On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.
On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.
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利用偏微分方程方法从光散射数据确定三元混合物的自由能和共存相组成。
DOI：
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发表时间：
2008
影响因子：
4.4
通讯作者：
Carl Lutzer
中科院分区：
文献类型：
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作者：
D. Ross;G. Thurston;Carl Lutzer
本文提出了一种利用光散射数据确定三元混合物自由能的方法。我们使用一种适合于液体混合物的近似，我们将其表述为二阶非线性偏微分方程。该偏微分方程（PDE）将强自由能的黑森量与正向光散射效率联系起来。这个基本方程适用于相图中混合物热力学稳定的区域。在混合物不稳定或亚稳的区域，适当的偏微分方程是凸壳的非线性方程。我们将该方程与两个方程在云点轨迹上的过渡的连续性条件一起表述。我们展示了如何离散这个问题，以获得它的有限差分逼近，我们提出了一个迭代的方法来解决离散问题。我们给出了用实现我们方法的计算机程序完成的计算结果。这些计算表明，我们的方法能够从模拟光散射数据重建测试自由能函数。如果云点位置已知，该方法还可以找到描述两种或三种液相之间热力学平衡的系线和系三角形。一种解决这种偏微分方程问题的鲁棒方法，如本文所提出的方法，可以成为表征多组分混合物热力学的光学、非侵入性方法的基础。
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 lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.
影响因子：
8.6
作者：
Bloustine, J;Virmani, T;Fraden, S
通讯作者：
Fraden, S