Effect of Concentration and Intermolecular Forces on the Sedimentation of Polystyrene Spheres

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Abstract
At low concentration, the sedimentation coefficient s can be related to the sedimentation coefficient at zero concentration s0 through a power series expansion in the volume fraction Φ, i.e., s = s0(1 + KΦ···). We discuss the calculation of the constant K for sedimenting charged spheres. The spheres interact hydrodynamically as well as through a potential consisting of a hard-core repulsion, a screened Coulomb repulsion, and a London–van der Waals attraction. To calculate K one must know the value of the electrostatic potential in the vicinity of the surface of the sedimenting sphere ψδ, and the Hamaker constant, the constant which measures the strength of the London–van der Waals attraction. It is shown that knowledge of any two of the three quantities K, ψδ, and the Hamaker constant allows one to find the third. It is also shown that if both ψδ and the Hamaker constant are unknown the experimental determination of K can be used to obtain upper and lower bounds on the Hamaker constant. Using Cheng and Schachman's experimental value of K for polystyrene latex spheres, the following bounds for the Hamaker constant for polystyrene in aqueous solution are found: 3–8 × 10−14 erg. These bounds are in good agreement with previous experimental determinations.