NUCLEAR MAGNETIC RESONANCE Dr. Nermin Salah 6th Lecture 16-10-2011

Objectives Properties of the nucleus Nuclear spin Nuclear magnetic moments The nucleus in a magnetic field Precession of nuclei in a field The “Resonance” Phenomenon NMR techniques Continuous wave Pulsed or Fourier transform (FT-NMR) Instrumentation

NMR Spectroscopy NMR spectroscopy is a form of absorption spectrometry. Most absorption techniques (e.g. – Ultraviolet-Visible and Infrared) involve the electrons… in the case of NMR, it is the nucleus of the atom which determines the response. An applied (magnetic) field is necessary to for the absorption to occur.

Spectral Properties, Application and Interactions of Electromagnetic Radiation Energy Wave Number V Wavelength λ Frequency υ Type Radiation Type spectroscopy Type Quantum Transition Kcal/mol Electron volts, eV cm-1 cm Hz 9.4 x 107 4.9 x 106 3.3 x 1010 3 x 10-11 1021 9.4 x 103 4.9 x 102 3.3 x 106 3 x 10-7 1017 9.4 x 101 4.9 x 100 3.3 x 104 3 x 10-5 1015 9.4 x 10-1 4.9 x 10-2 3.3 x 102 3 x 10-3 1013 9.4 x 10-3 4.9 x 10-4 3.3 x 100 3 x 10-1 1011 9.4 x 10-7 4.9 x 10-8 3.3 x 10-4 3 x 103 107 Gamma ray Gamma ray emission Nuclear X-ray absorption, emission Electronic (inner shell) X-ray Ultra violet UV absorption Electronic (outer shell) Visible Infrared IR absorption Molecular vibration Molecular rotation Micro-wave Microwave absorption Magnetically induced spin states Nuclear magnetic resonance Radio 4

Nuclear Spin Nuclear spin angular momentum is a quantized property of the nucleus in each atom, it is assigned based on the properties of neutrons and protons. The nuclear spin angular momentum of each atom is represented by a nuclear spin quantum number (I). All nuclei with even mass numbers have I = 0,1,2… All nuclei with odd mass numbers have I = 1/2, 3/2... NMR is possible with all nuclei except I = 0, but I = 1/2 has simplest physics.

SPIN QUANTUM NUMBERS OF SOME COMMON NUCLEI The most abundant isotopes of C and O do not have spin. Element 1H 2H 12C 13C 14N 16O 19F Nuclear Spin Quantum No 1/2 1 0 1/2 1 0 1/2 ( I ) No. of Spin 2 3 0 2 3 0 2 States In many atoms, these spins are paired against each other, such that the nucleus of the atom has no overall spin such as 12C, 16O, 32S. However, in some atoms (such as 1H, 13C, 19F, 31P ) the nucleus does possess an overall spin (odd no. of protons or neutrons [odd mass number or odd atomic number]). The nucleus with spin quantum no. I  0, can assume (2I +1) possible orientations (states). A nucleus with spin 1/2 will have 2 possible orientations (i.e. two possible energy states) described by magnetic quantum number mI=+1/2 and mI=-1/2 Elements with either odd number of protons or neutrons (odd mass number 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.

NUCLEAR SPIN STATES – MAGNETIC MOMENT A spinning, charged nucleus creates a magnetic field. Thus, the spinning charged nucleus is characterized by a certain magnetic moment, . Since a nucleus is a charged particle in motion, it will develop a magnetic field, they behave in a similar fashion to a simple, tiny bar magnet. In the absence of a magnetic field, these are randomly oriented. When a magnetic field is applied the nuclei line up parallel to the applied field, either spin aligned or spin opposed.   Always consider hydrogen nuclei for simplicity, the whole nuclei contains only one proton. More nuclei align with the applied magnetic field as it is the lower energy spin state .

