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NMR Theory

RF PULSE. All types of hydrogen are excited. simultaneously with the ... COMPUTER-BASED METHOD. The excitation pulse, the data collection (FID), and. the computer ...

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NMR Theory

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    NUCLEAR MAGNETIC RESONANCE The nuclei of some atoms have a property called “SPIN”. NUCLEAR SPIN These nuclei behave as if they were spinning. This is like the spin property of an electron, which can have two spins: +1/2 and -1/2 . Each spin-active nucleus has a number of spins defined by its spin quantum number, I. ….. we don’t know if they actually do spin! The spin quantum numbers of some common nuclei follow ….. Element 1H 2H 12C 13C 14N 16O 17O 19F Nuclear Spin Quantum No 1/2 1 0 1/2 1 0 5/2 1/2 ( I ) No. of Spin 2 3 0 2 3 0 6 2 States Spin Quantum Numbers of Some Common Nuclei Elements with either odd mass or odd atomic number have the property of nuclear “spin”. The number of spin states is 2I + 1, where I is the spin quantum number. The most abundant isotopes of C and O do not have spin. THE PROTON Although interest is increasing in other nuclei, particulary C-13, the hydrogen nucleus (proton) is studied most frequently, and we will devote our attention to it first. NUCLEAR SPIN STATES - HYDROGEN NUCLEUS + 1/2 - 1/2 The two states are equivalent in energy in the absence of a magnetic or an electric field. + + The spin of the positively charged nucleus generates a magnetic moment vector, m. m m TWO SPIN STATES THE “RESONANCE” PHENOMENON absorption of energy by the spinning nucleus

    Slide 7:Nuclear Spin Energy Levels

    Bo +1/2 -1/2 In a strong magnetic field (Bo) the two spin states differ in energy. aligned unaligned N S

    Slide 8:Absorption of Energy

    Bo +1/2 -1/2 +1/2 -1/2 DE = hn DE quantized Radiofrequency Applied Field Aligned Opposed

    Bo DE + 1/2 - 1/2 = kBo = hn degenerate at Bo = 0 increasing magnetic field strength THE ENERGY SEPARATION DEPENDS ON Bo

    Slide 10:The Larmor Equation!!!

    gB0 n = 2p g n = 2p Bo g is a constant which is different for each atomic nucleus (H, C, N, etc) DE = kBo = hn can be transformed into gyromagnetic ratio g strength of the magnetic field frequency of the incoming radiation that will cause a transition

    WHEN A SPIN-ACTIVE HYDROGEN ATOM IS PLACED IN A STRONG MAGNETIC FIELD ….. IT BEGINS TO PRECESS A SECOND EFFECT OF A STRONG MAGNETIC FIELD OPERATION OF AN NMR SPECTROMETER DEPENDS ON THIS RESULT N S w Nuclei precess at frequency w when placed in a strong magnetic field. hn If n = w then energy will be absorbed and the spin will invert. NUCLEAR MAGNETIC RESONANCE NMR RADIOFREQUENCY 40 - 600 MHz 1H 99.98% 1.00 42.6 267.53 1.41 60.0 2.35 100.0 7.05 300.0 2H 0.0156% 1.00 6.5 41.1 7.05 45.8 13C 1.108% 1.00 10.7 67.28 2.35 25.0 7.05 75.0 19F 100.0% 1.00 40.0 251.7 Resonance Frequencies of Selected Nuclei Isotope Abundance Bo (Tesla) Frequency(MHz) g(radians/Tesla)

    Slide 14:The strength of the NMR signal depends on the Population Difference of the two spin states

    resonance induced emission excess population Radiation induces both upward and downward transitions. For a net positive signal there must be an excess of spins in the lower state. Saturation = equal populations = no signal POPULATION AND SIGNAL STRENGTH

    CLASSICAL INSTRUMENTATION typical before 1960 field is scanned

    Slide 16:A Simplified 60 MHz NMR Spectrometer

    Transmitter Receiver Probe hn S N RF Detector Recorder RF (60 MHz) Oscillator ~ 1.41 Tesla (+/-) a few ppm absorption signal MAGNET MAGNET

    scan increasing Bo HIGH FIELD LOW FIELD UPFIELD DOWNFIELD IN THE CLASSICAL NMR EXPERIMENT THE INSTRUMENT SCANS FROM “LOW FIELD” TO “HIGH FIELD” NMR CHART NOTICE THAT EACH DIFFERENT TYPE OF PROTON COMES AT A DIFFERENT PLACE - YOU CAN TELL HOW MANY DIFFERENT TYPES OF HYDROGEN THERE ARE NMR Spectrum of Phenylacetone MODERN INSTRUMENTATION PULSED FOURIER TRANSFORM TECHNOLOGY requires a computer FT-NMR PULSED EXCITATION BROADBAND RF PULSE All types of hydrogen are excited simultaneously with the single RF pulse. contains a range of frequencies N S n1 n2 n3 (n1 ..... nn) FREE INDUCTION DECAY ( relaxation ) n1 n2 n3 n1, n2, n3 have different half lifes COMPOSITE FID “time domain“ spectrum n1 + n2 + n3 + ...... time FOURIER TRANSFORM A mathematical technique that resolves a complex FID signal into the individual frequencies that add together to make it. COMPLEX SIGNAL n1 + n2 + n3 + ...... computer Fourier Transform FT-NMR individual frequencies TIME DOMAIN FREQUENCY DOMAIN a mixture of frequencies decaying (with time) converted to converted to a spectrum ( Details not given here. ) FID NMR SPECTRUM DOMAINS ARE MATHEMATICAL TERMS

    Slide 24:The Composite FID is Transformed into a classical NMR Spectrum :

    “frequency domain” spectrum

    COMPARISON OF CW AND FT TECHNIQUES CONTINUOUS WAVE (CW) METHOD The magnetic field is “scanned” from a low field strength to a higher field strength while a constant beam of radiofrequency (continuous wave) is supplied at a fixed frequency (say 100 MHz). Using this method, it requires several minutes to plot an NMR spectrum. THE OLDER, CLASSICAL METHOD SLOW, HIGH NOISE LEVEL PULSED FOURIER TRANSFORM (FT) METHOD THE NEWER COMPUTER-BASED METHOD The excitation pulse, the data collection (FID), and the computer-driven Fourier Transform (FT) take only a few seconds. Most protons relax (decay) from their excited states very quickly (within a second). The pulse and data collection cycles may be repeated every few seconds. Many repetitions can be performed in a very short time, leading to improved signal ….. FAST LOW NOISE By adding the signals from many pulses together, the signal strength may be increased above the noise level. IMPROVED SIGNAL-TO-NOISE RATIO noise signal add many pulses noise is random and cancels out etc. 1st pulse 2nd pulse nth pulse enhanced signal
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