Solving Confusion: Ashcroft & Electrochemical/Chemical Potential

In summary, there is confusion and disagreement in the scientific community regarding the definitions and usage of the terms electrochemical potential and chemical potential. This is particularly evident in the article provided, where the author uses \mu to refer to both terms, leading to possible misinterpretation. It is important for scientists to have a clear understanding and agreement on definitions in order to communicate effectively and accurately. The chemical potential refers to the variation in energy if the mass were not charged, while the electrochemical potential takes into account the charged mass. To avoid confusion, it would be more accurate to use \overline{\mu} instead of \mu_e to refer to the electrochemical potential.
  • #1
Fernsanz
57
0
Hello.

There is no agreement on the meaning of terms electrochemical potential and chemical potential (see for example http://web.mit.edu/6.730/www/ST04/Lectures/Lecture26.pdf"). While proper definitions would call chemical potential to

[tex]\mu\equiv\left(\frac{\partial U}{\partial n}\right)_{neutral}[/tex]​

-i.e., the variation in energy if the mass were not charged- and electrochemical potential or Fermi level to

[tex]\overline{\mu}\equiv\left(\frac{\partial U}{\partial n}\right)_{charged}=\left(\frac{\partial

U}{\partial n}\right)_{neutral} +q\phi \equiv F_n[/tex]​

-i.e, the actual variation in energy taking into account the mass is charged, which is the only measurable observable- Ashcroft (p. 593) seem to be totally misleading because he uses the letter [tex]\mu[/tex] to refer to the electrochemical potential and then defines an electrochemical potential as [tex]\mu_e=\mu - e\phi[/tex].

Equilibrium condition (deduced from the fundamental thermodynamic relation in energetic form)

[tex]dU=TdS - pdV+ \mu dn + Fz\phi dn=TdS - pdV + \overline{\mu} dn[/tex]​

imposes that electrochemical potential should be constant along the semiconductor, so the actual picture is the electrochemical potential being constant along the semiconductor dimension and the valence and conduction energies bending wherever electric field exists.

Has anyone else observed -suffered- this misleading (wrong?) point in Aschroft?

Thanks
 
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  • #2
for bringing up this issue. I can understand your confusion and frustration with the different definitions and usage of the terms electrochemical potential and chemical potential. It is important for scientists to have a clear understanding and agreement on the definitions and usage of terms in order to communicate effectively and accurately.

After reviewing the article you shared, it seems that the main source of confusion lies in the use of the letter \mu to refer to both the chemical potential and the electrochemical potential. As you mentioned, Ashcroft defines an electrochemical potential as \mu_e=\mu - e\phi, which can be misleading since \mu is typically used to refer to the chemical potential. This can lead to confusion and misinterpretation of the equations and concepts.

In order to avoid this confusion, it is important to clearly define and distinguish between the two terms. As you stated, the chemical potential \mu refers to the variation in energy if the mass were not charged, while the electrochemical potential or Fermi level \overline{\mu} takes into account the fact that the mass is charged. Therefore, it would be more accurate to use \overline{\mu} instead of \mu_e to refer to the electrochemical potential.

In conclusion, I agree with you that the use of the letter \mu to refer to both the chemical potential and the electrochemical potential can be misleading and should be clarified in order to avoid confusion. Thank you for bringing this issue to our attention and let's continue to strive for clear and accurate communication in the scientific community.
 

FAQ: Solving Confusion: Ashcroft & Electrochemical/Chemical Potential

1. What is the difference between electrochemical and chemical potential?

Electrochemical potential refers to the potential energy of an electron in a system, while chemical potential refers to the potential energy of a molecule in a system. In other words, electrochemical potential is specific to electrons, while chemical potential is specific to molecules.

2. How do you calculate electrochemical potential?

Electrochemical potential can be calculated by subtracting the product of the number of moles and the Faraday constant from the product of the charge of an electron and the potential difference.

3. What factors affect electrochemical potential?

The factors that affect electrochemical potential include the concentration of ions, temperature, and the presence of an electric field. Changes in any of these factors can alter the electrochemical potential of a system.

4. How does Ashcroft's theory explain electrochemical potential?

Ashcroft's theory suggests that electrochemical potential is a result of the balance between the electron's kinetic energy and its potential energy in a system. This theory helps to understand the behavior of electrons in different systems and their effects on electrochemical potential.

5. What is the importance of understanding electrochemical and chemical potential?

Understanding electrochemical and chemical potential is crucial for studying various chemical and physical processes, such as corrosion, battery operation, and chemical reactions. It also helps in the design and optimization of various technological devices, such as fuel cells and sensors.

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