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| [[File:Ostwaldpic.png|right|thumb|300px|Basic schematic of the Ostwald ripening process]] '''Ostwald ripening''' is an observed phenomenon in solid solutions or liquid [[sol (colloid)|sols]] that describes the change of an inhomogeneous structure over time, i.e., small crystals or sol particles dissolve, and redeposit onto larger crystals or sol particles.<ref>{{GoldBookRef | title = Ostwald ripening | file = O04348}}</ref>
| | Hi there, I am Andrew Berryhill. To play lacross is one of the things she enjoys most. Distributing manufacturing has been his occupation for some time. Ohio is exactly where her home is.<br><br>My page; spirit messages; [http://help.ksu.edu.sa/node/65129 http://help.ksu.edu.sa], |
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| Dissolution of small crystals or sol particles and the redeposition of the dissolved species on the surfaces of larger crystals or sol particles was first described by [[Wilhelm Ostwald]] in 1896.<ref>W. Ostwald. '''1896'''. ''Lehrbuch der Allgemeinen Chemie'', vol. 2, part 1. Leipzig, Germany.</ref><ref>See also: Ostwald, W. (1897) [http://books.google.com/books?id=WwhLAAAAYAAJ&pg=PA289#v=onepage&q&f=false "Studien über die Bildung und Umwandlung fester Körper"] (Studies on the formation and transformation of solid bodies), ''Zeitschrift für physikalische Chemie'', '''22''' : 289-330.</ref> Ostwald ripening is generally found in water-in-oil [[emulsion]]s, while [[flocculation]] is found in oil-in-water emulsions.<ref name="Hubbard 2004 4230">{{cite book
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| | last = Hubbard
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| | first = Arthur T.
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| | title = Encyclopedia of Surface and Colloid Science
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| | publisher = CRC Press
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| | year = 2004
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| | url = http://books.google.com/?id=vnb2X7Q8_cYC&pg=PA4230&lpg=PA4230&dq=ostwald+ripening+emulsion+polymerization
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| | accessdate = 2007-11-13
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| | isbn = 0-8247-0759-1
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| | page = 4230 }}</ref>
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| ==Mechanism==
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| This [[thermodynamics|thermodynamically]]-driven spontaneous process occurs because larger particles are more energetically favored than smaller particles.<ref name="GandC">{{cite book
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| | last = Ratke
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| | first = Lorenz
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| | coauthors = Voorhees, Peter W.
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| | title = Growth and Coarsening: Ostwald Ripening in Material Processing
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| | publisher = Springer
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| | year = 2002
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| | url = http://books.google.com/?id=baKRnEuSBXkC&dq=ostwald+ripening&printsec=frontcover
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| | accessdate = 2007-11-15
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| | pages = 117–118
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| | isbn = 3-540-42563-2 }}</ref> This stems from the fact that molecules on the surface of a particle are energetically less stable than the ones in the interior.[[File:Sodium-chloride-3D-ionic.png|thumb|Cubic crystal structure (sodium chloride)]]Consider a cubic crystal of atoms: all the atoms inside are bonded to 6 neighbors and are quite stable, but atoms on the surface are only bonded to 5 neighbors or fewer, which makes these surface atoms less stable. Large particles are more energetically favorable since, continuing with this example, more atoms are bonded to 6 neighbors and fewer atoms are at the unfavorable surface. As the [[Thermodynamic system|system]] tries to lower its overall energy, molecules on the surface of a small particle (energetically unfavorable, with only 3 or 4 or 5 bonded neighbors) will tend to detach from the particle, as per the [[Kelvin equation]], and diffuse into the solution. When all small particles do this, it increases the concentration of free molecules in solution. When the free molecules in solution are [[supersaturation|supersaturated]], the free molecules have a tendency to [[condensation|condense]] on the surface of larger particles.<ref name="GandC" /> Therefore, all smaller particles shrink, while larger particles grow, and overall the average size will increase. As time tends to infinity, the entire population of particles becomes one large spherical particle to minimize the total surface area.
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| In 1961, Lifshitz and Slyozov <ref>{{cite journal |author=I.M. Lifshitz, V.V. Slyozov |title=The Kinetics of Precipitation from Supersaturated Solid Solutions |journal=Journal of Physics and Chemistry of Solids |volume=19 |issue=1–2 |pages=35–50 |year=1961|bibcode = 1961JPCS...19...35L |doi = 10.1016/0022-3697(61)90054-3 }}</ref> performed a mathematical investigation of Ostwald ripening in the case where [[diffusion]] of material is the slowest process. They began by stating how a single particle grows in a solution. This equation describes where the boundary is between small, shrinking particles and large, growing particles. They finally conclude that the average radius of the particles ⟨R⟩, grows as follows:
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| :<math>\langle R \rangle ^3 - \langle R \rangle _0 ^3 = \frac {8 \gamma c_{\infty}v^2D} {9R_g T} t </math>
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| where
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| {|
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| |-
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| | align = "right" | <math> \langle R \rangle </math> || = || average radius of all the particles
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| |-
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| | align = "right" | <math> \gamma </math> || = || particle [[surface tension]] or [[surface energy]]
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| |-
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| | align = "right" | <math> c_{\infty} </math> || = || [[solubility]] of the particle material
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| |-
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| | align = "right" | <math> v </math> || = || [[molar volume]] of the particle material
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| |-
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| | align = "right" | <math> D </math> || = || [[mass diffusivity|diffusion coefficient]] of the particle material
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| |-
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| | align = "right" | <math> R_g </math> || = || [[gas constant|ideal gas constant]]
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| |-
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| | align = "right" | <math> T </math> || = || [[Thermodynamic temperature|absolute temperature]] and
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| |-
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| | align = "right" | <math> t </math> || = ||time.
