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95-571: The results from AGASA were used to calculate the energy spectrum and anisotropy of cosmic rays. The results helped to confirm the existence of ultra-high energy cosmic rays ( > 5 × 10 eV ), such as the so-called " Oh-My-God " particle that was observed by the Fly's Eye experiment run by the University of Utah . The Telescope Array , a merger of the AGASA and High Resolution Fly's Eye (HiRes) groups, and

190-422: A r = G E / [ 2 ( 1 + ν ) ] = 2 ( 1 + ν ) G E ≡ 2 C 44 C 11 − C 12 . {\displaystyle a_{r}={\frac {G}{E/[2(1+\nu )]}}={\frac {2(1+\nu )G}{E}}\equiv {\frac {2C_{44}}{C_{11}-C_{12}}}.} The latter expression

285-464: A molecule , particularly for molecules that are too complicated to work with using one-dimensional NMR. The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at Université Libre de Bruxelles, in 1971. This experiment was later implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst , who published their work in 1976. A variety of physical circumstances do not allow molecules to be studied in solution, and at

380-408: A plasma , so that its magnetic field is oriented in a preferred direction. Plasmas may also show "filamentation" (such as that seen in lightning or a plasma globe ) that is directional. An anisotropic liquid has the fluidity of a normal liquid, but has an average structural order relative to each other along the molecular axis, unlike water or chloroform , which contain no structural ordering of

475-576: A better sensitivity and higher resolution of the peaks, and it is preferred for research purposes. Credit for the discovery of NMR goes to Isidor Isaac Rabi , who received the Nobel Prize in Physics in 1944. The Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared

570-544: A difficult quantity to calculate. In remote sensing applications, anisotropy functions can be derived for specific scenes, immensely simplifying the calculation of the net reflectance or (thereby) the net irradiance of a scene. For example, let the BRDF be γ ( Ω i , Ω v ) {\displaystyle \gamma (\Omega _{i},\Omega _{v})} where 'i' denotes incident direction and 'v' denotes viewing direction (as if from

665-544: A high aspect ratio . These features are commonly used in MEMS (microelectromechanical systems) and microfluidic devices, where the anisotropy of the features is needed to impart desired optical, electrical, or physical properties to the device. Anisotropic etching can also refer to certain chemical etchants used to etch a certain material preferentially over certain crystallographic planes (e.g., KOH etching of silicon [100] produces pyramid-like structures) Diffusion tensor imaging

760-431: A molecule change slightly between solvents, and therefore the solvent used is almost always reported with chemical shifts. Proton NMR spectra are often calibrated against the known solvent residual proton peak as an internal standard instead of adding tetramethylsilane (TMS), which is conventionally defined as having a chemical shift of zero. To detect the very small frequency shifts due to nuclear magnetic resonance,

855-600: A nuclear magnetic resonance response – a free induction decay (FID) – is obtained. It is a very weak signal and requires sensitive radio receivers to pick up. A Fourier transform is carried out to extract the frequency-domain spectrum from the raw time-domain FID. A spectrum from a single FID has a low signal-to-noise ratio , but it improves readily with averaging of repeated acquisitions. Good H NMR spectra can be acquired with 16 repeats, which takes only minutes. However, for elements heavier than hydrogen,

950-933: A satellite or other instrument). And let P be the Planar Albedo, which represents the total reflectance from the scene. P ( Ω i ) = ∫ Ω v γ ( Ω i , Ω v ) n ^ ⋅ d Ω ^ v {\displaystyle P(\Omega _{i})=\int _{\Omega _{v}}\gamma (\Omega _{i},\Omega _{v}){\hat {n}}\cdot d{\hat {\Omega }}_{v}} A ( Ω i , Ω v ) = γ ( Ω i , Ω v ) P ( Ω i ) {\displaystyle A(\Omega _{i},\Omega _{v})={\frac {\gamma (\Omega _{i},\Omega _{v})}{P(\Omega _{i})}}} It

1045-440: A separate lock unit, which is essentially an additional transmitter and RF processor tuned to the lock nucleus (deuterium) rather than the nuclei of the sample of interest. In modern NMR spectrometers shimming is adjusted automatically, though in some cases the operator has to optimize the shim parameters manually to obtain the best possible resolution. Upon excitation of the sample with a radio frequency (60–1000 MHz) pulse,

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1140-431: A significant broadening of spectral lines. A variety of techniques allows establishing high-resolution conditions, that can, at least for C spectra, be comparable to solution-state NMR spectra. Two important concepts for high-resolution solid-state NMR spectroscopy are the limitation of possible molecular orientation by sample orientation, and the reduction of anisotropic nuclear magnetic interactions by sample spinning. Of

