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The glass transition of amorphous polymers: About a continuous equation of state and its derivatives

机译：无定形聚合物的玻璃化转变：关于状态的连续等式及其衍生物

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摘要

Describing the pressure-volume-temperature (PVT) behavior of polymers is often hindered due to limitations of models and theories. In this work, we propose the logistic function to derive a phenomenological equation of state (EOS) that overcomes these limitations. Without dividing the temperature domain into several intervals, this continuous EOS describes the PVT behavior of amorphous polymers in the equilibrium state, the vitreous state and at glass transition. Discontinuities at glass transition are inherently eliminated. The EOS is continuously differentiable with respect to temperature and pressure. The thermal expansion coefficient and compression modulus thus can be determined at any valid reference state. The EOS linearly depends on temperature both in the equilibrium state and vitreous state. Furthermore, a parameter of the EOS is interpreted as the pressure-dependent glass transition temperature. Using PVT data of polyethersulfone (PES), measured in the temperature range of 20 - 360 degrees C and pressure range of 10 - 200 MPa in both the isobaric and standard isothermal mode, the validity of the EOS is discussed. Polymer processing simulation and solid mechanics benefit from the EOS and its derivatives, respectively. In addition, the EOS can be used to determine the glass transition temperature from PVT data.
机译：由于模型和理论的局限性，描述聚合物的压力-体积-温度（PVT）行为常常受到阻碍。在这项工作中，我们提出了逻辑函数来推导克服这些限制的唯象状态方程（EOS）。在不将温度域划分为几个区间的情况下，这种连续状态方程描述了非晶态聚合物在平衡态、玻璃态和玻璃化转变时的PVT行为。玻璃化转变的不连续性本质上被消除。EOS在温度和压力方面是连续可微的。因此，可以在任何有效参考状态下确定热膨胀系数和压缩模量。在平衡态和玻璃态下，物态方程与温度呈线性关系。此外，EOS的一个参数被解释为与压力有关的玻璃化转变温度。利用聚醚砜（PES）的PVT数据，在20-360°C的温度范围和10-200 MPa的压力范围内，在等压和标准等温模式下测量，讨论了EOS的有效性。聚合物加工模拟和固体力学分别受益于EOS及其衍生物。此外，EOS可用于根据PVT数据确定玻璃化转变温度。

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