Behavior of spinning protons with external magnetic field (-spin state) (β-spin state)

THE PROTON Although interest is increasing in other nuclei, particularly C-13, the hydrogen nucleus (proton) is studied most frequently, and we will devote our attention to the proton at first. Now on, the acronym “NMR” is generally assumed to mean 1H-NMR (Proton Magnetic Resonance)

NUCLEAR SPIN STATES - HYDROGEN NUCLEUS m + Clockwise spin Anticlockwise spin Hydrogen Nucleus One Proton I = 1/2 Two states (2I+1 = 2) mI= + ½ & mI= - ½ -spin state, mI= + ½ -Spin state, mI= - ½ (magnetic quantum number) TWO SPIN STATES two possible orientations (two possible energy states)

In a strong magnetic field (Bo) the two spin states differ in energy THE NUCLEUS IN A MAGNETIC FIELD When nuclei are exposed to external magnetic field of strength B0, their spins line up parallel to the applied field, either spin aligned (-spin state) or spin opposed (-spin state) to the external field. Bo aligned opposing N S Nuclear Spin Energy Levels + ½  ½ higher in energy lower in energy -spin state -spin state Imagine as if in a magnetic field : E0-E1 In a strong magnetic field (Bo) the two spin states differ in energy

THE “RESONANCE” PHENOMENON absorption of energy by spinning nuclei in a magnetic field

A Quantum Description of NMR When sample is subjected to a pulse of radiation whose energy corresponds to the difference in energy (E) between the -spin state and the -spin state, the nuclei in the -spin state flip their spin and are promoted to the -spin state. The term resonance refers to the spin flipping back and forth between the - and -spin states in response to rf radiations. Bo DE = hn DE quantized Radiofrequency Applied Field Aligned Opposed + ½  ½ -spin state -spin state

POPULATION AND SIGNAL STRENGTH The strength of the NMR signal depends on the Population Difference of the two spin states In external magnetic field, the  and  states will be populated (occupied by nuclei) and the population difference is dependent on the nuclear species under observation. The difference in population is very small with only about 20 out of 1 million in excess in the lower energy state. The NMR signal depends essentially on a such a small difference. Ground state Resonance Absorption of rf spin flip Excited state For a net positive signal, there must be an excess of spins in the lower state.

THE ENERGY SEPARATION DEPENDS ON Bo The stronger the external magnetic field, the higher the energy of the excited state, the higher the energy required to flip the nuclear spin. - 1/2 -spin state DE Bo = 0 all nuclei have the same energy + 1/2 -spin state Bo increasing magnetic field strength

Energy difference between the two state Energy of spinning nuclei The energy of the nucleus in these two states (orientations) is given by: Energy of -state (spin aligned) Energy of -state (spin opposed) Energy difference between the two state Absorption of electromagnetic radiation of frequency  that correspond to in energy to E

THE LARMOR EQUATION g is a constant which is different for gyromagnetic ratio g Frequency of the incoming radiation that will cause a transition strength of the magnetic field g is a constant which is different for each atomic nucleus (H, C, N, etc)

Rf Frequencies for different nuclei

“Where the Quantum Explanation Ends, and the Classical One Takes Over” To understand the absorption process , and in particular the measurement of absorption, a classical picture of the behavior of a charged particle in a magnetic field is helpful. Since the nuclei are spinning rapidly around its axis, the magnetic field applied to the axis of rotation forces the nuclei to move in a circular path. The rotational axis of the nuclei precess around the vector representing the applied magnetic field. The nuclei is precessing with angular velocity ω or better say with frequency of precession (Larmor frequency) Same derived from quantum mechanics

If nradiation = wprecession Nuclei precess at frequency  (Larmor precession frequency) when placed in a strong magnetic field.   B0   Energy will be absorbed and the spin will invert If nradiation = wprecession w hn NUCLEAR MAGNETIC RESONANCE Applied Field Bo RADIOFREQUENCY 80 - 900 MHz NMR S

CLASSICAL INSTRUMENTATION Before 1970 Continuous wave NMR : The sample is held in a strong magnetic field, and the frequency of the source is slowly scanned or vice versa, the source frequency is held constant, and the magnetic field is scanned. Disadvantages The magnitude of the energy changes involved in NMR spectroscopy are small Slow scanning Fourier – Transform NMR were introduced in 1970. Low sensitivity Hard to improve S/N ratio

A Simplified 60 MHz NMR Spectrometer hn RF (60 MHz) Oscillator RF Detector absorption signal Recorder Radiation source, its magnetic field is what matters Receiver MAGNET MAGNET N S ~ 1.41 Tesla (+/-) a few ppm Probe For protons (1H), affected by magnetic field of 1.41 Tesla (~14000 gauss), the needed frequency was found to be 60 MHz

