Anisotropic relaxation and motion of half-integer quadrupole nuclei studied by central transition nuclear magnetic resonance spectroscopy

An efficient theoretical formalism and advanced experimental methods are presented for studying the effects of anisotropic molecular motion and relaxation on solid-state central transition NMR spectra of half-integer quadrupole nuclei. The theoretical formalism is based on density operator algebra and involves the stochastic Liouville–von Neumann equation. In this approach the nuclear spin interactions are represented by the Hamiltonian while the motion is described by a discrete stochastic operator. The nuclear spin interactions fluctuate randomly in the presence of molecular motion. These fluctuations may stimulate the relaxation of the system and are represented by a discrete relaxation operator. This is derived from second-order perturbation theory and involves the spectral densities of the system. Although the relaxation operator is valid only for small time intervals it may be used recursively to obtain the density operator at any time. The spectral densities are allowed to be explicitly time dependent making the approach valid for all motional regimes. The formalism has been applied to simulate partially relaxed central transition ¹⁷O NMR spectra of representative model systems. The results have revealed that partially relaxed central transition lineshapes are defined not only by the nuclear spin interactions but also by anisotropic motion and relaxation. This has formed the basis for the development of central transition spin-echo and inversion-recovery NMR experiments for investigating molecular motion in solids. As an example we have acquired central transition spin-echo and inversion-recovery ¹⁷O NMR spectra of polycrystalline cristobalite (SiO₂) at temperatures both below and above the α–β phase transition. It is found that the oxygen atoms exhibit slow motion in α-cristobalite. This motion has no significant effects on the fully relaxed lineshapes but may be monitored by studying the partially relaxed spectra. The α–β phase transition is characterized by structural and motional changes involving a slight increase in the Si–O–Si bond angle and a substantial increase in the mobility of the oxygen atoms. The increase in the Si–O–Si angle is supported by the results of ¹⁷O and ²⁹Si NMR spectroscopy. The oxygen motion is shown to be orders of magnitude faster in β-cristobalite resulting in much faster relaxation and characteristic lineshapes. The measured oscillation frequencies are consistent with the rigid unit mode model. This shows that solid-state NMR and lattice dynamics simulations agree and may be used in combination to provide more detailed models of solid materials.     

A Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. In this paper, we show how commonly used NMR relaxation data (R(1), R(2), and NOE) obtained at two spectrometer frequencies can be analyzed using a Bayesian statistical approach to reliably detect and quantify the degree of rotational diffusion anisotropy. Our approach differs from previous methods in that it does not make assumptions concerning the internal motions experienced by the residues which are used to quantify the diffusion anisotropy, but rather averages the results over all internal motions consistent with the data. We demonstrate our method using synthetic data corresponding to isotropic, axially symmetric anisotropic, and fully asymmetric anisotropic rotational diffusion, as well as experimental NMR data. We compare the Bayesian statistical approach with a widely used method for extracting tumbling parameters using both synthetic and experimental data. While it can be difficult to separate the effects of chemical exchange from rotational anisotropy using this "standard" method, these effects are readily separated using Bayesian statistics. In addition, we find that the Bayesian statistical approach requires considerably less CPU time than an equivalent standard analysis.     

Flow-enhanced molecular reorientations and interfacial slip probed by field-cycling NMR relaxometry in microscopic pores

It is shown that hydrodynamic flow has an effect on spin-lattice relaxation in water filled into a porous monolithic silica material. This is a rotational analogue of translational hydrodynamic (or Taylor-Aris) dispersion arising from incoherent Brownian motion in combination with coherent flow. The effect is demonstrated with the aid of field-cycling NMR relaxometry and confirmed by theoretical considerations. The results directly verify bulk mediated surface diffusion and reveal interfacial slip at fluid-solid interfaces.     

High-resolution study of nuclear magnetic relaxation dispersion of purine nucleotides: effects of spin-spin coupling

By combining magnetic field cycling in the range from 0.1mT to 7T with high-resolution NMR detection the T(1) relaxation dispersion (nuclear magnetic relaxation dispersion (NMRD)) of protons in the nucleotides adenosine mono-phosphate and guanosine mono-phosphate was measured in a site-specific way. While at high field the individual spins have distinctly different T(1) times, their scalar spin-spin interaction fulfills at low field the condition of strong coupling and leads to convergence of their T(1) dispersion curves. In addition, the spin-spin coupling can lead to oscillatory components in the relaxation kinetics traceable to a coupling between spin polarization and coherence in the relaxation process. As a consequence the NMRD curves do not directly reflect the spectral density function of the motional processes, but the effects of motion and spin coupling must be separated for a reliable evaluation. A theoretical approach is described allowing such an analysis.     

