Tanaka Hajime
Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 1):011505. doi: 10.1103/PhysRevE.68.011505. Epub 2003 Jul 18.
Generally, the entropy of the supercooled liquid decreases more rapidly than that of the crystal. Thus, the former, if we extrapolate it smoothly below the glass-transition temperature T(g), becomes equal to the latter at the so-called Kauzmann temperature T(K). Further extrapolation below T(K) leads to the unphysical situation that the entropy of disordered liquid is lower than the ordered crystal, which results in the violation of the third law of thermodynamics. This is known as the "Kauzmann paradox" which has been the key problem of liquid-glass transition for a long time. Here we propose a simple resolution of the Kauzmann paradox by answering a fundamental question of how deeply we can supercool a liquid. We argue that the lower metastable limit T(LML), below which a liquid should crystallize before its structural relaxation, is located above the Kauzmann temperature T(K). Thus, the entropy crisis at T(K) is naturally avoided by crystallization. We suggest that it is dynamic heterogeneity that destabilizes a deeply supercooled "equilibrium" liquid state as well as a glassy state against crystallization. This may have a significant implication on the stability of a glassy state, which is of industrial importance in relation to the storage of glassy material.
一般来说，过冷液体的熵比晶体的熵下降得更快。因此，如果我们将前者在玻璃化转变温度T(g)以下平滑外推，在所谓的考兹曼温度T(K)时它将等于后者。在T(K)以下进一步外推会导致无序液体的熵低于有序晶体这种不符合物理实际的情况，这就导致了热力学第三定律的违背。这就是所谓的“考兹曼悖论”，长期以来一直是液 - 玻璃转变的关键问题。在此，我们通过回答一个关于液体能够被过冷到何种程度的基本问题，提出了一种解决考兹曼悖论的简单方法。我们认为，较低的亚稳极限T(LML)，即在该温度以下液体在结构弛豫之前就会结晶，位于考兹曼温度T(K)之上。因此，通过结晶自然地避免了T(K)处的熵危机。我们认为，是动态非均匀性破坏了深度过冷的“平衡”液态以及玻璃态对结晶的稳定性。这可能对玻璃态的稳定性具有重要意义，而玻璃态的稳定性在玻璃材料的储存方面具有工业重要性。
