Classical Nucleation theory two dimensions

[Yoran91]

Hi everyone,

I'm having trouble understanding a problem on CNT in 2d.
I'm given the equation

$\Delta G = \frac{4}{3} \pi R^3 \rho_s \Delta \mu + 4\pi R^2 \gamma$

for nucleation in 3d. Here mu is the difference in chemical potential between the solid and liquid phase, R is the radius of the spherical solid that forms, gamma is the surface tension. Now I'm trying to the find the analogous formula for nucleation in 2 dimensions.

What is that equation? I have only found things that produce nonsense.

 

[eljose79]

Hi there,

I understand your confusion with finding the formula for nucleation in 2 dimensions. The reason for this is because the equations for nucleation in 2 and 3 dimensions are different. In 2 dimensions, the equation for nucleation is given by:

\Delta G = \pi R^2 \rho_s \Delta \mu + 2\pi R \gamma

As you can see, the main difference is the absence of the 4/3 factor in the first term and the change in the second term from 4\pi R^2 to 2\pi R. This is due to the difference in surface area between a 2-dimensional circle (πR^2) and a 3-dimensional sphere (4/3πR^3).

I hope this helps clarify the equation for you. Please let me know if you have any further questions. Keep up the good work with your research on CNTs!