Are Polymer NMR Peaks Always Broad?

Solution NMR peak widths are mostly determined by two factors, homogeneous broadening and inhomogeneous broadening. Homogeneous broadening is governed by T2 relaxation, which is driven by the dynamics of the molecular segments. Small molecules rotate very fast in solution (>> 109 s-1), resulting in long T2 (~ seconds) and thus very sharp peaks (intrinsic peak width usually < 0.5 Hz). For polymers, there are different situations. For hydrocarbon polymers, each bond of the backbone rotates independent of the bonds that are more than 4-5 bonds away, and such rotations are almost as fast as those of small molecules. Therefore, NMR peaks of hydrocarbon polymers are almost as sharp as those of small molecules, and the peak widths are largely independent of molecular weight. For polymers that have strong interactions with solvents, the bond rotations might not be that free, resulting in shorter T2 and thus broader peak widths. You could think of the former case as a snake freely swirling in water while the latter case as a stiff coil of steel wire.

Inhomogeneous broadening is governed by the heterogeneity of chemical structure of the molecule. For example, a purely isotactic polymer has a uniform chemical structure throughout the backbone, while an atactic polymer has many different local structures (mmr, mrm, mrr, etc.). Therefore, an isotactic polystyrene has very sharp NMR peaks, while an atactic polystyrene has quite broad NMR peaks. The difference here is not homogeneous broadening due to T2 relaxation, but due to inhomogeneous broadening due to tacticity. In other words, the broad peaks on polystyrene NMR spectra are in fact many sharp peaks right next to each other.

In summary, polymer peaks are not always broad, and shimming is generally recommended for polymer samples. In fact, the extent of the peak broadening tells you a lot about the behavior of these molecules and their interaction with their surrounding environment.

Hydrogen Bonding Probed by 15N NMR

The nitrogen site of pyridine is a hydrogen bond acceptor. In the presence of a hydrogen bond donor, its 15N peak shifted upfield by more than 1 ppm. See picture below (blue: pyridine; red: pyridine + H donor). This is one way of probing the presence of hydrogen bond in solution.

a

How to Compare Integrations for Different Data Files

You can compare the signal integration of different data files. They will need to be acquired with the same receiver gain (rg). To ensure this, before you run your first sample, run rga, then type rg to record the receiver gain that has been determined. When you run your other samples, instead of running rga, you type rg and input the receiver gain that you wrote down for your first sample. This will ensure all the spectra that you want to compare signal areas against have been run with the same receiver gain.

It is possible to use different ns for different samples, but you will need to remember that signal area is proportional to number of scans and thus properly normalize your peak areas against ns.

When comparing peak areas, after integrating your first sample, save the integration results and return to main menu. Then do your second sample. Before you exit the integration mode, right click on the integration screen and select “Use lastscale for calibration” (see picture below). The peak areas will be rescaled such that the peak areas for your current sample will be quantitatively comparable to your last one.

Why don’t some protons have signals on 2D spectra?

This small molecule has good signals on 1H-15N HMBC:

However, upon incorporation into a polymer, the region expected to show correlation peaks is completely noise:

Why?

If you look at the 1D proton signals, plotted on top of the 2D spectra, the aromatic protons in the small molecule have sharp peaks, while those in the polymer have much broader peaks. The broadening is due to short T2. A simple though not the most rigorous way to estimate T2 is T2 = 1/(pi*Delta), while Delta is proton peak width in Hz.

Some 2D pulse sequences keep magnetizations on the xy plane for a long time (a few ms to > 100 ms). For protons with short T2, unfortunately, their signals cannot survive these pulse sequences. HMBC has the harshest requirements for T2.

While the no-show on 2D spectra is a bit disappointing, a short T2 does tell you important information about the dynamics of your molecules – it often indicates that they interact poorly with the solvent and are aggregating.

Correct Baseline for Pseudo-2D Data

Baseline correction is essential for T1, T2 and diffusion experiments as our target peaks are often broad and short, so any baseline imperfection can cause large errors.

Baseline correction is done by computer fitting of the baseline by a fifth order polynomial: y = A + Bx + Cx2 + Dx3 +Ex4 + Fx5. Since the baseline shapes cannot always be perfectly fit by such a polynomial and sometimes some peaks are so broad that the computer is having a hard time decide whether it is a peak or part of the baseline, we need to be aware of the limitations of the fitting algorithm and tweak strategy if the correction result is not good.

To check if your slices have good baselines, go to the Multiple Display mode. Make the peaks very tall so you can see the baseline well. When you do Scan Rows, zero intensity of each spectrum is at the middle line of the window. This means that a good baseline would not shift downward or upward if you adjust peak heights (remember: ten times zero is zero!). If, when you left click to make the peaks taller, the baseline sinks or rises, the baseline is not good and needs correction. Note that the vertical scale is erroneous – zero intensity of a slice is at the middle line of the window, while the 0 as indicated by the scale is at the bottom of the window.

