Equivalent radii of humic macromolecules from acid-base titration

The macromolecular nature of humic substances is well established, and cylindrical geometry appears most likely although molecular dimensions have not been published. Previous analyses of acid-base titrations of humic acids have largely ignored the macromolecular nature of the humic molecule and the effect of ionization of titrated groups on the hydronium ion concentration in the vicinity of untitrated groups. In this work, humic macromolecules are modeled as cylinders with surface potentials generated by the ionization of acidic groups. Based on data collected from titrations of two humic acids at ionic strengths between 0.001 and 0.100 M NaCl and numerical solutions of the Poisson-Boltzmann equation for surface potentials, the radii of ideal charged cylinders that would display the same titration behavior in response to humic charge density and ionic strength were calculated. The results of these calculations show that humic macromolecules have equivalent radii ranging from about 1.1 nm at 10% ionization to 0.24 nm at 90% ionization. This change in equivalent radius may be conceptualized as the quantitative expression of changes in configuration as a result of uncoiling and extension due to electrostatic repulsion among charged groups on the same molecule. The derived charge densities reach relatively constant values of 1.3 to 1.5 × 10⁴ esu cm⁻² at 50 to 90% ionization. The data also support the concept of at least two different weakly acidic groups with different acid strengths or a Gaussian distribution of acidic groups about a central pK value.