無機物理方法(核磁共振部分)
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無機物理方法(核磁共振部分). The Physical Methods in Inorganic Chemistry (Fall Term, 2004) (Fall Term, 2005) Department of Chemistry National Sun Yat-sen University. Chapter 4. Chapter 4. 90 o pulse width T 1 measurement T 2 measurement Chemical exchange. π. π /2. Fine Tuning until t π.

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無機物理方法(核磁共振部分)

The Physical Methods in Inorganic Chemistry(Fall Term, 2004)(Fall Term, 2005)Department of ChemistryNational Sun Yat-sen University

Chapter 4


Chapter 4

Chapter 4

  • 90o pulse width

  • T1 measurement

  • T2 measurement

  • Chemical exchange


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π

π/2


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Fine Tuning until tπ

90o pulse width= tπ/2

Any degree (n)-pulse = tπ*n/180.


Spin relaxation

Spin Relaxation

  • Any system that is prepared to off-equilibrium “state” tends to restore to its equilibrium state. Random forces are the origin of relaxation.

  • Nuclear spin relaxation is driven by random magnetic fields. The transverse component of the random magnetic field causes longitudinal relaxation (T1) and the longitudinal component of the random magnetic field causes transverse relaxation (T2).

  • Random magnetic field being generated by the molecular motions, relaxation measurement offers information on dynamics.


Inversion recovery

Inversion-Recovery

π_2

π

τ

My

FT

τ


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τ


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When magnetic field inhomogeneity Δν is not negligible, it

Introduces observable contributions to signal decay:


T 2 effect

T2 Effect


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π/2

π

τ1

τ2

τ1 = τ2

τ1 = T2

τ1


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τ1 = τ2

τ2


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τ

τ

2τ=T2


Cpmg sequence for t 2 measurement

n

πxy

π/2xy

δ

δ

CPMG Sequence for T2 Measurement


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Mx

n

2nδ

πxy

π/2xy

2nδ=T2

δ

2nδ

δ


T 1 t 2 and dynamics just a little example

T1, T2 and Dynamics…Just A Little Example

S

I

rIS

How far between two nuclei

How fast the molecule tumbles.


Example of relaxation dipolar relaxation

Example of relaxation: dipolar relaxation


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How does the magnetization relax back to equilibrium after applying a

radiofrequency pulse?


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Thus, to bring the bulk magnetization back

to the z axis, an oscillating field (oscillating

at the Larmor frequency of the transition)

that is orthogonal to the Zeeman field is

required. The source of these additional

fields is easy to see, the other nuclei which

have magnetic moments nearby.  Thus, the

dipole-dipole interaction can actually

provide a mechanism for relaxation.


How does the spectra density j depend on the correlation time

How does the spectra density J depend on the correlation time?


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  • The following gives the relaxation rate when it is dominated by dipolar interaction.  It should be noted that relaxation can be afforded by other mechanisms such as chemical shift anisotropy, scalar relaxation, spin-rotation and quadrupolar interaction.  For protons, in solution free of molecular oxygen, the dipolar mechanism usually dominates.

In the extreme narrowing limit (very fast motion and very short correlation time), the following holds.


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  • Can one use one correlation time for all the sites in a molecule?  That depends.  This is true only if the motion is isotropic and NOT segmental.  Below are examples where the motion is segmental (first example).  Listed are the T1 values for each of the carbons in this long-chain alcohol.  Clearly, motion is restricted near the -OH end of the molecule (presumably due to hydrogen bonding).  As a result, these protons have relatively shorter relaxation times (or faster relaxation rates) as the motions get slower and approach the Larmor frequency.  The second example illustrates anisotropy.  Listed are the T1 values for some of the carbons in phenol.  The relaxation time of the C directly attached to the -OH group illustrates the importance of nearby protons in the relaxation of C spins.  Since this C is not directly attached to any proton, its relaxation time is appreciable long.  The anisotropic motion of the ring (it prefers rotation about the axis that contains -OH) leads to appreciably longer relaxation times for the C's that do not lie on this rotational axis.


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Listed are the T1 values for each of the carbons in this long-chain alcohol. 

Clearly, motion is restricted near the -OH end of the molecule (presumably

due to hydrogen bonding).  As a result, these protons have relatively shorter

relaxation times (or faster relaxation rates) as the motions get slower and

approach the Larmor frequency. 


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This example illustrates anisotropy.  Listed are the T1 values for

some of the carbons in phenol.  The relaxation time of the C directly

attached to the -OH group illustrates the importance of nearby protons

in the relaxation of C spins.  Since this C is not directly attached to any

proton, its relaxation time is appreciable long.  The anisotropic motion

of the ring (it prefers rotation about the axis that contains -OH) leads to

appreciably longer relaxation times for the C's that do not lie on this

rotational axis.


The effect of t 1 on the setting of recycle delay d1

M0

M0

Pulse

sequence

(If d1 is long enough)

d1

d1

M0’

(If d1 is not long enough)

The effect of T1 on the setting of recycle delay (d1)


Saturation bad

M0

Pulse

sequence

Pulse

sequence

Pulse

sequence

M0’

d1

d1

d1

M0’’

……

Saturation:Bad!

No more signal added to the total signal after a few scans.


Steady state not bad maybe

Pulse

sequence

Pulse

sequence

Pulse

sequence

M0

M0

M0

M0

M0

M0’

M0’’

M0’’

M0’’

d1

d1

d1

M0’’

……

Steady State:Not Bad, Maybe.

Signal for each scan is lower than single 90 degree pulse but the transients

can be added up.


Ernst angle

Ernst Angle

d1/T1


Many more relaxation rates

Many More Relaxation Rates…

T1, T2 and K are just a small tip of the iceberg of relaxation/exchange rates.


Chemical exchange

Chemical Exchange

dimethylamino-7-methyl-1,2,4-benzotriazine.


Chemical exchange1

Chemical Exchange

General Cases:


Modified bloch equations

Modified Bloch Equations


Example of chemical exchange

116 Hz

Example of Chemical Exchange

dimethylamino-7-methyl-1,2,4-benzotriazine.

When exchange rate is larger than

chemical shift difference, coalescence

between two signals occurs.


Another example

6

2

2

6

5

3

3

5

Another Example


Simulation

Simulation


Lab phase cycling

Lab: Phase Cycling


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