NMR spektroszkópia (vegyész mesterkurzus: VEMKSI

4312S)

7. rész: Diffúzió-szelektált 2D NMR spektroszkópia

Szalontai Gábor2014. december (45 ábra)

Diffusion Ordered SpectroscopY (DOSY)

MOBility Ordered NMR SpectroscopY (MOBY)

Two-dimensional spectroscopy, 2D

Mérés két időváltozó (t1 és t2 ) szerint….

Cél: - a spektrális felbontás javítása és ezáltal a spektrum

információtartalmának lényegesen jobb hasznosítása …- a mérés hatékonyságának javítása (információ/idő tényező) …

Eredmény:nagyobb molekulák váltak vizsgálhatóvá.

Három-, n-dimenziós spektroszkópia, 3D, nD.

előkészítés keveredéskifejlődés(t1) mérés(t2)

2D NMR: „abundant” nuclei (1H, 19F, 31P, …) correlation spectroscopy, the COSY experiment (vector model)

90o(x) t2 constant90o(x)t1(variable)

B1(90o)x

Mx=Msin2t1

Mz=Mcos2t1

B1(90o)x

Codein: 2D (COSY) spectrum

Correlations are detected between J-coupled nuclei ...

1D spectrum

Question: can we use the second dimension (evolution period: t1 ) to study a molecular property (such as shape, size, diffusion, etc.)

rather than the usual spin Hamiltonian (J-coupling, chemical

shifts, etc,)?

Answer: yes, provided these properties have an impact on the spectrum !!.

Results: a 2D NMR spectrum

1D NMR spectrum (t2 modulation)

1. relaxation times

molecular properties (examples of t1 modulation)

2. translational diffusion coefficients3. electrophoretic mobilities

t1

The effect of changing

stream gradient on

zanders

(without diffusion)

The diffusion

phenomenon

destroys the order!

The effect of changing

stream: small and big fishes

with diffusion (harcsa)

phenomenon

The large fishes hardly move !

PFG (PGSE) –NMR: a Carr-Purcell spin-echo

(C.S. Johnson 1999 Progress in NMR)

Disadvantages: short T2 values limits the applications to small to medium size molecules,

J-modulation prevent complete refocusing!

Echo amplitude at 2:

S(2) = Moexp(-2/T2)*

exp[-Dq2(- /3)]Advantages

the maximum signal strength is recovered,

The chemical shifts are refocused!

time is left for the molecules to move, the larger

the molecule is the longer time is

required, however, the larger they are

the shorter they live due to their short T2 values!

A gradiensek a térbeli kódolást végzik !!

A második gradiens a 180y-as átfordító

impulzus után „visszatolja” a spinek

fázisát az eredeti poziciójukba! Cohen

2005

Applications: Pulse (Field) Gradient Spin Echo experiment

• Determination of

– Translational self-diffusion coefficient, Dt

– Hydrodynamic radius, rH

– Hydrodynamic volume, VH

Theory• Diffusion ordered NMR: translational

diffusion coefficient (Stokes-Einstein relation)

a

TkD Bt

00 6

• a = molecular radius, o= solvent viscosity

Theory: (Relaxation) rotational diffusion coefficient (Debye-Stokes-

Einstein relation)

a = molecular radius, C = molecular rotational

correlation time, = solvent viscosity

(Dr = 1/3C)

It follows that e.g. T1 relaxation rates must be sensitive indicators of the molecular size too.

'30

0 8 a

TkD Br

kT

aC 3

4 3

Most common experiments

• PGSE-STE (STimulated Echo)

• PGSE-LED ( Longitudional Eddy current Delay)

• BPP-LED (Bipolar Pulse Pairs)

PFG (PGSE) –NMR: stimulated spin-echo (STE)

(C.S. Johnson 1999 Progress)

Echo amplitude at T+2:

S(T+2) = Moexp[(-2/T2)*

-/T/T1)]exp[-Dq2(- /3)]Advantages:

If 2 << T the relaxation depends mainly on T1, (even macromolecules can be studied)

If << 1/J the J-modulation is insignificant!

The sensitivity loss is normally overcompensated!

time is given to the molecules to relax

according to T1, out of the extreme narrowing conditions the larger

the molecule the longer T1 is. The

periods are kept short not to loose much

signal due to short T2 values!

