A.- F. Miller 2012 T1&T2 Measurement 1 Practicum 3, Fall 2012 Measuring the longitudinal relaxation time: T1. Strychnine, dissolved CDCl3 The T1 is the characteristic time of relaxation of Z- magnetization, also known as the longitudinal relaxation time. Knowledge of T1 enables you to make an informed choice of the duration of delay between scans. If too short a relaxation delay is chosen, then the peaks of slowly recovering protons will be smaller than they should be, and it will not be possible to compare peak areas to learn about proton numbers. Also, we use the T1s our first estimate for choosing mix times in NOESY spectra, and 3xT1 as our relaxation delay in NOESY spectra. Hence the need to know T1. Start with a beautiful 1d spectrum, and a calibrated pw90 (recall that this varies with the choice of power). (It turns out that the default value in the probe file is a good compromise for people in a rush or not bothered about perfection.) Fine point: phase up the spectrum and then type setlp0. This sets up the delay between the end of the read pulse and the start of data collection so that no zero- order phase correction is needed and all spectra will be positive absorptive. Recollect to embed the new delay in your parameter set. Under the Experiments choose 'convert current parameters to do... > Relax. Measurements > T1' This will retain your current sw, tof and pw90, but it will add a few features to the experiment to support measurement of the magnetization's recovery after inversion. To see the pulse sequence click Sequence in Figure 1. The first pulse is a 180 pulse (p1=2*pw90) that will invert magnetization. This places it in a high- energy state with respect to the field, so it will 'decay' back to the resting state. Time is allowed for this process, in the form of a delay called d2. So far all magnetization is still along Z, but its amplitude is recovering with time. To determine what the amplitude is after a given time d2, we use a 90 pulse (pw) [4] to 'read' our magnetization by rotating it into the XY plane where our receiver coils detect it [5]. We cannot monitor recovery continuously, instead we repeat the experiment 6 or more times, waiting a different amount of time d2 in each repeat before executing the read pulse. Thus we end up with a series of 1d spectra, each representing a different duration of recovery after the inversion pulse. In Acquire>Defaults, a set of three boxes invites you to enter first- guesses of the T1s you sample may have, and Agilent uses these to set the delays in the experiment to perform a measurement. Set T1 Mode to inversion recovery [6] (ignore the NOE choice unless you are measuring 13 C T1s. [7]), then set Min T1 to the shortest T1 you expect to be present among your resonances (say 0.5 sec.: enter 0.5) [8], Max T1 to the longest T1 you anticipate (err on the long side here, say 5 (seconds)) [9] and the time you are willing to devote to the experiment (eg. 0.1 (hours)) [10].
A.- F. Miller 2012 T1&T2 Measurement 2 The Min. and especially the Max times will be used to choose an array of d2 values ranging from very short to something on the order of your maximum estimate. You can see these by clicking on 'Arrays'. [11]. The experiment takes a long time in part due to the long relaxation time d1 allowed between scans [12]. This is chosen to be 5 times your estimated longest T1 you guessed ([9]). The duration of the experiment also increases in proportion to the number of scans collected for each value of the delay d2. Although the number of scans appears in this panel, you are not allowed to change it to something smaller than 4. For a good value of T1 it is wise to use multiples of 4 scans, but for a first quick check on a strong sample one scan will do. Therefore, go to Acquire>Acquisition and change the number of scans to 1. Make sure that gain is a number, not autogain [13]. You may also want to go into the 'Array' panel and decrease the number of values of d2 used (Click [11] in Figure 1). Because we are expecting an exponential recovery, we anticipate that an exponential array will be a better choice than a linear array (Figure 2). Thus in this case successive values of d2 are 2x the previous value, rather than being some value plus the previous value. The increment is the ln(2). If you want to triple each value to get the next one, use an increment of ln(3)=1.1. If I am rushing I choose an array size of 6 (the minimum allowed) and an increment 1.1. The resulting array covers a factor of approximately 700. Thus for a longest estimate of 3 seconds I want a