On dynamic self-organization: examples from magmatic and other geochemical systems

Abstract

Standard Liesegang banding is the display of parallel bands of precipitate formed periodically when co-precipitate ions interdiffuse in a gel medium. The most striking resemblance with Liesegang patterns in Nature lies in the diverse scenery of banded textural features commonly observed in some geological materials, such as geodes, agates, malachites, as well as stratigraphic units of certain rock formations. Here, we explore the possible relationship between the Liesegang banding scenario and magmatic-type pattern formation, such as zonations in km-scale circular zoned plutons and anorogenic ring complexes, cyclic layering in large mafic-ultramafic layered intrusions and orbicular granites, as well as in mm-scale crystal zonations. We also investigate magmatic processes such as fractional crystallization, and the ranges of T and p that are compatible with operating conditions for Liesegang banding. For geochemical selforganization to operate via a Liesegang-type mechanism, a necessary condition is that the system be transiently out of equilibrium, and be described by complex nonlinear kinetic laws. We examine the viability of the development of geochemical patterns, in relation with the various requirements for the growth of Liesegang structures. Keywords Liesegang, precipitate patterns, geochemical self-organization, magmatic ring complexes, layered intrusions.On dynamic self-organization: examples from magmatic and other geochemical systems INTRODUCTIONOne of the fascinating and visually most attractive phenomena, widely studied and documented in the physical chemistry literature, is that of periodic precipitation commonly known as Liesegang banding [1][2][3]. Liesegang bands of precipitate appear when a solution of a specific ion (say Cr 2 O 7 2 ) diffuses in a tubular gel medium containing its co-precipitate ion (such as Ag + ). The sparingly soluble Ag 2 Cr 2 O 7 precipitate forms a set of discotic strata perpendicular to the tube axis. A panorama of banded Liesegang patterns for different precipitate systems is displayed in Fig. 1. The mechanism of the Liesegang banding phenomenon is not one of universal character. Most scientists believe that the first band forms away from the first precipitation region, delayed by diffusion over a zone initially depleted in the diffusing ion, until the concentration product builds up and exceeds the supersaturation and nucleation thresholds. Then this cycle is repeated, and hence causes the formation of the next bands periodically, in a concerted scenario known as the supersaturation-nucleation-depletion cycle, first elucidated by Wilhelm Ostwald [4]. Another group of scientists believe that bands emerge from the break-up of a pre-formed uniform colloidal sol, due to a competitive particle growth mechanism mediated by the surface tensions of the various colloid particles having a broad distribution of sizes [5][6][7]. Due to larger surface tension, the small particles dissolve and the newly-formed aqueous species diffuse, driven by the concentration gradient t...

Chemical Tracking of Temperature by Concurrent Periodic Precipitation Pattern Formation in Polyacrylamide Gels

“…LPs can form in various porous media. 25 − 28 Our choice was PAm hydrogel since this is a covalently cross-linked hydrogel with a glass transition temperature above 190 °C. 29 This gel provides a homogeneous medium for the formation of CuCrO 4 patterns, as we have reported before.…”

Self-organization in precipitation reactions far from the equilibrium

“…Other structures that emerge at different reaction conditions include helicoidal precipitates, fractal patterns, and regular crystals ( 123 – 126 ). Because of the simplicity of the underlying chemical principles, Liesegang patterns have been observed for a broad range of systems involving metals (such as Ag + , Pb 2+ , Fe 2+ , Zn 2+ , Ca 2+ , and Mg 2+ ) and their precipitate counter-anions (I − , F − , S 2− , OH − , CrO 4 2− , Cr 2 O 7 2− , and SO 4 2− ), even extending beyond the laboratory to geochemical and mineralogical environments ( 127 , 128 ).…”

Complex Patterning of Matter with Liesegang Patterns Propagating through Different Concentration Media─Gel Lenses for Liesegang Waves

“…Despite the development of material manufacturing at all levels, biomimetic artificial chemical systems are far from reaching the complexity of natural systems. , One platform that displays this natural complexity is macroscopic material patterns in nature. These patterns can be found in numerous places, on rocks and animal skins, in tree trunks and beehives, and in bacteria colonies. , The beautiful natural self-assembled patterns are complex because of the variety of environmental conditions under which they develop. In addition, these conditions may concurrently change during pattern formation.…”

“…These patterns can be found in numerous places, on rocks and animal skins, in tree trunks and beehives, and in bacteria colonies. 4,5 The beautiful natural self-assembled patterns are complex because of the variety of environmental conditions under which they develop. In addition, these conditions may concurrently change during pattern formation.…”