Main obstacle against good resolution: Eddy–current caused by the gradient pulse current

Possible solutions:

-special RF coil design

-gradient pulse shaping

-active shielding of the gradient coils

-special pulse sequences (LED, BPP-LED)

PGSE – Longitudional Eddy–current Delay sequence (LED)

90o(x) t2 90o(x)T

Te

90o(-x) 90o(-x) 90o(x)

The fourth pulse stores the magnetization for a while (Te = the time allowed for the Eddy currents to vanish) again along the z axis, the fifth one brings it back to the x,y plane…

g

BPP-BiPolar Pulse – LED

90o(x)t2

90o(x)

T

Te

90o(-x) 90o(-x) 90o(x)

Often the method of choise: the composite bipolar gradient pulse combination (g-180o-(-)g) provides self-compensation of the Eddy current (for short ~ 95%).

180o(x)

180o(x)

g

Attenuation factor:

(++2) = exp[-Dq2(- /3-/2)]

The 180 pulses cause some loss of signal, but eliminate the effect of background

gradients and refocus

chemical shifts and produce

distortion free signals!

PGSE –NMR: (B.Antalek 2007 Concepts)

Essential components:

The PSGE sequence

The Pulse Gradient STimulated Echo sequence

The Bipolar Gradient Pulse sequence

Data collection stategies

To save time and increase the S/N ratio select the minimum number q2 values (q=g )

How much is the minimum?, one has to characterize properly even the fastest decay!

Gradient strength, g increase must be adjusted to the actual sample, i.e. to the distribution of the diffusion coefficients of the components!

Data collection: according to linear, squared and exponential functions in 8

steps from 2% to 95% amplifier power

Applications: separation of mixture based on the components diffusion constants (Diffusion Ordered Spectroscopy)

•DOSY: not much more then a convenient 2D data processing and displaying method (Johnson

1996) • In comparison with P(F)GSE it can

separate components of a mixture along the diffusion dimension if their translational diffusion differ.

PFG (PGSE) –NMR: inverz Laplace transformation (ILT) (C.S. Johnson 1999 Progress)

Inverze Laplace transformation:not so trivial if the

decays are not mono-exponantials

(e.g. if the peaks overlap)

Accuracy: 3-1 % in Dt!

Data analysis methods: inversion and display in the case of monodisperse

samples

Single exponantial (Levenberg-Marquardt)

DISCRETE, SPLMOD

Limitations: if diffusion coefficient for overlapping signals differ by less than a factor of two (three?) and/or their S/N ratio is low (…), they cannot be resolved in the diffusion dimension.

Data analysis methods: inversion and display in the case of

polydisperse samples

biexponantial fitting (SPLMOD)

DECRA

Continuous distribution analyses (CONTIN)

MaxEnt

Outlook of a DOSY spectrum

Log D (m2/s)

Dt

1H (or X) chem.shift / ppm

or

D (m2/s)

Data inversion and display

Task: n absorption mode spectra have been recorded with n predetermined values of q2(), (each having frequency points or channels), these must be transformed into 2D spectra with chemical shifts on one axis and the distribution of diffusion coefficients on the other.

q = gpulse area, = gradient pulse shape factor

I(q, m) = nAn(m)exp[-Dnq2(- )]

Ideal conditions: basic requirements

• Complete separation of signals• Good signal to noise ratio• Strong and linear Bo pulse gradients• Low constant background gradient• Low internal magnetic field gradient

caused by susceptibility changes over the sample

• No heat convection in the sample !• Low to medium solvent viscosity (?)

Higher fields or the use of other nuclei such as 19F, 31P or 13C will help a lot!

This means much longer acq. time

for e.g. 13C, but it may be

worthwhile!!

The stronger the gradient is the

larger molecules can be considered, but also the Eddy current effect is proportionally

larger!

Artifacts and pitfalls (Ref.: Aksnes MRC 40 (2002) S139)

•Calibration of the gradient strength

•Eddy current effects•Constant background gradients•Unwanted flow within the sample•Correction of effective diffusion

times

Calibration of the gradient strength Ref.: Holz JMR 92 (1991) 115-125

• We need absolute values in G/cm or T/m

• Gradient coil factor = gradient calibration constant?

