1 H DOSY analysis of high molecular weight acrylamide-based copolymer electrolytes using an inverse-geometry diffusion probe

Copolymers of [2-(acryloyloxy)ethyl]trimethylammonium chloride (AETAC) and acrylamide (AAm) (AETAC- co -AAm) are polyelectrolytes used as ﬂ occulants in wastewater puri ﬁ cation. Diffusion-ordered two-dimensional NMR spectroscopy (DOSY) experiments for AETAC- co -AAm samples with M w ranging from 1.9 to 3.9 million and a polyacrylamide sample with M w of 1.3 million were carried out in pure D 2 O and in D 2 O containing 0.1 or 1 M NaCl using an inverse-geometry diffusion probe system. Projections of the DOSY contour plots onto the diffusion coef ﬁ cient ( D ) dimension gave distributions of D for the AETAC and AAm units in the samples. The D values at the maximum point of the distribution ( D p ) agreed fairly well with those determined by dynamic light scattering.

The properties of AETAC-co-AAm in aqueous media have been studied by light scattering and viscometry [4]. The relationships between the weight average molecular weight (M w ), root mean square radius of gyration (R g in nm) and intrinsic viscosity ([η] in dL/g) were determined for AETAC-co-AAm with 30% AETAC: R g = 0.033 M w 0.54 , (1 M NaCl 25°C, 4.5 × 10 5 ≤ M w ≤ 2.7 × 10 6 ). The effect of ionic strength on [η] was also investigated for NaCl concentrations (C s ) between 10 −2 and 1 mol/L, with a semirigid configuration of the copolymer chains at low C s values being suggested owing to the absence of a linear relationship between [η] and C s −1/2 [4]. The interaction between AETAC-co-AAm and an anionic perfluorinated surfactant was studied by NMR spectroscopy to elucidate the mechanism of flocculation [6]. Full spectral assignment of 1 H and 13 C resonances was achieved with 1D and 2D experiments. The 1 H NMR spectra of AETAC-co-AAm with 14% and 23% AETAC in D 2 O (1% w/v) showed a higher multiplicity than the corresponding spectra of AETAC-co-AAm with 42% and 54% AETAC, and a stiff rod-like structure of the copolymer chains at higher AETAC compositions was suggested. This interpretation was consistent with the 13 C NMR spectra of AETAC-co-AAm, in which the number of resonances with higher AETAC compositions was smaller than that with lower AETAC compositions [6].
One of the most commonly used pulse sequences for DOSY experiments is the bipolar pulse pair stimulated echo sequence with a longitudinal eddy current delay (bpp-steled) (Fig. 2) [45]. The observed echo intensity f(G) at a given PFG strength G (in G/cm) is given by the Stejskal-Tanner expression: where G 1 represents the first (the smallest) value of the gradient ramp steps; τ 1 , τ 2 , δ, and Δ are delays, which are shown in Fig. 2; γ is the magnetogyric ratio of the observed nuclide; and T 1 and T 2 are the longitudinal and transverse relaxation times, respectively. Modern NMR spectrometers are generally equipped with a PFG system (probe and amplifier) generating a maximum G of several tens to 60 G/ cm and a maximum δ of several milliseconds. To obtain 5% echo attenuation f(G)/f(G 1 ), which is required for reliable DOSY experiments, a delay, Δ, of approximately 460 ms (Eq. 1) is required to determine a D of 10 −11 m 2 /s under the following experimental parameters: a maximum G of 60 G/ cm and a δ of 5 ms. A larger Δ is necessary as D decreases and as M w of the solute polymer increases because the relationship between D and M w roughly obeys D ∝ M w −0.6 .
Applying a large Δ for DOSY experiments of AETAC-co-AAm severely reduces the f(G) intensity because T 2 of the copolymer resonances is expected to be less than several tens of milliseconds (see Eq. 1 and Supplemental Material) owing to low segmental mobility, as described above. In our previous studies [37,46], DOSY experiments of AETACco-AAm with M w ranging from 5.1 × 10 6 to 1.5 × 10 7 were carried out using a diffusion probe system with a maximum G of 1200 G/cm. The D values determined by DOSY agreed with those determined by dynamic light scattering (DLS). However, the DOSY experiments gave broad distributions of D owing to the low signal-to-noise ratio (S/N) and poor resolution of the spectra. Recently, an inverse-geometry diffusion probe system (with a maximum G of 1800 G/cm) optimized to perform 1 H NMR diffusometry was devised. In contrast to conventional (normal geometry) diffusion probes, which are useful for NMR diffusometry of low γ nuclei, the inverse-geometry diffusion probe is optimized for 1 H DOSY experiments of high molecular weight polymers. For example, Lopez and coworkers reported 1 H NMR diffusometry experiments for polystyrene sulfonates with M w up to 3.4 × 10 5 in D 2 O using this inverse-geometry diffusion probe [47]. The M w values of AETAC-co-AAm investigated in our present study are larger than those of polystyrene sulfonates by one order of magnitude. This inverse-geometry diffusion probe enabled us to obtain 1 H DOSY spectra with greater resolution than those obtained in our previous studies.

