Fundamentals of Magnetic Resonance Flashcards
What is the nuclear spin quantum number
I - describes the intrinsic spin of the nuclei
What is the nuclear spin quantum number associated with the z-component?
m - values range from +I to -I in steps of 1
What types of nuclei have spin magnetic moment?
Nuclei with nuclear spin > 0
What is the Zeeman interaction?
The nuclear magnetic moment will interact with any applied magnetic field. The energy of this interaction can be described by the Zeeman Hamiltonian
What can be used to determine the transition frequency from one spin state to another
𝛥E between spin states
Limitations of the energy level picture of NMR
NMR is not emission/ absorption spectroscopy, it is a resonance technique
What are vectors
Vectors are quantities with both magnitude and a direction defined in terms of a coordinate system
What is torque
A twisting force that acts perpendicular to interacting vectors - this causes M to precess around B
Net magnestisation
vector sum of all magnetic moments of all spins in sample
In absence of magnetic field what is what is the net magnetisation?
zero - no net magnetisation as there is no preference for direction so they all cancel out
What happens when 2 magnetic moments are out of phase?
Mostly cancel each other out - destructive interference
What happens when 2 magnetic moments are in phase?
The magnetic moments add up - constructive interference
When can there only be net magnetisation in Mxy plane
if there is phase coherence - when nuclear magnetic moments precess in sync with one another at same frequency and same initial phase
What is the net magnetisation in Mxy plane at thermal equilibrium?
At thermal eqm all spins point in arbitrary directions so Mxy = 0 as there is no phase coherence
What happens when we rotate net magnetisation (Mo) into xy plane
Magnetic moments are precessing in sync so add up in xy plane Mxy > 0
Destroy longitudinal magnetisation Mz now = 0 equal popn between energy states
Mo precesses around Bo at Larmor frequency
How do we rotate Mo into xy plane?
Generate RF pulse - an oscillating voltage passed through a coil of wire will generate oscillating magnetic field
Radio frequency pulse at Larmor frequency to induce transitions between 2 energy states.
New magnetic field B1 oscillates at larmor frequency perpendicular to Bo
What does applying a second magnetic field B1 on x axis perpendicular Bo do?
This causes Mo net magnetisation to precess around B1 in the rotating frame. If we apply the pulse for exactly the right amount of time we can rotate magnetisation from z into xy plane
What is NMR receptivity?
NMR receptivity is a measure of how easy it is to detect the NMR signal of a given nucleus - it is quoted relatitive to another nucleus e.g. 1H or 13C
Longitudinal relaxation
T1
This process generates the eqm population difference across zeeman energy levels and establishes Mo along z axis
Transverse relaxation
T2
process that causes xy magnetisation to decay to zero. Mxy comes from phase coherence so relaxation must be due to loss of phase coherence - randomisation of phase
What is the rate of change of longitudinal magnetisation proportional to?
Proportional to the difference between current magnetisation and equilibrium magnetisation
what is it called if Mz is larger than equilibrium magnetisation?
Hyperpoarisation
Mz will decay time due to T1 relaxation
what is the rate of transverse relaxation proportional to?
magnetisation in xy plane, Mxy
What is the rate of longitudinal relaxation proportional to?
The difference between current magnetisation and eqm magnetisation
What is effective transverse relaxation T2*?
the rate at which transverse magnetisation decays faster than expected in NMR experiments
Mxy can also decay due to reversible dephasing - this comes from nuclei experiencing different larmor frequencies (e.g. bubble in NMR tube)
If nuclei in different parts of sample will experience different fields so precess at different frequencies and dephase as time goes on
What effect does short T2* have on NMR spectra?
Short T2* (fast relaxation) leads to broad peaks in NMR spectrum - reduced resolution and signal to noise ratio
What effect does long T2* have on NMR spectra
This means slow relaxation which leads to narrow peaks with higher signal
What is shimming?
Shimming is the process of improving the homogeneity of Bo by applying small additional fields to cancel out small variations across the sample
What causes T1 relaxation?
Exchange of energy with the environment re-establishing the equilibrium population difference across the nuclear spin energy levels
What causes T2 relaxation?
Interaction between spins and the environment - doesn’t require exchange of energy.
Causes loss of phase coherence between precessing spins
What is dipole-dipole coupling?
direct magnetic spin-spin interaction between nuclei, occurs through space
the size of the interaction is determined by the coupling constants
As it is an anisotropic interaction it averages out in liquids
What is J coupling
indirect magnetic spin-spin interaction mediated by the electrons, occurs through chemical bonds
What is Quadrupolar interactions?
Electronic interaction of electric quadrupole moment (eQ) of spins with I > 1/2 with surrounding electric field
The more anisotropic the distribution of charge the larger the eQ
What are hyperfine interactions?
Interaction between a nuclear spin and an unpaired electron spin, similar in origin to J coupling
What makes an interaction an isotropic interaction?
The size of the interaction is independent of the relative orientation of the molecule and the magnetic field
Some examples of isotropic interactions?
J coupling
Hyperfine
Zeeman interaction
isotropic chemical shift
what makes an interaction an anisotropic interaction
The size of the interaction depends on the orientation of the molecule with respect to the magnetic field
Example of anisotropic interaction
Dipole-dipole coupling
Quadrupole coupling
Chemical shift anisotropy
What are the effects of anisotropic interactions on NMR spectra
Cause different frequency shifts depending on orientation of molecule relative to Bo
(Not observed in liquid due to molecular tumbling - anisotropic interactions average to zero)
What does the size of J-Coupling depend on?
Gyromagnetic ratio of each nucleus
number of bonds/ bond angle between nuclei
What is chemical equivalence?
Where 2 spins have the same chemical shift, appears as a singlet, no coupling between A and B is observed
when are two nuclei magnetically inequivalent?
if they couple differently to a 3rd nucleus.
For example in an octahedral complex one H couples cis to a P spin up nuclei and one H couples trans to the same P spin up nuclei
If the difference in chemical shift of 2 nuclei is much bigger than the J coupling
get weak coupling
standard multiplets
If the difference in chemical shift is approximately the same as the J value
Means there is strong coupling
Lots of roofing
If 2 nuclei have the same chemical shift?
they are chemically equivalent - see a singlet
What is chemical shift anisotropy
in the presence of a strong applied field, the electrons in the molecule give rise to a small induced field at the nucleus that opposes Bo
What do hyperfine interactions cause in NMR spectroscopy?
causes fast T2 relaxation meaning NMR spectra can often not be obtained for paramagnetic species
What is magic angle spinning
Technique used in solid state NMR to average out anisotropic interactions to simplify spectra and recover isotropic chem shift info
Averages out anisotropic interactions in a similar way to motional averaging but not random, it is at a fixed rotation frequency at a single specific axis.
Rotation axis oriented at 54.7 bc due to symmetry the dipole dipole and CSA interactions are zero at this angle
