Corsi Andrea, Gujrati P D
Department of Polymer Science, The University of Akron, Akron, Ohio 44325, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 1):031502. doi: 10.1103/PhysRevE.68.031502. Epub 2003 Sep 5.
We investigate an extension of the lattice model of melting of semiflexible polymers originally proposed by Flory. Along with a bending penalty epsilon, present in the original model and involving three sites of the lattice, we introduce an interaction energy epsilon (p), corresponding to the presence of a pair of parallel bonds and an interaction energy epsilon (h), associated with a hairpin turn. Both these new terms represent four-site interactions. The model is solved exactly on a Husimi cactus, which approximates a square lattice. We study the phase diagram of the system as a function of the energies. For a proper choice of the interaction energies, the model exhibits a first-order melting transition between a liquid and a crystalline phase at a temperature T(M). The continuation of the liquid phase below T(M) gives rise to a supercooled liquid, which turns continuously into a new low-temperature phase, called metastable liquid, at T(MC)<T(M). This liquid-liquid transition seems to have some features that are characteristic of the critical transition predicted by the mode-coupling theory. The exact calculation provides a thermodynamic justification for the entropy crisis (entropy becoming negative), generally known as the Kauzmann paradox, caused by the rapid drop of the entropy near the Kauzmann temperature. It occurs not in the supercooled liquid, but in the metastable liquid phase since its Helmholtz free energy equals the absolute zero equilibrium free energy at a positive temperature. A continuous ideal glass transition occurs to avoid the crisis when the metastable liquid entropy, and not the excess entropy, goes to zero. The melting transition in the original Flory model, corresponding to the vanishing of the four-site interactions, appears as a tricritical point of the model.
我们研究了弗洛里最初提出的半柔性聚合物熔化晶格模型的一种扩展。除了原始模型中存在的、涉及晶格三个位点的弯曲罚分ε外，我们引入了与一对平行键的存在相对应的相互作用能ε(p)以及与发夹弯相关的相互作用能ε(h)。这两个新项均代表四点相互作用。该模型在近似于正方形晶格的胡西米仙人掌图上得到了精确求解。我们研究了该系统作为能量函数的相图。对于相互作用能的适当选择，该模型在温度T(M)下表现出液相和晶相之间的一级熔化转变。液相在T(M)以下的延续产生了过冷液体，它在T(MC)<T(M)时连续转变为一种新的低温相，称为亚稳液体。这种液 - 液转变似乎具有一些模式耦合理论所预测的临界转变的特征。精确计算为熵危机（熵变为负）提供了热力学依据，熵危机通常被称为考兹曼悖论，它是由考兹曼温度附近熵的快速下降引起的。它并非发生在过冷液体中，而是发生在亚稳液相中，因为其亥姆霍兹自由能在正温度下等于绝对零平衡自由能。当亚稳液体熵而非过剩熵趋于零时，会发生连续的理想玻璃化转变以避免危机。原始弗洛里模型中的熔化转变对应于四点相互作用的消失，它表现为该模型的一个三临界点。
