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Ostwald ripening is a phenomenon observed in solid solutions or liquid 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. 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. For
colloid A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
al systems, Ostwald ripening is also found in water-in-oil
emulsion An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloids. Alth ...
s, while
flocculation Flocculation, in the field of chemistry, is a process by which colloidal particles come out of suspension to sediment under the form of floc or flake, either spontaneously or due to the addition of a clarifying agent. The action differs from ...
is found in oil-in-water emulsions.


Mechanism

This thermodynamically-driven spontaneous process occurs because larger particles are more energetically favored than smaller particles. This stems from the fact that molecules on the surface of a particle are energetically less stable than the ones in the interior. Consider a cubic crystal of atoms: all the atoms inside are bonded to 6 neighbours 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 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 and diffuse into the solution. Kelvin's equation describes the relationship between the radius of curvature and the chemical potential between the surface and the inner volume: :\Delta \mu = \frac where \mu corresponds to the
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a speci ...
, \sigma to the
surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) t ...
, \nu_ to the atomic volume and r to the radius of the particle. The chemical potential of an ideal solution can also be expressed as a function of the solute’s concentration if liquid and solid phases are in equilibrium. :\mu = K_B T ln(C_) where K_B corresponds to the
Boltzmann Constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
, T to the temperature and C_ to the solute concentration in a solution in which the solid and the liquid phase are in equilibrium. Combining both expressions the following equation is obtained: :K_B T ln\left(\frac \right) = \frac \rightarrow C_(r) = C_(\infty) e^ Thus, the equilibrium concentration, C_, is lower around bigger particles than it is around smaller particles. :C_(r) > C_ (R) where r and R are the particles radius, and r < R. Inferring from Fick’s first law of diffusion, the particles will move from big concentrations, corresponding to areas surrounding small particles, to small concentrations, corresponding to areas surrounding large nanoparticles. Thus, the small particles will tend to shrink while the big particles will grow. As a result, the average size of the nanoparticles in the solution will grow, and the dispersion of sizes will decrease. Therefore, if a solution is left for a long time, in the extreme case of t \rightarrow \infty, its particles would evolve until they would finally form a single huge spherical particle to minimize the total surface area. The history of research progress in quantitatively modeling Ostwald ripening is long, with many derivations. In 1958, Lifshitz and Slyozov performed a mathematical investigation of Ostwald ripening in the case where
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
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: :\langle R \rangle ^3 - \langle R \rangle _0 ^3 = \frac t where Note that the quantity is different from , and only the latter one can be used to calculate average volume, and that the statement that ⟨R⟩ goes as relies on being zero; but because
nucleation In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that deter ...
is a separate process from growth, this places outside the bounds of validity of the equation. In contexts where the actual value of is irrelevant, an approach that respects the meanings of all terms is to take the time derivative of the equation to eliminate and . Another such approach is to change the to with the initial time having a positive value. Also contained in the Lifshitz and Slyozov derivation is an equation for the size distribution function of particles. For convenience, the radius of particles is divided by the average radius to form a new variable, ρ = . : f(R,t) = \frac \rho^2 \left(\frac \right)^\frac \left(\frac \right)^\frac \exp \left(- \frac \right), \rho < 1.5 Three years after that Lifshitz and Slyozov published their findings (in Russian, 1958),
Carl Wagner Carl Wilhelm Wagner (May 25, 1901 – December 10, 1977) was a German Physical chemist. He is best known for his pioneering work on Solid-state chemistry, where his work on oxidation rate theory, counter diffusion of ions and defect chemistry ...
performed his own mathematical investigation of Ostwald ripening, examining both systems where
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
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 The Iron Curtain was the political boundary dividing Europe into two separate areas from the end of World War II in 1945 until the end of the Cold War in 1991. The term symbolizes the efforts by the Soviet Union (USSR) to block itself and its ...
in 1961. It was not until 1975 that Kahlweit addressed the fact that the theories were identical 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 Spinodal decomposition is a mechanism by which a single thermodynamic phase spontaneously separates into two phases (without nucleation). Decomposition occurs when there is no thermodynamic barrier to phase separation. As a result, phase separation ...
have been shown to
quantitatively Quantitative research is a research strategy that focuses on quantifying the collection and analysis of data. It is formed from a deductive approach where emphasis is placed on the testing of theory, shaped by empiricist and positivist philosop ...
obey LSW theory after initial stages of growth. Wagner derived that when attachment and detachment of molecules is slower than diffusion, then the growth rate becomes : \langle R \rangle ^2 = \frac t where is the
reaction rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction. For a reaction between reactants A and B to form product C the reaction rate is often found to have the ...
of attachment with 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. 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. In this case, Ostwald ripening causes the
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
of
monomer In chemistry, a monomer ( ; '' mono-'', "one" + '' -mer'', "part") is a molecule that can react together with other monomer molecules to form a larger polymer chain or three-dimensional network in a process called polymerization. Classification ...
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).


