Liao CY, Chen SH, Sette F
Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):1518-26. doi: 10.1103/physreve.61.1518.
We analyze a set of high-resolution inelastic x-ray scattering (IXS) spectra from H2O measured at T=259, 273, and 294 K using two different phenomenological models. Model I, called the "dynamic cage model," combines the short time in-cage dynamics described by a generalized Enskog kinetic theory with a long-time cage relaxation dynamics described by an alpha relaxation. This model is appropriate for supercooled water where the cage effect is dominant and the existence of an alpha relaxation is evident from molecular-dynamics (MD) simulation data of extended simple point charge (SPC/E) model water. Model II is essentially a generalized hydrodynamic theory called the "three effective eigenmode theory" by de Schepper et al. 11. This model is appropriate for normal liquid water where the cage effect is less prominent and there is no evidence of the alpha relaxation from the MD data. We use the model I to analyze IXS data at T=259 K (supercooled water). We successfully extract the Debye-Waller factor, the cage relaxation time from the long-time dynamics, and the dispersion relation of high-frequency sound from the short time dynamics. We then use the model II to analyze IXS data at all three temperatures, from which we are able to extract the relaxation rate of the central mode and the damping of the sound mode as well as the dispersion relation for the high-frequency sound. It turns out that the dispersion relations extracted from the two models at their respective temperatures agree with each other giving the high-frequency sound speed of 2900+/-300 m/s. This is to be compared with a slightly higher value reported previously, 3200+/-320 m/s, by analyzing similar IXS data with a phenomenological-damped harmonic oscillator model 22. This latter model has traditionally been used exclusively for the analysis of inelastic scattering spectra of water. The k-dependent sound damping and central mode relaxation rate extracted from our model analyses are compared with the known values in the hydrodynamic limit.
我们使用两种不同的唯象模型分析了在T = 259、273和294 K下测量的一组来自H₂O的高分辨率非弹性X射线散射（IXS）光谱。模型I，称为“动态笼模型”，将由广义恩斯科格动力学理论描述的短时间笼内动力学与由α弛豫描述的长时间笼弛豫动力学相结合。该模型适用于过冷水，其中笼效应占主导，并且从扩展简单点电荷（SPC/E）模型水的分子动力学（MD）模拟数据中可以明显看出α弛豫的存在。模型II本质上是一种广义流体动力学理论，被德·谢珀等人称为“三种有效本征模理论”。该模型适用于普通液态水，其中笼效应不太突出，并且MD数据中没有α弛豫的证据。我们使用模型I分析T = 259 K（过冷水）时的IXS数据。我们成功地从长时间动力学中提取了德拜-瓦勒因子、笼弛豫时间，并从短时间动力学中提取了高频声的色散关系。然后我们使用模型II分析所有三个温度下的IXS数据，从中我们能够提取中心模的弛豫率和声模的阻尼以及高频声的色散关系。结果表明，在各自温度下从两个模型中提取的色散关系相互吻合，给出的高频声速为2900±300 m/s。这与之前通过使用唯象阻尼谐振子模型分析类似IXS数据报道的略高的值3200±320 m/s进行比较。后一种模型传统上一直专门用于分析水的非弹性散射光谱。我们从模型分析中提取的与k相关的声阻尼和中心模弛豫率与流体动力学极限中的已知值进行了比较。