shortest value of 0.004. I go back and make adjustments to the first value and increment as needed to get the last value I want. As always, close the Array box, check Sequence, Show Time and then Acquire. The result should be a series of spectra in which we see that spins are initially inverted and then gradually recover as the delay d2 is made longer (Figure 3). In the LHS (left- hand side) panel, with the 'Arrayed Spectra' tab active [0], choose to display spectra stacked vertically (activate the radio button ( ). Check the 'values' box to show the duration of d2 corresponding to each spectrum. Change values in 'Chart Dimensions' to alter the vertical spacing and heights of the individual spectra. For Vert. Pos. use 20 (from 90) Vert Height 300 [4] (from 900). Under Offset Vertical change this interactively (step size of 10) [5] with +10, it gives 17.7 (a good display) and in "Show". You see that different peaks recover in different times. The null represents approx T1 *0.7. Divide null time by 0.7 to estimate T1 1 sec/.7 = 1.4 sec for peak at 6 ppm. 0.5 s /.7 = 0.7 S for aliphatics. In Process>T1 Analysis (Figure 4 ), click on Display Last Spectrum. It should be upright as shown. If it is not, you will have to phase it manually (after activating the additional options on the right- hand- side of the graphical display window ). Figure 4 shows a case where the software picked a ridiculous number of lines.
A.- F. Miller 2012 T1&T2 Measurement 3 Activate the action buttons on the RHS of the graphics display window and activate threshold (Figure 5 ). Move the threshold up to be more selective. You can also use the cursors to restrict your analysis to one region of the spectrum by placing cursors around it and clicking the '+' magnifying glass. Then click on 'Do T1 Analysis' [4]. All the lines the instrument picked will be in the table in the RHS box [5]. First, all the picked peaks are listed and each is assigned an 'index' number, which will be used below to provide the T1 for the corresponding peak. Next there is a summary of the analysis in which each peak's T1 is provided along with the associated error. Finally a detailed analysis follows for each picked peak (just beginning to appear in the box [5]). You can see the recovery of each peak after inversion by clicking "Display all Peaks" [6], this is valuable because it allows you to confirm that the recoveries do in fact conform to single- exponential recoveries. However there is often too much data to be able to distinguish different build- ups. You can also display the data for selected resonances only. Using the chemical shifts provided with the spectrum (Figure 6 ) in conjunction with the numerical output telling you which index number corresponds to each chemical shift value you can select a few lines and plot the peak amplitude vs. duration of recovery d2 for them. Next to 'Display Selected Fits' enter the line numbers for the lines you would like information on, for example "1, 10, 36". Then <return>. A time course of magnetization recovery is produced for the peaks number 1, 10 and 36 in the line list (Figure 7). Don't believe T1 values derived from curves that don't fit the data well. Don't believe any values whose errors are more than 10% the value (read the numerical output in the summary of analysis section). Don't believe a T1 that are more than one third of the recovery time you used between scans (=d1+at). If the T1s you get are longer than (d1+at)/3, repeat the experiment with a longer d1, roughly 5 times the longest T1 you got. To get a copy of the graphical output, use the drag- down menu at the top of the screen File>Print Screen. In the window that opens (Figure 8) select PSland, ( ) file, give name with path (eg. che555/data/yourname/yourfile (omit the.ps), POSTSCRIPT, Mono/Color... Save, then Close. A digital copy of the graphics window will be saved for you to place in documents, presentations etc. If you want a white background, be sure to change the graphics window in advance (and change it back afterwards) by dragging down under Edit to Display. It is often helpful to be able to take the peak amplitudes out of the Agilent software for analysis in a spread- sheet or analysis software of your choice. To do this, select all the text you want in the text output window (Figure 9, ). Copy it (Ctrl C). Then go to the Linux drag- down menu called 'Applications' and select Accessories, then Text Editor. In the editor, Paste (Ctrl V), and the text you selected should appear. Save this document in your own folder in CHE555/data/YOUR- INITIALS.