Specific examples

One example of Ostwald ripening is the re-crystallization of water within
ice cream Ice cream is a sweetened frozen food typically eaten as a snack or dessert. It may be made from milk or cream and is flavoured with a sweetener, either sugar or an alternative, and a spice, such as cocoa or vanilla, or with fruit such as ...
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. Another gastronomical example is the ouzo effect, where the droplets in the cloudy microemulsion grow by Ostwald ripening. In
geology Geology () is a branch of natural science concerned with Earth and other Astronomical object, astronomical objects, the features or rock (geology), rocks of which it is composed, and the processes by which they change over time. Modern geology ...
, it is the textural coarsening, aging or growth of phenocrysts and crystals in solid rock which is below the solidus temperature. It is often ascribed as a process in the formation of
orthoclase Orthoclase, or orthoclase feldspar ( endmember formula K Al Si3 O8), is an important tectosilicate mineral which forms igneous rock. The name is from the Ancient Greek for "straight fracture," because its two cleavage planes are at right angles ...
megacrysts, as an alternative to the physical processes governing crystal growth from
nucleation In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that deter ...
and growth rate
thermochemical Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or phase changes such as melting and boiling. A reaction may release or absorb energy, and a phase change may do the same. Thermochemistry focuses on ...
limitations. In
aqueous solution An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be r ...
chemistry and precipitates ageing, 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 (''nuclei'') slowly disappear, except for a few that grow larger, at the expense of the small crystals (''crystal growth''). 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 Quantum dots (QDs) are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology. When the ...
s. Ostwald ripening is also the key process in the
digestion Digestion is the breakdown of large insoluble food molecules into small water-soluble food molecules so that they can be absorbed into the watery blood plasma. In certain organisms, these smaller substances are absorbed through the small intest ...
and aging of precipitates, an important step in gravimetric analysis. The digested precipitate is generally purer, and easier to wash and filter. Ostwald ripening can also occur in
emulsion An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloids. Alth ...
systems, with molecules diffusing from small droplets to large ones through the continuous phase. When a miniemulsion is desired, an extremely
hydrophobic In chemistry, hydrophobicity is the physical property of a molecule that is seemingly repelled from a mass of water (known as a hydrophobe). In contrast, hydrophiles are attracted to water. Hydrophobic molecules tend to be nonpolar and, ...
compound is added to stop this process from taking place. Diffusional growth of larger drops in liquid water
cloud In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, frozen crystals, or other particles suspended in the atmosphere of a planetary body or similar space. Water or various other chemicals may ...
s in the atmosphere at the expense of smaller drops is also characterized as Ostwald Ripening.


See also

* Aggregation *
Coalescence (chemistry) In chemistry, coalescence is a process in which two phase domains of the same composition come together and form a larger phase domain. In other words, the process by which two or more separate masses of miscible substances seem to "pull" each ...
*
Coalescence (physics) Coalescence is the process by which two or more droplets, bubbles or particles merge during contact to form a single daughter droplet, bubble or particle. It can take place in many processes, ranging from meteorology to astrophysics. For example ...
* Critical radius *
Flocculation Flocculation, in the field of chemistry, is a process by which colloidal particles come out of suspension to sediment under the form of floc or flake, either spontaneously or due to the addition of a clarifying agent. The action differs from ...
*
Kelvin equation The Kelvin equation describes the change in vapour pressure due to a curved liquid–vapor interface, such as the surface of a droplet. The vapor pressure at a convex curved surface is higher than that at a flat surface. The Kelvin equation is de ...
* Kirkendall effect * Rock microstructure * *
Nucleation In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that deter ...
* Crystal growth * Viedma ripening


References


External links


Ostwald Ripening
a 3D Kinetic Monte Carlo simulation {{DEFAULTSORT:Ostwald Ripening Physical chemistry Chemical engineering thermodynamics Colloidal chemistry Crystallographic defects Precipitation