Editing Supersaturation (section)

== History ==
[[File:Na2SO4 solubility.svg|thumb|upright=1.3|Solubility of Na<sub>2</sub>SO<sub>4</sub> in water as a function of temperature.]]
Early studies of the phenomenon were conducted with [[sodium sulfate]], also known as Glauber's Salt because, unusually, the solubility of this salt in water may decrease with increasing temperature. Early studies have been summarised by Tomlinson.<ref>{{Cite journal|title = On Supersaturated Saline Solutions|journal = Philosophical Transactions of the Royal Society of London|date = 1868-01-01|issn = 0261-0523|pages = 659–673|volume = 158|doi = 10.1098/rstl.1868.0028|first = Charles|last = Tomlinson|s2cid = 110079029}}</ref> It was shown that the crystallization of a supersaturated solution does not simply come from its agitation, (the previous belief) but from solid matter entering and acting as a "starting" site for crystals to form, now called "seeds" (for more information, see [[nucleation]]). Expanding upon this, [[Joseph Louis Gay-Lussac|Gay-Lussac]] brought attention to the [[kinematics]] of salt ions and the characteristics of the container having an impact on the supersaturation state. He was also able to expand upon the number of salts with which a supersaturated solution can be obtained. Later Henri Löwel came to the conclusion that both nuclei of the solution and the walls of the container have a catalyzing effect on the solution that cause crystallization. Explaining and providing a model for this phenomenon has been a task taken on by more recent research. Désiré Gernez contributed to this research by discovering that nuclei must be of the same salt that is being crystallized in order to promote crystallization.

[[File:LaMer diagram.png|thumb|Time evolution of the concentration of a solute in a solution when it receives a constant inflow of the solute, according to the LaMer model.]]
Furthermore, in 1950, [[Victor LaMer|Victor K. LaMer]] proposed another theory for [[nucleation]],<ref>{{Cite journal|title = Theory, Production and Mechanism of Formation of Monodispersed Hydrosols|journal = Journal of the American Chemical Society|date = 1950-11-01|volume = 72|issue=11|pages = 4847–4854|doi = 10.1021/ja01167a001|first1 = Victor|last1 = K. LaMer|first2 = Robert|last2 = H. Dinegar|s2cid = 98025629}}</ref> in which he described the nucleation and growth of [[sulfur]] nuclei in a solution where a [[chemical reaction]] provided a constant inflow of molecularly dissolved sulfur. This theory, however, is not confined to this specific case and can be generalised as shown in LaMer’s diagram,<ref>{{Cite journal|title = LaMer diagram approach to study the nucleation and growth of Cu2O nanoparticles using supersaturation theory|journal = Korean Journal of Chemical Engineering|date = 2014-07-31|volume = 31|issue=11|pages = 2020–2026|doi = 10.1007/s11814-014-0130-3|first1 = S.|last1 = Arshadi|first2 = J. |last2 = Moghaddam|first3 = M.|last3 = Eskandarian|s2cid = 97983025|issn = 1975-7220}}</ref><ref>{{Cite journal|title = Spontaneous nucleation of monodisperse silver halide particles from homogeneous gelatin solution I: silver chloride|journal = Colloids and Surfaces A: Physicochemical and Engineering Aspects|date = 2000-05-15|volume = 164|issue=2-3|pages = 183-203|doi = 10.1016/S0927-7757(99)00365-9|first1 = T.|last1 = Sugimoto|first2 = F. |last2 = Shiba|first3 = T.|last3 = Sekiguchi|first4 = H.|last4 = Itoh|s2cid = 96100186}}</ref><ref>{{Cite journal|title = Underlying mechanisms in size control of uniform nanoparticles|journal = Journal of Colloid and Interface Science|date = 2007-05-01|volume = 309|issue=1|pages = 106-118|doi = 10.1016/J.JCIS.2007.01.036|first1 = T.|last1 = Sugimoto|s2cid = 43843460}}</ref> provided in the second figure of this section.

[[File:Phase diagram of a solution.png|thumb|Dependance of equilibrium (saturation) concentration of a solute with temperature. The leftmost function represents the equilibrium between an undersaturated solution and a supersaturated solution, while the rightmost function represents the equilibrium between a supersaturated solution and a solid (where the solute has fully crystallised). At a constant temperature, solute is added to the solution, so that its concentration evolves following the arrows. The solution will become saturated upon reaching <math> c_L^{eq} \,\!</math>, and will fully crystallise upon reaching <math> c_S^{eq} \,\!</math>.]]

In section (I), the concentration of solute grows linearly, as it is formed (or added) to the solution. Upon reaching <math> c_L^{eq} \,\!</math>, it will become saturated, but it won’t start depositing solute right away. Instead, it will keep absorbing it, becoming supersaturated. 

In section (II), concentration reaches critical saturation levels, <math> c_{min} \,\!</math>, when solute crystals begin nucleating. The appearance of nuclei partially relieves the supersaturation, at least rapidly enough that the rate of nucleation falls almost immediately to zero. The system rapidly reaches a balance between the solute supply and the consumption rate for the nucleation and its growth, slowing down the increase in its concentration. After reaching the peak, the curve declines owing to the increasing consumption of the solute for the growth of nuclei and reaches again the critical level of nucleation, <math> c_{min} \,\!</math>, ending the nucleation stage. Given optimal conditions, having the solute be introduced to the solution very steadily while keeping the system free from perturbations and nucleation seeds, the maximum concentration that can be achieved in this way is defined as <math> c_{max} \,\!</math>. 

In section (III), the supersaturation becomes too low for any more crystals to nucleate, so no new crystals are formed. However, as the solution is still supersaturated, the existing crystals grow by solute [[diffusion]]. As time passes by, the growth rate of the crystal equals the rate of solute supply, so the concentration converges to the saturation value <math> c_L^{eq} \,\!</math>.