b) A coating consists of consisting of 55vol%TiO_(2) (spherical, surface-treated pigment particles), 32vol% emulsion, and 13vol% water (containing some dissolved compounds). The oil content of the emulsion is 50vol.%. The oil droplet and TiO_(2) particle diameters are 1.2 and 0.3mu m, respectively. The temperature is 25deg C and the viscosity of the medium (thickened aqueous phase) is 1kgm^(-1)s^(-1). The Hamaker constants of the oil and of TiO_(2) in vacuum are 5 imes 10^(-20) and 15 imes 10^(-20)J, respectively. The Hamaker constant of the aqueous medium in vacuum is 3.75 imes 10^(-20)J. The medium concentration of salt, NH_(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 kappa ^(-1)=(0.304)/(sqrt())C.
i) Calculate the attractive Van der Waals interaction energy between two orl droplets, between two TiO_(2) particles, and between an oil droplet and a TiO_(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 TiO_(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 TiO_(2) particles in the coating?
b A coating consists of consisting of 55 vol% TiO (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 TiO particle diameters are 1.2 and 0.3 um, respectively. The temperature is 25C and the viscosity of the medium (thickened aqueous phaseis l kg m-s-The Hamaker constants of the oil and of TiO in vacuum are 5 10-20 and 15 10-20 J,respectively.The Hamaker constant of the aqueous medium in vacuum is 3.75 10-20 J.The medium concentration of salt,NH4OH applied to control pH to basic conditions),in the coating formulation is 10- M.The relative permittivity of the medium is 80. The medium is water with a salt,NHOH 1 : I salt at 10-M and K- is calculated using the formulaK-1=0.304/VC. i Calculate the attractive Van der Waals interaction energy between two oil droplets between two TiO particles,and between an oil droplet and a TiO particle in the coating when the distance between the colloids (in all cases) is l5 nm.Comment on the result. ii It has been decided to stabilize both pigments and oil droplets electrostatically.The surface potential for both colloids is -50 mV.Calculate the electrostatic and composite overall interaction energies between an oil droplet and a TiO particle in the coating when the distance between them is l0 nm. Based on these calculations,what can you conclude more generally about the interaction of oil droplets and TiO particles in the coating?