Preparation of polyacrylamide and AETAC-AAm copolymers
Radical polymerization was performed in water at 40°C for 15 h with V-50 as the initiator. Polyacrylamide (sample A) and AETAC-co-AAm (samples B, C, D) with different monomer compositions and molecular weights were synthesized by changing the concentration of V-50 from 0.01 to 1.06 mol% in the monomer mixture. The reactions were Fig. 1 The chemical structure of AETAC-co-AAm Fig. 2 The bpp-ste-led pulse sequence [45]. The encoding gradients of a stimulated echo (ste) sequence were applied as symmetrical bipolar pulse pairs (bpp) of the total duration, δ. The longitudinal eddy-current delay (led) sequence was extended with a delay period, T e stopped by cooling, and the polymers were isolated by repeated precipitation in acetone. Polyacrylamide and AETAC-co-AAm powders were obtained by vacuum drying at room temperature.

NMR measurements
The polyacrylamide and AETAC-co-AAm powders were dissolved in D 2 O (99.9 atom% D), 0.1 M NaCl in D 2 O or 1 M NaCl in D 2 O containing 0.05% trimethylsilylpropanoic acid to prepare samples of 0.2 wt% polymer or copolymer. The powders of sample A (or C) and sample D were mixed, and then the solvent was added. These sample solutions were transferred to a sample tube with a 5-mm outer diameter, and the liquid height was adjusted to 30 mm. DOSY measurements were performed using a Bruker AVANCE NEO 400 spectrometer equipped with the Diff BBI probe and the Diff-5-3 program implemented in TopSpin 4.1.0 software. For the measurements of the polymer samples in D 2 O containing 1 M NaCl at 30°C, data were acquired using the bpp-ste-led sequence [45] (PULPROG: diffSteBp) with a gradient pulse length (δ) of 3.2 ms (gradient pulse shape: smsq), a diffusion delay (Δ) of 10 ms, an eddy current delay (T e ) of 5 ms, and a gradient recovery delay (t g ) of 0.5 μs. The parameters for the measurements under other conditions are given in the figure legends. All experiments were recorded using 128 scans for each gradient strength in 128 linear G lamp steps. The acquisition time was 0.84 s with a relaxation delay of 4.16 s using 8192 data points for the F 2 dimension covering 4850 Hz. The transmitter frequency offset was adjusted to the frequency of the N(CH 3 ) 3 + resonance. An exponential window with a broadening factor of 3 Hz was applied prior to Fourier transform along the F 2 dimension. Careful phase adjustment and baseline correction were performed. The CONTIN method [48,49] implemented in the TopSpin 4.1.4 software was adopted for inversion of the Laplace transform along the F 1 dimension.

