NMR Hahn echo decays in deuterated polyethylene oxide melts

Sample Preparation & Technical Details
The PEO samples were placed in 3 mm outer diameter NMR tubes to a height of roughly 15 to 20 mm, covered with argon to minimize the presence of oxygen near the PEO, and flame sealed to a maximum length of 35 mm.

The measurements were performed on a Bruker Avance III NMR spectrometer, equipped with a solid state probe head (HP WB 73 B MAS 4 BL CP BB WVT). Due to their length and the tilt of the sample chamber (magic angle), the glass tubes could not be inserted conventionally into the probe head using the sample transport tube. Therefore, the probe head was dismantled until the sample chamber could directly be accessed to place the sample tube within.

To prevent any movement (i.e. rotation) of the sample tube (Ø=3mm) inside the sample chamber (Ø=4mm), a 4mm glass rod was placed on top of the sample tube. A silicone piece between the glass rod and the wall of the sample transport channel was used to fix the position of the glass rod and prevent any movements of it. Then the probe head was fully reassembled again.

Temperature Calibration
The inflow temperature (T_i) of an air stream (1200 l/h) around the sample is used to control the sample temperature. Especially at high temperatures, the real sample temperature (T_s) differs not negligible from the displayed inflow temperature, that is T_s>T_i. This is partially due to the different dimension of the glass tubes compared to standard MAS rotors and the partially blocked sample transport channel. Therefore, before each sample insertion, the dependence between inflow and sample temperature is checked using the temperature dependence of the peak-to-peak distance between the OH and the CH₂ peak in an ethylene glycol ¹H NMR spectrum.

The ethylene glycol reference sample is prepared similar to the PEO-d₄ samples (~20mm height in a ~35mm x 3mm NMR glass tube) and inserted the same way into the probe head, including the described fixation with the same 4mm glass rod and silicone piece, to achieve a measurement situation as similar as possible.

The ¹H NMR spectrum of ethylene glycol is measured at different temperatures, after an equilibrium time (~15 min) to ensure a stable temperature condition in the sample chamber, using the FID sequence (π/2-pulse). From the spectra, the distance Δ between the OH and CH₂ peak is extracted, and the sample temperature is calculated according to [1,2]
T_s = 466.5 - 101.42*|Δ|  (Δ in ppm, T_s in K)

A linear regression is then used to link the inflow temperature with the sample temperature, and the regression equation is used to determine the needed inflow temperatures for the desired sample temperatures in the PEO-d₄ experiments.
[1] D. S. Raiford, C. L. Fisk and E. D. Becker, Anal. Chem., 1979, 51, 2050. DOI: 10.1021/ac50048a040
[2] A. G. Webb, Ann. R. NMR. S., 2002, 45, 1, Table 2. DOI: 10.1016/S0066-4103(02)45009-0

Measurements & Evaluation
The transverse relaxation decay of the deuterons was measured at a ²H resonance frequency of 46.1 MHz, using a Hahn echo (HE) pulse sequence (π/2 - τ - π - τ). The applied 16-step phase cycling can be found in the Bruker file "pulseprogram". The duration of the π-pulse, typically 10 µs, was twice the length of the π/2-pulse. The measurements were carried out in the completely molten state of the polymers at different temperatures between the melting point and 373 K.

The longitudinal relaxation time T₁ was measured using the inversion recovery pulse sequence (π - τ - π/2) and increases for all samples with temperature from roughly 40 ms (T_m) to about 100 ms (373 K). A recycle delay of 5 T₁ was applied between the repetitions of the pulse sequence to allow for complete spin-lattice relaxation. Starting from the end of the second waiting time τ, the second half of the spin-echo was acquired and Fourier transformed to the frequency domain. The transverse relaxation decay is then the evolution of the PEO peak area with time, where a time point is twice the waiting time τ plus the duration of the π-pulse.

The measurement of the transverse relaxation decay is repeated up to five times for either short & long waiting times or all waiting times, normalized to its maximum value and then averaged over the measurements. This procedure reduces the scattering of the data in the relevant regions, i.e. the region of high signal-to-noise ratio but small differences in signal (short waiting times) and the region of low signal to-noise ratio (long waiting times). In addition, repetitions in the region of low signal-to-noise ratio can be restricted to the longest waiting times (and one short waiting time for normalization), so that more scans could be used to increase the signal-to-noise ratio without prolonging the measurement time extraordinary.

