I am trying to calculate the distance between two micelles in which potential switches from attractive to repulsive in water.

I been given the following information [also attached].

- Hydrophobic chain-water interfacial energy

My approach is to plot the curve of overall potential against distance by using DLVO theory:

net potential = attractive potential + repulsive potential

V

_{n} = V

_{A} + V

_{R}Then read distance off x axis at turning point from the curve.

I have the information and equation to calculate the potential of the attractive forces, but I can't seem to figure out how to calculate the repulsive forces from the given information. I was trying with the Debye-Hückel approximation:

V

_{R} = Ψ

_{0} exp

^{-KD}I have K, but I'm unsure how to find Ψ

_{0}.

There is also another equation where repulsive energy between two spheres of radius R can be calculated:

V

_{R} = (64*n

_{0}*K

_{B}T*pi*R* γ

^{2}*e

^{-KD}) / K

^{2} but it involves parameters: reduced surface potential (γ) & ionic concentration in the bulk solution (n

_{0}).

Which are two things not directly given in the question, is it possible to somehow calculate these two things?

Is there another equation I can use to do this?