1235-733: A smaller percentage of hydrogen atoms, which are the atoms usually observed in NMR spectroscopy, and because nucleic acid double helices are stiff and roughly linear, they do not fold back on themselves to give "long-range" correlations. The types of NMR usually done with nucleic acids are H or proton NMR , C NMR , N NMR , and P NMR . Two-dimensional NMR methods are almost always used, such as correlation spectroscopy (COSY) and total coherence transfer spectroscopy (TOCSY) to detect through-bond nuclear couplings, and nuclear Overhauser effect spectroscopy (NOESY) to detect couplings between nuclei that are close to each other in space. Parameters taken from

1330-410: A spin quantum number of 1/2, are of great significance in NMR spectroscopy. Examples include H, C, N, and P. Some atoms with very high spin (as 9/2 for Tc atom) are also extensively studied with NMR spectroscopy. When placed in a magnetic field, NMR active nuclei (such as H or C) absorb electromagnetic radiation at a frequency characteristic of the isotope . The resonant frequency, energy of

1425-429: A spinning sample-holder inside a very strong magnet, a radio-frequency emitter, and a receiver with a probe (an antenna assembly) that goes inside the magnet to surround the sample, optionally gradient coils for diffusion measurements, and electronics to control the system. Spinning the sample is usually necessary to average out diffusional motion, however, some experiments call for a stationary sample when solution movement

1520-960: A very strong, large and expensive liquid-helium -cooled superconducting magnet, because resolution directly depends on magnetic field strength. Higher magnetic field also improves the sensitivity of the NMR spectroscopy, which depends on the population difference between the two nuclear levels, which increases exponentially with the magnetic field strength. Less expensive machines using permanent magnets and lower resolution are also available, which still give sufficient performance for certain applications such as reaction monitoring and quick checking of samples. There are even benchtop nuclear magnetic resonance spectrometers . NMR spectra of protons ( H nuclei) can be observed even in Earth magnetic field . Low-resolution NMR produces broader peaks, which can easily overlap one another, causing issues in resolving complex structures. The use of higher-strength magnetic fields result in

1615-411: Is a spectroscopic technique based on re-orientation of atomic nuclei with non-zero nuclear spins in an external magnetic field. This re-orientation occurs with absorption of electromagnetic radiation in the radio frequency region from roughly 4 to 900 MHz, which depends on the isotopic nature of the nucleus and increased proportionally to the strength of the external magnetic field. Notably,

1710-581: Is a stub . You can help Misplaced Pages by expanding it . Anisotropy Anisotropy ( / ˌ æ n aɪ ˈ s ɒ t r ə p i , ˌ æ n ɪ -/ ) is the structural property of non-uniformity in different directions, as opposed to isotropy . An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical or mechanical properties when measured along different axes, e.g. absorbance , refractive index , conductivity , and tensile strength . An example of anisotropy

1805-479: Is a development of ordinary NMR. In two-dimensional NMR , the emission is centered around a single frequency, and correlated resonances are observed. This allows identifying the neighboring substituents of the observed functional group, allowing unambiguous identification of the resonances. There are also more complex 3D and 4D methods and a variety of methods designed to suppress or amplify particular types of resonances. In nuclear Overhauser effect (NOE) spectroscopy,

1900-448: Is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the proximal regions filter out larger particles and distal regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration. In fluorescence spectroscopy , the fluorescence anisotropy , calculated from the polarization properties of fluorescence from samples excited with plane-polarized light,

1995-475: Is a method of enhancing the image quality of textures on surfaces that are far away and steeply angled with respect to the point of view. Older techniques, such as bilinear and trilinear filtering , do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily. A chemical anisotropic filter , as used to filter particles,

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2090-405: Is also possible. The timescale of NMR is relatively long, and thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. Although large amounts of impurities do show on an NMR spectrum, better methods exist for detecting impurities, as NMR is inherently not very sensitive – though at higher frequencies, sensitivity is higher. Correlation spectroscopy

2185-464: Is also useful for probing the binding of nucleic acid molecules to other molecules, such as proteins or drugs, by seeing which resonances are shifted upon binding of the other molecule. Carbohydrate NMR spectroscopy addresses questions on the structure and conformation of carbohydrates . The analysis of carbohydrates by 1H NMR is challenging due to the limited variation in functional groups, which leads to 1H resonances concentrated in narrow bands of

2280-423: Is an MRI technique that involves measuring the fractional anisotropy of the random motion ( Brownian motion ) of water molecules in the brain. Water molecules located in fiber tracts are more likely to move anisotropically, since they are restricted in their movement (they move more in the dimension parallel to the fiber tract rather than in the two dimensions orthogonal to it), whereas water molecules dispersed in

