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| [[File:HahnEcho GWM.gif|right|thumb|400px|[[Spin echo]] animation showing the response of electron spins (red arrows) in the blue [[Bloch sphere]] to the green [[pulse sequence]] ]]
| | If you are overweight as well as make an impact in your body, discover walk alot more. You may not realize that your particular simple walk can have such a large impact with regards to your body's inches. A body that is lethargic will amass more fat than a shape that is in motion. Little walk can make a huge difference in your weight.<br><br>Rush health and fitness club if you wish to get rid of extra mass. Use more weights to burn calories. If you want eliminate weight, work with heavy barbells. The exercise duration has to 25 to 30 minutes. Focus on one muscle every single day. It is recommended to be able to the gym 3 to 4 days in full week. So if you go 4 days a week, you have 4 different muscles to target upon around the week. One muscle per day, big names and half hour per day.<br><br>In self-worth and phase, you need to start doing proper and regular exercise. You can choose any sort of exercise, on the other hand prefer jogging or rushing. There is no need to become listed on a gym instead when jog 1 to 2 miles just a day that's adequately. Even if frustration to lessen body fat, [http://raspberrytrimdiet.net/ Raspberry Trim Review] it is an effective habit to jog daily because it'll help you keep fit, active and will assist fight .<br><br>There has become lot of hype about the benefits of [http://raspberrytrimdiet.net/ Raspberry Trim] ketone and some tips it behaves as a weight reducing agent. You'll find a regarding articles, blog posts, reviews and alike about subject of enzyme over the internet. Most of the people especially victims unaware on the real facts and figures usually get impressed get started using which it. And believe me, you will find thousands of individuals who are utilizing it and your current hundreds of companies which manufacturing and selling subject enzyme.<br><br>Avoid temptation at projects. If possible, stay faraway from break rooms where other people may have died their high-calorie leftovers. Maintain your desk stocked with healthy snacks, and pack a lunch each day rather than going in order to eat. An individual are have a lunch appointment, eat an extra side of vegetables or a salad associated with high fat options.<br><br>How old are you can? This is another question deal with as begin your attempt to find the best weight loss pills. Prone to are within your 20s you will not desire to use exact supplement as somebody which over age of 44. The older you receive the more you do focus towards the products which can be on the market, also as what's safest for any body at the time of one's life.<br><br>Losing weight starts along with a plan together motivational factor. If either principle or the motivational factor is missing, you cannot lose surplus. Chart a plan as to how many pounds you actually lose exactly what is the deadline for your same. For motivational factor, you need be highly motivated a person need to read success anecdotes. Usually motivational factor exists as if it doesn't, the individual is not going to think of weight loss [http://raspberrytrimdiet.net/ Raspberry Trim] at directory submission place.<br><br>1- Be certain that you're is to plan and set a realistic goal. You need to decide seeking how much fat you require lose? The time you to be able to lose so much weight? How one can will in order to be achieve aim? You must write down answers to all of these examination questions. Start off with a clear mission, plan and idea. Make sure your goals should be realistic. I mean you cannot lose 20 pounds in the month, as it were set such unrealistic targets, it will create problems a person personally and in the end, you will get de-motivated. |
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| '''Pulsed [[electron paramagnetic resonance]]''' (EPR) is a [[Spectroscopy|spectroscopic technique]] related to common [[nuclear magnetic resonance]] (NMR). Its most basic form involves the alignment of the net magnetization vector of the [[Electron magnetic dipole moment|electron spins]] in a constant [[magnetic field]]. This alignment is perturbed by applying a short oscillating field, usually a microwave pulse. One can then measure the emitted microwave signal which is created by the sample magnetization. [[Fourier transform]]ation of the microwave signal yields an EPR spectrum in the frequency domain. With a vast variety of pulse sequences it is possible to gain extensive knowledge on structural and dynamical properties of paramagnetic compounds. Pulsed EPR techniques such as electron [[spin echo]] envelope modulation (ESEEM) or pulsed [[electron nuclear double resonance]] (ENDOR) can reveal the interactions of the electron spin with its surrounding [[Spin (physics)|nuclear spins]].
