[NotSureReally]

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 

• Hamaker Constant

• Interaction constant

• Debye Length

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 = Ψ₀ exp^-KD

I have K, but I'm unsure how to find Ψ₀.

There is also another equation where repulsive energy between two spheres of radius R can be calculated:
V_R = (64*n₀*K_BT*pi*R* γ²*e^-KD) / K ²

but it involves parameters: reduced surface potential (γ) & ionic concentration in the bulk solution (n₀).

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?