2375-479: Is an important variable. For instance, measurements of diffusion constants ( diffusion ordered spectroscopy or DOSY) are done using a stationary sample with spinning off, and flow cells can be used for online analysis of process flows. The vast majority of molecules in a solution are solvent molecules, and most regular solvents are hydrocarbons and so contain NMR-active hydrogen-1 nuclei. In order to avoid having

2470-416: Is called a transversely isotropic material . Tensor descriptions of material properties can be used to determine the directional dependence of that property. For a monocrystalline material, anisotropy is associated with the crystal symmetry in the sense that more symmetric crystal types have fewer independent coefficients in the tensor description of a given property. When a material is polycrystalline ,

2565-422: Is called the dispersion. It is rather small for H signals, but much larger for other nuclei. NMR signals are reported relative to a reference signal, usually that of TMS ( tetramethylsilane ). Additionally, since the distribution of NMR signals is field-dependent, these frequencies are divided by the spectrometer frequency. However, since we are dividing Hz by MHz, the resulting number would be too small, and thus it

2660-411: Is centered on the peak of an individual nucleus; if its magnetic field is correlated with another nucleus by through-bond (COSY, HSQC, etc.) or through-space (NOE) coupling, a response can also be detected on the frequency of the correlated nucleus. Two-dimensional NMR spectra provide more information about a molecule than one-dimensional NMR spectra and are especially useful in determining the structure of

2755-412: Is due to the fact that FDM is designed to extrude and print layers of thermoplastic materials. This creates materials that are strong when tensile stress is applied in parallel to the layers and weak when the material is perpendicular to the layers. Anisotropic etching techniques (such as deep reactive-ion etching ) are used in microfabrication processes to create well defined microscopic features with

2850-399: Is its poor sensitivity (compared to other analytical methods, such as mass spectrometry ). Typically 2–50 mg of a substance is required to record a decent-quality NMR spectrum. The NMR method is non-destructive, thus the substance may be recovered. To obtain high-resolution NMR spectra, solid substances are usually dissolved to make liquid solutions, although solid-state NMR spectroscopy

2945-563: Is known as the Zener ratio , a r {\displaystyle a_{r}} , where C i j {\displaystyle C_{ij}} refers to elastic constants in Voigt (vector-matrix) notation . For an isotropic material, the ratio is one. Limitation of the Zener ratio to cubic materials is waived in the Tensorial anisotropy index A that takes into consideration all

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3040-421: Is light coming through a polarizer . Another is wood , which is easier to split along its grain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions). In the field of computer graphics , an anisotropic surface changes in appearance as it rotates about its geometric normal , as is the case with velvet . Anisotropic filtering (AF)

3135-513: Is multiplied by a million. This operation therefore gives a locator number called the "chemical shift" with units of parts per million. The chemical shift provides structural information. The conversion of chemical shifts (and J's, see below) is called assigning the spectrum. For diamagnetic organic compounds, assignments of H and C NMR spectra are extremely sophisticated because of the large databases and easy computational tools. In general, chemical shifts for protons are highly predictable, since

3230-399: Is now a common tool for the determination of Conformation Activity Relationships where the structure before and after interaction with, for example, a drug candidate is compared to its known biochemical activity. Proteins are orders of magnitude larger than the small organic molecules discussed earlier in this article, but the basic NMR techniques and some NMR theory also applies. Because of

3325-590: Is of interest because, with knowledge of the anisotropy function as defined, a measurement of the BRDF from a single viewing direction (say, Ω v {\displaystyle \Omega _{v}} ) yields a measure of the total scene reflectance (planar albedo ) for that specific incident geometry (say, Ω i {\displaystyle \Omega _{i}} ). Nuclear magnetic resonance spectroscopy Nuclear magnetic resonance spectroscopy , most commonly known as NMR spectroscopy or magnetic resonance spectroscopy ( MRS ),

3420-420: Is often the only way to distinguish different nuclei. The magnitude of the coupling (the coupling constant J ) is an effect of how strongly the nuclei are coupled to each other. For simple cases, this is an effect of the bonding distance between the nuclei, the magnetic moment of the nuclei, and the dihedral angle between them. The above description assumes that the coupling constant is small in comparison with

3515-412: Is proportional to the magnetic field ( Zeeman effect ). Δ E is also sensitive to electronic environment of the nucleus, giving rise to what is known as the chemical shift, δ. The simplest types of NMR graphs are plots of the different chemical shifts of the nuclei being studied in the molecule. The value of δ is often expressed in terms of "shielding": shielded nuclei have higher Δ E . The range of δ values

