Unveiling an NMR-Invisible Fraction of Polymers in Solution by Saturation Transfer Difference

The observation of signals in solution NMR requires nuclei with sufficiently large transverse relaxation times (T2). Otherwise, broad signals embedded in the baseline afford an invisible fraction of nuclei (IF). Based on the STD (saturation transfer difference) sequence, IF-STD is presented as a quick tool to unveil IF in the 1H NMR spectra of polymers. The saturation of a polymer in a region of the NMR spectrum with IF (very short 1H T2) results in an efficient propagation of the magnetization by spin diffusion through the network of protons to a visible–invisible interphase with larger 1H T2 (STDon). Subtracting this spectrum from one recorded without saturation (STDoff) produces a difference spectrum (STDoff-on), with the nuclei at the visible–invisible interphase, that confirms the presence of an IF. Analysis of a wide collection of polymers by IF-STD reveals IF more common than previously thought, with relevant IF figures when STD > 0.4% at 750 MHz. A fundamental property of the IF-STD experiment is that the signal is generated within a single state comprising polymer domains with different dynamics, as opposed to several states in exchange with different degrees of aggregation. Contrary to a reductionist visible–invisible dichotomy, our results confirm a continuous distribution of nuclei with diverse dynamics. Since nuclei observed (edited) by IF-STD at the visible–invisible interphase are in close spatial proximity to the IF (tunable with the saturation time), they emerge as a privileged platform from which gaining an insight into the IF itself.


Nuclear Magnetic Resonance
CS was dissolved in a pD 4.5 buffer solution consisting of 350 mM CD3CO2D / 135 mM NaOD in D2O. All other polymer solutions were prepared in D2O, unless noted. NMR spectra were acquired on an Agilent Inova or Bruker NEO spectrometers operating at 17.6 T (750 MHz resonance of proton), Bruker DRX-500 (operating at 11.74 T, 500 MHz resonance of proton), Varian Inova 400 (operating at 9.39 T, 400 MHz resonance of proton) or Bruker 250 MHz resonance of proton) spectrometers. Spectra were processed and analyzed with Mnova software (Mestrelab Research S.L.). Table 1 were determined at 750 MHz. To this end, the integral of the 1 H NMR signals indicated in Table   S1 was compared to that of an external reference (maleic acid or trimethylsilyl propionic acid placed in a coaxial capillary inside the NMR tube) in a series of quantitative 1 H NMR spectra recorded at increasing temperatures (278, 298, 313, 328, and 343 K). The IF% at any T is defined as shown in Eq S1. IF figures lower than 1.5% were considered as zero.

%
x 100 Eq S1 S5  (128) and . Unless otherwise mentioned, the inter-scan delay (d1) was 6 s immediately followed by a saturation time of 3 s. The on-and off-saturation consisted of a train of low power saturation pulses of gaussian shape with nominal duration of 35.4 ms and separated by a 1 ms delay. The effective band-width of the saturation applied (BW eff ) was 130 Hz, a value that was determined experimentally in the spectrometer with a sucrose sample following the method described below. The frequency of the on-saturation was placed in an empty region of the 1 H spectrum, at a frequency -1125 Hz from the right end (starting of noise) of the lowest ppm visible signal in the NMR spectrum of each polymer.
This frequency is equivalent to -1.5 ppm in our spectrometer operating at 750 MHz. The frequency of the off-saturation was placed at 20 ppm, a position that is more than 10000 Hz away from any visible signal in all the 1 H spectra analyzed. STDoff-on spectra were obtained with the scans corresponding to the STDon and STDoff experiments interleaved during the acquisition and the corresponding FIDs subtracted automatically by the phase cycle. STDoff control spectra were acquired by application of the off-saturation pulse train only, without any FID subtraction. STD factors were calculated from the integrals of the STDoff-on and STDoff spectra using equation S2.

TD% x 100
Eq S2 For this purpose, the two spectra were processed identically. Integration ranges of the polymer signals are shown in Table S1. STD factors lower than 0.05% were considered as zero.