Gravitomagnetic time-varying effects on the motion of a test particle

We study the effects of a time-varying gravitomagnetic field on the motion of test particles. Starting from recent results, we consider the gravitomagnetic field of a source whose spin angular momentum has a linearly time-varying magnitude. The acceleration due to such a time-varying gravitomagnetic field is considered as a perturbation of the Newtonian motion, and we explicitly evaluate the effects of this perturbation on the Keplerian elements of a closed orbit. The theoretical predictions are compared with actual astronomical and astrophysical scenarios, both in the solar system and in binary pulsars systems, in order to evaluate the impact of these effects on real systems.     

核磁共振扩散测量和q-空间成像进展(英文)

在过去的近半个世纪, NMR扩散测量在理论和实践方面都不断取得进展,使得测量更加可靠和准确,并能获取越来越多的信息.随着扩散测量技术的发展,其科学应用范围也不断增加,覆盖从物理化学到临床医学等各个领域. NMR扩散测量不仅能提供分子的平移运动动力学信息,而且也可以提供影响平移运动的局部几何结构的信息,后一种应用通常称为q-空间成像.该综述聚焦于过去10年中的NMR扩散研究方面一些重大的进展.     

影响空心旋转液体射流初始阶段运动的无量纲参数的分析

本文以描述空心旋转时流初始阶段运动规律的理论模型[1]为依据,重点讨论了影响射流运动的无量纲参数：韦伯数,液膜内外压力差,液膜初始内外环半径比,初始旋流度;初始径向速度等。从而进一步加深了对旋流喷嘴所产生的空心旋转射流初始阶段运动及发展规律的认识。     

Investigation of a sample-NMR sensor for relative motion

The present work is concerned with theoretical and experimental investigations of the parameters of a free nuclear induction signal when the direction of the exciting field changes along the motion trajectory of a liquid under study. The nuclear magnetic resonance (NMR) experiments are carried out in the geomagnetic field by use of special sensors, namely, a toroid and sensors having linear or cycle displacement of frame coils. The main theoretical approach is based on the usage of the signal of the free induction decay in the integral form derived from the reciprocity principle. The obtained results allowed us to define the physical origin of the NMR frequency shift and to propose a general analytic expression of this shift for the three sensors. The condition of the equality of the sample or sensor motion is proposed also.     

Quantum Discord in Nuclear Magnetic Resonance Systems at Room Temperature

We review the theoretical and the experimental researches aimed at quantifying or identifying quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We first overview, at the formal level, a method to determine the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we describe an experimental implementation of that method. Previous theoretical analysis of quantum discord decoherence had predicted the time dependence of the discord to change suddenly under the influence of phase noise. The experiment attests to the robustness of the effect, sufficient to confirm the theoretical prediction even under the additional influence of a thermal environment. Finally, we discuss an observable witness for the quantumness of correlations in two-qubit systems and its first NMR implementation. Should the nature, not the amount, of the correlation be under scrutiny, the witness offers the most attractive alternative.     

Volume-exclusion effects in tethered-particle experiments: bead size matters

We give a theoretical analysis of bead motion in tethered-particle experiments, a single-molecule technique that has been used to explore the dynamics of a variety of macromolecules of biological interest. Our analysis reveals that the proximity of the tethered bead to a nearby surface gives rise to a volume-exclusion effect, resulting in an entropic stretching-force on the molecule that changes its statistical properties. In addition, volume exclusion brings about intriguing scaling relations between key observables (statistical moments of the bead) and parameters such as bead size and contour length of the molecule. We present analytic and numerical results for these effects in both flexible and semiflexible tethers. Finally, our results give a precise, experimentally testable prediction for the probability distribution of the bead center measured from the polymer attachment point.     

用异核多维NMR技术研究蛋白质动力学

蛋白质在溶液中的三维空间结构、动力学与蛋白质生物功能的关系是在分子水平上理解生命现象的重要基础. NMR技术在研究蛋白质动力学方面具有独特的优势,所能表征的运动过程相关时间尺度很广. 文章综述了异核多维NMR技术研究蛋白质动力学的实验技术和理论方法,介绍了描述蛋白质动力学的内运动参量的意义和Model-Free 方法,并举例说明¹⁵N弛豫测量实验被用于研究蛋白质及其与配体复合物的动力学.      

