HOME

TheInfoList



OR:

In
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...
, nucleation is the first step in the formation of either a new thermodynamic phase or
structure A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such a ...
via self-assembly or
self-organization Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when suffic ...
within a substance or
mixture In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the ...
. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
is cooled (at atmospheric pressure) below 0°C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0°C often stay completely free of ice for long periods ( supercooling). At these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
s appear after little or no delay. Nucleation is a common mechanism which generates first-order
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states ...
s, and it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immediately. Nucleation is often very sensitive to
impurities In chemistry and materials science, impurities are chemical substances inside a confined amount of liquid, gas, or solid, which differ from the chemical composition of the material or compound. Firstly, a pure chemical should appear thermodynami ...
in the system. These impurities may be too small to be seen by the naked eye, but still can control the rate of nucleation. Because of this, it is often important to distinguish between heterogeneous nucleation and homogeneous nucleation. Heterogeneous nucleation occurs at ''nucleation sites'' on surfaces in the system. Homogeneous nucleation occurs away from a surface.


Characteristics

Nucleation is usually a
stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
(random) process, so even in two identical systems nucleation will occur at different times. A common mechanism is illustrated in the animation to the right. This shows nucleation of a new phase (shown in red) in an existing phase (white). In the existing phase microscopic fluctuations of the red phase appear and decay continuously, until an unusually large fluctuation of the new red phase is so large it is more favourable for it to grow than to shrink back to nothing. This nucleus of the red phase then grows and converts the system to this phase. The standard theory that describes this behaviour for the nucleation of a new thermodynamic phase is called classical nucleation theory. However, the CNT fails in describing experimental results of vapour to liquid nucleation even for model substances like argon by several orders of magnitude. For nucleation of a new thermodynamic phase, such as the formation of ice in water below 0°C, if the system is not evolving with time and nucleation occurs in one step, then the probability that nucleation has ''not'' occurred should undergo
exponential decay A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate ...
. This is seen for example in the nucleation of ice in
supercooled Supercooling, also known as undercooling, is the process of lowering the temperature of a liquid or a gas below its melting point without it becoming a solid. It achieves this in the absence of a seed crystal or nucleus around which a crysta ...
small water droplets. The decay rate of the exponential gives the nucleation rate. Classical nucleation theory is a widely used approximate theory for estimating these rates, and how they vary with variables such as temperature. It correctly predicts that the time you have to wait for nucleation decreases extremely rapidly when
supersaturated In physical chemistry, supersaturation occurs with a solution when the concentration of a solute exceeds the concentration specified by the value of solubility at equilibrium. Most commonly the term is applied to a solution of a solid in a li ...
. It is not just new phases such as liquids and crystals that form via nucleation followed by growth. The self-assembly process that forms objects like the amyloid aggregates associated with
Alzheimer's disease Alzheimer's disease (AD) is a neurodegenerative disease that usually starts slowly and progressively worsens. It is the cause of 60–70% of cases of dementia. The most common early symptom is difficulty in remembering recent events. As ...
also starts with nucleation. Energy consuming self-organising systems such as the
microtubules Microtubules are polymers of tubulin that form part of the cytoskeleton and provide structure and shape to eukaryotic cells. Microtubules can be as long as 50 micrometres, as wide as 23 to 27  nm and have an inner diameter between 11 a ...
in cells also show nucleation and growth.


Heterogeneous nucleation often dominates homogeneous nucleation

Heterogeneous nucleation, nucleation with the nucleus at a surface, is much more common than homogeneous nucleation. For example, in the nucleation of ice from supercooled water droplets, purifying the water to remove all or almost all impurities results in water droplets that freeze below around −35°C, whereas water that contains impurities may freeze at −5°C or warmer. This observation that heterogeneous nucleation can occur when the rate of homogeneous nucleation is essentially zero, is often understood using classical nucleation theory. This predicts that the nucleation slows exponentially with the height of a free energy barrier ΔG*. This barrier comes from the free energy penalty of forming the surface of the growing nucleus. For homogeneous nucleation the nucleus is approximated by a sphere, but as we can see in the schematic of macroscopic droplets to the right, droplets on surfaces are not complete spheres and so the area of the interface between the droplet and the surrounding fluid is less than a sphere's 4\pi r^2 . This reduction in surface area of the nucleus reduces the height of the barrier to nucleation and so speeds nucleation up exponentially. Nucleation can also start at the surface of a liquid. For example, computer simulations of gold nanoparticles show that the crystal phase nucleates at the liquid-gold surface.


