在密度标度范围内寻找粘性液体的不变量：动力学和热力学模量的研究
In search of invariants for viscous liquids in the density scaling regime: Investigations of dynamic and thermodynamic moduli
摘要：
在本文中，我们报告的非平凡的结果，我们的调查的动力学和热力学模量在寻找不变量的粘性液体的密度标度制度，使用选定的过冷范德华液体作为代表材料。以前，动态模量$M_{p-T}$（在压力-温度表示中由等压活化能和活化体积的比率定义）以及比率$B_{T}/M_{p-T}$（其中$B_T$是定义为逆等温压缩率的热力学模量）已经被建议为某种材料常数。我们已经确定，他们是无效的，在探索广泛的温度范围$T$超过几十年的结构弛豫时间$τ$。$M_{p-T}$和$B_T/M_{p-T}$的温度依赖性已经通过与众所周知的温度和密度波动对接近玻璃化转变的分子动力学的相对贡献的测量进行比较而阐明，即，等容和等压活化能之比，$E^{act}_{V}/E^{act}_{p}$。然后，我们实现了一种思想，将动态模量$M_{p-T}$的定义从p-T表示转换为V-T表示。这个想法依赖于在等压参数中涉及的组合温度和密度波动的解纠缠，导致在密度标度制度中找到粘性液体的不变量，这是热力学和动力学模量的比率，$B_{T}/M_{V-T}$。这样，我们就建立了热力学和分子动力学的一个特征，对于给定的物质，该特征在过冷液体下保持不变，其分子动力学服从功率密度标度律。
英文摘要：
In this paper, we report on 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 $M_{p-T}$ (defined in the pressure-temperature representation by the ratio of isobaric activation energy and activation volume) as well as the ratio $B_{T}/M_{p-T}$ (where $B_T$ is the thermodynamic modulus defined as the inverse isothermal compressibility) have been suggested as some kind of material constants. We have established that they are not valid in the explored wide range of temperatures $T$ over dozen decades of structural relaxation times $τ$. The temperature dependences of $M_{p-T}$ and $B_T/M_{p-T}$ 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 the isochoric and isobaric activation energies, $E^{act}_{V}/E^{act}_{p}$. Then, we have implemented an idea to transform the definition of the dynamic modulus $M_{p-T}$ 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 has resulted in finding an invariant for viscous liquids in the density scaling regime, which is the ratio of the thermodynamic and dynamic moduli, $B_{T}/M_{V-T}$. 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.
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