3610-481: Is the shear modulus , E {\displaystyle E} is the Young's modulus , and ν {\displaystyle \nu } is the material's Poisson's ratio . Therefore, for cubic materials, we can think of anisotropy, a r {\displaystyle a_{r}} , as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent:

3705-453: Is the variation of seismic wavespeed with direction. Seismic anisotropy is an indicator of long range order in a material, where features smaller than the seismic wavelength (e.g., crystals, cracks, pores, layers, or inclusions) have a dominant alignment. This alignment leads to a directional variation of elasticity wavespeed. Measuring the effects of anisotropy in seismic data can provide important information about processes and mineralogy in

3800-425: Is to obtain high resolution 3-dimensional structures of the protein, similar to what can be achieved by X-ray crystallography . In contrast to X-ray crystallography, NMR spectroscopy is usually limited to proteins smaller than 35 kDa , although larger structures have been solved. NMR spectroscopy is often the only way to obtain high resolution information on partially or wholly intrinsically unstructured proteins . It

3895-466: Is used, e.g., to determine the shape of a macromolecule. Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photon. In NMR spectroscopy , the orientation of nuclei with respect to the applied magnetic field determines their chemical shift . In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like

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3990-534: The Pierre Auger Observatory have improved on the results from AGASA by building larger, hybrid detectors and collecting greater quantities of more precise data. 35°47′13″N 138°28′34″E  /  35.786966°N 138.47625°E  / 35.786966; 138.47625 This article about a specific observatory, telescope or astronomical instrument is a stub . You can help Misplaced Pages by expanding it . This particle physics –related article

4085-486: The relaxation of the resonances is observed. As NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows construction of a three-dimensional model of the molecule. NMR spectrometers are relatively expensive; universities usually have them, but they are less common in private companies. Between 2000 and 2015, an NMR spectrometer cost around 0.5–5 million  USD . Modern NMR spectrometers have

4180-400: The (signed) intensity as a function of pulse width. It follows a sine curve and, accordingly, changes sign at pulse widths corresponding to 180° and 360° pulses. Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, slower for heavier nuclei and in solutions, and can be very long in gases. If

4275-532: The 1952 Nobel Prize in Physics for their inventions. The key determinant of NMR activity in atomic nuclei is the nuclear spin quantum number ( I ). This intrinsic quantum property, similar to an atom's " spin ", characterizes the angular momentum of the nucleus. To be NMR-active, a nucleus must have a non-zero nuclear spin ( I ≠ 0). It is this non-zero spin that enables nuclei to interact with external magnetic fields and show signals in NMR. Atoms with an odd sum of protons and neutrons exhibit half-integer values for

4370-486: The 27 components of the fully anisotropic stiffness tensor. It is composed of two major parts A I {\displaystyle A^{I}} and A A {\displaystyle A^{A}} , the former referring to components existing in cubic tensor and the latter in anisotropic tensor so that A T = A I + A A . {\displaystyle A^{T}=A^{I}+A^{A}.} This first component includes

4465-491: The 4 H sites of 1,2-dichlorobenzene divide into two chemically equivalent pairs by symmetry, but an individual member of one of the pairs has different couplings to the spins making up the other pair. Magnetic inequivalence can lead to highly complex spectra, which can only be analyzed by computational modeling. Such effects are more common in NMR spectra of aromatic and other non-flexible systems, while conformational averaging about C−C bonds in flexible molecules tends to equalize

4560-741: The Earth; significant seismic anisotropy has been detected in the Earth's crust , mantle , and inner core . Geological formations with distinct layers of sedimentary material can exhibit electrical anisotropy; electrical conductivity in one direction (e.g. parallel to a layer), is different from that in another (e.g. perpendicular to a layer). This property is used in the gas and oil exploration industry to identify hydrocarbon -bearing sands in sequences of sand and shale . Sand-bearing hydrocarbon assets have high resistivity (low conductivity), whereas shales have lower resistivity. Formation evaluation instruments measure this conductivity or resistivity, and

4655-799: The NMR spectrum. In other words, there is poor spectral dispersion. The anomeric proton resonances are segregated from the others due to fact that the anomeric carbons bear two oxygen atoms. For smaller carbohydrates, the dispersion of the anomeric proton resonances facilitates the use of 1D TOCSY experiments to investigate the entire spin systems of individual carbohydrate residues. Knowledge of energy minima and rotational energy barriers of small molecules in solution can be found using NMR, e.g. looking at free ligand conformational preferences and conformational dynamics, respectively. This can be used to guide drug design hypotheses, since experimental and calculated values are comparable. For example, AstraZeneca uses NMR for its oncology research & development. One of