Computer simulation studies of simple models

Classical nucleation theory makes a number of assumptions, for example it treats a microscopic nucleus as if it is a macroscopic droplet with a well-defined surface whose free energy is estimated using an equilibrium property: the interfacial tension σ. For a nucleus that may be only of order ten molecules across it is not always clear that we can treat something so small as a volume plus a surface. Also nucleation is an inherently out of
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In the ...
phenomenon so it is not always obvious that its rate can be estimated using equilibrium properties. However, modern computers are powerful enough to calculate essentially exact nucleation rates for simple models. These have been compared with the classical theory, for example for the case of nucleation of the crystal phase in the model of hard spheres. This is a model of perfectly hard spheres in thermal motion, and is a simple model of some colloids. For the crystallization of hard spheres the classical theory is a very reasonable approximate theory. So for the simple models we can study, classical nucleation theory works quite well, but we do not know if it works equally well for (say) complex molecules crystallising out of solution.


The spinodal region

Phase-transition processes can also be explained in terms of
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 ...
, where phase separation is delayed until the system enters the unstable region where a small perturbation in composition leads to a decrease in energy and, thus, spontaneous growth of the perturbation. This region of a phase diagram is known as the spinodal region and the phase separation process is known as spinodal decomposition and may be governed by the Cahn–Hilliard equation.


The nucleation of crystals

In many cases, liquids and solutions can be cooled down or concentrated up to conditions where the liquid or solution is significantly less thermodynamically stable than the crystal, but where no crystals will form for minutes, hours, weeks or longer. Nucleation of the crystal is then being prevented by a substantial barrier. This has consequences, for example cold high altitude clouds may contain large numbers of small liquid water droplets that are far below 0°C. In small volumes, such as in small droplets, only one nucleation event may be needed for crystallisation. In these small volumes, the time until the first crystal appears is usually defined to be the nucleation time. Visualization of the initial stage of crystal nucleation of sodium chloride was achieved through atomic-resolution real-time video imaging. Calcium carbonate crystal nucleation depends not only on degree of supersaturation but also the ratio of calcium to carbonate ions in aqueous solutions. In larger volumes many nucleation events will occur. A simple model for crystallisation in that case, that combines nucleation and growth is the KJMA or Avrami model.


Primary and secondary nucleation

The time until the appearance of the first crystal is also called primary nucleation time, to distinguish it from secondary nucleation times. Primary here refers to the first nucleus to form, while secondary nuclei are crystal nuclei produced from a preexisting crystal. Primary nucleation describes the transition to a new phase that does not rely on the new phase already being present, either because it is the very first nucleus of that phase to form, or because the nucleus forms far from any pre-existing piece of the new phase. Particularly in the study of crystallisation, secondary nucleation can be important. This is the formation of nuclei of a new crystal directly caused by pre-existing crystals. For example, if the crystals are in a solution and the system is subject to shearing forces, small crystal nuclei could be sheared off a growing crystal, thus increasing the number of crystals in the system. So both primary and secondary nucleation increase the number of crystals in the system but their mechanisms are very different, and secondary nucleation relies on crystals already being present.


Experimental observations on the nucleation times for the crystallisation of small volumes

It is typically difficult to experimentally study the nucleation of crystals. The nucleus is microscopic, and thus too small to be directly observed. In large liquid volumes there are typically multiple nucleation events, and it is difficult to disentangle the effects of nucleation from those of growth of the nucleated phase. These problems can be overcome by working with small droplets. As nucleation is
stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
, many droplets are needed so that statistics for the nucleation events can be obtained. To the right is shown an example set of nucleation data. It is for the nucleation at constant temperature and hence supersaturation of the crystal phase in small droplets of supercooled liquid tin; this is the work of Pound and La Mer. Nucleation occurs in different droplets at different times, hence the fraction is not a simple step function that drops sharply from one to zero at one particular time. The red curve is a fit of a Gompertz function to the data. This is a simplified version of the model Pound and La Mer used to model their data. The model assumes that nucleation occurs due to impurity particles in the liquid tin droplets, and it makes the simplifying assumption that all impurity particles produce nucleation at the same rate. It also assumes that these particles are Poisson distributed among the liquid tin droplets. The fit values are that the nucleation rate due to a single impurity particle is 0.02/s, and the average number of impurity particles per droplet is 1.2. Note that about 30% of the tin droplets never freeze; the data plateau at a fraction of about 0.3. Within the model this is assumed to be because, by chance, these droplets do not have even one impurity particle and so there is no heterogeneous nucleation. Homogeneous nucleation is assumed to be negligible on the timescale of this experiment. The remaining droplets freeze in a stochastic way, at rates 0.02/s if they have one impurity particle, 0.04/s if they have two, and so on. These data are just one example, but they illustrate common features of the nucleation of crystals in that there is clear evidence for heterogeneous nucleation, and that nucleation is clearly stochastic.


