b$)$ A coating consists of consisting of $55$vol$\%Ti{O}_2($spherical$,$ surface$-$treated pigment particles$),32$vol$\%$ emulsion, and $13$vol$\%$ water $($containing some dissolved compounds$).$ The oil content of the emulsion is $50$vol.$\%.$ The oil droplet and $Ti{O}_2$ particle diameters are $1\mathrm{.}2$ and $0\mathrm{.}3m,$ respectively. The temperature is $25C$ and the viscosity of the medium $($thickened aqueous phase$)$ is $1kg{m}^{-1}{s}^{-1}.$ The Hamaker constants of the oil and of $Ti{O}_2$ in vacuum are $5{10}^{-20}$ and $15{10}^{-20}J,$ respectively. The Hamaker constant of the aqueous medium in vacuum is $3\mathrm{.}75{10}^{-20}J.$ The medium concentration of salt, $N{H}_{4}OH($applied to control $pH$ to basic conditions$),$ in the coating formulation is ${10}^{-5}M.$ The relative permittivity of the medium is $80.$ The medium is water with a salt, salt$)$ at ${10}^{-5}M$ and $K^{-1}$ is calculated using the formula ${}^{-1}=\frac{0\mathrm{.}304}{\sqrt[\phantom{2}]{?}}C.$

i$)$ Calculate the attractive Van der Waals interaction energy between two orl droplets, between two $Ti{O}_2$ particles, and between an oil droplet and a $Ti{O}_2$ particle in the coating when the distance between the colloids $($in all cases$)$ is $15nm.$ Comment on the result.

ii$)$ It has been decided to stabilize both pigments and oil droplets electrostatically. The surface potential for both colloids is $-50mV.$ Calculate the electrostatic and composite $($overall$)$ interaction energies between an oil droplet and a $Ti{O}_2$ particle in the coating when the distance between them is $10nm.$ Based on these calculations, what can you conclude more generally about the interaction of oil droplets and $Ti{O}_2$ particles in the coating?