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| ==Scope==
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| Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) is a spectroscopic technique widely used in biology, chemistry, medicine and physics to study systems with one or more unpaired electrons. Because of the specific relation between the magnetic parameters, electronic wavefunction and the configuration of the surrounding non-zero spin nuclei, EPR and ENDOR provide information on the structure, dynamics and the spatial distribution of the paramagnetic species. However, these techniques are limited in spectral and time resolution when used with traditional continuous wave methods. This resolution can be improved in pulsed EPR by investigating interactions separately from each other via pulse sequences.
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| ==Historical overview==
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| R. J. Blume reported the first electron [[spin echo]] in 1958, which came from a solution of sodium in ammonia at room temperature.<ref name=blume>
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| {{cite journal
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| | author = Blume, R. J.
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| | title = Electron Spin Relaxation Times in Sodium-Ammonia Solutions
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| | journal = Physical Review
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| | year = 1958
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| | volume = 109
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| | pages = 1867–1873
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| | doi = 10.1103/PhysRev.109.1867
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| |bibcode = 1958PhRv..109.1867B }}</ref> A magnetic field of 0.62 mT was used requiring a frequency of 17.4 MHz. The first microwave electron spin echoes were reported in the same year by Gordon and Bowers using 23 GHz excitation of dopants in [[silicon]].<ref name=gordon>
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| {{cite journal
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| | author = Gordon, J. P.; Bowers, K. D.
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| | title = Microwave Spin Echoes from Donor Electrons in Silicon
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| | journal = Physical Review Letters
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| | year = 1958
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| | volume = 1
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| | pages = 368–370
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| | doi = 10.1103/PhysRevLett.1.368
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| |bibcode = 1958PhRvL...1..368G }}</ref>
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| Much of the pioneering early pulsed EPR was conducted in the group of W. B. Mims at [[Bell Labs]] during the 1960s. In the first decade only a small number of groups worked the field, because of the expensive instrumentation, the lack of suitable microwave components and slow digital electronics. The first observation of electron spin echo envelope modulation (ESEEM) was made in 1961 by Mims, Nassau and McGee.<ref name=ESEEM>
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| {{cite journal
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| | author = Mims, W. B.; Nassau, K.; McGee J. D.
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| | title = Spectral Diffusion in Electron Resonance Lines
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| | journal = Physical Review
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| | year = 1961
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| | volume = 123
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| | pages = 2059–2069
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| | doi = 10.1103/PhysRev.123.2059
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| |bibcode = 1961PhRv..123.2059M }}</ref> Pulsed [[electron nuclear double resonance]] (ENDOR) was invented in 1965 by Mims.<ref name=PENDOR>
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| {{cite journal
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| | author = Mims, W. B.
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| | title = Pulsed endor experiments
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| | journal = [[Proceedings of the Royal Society A]]
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| | year = 1965
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| | volume = 283
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| | pages = 452–457
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| | doi = 10.1098/rspa.1965.0034
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| |bibcode = 1965RSPSA.283..452M }}</ref> In this experiment, pulsed [[NMR]] transitions are detected with pulsed EPR. ESEEM and pulsed ENDOR continue to be important for studying nuclear spins coupled to electron spins.
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| In the 1980s, the upcoming of the first commercial pulsed EPR and ENDOR spectrometers in the [[X band]] frequency range, lead to a fast growth of the field. In the 1990s, parallel to the upcoming high-field EPR, pulsed EPR and ENDOR became a new fast advancing magnetic resonance spectroscopy tool and the first commercial pulsed EPR and ENDOR spectrometer at [[W band]] frequencies appeared on the market.
