A new model of periodic precipitation incorporating nucleation, growth and ripening

Chacron, Maurice J.; L’Heureux, Ivan

doi:10.1016/s0375-9601(99)00709-4

Cited by 42 publications

(50 citation statements)

References 25 publications

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“…While the front properties have been thoroughly studied and understood both theoretically [17,18] and experimentally [19,20], the dynamics of precipitation is more debated [13,18]. The competing pre-and post-nucleation views can be combined [18,21], and we shall use a simple version [14] based on the Cahn-Hilliard equation with noise added [22][23][24]. This equation features spinodal-decomposition-type fast dynamics, as well as slower, nucleation-and-growth processes [25].…”

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Probability of the Emergence of Helical Precipitation Patterns in the Wake of Reaction-Diffusion Fronts

et al. 2013

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Helical and helicoidal precipitation patterns emerging in the wake of reaction-diffusion fronts are studied. In our experiments, these chiral structures arise with well defined probabilities PH controlled by conditions such as e.g., the initial concentration of the reagents. We develop a model which describes the observed experimental trends. The results suggest that PH is determined by a delicate interplay among the time-and length-scales related to the front and to the unstable precipitation modes and, furthermore, the noise amplitude also plays a quantifiable role.PACS numbers: 68.35.Ct Helices and helicoids are present from nano-to macroscale (ZnO nanohelices [1], macromolecules and inorganic crystals with a helical structure [2, 3], precipitation helices [4][5][6], fiber geometry of heart walls [7]). Formation of these fascinating structures generally follows two routes. First, templates with chiral symmetry (e.g., oragogel fibers) may exist in the system, and the symmetry is just transcribed to a structure (e.g., inorganic materials [8]) at a larger scale. Second, spontaneous symmetry breaking may occur through the self-assembly of achiral building blocks into a helical/helicoidal structure, as e.g. in case of crystals with chiral morphology [2,9].Theoretically, the symmetry-breaking route is more interesting. Universal aspects may emerge and the robust features of this self-organization process may be important for applications as well. Indeed, control over creating helical structures would make engineering (in particular, the bottom-up design of micro-patterns [10]) more flexible since chiral morphology of materials are known to affect their physical (electronic) properties [6,11].In order to develop insight into the genesis of helices/helicoids, we investigate an emblematic example of pattern formation, namely the formation of precipitation patterns in the wake of reaction-diffusion fronts [12,13]. The motivation for this choice comes from the observation that helicoidal structures have an axis, and the correlations are simple in the plane perpendicular to the axis. This suggests that building the perpendicular correlations in the wake of an advancing planar front may be a simple and natural mechanism of creating helices/helicoids. Additional motivation comes from the existence of a large body of knowledge in the related Liesegang phenomena [12,13]. It allows the use of well-established experimental and theoretical approaches, thus making it easier to develop a novel view on the formation of helical structures.Our main results concern the probabilistic aspects of the symmetry-breaking route. We determine the probability P H of the emergence of single helices/helicoids in Liesegang-type experiments as the conditions such as the initial concentration of inner or outer electrolytes, or the temperature are changed. P H is found to be well reproducible and large (P H > 0.5 for some parameter range). The results are understood by expanding and simulating a model of formation of precipitation patterns [14]...

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Probability of the Emergence of Helical Precipitation Patterns in the Wake of Reaction-Diffusion Fronts

et al. 2013

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“…The count dynamics suggested that, after the second addition, initially some previously formed nuclei in channel 0-10 :m were able to grow into bigger nuclei or particles in channel 50-150 :m. This observed experimental phenomenon, that is, an increase larger crystals at the expense of smaller ones, could be well explained by the Ostwald ripening theory. 40 However, the newly formed nuclei at both channels were unable to survive in the system too long because some of them were dissolved afterwards. For the chords at channel 50-150 :m, the only plateau around 128 counts/ sec occurred between the second and the third additions.…”

Section: Exploratory Results For Real-time Fbrm Monitoring Of Nucleatmentioning

confidence: 99%

Quality-by-Design: An Integrated Process Analytical Technology Approach to Determine the Nucleation and Growth Mechanisms During a Dynamic Pharmaceutical Coprecipitation Process

Wu¹,

Khan²

2011

Journal of Pharmaceutical Sciences

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“…These models are consistent with the Jablczynski law, the Matalon-Packter law and the time scaling law. In particular, Dee's model [13] can be reformulated as a set of seven coupled nonlinear partial differential equations (one each for the concentration of species A, B, C and P plus the number density of crystallites, their average size and area) and has been found to be quite useful [14][15][16].…”

Section: Liesegang Patterns: General Considerationsmentioning

confidence: 99%

“…This characteristic pattern is due to the high flux of dissolved inter-band material that favours growth on both margins of the band, followed by intra-band ripening. Models that combine both pre-nucleation and post-nucleation mechanisms are also available [15,16,18].…”

Section: Liesegang Patterns: General Considerationsmentioning

confidence: 99%

Self-organized rhythmic patterns in geochemical systems

L’Heureux

2013

Phil. Trans. R. Soc. A.

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Chemical oscillating patterns are ubiquitous in geochemical systems. Although many such patterns result from systematic variations in the external environmental conditions, it is recognized that some patterns are due to intrinsic self-organized processes in a non-equilibrium nonlinear system with positive feedback. In rocks and minerals, periodic precipitation (Liesegang bands) and oscillatory zoning constitute good examples of patterns that can be explained using concepts from nonlinear dynamics. Generally, as the system parameters exceed some threshold values, the steady (time-independent) state characterizing the system loses its stability. The system then evolves towards other time-dependent solutions (‘attractors’) that may have an oscillatory behaviour or a complex chaotic one. In this review, we describe many of these pattern types taken from a variety of geological environments: eruptive, sedimentary, hydrothermal or metamorphic. One particular example (periodic precipitation of pyrite bands in an evolving sapropel sediment) is presented here for the first time. This will help in convincing the reader that the tools of nonlinear dynamics may be useful to understand the history of our planet.

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A new model of periodic precipitation incorporating nucleation, growth and ripening

Cited by 42 publications

References 25 publications

Probability of the Emergence of Helical Precipitation Patterns in the Wake of Reaction-Diffusion Fronts

Probability of the Emergence of Helical Precipitation Patterns in the Wake of Reaction-Diffusion Fronts

Quality-by-Design: An Integrated Process Analytical Technology Approach to Determine the Nucleation and Growth Mechanisms During a Dynamic Pharmaceutical Coprecipitation Process

Self-organized rhythmic patterns in geochemical systems

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