MRI 本质上还是一维 NMR ，只不过多个方向上扫描。 二维 NMR 一般包括： correlation spectroscopy (COSY), J-spectroscopy, exchange spectroscopy (EXSY), and nuclear Overhauser effect spectroscopy (NOESY) 。 COSY 原理很简单，可以找出两个有关联的 chemical shift 。会出现 diagonal peaks 和 cross peaks 。 TOCSY （ Total correlation spectroscopy ）跟 COSY 很类似，但除了可以观测到直接关联的 cross peaks ，还可以观测到间接关联在一起的 cross peaks. 【历史】 The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at the Université Libre de Bruxelles, in 1971. (Theoretically) This experiment was later implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst (1991 Nobel prize), who published their work in 1976. Ernst出席了13届生物物理大会(IUPAB)，我参加的是第8届生物物理大会（IUPAP），不要混淆。 【 chemical shift 】 In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of a nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of amolecule . 参考复旦的实验原理！劈裂成两个方向，说明出现了类似 ising model 一样的两种自旋方向。当 RF 为二者之差时，低能向高能跃迁。 拉莫尔公式： 其中 γ 为旋磁比。进一步，原子核在磁场下的分裂的能级间距为： 质子的拉莫尔频率为 42.5MHz 。 Chemical shift δ is usually expressed in parts per million (ppm) ： 所以 ， 1ppm=1Hz per 100MHz ， 也就是 42.5Hz chemical shift。
碳，作为一种非常常见的元素，对有机物有着重要的意义。单质碳材料有零维，一维，二维和三维。这里主要介绍一下富勒烯，碳纳米管和石墨烯这三种材料。 富勒烯(巴基球，足球烯，Fullerene，C60)： 作为零维材料，在1985年英国H. W. Kroto和美国R. E. Smalley等人在氦气流中以激光汽化蒸发石墨实验中发现C60。由五元环、六元环等构成的封闭式空心球形或椭球形结构的共轭烯。 1985年文章 C60 Buckminsterfullerene 。 在碳纳米管发现之前，它是研究的热点，在生物和医学有着重要的意义。此外还有C78、C82、C84、C90、C96等。 碳纳米管(carbon naotubes) 作为一维纳米材料，自1991年被S. Iijima发现以来一直是研究的热点。根据层数可分为单壁(single-wall carbon nanotubes)和多壁(multiwall carbon nanotubes)。根据手性可分为非手性(armchair和zigzag)和手性(chiral)结构。中空结构，一般可认为是单层石墨卷曲而成。它在很多领域都有着广泛的应用和前景。正如美国Alex Zettl 教授说，就应用前景对C60和碳纳米管进行全面的比较，C60可以用一页纸概括，而碳纳米管需要一本书来完成。推荐一本书Physical properties of carbon nanotubes(R. Saito, G. Dresselhaus, and M.S. Dresselhaus 1998，Imperial College Press ，世图有卖：39元)。 The field of nanotubes is still rapidly growing. As emphasized, many questions are still unanswered. The dynamics of hot electrons (and electron-hole pairs) in optical experiments, the nature of the contact resistance at metallic electrode interfaces, the effect of an out-of- equilibrium phonon distribution on inelastic scattering, and the domain of existence of the Luttinger-liquid, charge-density-wave, and superconducting phases are still subjects which require a considerable amount of work and understanding. Further, and beyond the intrinsic properties of nanotubes, the physics of functionalized, chemisorbed, doped, or excited CNTs is driven by potential applications in molecular electronics, optoelectronics, and sensors. Such themes are still largely unexplored areas for theorists: while early theoretical papers preceded experiments on the discussion of the basic electronic properties of pristine tubes, such complex systems and applications have now been demonstrated experimentally and theory is lagging behind. The field of nanotubes has fostered much interest in related systems such as graphene or semiconducting nanowires.（摘自Rev. Mod. Phys., Vol. 79, No. 2，667-732，2007.见下面RMP文章）. Iijima91年Natrue文章 07年RMP综述文章 Electronic and transport properties of nanotubes 石墨烯(单层石墨，graphene) 作为二维材料，一般厚度方向为单原子层或双原子层碳原子。完美的石墨烯包括六角元胞(等角六边形)。2004年被英国A.K.Geim发现。石墨烯有众多优异的物理性质，在很多现象中有很多异常的行为如整数量子霍尔效应，准粒子激发谱可用2+1维无质量的相对论Dirac方程描述等等。近几年研究的特别热。 Graphene is a unique system in many ways. It is truly 2D, has unusual electronic excitations described in terms of Dirac fermions that move in a curved space, is an interesting mix of a semiconductor (zero density of states) and a metal (gaplessness), and has properties of soft matter. The electrons in graphene seem to be almost insensitive to disorder and electron-electron interactions and have very long mean free paths. Hence, graphene's properties are different from what is found in usual metals and semiconductors. Graphene has also a robust but flexible structure with unusual phonon modes that do not exist in ordinary 3D solids. In some sense, grapheme brings together issues in quantum gravity and particle physics, and also from soft and hard condensed matter. Interestingly enough, these properties can be easily modified with the application of electric and magnetic fields, addition of layers, control of its geometry, and chemical doping. Moreover, graphene can be directly and relatively easily probed by various scanning probe techniques from mesoscopic down to atomic scales, because it is not buried inside a 3D structure. This makes graphene one of the most versatile systems in condensed-matter research。（摘自Rev. Mod. Phys., Vol. 81,No. 1,109-162,2009.文章见下面）. 09年RMP综述文章 The electronic properties of graphene
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