While in the Multiple Display mode, you need to decide two factors for baseline correction: (1) a chemical shift range of spectrum in which you want baseline correction. Since it is often difficult to perfectly correct baseline across the entire spectrum, only correcting a smaller range often produces better result. For this, you will need to properly choose the left and right limit of the range that you want the baseline correction be done. Choose the limits such that tails of peaks do not extend there, i.e., there is only baseline or noise near there. In the figure below, I chose the limits to be 4.5 and 0 ppm. Write your choices down for the next step. (2) shape of the polynomial. I often find that lower orders of polynomial (linear, which means I only use the shape A + Bx; or quadratic, which means I only use the shape A + Bx + Cx2) do a better job than the ones that use all five orders, which often overdo the job.

Exit Multiple Display mode.

Click the tab ProcBars (on top row of the spectrum window). In Baseline Correction category, set ABSG to 1. This means that you allow the computer to fit the baseline with only a linear function (A + Bx), not the entire five orders of polynomial. I found this usually produces good result. Sometimes 2 is better. Experiment with it yourself. Set ABSF1 and ABSF2 to the left and right limits of your choice. Do this only for F2 dimension. F1 dimension is not used.

Click the Spectrum tab. On the command line, type abs2. This will perform an automatic baseline correction in the range of spectrum that you chose. Go back to Multiple Display and check the slices. It should look like the figure below. Note that the baseline of the spectrum between 4.5 and 0 ppm has been corrected. There are step changes at 4.5 and 0 ppm, which is because the spectrum within the window has been corrected for baseline and that outside the window still has very negative baseline. This is normal.

baseline

If you don’t like the correction result, just type xf2 again. This will erase all the baseline corrections that you have done. Start fresh from here.

The Multiple Display Function

The Multiple Display module can be accessed by clicking the Topspin icon that shows two spectra on top of each other. This module has two very useful functions: 1. compare a number of different 1D spectra; and 2. view each 1D slice of a 2D or pseudo-2D spectrum.

When you are done with the Multiple Display module, you should click the Return button on the far right end of the Multiple Display submenu to go back to the main menu.

To compare two 1D spectra, let’s say spectrum A and B, (1) load A onto the display; (2) click Multiple Display button; (3) find B in the browser, and drag it into the Multiple Display window. See the picture below. You can highlight one of the spectrum in the lower left window (the one below the Browser), then use the buttons to move or rescale it.

md-1d

To view each slice of a 2D or pseudo-2D spectrum, first go into Multiple Display mode, then click the Scan Rows button (the highlighted button in the figure below). Then hover the mouse above the contour lines and you will see the slice. The first slice is at the very bottom while the last slice is at the top. You can use left click to make the peaks bigger, or click the mouse wheel to make them smaller. Making the peaks taller will help you better see if phase correction and/or baseline correction is needed.

scanrows

The picture below shows one slice (slice #2, as the info box on the upper left corner shows “Index = 2”) of a pseudo-2D file.

baseline

Phase Correction for Pseudo-2D data

A pseudo-2D file is very similar to a 2D file, with the only difference being that the former only does Fourier Transformation in the horizontal dimension (by command xf2) while the latter needs FT in both dimensions (by command xfb). The data in these files are arranged in a matrix, with rows and columns. In pseudo-2D data, we only do phase correction and baseline correction on rows.

You can phase correct a pseudo-2D file by clicking the menu Processing -> Phase Correction, or by clicking the icon with a little distorted peak picture. In the new window, you need to select 2-3 slices as “representatives” of all the slices. Right click on the bottom-most slice, which is the first slice (you can tell that by the message “row: … Index = 1” in the info window on the top left corner), select Add. You will see a red circle being marked for the slice. Move mouse to one of the middle slices, repeat the Add operation. Repeat again for the last slice. Then click the button “R” (which means phase correcting rows), and you will see a window showing the three slices that you picked, like this:

phasecorr

Now you can phase correct the pseudo-2D file just like the way you correct 1D files. Drag the button 0 and 1 up and down so that all the peaks on all the slices have positive intensity and the baseline are not distorted. Click the Save and Return button. Then click Return, to go back to the main menu.

Note that for Inversion Recovery experiments, the first few rows are negative.

Then use the Multiple Display function to visually make sure each slice indeed has good phase. You are done.

13C Integration Can Be Very Helpful If Used Wisely

Although 13C spectra are commonly known as not being quantitative, peak integrations can be helpful in many situations. All protonated carbons have similar integration values, as you can see in this example:

13cinteg-aroma

Figure 1 is aromatic area, in which all protonated carbons have integration values of ca. 1.0. All unprotonated carbons have values of 0.4-0.5. The tallest peak is solvent.

13cinteg-aliph

Figure 2 is aliphatic area, in which each carbon (all are protonated) has an area of 1.1, slightly bigger than the protonated aromatic ones, but quite close.

Integrations can also help to solve puzzles of missing peaks. In this molecule, seven aromatic carbon peaks are expected, but only six show up on Figure 1. Why?

