Jedrzejowska Agnieszka, Grzybowski Andrzej, Paluch Marian
Institute of Physics, University of Silesia in Katowice, Uniwersytecka 4, 40-007 Katowice, Poland.
Phys Chem Chem Phys. 2017 Jul 19;19(28):18348-18355. doi: 10.1039/c7cp01144j.
In this paper, we report the nontrivial results of our investigations of dynamic and thermodynamic moduli in search of invariants for viscous liquids in the density scaling regime by using selected supercooled van der Waals liquids as representative materials. Previously, the dynamic modulus M (defined in the pressure-temperature representation by the ratio of isobaric activation energy and activation volume) as well as the ratio B/M (where B is the thermodynamic modulus defined as the inverse isothermal compressibility) have been suggested as some kinds of material constants. We have established that they are not valid in the explored wide range of temperatures T over a dozen decades of structural relaxation times τ. The temperature dependences of M and B/M have been elucidated by comparison with the well-known measure of the relative contribution of temperature and density fluctuations to molecular dynamics near the glass transition, i.e., the ratio of isochoric and isobaric activation energies. Then, we have implemented an idea to transform the definition of the dynamic modulus M from the p-T representation to the V-T one. This idea relied on the disentanglement of combined temperature and density fluctuations involved in isobaric parameters and has resulted in finding an invariant for viscous liquids in the density scaling regime, which is the ratio of thermodynamic and dynamic moduli, B/M. In this way, we have constituted a characteristic of thermodynamics and molecular dynamics, which remains unchanged in the supercooled liquid state for a given material, the molecular dynamics of which obeys the power density scaling law.
在本文中，我们报告了通过使用选定的过冷范德瓦尔斯液体作为代表性材料，在密度标度范围内寻找粘性液体不变量的动态和热力学模量研究的重要结果。此前，动态模量M（在压力-温度表示中定义为等压活化能与活化体积之比）以及B/M之比（其中B是定义为等温压缩率倒数的热力学模量）已被提议作为某种材料常数。我们已经确定，在跨越十几个数量级的结构弛豫时间τ的广泛温度T范围内，它们是无效的。通过与玻璃化转变附近温度和密度涨落对分子动力学相对贡献的著名度量，即等容和等压活化能之比进行比较，阐明了M和B/M的温度依赖性。然后，我们实施了一个想法，将动态模量M的定义从p-T表示转换为V-T表示。这个想法依赖于对等压参数中涉及的温度和密度涨落组合的解缠，并导致在密度标度范围内找到了粘性液体的一个不变量，即热力学模量与动态模量之比B/M。通过这种方式，我们构建了一种热力学和分子动力学的特征，对于给定的材料，在过冷液态中保持不变，其分子动力学服从幂密度标度律。
