Analytical Chem-Exam 4-NMR

What is Nuclear Magnetic Resonance?

Nuclear Magnetic Resonance (NMR) measures the absorption of electromagnetic radiation in the radio-frequency region (~4-900 MHz)

o   Nuclei (instead of outer electrons) are involved in absorption process

o   Sample needs to be placed in magnetic field to cause different energy states

-       NMR was first experimentally observed by Bloch and Purcell in 1946 (received Nobel Prize in 1952) and quickly became commercially available and widely used.

-       Probe the Composition, Structure, Dynamics and Function of the Complete Range of Chemical Entities: from small organic molecules to large molecular weight polymers and proteins

-       NMR is routinely and widely used as the preferred technique to rapidly elucidate the chemical structure of most organic compounds.

-       One of the MOST Routinely used Analytical Techniques

NMR History

First NMR Spectra: on Water

-Electrons spin clock-wise or counter-clockwise

-Nucleus also has nuclear-spin. So, like a magnet, it will be attracted to one part of the field

-Back to spectroscopy

-Proved that nuclei had spin

-Then discovered chemical shift when doing NMR of Ethanol

            -Every molecule absorbs differently based on different chemical environments

            -Results in different peaks

            -Each chemical has a fingerprint

Typical Applications of NMR: Structural (chemical) elucidation

a.     Natural product chemistry

b.     Synthetic organic chemistry

                                               i.     Analytical tool of choice of synthetic chemists

                                             ii.     Used in conjunction with MS and IR

Typical Applications of NMR: Study of Dynamic Processes

a.     Reaction kinetics

b.     Study of equilibrium (chemical or structural)

Typical Applications of NMR: Drug Design

Structure Activity Relationships by NMR

Typical Applications of NMR: Others

1.)   Medicine-MRI

2.)   Metabolomics-disease biomarkers

Information in an NMR Spectrum: Absorption

electromagnetic (light) energy is transferred to atoms, ions, or molecules in the sample. Results in the transition to a higher energy state.

Information in an NMR Spectrum: Wave model

Represented by a sinusoidal wave traveling space with an oscillating electric field and perpendicular magnetic field (NMR responds to magnetic field)

What is Electromagnetic Theory?

-       A perpendicular external magnetic field will induce an electric current in a closed loop

-       Magnetic field produced by circulating electron

-       An electric current in a closed loop will create a perpendicular magnetic field

Theory of NMR: Quantum Description

-       Nuclear Spin (think Electron Spin)

a)  Nucleus rotates about its axis (spin

b) Nuclei with spin have angular momentum

      -Quantized, spin quantum number I

      -2I + 1 states: I, I-1, I-2

      -idenitcal energyies in absence of external magnetic field

c) NMR “active” Nuclear Spin (I)= ½

      ¹H, ¹³C, ¹⁵N, ¹⁹F, ³¹P

      Odd atomic mass

      I= +1/2 & -1/2

NMR “inactive” Nuclear Spin (I)=0

¹²C,¹⁶O

Even atomic mass and Number

Quadrupole Nuclei Nuclear Spin (I)>1/2

What is a magnetic moment?

  spinning charged nucleus creates a magnetic field

Similar to magnetic field created by electric current flowing in a coil

a)     Magnetic moment is created along axis of nuclear spin

a.     U=yp

Where:

            p-angular momentum

            y-gyromagnetic ratio (different value for each type of nucleus)

b)    Magnetic moment is quantized (m)

a.     M=I, I-1, I-2…, -I

For common nuclei of interest:

M=1/2 & -1/2

What is Magnetic Alignment?

Without magnetic field the nucleus does not prefer any particular alignment.

·      Add a strong external field (B_o). and the nuclear magnetic moment aligns with (low energy) against (high-energy)

·      To sense these magnetic moments, we have to put it into a magnetic field

o   Can’t detect a signal if there is no change in energy

Zeeman Effect

Magnetic moments are oriented in one of two directions in a magnetic field

Energy Levels in a Magnetic Field

  Transition from the low energy to high energy spin state occurs through an absorption of a photon of radio-frequency (RF) energy

NMR Theory: Classical Description

Spinning particle precesses around an applied magnetic field

a) Angular velocity of this motion is given by:

ω_o=γB_o

Net Magnetization in A Magnetic Field: Classic View

Nuclei either align with or against external magnetic field along the z-axis

- Since more nuclei align with field, not magnetization (M_o) exists parallel to external magnetic field

Net Magnetization in A Magnetic Field: Quantum Description

-       Nuclei either populate low energy (α, aligned with field) or high energy (β, aligned against field)

-       Net population in α energy level.

-       Absorption of radio-frequency promotes nuclear spins from α-β

Resonant conditions

frequency (ω₁) of B₁ matches Lamor frequency (ω_o) energy is absorbed and population of α and β states are perturbed

And/or

M_o, now precess about B₁ (similar to B_o) for as long as the B₁ field is applied

Classical Description: Observe NMR Signal

o   Need to perturb system from equilibrium

§  B₁ field (radio frequency pulse with γB_o/2π frequency

o   Net magnetization (M_o) now precesses about B_o and B₁

§  M_x  and M_y are non-zero

§  M_x and M_y rotate at Larmor frequency

§  System absorbs energy with transitions between aligned and unaligned states

o   Precession about B₁ stopped when B₁ is turned off

The B₁ field is turned off and M_xy continues to precess about B_o at a frequency ω_o

The oscillation of Mxy generates a fluctuating magnetic field which can be used to generate a current in a receiver coil to detect the NMR signal

-       A magnetic field perpendicular to a circular loop will induce a current in the loop.

NMR Signal Detection- Fourier Transform

So, the NMR signal is collected in the Time-domain

Fourier Transform is a mathematical procedure that transforms time domain data into frequency domain

After the NMR signal is generated and the B1 field is removed, the net magnetization will relax back to equilibrium aligned along the Z-axis

V_1/2 = 1/πT₂

Two types of relaxation processes, on in the x, y plane and one along the x-axis

Peak shape also affected by magnetic field homogeneity or shimming

NMR Relaxation

No spontaneous reemission of photons to relax down to ground state

            Probability too low- cube of the frequency

NMR Relaxation: Spin-lattice or longitudinal relaxation (T₁)

                                               i.     Transfer energy to the lattice or solvent material

                                             ii.     Coupling of nuclei magnetic field with magnetic fields created by the ensemble of vibrational and rotational motion of the lattice or solvent

                                           iii.      Results in a minimal temperature increase in sample

Mz=Mo (1-e^-t/T1)

NMR Relaxation: Spin-Spin or transverse relaxation (T₂)

i.      Exchange of energy between excited nucleus and low energy state nucleus

                                               i.    Randomization of spins or magnetic moment in x,y-plane

                                             ii.     Related to NMR peak line width

Mx=My=Moexp(-t/T2)