SEC-MALS measurements
Size exclusion chromatography coupled with multiangle light scattering (SEC-MALS) measurements were performed in 1 M NaCl at 25°C to determine the M w , M w /M n , and root mean square radius of gyration (R g ) of the polyacrylamide and AETAC-co-AAm samples. The powders of these samples were dissolved in 1 M NaCl to give 0.2 wt% solutions. An MALS detector (WYATT DAWN HELEOS-II) and two SEC columns (Shodex OHpak SB-806 M HQ with a maximum porosity of 2 million and OHpak SB-807 HQ with a maximum porosity of 50 million) were used for the analysis. Aqueous NaCl (1 M) was used as the eluent, and the flow rate was 0.6 mL/min. A Wyatt Optilab T-rEx differential refractometer was calibrated using a series of 1 M NaCl solutions of known concentrations [50].

Dynamic light scattering measurements
DLS measurements of the polymer samples were carried out for 0.2 wt% solutions in 1 M NaCl at 30°C using a Malvern Panalytical Zetasizer Nano ZSP system and a 10-mm polystyrene cell. The powders of polyacrylamide and AETAC-co-AAm were dissolved in 1 M NaCl to prepare samples of 0.2 wt% polymer or copolymer. The powders of sample A and sample D were mixed, and then the solvent was added. Inversion of the Laplace transform was conducted using the CONTIN method implemented in Zatasizer software (version 8.02).

Intrinsic viscosity measurements
The [η] of the polymers was measured in 1 M NaCl at 25°C using a Cannon-Fenske viscometer (size 75). The intrinsic viscosity values were extrapolated from the linear plots of the reduced specific viscosity as a function of concentration [50]. and R g is affected by M w but not by the composition of AETAC-co-AAm [4]. Figure 3b shows the 1D NMR spectrum extracted from the DOSY data of sample B measured in D 2 O at 40°C. The spectrum was acquired at the first gradient step, G 1 . The parameters for the DOSY experiment are shown in Table 2 as Run 2. According to the assignments by Proietti et al. [6], the broad resonances at 1.35-2.41 and 2.41-3.04 ppm can be assigned to the CH 2 (1) and CH (2) groups of the copolymer main chain, respectively. We assigned the strong resonance at 3.24 ppm to the (CH 3 ) 3 N + group (5) and the resonances at 3.77 and 4.59 ppm to the CH 2 groups of the AETAC side chain (3,4). A comparison of this spectrum with that of Fig. 3a in our previous study [37,46] (the parameters are shown in Table 2 as Run 1) reveals that the intensities of resonances 1-4 were higher than that of resonance 5. We mainly attribute this increase to the reduction of the diffusion time (Δ) from 100 ms (Run 1) to 10 ms (Run 2), which was made possible by the use of the Diff BBI probe. The T 2 values for resonances 1-4 were smaller than that of resonance 5 (see Supplementary Material). Thus, using a large Δ leads to severe loss of the echo intensity for small T 2 resonances (see Eq. 1). Fig. 3 1D NMR spectra extracted from the DOSY data of sample B in D 2 O at 40°C. The spectra were acquired at the first gradient step, G 1 . The DOSY experiments were performed using the GR probe (previous study, Run 1) (a) and the Diff BBI probe (present study, Run 2) (b). See Table 2 for the parameters of these experiments  Fig. 1 for the other abbreviations of the delay times (Δ, δ, T e )); n is the number of gradient steps (linear G ramp); and G 1 and G max are the strengths of the minimum (the first) and maximum (the n-th) gradients, respectively b Signal-to-noise ratio for the 1D spectrum obtained at G 1 . An exponential apodization function (LB = 3.0 Hz) was applied prior to the Fourier transform along the F 2 dimension. The noise region for the S/N calculations was 6.5-10.0 ppm Figure 4 shows the DOSY contour plots with F 1 (the D dimension) and F 2 (the chemical shift dimension) projections obtained from the CONTIN analysis of samples A and D and a 1:1 mixture of A and D in D 2 O at 40°C. The plots for sample A (Fig. 4a) show the resonances due to the CH 2 (6) and CH (7) groups of the polyacrylamide main chain and the log-Gaussian distribution of D with the peak maximum (D p ) at a log D of −11.52 m 2 /s. In contrast, almost no resonances other than that due to the (CH 3 ) 3 N + group (5) of the AETAC side chain were observed in the plots for sample D (Fig. 4c). The log D p was found at −12.33 m 2 /s. The plots for the mixture of samples A and D (Fig. 4b) showed resonances 6 and 7 of polyacrylamide and resonance 5 of AETAC-co-AAm. The distributions of D for samples A and D were well separated, with log D p values at −12.09 and −12.27 m 2 /s, respectively. Polyacrylamide (sample A) is uncharged and has a flexible chain structure, whereas AETAC-co-AAm (sample D) is a polyelectrolyte, which we assume has a relatively expanded chain structure in D 2 O owing to electrostatic repulsion between the charged AETAC units. We consider that the expansion of AETACco-AAm chains reduces the segmental mobility of the main chain and makes T 2 of resonances 1-4 very small. Even with a small Δ of 12 ms, which was achieved by the use of the Diff BBI probe, it seems difficult to observe resonances 1-4 from DOSY experiments in pure D 2 O.

