# Supersaturation

Supersaturation is a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances. It can also refer to a vapor of a compound that has a higher (partial) pressure than the vapor pressure of that compound.

## Preparation

Special conditions need to be met in order to generate a supersaturated solution. One of the easiest ways to do this relies on the temperature dependence of solubility. As a general rule, the more heat is added to a system, the more soluble a substance becomes. (There are exceptions where the opposite is true). Therefore, at high temperatures, more solute can be dissolved than at lower temperatures. If this solution were to be suddenly cooled at a rate faster than the rate of precipitation, the solution will become supersaturated until the solute precipitates to the temperature-determined saturation point. The precipitation or crystallization of the solute takes longer than the actual cooling time because the molecules need to meet up and form the precipitate without being knocked apart by the solvent. Thus, the larger the molecule, the longer the solute will take to crystallize due to the principles of Brownian motion.

The condition of supersaturation does not necessarily have to be reached through the manipulation of heat. The ideal gas law

${\displaystyle PV=nRT}$

suggests that pressure and volume can also be changed to force a system into a supersaturated state. If the volume of solvent is decreased, the concentration of the solute can be above the saturation point and thus create a supersaturated solution. The decrease in volume is most commonly generated through evaporation. Similarly, an increase in pressure can drive a solution to a supersaturated state. All three of these mechanisms rely on the fact that the conditions of the solution can be changed quicker than the solute can precipitate or crystallize out.

## Phase change (crystallization and condensation)

Supersaturated solutions will also undergo crystallization under specific conditions.[1][2] In a normal solution, once the maximum amount of solute is dissolved, adding more solute would either cause the dissolved solute to precipitate out and/or for the solute to not dissolve at all.[3] Similarly, there are cases wherein solubility of a saturated solution is decreased by manipulating temperature, pressure, or volume but a supersaturated state does not occur.[4] In these cases, the solute will simply precipitate out. This is because a supersaturated solution is in a higher energy state than a saturated solution.

A supersaturated solution of gases in a liquid may form bubbles if suitable nucleation sites exist. Supersaturation may be defined as a sum of all gas partial pressures in the liquid which exceeds the ambient pressure in the liquid.[5]

Crystallization will occur to allow the solution to reach a lower energy state.(Keep in mind that this process can be exothermic or endothermic). The activation energy comes in the form of a nuclei crystal being added to the liquid solution (or a condensation nuclei when the solution is gaseous). This nuclei can be either added from another source, which is known as seeding, or can spontaneously form within the solution due partly to ion and molecule interactions. This process is known as primary nucleation. It is necessary for the nuclei to be identical to the solute that is crystallizing.[6] This will allow for the dissolved ions to build up on the nuclei and then each other in the process of crystal growth or secondary nucleation.[7] There are a multitude of factors that will affect the rate and order of magnitude with which crystallization proceeds as well as the difference in formation of crystallites and single crystals.

A crystallization phase diagram shows where undersaturation, saturation, and supersaturation occur at certain concentrations. Concentrations below the solubility curve result in an undersaturation solution. Saturation occurs when the concentrations are on the solubility curve. If the concentrations are above the solubility curve, the solution is considered supersaturated. There are three mechanisms with which supersaturation occurs: precipitation, nucleation, and metastable. In the precipitation zone, the molecules in a solution are in excess and will separate from the solution to form amorphous aggregates. The excess of molecules aggregate to form a crystalline structure when in the nucleation zone. In the metastable zone, the solution takes time to nucleate. In order to grow crystals while in the metastable zone, the conditions would require the formation of one nucleus while in the nucleation zone, just past the metastable region. The supersaturated solution can then return to the metastable region.[8]

## Supersaturation in Vapors

Supersaturation in vapor phase is related to the surface tension of liquids through the Kelvin equation, the Gibbs–Thomson effect and the Poynting effect[9].

The International Association for the Properties of Water and Steam (IAPWS) provides a special equation for the Gibbs free energy in the metastable-vapor region of water in its Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. All thermodynamic properties for the metastable-vapor region of water can be derived from this equation by means of the appropriate relations of thermodynamic properties to the Gibbs free energy.[10]

## Methodologies of measurement

Measurement Technique Measurement Method Measurand
Acoustics Ultrasonic Sonic speed, phase shift
Chemistry Titration, indicators Concentration, tinct
Conductometry Kohlrausch-cell, inductive measurements Electrolytic conductivity
Gravimetry Densimeter Density
Optics Refractometry, interferometry, polarimetry, turbidmetry Refraction of index, interference, rotation of polarization plane, turbidity
Particle Analysis Particle analyzer Size distribution, particle density
Viscometry Viscometer, quartz-crystal oscillator Viscosity
Potentiometry Ionspecific electrodes, ionspecific membrands Ionic conductivity
Spectroscopy Spectrophotometry, infrared spectroscopy Absorption spectra