Effects of localized impurity on a dark soliton in a Bose--Einstein condensate with an external magnetic trap

The dynamics of a dark soliton has been investigated in a Bose--Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.     

湍流理论的近代发展

这篇论文的内容是关於不可压缩流体的湍流理论近代发展的综合性介绍舆分析。我们首先评述了根据Reynolds的平均运动方程所建立的混合长度理论。其次,分析关於均匀各向同性湍流的主要理论工作。第三,讨论了运用Reynolds的平均运动方程和根据速度涨落方程求得的速度关联函数的动力学方程来处理具有Reynolds剪应力的普通湍流运动问题。同时说明这个方法虽然能够给出比混合长度理论舆实验较为接近的理论结果并能提出速度涨落平方平均值的理论分布,但是由於在求出的速度关联的动力学方程中出现高次元的速度关联,它继续地导致不封闭的微分方程组因而遇到不易克服的困难。因此,从以上湍流理论发展的回顾和最近关於均匀各向同性湍流在后期衰变运动的涡性结构工作,我们在最后提出了对今后湍流理论研究工作的新看法:湍流运动的基本组成部分是流体粘性作用所引起的涡旋运动;这个涡旋运动的动力学根据是用平均的方法后Navier-Stokes方程所导出的Reyonlds的平均运动方程典带度涨落方程。我们并着重说明Reynolds认识到湍流运动可分作平均运动与涨落运动的重要性。今后的理论工作则在於求这两组动力学方程的涡旋运动解,而这种类型的解并须满足像Колмогоров在高Reynolds数运动的局部各向同性湍流理论中所提出的统计条件,方能使解满足惟一性并可舆实验结果相比较。     

Effects of various types of molecular dynamics on 1D and 2D (2)H NMR studied by random walk simulations

By carrying out random walk simulations we systematically study the effects of various types of complex molecular dynamics on (2)H NMR experiments in solids. More precisely, we calculate one-dimensional (1D) (2)H NMR spectra and the results of two dimensional (2D) (2)H NMR experiments in time domain, taking into account isotropic as well as highly restricted motions which involve rotational jumps about different finite angles. Although the dynamical models are chosen to mimic the primary and secondary relaxation in supercooled liquids and glasses, we do not intend to describe experimental results quantitatively but rather to show general effects appearing for complex reorientations. We carefully investigate whether 2D (2)H NMR in time domain, which was originally designed to measure correlation times of ultraslow motions (tau >/= 1 ms), can be used to obtain shorter tau, too. It is demonstrated that an extension of the time window to tau >/= 10 &mgr;s is possible when dealing with exponential relaxation, but that it will fail if there is a distribution of correlation times G(lgtau). Vice versa, we show that 1D (2)H NMR spectra, usually recorded to look at dynamics with tau in the microsecond regime, are also applicable for studying ultraslow motions provided that the loss of correlation is achieved step by step. Therefore, it is useful to carry out 1D and 2D NMR experiments simultaneously in order to reveal the mechanism of complex molecular motions. In addition, we demonstrate that highly restricted dynamics can be clearly observed in 1D spectra and in 2D NMR in time domain if long solid-echo delays and large evolution times are applied, respectively. Finally, unexpected observations are described which appear in the latter experiment when considering very broad distributions G(lgtau). Because of these effects, time scale and geometry of a considered motion cannot be extracted from a straightforward analysis of experimental results. Copyright 2000 Academic Press.     

Dynamics of vortex dipoles in confined Bose-Einstein condensates

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.     

