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How To Measure T1 and T2For TopSpin 2.1.5

By Mike Brown 11192009.ver.24

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What we will cover• The sample

• How to measure the 90 degree pulse width

• Some definitions

• Estimation of the T1

• Setup of the T1 experiment

• Processing and analysis of the T1 experiment

• Analysis and print out of the results

• Estimation of the T2

• Setup of the T2 experiment

• Spread sheets

• Processing and analysis of the T2 experiment

• Analysis and print out of the results

• Export of the data

• Helpful hints and tips

• Some macros and AU program to help you

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The Sample

• The sample we are using for this experiment is a sample of DOPED 1% H2O in 99% D2O.

• It also has some Labeled Methanol.

• It is doped with Gadolinium Chloride (0.1mg/mL GdCl3)

• You may know this sample as the HWT sample

Labeled Methanol

1% H2O

Part Numbers CIL: 92265Bruker: Z10246Wilmad: WGH-90Cost: ≈ $200 USD

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• Some organic solvents will produce T1’s that can be very long

• If the sample is degassed you may have very long T2’s

• Try to use as much sample as you can (with out affecting the shimming) to get better S/N in less scans

• If your solvent is H2O (more than about 10%) be aware of radiation damping effects.

• pH, temperature, concentration and solvent effects may be observed in T2 measurements. And they can be quite severe.

• T1’s can be affected by concentration and temperature.

Other Samples

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It is extremely important to have accurate 90 degree PW’s for T1 and T2measurements. You are moving spins and it must be accurate movement.

• Tune the Probe very carefully

• Make sure d1 is long enough (d1 + aq must be greater than 5 X T1)

• Shim the system as well as you can

• Make sure you are on resonance exactly

• Use zg as the pulse program

• Use the AU program “paropt”

• Or you can use the Module “popt”

• Or you can run the experiment manually.

• Set the 90 degree pulse width as short as possible for your probe and system (6 usec is minimum for 1H)

• Report or record the power level as well as the pulse width

Measuring the 90 degree Pulse Width and Power Level

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On ResonanceOn Resonance

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You can easily put the system on resonance by using the “gs” mode or you can simply use the icon after placing the cursor on top of the peak.

Off Resonance

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Measuring the 90 degree pulse width and power level with the AU program “paropt”

On the command line enter: “xau paropt”Answer the questions and the system will automatically run an array with p1 incremented properly

Its almost always better to find the 360 and divide by 4

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Measuring the 90 degree Pulse Width and Power Level with the module “popt”

You must set up the “user defined ft”, a command called: trf

Change PH_mod to “pk”Change FT_mod to “fqr”

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Measuring the 90 degree Pulse Width and Power Level with the module “popt”

Once you click “Save” the NEXP is calculated for you, from the STARTVAL, ENDVAL and INC.

Convenient

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Measuring the 90 degree pulse width and power level with the module “popt”

First null is at 17.49 usec (180 degree ) 90 degree PW is 8.745 usec at pl1 = -2.02 dB

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We would have better accuracy if we started at the approximate 270.

Continued on past the 360 to the 450 degree pulse. Then the first null would be the 360 degree pulse width, we would then divide by 4 to get the true 90 degree pulse width.

Measuring the 90 degree pulse width and power level with the module “popt”

360

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Some helpful definitions: T1

• T1: Spin-lattice relaxation time T1 characterizes the rate at which the longitudinal Mz component of the magnetization vector recovers. It is thus the time it takes for the signal to recover 63% [1-(1/e)] of its initial value after being flipped into the magnetic transverse plane. Hence the relation:

• Nuclei are held within a lattice structure, and are in constant vibrational and rotational motion, creating a complex magnetic field. The magnetic field caused by motion of nuclei within the lattice is called the lattice field. The lattice field of a nucleus in a lower energy state can interact with nuclei in a higher energy state, causing the energy of the higher energy state to distribute itself between the two nuclei. Therefore, the energy gained by nuclei from the RF pulse is dissipated as increased vibration and rotation within the lattice, which can slightly increase the temperature of the sample. The name spin-lattice relaxation refers to the time it takes for the spins to give the energy they obtained from the RF pulse back to the surrounding lattice, thereby restoring their equilibrium state.

• Also called longitudinal relaxation

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Is T1 always longer than T2?

The following almost always holds true:

In most situations (but not in principle) T1 is greater than T2.

If T2 were to be greater than 2T1, then (during relaxation) the vector sum of the transversal and longitudinal magnetizations would become greater than the equilibrium magnetization, this is physically impossible.

A relationship

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• T2 characterizes the rate at which the Mxy component of the magnetization vector decays in the transverse magnetic plane. It is the time it takes for the transverse signal to reach 37% (1/e) of its initial value after flipping into the magnetic transverse plane. Hence the relation:

• T2 decay occurs 5 to 10 times more rapidly than T1 recovery.

