Pattern Formation in Precipitation Reactions: the Liesegang Phenomenon.

Pattern formation is a frequent phenomenon in physics, chemistry, biology and material science. Bottom-up pattern formation occurs usually in the interaction of the transport phenomena of chemical species with their chemical reaction. The oldest pattern formation is the Liesegang phenomenon (or periodic precipitation), which was discovered and described by Raphael Edward Liesegang in 1896, who was a German chemist and photographer, and he was born 150 years ago. The purpose of this review is to provide a comprehensive overview of this type of pattern formation. Liesegang banding occurs due to the coupling of the diffusion process of the reagents to their chemical reactions in solid hydrogels. We will discuss several phenomena observed and discovered in the past century including reverse patterns, precipitation patterns with dissolution (due to complex formation), helicoidal patterns, and precipitation waves. Additionally, we will review all existing models of the Liesegang phenomenon including pre- and post-nucleation scenarios. Finally, we will highlight several applications of periodic precipitation.

[1]  B. Baytekin,et al.  Mechanical Control of Periodic Precipitation in Stretchable Gels to Retrieve Information on Elastic Deformation and for the Complex Patterning of Matter , 2020, Advanced materials.

[2]  Mohamad Hmadeh,et al.  Liesegang Banding for Controlled Size and Growth of Zeolitic-Imidazolate Frameworks. , 2019, Small.

[3]  Min N. Wu,et al.  Preparation of isometric Liesegang patterns and application in multi-pulsed drug release system , 2019, Journal of Sol-Gel Science and Technology.

[4]  G. Holló,et al.  Existence of a Precipitation Threshold in the Electrostatic Precipitation of Oppositely Charged Nanoparticles. , 2018, Angewandte Chemie.

[5]  H. Nabika,et al.  Role of Electrolyte in Liesegang Pattern Formation. , 2018, Langmuir : the ACS journal of surfaces and colloids.

[6]  R. Sultan,et al.  Revisited Chaos in a Diffusion-Precipitation-Redissolution Liesegang System. , 2018, The journal of physical chemistry. A.

[7]  H. Nabika,et al.  Role of Nuclei in Liesegang Pattern Formation: Insights from Experiment and Reaction-Diffusion Simulation , 2018 .

[8]  Houssam El-Rassy,et al.  Liesegang Bands versus Random Crystallites in Ag 2 Cr 2 O 7 - Single and Mixed Gelled Media , 2018 .

[9]  Mohamad Hmadeh,et al.  Crystal Growth of ZIF-8, ZIF-67, and Their Mixed-Metal Derivatives. , 2018, Journal of the American Chemical Society.

[10]  M. José-Yacamán,et al.  Surface-Enhanced Raman Spectroscopy of Acetil-neuraminic Acid on Silver Nanoparticles: Role of the Passivating Agent on the Adsorption Efficiency and Amplification of the Raman Signal , 2017 .

[11]  O. Steinbock,et al.  Self-organization in precipitation reactions far from the equilibrium , 2016, Science Advances.

[12]  T. Ban,et al.  Propagation Properties of the Precipitation Band in an AlCl₃/NaOH System. , 2016, Langmuir : the ACS journal of surfaces and colloids.

[13]  K. Showalter,et al.  Three-dimensional modeling of propagating precipitation waves. , 2015, Chaos.

[14]  Z. Rácz,et al.  Growth of nanoparticles and microparticles by controlled reaction-diffusion processes. , 2015, Langmuir : the ACS journal of surfaces and colloids.

[15]  I. Lagzi,et al.  Chemical waves in heterogeneous media. , 2014, The journal of physical chemistry. A.

[16]  Yu-lu Chen,et al.  Three dimension Liesegang rings of calcium hydrophosphate in gelatin , 2014, Journal of Sol-Gel Science and Technology.

[17]  M. Al-Ghoul,et al.  Superdiffusive cusp-like waves in the mercuric iodide precipitate system and their transition to regular reaction bands. , 2014, The journal of physical chemistry. A.

[18]  H. Nabika,et al.  Liesegang patterns engineered by a chemical reaction assisted by complex formation. , 2014, Langmuir : the ACS journal of surfaces and colloids.

