Relative permittivity (dielectric constant) determines the relation between the electric field and the electric flux density. If there is a constant electric charge at a certain point in space, the permittivity can determine the rate of attenuation of the electric field and voltage by increasing the distance from the charge source. Therefore, in cases in which a constant charge is existing and it is required to minimize the attenuation of the electric field and voltage by increasing the distance from the charge, a material with a high permittivity is desired.
In solid-state batteries, having a larger electric field throughout the electrolyte may be helpful to exert a larger force on the moving ions and facilitate ion migration through the electrolyte. However, I cannot see any relation between the electric field (and the resultant force) and the permittivity of the electrolyte material in batteries. The electric field of the solid electrolyte is not necessarily generated by electric charges. In the discharging mode, a voltage is existing between the anode and cathode which is generated by the inherent difference between the reduction potentials of the two electrodes and the gradient of this voltage is the electric field. Hence, having a high permittivity through the electrolyte cannot strengthen the electric field. The electric field which is generated by the electric charges has also a parasitic effect in the double-layer space charge regions at the interfaces.
On the other hand, when the battery is being charged, a particular voltage is exerted from an external circuit and again the gradient of this voltage is the electric field. If instead of charging the battery by a voltage source, the electric charges injected to the electrodes were constant, the permittivity of the electrolyte could have an impact on the electric field and the voltage, but because the voltage is directly determined by the charger circuit, the electric field is also directly fixed by the voltage and permittivity could not have any effect on the electric field.
So why are the researchers seeking materials with high permittivity for solid electrolytes?
Dear friend Kianoosh Karimi
The permittivity of a material is a measure of its ability to store an electric charge in an electric field. In solid-state batteries, having a larger electric field throughout the electrolyte can exert a larger force on the moving ions and facilitate ion migration through the electrolyte. Therefore, in cases in which a constant charge is existing and it is required to minimize the attenuation of the electric field and voltage by increasing the distance from the charge, a material with a high permittivity is desired. However, I cannot see any relation between the electric field (and the resultant force) and the permittivity of the electrolyte material in batteries. The electric field of the solid electrolyte is not necessarily generated by electric charges. In the discharging mode, a voltage is existing between the anode and cathode which is generated by the inherent difference between the reduction potentials of the electrodes with each other and the gradient of this voltage is the electric field. Hence, having a high permittivity through the electrolyte cannot strengthen the electric field. The electric field which is generated by the electric charges has also a parasitic effect in the double-layer space charge regions at the interfaces. On the other hand, when the battery is charging, a particular voltage is exerted from an external circuit and again the gradient of this voltage is the electric field through the electrolyte. If instead of charging the battery by a voltage source, the electric charges injected to the electrodes were constant, then permittivity of electrolyte could have an impact on electric field and voltage.
Here are some references that might help you understand the relationship between permittivity and solid-state batteries:
- [Solid-state batteries: An overview of current progress and future prospects](https://www.sciencedirect.com/science/article/pii/S1364032119306971)
- [Solid-state batteries: Challenges and prospects](https://www.sciencedirect.com/science/article/pii/S1369702117306999)
- [Solid-state batteries: Opportunities beyond Li-ion](https://www.nature.com/articles/s41560-019-0468-9)
I hope that helps! Let me know if you have any other questions.
Dear all,
(re-)consider, please, that the permittivity has very different roles (impacts and specs) depending on the:
i) materials (single phases: electrolytes, and electrode materials) offering a high ionic mobility[1]),
and very demanding roles at the local (complex)
ii) interface(s') specs of the devices (3-phases/2-interfaces: batteries, and solid-state batteries), offering a wider (Potential) window(s) stability.
1. ...high (only) ionic electrolytes' conductivity and high mixed (e+i) conductivity in electrode materials.
Dear Mr. Rana Hamza Shakil
,Thank you for your answer and comprehensive explanations.
The contradiction that I faced in the role of permittivity in allowing a stronger electric field is not still solved and the effects of permittivity on ionic conductivity and ion shunting that you explained were both based on the presumption of being permittivity effective in the electric field of the solid electrolytes.
The battery's voltage is determined by the inherent difference between the reduction potentials of the anode and cathode and the electric field is just the gradient of voltage. I cannot see any relation between the electric field and permittivity when the voltage is determined by the inherent electrochemical properties of the electrodes and the state of charge of the battery. The electric field would be strengthened by increasing the permittivity if there was a fixed electric charge, and the voltage and electric field were just the effects of the electric charge, but when the voltage is fixed by inherent electrochemical properties, the electric field is also fixed by them and permittivity cannot increase it.
My problem is in the equations that determine the relationship between these parameters and based on the physical relation between electric field and voltage (E = - gradient {V} & V = - integral {E.dl}) and being the voltage independent of permittivity, I cannot understand how can permittivity increase the electric field when the voltage is constant.
Dear Mr. Rana Hamza Shakil
,Thanks again for your complete explanations and your time.
I understand that when the permittivity is higher, the concentration of electric dipoles is higher, so the material can support stronger electric fields. The contradiction between a constant voltage and having a strengthened electric field by enlargening the permittivity still exists.
If we consider a homogeneous material as the solid electrolyte and simplify the problem to a 1-dimensional analysis, the relation between the voltage and electric field would be simply V = - Ed. There is no permittivity in this equation and the only parameter other than voltage is the thickness of the solid electrolyte.
Even if the material is nonhomogenous, this relation would be in the form of V = - integral {E.dl}, and again the integral of the values of E throughout the thickness of the electrolyte is constant and equal to V. Therefore, the average electric field would be again equal to V/d based on the mean value theorem for integrals.
The question is still unanswered how (based on which physical equations) strengthening the electric field in a constant voltage by increasing the permittivity could be explained.
Thank you in advance.
Dear Rana Hamza Shakil
,When we have the equation "V = - intergal{E.dl}" for any nonhomogeneous material, if the two ending points of the electrolyte are called "a" and "b", the mean value of E is (V(a) - V(b))/|a - b| based on the mean value theorem for integrals, where |a - b| is the thickness of the electrolyte and (V(a) - V(b)) is the voltage. Electric potential is the primitive function of the electric field. Why should we consider the value of electric potential as the weight of computing the average value of the electric field? The electric field at any point of a nonhomogenous material is only proportional to the derivative of the voltage, not the voltage itself. The right and left sides of your proposed equation do not have equal dimensions and it does not also include permittivity.
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