Temperature Choice
The melting temperature T_m was determined as the peak temperature in the second heating run at 1 K/min, using a DSC6000 from Perkin Elmer (T_min=-70°C/0°C, T_max=100°C, t_eq=3 min/5 min). For the samples 3.5k, 33k and 75k a melting temperature slightly higher than 55°C was found, while the melting temperature for 300k lies below 50°C. 100°C was set as the upper temperature limit, to avoid/minimize oxidative thermal degradation of the samples. Taking the described temperature control and calibration into account, the investigation temperatures were set to 55°C, 70°C, 85°C and 100°C. However, the Hahn Echo decay of PEO-d₄ 75k at 55°C differs significantly from the decays at the higher temperatures, which indicates that the fully molten state is not yet reached at 55°C for this sample. Therefore, for the PEO-d₄ 75k sample, the measurement at 55°C was replaced by a measurement at 60°C. The similarity between the Hahn Echo decays at 100°C, 85°C, 70°C and 55°C/60°C in the log(-ln(g^D)) over log(t/T₂^eff) representation confirms the molten state of the samples at the investigated temperatures.

Dataset structure
In the following the structure and content of the dataset is explained.
The dataset contains a zip folder for each sample (sample folder), e.g. each molecular weight ("Sample_MolarMass") and the zip folder "Code", which contains the Matlab scripts for extracting T₂^eff and calculating the Hahn echo decays according to the respective equations in the publication 10.1063/5.0099293, as well as ASCII text files containing the parameters and results of the calculations used in the publication.

Within the sample folder you find

• a text file containing the parameters and data of the DSC measurements.
• a folder called "Relaxation", containing the parameters, raw and processed data from the ²H NMR HE & IR measurements in subfolders for each temperature.
• a folder called "Temperature_Calibration", containing the parameters, raw and processed data from the ¹H NMR FID (e.g. Spectrum) measurements of Ethylenglycol

Within the Code folder you find

• the matlab script T2eff to extract the effective transverse relaxation T₂^eff = t(g^D=1/e)
• the matlab script Rouse to generate the Hahn echo decay according to eq. (6) from 10.1063/5.0099293.
• the matlab script Crossover to generate the Hahn echo decay according to eq. (3)=(4)*(12) from 10.1063/5.0099293.
• the matlab script Reptation to generate the Hahn echo decay according to eq. (3)=(4)*(13(1, 14, 15)) from 10.1063/5.0099293.
• The with the latter three scipts generated Hahn echo decays for the experimental data at 85°C using the given parameters in the scripts.

All matlab scripts expect a tabstop seperated txt file with 25 headerlines, where they use only the first two columns. They all work with the PEO-d4_M_T.txt file in PEO-d4_M > Relaxation > T without further adjustments.

Data format
The DSC parameters and data are present in a tab stop seperated ASCII text file.
The NMR data in "Relaxation" or "Temperature_Calibration" are present in form of the original Bruker files (folder "Sample_MolarMass_Temperature") and a JCAMP-DX file ("Sample_MolarMass_Temperature.dx"), a text-based standard file format of the IUPAC for spectroscopic data, which combines all files generated during the acquisition and processing in a single file. The used compression mode is DIFF/DUP, e.g. the difference between successive values is encoded and the repetition of successive equal values is suppressed. In addition an ASCII text file ("Sample_MolarMass_Temperature.txt") containing the final results after data processing & evaluation can be found.

• "Relaxation" > PEO-d4_M_T.txt: Normalized Hahn echo decays after averaging of up to five measurements.
• "Temperature_Calibration" > TC_PEO-d4_M.txt: table relating the inflow temperature Ti of the compressed air with the real sample temperature Ts.

How to handle the NMR data & useful files
Since the NMR data was generated using a Bruker Avance III in combination with the Bruker software TopSpin (v2.1 & v.3.6.4), the easiest way to view and process the data further is with the help of the TopSin software, which is widespread in the NMR community and (currently) available under a free academic license. You can either add the whole folder "Sample_M_T" to the in TopSpin specified data directory or simply drag and drop the JCAMP-DX in the TopSpin window, which will generate the same folder structure in the current data directory.

Alternatively all parameters, raw and processed data are directly accessible in the text-based JCAMP-DX file or in the Bruker original files:

• fid/ser file contains the 1D/2D raw data (binary file)
• 1i/2ii & 1r/2rr files contain the 1D/2D imaginary & real processed data (binary file)
• vdlist contains the list of waiting times (ASCII file)