A.- F. Miller 2012 T1&T2 Measurement 4 As usual, you can save your data set as a.fid file using the diskette icon in upper left of the VNMR window. Please save all your things in the directory with your own initials, in CHE555/data. Illustration of why the relaxation delay must be longer than T 1 If you do not allow sufficient time between scans for resonances to recover, they will be smaller in subsequent scans. If the total recycle time (d1+at) is shorter than the T1s of some resonances but longer than the T1s of others, then the former resonances will be shrunken more than the others, in your spectra. Thus, peak areas will no longer be proportional to the numbers of protons associated with each peak. Figure 11 compares the results of using four different d1 values all in combination with an at of 0.5. Thus, the total recycle times were 11.5, 3.8, 1.5 and 0.8 s (for d1 values of 11, 3.3, 1.0 and 0.3 s). The results show that the 0.8 s recycle time causes aromatic resonances, in particular, to be proportionaltely smaller (Figure 12). Note that the TMS line is also much smaller compared to the other lines when recycling is fast. The above partial saturation of slow- relaxing resonances can be prevented either by choosing a longer (d1 + at) or by using a smaller tip- angle pulse. If you use a 45 pulse then you do not have to wait as long between scans, because magnetization does not need to recover as much. Using a smaller tip angle in combination with a shorter recycle time allows you to get the best data per hour of spectrometer time. This is invaluable for weak spectra such as 13 C 1ds, or samples that are not stable. Once you know T1 the software can calculate the optimal pulse width and tip angle given a choice of d1. In the command line type 'ernst(3.4, 13.6)' for the example of a case where the T1 is 3.4 s. and the pw90 is 13.6 us. Thus the general form of the command is 'ernst(t1_est, pw90)'. This causes the software will update the pulse width and tip angle of the experiment for maximal sensitivity per hour of spectrometer time, given the d1 value in your parameter set. Measuring the transverse relaxation time T2 As for T1 measurement, begin with a beautiful 1d spectrum and a calibrated pw90. For best results phase up a nice 1d spectrum and type setlp0 to obtain delays that automatically produce an upright spectrum, then recollect to embed the new delay in your parameter set. Although the NMR experiment is a different one, the workflow is very similar to that employed to measure T1. But first... have a look at the FID from your beautiful 1d.
A.- F. Miller 2012 T1&T2 Measurement 5 Figure 12 shows that the amplitude, whether positive or negative, decays with what looks like a single exponential (roughly). We can estimate the characteristic time of the decay by looking for the time at which the amplitude has dropped to half of its starting value, in this case 0.2 s. This gives an estimate for T2, called T2* of T2*=τ1/2/0.7 = 0.2/0.7 0.3 s. However this is not the actual T2 because the FID amplitude decays not only to spin randomization but also due to magnetic field inhomogeneity, J- coupling, and other coherent effects. To measure the actual T2s of the spins, and thus get at a number that informs us about chemical exchange and other dynamics, we need to cancel out the other effects (more in lecture). To do this, we use a Carr- Purcell- Meiboom- Gill (CPMG) refocussing sequence. Obtain the NMR experiment employing the CPMG, use the draw- down menu Experiments>Convert current param. to do...>relax. Measurements>T2 Meas. Figure 13 shows the NMR experiment. To measure T2 (rather than T1) the first thing we do is employ a 90 pulse to put magnetization into the XY plane. Next we want to let it relax (transverse relaxation) and we will collect a whole series of spectra each resulting from a different duration of relaxation. During the relaxation we have the CPMG pulses going and the pulse sequence shows this train of pulses as the contents of the red parentheses (think of the drumming that runs in the background of rock songs). The number above and to the left of the red parentheses tells us how many times the parenthetical pulse train is repeated. Because there needs to be an integer number of repeats, the delay d2 can only be multiples of the duration of one repeat. Software takes care of this for us. In Acquire>Defaults [4], we enter our best guesses