Talk:Nucleation

Cosmological confusion

Can anyone provide some cites and some discussion of nucleation in cosmology? Nucleation is a key concept in false vacuum inflation, it would be nice to get some treatment of that. --Keflavich 19:51, 1 April 2006 (UTC)

I was just about to ask a similar question! What about gravitational nucleation? when the universe was finding its feet, it was a uniform cloud, no? What caused it to form nebulae, stars, and planets? - jak (talk) 03:06, 13 June 2006 (UTC)

Fix it. DCDuring 16:41, 24 September 2007 (UTC)

Can you write who discovered nucleation? i need to know for a project. —Preceding unsigned comment added by 72.54.128.137 (talk) 14:11, 1 October 2008 (UTC)

Help Request

I noticed that this page has an external link to a page about the coke and mentos experience. I created a page about the mentos eruption phenomenon (Mentos eruption). But I'm not a scientist so any help you could provide editing it (especially the scientific explanation section) would be great. I'm sure that you would do much better at it than me. (Toritaiyo 17:39, 7 August 2006 (UTC))

Heterogeneous nucleation form factor

I get a different result for the form factor relating the free energy for heterogeneous nucleation as a proportion of the free energy of homogeneous nucleation. Can anyone add a source to confirm?

$f(\theta )={\frac {1}{4}}\left(2-\cos \theta +\cos ^{3}\theta \right)$

Grunkhead (talk) 14:25, 11 April 2010 (UTC)

This rate is valid only if the heterogeneous nucleation takes place on a plane surface. In other cases the "geometric factor" has more complicated form. You can check any of text books for nucleation for further reference. —Preceding unsigned comment added by 128.252.20.193 (talk) 21:20, 28 June 2010 (UTC)

The original expression in the page was right, but as note above applies only to the (unrealistic) case of a perfectly smooth surface, so I have replaced the equation with a qualitative discussion of the effect of contact angle and surface geometry on nucleation. rpsear 26th Dec 2013 — Preceding unsigned comment added by Rpsear (talk • contribs) 19:35, 26 December 2013 (UTC)

Ambiguity regarding the example of chemical nucleation

"Most nucleation processes are physical, rather than chemical, but a few exceptions do exist (e.g. electrochemical nucleation) . A good example would be the famous Diet Coke and Mentos eruption". First of all, is electrochemical nucleation the only exception, the only form of chemical nucleation, or there are more? If it is the only one, then it's supposed to be "i.e." ("id est", "that is"), not "e.g." (example gratia). Secondly, is the diet(?)-coke-and-menthos case a sort of electrochemical nucleation, or is it just other sort of chemical nucleation, but not electrochemical? --Extremophile (talk) 02:54, 21 April 2010 (UTC)

free energy vs radius graph jpg needs redrawing.

The interfacial energy + the volume free energy should add up to give the free energy of the system (line in the middle). I understand that it's a sketch but you can see clearly that this line is in the wrong place and therefore may cause confusion. —Preceding unsigned comment added by 82.4.86.255 (talk) 00:46, 14 November 2010 (UTC)

Fixed. I did an improved figure (PNG format) and the page now uses this image - Richard Sear (rpsear) 9th Jan 2014 — Preceding unsigned comment added by Rpsear (talk • contribs) 18:22, 9 January 2014 (UTC)

Modern Theory equation documentation error?

Is "ΔG" vs "Δs" in this example correct from gibbs free energy equation? Can one substitute "s" here? This does not look correct.

$\Delta G\ =\ (4\pi r^{2}-s)\sigma -(n-1)k_{B}T\ln S$

Where:

• Δs is critical free energy needed.
• k_B is the Boltzmann constant
• S=p_v/p_o is the supersaturation
• s is the surface area of a monomer

Sativarg (talk) 18:08, 29 June 2011 (UTC)

Sodium acetate nucleation with snapping disk

The snap disk in warming packs apparently nucleates solidification by exposing microcrystals in small cracks in the metal surface, according to Rogerson, Mansel A, and Silvana S. S Cardoso. 2003. Solidification in heat packs: III. Metallic trigger. AIChE Journal 49(2):522-529. This is according to the abstract, I don't have access to the full paper. This should also be clarified in the article sodium acetate. Robert Hiller (talk) 06:42, 8 March 2012 (UTC)

Another citation along those same lines is B. Sandnes, The physics and the chemistry of the heat pad, Am. J. Phys. 76, 546 (2008); http://dx.doi.org/10.1119/1.2830533 Dder (talk) 14:22, 16 November 2014 (UTC)

Homogeneous and Heterogeneous Nucleation

We are a group of physics master's students who are taking the subject of nanomaterials. We have seen that we can add more information on this topic. Our idea is to put it under the "characteristics" section and remove the "Heterogeneous nucleation often dominates homogeneous nucleation" section, because we think we already explained it. We leave the content below.

