There is always (rightfully) some confusion as to how the free energy of mixing can be written three different ways. Here is some elaboration of my answer to the question raised around 12:30. Consider the following equations: 1) deltaGm/RT = (n1 ln x1 + n2 ln x2 + n1 x2 chi) for the system (Lodge eq. 7.2.11a) 2) deltaGm/kT = (x1 ln x1 + x2 ln x2 + x1 x2 chi) per site (Lodge eq. 7.2.11b) 3) deltaGm/RT = (x1 ln x1 + x2 ln x2 + x1 x2 chi) per mole (Lodge eq. 7.5.1) Specifically, how they can possibly all be true at the same time? It all depends on your perspective. Are you looking at the change in free energy for the whole entire system (that is, with a finite number of atoms, moles, stuff in a lattice of finite size), for one site in a lattice of arbitrary size, or per mole of sites. In each case, deltaGm is going to be different to compensate for the fact that in (2) we are talking about individual sites and in (3) we are talking about per 10^23 sites. In (1), deltaGm will be whatever it is. Big for a big lattice, small for a small lattice. The right hand side is unitless in all three cases. The cloud point diagrams are constructed from equations like (3). REALLY though, we should be using some kind of superscript to differentiate between the three meanings of deltaGm. This is, however, rarely done. Hope this helps, Darren
There is always (rightfully) some confusion as to how the free energy of mixing can be written three different ways. Here is some elaboration of my answer to the question raised around 12:30. Consider the following equations:
1) deltaGm/RT = (n1 ln x1 + n2 ln x2 + n1 x2 chi) for the system (Lodge eq. 7.2.11a)
2) deltaGm/kT = (x1 ln x1 + x2 ln x2 + x1 x2 chi) per site (Lodge eq. 7.2.11b)
3) deltaGm/RT = (x1 ln x1 + x2 ln x2 + x1 x2 chi) per mole (Lodge eq. 7.5.1)
Specifically, how they can possibly all be true at the same time? It all depends on your perspective. Are you looking at the change in free energy for the whole entire system (that is, with a finite number of atoms, moles, stuff in a lattice of finite size), for one site in a lattice of arbitrary size, or per mole of sites. In each case, deltaGm is going to be different to compensate for the fact that in (2) we are talking about individual sites and in (3) we are talking about per 10^23 sites. In (1), deltaGm will be whatever it is. Big for a big lattice, small for a small lattice. The right hand side is unitless in all three cases. The cloud point diagrams are constructed from equations like (3).
REALLY though, we should be using some kind of superscript to differentiate between the three meanings of deltaGm. This is, however, rarely done.
Hope this helps,
Darren
Darren Lipomi i need polymer phase diagram pls help me
Thank you for the wonderful lectures! Which textbook(s) do you use for this course?
Thanks! I use Hiemenz and Lodge, Polymer Chemistry.
Sir can I have your email