# Additional models to Poisson-Boltzmann equation?

• e15
In summary, the conversation discusses two models, the Poisson-Boltzmann equation and the Debye-Huckel approximation, which are used to study the effects of ions in solutions. The Debye-Huckel approximation is used at low ionic strengths and dilute solutions, while the Poisson-Boltzmann equation focuses on the charged interface. The Stern layer, which takes into account the finite size of ions, is also mentioned. Other models and important details about the Stern layer and Debye-Huckel approximation are also brought up in the conversation.
e15
I'm not sure my question belongs here or in the physics section

I'm aware that in addition to the poisson-boltzmann equation, there's also the Debye-Huckel approximation, which is used at low ionic strengths and dilute solutions. I also know that the Stern layer includes the finite size of ions and studies how surfaces are affected

However, what other models exist? And what other details about the Stern layer and Debye-Huckel approximation are important that I forgot to mention?

e15 said:
in addition to the poisson-boltzmann equation, there's also the Debye-Huckel approximation

Isn't it apples and oranges? AFAIR PB is mostly about what happens at the phase interface, while DH describes ions in the bulk solution.

Borek said:
Isn't it apples and oranges? AFAIR PB is mostly about what happens at the phase interface, while DH describes ions in the bulk solution.
Not quite. The PB equation is used to set up Debye Hueckel. Instead of a charged interface you consider the charged surface of an ion.

I see. I stand corrected.

Not for the first, not for the last time

## 1. What is the Poisson-Boltzmann equation?

The Poisson-Boltzmann equation is a mathematical model used to describe the electrostatic interactions between charged particles in a solution. It takes into account the effects of both the electrostatic potential and the thermal energy of the ions in the solution.

## 2. Why are additional models needed for the Poisson-Boltzmann equation?

While the Poisson-Boltzmann equation is a useful model, it is not always accurate for complex systems. Additional models may be needed to account for factors such as ion size, ion-ion correlations, and non-electrostatic interactions.

## 3. What are some examples of additional models to the Poisson-Boltzmann equation?

Additional models to the Poisson-Boltzmann equation include the mean spherical approximation (MSA), the Debye-Hückel theory, and the generalized Poisson-Boltzmann equation. These models aim to improve upon the limitations of the original equation and provide more accurate predictions for systems with high ion concentrations or complex geometries.

## 4. How are these additional models validated?

Additional models to the Poisson-Boltzmann equation are typically validated through comparisons with experimental data or more accurate theoretical models. They may also be tested by applying them to systems with known solutions or by conducting sensitivity analyses to determine their robustness.

## 5. What are the potential applications of these additional models?

Additional models to the Poisson-Boltzmann equation have a wide range of potential applications, particularly in the fields of biophysics, biochemistry, and materials science. They can be used to study the behavior of charged particles in biological systems, as well as to design and optimize materials with specific electrostatic properties.

Replies
1
Views
619
Replies
25
Views
2K
Replies
5
Views
2K
Replies
1
Views
2K
Replies
12
Views
9K
Replies
6
Views
2K
Replies
0
Views
2K
Replies
2
Views
3K
Replies
2
Views
1K
Replies
1
Views
3K