of the shortest T2 we expect [5] and the longest T2 [6], we also enter the amount of time we are willing to spend varies depending on the accuracy desired. For 1 H work we can ignore the NOE choices [7] (check in Acquire>Channels that this is true and see the Observe/Decouple statement). Then click "Array Relaxation Delay" [8], and the software will set up an array with a series of d2 values. Click on the Arrays button to see the d2 values suggested and make changes if you want (see above). Also change the number of scans as needed, in Acquire>Acquisition. Close the Array box, check Sequence, Show Time and then Acquire. When the experiment finishes it will automatically perform the analysis based on its choice of threshold etc. However we can look behind the scenes to see the spectra collected (Figure 14). In this display (produced using "arrayed Spectra" ) the result of a short relaxation delay is on the bottom and results of increasingly long delays are the spectra are stacked vertically above (showing the delay duration used for each spectrum ). Note that different peaks decay at different rates, in that the resonances on the left- hand side are essentially gone after 6.4 seconds whereas the three peaks on the right have decreased by a factor of 4 but are still visible. Figure 15 shows the spectrum that will appear when the experiment completes (Assumes that Acquire>Future Actions contains "process" as the "when experiment
A.- F. Miller 2012 T1&T2 Measurement 6 finishes".) As often, the software has chosen a reasonable threshold for peak detection, but it may not produce the results you want. In Process>T2 Analysis, you may need to go through the ppm peak list to identify the indices of the peaks you care about so that you can look up the T2s of those values in the large list of T2s for all peaks [4]. It is helpful when sorting through long lists of peaks, to have the spectrum itself be labeled. You can type dpf in the command line [5] to get ppm labels on the peaks, as shown here. If you want more peaks you will need to set a threshold yourself. As shown in Figure 16, click on "Display First Spectrum", activate the spectral analysis tools that normally appear to the right of the spectrum by clicking on the top icon, this will cause the rest of the icons to appear, including the one that allows you to set a threshold. After setting the threshold, click on "Do T2 Analysis" [4]. In this example, I raised the threshold so that only 6 peaks were analyzed [5]. In the text output box I have scrolled down a little [6] to show that beneath the list of peaks, and the list of their T2s and associated errors, the software provides details of the quality of the fits in the form of the calculated amplitude for each relaxation time for comparison with the actual amplitude [7]. As described for T1 analysis, you can select all of this text, copy it and paste it into a text file that you can copy to a thumb- drive and then read into spread sheet of mathematical software for more detailed analysis. Figure 17 shows the same text data output a little higher up, where the summary of the T2 results appears. Note the modest differences among the T2s of different resonances. In molecules where a proton is exchanging with solvent, or a portion of the molecule undergoes intermediate time- scale motions, you can see T2 values that are 10- fold shorter (or more) than the T2s of rigid non- exchanging Hs. Upon clicking "Display All Fits" (Figure 18) we see that the model (single exponential decay) provides a good description of the data, indicating that the T2 values have value, this along with the relatively low errors make these values trustworthy. Knowledge of the T2s is helpful when setting up 2D experiments that require resonances to persist in the XY plane for some delay within the pulse sequences. Examples include COSY and TOCSY.
[4] [5] T1 and T2, Figure 1 [6] [8] [9] [7] [10] [11] [12] [13] T1 and T2, Figure 2
[0] T1 and T2, Figure 3 [4] [5] T1 and T2, Figure 4
T1 and T2, Figure 5 [5] [6] [4] T1 and T2, Figure 6
T1 and T2, Figure 7 T1 and T2, Figure 8
T1 and T2, Figure 9 T1 and T2, Figure 10
T1 and T2, Figure 11 Recovery delay (s) 0.3 1.0 3.3 11 Often the relevant time is d1 + at. T1 and T2, Figure 12
T1 and T2, Figure 13 [4] [5] [7] [6] [8] T1 and T2, Figure 14
[5] T1 and T2, Figure 15 [4] T1 and T2, Figure 16 [5] [6] [8] [4] [7]
T1 and T2, Figure 17 T1 and T2, Figure 18