13cinteg-aroma2

Let’s look at the 134.6ppm peak closely.  Integration of this is 1.4 – this means that this is not just one protonated carbon (area = 1), but contains two overlapping peaks – one protonated and one unprotonated, which would have a total area of ca. 1.4. This solves the mystery of the missing carbon.

 

Processing T1/T2, kinetics, and diffusion data using Dynamics Center

Topspin’s new feature Dynamics Center does everything the old T1/T2 module does, and with much more capability and much less buggy issues. It also processes diffusion data better than the dosy2d command.

To set up T1/T2/kinetics experiments, please visit this entry. An example of a kinetics experiment can be found here.

Click here for instructions on how to set up diffusion experiments.

The data from these experiments are in pseudo-2D format. Each pseudo-2D file consists of many 1D spectra, each of which is called a slice. To process these data, follow these steps:

First, you need to properly phase correct your spectra. When done, examine each slice of the pseudo-2D file in Multiple Display mode. Scan through each slice to see if phase correction is good.

Next, you need to perform baseline correction. This is especially imperative if you are tracking some small peaks when there are other much larger peaks present on the spectra, in which imperfect baseline will severely skew your results.

Then you can launch the Dynamics Center in Analysis -> T1/T2 module -> Dynamics Center. Or you can type dync at the command line. It opens up a new window “Dynamics Center”:
dyncenter

Click the option that you need (T1; T2; diffusion; etc). Then click each step within the option: Sample -> Data -> …  For the Data step, you will need to look for the “2rr” file that has been generated by your experiment, as shown in the above figure (unfortunately there are many layers of folders that you will have to dig through). The 2rr file stores the pseudo-2D data, which contains a number of 1D spectra.

Using peak areas is often more desired than using peak intensities, especially your target peaks are broad and ugly (which is actually often the case for interesting objects of relaxation and diffusion study!). In the Data step, after finding the 2rr file in the Spectra tab, click the Integrals tab, select “Use peak areas (user defined) integrals”.

dync-select-integral

After clicking OK, a spectrum will be displayed. You can define your interested peaks and peak integration limits here. There might be a number of peaks that the computer has picked for you that you don’t really care about. Move cursor near one of the peaks, right click, select Delete in a region. Then drag a box around all the computer-picked peaks that you want to get rid of. This will delete these selections.

dync-define-integral

Next, select the peaks that you are interested in. move the cursor near the peak, right click, then select Add peak integration area. A black bar will appear on the bottom of the peak (see the figure below). You can drag the bar around or resize it.  Repeat for all the peaks you are interested in. You could also right click near a peak and select “Resize All” option to change the width of the integral for all the peaks. Note: for broader peaks, their tails can extend quite far, so if you define the integration limits to include all the visible intensities of that peak, you will end up integrating over a very wide range. The potential problem with this is that if your baseline correction is not that perfect and if that peak is not that much taller than the baseline imperfection, you will introduce a lot of errors. My strategy in dealing with this problem is to integrate only the majority, not the entirety, of the peak area. I usually define the integration limits by the places when the intensities are at ca. 10% of the peak intensity. For example, if my target peak has peak position at 1.0 ppm, and with peak intensity of X, and the intensity falls to about X/10 at 1.2 and 0.8 ppm, then I define [1.2, 0.8] as my integration limits. Since we are not interested in the absolute peak area in each slice, but rather the change of area between different slices, as long as the integration limits remain the same for all slices, we are fine, and we minimize the problem of baseline imperfection.

selectpeakarea

In Analysis, you can define the function that you want to fit, and various fitting parameters. For T1 experiment by Inversion Recovery, pick the following fitting function:

t1function

In View, you can define various options for display. Then you should get a window like this:

dyncenter2

You can get a decay curve for each peak you pick (lower left window; move your mouse to other defined peaks in the upper left window to see decay curves for other peaks in the lower left window), and a 2D spectrum (upper right window) with the vertical dimension displaying the dynamics information (T1, T2, diffusion coefficients, etc). For diffusion data, the upper right figure would be a DOSY spectrum (I think the Dynamics Center does a better job than the “dosy2d” command).

The Report function summarizes all the fitting results. You should pay particular attention to the “error” column, which is the standard deviation of your fitting. Usually, relative standard deviation should be < 5% to indicate a high-quality fit. High errors usually indicate either poor data processing (phase correction; baseline correction) or multiple dynamic components existing in your sample.

The Export function can export the fitting results to an Excel file.

The Help menu has a manual in which you can find the information on how to navigate this relatively easy software package.

Rotors for Solid-State NMR

Users need to order a rotor (container for your sample) from Bruker online store. The part number is B200147 (4 mm rotor with 3 Kel-F caps). It is kind of expensive but it can be used many times.

The rotor spins at very high speed (usually >=4khz) during experiments. The acceleration can reach several thousand g. No liquid is allowed in the rotor as it will be squeezed out during spinning. This would contaminate the probe and cause arcing, and make the spinning difficult. A poorly spinning rotor could explode inside the probe and incur thousands of dollars of repairs.