Polymer Free Volume and Its Connection to the Glass Transition,Macromolecules

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Polymer Free Volume and Its Connection to the Glass Transition
Macromolecules ( IF 5.1 ) Pub Date : 2016-05-23 00:00:00 , DOI: 10.1021/acs.macromol.6b00215
Ronald P. White ₁ , Jane E. G. Lipson ₁

Affiliation

In this Perspective we summarize the most widely used definitions of free volume and illustrate the differences between them, including the important distinction between total free volume and excess free volume. We discuss the implications when alternative estimates for free volume are inserted into relationships that connect experimentally measured properties (e.g., the viscosity) to free volume, such as those proposed by Doolittle, Fox and Flory, Simha and Boyer, Cohen and Turnbull, and Williams, Landel, and Ferry. Turning to the results of our own locally correlated lattice (LCL) model, we demonstrate, by analyzing data for a set of over 50 polymers, that our calculations for total percent free volume not only lead to a predictive relationship with experimental glass transition temperatures but also allow us to place the different definitions of free volume within a physical picture of what the proposed contributions represent. We find that melts go glassy upon reaching a “boundary” of minimum (total) percent free volume that depends roughly linearly on temperature. We interpret this boundary as being close to the T-dependent free volume associated with solid-like segmental vibrational motions. Since the LCL model is a first-principles thermodynamic theory, we are also able to link our free volume predictions to similar patterns that we find in the predicted entropy per theoretical segment. Our results are consistent with a picture wherein the difference in entropy between the melt (liquid) state and corresponding solid state vanishes as the glass transition is approached. This leads us to a new connection with the work of Adams and Gibbs, whose model reflects a similar vanishing of the configurational entropy. We conclude by discussing why the approach to the glassy state is best viewed as being controlled via the linked contributions of free volume and temperature.

中文翻译：

聚合物自由体积及其与玻璃化转变的关系

在本《观点》中，我们总结了最广泛使用的自由交易量定义，并说明了它们之间的区别，包括总自由交易量与超额交易量之间的重要区别。免费卷。我们讨论了将自由体积的替代估计值插入将实验测量的特性（例如粘度）与自由体积联系起来的关系时的含义，例如Doolittle，Fox和Flory，Simha和Boyer，Cohen和Turnbull和Williams提出的那些，Landel和Ferry。转到我们自己的局部相关晶格（LCL）模型的结果，我们通过分析一组50多种聚合物的数据证明，我们对总自由体积百分比的计算不仅导致与实验玻璃化转变温度的预测关系，而且还允许我们将不同的免费量定义放在拟议捐助所代表的物理图片中。我们发现，熔体达到最小（总）自由体积的“边界”时呈玻璃状，该体积大致上线性依赖于温度。我们认为此边界接近T依赖的自由体积，与固体分段振动运动相关。由于LCL模型是第一性原理热力学理论，所以我们也能够将我们的自由体积预测链接到在每个理论段的预测熵中找到的相似模式。我们的结果与一幅图片是一致的，其中随着接近玻璃化转变，熔体（液态）状态和相应的固态之间的熵差消失了。这使我们与亚当斯和吉布斯的工作有了新的联系，他们的模型反映了结构熵的相似消失。我们以讨论为什么玻璃态最好的方法是通过自由体积和温度的相互联系来控制来得出结论。

更新日期：2016-05-23

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