MSE 201 S21 Lecture 37 - Module 1 - Free Energy of Nucleation

Summary

This module explores nucleation and the free energy involved in the process. It explains the roles of surface and bulk free energy during phase formation, with surface energy being destabilizing and volume energy being stabilizing. The total free energy of the system changes based on these interactions, leading to the concept of a critical nucleus. Once a nucleus reaches a critical radius (r*), it stabilizes and grows. The summary also highlights the formulas used to calculate the critical radius and energy, emphasizing how supercooling influences nucleation behavior.

Takeaways

• 🔬 Nucleation involves analyzing free energy, where negative values indicate favorability, and positive values imply that something is unlikely to occur.
• 🟥 The surface free energy is a positive term, representing the energy required to create a boundary between the solid and liquid phases. This destabilizes the nucleus and increases with particle radius.
• ⚖️ The surface free energy can be expressed as 4πr² multiplied by the surface tension between the interfaces.
• 🟩 The bulk free energy, a stabilizing factor, is related to the formation of a new solid phase and decreases as the particle radius increases.
• 📉 The bulk free energy term is proportional to the volume (r³) and decreases more rapidly than the surface term, which is proportional to r².
• 🌀 The total free energy of the system initially increases, reaching a maximum at a critical radius (r*), after which it decreases, indicating favorability for nucleation.
• 💡 The critical value (ΔG*) represents the energy required for nucleation to become stable, and once the radius exceeds r*, the nucleus will continue to grow.
• 📐 The critical radius (r*) is calculated using surface tension, melting temperature, latent heat of solidification, and the degree of supercooling (ΔT).
• ❄️ The critical nucleus size decreases as the supercooling increases, typically reaching about 10 nanometers for common supercooling values.
• ⚙️ The energy barrier for nucleation (ΔG*) also decreases with decreasing temperature, driven by the same variables that influence the critical radius.

Q & A

What is the basic concept of free energy in nucleation?

Free energy in nucleation helps determine whether a process is favorable or not. A negative free energy value indicates that the process is likely to occur, while a positive value means it is not likely to occur.

What are the two terms involved in the free energy of nucleation?

The two terms involved in the free energy of nucleation are the surface free energy (positive term) and the volume or bulk free energy (negative term). The surface free energy represents the energy required to create a surface between solid and liquid, while the volume free energy stabilizes the system by forming a new solid phase.

Why is the surface free energy term considered destabilizing?

The surface free energy term is considered destabilizing because forming a new boundary between the solid and liquid requires energy, making the nucleation process less favorable. This term increases with the radius of the particle.

How does the volume free energy term affect the nucleation process?

The volume free energy term is stabilizing and favorable for the system because it represents the energy behind forming a new solid phase. As the radius of the particle increases, the volume term decreases and becomes more negative, helping drive the nucleation process.

What happens when both surface and volume free energy terms are combined?

When the surface and volume free energy terms are combined, the total free energy initially increases but eventually starts to decrease once the volume term dominates. This leads to a critical value where the free energy becomes favorable for nucleation.

What is the significance of the critical radius (r*) in nucleation?

The critical radius (r*) is the size at which the nucleus becomes stable and will continue to grow. Before reaching this critical radius, the nucleus is just as likely to shrink as to grow. Once the radius exceeds r*, the nucleus becomes stable and can grow to further reduce the system's free energy.

What is delta G* in the context of nucleation?

Delta G* represents the critical amount of free energy that must be supplied to the nucleus for it to reach the stable size (r*). It is the energy barrier that must be overcome for nucleation to proceed.

How is the critical radius (r*) calculated?

The critical radius (r*) is calculated using the formula: r* = -2 * (surface tension or free energy) * (melting temperature) / (latent heat of solidification) * (degree of supercooling).

How does supercooling affect the critical radius and nucleation process?

As supercooling increases (i.e., the temperature decreases), the critical radius (r*) decreases. This means that smaller nuclei become stable at lower temperatures, making the nucleation process more likely.

What happens to the energy barrier for nucleation as the temperature decreases?

As the temperature decreases (with increasing supercooling), the energy barrier for nucleation (delta G*) decreases. This means it becomes easier for nuclei to form, which enhances the nucleation process.