Experimental Determination of the Effective Band-width (BW eff ) Covered by the Saturation in
an IF-STD Experiment. BW eff (in Hz) depends on several experimental parameters, including the shape of the pulse, its nominal duration and power level, the inter-pulse delay used in the saturation train as well as the spectrometer hardware (RF amplifier and probe). In this section, a method is proposed for measuring BW eff in any modern spectrometer ( For small molecules in solution, as sucrose in D2O, at the typical frequencies of the NMR spectrometers, the subtracted STDoff-on spectrum shows the highest intensity for the peak/s that S9 is/are being affected by the saturation. In the same spectrum, the presence of NOE peaks that denote proton-proton proximity are of very low intensity (a few percent of the saturated peak/s) and can be easily identified as they appear with opposite sign respect to the peak/s that is/are being saturated. Other possible peaks are those generated by spin-diffusion phenomena (three spin effects), which may have the same sign that the saturated peak/s but their intensity is very modest and comparable to that of the NOE. The remaining peaks are those that are neither affected by the saturation, NOE or spin-diffusion; they will appear with null intensity in the STDoff-on spectrum.
Under these premises, it is straightforward to distinguish in a STDoff-on spectrum of sucrose the peak/s that is/are being affected by the on-saturation, and to determine experimentally an upper and lower limit values of BW eff by measuring the distance in Hz from the central frequency position at which the on-saturation is applied to (a) the furthest peak identified as saturated (lower limit, BW eff_lowerlimit ) and (b) the closest peak identified as not saturated (upper limit, BW eff_upperlimit ). The lower and upper limits of BW eff were measured for sucrose using the above series of gaussian saturation pulse-lengths in a Bruker NEO 750 MHz spectrometer ( Figure S1). The results obtained are given in Table S2. Figure S2 represents BW calc , this is the excitation band-width calculated with the spectrometer software, and the experimentally determined BW eff_lowerlimit and BW eff_upperlimit at each pulse-length. As a linear relationship can be expected between BW calc and BW eff , the points were fitted to a straight line so that at each pulse-length, the value of BW eff passes in between BW eff_lowerlimit and BW eff_upperlimit . Such a linear dependence provides BW eff_fit that is equivalent to BW eff in the IF-STD experiment ( Figure S2 and  The position of the on-saturation at 3.737 ppm is shown by an arrow. At the bottom is the STDoff spectrum (reference). In each STDoff-on spectrum the distance between the pair of stripped lines (in Hz) corresponds to the BW eff_fit shown in Table S2.  Figure S2 to a straight line. Average BW eff = (BW eff_upperlimit + BW eff_lowerlimit )/2 S13
The CPMG duration (t) was linearly varied along 16 steps between a minimum value of 1.4 ms (n = 1) and a maximum of ca. 6 to 7 times the highest T2. At each step, a spectrum was acquired with 64 scans. The interscan relaxation delay (d1) was larger than 5 times the highest 1 H T1 in the sample.
The absolute signal integral (I) at each value of t was fitted to the mono-exponential equation S3 to determine the relaxation time T2: where I(t) and I0 are the observed signal integrals at a certain value of t and for t equal to the minimum value of the series (t =1.4 ms), respectively. OriginPro 9.0 Software (Originlab Corporation) was used to perform the exponential fittings to obtain the 1 H relaxation times T2.

Determination of 1 H T2 values at the visible-invisible interphase of polymers was performed by
means of an IF-STD-CPMG experiment. This hybrid pulse sequence was built with a T2 filter based on the conventional CPMG sequence. 3 The experimental conditions used for STDoff-CPMG and STDoff-on-CPMG experiments were identical to those described above for the CPMG and IF-STD experiments, using 64 scans.

Determination of Translational Diffusion Coefficients. Translational diffusion coefficients (D)
were measured at 750 MHz with the BPPSTE experiment based on the stimulated echo and bipolar pulse field gradients (PFG) (sequences Doneshot in the Agilent and ledbpgp2s in the Bruker pulse sequence libraries, respectively). 4 The PFG strength was calibrated with a reference sample of D2O 99.9% at 298 K, D= 1.87ꞏ10 -9 m 2 s -1 . For the measurements with polymers, the diffusion delay was S14 set to 3 s, the duration  of the PFG encoding diffusion was set to 4 ms. The strength of the PFG was linearly varied between 4 and 58 Gꞏcm -1 along 20 steps, each one with acquisition of an FID.
Diffusion coefficients were determined by analysis of the signal integrals along the 20 spectra and non-linear fitting to the Stejskal-Tanner equation governing the integral attenuation in the experiment.
Determination of diffusion values was also performed with an IF-STD-BPPSTE experiment that used identical parameters. The later pulse sequence was built by incorporating the IF-STD scheme and the parameters described above to the conventional BPPSTE pulse sequence.