Table 1. Supersaturation measurement methods (Profos, 1987).[11]

## History

Supersaturation has been a frequent topic of research throughout history. Early studies of these solutions were normally conducted with sodium sulfate, also known as Glauber’s Salt, due to the stability of the crystal and the rising role it had in industry. Through the use of this salt, an important scientific discovery was made by Jean-Baptiste Ziz, a botanist from Mayence, in 1809.[12] His experiments allowed him to conclude 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 nuclei sites. Expanding upon this, 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 yield crystallization.

## Applications

Supersaturation is a widely encountered phenomenon both found in environmental processes and exploited in commercial manufacturing. For example, honey, the sweet nectar-derived food source, is a supersaturated aqueous solution of sugars. Nectar itself is a sugary solution below the point of saturation. Once bees harvest the nectar, they fan it rapidly with their wings to force evaporation. This forces the solution into a supersaturated state, creating honey. This explains why honey crystallizes; the solution is simply returning to its saturated state.[13]

Certain candies are made by crystallizing supersaturated solutions of sugar. To make rock candy, manufacturers can raise a solvent to a high temperature, add sugar to reach a high concentration, and then lower the temperature. If a string or stick is present in the solution as it cools, the crystallization will occur on that solid and create a candy. This is the same principle that leads maple syrup to crystallize.[14]

The carbonation of water is also reliant upon the behavior of supersaturated solutions. In this case, the solution is supersaturated with a gas. To create sodas and seltzer water, carbon dioxide gas is forced to dissolve in water beyond its saturation point. This is done by applying high amounts of pressure to the gas in the presence of water followed by sealing the system in an airtight manner.

The characteristics of supersaturation have practical applications in terms of pharmaceuticals. By creating a supersaturated solution of a certain drug, it can be ingested in liquid form. The drug can be made driven into a supersaturated state through any normal mechanism and then prevented from precipitating out by adding precipitation inhibitors.[15] Drugs in this state are referred to as "supersaturating drug delivery services," or "SDDS."[16] Oral consumption of a drug in this form is simple and allows for the measurement of very precise dosages. Primarily, it provides a means for drugs with very low solubility to be made into aqueous solutions.[17][18] In addition, some drugs can undergo supersaturation inside the body despite being ingested in a crystalline form [19]. This phenomenon is known as in vivo supersaturation.

The identification of supersaturated solutions can be used as a tool for marine ecologists to study the activity of organisms and populations. Photosynthetic organisms release O2 gas into the water. Thus, an area of the ocean supersaturated with O2 gas can likely determined to be rich with photosynthetic activity. Though some O2 will naturally be found in the ocean due to simple physical chemical properties, upwards of 70% of all oxygen gas found in supersaturated regions can be attributed to photosynthetic activity.[20]

Supersaturation in vapor phase is usually present in the expansion process through steam nozzles operating with dry, saturated steam at the inlet, becoming an important factor to be taken into account in the design of steam turbines, as this results in an actual mass flow of steam through the nozzle being about 1 to 3% greater than the theoretically calculated value that would be expected if the expanding steam underwent a reversible adiabatic process through equilibrium states. In these cases supersaturation occurs due to the fact that the expansion process develops so rapidly and in such a short time, that the expanding vapor cannot reach its equilibrium state in the process, behaving as if it were superheated. Hence the determination of the expansion ratio, relevant to the calculation of the mass flow through the nozzle, must be done using an adiabatic index of approximately 1.3, like that of the superheated steam, instead of 1.135, which is the value that should have to be used for a quasi-static adiabatic expansion in the saturated region[21].

The study of supersaturation is also relevant to atmospheric studies. Since the 1940s, the presence of supersaturation in the atmosphere has been known. When water is supersaturated in the troposphere, the formation of ice lattices is frequently observed. In a state of saturation, the water particles will not form ice under tropospheric conditions. It is not enough for molecules of water to form an ice lattice at saturation pressures; they require a surface to condense on to or conglomerations of liquid water molecules of water to freeze. For these reasons, relative humidities over ice in the atmosphere can be found above 100%, meaning supersaturation has occurred. Supersaturation of water is actually very common in the upper troposphere, occurring between 20% and 40% of the time.[22] This can be determined using satellite data from the Atmospheric Infrared Sounder.[23] Evidence of supersaturation in the troposphere can be seen in the contrails of airplanes and rocket ships, which need to reach a humidity above that of ice saturation in order to form.

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