Liesegang Rings: 3 – Theory and Practice

Liesegang Rings - Theory and Practice

The previous post examined the natural diversity of patterns associated with the Liesegang Phenomenon [including rings, spirals, helices and polygons].

The Liesegang Phenomenon has been studied for over a 100 years and academia has generated a plethora of theories that attempt to explain the underlying science.

Super Saturation Theory
The first theory of periodic precipitation was published in 1897 by Wilhelm Ostwald in his book about general chemistry. It is well known, that in some situations, nucleation of crystals can be kinetically hindered, and precipitation can start only at a certain level of super saturation. This experimental finding formed the basis of Ostwald’s “super saturation theory”. According to this scenario the system remains supersaturated until the formation of the first crystal. At this point a local “explosion” happens because the surrounding zone is very far from equilibrium. “Explosion” means that the chemical reaction becomes so fast, that diffusion is not able to feed it and a wide depleted zone will be formed around the precipitate. This series of events happens repeatedly and causes a spatiotemporal periodicity.

The Sol Coagulation Theory
The main feature of the sol coagulation theory is that the material to be precipitated is produced first as a colloid dispersion. The visible precipitate will emerge when the stability of this dispersion ceases because of the high concentration of the outer electrolyte.

Diffusing Intermedier Models
To surmount the mentioned theoretical problem with the sol-coagulation model, many authors tried to describe Liesegang patterning by models, in which the diffusing ions form molecules or very small particles at first. These particles can move by diffusion with practically the same velocity as ions, and when their concentration reaches a threshold, they precipitate. The basic difference between these models lies in the kinetics of precipitation.

Competitive Particle Growth Model
There are some experimental findings showing that precipitate patterns can form without imposed external concentration gradients. In a gelatine gel containing evenly distributed lead-iodide sol spontaneous pattern formation takes place by a ripening mechanism.
According to the competitive particle growth theory this is due to a thermodynamic instability (Lifshitz-Slyozov instability), that is caused by the non-homogeneous size distribution of sol particles. Smaller particles have greater surface tension, which causes their solubility to be something higher, than that of the greater ones. This means, that in such a non-homogeneous system the large particles can grow at the expense of smaller ones. The latter finally completely dissolve and leave clear regions between the precipitate zones.

Diffusion Wave Theory
Basis of every really functioning Liesegang model is the assumption of at least one autocatalytic reaction step in the mechanism of precipitation. In this respect diffusion wave theory is rather exceptional, because it is based on autoinhibition. When two electrolytes react with each other formation of precipitate is always followed by formation of a by-product. There are many cases too, when the reaction can be reversed by excess of this material. For example if the two reactants are MgCl2 and NH4OH the by-product will be NH4Cl, in excess of which the Mg(OH)2 precipitate can be re-dissolved.
According to the diffusion wave theory spatiotemporal periodicity of Liesegang patterns is caused by the by-product of precipitation. Where a greater amount of precipitate forms concentration of the by-product increases too. This locally increases the solubility product and hinders formation of more precipitate. This inhibition effect remains until the concentration peak is bleared by slow diffusion.

Adsorption Theory
Adsorption theory gives a very straightforward but – from practical point of view – hardly believable explanation for spatiotemporal periodicity of Liesegang patterns. According to this model appearance of void depleted spaces is caused by adsorption of electrolytes on surfaces of precipitate particles.

The Spinodal Decomposition Scenario
This model has been suggested recently by Zoltán Rácz and can be regarded as a special variant of the diffusing intermedier models.
According to this description the two electrolytes form a metastable product that can move in the system by diffusion. When its stability ceases it decomposes into immobile precipitate.

Lattice-Boltzmann Model
This is essentially a cellular automata model of Liesegang patterning developed recently by Chopard and others. Both reactants are treated as an ensamble of discrete particles walking randomly on a lattice. When two different particles occupy the same lattice position they can react with eachother according to certain automata rules and form an immobile phase (precipitate)

Existing Theories and Qualitative Models – András Büki
http://www.insilico.hu/liesegang/theories/theories.html

Ultimately, no single theory has managed to explain all forms of the Liesegang Phenomenon and many scientists believe that periodic precipitation is not the result of a single effect.

Due to the fact that since 1896 nobody was able to suggest a general theory, most of the scientists believe that periodic precipitation is not a single effect, and such a general description does not exist at all.

Effects, Anomalies and Natural Occurrences of Liesegang Patterns – András Büki
http://www.insilico.hu/liesegang/effects/effects.html

The solution of the diffusion equation with proper boundary conditions, and a set of good assumptions on supersaturation, adsorption, auto-catalysis, and coagulation alone, or in some combination, has not been done yet, it appears, at least in a way that makes a quantitative comparison with experiment possible.

https://en.wikipedia.org/wiki/Liesegang_rings

Not many of the reactions are fully understood, including some that have been observed for upward of a century, such as the phenomenon of the Liesegang rings.

Many theories have h been advanced in explanation of this periodic precipitation but I have not been able to make much sense of them.

Most suggest that a band precipitates when more salt has diffused into the solution than the solution can hold, and nucleation occurs. Crystals then grow on the nuclei, deplete the solution and enable the migration to continue for a certain distance until supersaturation is again reached and another band of crystals is deposited.

My personal reaction to this explanation is best expressed in the words of Omar Khayyám, as translated by Edward Fitzgerald:

Myself, when young, did eagerly frequent
Doctor and Saint, and heard great argument
About it and about: but evermore
Came out by the same door where in I went.

Growing Crystals in Silica Gel Mimics Natural Mineralization – C. L. Stong – 1962
http://jesseenterprises.net/amsci/1962/03/1962-03-fs.html

Unsurprisingly, the lack of a comprehensive scientific explanation has frustrated some observers.

