Brownian flocculation of polymer colloids in the presence of a secondary minimum

Most analyses of Brownian flocculation apply to conditions where London–van der Waals attractive forces cause particles to be strongly bound in a deep interparticle potential well. In this paper, results are reported that show the interaction between primary- and secondary-minimum flocculation when the interparticle potential curve reflects both attractive and electrostatic repulsive forces. The process is highly time-dependent because of transfer of particles from secondary- to primary-minimum flocculation. Essential features of the analysis are corroborated by experiments with 0.80-μm polystyrene spheres suspended in aqueous solutions of NaCl over a range of ionic strengths. In all cases, experiments were restricted to the initial stage of coagulation, where singlets and doublets predominate.

Quantification of the hydrophobic interaction by simulations of the aggregation of small hydrophobic solutes in water

The hydrophobic interaction, the tendency for nonpolar molecules to aggregate in solution, is a major driving force in biology. In a direct approach to the physical basis of the hydrophobic effect, nanosecond molecular dynamics simulations were performed on increasing numbers of hydrocarbon solute molecules in water-filled boxes of different sizes. The intermittent formation of solute clusters gives a free energy that is proportional to the loss in exposed molecular surface area with a constant of proportionality of 45 ± 6 cal/mol⋅Å2. The molecular surface area is the envelope of the solute cluster that is impenetrable by solvent and is somewhat smaller than the more traditional solvent-accessible surface area, which is the area transcribed by the radius of a solvent molecule rolled over the surface of the cluster. When we apply a factor relating molecular surface area to solvent-accessible surface area, we obtain 24 cal/mol⋅Å2. Ours is the first direct calculation, to our knowledge, of the hydrophobic interaction from molecular dynamics simulations; the excellent qualitative and quantitative agreement with experiment proves that simple van der Waals interactions and atomic point-charge electrostatics account for the most important driving force in biology.