So that's our delta G of homogeneous nucleation.
The next term is what we're calling our wedding term, which is f of theta.
And so it's going to be,
as we change the angle theta we're going to change the values of f of theta.
And now we need to examine how those variables change, that is with f of theta.
So now what we've done is we're going to write the barrier to the heterogeneous
nucleation process in terms of first, homogeneous nucleation, and secondly,
times the associated wedding of that particular interface.
And what we're going to see is that that function,
f of theta, lies between two values.
It goes between 0 and 1 as you change the wedding angle from 0 to 180 degrees.
So what this tells us is, if we look at the bottom of the equation,
what that's telling [COUGH] us is that in one case,
when the value of f of theta is equal to 1,
it means we have no wedding associated with that particular interface.
And consequently, the only type of nucleation that we can have in
the absence of something that is wedding is homogenous nucleation.
Alternatively, if we look at the lower limit, when that value is equal to 0,
what that tells me is I have effectively complete wedding, and
the barrier to the nucleation process, is essentially equal to 0.
And one of the things that becomes important is the fact that
the radius is not going to be changed or altered that we calculated for
homogeneous nucleation, it's going to be the same r star.
And the reason, of course, for that is,
even though we have introduced the substrate, the behavior associated with
the interface separating the liquid and the solid has not changed.
But what has changed is the barrier to the nucleation process.
And the barrier looks exactly the same as
the homogeneous barrier that we described previously, but
this time it's modified by the presence of that wedding angle f of theta.
So by beginning the process of heterogeneous nucleation,
we're able to use homogeneous nucleation as a starting point and
develop how we can modify that particular behavior with respect
to the effectiveness of the wedding of the material as the substrate f of theta.
Thank you.