Texts: A monodisperse colloid of spherical silica particles with a diameter of approximately 1.0 μm in water at room temperature (25°C) has been produced using the Stöber method. If the particle concentration in the above dispersion is 0.01 vol%, the following calculations can be made:
i) Assuming no particle aggregation, estimate the time required for the particles to settle to the bottom of a 10-cm deep vessel. The particle density is ρp = 2.10 g/cm³.
ii) Again, assuming no aggregation, calculate the time required to centrifuge this colloid (i.e., settle out all the particles) in a 10-cm long centrifuge tube spun at 5,000 RPM about an axis 3.0 cm from the top of the tube.
iii) Estimate the half-life, t1/2, of the dispersion with respect to rapid (Smoluchowski) aggregation.
iv) Consider an aggregate of two of the above particles in "direct" contact. What is the probability that this aggregate will spontaneously break apart due to thermal agitation at T = 25°C? The relevant Hamaker constant is A = 10⁻¹⁹ J.