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| |}
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| Note that the quantity {{math|⟨R⟩<sup>3</sup>}} is different from {{math|⟨R<sup>3</sup>⟩}}, and only the latter one can be used to calculate average volume, and that the statement that ⟨R⟩ goes as {{math|t<sup>1/3</sup>}} relies on {{math|⟨R⟩<sub>0</sub>}} being zero; but because [[nucleation]] is a separate process from growth, this places {{math|⟨R⟩<sub>0</sub>}} outside the bounds of validity of the equation. In contexts where the actual value of {{math|⟨R⟩<sub>0</sub>}} is irrelevant, an approach that respects the meanings of all terms is to take the time derivative of the equation to eliminate {{math|⟨R⟩<sub>0</sub>}} and {{math|t}}. Another such approach is to change the {{math|⟨R⟩<sub>0</sub>}} to {{math|⟨R⟩<sub>i</sub>}} with the initial time {{math|i}} having a positive value.
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| Also contained in the Lifshitz and Slyozov derivation is an equation for the size [[distribution function]] {{math|f(R, t)}} of particles. For convenience, the radius of particles is divided by the average radius to form a new variable, ρ = {{math|R(⟨R⟩)<sup>-1</sup>}}.
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| :<math> f(R,t) = \frac {4}{9} \left(\frac {3}{3+\rho}\right)^\frac {7}{3} \left(\frac {1.5} {1.5 - \rho}\right)^\frac {11}{3} \exp \left(- \frac {1.5}{1.5 - \rho}\right) \rho < 1.5 </math>
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| At the same time that Lifshitz and Slyozov published their findings, Carl Wagner performed his own mathematical investigation of Ostwald ripening,<ref>{{cite journal |author=C. Wagner |title= Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald-Reifung)|trans_title=Theory of the aging of precipitates by dissolution-reprecipitation (Ostwald ripening)|journal=Zeitschrift für Elektrochemie |volume=65 |issue=7 |pages=581–591 |year=1961}}</ref> examining both systems where [[diffusion]] was slow and also where attachment and detachment at the particle surface was slow. Although his calculations and approach were different, Wagner came to the same conclusions as Lifshitz and Slyozov for slow-diffusion systems. This duplicate derivation went unnoticed for years because the two scientific papers were published on opposite sides of the [[Iron Curtain]] in 1961.{{Citation needed|date=September 2011}} It was not until 1975 that Kahlweit addressed the fact that the theories were identical<ref>{{cite journal |author=M. Kahlweit |title = Ostwald Ripening of Precipitates | journal=Advances in Colloid and Interface Science |volume=5 |issue=1 |pages=1–35 |year=1975 |doi=10.1016/0001-8686(75)85001-9}}</ref> and combined them into the Lifshitz-Slyozov-Wagner or LSW Theory of Ostwald ripening. Many experiments and [[simulations]] have shown LSW theory to be robust and accurate. Even some systems that undergo [[spinodal decomposition]] have been shown to [[quantitatively]] obey LSW theory after initial stages of growth.<ref>{{cite journal |author=N. Vladimirova, A. Malagoli, R. Mauri |title=Diffusion-driven phase separation of deeply quenched mixtures |journal=Physical Review E |volume=58 |issue=6 |pages=7691–7699 |year=1998|bibcode = 1998PhRvE..58.7691V |doi = 10.1103/PhysRevE.58.7691 }}</ref>
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| Wagner derived that when attachment and detachment of molecules is slower than diffusion, then the growth rate becomes
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| :<math> \langle R \rangle ^2 = \frac {64 \gamma c_{\infty} v^2 k_s} {81 R_g T} t </math>
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| where {{math|k<sub>s</sub>}} is the [[reaction rate constant]] of attachment with [[Units of measurement|units]] of length per time. Since the average radius is usually something that can be measured in experiments, it is fairly easy to tell if a system is obeying the slow-diffusion equation or the slow-attachment equation. If the experimental data obeys neither equation, then it is likely that another mechanism is taking place and Ostwald ripening is not occurring. | |
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| Although LSW theory and Ostwald ripening were intended for solids ripening in a fluid, Ostwald ripening is also observed in liquid-liquid systems, for example, in an oil-in-water [[emulsion polymerization]].<ref name="Hubbard 2004 4230"/> In this case, Ostwald ripening causes the [[diffusion]] of [[monomer]]s (i.e. individual molecules or atoms) from smaller droplets to larger droplets due to greater solubility of the single monomer molecules in the larger monomer droplets. The rate of this diffusion process is linked to the solubility of the monomer in the continuous (water) phase of the emulsion. This can lead to the destabilization of emulsions (for example, by creaming and sedimentation).<ref>{{cite book
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| | last = Branen
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| | first = Alfred Larry
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| | title = Food Additives
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| | publisher = CRC Press
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| | year = 2002
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| | url = http://books.google.com/?id=K8urEPJvXNsC&pg=PA724&lpg=PA724&dq=ostwald+ripening+destabilization+emulsion
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| | accessdate = 2007-11-15
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| | isbn = 0-8247-9343-9