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| ==Principle==
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| The basic principle of pulsed EPR is similar to NMR spectroscopy. Differences can be found in the relative size of the magnetic interactions and in the relaxation rates which are orders of magnitudes larger in EPR than NMR. A full description of the theory is given within the quantum mechanical formalism, but since the magnetization is being measured as a bulk property, a more intuitive picture can be obtained with a classical description. For a better understanding of the concept of pulsed EPR let us consider the effects on the magnetization vector in the [[Laboratory frame of reference|laboratory frame]] as well as in the [[Rotating reference frame|rotating frame]]. As the animation below shows, in the laboratory frame the static magnetic field B<sub>0</sub> is assumed to be parallel to the z-axis and the microwave field B<sub>1</sub> parallel to the x-axis. When an electron spin is placed in magnetic field it experiences a torque which causes its [[magnetic moment]] to precess around the magnetic field. The precession frequency is known as the [[Larmor precession|Larmor frequency]] ω<sub>L</sub> (see page 18 of ref <ref name=Schweiger>{{cite book |author= Schweiger, A. and Jeschke, G. |title= Principles of pulse electron paramagnetic resonance|url=http://books.google.com/books?id=tkvQQElkW1wC&printsec=frontcover|isbn=0-19-850634-1 |publisher= Oxford University Press, New York |year= 2001}}
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| </ref>). | |
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| :<math> \omega_{L} = -\gamma B_{0} </math>
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| where γ is the [[gyromagnetic ratio]] and B<sub>0</sub> the magnetic field. The electron spins are characterized by two quantum mechanical states, one parallel and one antiparallel to B<sub>0</sub>. Because of the lower energy of the parallel state more electron spins can be found in this state according to the [[Boltzmann distribution]]. This results in a net magnetization, which is the [[vector sum]] of all magnetic moments in the sample, parallel to the z-axis and the magnetic field. To better comprehend the effects of the microwave field B<sub>1</sub> it is easier to move to the rotating frame.
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| [[File:Animated Rotating Frame.gif|Animation showing the rotating frame. The red arrow is a spin in the [[Bloch sphere]] which precesses in the laboratory frame due to a static magnetic field. In the rotating frame the spin remains still until a resonantly oscillating magnetic field drives magnetic resonance.]]
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| EPR experiments usually use a microwave resonator designed to create a [[Linear polarization|linearly polarized]] microwave field B<sub>1</sub>, perpendicular to the much stronger applied magnetic field B<sub>0</sub>. The rotating frame is fixed to the rotating B<sub>1</sub> components. First we assume to be on resonance with the precessing magnetization vector M<sub>0</sub>.
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| :<math> \omega_{L} = \omega_{0} </math>
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| Therefore the component of B<sub>1</sub> will appear stationary. In this frame also the precessing magnetization components appear to be stationary that leads to the disappearance of B<sub>0</sub>, and we need only to consider B<sub>1</sub> and M<sub>0</sub>. The M<sub>0</sub> vector is under the influence of the stationary field B<sub>1</sub>, leading to another precession of M<sub>0</sub>, this time around B<sub>1</sub> at the frequency ω<sub>1</sub>.
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| :<math> \omega_{1} = -\gamma B_{1} </math>
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| This angular frequency ω<sub>1</sub> is also called the [[Rabi frequency]]. Assuming B<sub>1</sub> to be parallel to the x-axis, the magnetization vector will rotate around the +x-axis in the zy-plane as long as the microwaves are applied. The angle by which M<sub>0</sub> is rotated is called the tip angle α and is given by:
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| :<math> \alpha = -\gamma|B_{1}|t_{p} </math>
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| Here t<sub>p</sub> is the duration for which B<sub>1</sub> is applied, also called the pulse length. The pulses are labeled by the rotation of M<sub>0</sub> which they cause and the direction from which they are coming from, since the microwaves can be phase-shifted from the x-axis on to the y-axis. For example, a +y π/2 pulse means that a B<sub>1</sub> field, which has been 90 degrees phase-shifted out of the +x into the +y direction, has rotated M<sub>0</sub> by a tip angle of π/2, hence the magnetization would end up along the –x-axis. That means the end position of the magnetization vector M<sub>0</sub> depends on the length, the magnitude and direction of the microwave pulse B<sub>1</sub>. In order to understand how the sample emits microwaves after the intense microwave pulse we need to go back to the laboratory frame. In the rotating frame and on resonance the magnetization appeared to be stationary along the x or y-axis after the pulse. In the laboratory frame it becomes a rotating magnetization in the x-y plane at the Larmor frequency. This rotation generates a signal which is maximized if the magnetization vector is exactly in the xy-plane. This microwave signal generated by the rotating magnetization vector is called [[free induction decay]] (FID) (see page 175 of ref <ref name=Schweiger/>).