典型高分子材料的固体核磁共振研究

本论文通过固体核磁共振（NMR）谱及动力学参量的测量,并结合X-射线衍射技术和DSC测量等研究了两种典型高分子材料的相结构、链的运动以及相与相之间的关系.  乙烯-醋酸乙烯共聚物( EVA) 是最主要的乙烯共聚物之一. 研究发现,EVA的相组成非常复杂,共有5个不同的组分. 除了PE中所观察到的常规单斜晶相和刚性的正交晶相外,我们发现还存在第三个晶相分量－运动性较强的晶相（SOCP,可能是转动相）. 它不仅拥有自己的熔点,而且它的化学位移和分子运动性不同于刚性正交晶相（LOCP）. 另一方面,非晶相也由两种不同的分量组成：运动受限的各相异性的非晶界面相和高度可动的橡胶型的非晶相. 我们进一步详细研究了EVA中的晶区链动力学和非晶区的低温冻结行为. 实验发现,在正交晶相中,高分子链以180° flip-flop方式运动,同时伴随沿链方向的平移型跳跃运动,并引起正交晶相和非晶相之间的长程链扩散,通过NOE的测量证实了这种相间链扩散的存在,并进一步通过实验证实这种相间链扩散是一种受限扩散而不是自由扩散. 同时非晶相的两个组分具有不同的低温冻结行为：当温度低于-弛豫转变温度时,橡胶型的非晶相中的长程分子运动被冻结,但仍存在分子的局域运动;而界面非晶在低温时冻结成一种有序取向结构,并用质子自旋扩散实验证实该有序结构与正交晶相相邻近.  少量纳米级片层状粘土分散在聚合物中就可赋予材料许多优异的性能,我们用固体NMR技术对EVA/REC复合材料的结构和其中粘土的分散性质进行研究,发现上述复合材料中所形成的晶体类型不仅依赖于各组分的性质还依赖于所形成的复合材料的类型.  偏氟乙烯/三氟乙烯共聚物（P（VDF-TrFE））是最主要的铁电高聚物之一. 我们利用变温固体¹⁹F MAS NMR 谱及弛豫数据的测量详细研究了电子辐照对P(VDF-TrFE)共聚物的分子结构、构型、运动性以及相变等的影响. 发现,电子辐照不仅改变了分子链段的构型和运动性,同时也改变了局部分子化学结构. 电子辐照促使铁电相向顺电相(或者非晶相)转变,与此同时诱发了富含VDF和含-TrFE链段从全反式的构型到混合的反式-旁式构型的转变. 电子辐照加剧顺电区域中的分子运动而在高温熔融态中(>100 ℃）,分子的运动反而受限.     

Time-dependence of nuclear magnetic resonance quadrupole interactions for polymers under shear

We consider the problem of performing NMR spectroscopy under conditions of flow, a central issue in Rheo-NMR. By way of example, the effects of rotational motion on the deuterium NMR spectrum are considered for Couette cell experiments involving deformation of polymers under shearing conditions. The polymer was modelled as a power law fluid and for each streamline, the spin Hamiltonian evolved to allow for flow reorientation. The gap-integral spectra are compared with the 'ideal' spectra for a polymer under shear, but without reorientation. It is found that flow does affect the shape of the deuterium spectra, as well as slightly perturbing the splittings.     

NMR studies of carrier-mediated transport across lipid bilayer membranes

Two theoretical models are presented which show how the various kinetic steps involved in transport across lipid bilayer membranes affect NMR spectral lineshapes and relaxation times. The first model applies whenever the transported material moves across the membrane by restricted diffusion. The second model applies when the motion can be described as a jump between membrane interfaces. Both carrier-mediated and carrier-independent cases are treated. Special attention is given to the effects of relaxation in the membrane and to morphology. Exact analytical solutions for the simplest one-dimensional geometry are presented. More complicated morphologies are best treated numerically.     

Four‐component relativistic chemical shift calculations of halogenated organic compounds

The calculation of nuclear magnetic resonance (NMR) properties of organic compounds with heavy elements has been a computational challenge due to the importance of relativistic effects and the cost of relativistic calculations capable of capturing these effects. The heavy‐atom effect on the chemical shift of light atoms also challenges the interpretation of NMR spectra of organic compounds, since relativistic effects can affect the predicted values of protons bonded to heavy atoms by as much as 20 ppm. Here, we investigate the chemical shifts of six organic compounds with/without halogen atoms using non‐relativistic and state‐of‐the‐art four‐component relativistic methods, comparing the results to available experimental data. Our study confirms the importance of relativistic effects in modeling NMR properties of organic compounds involving heavy atoms and shows that these effects cannot be properly described by non‐relativistic methods. We also demonstrate that relativistic four‐component calculations of NMR chemical shifts now have reached a level of maturity that allows these methods to be used routinely in theoretical studies of NMR properties of large organic compounds containing heavy elements. The accuracy of these calculations is high enough to allow them to be used in assisting in the structural characterization of natural compounds. Comparison of the GGA functionals used in the four‐component relativistic density functional theory calculations shows that the PBE functional seems to be well suited for such studies. Copyright © 2013 John Wiley & Sons, Ltd.