Proton binding to humic nano particles: electrostatic interaction and the condensation approximation
PHYSICAL CHEMISTRY CHEMICAL PHYSICS(2022)
摘要
Proton binding to "carboxylic" and "phenolic" sites of humic nano particles (HNPs) is determined by the total proton affinity that is due to a specific and an electrostatic affinity. Both affinities are accounted for in the bi-modal Langmuir-Freundlich (bi-LF)-equation extended with a Boltzmann factor that includes the electrostatic site potential(s), y. For y -> 0 the equation reduces to the bi-LF Master Curve (MC). Commonly, an electrical double layer model is used to obtain y, e.g., the bi-LF-Donnan-V-app (monocomponent NICA-Donnan) model and bi-LF-soft-particle-Poison-Boltzmann-Theory (SPBT). A new method is presented that combines the "condensation approximation" (CA) with the MC concept (CA-MC). With the CA, the proton binding curve and MC can be transformed in, respectively, the total and specific affinity distribution. The difference at a given charge density provides the electrostatic affinity and CA-potentials vs. charge density. The MC can be obtained theoretically or by using the convention that the electrostatic interaction is negligible at 1 M salt concentration. For five HNPs CA-potentials corresponding with the bi-LF-SPBT are compared with results of the bi-LF-Donnan-V-app model using the MC(SPBT). The bi-LF-Donnan-V-app model fails when the Debye length > hydrated particle radius. The CA-MC(1M) method does not require characteristics of the HNPs. Combination of the bi-LF-eq. with the CA-MC(1 M) method gives the bi-LF-CA-MC(1 M) model. The CA-MC(1 M) differs from the MC(SPBT); therefore, resulting parameters can only be compared when the same method is used.
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