Todays Lecture

1
Todays Lecture
2) Fri, Oct 2 Behavior of nuclear spins in a
magnetic field II a. Bloch equations b.
Phenomenological introduction to T1 and T2 c. RF
Pulses d. Teach Spin apparatus
2
Bulk Magnetization
Recall from lecture 1
Unfortunately, the vast majority of the magnetic
moments cancel one another. The Boltzmann
excess in the a state add together to create
bulk angular momentum (J) and magnetization (M).
3
Gyroscopes!
Classical physics tells us about the motion of a
magnet in a magnetic field
4
Bloch Equations
We can make the equations easier to deal with by
multiplying both sides by g
Multiply by g
(Remember that mgI)
5
Bloch Equations
What does this equation describe?
After suitable choices for B, this equation
predicts that nuclear magnetization will precess
at a frequency w0gB0 FOREVER. Nothing in the
equation is a restoring force to cause the
magnetization to relax back to equilibrium.
However, real-life NMR experiments relax.
6
Bloch Equations
Therefore, Felix Bloch made the following
modifications to the basic equation
Empirical modification in which a relaxation
matrix R acts on magnetization that is different
from the equilibrium state, M0
7
Bloch Equations
8
Changing the frame of reference
PROBLEM The Bloch equations we have shown so
far are helpful but still too complicated. The
problem is that as soon as magnetization is put
into the x-y plane, it starts to precess (we will
see that soon) at NMR frequencies (e.g. 500 MHz).
Thus, the actual trajectory of the motion is
VERY COMPLICATED.
SOLUTION We will define a coordinate system
that rotates around the z-axis at the same NMR
frequency. This is accomplished by defining the
following
wrf is the frequency of the NMR transmitter and
gB0 is the frequency of the peak we are
interested in observing. If the two are the
same, this is called on-resonance. In this
case, the effective magnetic field strength
along the z-axis is 0.
9
Bloch Equations in the Rotating Frame
Substituting W-gB0-wrf (where B0Bz and is not
time-dependent) into the Bloch equations yields
The r superscript refers to a magnetic field in
the rotating frame
Now try some Mathematica simulations to see what
these mean!
10
Teach Spin
11
Next Mondays Lecture
3) Mon, Oct 6 Introduction to NMR Parameters a.
Chemical shiftBMRB database b. J
couplingKarplus equation c. T1 d. T2 e. NOE f.
Dipolar Couplings