Homogeneous Nucleation

Introduction

Homogeneous nucleation refers to the process where a new phase (like a crystal) forms uniformly throughout a parent phase (like a liquid or gas) without any preferential nucleation sites. This process requires a phase change and can be initiated from a liquid, gas, or solid state.

Phase Change and Formation of Aggregates

When starting from a liquid, small aggregates or embryos, consisting of a few atoms, form randomly. If the conditions are right, these aggregates grow into the desired crystal. The conditions necessary for the growth of these aggregates are determined by the energy required for the phase change.

Interfacial Formation and Surface Tension

To grow a nucleus, an interface that separates the two phases must form, which has an associated energy cost. This interface has a characteristic surface tension given by:

$\sigma ={\frac {\partial G}{\partial S}},$

where $\partial G$ is the energy difference required to form the surface.

Energy Considerations

The free energy to create the surface, $\Delta G_{S}$, is given by:

$\Delta G_{S}=4\pi r^{2}\sigma ,$

where $\sigma >0$, meaning there is always an energy cost.

The free energy difference per unit volume, $\Delta G_{V}$, can be positive or negative and is given by:

$\Delta G_{V}={\frac {4}{3}}\pi r^{3}\Delta g_{V},$

where $\Delta g_{V}$ depends on temperature (T), pressure (P), and composition (c).

Total Free Energy Change

The total free energy required for nucleation, combining surface and volume terms, is:

$\Delta G=\Delta G_{S}+\Delta G_{V}=4\pi r^{2}\sigma +{\frac {4}{3}}\pi r^{3}\Delta g_{V}.$

Critical Radius and Free Energy

The relationship between free energy and the radius of the nanoparticle reveals that there's a critical radius, $r^{*}$, where the free energy is maximized:

$r^{*}={\frac {2\sigma }{|\Delta g_{V}|}},$

$\Delta G^{*}={\frac {16\pi \sigma ^{3}}{3|\Delta g_{V}|^{2}}}.$

If the radius $r$ is smaller than $r^{*}$, the particles will dissolve. If $r\geq r^{*}$, the particles can continue to grow.

Influence of Surface and Volume Terms

For small radii, the surface term predominates, while for larger radii, the volume term dominates. This indicates that the initial stages of nucleation are controlled by surface energy, but as the nucleus grows, volume energy becomes more significant.

Critical Radius and Temperature Dependence

By evaluating the free energy change at the freezing temperature, \( T_f \), and the degree of undercooling, \( \Delta T = T_f - T \):

$\Delta G=\Delta H_{f}{\frac {\Delta T}{T_{f}}},$

the critical radius \( r^* \) and the critical free energy \( \Delta G^* \) are:

$r^{*}=\left({\frac {2\sigma T_{f}}{\Delta H_{f}}}\right){\frac {1}{\Delta T}},$

$\Delta G^{*}={\frac {16\pi \sigma ^{3}T_{f}^{2}}{3(\Delta H_{f})^{2}\Delta T^{2}}}.$

The further the system is from the freezing temperature, the smaller the values of \( r^* \) and \( \Delta G^* \).

Examples of Supercooling and Superheating

• Supercooling: Cooling distilled water below 0°C without it freezing. Upon agitation, the water freezes instantly.
• Superheating: Heating water in a microwave above its boiling point without it boiling. Introducing a porous object can cause it to boil suddenly.

Heterogeneous Nucleation

Heterogeneous nucleation occurs when the nucleus forms at a surface, such as the walls of a container or a substrate.

Heterogeneous nucleation is important to understand the behavior of the nucleus in contact with a surface. The formation of different surfaces generates surface tension, with various forces \( \sigma \) acting to minimize these surfaces to reduce energy. At equilibrium, the relationship is described by:

$\sigma _{LS}=\sigma _{CS}+\sigma _{CL}\cos \theta .$

Here, \( \sigma_{LS} \), \( \sigma_{CS} \), and \( \sigma_{CL} \) represent the surface tensions between liquid-solid, crystal-solid, and crystal-liquid interfaces, respectively, and \( \theta \) is the wetting angle. The vertical component of \( \sigma_{CL} \) can deform the substrate, but this is usually negligible.

