On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data

The Journal of Chemical Physics
David S RossCarl V Lutzer

Abstract

In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie l...Continue Reading

Citations

Dec 22, 2010·Proceedings of the National Academy of Sciences of the United States of America·Priya R BanerjeeJayanti Pande
Oct 5, 2013·The Journal of Chemical Physics·Chris W WahleGeorge M Thurston
Jul 27, 2012·The Journal of Chemical Physics·Chris W WahleGeorge M Thurston
Jul 27, 2012·The Journal of Chemical Physics·Chris W WahleGeorge M Thurston
Feb 10, 2017·The Journal of Chemical Physics·Michael M BellGeorge M Thurston

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Methods Mentioned

BETA
light scattering
neutron scattering

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