Inferring Gibbs Free Energies from Light Scattering Data
| Faculty: | David Ross |
| George Thurston | |
| Carl Lutzer | |
| Chris Wahle |
Summary:
In this work we use a well-established relation for light scattering from liquid mixtures as a second-order nonlinear partial differential equation, which relates the inverse Hessian of the intensive free energy to the efficiency of light scattered near the forward direction. For ternary mixtures, this PDE is
where
The dielectric coefficient, 
, and the Rayleigh ratio, 
are known experimentally as functions of the mole fractions x and y. The Widom form of the Gibbs free energy ensures that the second normal derivatives of 
are logarithmically singular at the boundaries of the mixture triangle. This condition acts as a boundary condition. We have devised an algorithm that allows us to solve the PDE with this boundary condition to determine .
Publications:
- On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data, D.S. Ross, G.M. Thurston and C.V. Lutzer, J. Chem. Phys. 129, 064106 (2008).