Phase change is analyzed at the atomic level, considering the energies corresponding to each phase. The free energy change \( \Delta G \) is calculated by:

$\Delta G_{\text{het}}=\Delta G_{\text{hom}}f(\theta ),\quad {\text{with}}\quad f(\theta )={\frac {2-3\cos \theta +\cos ^{3}\theta }{4}}.$

The angle \( \theta \), defined as the wetting angle, depends on the forces \( \sigma \). When \( \theta = 180^{\circ} \), the crystal formed in contact with the substrate takes the shape of a sphere, and \( \Delta G_{\text{het}} = \Delta G_{\text{hom}} \). Conversely, if \( \theta = 0^{\circ} \), a continuous layer is formed.

Characteristics of Homogeneous and Heterogeneous Nucleation

Homogeneous Nucleation

Homogeneous nucleation occurs uniformly throughout the parent phase without any preferential nucleation sites. The main characteristics are:

• Uniformity: The nucleation sites are randomly distributed within the parent phase.
• Energy Requirement: It requires a higher energy barrier to overcome because it relies solely on the inherent properties of the phase change.
• Phase Change: It can start from a liquid, gas, or solid, involving the formation of small aggregates or embryos, which grow into the desired phase under the right conditions.
• Surface Tension: The creation of an interface between the two phases incurs an energy cost characterized by the surface tension, \( \sigma \).

Heterogeneous Nucleation

Heterogeneous nucleation, on the other hand, occurs on pre-existing surfaces or interfaces within the parent phase. Its main characteristics include:

• Preferential Sites: It typically occurs at surfaces, interfaces, or impurities, which act as nucleation sites.
• Lower Energy Barrier: The energy barrier for nucleation is significantly lower compared to homogeneous nucleation due to the presence of these sites.
• Enhanced Nucleation Rate: The presence of foreign surfaces or particles promotes nucleation, making the process more efficient.
• Surface Energy Contribution: The energy cost is reduced because part of the surface energy is

Energy Considerations and Critical Radius

For homogeneous nucleation, the entire energy required to create a new phase must come from the phase change itself, making the critical radius and free energy higher. In contrast, heterogeneous nucleation leverages the existing surfaces to lower the energy requirements:

$\Delta G_{\text{hetero}}<\Delta G_{\text{homo}}.$

The critical radius for heterogeneous nucleation is also typically smaller than that for homogeneous nucleation because the energy barrier to form a stable nucleus is reduced by the presence of the nucleation site.

Probability of forming a nucleus

The critical radius $(r^{*})$ is the same for both homogeneous and heterogeneous nucleation, but the associated energy values differ due to the factor $f(\theta )$, leading to $\Delta G_{\text{het}}^{*}\neq \Delta G_{\text{hom}}^{*}$. The probability of forming a nucleus with a critical radius $r^{*}$ is given by:

$P=\exp \left(-{\frac {\Delta G^{*}}{k_{B}T}}\right).$

The nucleation frequency, $I$ (nuclei/m³·s), is:

$I=P\cdot N\cdot \Gamma ,$

where $N$ is the number of potential nucleation sites, and $\Gamma$ is the jump frequency (how easily atoms move and meet). As $\Delta T$ increases, $\Delta G^{*}$ decreases, increasing $P$. However, at low temperatures, the jump frequency $\Gamma$ tends to zero due to slower particle movement, leading to a low $I$.

The jump frequency $\Gamma$ is given by:

$\Gamma ={\frac {1}{\tau }}={\frac {2D}{a_{0}^{2}}},$

where $\tau$ is the time between jumps and $D$ is the diffusion coefficient. The Einstein-Stokes relation gives $D$ as:

$D={\frac {k_{B}T}{6\pi \eta a_{0}}},$

where $\eta$ is the material's viscosity, often expressed as $\eta =A\exp \left({\frac {B}{T-T_{0}}}\right)$. At temperatures near $T_{f}$, particle speed increases, raising $\Gamma$, but $\Delta G^{*}$ also increases, reducing $P$ and thus decreasing $I$ overall. At very low temperatures, the system has low mobility, further decreasing $I$. Rapid cooling can prevent phase change, resulting in glass formation. For instance, cooling rates of about $10^{10}\,{\text{K/s}}$ are needed for pure metallic glass, achievable by reducing the system scale or using multiple atom types. Ana Planells (talk) 11:40, 21 May 2024 (UTC)