Dual Classical Electrostatic Equations

...from the History of Science literature

[The] most fundamental aspect of the incommensurability of competing paradigms... is that "the proponents of competing paradigms practice their trades in different worlds.

Scott L. Pratt (2009) Logic: Inquiry, Argument, and Order. p.8

Scientific development depends in part on a process of non-incremental or revolutionary change. Some revolutions are large, like those associated with the names of Copernicus, Newton, or Darwin, but most are much smaller, like the discovery of oxygen or the planet Uranus. The usual prelude to changes of this sort is, I believed, the awareness of anomaly, of an occurrence or set of occurrences that does not fit existing ways of ordering phenomena. The changes that result therefore require 'putting on a different kind of thinking-cap', one that renders the anomalous lawlike but that, in the process, also transforms the order exhibited by some other phenomena, previously unproblematic.

— Thomas S. Kuhn

the proponents of competing paradigms practice their trades in different worlds. … the two groups of scientists see different things when they look from the same point in the same direction. Again, that is not to say that they can see anything they please. Both are looking at the world, and what they look at has not changed. But in some areas they see different things, and they see them in different relations one to the other. That is why a law that cannot even be demonstrated to one group of scientists may occasionally seem intuitively obvious to another.

Stuart A. Umpleby and Eric B. Dent. (1999) "The Origins and Purposes of Several Traditions. in Systems Theory and Cybernetics". p.150

Distinct interpretations of Coulomb’s Law

Electrostatic analysis in physics is based on classical theory. Chemistry analysis is closely related to experimental conditions. Superficially, the two result in potential energy functions (PEFs) that differ by a factor of the permittivity, ε_r, but the full story is more interesting as well as useful. Utilizing the research from both fields raises potentialities for more accurate and stable molecular modeling - and it is the transition between the two perspectives that improves the calculations.

The transition function, D_eff, increases the magnitude of local terms as compared to cumulative long distance terms, it reduces distance dependence of the radial PEF within the induced charge layer, and it improves computational stability for some systems including substrate in dilute salt solution. Molecular modeling is used for development in pharmaceuticals, biotech, nanotech, and materials.

Published paper at: http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=53278

Alternate equations for PEF

Figure 1. (a) Analysis in chemistry is based on the empirical force between charges; D is frequently set to the permittivity, D=ε_r. (b) Physics uses a linear approximation to determine total charge (initial + induced). The force between charges is then calculated using vacuum Coulomb's Law.

A charge induces charge about itself. In chemistry, chemical interactions take place at the molecular scale which is within this induced charge layer. In physics, classical analysis is for interactions far outside the induced charge layer. An effective dielectric function, D_eff, resolves the different perspectives.

Effective dielectric function

For a particular distance, measuring the dielectric effect at that distance produces the correct result be it within or outside the induced charge layer. Outside the induced charge layer, the experimental data produces the theoretical result. D_eff is consistent with both Figure 1a and 1b. The experimental methodology of Figure 1a is very versatile in that it can handle the dielectric effect at any distance, within or outside the induced charge layer. The classical theoretical approach of Figure 1b can utilize the large databases of permittivities. It is particularly useful in situations where the electrostatic term is too small to measure.

From the pragmatic perspective of stabilizing computer simulations; the D_eff function increases the magnitude of local terms as compared to cumulative long distance terms, it reduces distance dependence of the radial PEF within the induced charge layer, and it improves computational stability for some systems including substrate in dilute salt solution.

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Dual Classical Equations

Distinct interpretations of Coulomb’s Law

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