Ice

The freezing of small water droplets to ice is an important process, particularly in the formation and dynamics of clouds. Water (at atmospheric pressure) does not freeze at 0°C, but rather at temperatures that tend to decrease as the volume of the water decreases and as the water impurity increases. Thus small droplets of water, as found in clouds, may remain liquid far below 0°C. An example of experimental data on the freezing of small water droplets is shown at the right. The plot shows the fraction of a large set of water droplets, that are still liquid water, i.e., have not yet frozen, as a function of temperature. Note that the highest temperature at which any of the droplets freezes is close to -19°C, while the last droplet to freeze does so at almost -35°C.


Examples


Examples of the nucleation of fluids (gases and liquids)

*
Clouds In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid drop (liquid), droplets, ice crystals, frozen crystals, or other particulates, particles suspended in the atmosphere of a planetary body or similar space. ...
form when wet air cools (often because the air rises) and many small water droplets nucleate from the supersaturated air.H. R. Pruppacher and J. D. Klett, ''Microphysics of Clouds and Precipitation'', Kluwer (1997). The amount of water vapour that air can carry decreases with lower temperatures. The excess vapor begins to nucleate and to form small water droplets which form a cloud. Nucleation of the droplets of liquid water is heterogeneous, occurring on particles referred to as
cloud condensation nuclei Cloud condensation nuclei (CCNs), also known as cloud seeds, are small particles typically 0.2 µm, or one hundredth the size of a cloud droplet. CCNs are a unique subset of aerosols in the atmosphere on which water vapour condenses. This c ...
.
Cloud seeding Cloud seeding is a type of weather modification that aims to change the amount or type of precipitation that falls from clouds by dispersing substances into the air that serve as cloud condensation or ice nuclei, which alter the microphysica ...
is the process of adding artificial condensation nuclei to quicken the formation of clouds. * Bubbles of
carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is t ...
nucleate shortly after the pressure is released from a container of carbonated liquid. * Nucleation in
boiling Boiling is the rapid vaporization of a liquid, which occurs when a liquid is heated to its boiling point, the temperature at which the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere. Th ...
can occur in the bulk
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, ...
if the pressure is reduced so that the liquid becomes superheated with respect to the pressure-dependent boiling point. More often, nucleation occurs on the heating surface, at nucleation sites. Typically, nucleation sites are tiny crevices where free gas-liquid surface is maintained or spots on the heating surface with lower
wetting Wetting is the ability of a liquid to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. This happens in presence of a gaseous phase or another liquid phase not miscible with ...
properties. Substantial superheating of a liquid can be achieved after the liquid is de-gassed and if the heating surfaces are clean, smooth and made of materials well wetted by the liquid. * Some champagne stirrers operate by providing many nucleation sites via high surface-area and sharp corners, speeding the release of bubbles and removing carbonation from the wine. * The
Diet Coke and Mentos eruption A Diet Coke and Mentos eruption (also known as a soda geyser) is a reaction between the carbonated beverage Diet Coke and Mentos mints that causes the beverage to be expelled from its container. The candies catalyze the release of gas from the ...
offers another example. The surface of Mentos candy provides nucleation sites for the formation of carbon-dioxide bubbles from carbonated soda. * Both the bubble chamber and the cloud chamber rely on nucleation, of bubbles and droplets, respectively.


Examples of the nucleation of crystals

* The most common crystallisation process on Earth is the formation of ice. Liquid water does not freeze at 0°C unless there is ice already present; cooling significantly below 0°C is required to nucleate ice and so for the water to freeze. For example, small droplets of very pure water can remain liquid down to below -30 °C although ice is the stable state below 0°C. * Many of the materials we make and use are crystalline, but are made from liquids, e.g. crystalline iron made from liquid iron cast into a mold, so the nucleation of crystalline materials is widely studied in industry. It is used heavily in the chemical industry for cases such as in the preparation of metallic ultradispersed powders that can serve as catalysts. For example, platinum deposited onto TiO2 nanoparticles catalyses the liberation of hydrogen from water. It is an important factor in the semiconductor industry, as the band gap energy in semiconductors is influenced by the size of nanoclusters.


Nucleation in solids

In addition to the nucleation and growth of crystals e.g. in non-crystalline glasses, the nucleation and growth of impurity precipitates in crystals at, and between, grain boundaries is quite important industrially. For example in metals solid-state nucleation and precipitate growth plays an important role e.g. in modifying mechanical properties like ductility, while in semiconductors it plays an important role e.g. in trapping impurities during integrated circuit manufacture.


References

{{Authority control Particle detectors Articles containing video clips Bubbles (physics)