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Measuring Kinetics of Dynamic Processes By NMR | CHEM 777, Study notes of Chemistry

Material Type: Notes; Class: Chem Spectroscopy; Subject: Chemistry; University: University of Massachusetts - Amherst; Term: Unknown 1989;

Typology: Study notes

Pre 2010

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Ch 777 Spring 03, page 33
16. Measuring kinetics of dynamic processes by NMR
What is the "NMR timescale"?
What dynamic processes can be monitored?
a) motion which enhances relaxation or averages an NMR parameter
examples:
1. Methyl group rotation at right frequency promotes T1 relaxation
2. Motion of lipid in different phases (bilayer in gel vs liquid crystal vs
vesicles…) averages lipid headgroup 31P spectrum in diagnostic ways
when motional frequency is faster than frequency range of parameter
being averaged
b) chemical exchange between 2 states which differ in or J or T1 or T2
Compare the rate k=1/τc of the dynamic process to
the NMR parameter being averaged: ∆δ or J or T1 or T2
timescale: slow exchange intermediate exchange fast exchange
δ>> 1
AB
1
AB
<< 1
AB
k<< AB kAB k>> AB
J>> 1
JAJB
1
JAJB
<< 1
AB
T1 or T2>> 1
1T1A1T
1B
etc etc
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16. Measuring kinetics of dynamic processes by NMR

What is the "NMR timescale"?

What dynamic processes can be monitored?

a) motion which enhances relaxation or averages an NMR parameter

examples:

1. Methyl group rotation at right frequency promotes T

1

relaxation

2. Motion of lipid in different phases (bilayer in gel vs liquid crystal vs

vesicles…) averages lipid headgroup

31

P spectrum in diagnostic ways

when motional frequency is faster than frequency range of parameter

being averaged

b) chemical exchange between 2 states which differ in or J or T

1

or T

2

Compare the rate k=1/τ

c

of the dynamic process to

the NMR parameter being averaged: ∆δ or ∆J or ∆T

1

or ∆T

2

timescale: slow exchange intermediate exchange fast exchange

A

B

A

B

A

B

k <<

A

B

k ≈

A

B

k >>

A

B

J >>

J

A

− J

B

J

A

− J

B

A

B

T

1

or T

2

T

1 A

T

1 B

etc etc

McConnell equations

Recall general Bloch equation

d

r

M

dt

r

M ×

r

B

0

r

M ×

r

B

1

(t )) −

(M

x

x + M

y

y)

T

2

(M

z

− M

0

)ˆz

T

1

express

r

B =

r

B

0

r

B

1

(t), then

d

r

M

dt

r

M ×

r

B) + relaxation terms

r

M ×

r

B =

x

y

z

M

x

M

y

M

z

B

x

B

y

B

z

x (M

y

B

z

− M

z

B

y

y(M

x

B

z

− M

z

B

x

z (M

x

B

y

− M

y

B

x

For

r

B

0

= B

z

and

r

B

1

= (B

1

cos t) ˆx + (B

1

sin t) ˆy

This is an x pulse: B

1

on Larmor frequency, starting on x in the

laboratory frame, fixed on x in the rotating frame.

dM

x

dt

= (M

y

B

0

− M

z

B

1

sin t) −

M

x

T

2

dM

y

dt

= − (M

x

B

0

− M

z

B

1

cos t) −

M

y

T

2

Now consider exchange process

d[A]

dt

= −k

1

[A] + k

− 1

[B]

d[B]

dt

= k

1

[A] − k

− 1

[B]

d[A]

dt

[A]

A

[B]

B

d[B]

dt

[A]

A

[B]

B

Then incorporate exchange into processes occuring to M

x

of A = M

Ax

M

Bx

, etc

dM

Ax

dt

= (M

Ay

B

0

− M

Az

B

1

sin t) −

M

Ax

T

2

M

Ax

A

M

Bx

B

= (M

Ay

B

0

− M

Az

B

1

sin t) −

M

Ax

T ′

2 A

M

Bx

B

dM

Ay

dt

= (M

Az

B

1

sin t − M

Ax

B

0

M

Ay

T

2

M

Ay

A

M

By

B

= (M

Az

B

1

sin t − M

Ax

B

0

M

Ay

T ′

2 A

M

By

B

and corresponding equations for M

Bx

, M

By

Equation shows that exchange increases relaxation rate, so broadens

resonance:

T ′

2 A

T

2 A

A

T ′

2 B

T

2 B

B

General equation is complex… (Evans pp 45-46)