• The corresponding transverse relaxation time constant is thus T2*, which is usually much smaller than T2. The relation between them is:

• where γ represents gyromagnetic ratio, and ΔB0 the difference in strength of the locally varying field.

• Unlike T2, T2* is influenced by magnetic field gradient irregularities. The T2* relaxation time is always shorter than the T2 relaxation time.

• Also called transverse relaxation

Some helpful definitions: T2

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Estimation of T1

• The pulse program is t1ir1d

• Set d1 + aq to 5 times the “estimated” value for T1

• Set p1 to the measured 90 degree pulse width at pl1

• Set d7 = d1

• The variable in this experiment is d7, decrease it until you see a null in signal amplitude

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Estimation of T1

d7 = 5 seconds is the reference

d7 = 100 milliseconds

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Estimation of T1*

d7 = 115 milliseconds is Tnull

Rough estimation of the T1 value from the null-point value by using T1= Tnull /ln(2).

T1 (estimated) is ≈ 165 milliseconds

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Measuring T1

• Call up the parameter set PROTONT1

• Pulse program is “t1ir”

• Make a vdlist• make the parameters make sense • Set d1 + aq to 5 times the estimated

T1• Set f1 td to the number of entries in

your vdlist (or the number of entries you want to use).

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Measuring T1

The VD List

#T1test

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5

2.5

1

0.7

0.5

0.25

0.1

0.07

0.05

0.025

0.01

0.007

The VD list units, by default is in seconds. There is no need to place units in the list.

You should put the “0” in front of the decimal point, it makes it easier to read and TopSpin will not complain.

You should start with the longest time and work down to the shortest (see below)

Usually, you want to choose a minimum number of entries (I chose 16 values for this presentation, way too many)

You want at least 2 (better 3) entries to be much longer than the estimated T1

You also want at least 2 values to “bracket” the estimated value of T1

For automation reverse the order. (For use in ICONNMR)

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Measuring T1

Data after tf2 (ft in F2 dimension only)

Data after phasing

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Measuring T1

Data after tf2 (ft in F2 dimension only)

Data after phasing

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Calculating T1

• Start the “T1/T2 Relaxation Guide” module

1. Extract a slice

2. Integrate

3. Peak Pick

4. Select the fitting Function

5. Calculate

6. Print it out

7. Plot it out

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Extract a row (FID)

Choose #1

(the longest VD time)

It will be displayed and

processed, and displayed

automatically

Then choose “Manual Integration” from the next window

Calculating T1; Extracting a slice

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• Integrate the peak (s) of interest

• Then export it to the Relaxation Module

Calculating T1; Integrate

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• Pick the peaks you want 1 per integrated region

• Export to the relaxation module.

Calculating T1; pick peak

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You should now select the:

Relaxation Window

This will open the actual calculation module.

This will immediately allow you to select the fitting function and its parameters

Calculating T1; Start Relaxation Module

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• Choose the longest vd time for this (#1 FID)

• Number of points to search for a peak

• Number of points in your list

• Choose uxnmrt1 as the function type

• Choose vdlist

• Use the default for everything else

• Click “OK” to start calculations

Calculating T1; Fitting function

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• You should have at least 2 points on the flat portion of the curve

• Delete any points that do not “fit”(within reason)

• Check the SD also

Calculating T1; Results

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A report like this can be obtained for each peak

It is a standard text file, it can be copied and pasted into another document or printed.

These results are close to our rough estimate of 165 milliseconds.

Calculating T1; The report

Dataset :

C:\Bruker\TOPSPIN/data/nmrsu/nmr/T1_D2O/2/pdata/1INTENSITY fit :I[t]=I[0]+P*exp(-t/T1)

16 points for Peak 1, Peak Point at 4.706 ppmResults Comp. 1

I[0] = 9.982e-001P = -1.917e+000T1 = 174.683mSD = 2.220e-002

tau ppm integral intensity

20.000s 4.706 4.3176e+009 5.0616e+00817.000s 4.706 4.3192e+009 5.0485e+00810.000s 4.706 4.3201e+009 5.063e+0087.000s 4.706 4.3202e+009 5.059e+0085.000s 4.706 4.3214e+009 5.0646e+0082.500s 4.706 4.322e+009 5.0843e+0081.000s 4.706 4.2999e+009 5.0247e+008

700.000m 4.706 4.1908e+009 4.9078e+008500.000m 4.706 3.8944e+009 4.5565e+008250.000m 4.706 2.4707e+009 2.9091e+008100.000m 4.709 -2.4617e+008 -6.1381e+00770.000m 4.703 -1.0029e+009 -1.4851e+00850.000m 4.705 -1.8621e+009 -2.0923e+00825.000m 4.707 -2.7757e+009 -3.6315e+00810.000m 4.707 -2.9985e+009 -4.1287e+0087.000m 4.705 -3.1515e+009 -4.0753e+008

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The layout is t1norm.xwp

Calculating T1; The Curve

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Use the au program hwcal to automatically get the half height line width of the peak of interest.