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| | page = 724 }}</ref>
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| ==Specific examples==
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| [[File:Pastis1.jpg|thumb|right|Oil droplets in pastis mixed with water grow by Ostwald ripening.]] | |
| An everyday example of Ostwald ripening is the re-crystallization of water within ice cream which gives old ice cream a gritty, crunchy texture. Larger ice crystals grow at the expense of smaller ones within the ice cream, creating a coarser texture.<ref>{{cite book
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| | last = Clark
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| | first = Chris
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| | title = The Science of Ice Cream
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| | publisher = Royal Society of Chemistry
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| | year = 2004
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| | pages = 78–79
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| | url = http://books.google.com/?id=bKZ1oICZWywC&pg=PA78&lpg=PA78&dq=ice+cream+ostwald
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| | accessdate = 2007-11-13
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| | isbn = 0-85404-629-1 }}</ref>
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| Another gastronomical example is in the [[ouzo effect]], where the droplets in the cloudy microemulsion grow by Ostwald ripening.
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| In [[geology]], it is the textural coarsening, aging or growth of [[phenocrysts]] and crystals in solid rock which is below the [[solidus (chemistry)|solidus]] temperature. It is often ascribed as a process in the formation of [[orthoclase]] [[megacryst]]s,<ref>{{cite journal |last= Mock |first= A. |year=2003 |title= Using Quantitative Textural Analysis to Understand the Emplacement of Shallow-Level Rhyolitic Laccoliths—a Case Study from the Halle Volcanic Complex, Germany|journal=Journal of Petrology |volume= 44|issue=5 |pages=Pp. 833–849 |id= |url=http://petrology.oxfordjournals.org/cgi/content/full/44/5/833 |accessdate= 2007-11-14 |quote= |doi= 10.1093/petrology/44.5.833 }}</ref> as an alternative to the physical processes governing crystal growth from [[nucleation]] and growth rate [[Thermochemistry|thermochemical]] limitations.
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| In chemistry, the term refers to the growth of larger crystals from those of smaller size which have a higher solubility than the larger ones. In the process, many small crystals formed initially slowly disappear, except for a few that grow larger, at the expense of the small crystals. The smaller crystals act as fuel for the growth of bigger crystals. Limiting Ostwald ripening is fundamental in modern technology for the solution synthesis of [[quantum dot]]s.<ref>{{cite journal |last=Vengrenovich |first=R.D. |date=December 2001 |title=Ostwald ripening of quantum-dot nanostructures |journal=Semiconductors |volume=35 |issue=12 |pages=pp.1378–1382 |doi=10.1134/1.1427975 |url=http://www.springerlink.com/content/814551gg47485391/ |accessdate= 2007-11-14 |last2=Gudyma |first2=Yu. V. |last3=Yarema |first3=S. V.|bibcode = 2001Semic..35.1378V }}</ref> Ostwald ripening is also the key process in the [[precipitation (chemistry)#Digestion|digestion]] of precipitates, an important step in [[gravimetric analysis]]. The digested precipitate is generally purer, and easier to wash and filter.
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| Ostwald ripening can also occur in [[emulsion]] systems, with molecules diffusing from small droplets to large ones through the continuous phase. When a [[miniemulsion]] is desired, an extremely [[hydrophobic]] compound is added to stop this process from taking place.{{Citation needed|date=April 2013}}
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| ==See also==
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| * [[Rock microstructure]]
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| * [[Kelvin equation]]
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| * [[Kirkendall effect]]
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| * [[Critical radius]]
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| * [[Solubility_equilibrium#Particle_size_effect]]
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| * [[Flocculation]]
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| * [[Particle aggregation|Aggregation]]
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| * [[Coalescence]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://www.roentzsch.org/OR/index.html Ostwald Ripening] a 3D Kinetic Monte Carlo simulation
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| {{Separation processes}}
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| {{DEFAULTSORT:Ostwald Ripening}}
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| [[Category:Geology]]
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| [[Category:Physical chemistry]]
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| [[Category:Chemical engineering]]
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| [[Category:Colloidal chemistry]]
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Hi there, I am Andrew Berryhill. To play lacross is one of the things she enjoys most. Distributing manufacturing has been his occupation for some time. Ohio is exactly where her home is.
My page; spirit messages; http://help.ksu.edu.sa,