The uncertainty around the theories of periodic precipitation would not be so surprising in case of a complicated reaction-diffusion system like for example the Belousov-Zhabotinsky reaction. But Liesegang patterning is the result of only one reaction taking place between two reactants…

Existing Theories and Qualitative Models – András Büki
http://www.insilico.hu/liesegang/theories/theories.html

However, there is clear evidence that indicates the Liesegang Phenomenon is not just a “chemical” process of periodic precipitation.

Unfortunately, this additional evidence seems to be generally ignored [probably because it involves the heretical involvement of the electromagnetic spectrum].

Firstly, it has been observed that “Liesegang bands will appear after the gel has been exposed to sunlight”.

A particularly attractive experiment involves the precipitation of metallic gold and the development of a banded pattern by exposing the gel to sunlight.

To make this experiment prepare a sodium silicate solution that includes one milliliter of a 1 percent solution (by weight) of yellow gold chloride. Transfer the mixture to a test tube and make it gel by adding an equal volume of 1.5M sulfuric acid. Gelling takes a week or so. Fill the space above the gel with a solution made by dissolving as much oxalic acid as possible in water, creating a saturated solution. Within a matter of days thousands of minute, sparkling crystals of gold will form in the gel.

If all has gone well, Liesegang bands will appear after the gel has been exposed to sunlight.

Salts React in a Gel to Make the Colorful Liesegang Bands – C. L. Stong – 1969
http://jesseenterprises.net/amsci/1969/06/1969-06-body.html

Herbert Freundlich, a specialist in colloidal chemistry, reports that gold crystals up to two millimeters in diameter have been grown in a gel containing sodium chloride and maintained at a temperature of 70 degrees centigrade.

He also states that the gold will deposit as a sheet at the interface between the gel and the oxalic acid, if the concentration of acid is low.

One other characteristic of gold reactions in gel merits special mention.

Colloidal gold forms only in the presence of ultraviolet light, whereas crystals of gold form in the dark.

Configurations of almost any desired shape can be grown in the colloidal region of the gel by exposing the preparation to sunlight through a mask. I once produced a fine grid pattern by exposing the test tube through window screening in the course of investigating the influence of light on the rate of reaction.

There appears to be no limit to the variety of reactions that may be undertaken in gel media. All can be entertaining, many are of academic interest and a few are of practical value.

There is much interest today, for example, in single crystals for electronic and ultrasonic applications. Only 3,000 different crystals that occur naturally have been described, but more than 12,000 others have been grown in the laboratory, mostly in aqueous solutions.

Growing Crystals in Silica Gel Mimics Natural Mineralization – C. L. Stong – 1962
http://jesseenterprises.net/amsci/1962/03/1962-03-fs.html

Secondly, there is evidence that suggests Liesegang Ring patterns can be regulated by an electric current so that information can be encoded into the precipitation pattern.

Material design at submicron scales would be profoundly affected if the formation of precipitation patterns could be easily controlled. It would allow the direct building of bulk structures, in contrast to traditional techniques which consist of removing material in order to create patterns.

Here, we discuss an extension of our recent proposal of using electrical currents to control precipitation bands which emerge in the wake of reaction fronts in A+ + B– → C reaction–diffusion processes.

Our main result, based on simulating the reaction–diffusion–precipitation equations, is that the dynamics of the charged agents can be guided by an appropriately designed time-dependent electric current so that, in addition to the control of the band spacing, the width of the precipitation bands can also be tuned.

This makes straightforward the encoding of information into precipitation patterns and, as an amusing example, we demonstrate the feasibility by showing how to encode a musical rhythm.

Liesegang Encoded Information

Encoding information into precipitation structures
Kirsten Martens, Ioana Bena, Michel Droz and Zoltan Rácz
Journal of Statistical Mechanics: Theory and Experiment – December 2008
http://iopscience.iop.org/1742-5468/2008/12/P12003;

Consequently, it seems highly likely that a combination of “effects” [or varying combination of “effects”] drive the Liesegang Phenomena.

However, it is unlikely that mainstream science will make much real progress with the Liesegang Phenomena because:
a) Very few mainstream scientists strictly follow the Scientific Method.
b) Post-normal science thrives by exploiting “gravy trains” that aren’t going anywhere.
c) Post-normal science has a preference for computer models.
d) Funding is usually a scarce commodity when it comes to investigating electromagnetic effects.
e) Investigating [heretical] electromagnetic effects can seriously damage your career.

Thus, science is in a very curious situation because the Liesegang Phenomena is only defined by the laboratory observations that are arbitrarily associated with the Liesegang Phenomena.

Beyond some artificial experiments Liesegang patterns can appear in nature in very different systems (bones, teeth, agate rocks, tumors, bacterial colonies, alloys etc.)

Therefore as a mineralogist stated somewhere during the 20th century anything that had a stripy pattern hardly avoided to be affiliated with Liesegang rings …

The greatest problem with the existing models of periodic precipitation was that although they use sometimes completely different approaches they are all partially successful.

From this naturally arises the question: who can decide which theory is correct, and how?

Effects, Anomalies and Natural Occurences of Liesegang Patterns – András Büki
http://www.insilico.hu/liesegang/effects/effects.html

Therefore, attributing any “real world” observation to the Liesegang Phenomena is equally arbitrary because there is no firm science that defines the Liesegang Phenomena.

The next post will examine the entertainment biologists have enjoyed exploiting this confusion [aka post-normal gravy train] regarding the Liesegang Phenomena.

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2 Responses to Liesegang Rings: 3 – Theory and Practice

  1. Pingback: As Above So Below – Georgi Gladyshev | MalagaBay

  2. Pingback: Liesegang Cavities: 1 – Hollow Rocks | MalagaBay

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