三元Polymer溶液中的质热扩散：经典不可逆热力学方法
Mass and Heat Diffusion in Ternary Polymer Solutions: A Classical Irreversible Thermodynamics Approach
摘要：
在经典不可逆热力学的框架下，利用Onsager变分原理推导了三组分体系中浓度和温度演化的控制方程，并给出了溶剂/溶剂/聚合物和溶剂/聚合物/聚合物体系的控制方程。推导是从平衡热力学的吉布斯方程出发，利用局部平衡假设、Onsager互易关系和力学平衡系统的Prigogine定理。结果表明，在三元系中的质量和热扩散现象的细节是完全由一个3 × 3矩阵，其条目是质量扩散系数（4个条目），热扩散系数（2个条目）和三个条目，描述在系统中的热的演变。扩散矩阵的元素与Onsager矩阵的元素有关，Onsager矩阵的元素被一些约束约束所限制，以满足系统中熵产生的正定性。扩散矩阵的所有元素都表示为组分交换化学势对浓度和温度的导数。由控制方程导出了三元高分子溶液的旋节曲线，并用自由能量密度的Hessian函数检验了其正确性。此外，还证明了将交叉扩散系数设为零会产生矛盾，没有交叉扩散系数的控制方程不能表达系统的实际相行为.
英文摘要：
Governing equations for evolution of concentration and temperature in three-component systems were derived in the framework of classical irreversible thermodynamics using Onsager variational principle and were presented for solvent/solvent/polymer and solvent/polymer/polymer systems. The derivation was developed from the Gibbs equation of equilibrium thermodynamics using the local equilibrium hypothesis, Onsager reciprocal relations and Prigogine theorem for systems in mechanical equilibrium. It was shown that the details of mass and heat diffusion phenomena in a ternary system are completely expressed by a 3x3 matrix whose entries are mass diffusion coefficients (4 entries), thermal diffusion coefficients (2 entries) and three entries that describe the evolution of heat in the system. The entries of the diffusion matrix are related to the elements of Onsager matrix that are bounded by some constraints to satisfy the positive definiteness of entropy production in the system. All the elements of diffusion matrix were expressed in terms of derivatives of exchange chemical potentials of the components with respect to concentration and temperature. The spinodal curves of ternary polymer solutions were derived from the governing equations and their correctness was checked by the Hessian of free energy density. Moreover, it was proved that setting cross-diffusion coefficients to zero results in a contradiction, and, the governing equations without cross-diffusion coefficients do not express the actual phase behavior of the system.
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