MODERN INSTRUMENTATION PULSED FOURIER TRANSFORM TECHNOLOGY FT-NMR requires a computer

Interval between pulses PULSED OR FOURIER TRANSFORM (FT-NMR) SPECTROMETERS Nuclei in a very strong magnetic field (constant strength) are subjected periodically to very brief pulses of intense radio-frequency radiation. Pulse duration or pulse width Interval between pulses Pulse train Each pulse is actually a packet of RF radiation

The NMR Experiment WHAT HAPPEN BEFORE IRRADIATION Before irradiation, the nuclei in both spin states are precessing with the Larmor frequency, but they are completely out of phase, i.e., randomly oriented around the z axis. The net nuclear magnetization M0 is aligned statically along the z axis (M0=Mz, Mxy=0) The NMR Experiment

WHAT HAPPEN DURING IRRADIATION Excitation is produced by a second magnetic field, B1, which oscillate at the appropriate radio-frequency. This field is induced from alternating current in a coil (source of radiation) wound perpendicular to B0. When irradiation begins: Under the effect of B1, the net magnetization M0 is displaced from equilibrium and is flipped toward the xy plane . The tip angle or the flip angle, , is determined by the power and duration of the electromagnetic irradiation (time for which B1 is turned on). Z z  x Mxy y B0 Mo y x B1 Y y x wo X  deg pulse 90 deg pulse

WHAT HAPPEN AFTER IRRADIATION CEASES After irradiation ceases, B1 turns off after the pulse, the magnetic moment M0 must now rotate in clockwise direction back to presses around the z axis. This motion gives rise to a signal (current) that can be detected by the same coil (along the x axis) that is used to produce the original pulse. As relaxation proceeds, this signal decreases exponentially and approach zero as the magnetic moment reaches the z axis. (Note that the coil acts as a receiver coil or detector that can sense only the magnetic field on the xy plane). This time domain signal is called the free induction decay (FID signal) FID: free of the influence of radio-frequency field, induced current in the coil and decaying back to equilibrium. z y Mxy x Mo 90y pulse relaxation B1 B1=0 B0 Transmitter (source) receiver (detector) Relaxation: Loss of excess energy in the system to surrounding (lattice) as heat

FREE INDUCTION DECAY SIGNAL z x Mxy y Mo Free Induction Decay (FID) - One frequency 90y pulse relaxation

The Pulse FT NMR Experiment equilibration 90º pulse detection of signals Experiment (t) Data Analysis Fourier Transform Time domain (t)

The Composite FID is Transformed into a classical NMR Spectrum “frequency domain” spectrum

COMPARISON OF CW AND FT TECHNIQUES

CONTINUOUS WAVE (CW) METHOD THE OLDER, CLASSICAL 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 60 MHz). Using this method, it requires several minutes to plot an NMR spectrum. SLOW, HIGH NOISE LEVEL

PULSED FOURIER TRANSFORM (FT) METHOD FAST LOW NOISE THE NEWER COMPUTER-BASED METHOD Most protons relax (decay) from their excited states very quickly (within a second). The excitation pulse, the data collection (FID), and the computer-driven Fourier Transform (FT) take only a few seconds. 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 to noise ratio.

NMR instrumentation N S Magnet - Normally Superconducting. Bo B1 Detector Frequency Generator Recorder Magnet Magnet - Normally Superconducting. Frequency generator Creates an alternating current that induces B1. Detector Recorder 34

NMR spectrometer in organic labs

The cost of NMR A superconducting magnet A Strong magnetic field Stable, homogenous field up to 21 Tesla (900MHz) Requires cooling to absolute zero (liquid Nitrogen or Helium) A Strong magnetic field requires special infrastructure to avoid any possible interference. NMR is a very expensive technique.

Is such a spectrum worth millions? Brainstorming Using a magnetic field of 2.4 Tesla, for an organic sample containing H- protons, absorbance of ν= 100 MHZ will occur. A spectrum with one signal indicating the presence of H- protons in the compound. Is such a spectrum worth millions? 100 MHz

Resources and references Textbook: Principles of Instrumental Analysis, Skoog, Holler, Nieman Recommended further reading: “Principles of instrumental analysis, 5th ed. by Skoog, Holler, Nieman” Chapter 19. Extra resources are available on the intranet. Relevant web sites http://www.chemguide.co.uk/analysismenu.html