Nucleation

Nucleation or nucleation is the first thread that initiates a phase transition of first order. Examples include the freezing of water to ice, blistering in the transition from the liquid to the gaseous phase (eg when opening a bottle of water with dissolved carbon dioxide) or the condensation of a gas.

General

An essential feature of nucleation is that the new, thermodynamically stable phase under the given conditions, is first formed by germs from the old metastable phase. The formation of these typically only nanometer-sized nuclei is initially kinetically inhibited. Liquids can be supercooled and overheat. The reason for this inhibition is the work that needs to be applied to (e.g., a spherical droplet ) to form the curved surface of a smallest nucleus of the new phase. For small droplets or crystals they work surface is greater than the energy gain from the transition to the new, stable phase. The resulting free energy barrier is called nucleation barrier. The work that must be applied to overcome this barrier, called nucleation work. The region of the phase diagram in which the seeds remain below the critical nucleus size is also called Ostwald - Miers region. However, if once germs that are larger than the so-called critical nucleus size, from thermal fluctuations formed, they grow rapidly at the macroscopic phase. Nucleation can thus be understood as a prototype of an activated process.

The nucleation rate describes the number of the new phase nuclei per volume and time unit are formed. This nucleation rate strongly depends exponentially on the nucleation work. The higher the nucleation work and thus the barrier for nucleation, the lower the rate.

Nucleation is a ubiquitous process. Thus, for example, the experiences of a volcano ejected lava a sudden fall in temperature and pressure, thus forming the typical, small gas bubbles interspersed rocks. Another example is weather phenomena such as the formation of rain, fog and snow. In medicine, you know, for example, the divers disease that is caused by too fast emerging. Here the previously dissolved nitrogen in the blood is outgassed by the pressure drop. Industry too is the knowledge of Keimbildungskinetik of the highest interest, for example, prevent to the drop impact in gas turbines or the formation of the contrail to control in jet aircraft.

The nucleation also plays a central role in process engineering of polymers, alloys and some ceramics and is also of great importance in meteorology.

Nucleation processes are systematically studied because of their great technical relevance since the beginning of the twentieth century. Substantial results have however been before, especially for the phase transition of gas-liquid, and crystallization for structural change in a few metals. The purpose established theories are often transferred to the remaining systems lack of an alternative.

The still prevailing theory is the so-called classical nucleation theory ( classical nucleation theory ) This is often used because of its simple structure, although especially for the gas-liquid transition has been repeatedly shown that the prediction of the theory typically differs by several orders of magnitude.

Recent studies of the gas-liquid phase transition of argon, for example, show deviations from the classical nucleation theory by more than 20 orders of magnitude. Deviations of this magnitude between theory and experiment are almost unique in contemporary science. This fact is all the more amazing than it essentially is a problem of classical physics.

Electrofreezing is a process by the crystallization of water or other liquids can be activated during the freezing process by the application of an electric field. This physical phenomenon is known since 1861.

Classical nucleation theory

The classical nucleation theory makes some basic, simplistic assumptions that put us in the position to describe the nucleation process. A majority of these approximations can be summarized under the term Kapillaritätsnäherung: With this approximation, it is assumed that even the smallest ( microscopic ) bacteria already the same ( macroscopic ) possess properties of the new phase. Illustrating the classical nucleation theory, we use the following, the example of the condensation of a droplet from a supersaturated vapor. In this case the process is typically considered at a constant temperature, and the driving force for nucleation is the supersaturation.

Thermodynamic aspect

We consider a super-saturated vapor, which means that at the given temperature, the current pressure is higher than the equilibrium vapor pressure. We now calculate the reversible work that is necessary to form in the supersaturated vapor phase, a liquid droplet. We consider a process at constant pressure, constant volume and constant number of particles. The relevant thermodynamic potential is thus the Gibbs free energy:

Specifically, for a pure vapor phase ( index v ) yields:

For a system that both steam and a liquid droplet ( index L ) consisting of particles, including concerns equally

Wherein the surface tension of a droplet with the surface. The nucleation energy of a droplet size in the gas phase is now just the difference between the Gibbs free energy of a system including a droplet size, and steam, as well as the pure steam system. It follows:

In this equation is just the difference between the chemical potentials of the vapor and the liquid. The classical nucleation theory now makes a number of simplifying assumptions:

• The liquid droplet is spherical, non-compressible and has a sharp interface.
• The liquid droplet has the same surface tension, density and vapor pressure as the macroscopic (flat) liquid phase.
• The vapor pressure can be described by means of the ideal gas law.

Using these assumptions it is now possible, the surface and the difference of the chemical potentials calculated easily ( with the help of the Gibbs -Duhem equation):

As well as

Here, the over-saturation, the average surface area required of a molecule that is the radius of the droplet and the mean volume of a molecule in the liquid phase. Thus results for the nucleation work

As you can see, the first term, also called volume term proportional to. This term is associated with the gain of energy resulting from the transition of a molecule from the vapor phase into the stable metastable liquid phase. On the other hand, the second term is associated with the work that needs to be applied to form the surface of such a liquid droplet. This term is just proportional to. For - and only in this case nucleation can use - shows that the surface term dominates for small droplet sizes up to a critical size above which the bulk term prevails. This gives the familiar picture of a barrier in the free energy.

The maximum is the nucleation work that needs to be applied to form a droplet of the critical size. This critical size and nucleation work are the determining parameters of nucleation: droplets that are smaller, have a higher probability to evaporate again than to continue to grow as connected for this evaporation with a gain of free energy. Only droplets larger than have a higher probability to grow further as to evaporate, and can thus serve as nuclei of the new phase. This is now understandable why a substance for a long time can be kept metastable: Although the new phase (in our example, the liquid phase) is the thermodynamically stable phase, the process must first pass through some energetically unfavorable steps to climb the barrier. The barrier and the critical nucleus size according to the classical nucleation theory are viewing:

And

Kinetics of nucleation

In order nucleation rate, ie to calculate the number of nuclei formed per unit volume and time, also the kinetics of nucleation must be considered. The stationary nucleation rate is usually calculated in the form of an Arrhenius approach:

The pre-factor is usually the kinetic prefactor called. On these, however, be discussed here in detail. The height of the barrier is usually due to the exponential dependence a much larger and decisive influence on the nucleation rate.

Homogeneous nucleation

If the nucleation in free space, ie, by a static coincidence of particles, it is called a homogeneous nucleation.

For this it is necessary that sufficient together and find a lot of slow particles without further assistance to larger structures in the case of condensation. Slow particles may be produced by the simultaneous concurrence of more than two particles ( third body ). In this case, a particle refers to a majority of the kinetic energy and leaves two slow particles. The supersaturation is about proportional to the probability of such a three shock, which leads to nucleation. Depending on the system under consideration can therefore remain very long in this state thermodynamically metastable systems.

Heterogeneous nucleation

In contrast, only very low supersaturation of you needs in the heterogeneous nucleation often even below one percent. This type of condensation is carried out in turn, in the case of condensation on existing surfaces, in other words usually in the gas phase of suspended solid particles, the condensation aerosol particles or nuclei. These act in relation to the respective gas as a kind of particle catcher, wherein substantially the radius and the chemical properties of the particle to determine how well it adhere to the gas particles. This also applies analogously for surfaces not of a particulate body, then one speaks of a fitting. In any case, heterogeneous particles or surfaces act as a catalyst for the nucleation by reducing the nucleation barrier significantly.