Becker Torsten, Smith Jeremy C
Computational Molecular Biophysics, Interdisciplinary Center for Computational Science (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 1):021904. doi: 10.1103/PhysRevE.67.021904. Epub 2003 Feb 18.
Incoherent neutron scattering is widely used to probe picosecond-nanosecond time scale dynamics of molecular systems. In systems of spatially confined atoms the relatively high intensity of elastic incoherent neutron scattering is often used to obtain a first estimate of the dynamics present. For many complex systems, however, experimental elastic scattering is difficult to interpret unambiguously using analytical dynamical models that go beyond the determination of an average mean-square displacement. To circumvent this problem a description of the scattering is derived here that encompasses a variety of analytical models in a common framework. The framework describes the time-converged part of the dynamic structure factor [the elastic incoherent scattering function (EISF)] and lends itself to practical use by explicitly incorporating effects due to the finite energy resolution of the instrument used. The dependence of the elastic scattering on wave vector is examined, and it is shown how heterogeneity in the distribution of mean-square displacements can be related to deviations of the scattering from Gaussian behavior. In this case, a correction to fourth order in the scattering vector can be used to extract the variance of the distribution of mean-square displacements. The formalism is used in a discussion of measurements on dynamics accompanying the glass transition in molecular systems. By fitting to experimental data obtained on a protein solution the present methodology is used to show how the existence of a temperature-dependent relaxation frequency can lead to a transition in the measured mean-square displacement in the absence of an EISF change.
非相干中子散射被广泛用于探测分子系统皮秒至纳秒时间尺度的动力学。在空间受限原子的系统中，弹性非相干中子散射的相对高强度常被用于初步估计存在的动力学。然而，对于许多复杂系统，使用超出平均均方位移测定的解析动力学模型来明确解释实验弹性散射是困难的。为解决这个问题，本文推导了一种散射描述，它在一个通用框架中涵盖了多种解析模型。该框架描述了动态结构因子的时间收敛部分[弹性非相干散射函数（EISF）]，并通过明确纳入所用仪器有限能量分辨率的影响而便于实际应用。研究了弹性散射对波矢的依赖性，并展示了均方位移分布中的不均匀性如何与散射偏离高斯行为相关。在这种情况下，散射矢量的四阶校正可用于提取均方位移分布的方差。该形式体系用于讨论分子系统中伴随玻璃化转变的动力学测量。通过拟合在蛋白质溶液上获得的实验数据，本方法用于展示温度依赖的弛豫频率的存在如何在EISF不变的情况下导致测量的均方位移发生转变。