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| Another assumption we have made was the exact resonance condition, in which the Larmor frequency is equal to the microwave frequency. In reality EPR spectra have many different frequencies and not all of them can be exactly on resonance, therefore we need to take off-resonance effects into account. The off-resonance effects lead to three main consequences. The first consequence can be better understood in the rotating frame. A π/2 pulse leaves magnetization in the xy-plane, but since the microwave field (and therefore the rotating frame) do not have the same frequency as the precessing magnetization vector, the magnetization vector rotates in the xy-plane, either faster or slower than the microwave magnetic field B<sub>1</sub>. The rotation rate is governed by the frequency difference Δω.
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| :<math> \Delta\omega = \omega - \omega_{0} </math>
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| If Δω is 0 then the microwave field rotates as fast as the magnetization vector and both appear to be stationary to each other. If Δω>0 then the magnetization rotates faster than the microwave field component in a counter-clockwise motion and if Δω<0 then the magnetization is slower and rotates clockwise. This means that the individual frequency components of the EPR spectrum, will appear as magnetization components rotating in the xy-plane with the rotation frequency Δω. The second consequence appears in the laboratory frame. Here B<sub>1</sub> tips the magnetization differently out of the z-axis, since B<sub>0</sub> does not disappear when not on resonance due to the precession of the magnetization vector at Δω. That means that the magnetization is now tipped by an effective magnetic field B<sub>eff</sub>, which originates from the vector sum of B<sub>1</sub> and B<sub>0</sub>. The magnetization is then tipped around B<sub>eff</sub> at a faster effective rate ω<sub>eff</sub>.
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| :<math> \omega_{eff}^{2} = (\omega_{1}^{2} + \Delta\omega^{2})^{1/2} </math>
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| This leads directly to the third consequence that the magnetization can not be efficiently tipped into the xy-plane because B<sub>eff</sub> does not lie in the xy-plane, as B<sub>1</sub> does. The motion of the magnetization now defines a cone. That means as Δω becomes larger, the magnetization is tipped less effectively into the xy-plane, and the FID signal decreases. In broad EPR spectra where Δω > ω<sub>1</sub> it is not possible to tip all the magnetization into the xy-plane to generate a strong FID signal. This is why it is important to maximize ω<sub>1</sub> or minimize the π/2 pulse length for broad EPR signals.
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| So far the magnetization was tipped into the xy-plane and it remained there with the same magnitude. However, in reality the electron spins interact with their surroundings and the magnetization in the xy-plane will decay and eventually return to alignment with the z-axis. This relaxation process is described by the [[spin-lattice relaxation]] time T<sub>1</sub>, which is a characteristic time needed by the magnetization to return to the z-axis, and by the [[spin-spin relaxation]] time T<sub>2</sub>, which describes the vanishing time of the magnetization in the xy-plane. The spin-lattice relaxation results from the urge of the system to return to thermal equilibrium after it has been perturbed by the B<sub>1</sub> pulse. Return of the magnetization parallel to B<sub>0</sub> is achieved through interactions with the surroundings, that is spin-lattice relaxation. The corresponding relaxation time needs to be considered when extracting a signal from noise, where the experiment needs to be repeated several times, as quickly as possible. In order to repeat the experiment, one needs to wait until the magnetization along the z-axis has recovered, because if there is no magnetization in z direction, then there is nothing to tip into the xy-plane to create a significant signal.
