2015
DOI: 10.1002/jcc.24209
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Ion strength limit of computed excess functions based on the linearized Poisson–Boltzmann equation

Abstract: The linearized Poisson-Boltzmann (L-PB) equation is examined for its κ-range of validity (κ, Debye reciprocal length). This is done for the Debye-Hückel (DH) theory, i.e., using a single ion size, and for the SiS treatment (D. Fraenkel, Mol. Phys. 2010, 108, 1435), which extends the DH theory to the case of ion-size dissimilarity (therefore dubbed DH-SiS). The linearization of the PB equation has been claimed responsible for the DH theory's failure to fit with experiment at > 0.1 m; but DH-SiS fits with data o… Show more

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Cited by 4 publications
(20 citation statements)
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“…The reason why Fraenkel insists in believing that the negative deviations should not existexcepting very particular situations in which strong interactions other than the usual coulomb forces are occurringis because he reached the conviction that L-PB is not considerably different from the full, nonlinearized PB equation, independently of the charges involved. He wrote in this regard a work reporting an evaluation of the series expansion terms of the PB equation beyond that of the linear form, which revealed no substantial contribution of those terms for, in particular, dilute solutions . It is not easy to carefully inspect all statements in his work to identify where, in his analysis, he introduced the item/items that make his conclusions nonapplicable to, or noncomparable with, the situations studied many years ago by Guggenheim, , who for 2–2 electrolytes found considerable differences between the L-PB and complete numerical integration of PB, in the charge density distributions around the central ion.…”
Section: Discussionmentioning
confidence: 99%
“…The reason why Fraenkel insists in believing that the negative deviations should not existexcepting very particular situations in which strong interactions other than the usual coulomb forces are occurringis because he reached the conviction that L-PB is not considerably different from the full, nonlinearized PB equation, independently of the charges involved. He wrote in this regard a work reporting an evaluation of the series expansion terms of the PB equation beyond that of the linear form, which revealed no substantial contribution of those terms for, in particular, dilute solutions . It is not easy to carefully inspect all statements in his work to identify where, in his analysis, he introduced the item/items that make his conclusions nonapplicable to, or noncomparable with, the situations studied many years ago by Guggenheim, , who for 2–2 electrolytes found considerable differences between the L-PB and complete numerical integration of PB, in the charge density distributions around the central ion.…”
Section: Discussionmentioning
confidence: 99%
“…However, the major literature on electrolyte solutions claims that, at very high dilution, the L-PB equation is physically correct; that is, the L-PB equation is as good as the nonlinearized PB equation when ion strength is very small. ,, Deviations between the two equations, when advocated, are related almost always to effects existing, or assumed to exist, at high concentration. There, the truncation of the series expansion of the exponential part of the PB equation after the second expansion term is believed by scholars to result in missing the contribution of higher terms. ,, (But as I have recently shown, including higher terms does not contribute much even at relatively high concentration.) The DH theory becomes gradually more accurate as dilution increases, up to a point at which the DHLL is a very effective representation of the physics of the system.…”
Section: Discussionmentioning
confidence: 99%
“…Biver and Malatesta mention two articles by Guggenheim, from 1959 and 1960, on numerical integration of the PB equation (the respective refs and 28 in Comment) and raise the question, why is my analysis of the full PB equation not coherent with that of Guggenheim (and those of others cited by him)? A few comments are in order on Guggenheim’s computations:…”
Section: Peculiar Behavior Of 2–2 Sulfates1: Difference Between Full...mentioning
confidence: 99%
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