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This Indian Institute of Technology Bombay press release quotes some research papers which claims to prove that homeopathic remedies do retain original substances even when diluted.

The paper reports the fascinating observation that certain high potency (highly diluted) homeopathic remedies made from metals still contain measurable amounts of the starting material, even at extreme dilutions of 1 part in 10 raised to 400 parts (200C). It is well known that a series of 1:99 dilutions done sequentially will produce a significant dilution of the starting material in very short order. Specifically, if the starting material is at one molar concentration (6.023x10e23 molecules per liter), then at about the 12th dilution (12C) there should be no or very nearly no molecules left of the starting material. At 200th dilution (200C) the likelihood of there being even one atom of the starting material approaches zero. However, dilution does not work so simply, according to this paper. Using electron microscopy (TEM), electron diffraction, and atomic spectroscopy, Chikramane et al. found that, contrary to the arithmetic, there are nanogram quantities of the starting material still present in these ‘high potency’ remedies in the form of nanoparticles.

This was published in a homeopathy journal and not a chemical engineering journal, although the department was chemical engineering.

A later paper, Why Extreme Dilutions Reach Non-zero Asymptotes: A Nanoparticulate Hypothesis Based on Froth Flotation suggests that nano-particles are distributed unevenly, floating to the top of the container, which may interfere with dilution predictions, public in a journal from the American Chemical Society.

However, physicochemical studies of these solutions have unequivocally established the presence of the starting raw materials in nanoparticulate form even in these extreme (super-Avogadro, >1023) dilutions. In this article, we propose and validate a hypothesis to explain how nanoparticles are retained even at such enormous dilution levels.

Another researcher in a Letter to the Editor that the original element was found may be be because those original elements were stuck to the inner walls of lab glass:

Further-more, soluble compounds can be captured by nanosized structure, often nanobubbles, lining the boron-silicate glasses with which dilutions, subjected to mechanical stresses, are made. Therefore, an imprecise fraction of compound may be dispersed into the solvent from the glass wall whenever a mechanical stress is applied to the dilution, possibly giving gelsemine concentration far from the theoretical evaluation into pure water.

(The "mechanical stress" presumably refers to the succussion during homeopathic preparation.)

In practice, are some of the original materials still found in 200C dilutions?

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    $\begingroup$ I see this was previously asked on Skeptics.SE. If a solution is not mixed perfectly in each step of successive dilution and sampling, then there's no way to be sure what the last solution's concentration is. Poorly mixed solutions could presumably carry solute far beyond the Avogadro limit of dilution. Whether this is actually the general case in homeopathy, I don't know. Either way, it is far from enough to prove its soundness. $\endgroup$ – Nicolau Saker Neto May 31 '15 at 15:56
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    $\begingroup$ In short, the paper in Langmuir shows that, if one tries to treat a suspension as a real solution, then dilutions won't work as arithmetic predicts. Which is quite obvious. The paper's contribution is in the fact that they show how these are not solutions, but really non-homogeneous suspensions. This explains how homeopaths may mistakenly make solutions that still contain some active principle, through poor technique when carrying out the dilution process. It in no way supports the extravagant claim that extreme dilution would retain any of that material, if it were done properly. $\endgroup$ – MarcoB May 31 '15 at 16:58
  • $\begingroup$ Think about it … a single belladonna dropped into a river out of which a town like Leipzig takes its drinking water … would create a higher atropine concentration than is sometimes ‘present’ in highly diluted homeopathetica (typo on purpose). $\endgroup$ – Jan Jun 1 '15 at 17:40

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