$8$ a$)$ Calculate Hamaker constant and Van der Waals interaction potential for $($i$)$ PTFEwater$-$PTFE, $($ii$)$ polyvinyl alcohol$-$water$-$polyvinyl alcohol, and for $($iii$)$ PTFE$-$waterpolyvinyl alcohol. Assume PTFE and polyvinyl alcohol are in the form of thin sheets and in each case the separation is $10nm\mathrm{.}10$ points

b$)$ Calculate Van der Waals interaction potential for two spheres of polystyrene of radii $500nm$ and $200nm$ dispersed in water at a distance of $1nm,10nm,$ and $100nm.$ Compare the interaction energy with $k_{B}T$ at $300K$ and whether this energy is sufficient to hold the particles together. How does the interaction energy change if the spheres are dispersed in toluene and separated by $1nm?15$ points