Using a minimal algebraic model for the thermodynamics of binary rod-polymer mixtures, we provide evidence for a quintuple phase equilibrium; an observation that seems to be at odds with the Gibbs phase rule for two-component systems. Our model is based on equations of state for the relevant liquid crystal phases that are in quantitative agreement with computer simulations. We argue that the appearance of a quintuple equilibrium, involving an isotropic fluid, a nematic and smectic liquid crystal, and two solid phases, can be reconciled with a generalized Gibbs phase rule in which the two intrinsic length scales of the athermal colloid-polymer mixture act as additional field variables.

中文翻译：

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违反吉布斯相位定律：胶体-聚合物混合物中熵驱动的五元点的证据

使用最小代数模型计算二元棒-聚合物混合物的热力学，我们提供了五重相平衡的证据。这种观察似乎与两组分系统的吉布斯相位定律不一致。我们的模型基于相关液晶相的状态方程，这些方程与计算机模拟在数量上是一致的。我们认为，包含各向同性流体，向列和近晶液晶以及两个固相的五元组平衡的出现可以与广义的吉布斯相变规则相协调，在该规则中，无热胶体-聚合物混合物的两个固有长度尺度充当其他字段变量。