• Shape factor = int(shape)/int(rectang.)

• Direct calibration with secondary standards

The usual high-resolution spectrometers can produce gradients of about 50-60 G/cm what is sufficient to analyze molecules up to 50 kGa.

Calibration of the gradient strength: 1H: proposed

primary standards

• Water self-diffusion coefficient: 25o C 2.3 *10-9 [m2/s]

• Benzene self-diffusion coefficient: 25o C 2.207 *10-9 [m2/s]

• H2O in D2O (trace) = 1.902 * 10-9 [m2/s]

• H2O in D2O (10 m %) = 1.935 * 10-9 [m2/s]

Calibration with secondary standards

(less-common nuclei) Ref.: Holz JMR 92 (1991) 115-125

• 13C: benzene self-diffusion coefficient: 25o C 2.207 *10-9 [m2/s]

• 31P: (C6H5)3P (3m) in C6D6 =

0.365 * 10-9 [m2/s]

19F: (C6H5F) = 2.395 * 10-9 [m2/s]

Applications: self-assemblies [(Pd(bifosz.)(N …..N)]1,2,3,4,5,6 tectons: 1H

DOSY

1:1

2:1

[Pd(dppp)]2+; L1

+ + +

+

+ + +

2a 3a 4a 5a

3aa 4aa 5aa 6aa

Applications: [(Pd(dppp)(N …..N)]1,2,3,4,5 tectons:

pyridine ortho protons, 1H DOSY in CD2Cl2

NN NNH

H H

H

Dt

1H chem.shift/ppm

Applications: [(Pd(dppp)(N …..N)]1,2,3,4,5 tectons: acenaphthane ortho protons 1H

DOSY in CD2Cl2

NN NN

H HDt

1H chem.shift/ppm

H HHH

Alkalmazások: önszerveződő rendszerek [(Pd(bifosz.)(N …..N)]1,2,3,4 tektonok: 1H

DOSY

Applications: a mixture of small to medium molecules: 1H DOSY in D2O

cyclodextrinecreatininpyridin

e

water

Conditionsg = 2 % - 95 %

number of steps = 8

data collection: linear

= 50 ms

= 1.7 ms

Alkalmazások: INEPT-DOSY [(Pd(bifosz.)(N …..N)]1,2,3,4 tektonok: 31P

DOSY

Alkalmazások: önszerveződő rendszerek [(Pd(bifosz.)(4,4’-bpy…)]1,2,3,4 tektonok: 31P

DOSY

Alkalmazások: önszerveződő rendszerek [(Pd(dppp)(4,4’-bpy…)]2,3,4,5 tektonok: 1H

DOSY

N NN N

12

34567

8

9

Alkalmazások: ruthenium complexes 1H DOSY dmso 298 K

[Ru(bpy)3]+

Dt = 180*10-12 m2/s

[Ru(methyl-bpy)3]+

Dt = 150*10-12 m2/s

[Ru(phenantroline)3]+

Dt = 165*10-12 m2/s

[Ru(diphenyl-phenantroline)3]+

Dt = 130*10-12 m2/s

Alkalmazások: inclusion complexes (CD – amino acids) 1H DOSY

Dt [*10-9 m2/s]

at 298 K

Viscosity [dyn s cm -

1] Ref.

-CD 0.30.264

saját

-CD

0.3180.98

10 mM

Larive Anal.Acta

-CD

0.320

Alkalmazások: szénhidrogének (alifás aminok keveréke) 13C DOSY

Lassúbb mérés, de lényegesen kevesebb az átfedő jel!

Chemical exchange in diffusion-ordered spectra, fast-exchange (Johnson, JMR 1993 102,

210)

D [m2/s]

[ppm]

D [m2/s]

[ppm]

Small diffusion-difference

Big diffusion-difference

Dobs = ffreeDfree + fboundDbound

ffree + fbound = 1

Chemical exchange in diffusion-ordered spectra, slow exchange (Johnson, JMR 1993 102,

210)

Small diffusion-difference

D [m2/s]

[ppm]

D [m2/s]

[ppm]

Big diffusion-difference