4750-473: The acidic hydroxyl proton often results in a loss of coupling information. Coupling to any spin-1/2 nuclei such as phosphorus-31 or fluorine-19 works in this fashion (although the magnitudes of the coupling constants may be very different). But the splitting patterns differ from those described above for nuclei with spin greater than 1/2 because the spin quantum number has more than two possible values. For instance, coupling to deuterium (a spin-1 nucleus) splits

4845-406: The applied magnetic field must be extremely uniform throughout the sample volume. High-resolution NMR spectrometers use shims to adjust the homogeneity of the magnetic field to parts per billion ( ppb ) in a volume of a few cubic centimeters. In order to detect and compensate for inhomogeneity and drift in the magnetic field, the spectrometer maintains a "lock" on the solvent deuterium frequency with

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4940-731: The background noise, although the integrated area under the peaks remains constant. In most high-field NMR, however, the distortions are usually modest, and the characteristic distortions ( roofing ) can in fact help to identify related peaks. Some of these patterns can be analyzed with the method published by John Pople , though it has limited scope. Second-order effects decrease as the frequency difference between multiplets increases, so that high-field (i.e. high-frequency) NMR spectra display less distortion than lower-frequency spectra. Early spectra at 60 MHz were more prone to distortion than spectra from later machines typically operating at frequencies at 200 MHz or above. Furthermore, as in

5035-443: The connectivity of atoms in a molecule. The multiplicity of the splitting is an effect of the spins of the nuclei that are coupled and the number of such nuclei involved in the coupling. Coupling to n equivalent spin-1/2 nuclei splits the signal into a n  + 1 multiplet with intensity ratios following Pascal's triangle as described in the table. Coupling to additional spins leads to further splittings of each component of

5130-543: The cosmic anisotropy in cosmic microwave background radiation in 1977. Their experiment demonstrated the Doppler shift caused by the movement of the earth with respect to the early Universe matter , the source of the radiation. Cosmic anisotropy has also been seen in the alignment of galaxies' rotation axes and polarization angles of quasars. Physicists use the term anisotropy to describe direction-dependent properties of materials. Magnetic anisotropy , for example, may occur in

5225-592: The couplings between protons on adjacent carbons, reducing problems with magnetic inequivalence. Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy or 2D-NMR . This type of NMR experiment is best known by its acronym , COSY . Other types of two-dimensional NMR include J-spectroscopy, exchange spectroscopy (EXSY), Nuclear Overhauser effect spectroscopy (NOESY), total correlation spectroscopy (TOCSY), and heteronuclear correlation experiments, such as HSQC , HMQC , and HMBC . In correlation spectroscopy, emission

5320-410: The difference between horizontal and vertical permeability must be taken into account; otherwise the results may be subject to error. Most common rock-forming minerals are anisotropic, including quartz and feldspar . Anisotropy in minerals is most reliably seen in their optical properties . An example of an isotropic mineral is garnet . Igneous rock like granite also shows the anisotropy due to

5415-421: The difference in NMR frequencies between the inequivalent spins. If the shift separation decreases (or the coupling strength increases), the multiplet intensity patterns are first distorted, and then become more complex and less easily analyzed (especially if more than two spins are involved). Intensification of some peaks in a multiplet is achieved at the expense of the remainder, which sometimes almost disappear in

5510-560: The direction of measurement. Fourth-rank tensor properties, like the elastic constants, are anisotropic, even for materials with cubic symmetry. The Young's modulus relates stress and strain when an isotropic material is elastically deformed; to describe elasticity in an anisotropic material, stiffness (or compliance) tensors are used instead. In metals, anisotropic elasticity behavior is present in all single crystals with three independent coefficients for cubic crystals, for example. For face-centered cubic materials such as nickel and copper,

5605-504: The directional dependence on properties is often related to the processing techniques it has undergone. A material with randomly oriented grains will be isotropic, whereas materials with texture will be often be anisotropic. Textured materials are often the result of processing techniques like cold rolling , wire drawing , and heat treatment . Mechanical properties of materials such as Young's modulus , ductility , yield strength , and high-temperature creep rate , are often dependent on

5700-400: The double helix does not have a compact interior and does not fold back upon itself. NMR is also useful for investigating nonstandard geometries such as bent helices , non-Watson–Crick basepairing, and coaxial stacking . It has been especially useful in probing the structure of natural RNA oligonucleotides, which tend to adopt complex conformations such as stem-loops and pseudoknots . NMR

