James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
J Chem Phys. 2013 Jun 21;138(23):234501. doi: 10.1063/1.4809991.
Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of a unique scaling function of the ratio ρ(γ)∕T, where ρ is the density, T is the temperature, and γ is a material dependent constant. Interest in the scaling is also heightened because the exponent γ enters prominently into considerations of the relative contributions to the dynamics from pressure effects (e.g., activation barriers) vs. volume effects (e.g., free volume). Although this scaling is clearly of great practical use, a molecular understanding of the scaling remains elusive. Providing this molecular understanding would greatly enhance the utility of the empirically observed scaling in assisting the rational design of materials by describing how controllable molecular factors, such as monomer structures, interactions, flexibility, etc., influence the scaling exponent γ and, hence, the dynamics. Given the successes of the generalized entropy theory in elucidating the influence of molecular details on the universal properties of glass-forming polymers, this theory is extended here to investigate the thermodynamic scaling in polymer melts. The predictions of theory are in accord with the appearance of thermodynamic scaling for pressures not in excess of ~50 MPa. (The failure at higher pressures arises due to inherent limitations of a lattice model.) In line with arguments relating the magnitude of γ to the steepness of the repulsive part of the intermolecular potential, the abrupt, square-well nature of the lattice model interactions lead, as expected, to much larger values of the scaling exponent. Nevertheless, the theory is employed to study how individual molecular parameters affect the scaling exponent in order to extract a molecular understanding of the information content contained in the exponent. The chain rigidity, cohesive energy, chain length, and the side group length are all found to significantly affect the magnitude of the scaling exponent, and the computed trends agree well with available experiments. The variations of γ with these molecular parameters are explained by establishing a correlation between the computed molecular dependence of the scaling exponent and the fragility. Thus, the efficiency of packing the polymers is established as the universal physical mechanism determining both the fragility and the scaling exponent γ.
许多玻璃形成液体表现出显著的热力学标度行为，其中动态特性，如粘度、弛豫时间和扩散常数，可以根据密度ρ(γ)∕T 的比值的唯一标度函数来描述，其中 ρ 是密度，T 是温度，γ 是与材料有关的常数。对这种标度的兴趣也增加了，因为指数 γ 突出地进入了对动力学的相对贡献的考虑，这些贡献来自于压力效应（例如，激活势垒）与体积效应（例如，自由体积）。尽管这种标度具有明显的实际用途，但对其分子理解仍然难以捉摸。提供这种分子理解将极大地增强经验观察到的标度在通过描述可控的分子因素，如单体结构、相互作用、柔韧性等，如何影响标度指数 γ，从而影响动力学，从而协助材料的合理设计方面的实用性。鉴于广义熵理论在阐明分子细节对玻璃形成聚合物的普遍性质的影响方面取得的成功，本文将该理论扩展到聚合物熔体的热力学标度研究中。理论的预测与压力不超过~50 MPa 时的热力学标度的出现是一致的。（在更高的压力下失败是由于晶格模型的固有限制。）与将 γ 的大小与分子间势能的排斥部分的陡峭度相关的论点一致，晶格模型相互作用的突然、方阱性质导致，正如预期的那样，标度指数的值大得多。然而，该理论被用于研究单个分子参数如何影响标度指数，以便从指数中提取分子理解的信息内容。发现链刚性、内聚能、链长和侧基长度都显著影响标度指数的大小，并且计算出的趋势与现有的实验很好地吻合。通过建立计算得出的标度指数的分子依赖性与脆性之间的相关性，解释了 γ 随这些分子参数的变化。因此，聚合物的包装效率被确立为决定脆性和标度指数 γ 的普遍物理机制。