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| The spin-spin relaxation time, also called the transverse relaxation time, is related to homogeneous and inhomogeneous broadening. An inhomogeneous broadening results from the fact that the different spins experience local magnetic field inhomogeneities (different surroundings) creating a large number of spin packets characterized by a distribution of Δω. As the net magnetization vector precesses, some spin packets slow down due to lower fields and others speed up due to higher fields leading to a fanning out of the magnetization vector that results in the decay of the EPR signal. The other packets contribute to the transverse magnetization decay due to the homogeneous broadening. In this process all the spin in one spin packet experience the same magnetic field and interact with each other that can lead to mutual and random spin flip-flops. These fluctuations contribute to a faster fanning out of the magnetization vector.
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| All the information about the frequency spectrum is encoded in the motion of the transverse magnetization. The frequency spectrum is reconstructed using the time behavior of the transverse magnetization made up of y- and x-axis components. It is convenient that these two can be treated as the real and imaginary components of a complex quantity and use the Fourier theory to transform the measured time domain signal into the frequency domain representation. This is possible because both the absorption (real) and the dispersion (imaginary) signals are detected.
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| The FID signal decays away and for very broad EPR spectra this decay is rather fast due to the inhomogeneous broadening. To obtain more information one can recover the disappeared signal with another microwave pulse to produce a [[Spin echo|Hahn echo]].<ref name=hahn>
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| {{cite journal
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| | author = Hahn, E.L.
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| | title = Spin echoes
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| | journal = Physical Review
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| | year = 1950
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| | volume = 80
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| | pages = 580–594
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| | doi = 10.1103/PhysRev.80.580|bibcode = 1950PhRv...80..580H }}
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| </ref> After applying a π/2 pulse (90°), the magnetization vector is tipped into the xy-plane producing an FID signal. Different frequencies in the EPR spectrum (inhomogeneous broadening) cause this signal to "fan out", meaning that the slower spin-packets trail behind the faster ones. After a certain time ''t'', a π pulse (180°) is applied to the system inverting the magnetization, and the fast spin-packets are then behind catching up with the slow spin-packets. A complete refocusing of the signal occurs then at time ''2t''. An accurate echo caused by a second microwave pulse can remove all inhomogeneous broadening effects. After all of the spin-packets bunch up, they will dephase again just like an FID. In other words, a spin echo is a reversed FID followed by a normal FID, which can be Fourier transformed to obtain the EPR spectrum. The longer the time between the pulses becomes, the smaller the echo will be due to spin relaxation. When this relaxation leads to an exponential decay in the echo height, the decay constant is the phase memory time T<sub>M</sub>, which can have many contributions such as transverse relaxation, spectral, spin and instantaneous diffusion. Changing the times between the pulses leads to a direct measurement of T<sub>M</sub> as shown in the spin echo decay animation below.
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| [[File:GWM HahnEchoDecay.gif]]
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| ==Applications==
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| ESEEM <ref name=ESEEM/><ref name=Schweiger/> and pulsed [[Electron nuclear double resonance|ENDOR]] <ref name=PENDOR/><ref name=Schweiger/> are widely used [[Spin echo|echo]] experiments, in which the interaction of electron spins with the nuclei in their environment can be studied and controlled. [[Quantum computing]] and [[spintronics]], in which spins are used to store information, have led to new lines of research in pulsed EPR.
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| One of the most popular pulsed EPR experiments currently is double electron-electron resonance (DEER), which is also known as pulsed electron-electron double resonance (PELDOR).<ref name=Schweiger/> This uses two different frequencies to control different spins in order to find out the strength of their coupling. The distance between the spins can then be inferred from their coupling strength, which is used to study structures of large bio-molecules.
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| ==See also==
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| *[[Electron paramagnetic resonance]]
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| *[[Spin echo]]
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| *[[Nuclear magnetic resonance]]
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| *[[Electron nuclear double resonance]]
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| ==References==
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| {{reflist|30em}}
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| ==External links==
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| *[http://www.bruker-biospin.com/pulse.html Pulse EPR] Bruker BioSpin
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| {{DEFAULTSORT:Pulsed EPR}}
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| [[Category:Spectroscopy]]
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| [[Category:Quantum mechanics]]
| |
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