Zhao Nanrong, Sugiyama Masaru, Ruggeri Tommaso
College of Chemistry, Sichuan University, Chengdu 610064, People's Republic of China.
J Chem Phys. 2008 Aug 7;129(5):054506. doi: 10.1063/1.2936990.
Dynamic phase transition induced by a shock wave in hard-sphere and hard-disk systems is studied on the basis of the system of Euler equations with caloric and thermal equations of state. First, Rankine-Hugoniot conditions are analyzed. The quantitative classification of Hugoniot types in terms of the thermodynamic quantities of the unperturbed state (the state before a shock wave) and the shock strength is made. Especially Hugoniot in typical two possible cases (P-1 and P-2) of the phase transition is analyzed in detail. In the case P-1 the phase transition occurs between a metastable liquid state and a stable solid state, and in the case P-2 the phase transition occurs through coexistence states, when the shock strength changes. Second, the admissibility of the two cases is discussed from a viewpoint of the recent mathematical theory of shock waves, and a rule with the use of the maximum entropy production rate is proposed as the rule for selecting the most probable one among the possible cases, that is, the most suitable constitutive equation that predicts the most probable shock wave. According to the rule, the constitutive equation in the case P-2 is the most promising one in the dynamic phase transition. It is emphasized that hard-sphere and hard-disk systems are suitable reference systems for studying shock wave phenomena including the shock-induced phase transition in more realistic condensed matters.
基于具有热状态方程和热传导方程的欧拉方程组，研究了硬球和硬盘系统中冲击波引起的动态相变。首先，分析了兰金 - 于戈尼奥条件。根据未受扰动状态（冲击波前的状态）的热力学量和冲击强度，对休格尼奥类型进行了定量分类。特别详细分析了典型的两种可能的相变情况（P - 1和P - 2）下的休格尼奥曲线。在P - 1情况下，相变发生在亚稳态液态和稳定固态之间；在P - 2情况下，当冲击强度变化时，相变通过共存态发生。其次，从最近的冲击波数学理论的角度讨论了这两种情况的可接受性，并提出了使用最大熵产生率的规则，作为在可能情况中选择最可能情况的规则，即预测最可能冲击波的最合适本构方程。根据该规则，P - 2情况下的本构方程在动态相变中最有前景。强调硬球和硬盘系统是研究冲击波现象（包括更现实凝聚态中的冲击诱导相变）的合适参考系统。
