive value of electron affinity than another is often called an electron acceptor and the less positive an electron donor. Together they may undergo charge-transfer ...
Under the free electron model, the electrons in a metal can be considered to form a Fermi gas. The number density N / V {\displaystyle N/V} of conduction electrons in metals ranges between approximately 10 28 and 10 29 electrons/m 3 , which is also the typical density of atoms in ordinary solid matter.
When a voltmeter is used to measure an electronic device, it does not quite measure the pure electric potential (also called Galvani potential).Instead, it measures the electrochemical potential, also called "fermi level difference", which is the total free energy difference per electron, including not only its electric potential energy but also all other forces and influences on the electron ...
In this case, the chemical potential of a body is the infinitesimal amount of work needed to increase the average number of electrons by an infinitesimal amount (even though the number of electrons at any time is an integer, the average number varies continuously.): ( ,) = ( ), where F(N, T) is the free energy function of the grand canonical ...
The chemical potential μ is, by definition, the energy of adding an extra electron to the fluid. This energy may be decomposed into a kinetic energy T part and the potential energy − eφ part. Since the chemical potential is kept constant, Δ μ = Δ T − e Δ ϕ = 0. {\displaystyle \Delta \mu =\Delta T-e\Delta \phi =0.}
The main assumption of the free electron model to describe the delocalized electrons in a metal can be derived from the Fermi gas. Since interactions are neglected due to screening effect , the problem of treating the equilibrium properties and dynamics of an ideal Fermi gas reduces to the study of the behaviour of single independent particles.