5795-603: The figure to the right, J-coupling can be used to identify ortho-meta-para substitution of a ring. Ortho coupling is the strongest at 15 Hz, Meta follows with an average of 2 Hz, and finally para coupling is usually insignificant for studies. More subtle effects can occur if chemically equivalent spins (i.e., nuclei related by symmetry and so having the same NMR frequency) have different coupling relationships to external spins. Spins that are chemically equivalent but are not indistinguishable (based on their coupling relationships) are termed magnetically inequivalent. For example,

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5890-588: The first scientific works devoted to the use of pressure as a variable parameter in NMR experiments was the work of J. Jonas published in the journal Annual Review of Biophysics in 1994. The use of high pressures in NMR spectroscopy was primarily driven by the desire to study biochemical systems, where the use of high pressure allows controlled changes in intermolecular interactions without significant perturbations. Of course, attempts have been made to solve scientific problems using high-pressure NMR spectroscopy. However, most of them were difficult to reproduce due to

5985-452: The heat source in electronics are often anisotropic. Many crystals are anisotropic to light ("optical anisotropy"), and exhibit properties such as birefringence . Crystal optics describes light propagation in these media. An "axis of anisotropy" is defined as the axis along which isotropy is broken (or an axis of symmetry, such as normal to crystalline layers). Some materials can have multiple such optical axes . Seismic anisotropy

6080-509: The interaction of different spin states through the chemical bonds of a molecule and results in the splitting of NMR signals. For a proton, the local magnetic field is slightly different depending on whether an adjacent nucleus points towards or against the spectrometer magnetic field, which gives rise to two signals per proton instead of one. These splitting patterns can be complex or simple and, likewise, can be straightforwardly interpretable or deceptive. This coupling provides detailed insight into

6175-602: The latter approach, fast spinning around the magic angle is a very prominent method, when the system comprises spin-1/2 nuclei. Spinning rates of about 20 kHz are used, which demands special equipment. A number of intermediate techniques, with samples of partial alignment or reduced mobility, is currently being used in NMR spectroscopy. Applications in which solid-state NMR effects occur are often related to structure investigations on membrane proteins, protein fibrils or all kinds of polymers, and chemical analysis in inorganic chemistry, but also include "exotic" applications like

6270-681: The material. Amorphous materials such as glass and polymers are typically isotropic. Due to the highly randomized orientation of macromolecules in polymeric materials, polymers are in general described as isotropic. However, mechanically gradient polymers can be engineered to have directionally dependent properties through processing techniques or introduction of anisotropy-inducing elements. Researchers have built composite materials with aligned fibers and voids to generate anisotropic hydrogels , in order to mimic hierarchically ordered biological soft matter. 3D printing, especially Fused Deposition Modeling, can introduce anisotropy into printed parts. This

6365-484: The modified Zener ratio and additionally accounts for directional differences in the material, which exist in orthotropic material, for instance. The second component of this index A A {\displaystyle A^{A}} covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise. Fiber-reinforced or layered composite materials exhibit anisotropic mechanical properties, due to orientation of

6460-619: The molecule. Subsequently, the distances obtained are used to generate a 3D structure of the molecule by solving a distance geometry problem. NMR can also be used to obtain information on the dynamics and conformational flexibility of different regions of a protein. Nucleic acid NMR is the use of NMR spectroscopy to obtain information about the structure and dynamics of poly nucleic acids , such as DNA or RNA . As of 2003 , nearly half of all known RNA structures had been determined by NMR spectroscopy. Nucleic acid and protein NMR spectroscopy are similar but differences exist. Nucleic acids have

6555-410: The molecules. Liquid crystals are examples of anisotropic liquids. Some materials conduct heat in a way that is isotropic, that is independent of spatial orientation around the heat source. Heat conduction is more commonly anisotropic, which implies that detailed geometric modeling of typically diverse materials being thermally managed is required. The materials used to transfer and reject heat from

6650-401: The much higher number of atoms present in a protein molecule in comparison with a small organic compound, the basic 1D spectra become crowded with overlapping signals to an extent where direct spectral analysis becomes untenable. Therefore, multidimensional (2, 3 or 4D) experiments have been devised to deal with this problem. To facilitate these experiments, it is desirable to isotopically label

6745-643: The multiplet, e.g. coupling to two different spin-1/2 nuclei with significantly different coupling constants leads to a doublet of doublets (abbreviation: dd). Note that coupling between nuclei that are chemically equivalent (that is, have the same chemical shift) has no effect on the NMR spectra, and couplings between nuclei that are distant (usually more than 3 bonds apart for protons in flexible molecules) are usually too small to cause observable splittings. Long-range couplings over more than three bonds can often be observed in cyclic and aromatic compounds, leading to more complex splitting patterns. For example, in