[19]  Leen Kalash,et al.  Dynamical profiles of the reactive components in direct and revert Liesegang patterns , 2013 .

[20]  K. Showalter,et al.  Propagating precipitation waves: experiments and modeling. , 2013, The journal of physical chemistry. A.

[21]  Z. Rácz,et al.  Matalon–Packter law for stretched helicoids formed in precipitation processes , 2013 .

[22]  I. Lagzi.  Controlling and engineering precipitation patterns. , 2012, Langmuir : the ACS journal of surfaces and colloids.

[23]  Nor Azowa Ibrahim,et al.  Synthesis of Silver Nanoparticles in Chitosan, Gelatin and Chitosan/Gelatin Bionanocomposites by a Chemical Reducing Agent and Their Characterization , 2011, Molecules.

[24]  Tony E. Karam,et al.  Mechanism of revert spacing in a PbCrO4 Liesegang system. , 2011, The journal of physical chemistry. A.

[25]  K. Nealson,et al.  Organic influences on inorganic patterns of diffusion-controlled precipitation in gels , 2010 .

[26]  Bartosz A Grzybowski,et al.  Liesegang rings engineered from charged nanoparticles. , 2010, Journal of the American Chemical Society.

[27]  H. Varma,et al.  Self-assembled right handed helical ribbons of the bone mineral hydroxyapatite , 2009, Journal of materials science. Materials in medicine.

[28]  I. Epstein,et al.  Precipitation patterns with polygonal boundaries between electrolytes. , 2009, Physical chemistry chemical physics : PCCP.

[29]  R. Sultan,et al.  Ring morphology and pH effects in 2D and 1D Co(OH)2 Liesegang systems. , 2009, The journal of physical chemistry. A.

[30]  Daishin Ueyama,et al.  Pattern transition between periodic Liesegang pattern and crystal growth regime in reaction-diffusion systems , 2009 .

[31]  F. Molnár,et al.  Design of equidistant and revert type precipitation patterns in reaction-diffusion systems. , 2008, Physical chemistry chemical physics : PCCP.

[32]  Ferenc Izsák,et al.  Pattern formation and self-organization in a simple precipitation system. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[33]  F. Izsák,et al.  Systematic front distortion and presence of consecutive fronts in a precipitation system. , 2006, The journal of physical chemistry. B.

[34]  B. Grzybowski,et al.  Nano- and microscopic surface wrinkles of linearly increasing heights prepared by periodic precipitation. , 2005, Journal of the American Chemical Society.

[35]  F. Izsák,et al.  Regular Liesegang patterns and precipitation waves in an open system. , 2005, Physical chemistry chemical physics : PCCP.

[36]  Yong Ding,et al.  Conversion of Zinc Oxide Nanobelts into Superlattice-Structured Nanohelices , 2005, Science.

[37]  S. Horvát,et al.  Pattern formation induced by ion-selective surfaces: models and simulations. , 2005, The Journal of chemical physics.

[38]  M. Fiałkowski,et al.  Self-organization of planar microlenses by periodic precipitation , 2005 .

[39]  F. Izsák,et al.  Simulation of a crossover from the precipitation wave to moving Liesegang pattern formation. , 2005, The journal of physical chemistry. A.

[40]  J. Partridge,et al.  Ion-Selective Membranes Involved in Pattern-Forming Processes , 2004 .

[41]  Bartosz A. Grzybowski,et al.  Multicolour micropatterning of thin films of dry gels , 2004, Nature materials.

[42]  I. Lagzi,et al.  Effect of geometry on the time law of Liesegang patterning , 2004 .

[43]  M. Fiałkowski,et al.  Arrays of microlenses of complex shapes prepared by reaction-diffusion in thin films of ionically doped gels , 2004 .

[44]  Zeina Shreif,et al.  Taming ring morphology in 2D Co(OH)2 Liesegang patterns , 2004 .

[45]  Stefan C. Müller,et al.  Spatial Structure Formation in Precipitation Reactions , 2003 .

