@JohnRennie hi

Hi :-)

Consider a positively charged AgCl sol, formed by adding KCl to AgNO3.

Some NO3- particles will be surrounding the positively charged sol.

Yes, the positive charge on the particles polarises the solution, just like polarising a dielectric. So near the particles there is an excess of nitrate ions.

If two experiments are done with this setup (with some values changed, say the concentration etc. I'm not sure), say it is observed that the particles of one sol have a higher zeta potential. Does this mean that the sol with higher zeta potential will have more NO3- ions surrounding the colloidal particles or less? I think it should be the former.

The zeta potential is the potential caused by the surface charge. The higher the surface charge the higher the zeta potential.

A higher zeta potential typically means a stronger electric field near the particles so a greater polarisation of the solution. So the higher zeta potential will have a higher nitrate concentration near the particles.

@JohnRennie ..isn't the zeta potential mainly due to the surrounding layer, not the surface charge? At least this wiki diagram seems to imply that it is not mainly due to the surface charge (which is negative in the diagram, but the zeta potential is positive)

You mean this diagram?

yes

The surface charge charge is positive i.e. the surface charge is due to the shell of cations that have stuck to the surface.

@JohnRennie ok, that was what I was thinking too, that a higher zeta potential will have a higher nitrate conc near the particles; but, a few days ago you had explained that upon the addition of an electrolyte (say KNO3), the sol flocculates due to more NO3- surrounding the colloid particles. This means that a higher zeta potential $\implies$ higher tendency to flocculate, but the wikipedia page says that the higher the zeta potential, more stable the sol

Hmm, wait, the diagram does have an arrow labelled Surface charge (negative)

That's weird ..

yes, exactly.

I don't know what that is supposed to mean.

> For molecules and particles that are small enough, a high zeta potential will confer stability, i.e., the solution or dispersion will resist aggregation.

That's correct.

could you explain why this reasoning is wrong then?

The zeta potential is basically just the equivalent to the potential of a charged sphere in electrostatics. It's more complicated in water since it's a dielectric and we get polarisation of the aqueous solution, but to a first approximation the zeta potential is just like a potential.

And when two spheres have the same sign charge then the higher the potential the higher the repulsive force between them. Yes?

yes

ok I see what you're saying...

So the higher the zeta potential of particles the more they repel each other and therefore the less likely they are to flocculate.

ok, yes but say in this example, you would agree that a higher zeta potential means that more nitrate ions will surround the surface?

The measured zeta potential is the potential including any rearrangement of ions near the particles.

Just like with electrostatics in a dielectric the field is the field after the dielectric has been polarised.

ah ok I got it. Higher the zeta potential means the surface charge must've been higher, which means that more NO3- ions must be sticking to the surface. But even though more NO3- ions are sticking to the surface, it doesn't matter since at the end the final potential (or you could say total charge) is higher, hence more repulsion.

is this correct?

Yes

and the wiki diagram would've been correct if they had flipped the graph about the x-axis, i.e since the surface charge is negative the zeta potential should also be negative?

I don't understand what the diagram means by saying the surface charge is negative.

In general the particle is overall neutral, and it picks up a charge because we get preferential adsorption of one of the ions on the surface.

In that diagram the cations preferentially adsorb on the surface forming an inner shell of tightly bound cations. So the surface charge is positive.

Either the diagram has a mistake or it means something too obscure for me to understand.

ah ok.

Also, I'd like to ask one more thing:

I think the surfactant will have very little effect on viscosity below the critical micellar concentration. Indeed, even after it has started forming micelles there isn't much effect on viscosity. It's only when we start getting rod or lamellar phases that the viscosity increases significantly.

ok, thanks.

hey can anyone help me

lim u tends to infinity (u-1)/(\sqrt(u^(2)-2u+2))

@TonyPhysicslover ans is 1

@napstablook Dividing numerator and denominator by u ?

@Wolgwang hmm