Humic substances are soft and permeable: Evidence from their electrophoretic mobilities

Due to the complexity of the humic substances (HS), mathematical models have often been employed to understand their roles in the environment. Since no consensus exists with respect to the structure and conformation of the HS, models have alternatively given them properties corresponding to impermeable hard spheres or fully permeable polyelectrolytes. In this study, the hydrodynamic permeability of standard HS (Suwannee River fulvic, humic, and peat humic acids) are evaluated as a function of pH and ionic strength. A detailed theoretical model is used to determine the softness parameter (lambda(0)), which characterizes the degree of flow penetration into the HS on the basis of measured values of electrophoretic mobilities, diffusion coefficients, and electric charge densities. Their motion in an electric field is evaluated by a rigorous numerical evaluation of the governing electrokinetic equations for soft particles. The hydrodynamic impact of the polyelectrolyte chains is accounted for by a distribution of Stokes resistance centers and partial dissociation of the hydrodynamically immobile ionogenic groups distributed throughout the polyelectrolyte. The results demonstrate that the studied HS are small (radius ca. 1 nm), highly charged (500-650 C g(-1) when all sites are dissociated), and very permeable (typical flow penetration length of 25-50% of the radius, depending on pH). The HS also coagulate slightly when lowering the pH of the solution. Modeling of the HS as hard spheres with a charge and slip plane located at the surface is thus physically inappropriate, as are a number of analytical theories for soft particles that hold for low to moderate electrostatic potentials and large colloids. The shortcomings of these simpler approaches, when interpreting the electrophoretic mobilities of HS, are highlighted by comparison with rigorous theoretical predictions.