6840-480: The nuclear spin quantum number ( I = 1/2, 3/2, 5/2, and so on). These atoms are NMR-active because they possess non-zero nuclear spin. Atoms with an even sum but both an odd number of protons and an odd number of neutrons exhibit integer nuclear spins ( I = 1, 2, 3, and so on). Conversely, atoms with an even number of both protons and neutrons have a nuclear spin quantum number of zero ( I = 0), and therefore are not NMR-active. NMR-active nuclei, particularly those with

6935-408: The orientation of the minerals during the solidification process. Anisotropy is also a well-known property in medical ultrasound imaging describing a different resulting echogenicity of soft tissues, such as tendons , when the angle of the transducer is changed. Tendon fibers appear hyperechoic (bright) when the transducer is perpendicular to the tendon, but can appear hypoechoic (darker) when

7030-475: The pi system of benzene . This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change. Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal). Physicists from University of California, Berkeley reported about their detection of

7125-524: The plant leaves and fuel cells. For example, Rahmani et al. studied the effect of pressure and temperature on the bicellar structures' self-assembly using deuterium NMR spectroscopy. Solid-state NMR is usefull also for metal structure understanding in case of X-ray amorphous metal samples (like nano-size refractory metal Tc) . Much of the innovation within NMR spectroscopy has been within the field of protein NMR spectroscopy, an important technique in structural biology . A common goal of these investigations

7220-427: The problem of equipment for creating and maintaining high pressure. In the most common types of NMR cells for realization of high-pressure NMR experiments are given. High-pressure NMR spectroscopy has been widely used for a variety of applications, mainly related to the characterization of the structure of protein molecules. However, in recent years, software and design solutions have been proposed to characterize

7315-410: The protein with C and N because the predominant naturally occurring isotope C is not NMR-active and the nuclear quadrupole moment of the predominant naturally occurring N isotope prevents high resolution information from being obtained from this nitrogen isotope. The most important method used for structure determination of proteins utilizes NOE experiments to measure distances between atoms within

7410-488: The proton spectrum for ethanol, the CH 3 group is split into a triplet with an intensity ratio of 1:2:1 by the two neighboring CH 2 protons. Similarly, the CH 2 is split into a quartet with an intensity ratio of 1:3:3:1 by the three neighboring CH 3 protons. In principle, the two CH 2 protons would also be split again into a doublet to form a doublet of quartets by the hydroxyl proton, but intermolecular exchange of

7505-520: The radiation absorbed, and the intensity of the signal are proportional to the strength of the magnetic field. For example, in a 21- tesla magnetic field, hydrogen nuclei ( protons ) resonate at 900 MHz. It is common to refer to a 21 T magnet as a 900  MHz magnet, since hydrogen is the most common nucleus detected. However, different nuclei will resonate at different frequencies at this field strength in proportion to their nuclear magnetic moments . An NMR spectrometer typically consists of

7600-518: The range is hundreds of ppm. In paramagnetic NMR spectroscopy , the samples are paramagnetic, i.e. they contain unpaired electrons. The paramagnetism gives rise to very diverse chemical shifts. In H NMR spectroscopy, the chemical shift range can span up to thousands of ppm. Some of the most useful information for structure determination in a one-dimensional NMR spectrum comes from J-coupling, or scalar coupling (a special case of spin–spin coupling ), between NMR active nuclei. This coupling arises from

7695-400: The reinforcement material. In many fiber-reinforced composites like carbon fiber or glass fiber based composites, the weave of the material (e.g. unidirectional or plain weave) can determine the extent of the anisotropy of the bulk material. The tunability of orientation of the fibers allows for application-based designs of composite materials, depending on the direction of stresses applied onto

7790-518: The relaxation time and thus the required delay between pulses. A 180° pulse, an adjustable delay, and a 90° pulse is transmitted. When the 90° pulse exactly cancels out the signal, the delay corresponds to the time needed for 90° of relaxation. Inversion recovery is worthwhile for quantitative C, D and other time-consuming experiments. NMR signals are ordinarily characterized by three variables: chemical shift, spin–spin coupling, and relaxation time. The energy difference Δ E between nuclear spin states

7885-464: The relaxation time is rather long, e.g. around 8 seconds for C. Thus, acquisition of quantitative heavy-element spectra can be time-consuming, taking tens of minutes to hours. Following the pulse, the nuclei are, on average, excited to a certain angle vs. the spectrometer magnetic field. The extent of excitation can be controlled with the pulse width, typically about 3–8 μs for the optimal 90° pulse. The pulse width can be determined by plotting

