Center for Studies in Physics and Biology, The Rockefeller University, 1230 York Avenue, New York, NY 10021, USA.
Proc Natl Acad Sci U S A. 2009 Dec 29;106(52):22130-4. doi: 10.1073/pnas.0911094106. Epub 2009 Dec 14.
We introduce the space-dependent correlation function C (Q)(r) and time-dependent autocorrelation function C (Q)(t) of the local tetrahedral order parameter Q identical with Q(r,t). By using computer simulations of 512 waterlike particles interacting through the transferable interaction potential with five points (TIP5 potential), we investigate C (Q)(r) in a broad region of the phase diagram. We find that at low temperatures C (Q)(t) exhibits a two-step time-dependent decay similar to the self-intermediate scattering function and that the corresponding correlation time tau(Q) displays a dynamic cross-over from non-Arrhenius behavior for T > T (W) to Arrhenius behavior for T < T (W), where T (W) denotes the Widom temperature where the correlation length has a maximum as T is decreased along a constant-pressure path. We define a tetrahedral entropy S (Q) associated with the local tetrahedral order of water molecules and find that it produces a major contribution to the specific heat maximum at the Widom line. Finally, we show that tau(Q) can be extracted from S (Q) by using an analog of the Adam-Gibbs relation.
我们引入了局部四面体形参数 Q 相同的空间相关函数 C(Q)(r)和时间相关自相关函数 C(Q)(t)。通过对通过具有五个点的可传递相互作用势（TIP5 势）相互作用的 512 个类水粒子进行计算机模拟，我们在相图的广阔区域研究了 C(Q)(r)。我们发现，在低温下，C(Q)(t)表现出类似于自中间散射函数的两步时间相关衰减，并且相应的相关时间 tau(Q)显示出从非 Arrhenius 行为（对于 T > T(W)）到 Arrhenius 行为（对于 T < T(W)）的动态交叉，其中 T(W)表示当沿着恒压路径降低温度时关联长度具有最大值的 Widom 温度。我们定义了与水分子局部四面体形序相关的四面体熵 S(Q)，并发现它对 Widom 线上的比热最大值有很大的贡献。最后，我们表明 tau(Q)可以通过使用 Adam-Gibbs 关系的类似物从 S(Q)中提取出来。
