I want to know is there any mathematical expression between zeta potential and charge on the nanoparticles?
Can we consider that biologically synthesized protein capped NPs will have a net negative surface charge at neutral pH?
Zeta potential depends on velocity of nanoparticles not on the charge.
Dear Mohd:
The mathematical relationship between the particle charge and its kinetic potential is not. If the dispersed system particles move to the negative electrode in electrophoresis, the nanoparticles are positively charged. Your protein amphoteric substance. The hydrogen ions and the hydroxyl group have a high adsorption capacity. Therefore, changing the pH of the medium can recharge nanoparticles.
Regards/
Unfortunately, it is not possible to relate the zeta potential quantitatively to the surface charge, since the build up of the Stern layer contains contributions due to specific ion adsorption and also requires to take the size of the ions into account. A Langmuir adsorption layer is typically assumed for this. (That is what Stern did.)
There are approximations to relate the surface charge to the surface potential though, The most common and straightforward one is the Grahame's equation. It is basically just assuming charge neutrality and using the Poisson equation for the charge distribution and then you get the result. You can google it or I can send you some of my lecture slides on it. The surface potential calculated in this way is however not the zeta potential mainly for the reason mentioned above.
For the second question, you can definitely not assume this since it depends on both the particle surface potential and the adsorbed protein layer. You cannot generalize anything like that.
Good luck with your work,
Erik
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