[46]  R. Sultan,et al.  Front Propagation in Patterned Precipitation. 2. Electric Effects in Precipitation−Dissolution Patterning Schemes , 2003 .

[47]  C. Rodriguez-Navarro,et al.  Liesegang pattern development in carbonating traditional lime mortars , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[48]  István Lagzi,et al.  Formation of Liesegang patterns in an electric field , 2002 .

[49]  R. Sultan,et al.  Front Propagation in Patterned Precipitation. 1. Simulation of a Migrating Co(OH)2 Liesegang Pattern , 2001 .

[50]  H. Hillhouse,et al.  Spontaneous Formation of Inorganic Helical Fibers and Rings , 2000 .

[51]  H. Krug,et al.  Morphological characteristics of Liesegang rings and their simulations , 1999 .

[52]  R. Sultan,et al.  Propagating Fronts and Chaotic Dynamics in Co(OH)2 Liesegang Systems , 1999 .

[53]  M. Droz,et al.  Liesegang patterns: studies on the width law , 1999, cond-mat/9901079.

[54]  T. Antal,et al.  Derivation of the Matalon-Packter law for Liesegang patterns , 1998, cond-mat/9807251.

[55]  R. Sultan,et al.  Patterning Trends and Chaotic Behavior in Co2+/NH4OH Liesegang Systems , 1996 .

[56]  M. Zrínyi,et al.  Computer simulation of regular Liesegang structures , 1995 .

[57]  A. Arkin,et al.  Experimental Evidence for Turing Structures , 1995 .

[58]  A. Polezhaev,et al.  Complexity of precipitation patterns: Comparison of simulation with experiment. , 1994, Chaos.

[59]  H. Henisch.  Crystals in Gels and Liesegang Rings: History and nature of the gel method , 1988 .

[60]  I. Das,et al.  Light Induced Periodic Precipitation and Chemical Instability in Lead Chromate Systems , 1988 .

[61]  J. Ross,et al.  Measurements and a hypothesis on periodic precipitation processes , 1987 .

[62]  A. Boudreau.  Pattern Formation During Crystallization and the Formation of Fine-Scale Layering , 1987 .

[63]  I. Das,et al.  Mechanism of periodic precipitation in an illuminated lead chromate system , 1987 .

[64]  D. Smith,et al.  On Ostwald’s supersaturation theory of rhythmic precipitation (Liesegang’s rings) , 1984 .

[65]  P. Ramasamy,et al.  Revert and direct Liesegang phenomenon of silver iodide: Factors influencing the transition point , 1983 .

[66]  J. Ross,et al.  Periodic precipitation patterns in the presence of concentration gradients. 2. Spatial bifurcation of precipitation bands and stochastic pattern formation , 1983 .

[67]  P. Ortoleva,et al.  Periodic precipitation and coarsening waves: Applications of the competitive particle growth modela) , 1983 .

[68]  J. Ross,et al.  Mesoscopic structure of pattern formation in initially uniform colloids , 1982 .

[69]  J. Ross,et al.  Periodic precipitation patterns in the presence of concentration gradients. 1. Dependence on ion product and concentration difference , 1982 .

[70]  J. Ross,et al.  Curiosities in Periodic Precipitation Patterns , 1982, Science.

[71]  P. Ortoleva,et al.  Spontaneous pattern formation in precipitating systems , 1978 .

[72]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

[73]  W. Carmody.  Variation of the solubility product constant with ionic strength , 1959 .

[74]  J. Hirschfelder,et al.  Liesegang Ring Formation Arising from Diffusion of Ammonia and Hydrogen Chlorine Gases through Air , 1951 .

[75]  S. C. BRADFORD,et al.  The Liesegang Phenomenon and Concretionary Structure in Rocks , 1916, Nature.

[76]  H. W. Morse,et al.  Diffusion und Übersättigung in Gelatine , 1903 .

[77]  R. Lorenz.  Lehrbuch der allgemeinen Chemie, von W. OSTWALD. II. Band. 2. Teil: Verwandtschaftslehre. 1. Lieferung. (Leipzig, 1896.) 5 Mark , 1897 .