To estimate the T2*

Use this equation:

T2* = 1 / [ π X (½ line width, Hertz ) ]

In our example

T2* = 123 millisecond.

Estimating T2

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• Create a VC list

• Choose a correct value for d20

• Use the Spread Sheet to create a VD List

• Call up the Parameter set PROTONT2

• Make sure the correct 90 degree pulse width and power level is entered

• Enter the VC and VD list in the proper places (eda)

• Adjust rg (from a 1H 1D experiment )

• Acquire data

• Process and calculate the value for T2

• Print and plot.

Measuring T2

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• Enter d20 (1 to 20 milliseconds)

• Enter p1 (1H 90 degree pulse width at pl1)

• Copy the VC list and paste in eda

• Copy the VD list and paste in eda

• Make sure the VD list makes sense

• You do not want the time for the VC loop to be too long

Measuring T2

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VC loop NS loop TD1 loop

1 # of entries in the VC list

2 (And VD list ) that you want

4 to use.

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etc

The pulse program, cpmg

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#t2count

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2

4

8

16

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64

128

256

512

1024

2048

The VC and VD list

#t2time

0.040

0.080

0.160

0.320

0.640

1.281

2.561

5.122

10.244

20.489

40.978

81.956

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The parameters in eda

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Notice the following:

The Y axis is in # of the FID’s

And we have several FID’s that appear to be “beaten down” this indicates we should have used less entries in our VC list.

The raw data

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Without mc in the F2 dimension

The processed data

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With mc in the F2 dimension

No phasing needed !

The processed data

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• Do the integrations and peak picking exactly as you did for T1

• Choose uxnmrt2 as the function type

• Adjust “Number of drift points”so that all points are considered

The relaxation module for T2

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• Notice the X axis is in seconds, not counts

• Adjust “Number of drift points” so that the X axis time agrees with the longest time in the VD list.

Calculation of T2

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• You should have at least 2 points (better 3) along the flat portion of the curve

• Delete any outliers (within reason)

Calculation of T2

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• Notice the calculated value of T2 is 153 milliseconds

• We estimated the T2*to be 123 millisecond

• Check the SD

Display the results

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Dataset :

C:\Bruker\TOPSPIN/data/nmrsu/nmr/T2_D2O/1/pdata/1

INTENSITY fit :

I[t]=P*exp(-t/T2)

12 points for Peak 1, Peak Point at 4.704 ppm

Results Comp. 1

P = 1.261e+000

T2 = 153.478m

SD = 1.563e-002

tau ppm integral intensity

40.000m 4.704 5.7346e+009 3.0006e+008

80.000m 4.704 4.3229e+009 2.2666e+008

160.000m 4.704 2.4668e+009 1.2908e+008

320.000m 4.704 8.4805e+008 4.3483e+007

640.000m 4.705 1.8778e+008 8.4876e+006

1.280s 4.706 1.1637e+008 4.6847e+006

2.561s 4.706 1.1578e+008 4.6752e+006

5.121s 4.706 1.1384e+008 4.5985e+006

10.242s 4.706 1.1445e+008 4.6077e+006

20.484s 4.706 1.1564e+008 4.6366e+006

40.969s 4.706 1.1549e+008 4.6454e+006

81.938s 4.706 1.1387e+008 4.588e+006

================================================================

Calculating T2; The report.

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• Keep temperature constant

• Repeat the test 3 times and average the results

• Make d1 + aq at least 5 times T1

• Tune the probe as well as you can

• Measure the 90 degree pulse width as accurately as possible

• Keep the 90 degree pulse width as short as possible (6 usec minimum for most probes) Do not exceed the power limits of the probe.

• Do not spin the sample

• Consider the effects of convection or diffusion of the sample (shorten d20 to fix this, or use mc for processing in the f2 dimension)

Tips for accurate results.

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The ZZ macro

p1

pl1

acqu

zg

em

ft

pk

abs

Macros

The TUNEA macro

acqu

atma

The TUNEMX macro

wbsw

acqu

atmm manWbsw

The tfp macro

lb

traf

ft

The ZZ macro is useful for calculating the 90 degree pulse width.

The TUNEMX and TUNEA macros are very useful for tuning the probe very precisely.

The tfp macro is very similar to efp, but you get much better results. The traf function can increase S/N and resolution at the same time.

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Name Short description

autot1 AU program for automatic processing of a 2D T1/T2 experiment with subsequent T1/T2 calculation.

decon_t1 AU program for automatic deconvolution of a 2D T1/T2experiment.

proc_2dt1 AU program for automatic processing of a 2D T1/T2experiment with subsequent T1/T2 calculation.

proc_t1 AU program for automatic processing of a 2D T1/T2experiment with subsequent T1/T2 calculation.

Read the header of each AU program to get more information

And usage instructions

AU programs that can helpful

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Thank you for your attention

Are there any questions ?