7980-723: The resonance frequency of each NMR-active nucleus depends on its chemical environment. As a result, NMR spectra provide information about individual functional groups present in the sample, as well as about connections between nearby nuclei in the same molecule. As the NMR spectra are unique or highly characteristic to individual compounds and functional groups , NMR spectroscopy is one of the most important methods to identify molecular structures, particularly of organic compounds . The principle of NMR usually involves three sequential steps: Similarly, biochemists use NMR to identify proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about

8075-430: The rest of the brain have less restricted movement and therefore display more isotropy. This difference in fractional anisotropy is exploited to create a map of the fiber tracts in the brains of the individual. Radiance fields (see Bidirectional reflectance distribution function (BRDF)) from a reflective surface are often not isotropic in nature. This makes calculations of the total energy being reflected from any scene

8170-434: The results are used to help find oil and gas in wells. The mechanical anisotropy measured for some of the sedimentary rocks like coal and shale can change with corresponding changes in their surface properties like sorption when gases are produced from the coal and shale reservoirs. The hydraulic conductivity of aquifers is often anisotropic for the same reason. When calculating groundwater flow to drains or to wells ,

8265-411: The same time not by other spectroscopic techniques to an atomic level, either. In solid-phase media, such as crystals, microcrystalline powders, gels, anisotropic solutions, etc., it is in particular the dipolar coupling and chemical shift anisotropy that become dominant to the behaviour of the nuclear spin systems. In conventional solution-state NMR spectroscopy, these additional interactions would lead to

8360-434: The second excitation pulse is sent prematurely before the relaxation is complete, the average magnetization vector has not decayed to ground state, which affects the strength of the signal in an unpredictable manner. In practice, the peak areas are then not proportional to the stoichiometry; only the presence, but not the amount of functional groups is possible to discern. An inversion recovery experiment can be done to determine

8455-548: The shifts are primarily determined by shielding effects (electron density). The chemical shifts for many heavier nuclei are more strongly influenced by other factors, including excited states ("paramagnetic" contribution to shielding tensor). This paramagnetic contribution, which is unrelated to paramagnetism ) not only disrupts trends in chemical shifts, which complicates assignments, but it also gives rise to very large chemical shift ranges. For example, most H NMR signals for most organic compounds are within 15 ppm. For P NMR,

8550-517: The signal into a 1:1:1 triplet because the spin 1 has three spin states. Similarly, a spin-3/2 nucleus such as Cl splits a signal into a 1:1:1:1 quartet and so on. Coupling combined with the chemical shift (and the integration for protons) tells us not only about the chemical environment of the nuclei, but also the number of neighboring NMR active nuclei within the molecule. In more complex spectra with multiple peaks at similar chemical shifts or in spectra of nuclei other than hydrogen, coupling

8645-477: The signals from solvent hydrogen atoms overwhelm the experiment and interfere in analysis of the dissolved analyte, deuterated solvents are used where >99% of the protons are replaced with deuterium (hydrogen-2). The most widely used deuterated solvent is deuterochloroform (CDCl 3 ), although other solvents may be used for various reasons, such as solubility of a sample, desire to control hydrogen bonding , or melting or boiling points. The chemical shifts of

8740-479: The spectrum, mainly NOESY cross-peaks and coupling constants , can be used to determine local structural features such as glycosidic bond angles, dihedral angles (using the Karplus equation ), and sugar pucker conformations. For large-scale structure, these local parameters must be supplemented with other structural assumptions or models, because errors add up as the double helix is traversed, and unlike with proteins,

8835-508: The stiffness is highest along the <111> direction, normal to the close-packed planes, and smallest parallel to <100>. Tungsten is so nearly isotropic at room temperature that it can be considered to have only two stiffness coefficients; aluminium is another metal that is nearly isotropic. For an isotropic material, G = E / [ 2 ( 1 + ν ) ] , {\displaystyle G=E/[2(1+\nu )],} where G {\displaystyle G}

8930-705: The structure, dynamics, reaction state, and chemical environment of molecules. The most common types of NMR are proton and carbon-13 NMR spectroscopy, but it is applicable to any kind of sample that contains nuclei possessing spin . NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules . Different functional groups are obviously distinguishable, and identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has largely replaced traditional wet chemistry tests such as color reagents or typical chromatography for identification. The most significant drawback of NMR spectroscopy

9025-412: The transducer is angled obliquely. This can be a source of interpretation error for inexperienced practitioners. Anisotropy, in materials science , is a material's directional dependence of a physical property . This is a critical consideration for materials selection in engineering applications. A material with physical properties that are symmetric about an axis that is normal to a plane of isotropy

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