Results and discussion
It should be noted that the log D p for sample A in Fig. 4b (−12.09 m 2 /s) was significantly smaller than that in Fig. 4a (−11.52 m 2 /s). We attribute the decrease in D p when sample A was mixed with sample D to the concentration of 0.2 wt% in D 2 O far exceeding the overlap concentration (c*). The individual polymer chains start to overlap as the concentration approaches c*, which is defined as the concentration at which a given dilute conformation's pervaded volume is equal to the solution concentration [51]. The need to use sufficiently low-concentration samples to determine the correct D by diffusometry has been noted in the literature [22,32,52,53]. However, DOSY experiments for AETAC-co-AAm samples at concentrations below 0.2 wt% were impractical in terms of sensitivity of the spectrometer in the present study. Figure 5 shows the DOSY contour plots with F 1 and F 2 projections of samples A and D and the mixture of samples A and D in 1 M NaCl in D 2 O at 30°C. In contrast with Fig. 4b, c, resonances 1-5 of AETAC-co-AAm were observed in Fig. 5b, c, and resonances 6 and 7 of polyacrylamide were observed in Fig. 5a, b. It was reported that the intramolecular electrostatic repulsion between charged segments by (CH 3 ) 3 N + in AETACco-AAm is screened by Cl − and that polymer chain expansion is not appreciable in D 2 O solution with salt [9]. As a result, the log D p for sample D increased markedly to −11.78 m 2 /s (Fig. 5c). The distributions of D for samples A and D in Fig. 5b separated well, with log D p values at −11.51 and −11.64 m 2 /s, respectively. These values agreed reasonably well with those determined by DLS-CONTIN analysis for sample A (−11.26 m 2 /s) and sample D (−11.58 m 2 /s) in 1 M NaCl in D 2 O at 30°C (Fig. 6). However, we note that the D determined by DLS is a mutual-diffusion coefficient in contrast with the self-diffusion coefficient determined by DOSY. Separations of samples A and D along the diffusion axis determined by DOSY (Fig. 5b) and DLS (Fig. 6) compare unfavorably with the SEC separation, which showed a bimodal distribution of molecular weight corresponding to samples A and D (Fig. 7). We attribute the insufficient separation in the SEC curve for the mixture of samples A and D to overloading of the sample solution in the SEC-MALS instrument. Figure 8b shows the DOSY contour plots with F 1 and F 2 projections of a 1:1 mixture of samples C and D in 0.1 M NaCl in D 2 O at 30°C. The M w of sample D (3.9 × 10 6 ) was twice as large as that of sample C (1.9 × 10 6 ), and the AETAC composition of sample D (80.9 mol%) was larger than that of sample C (59.4 mol%). However, the F 1 (the diffusion dimension) projection showed no sign of separation or broadening arising from the two copolymers. Thus, it appears difficult to separate the diffusion profiles of these samples by DOSY analysis under the conditions of this study.
Our results demonstrate that the inverse-geometry diffusion probe system is useful for the DOSY-CONTIN analysis of polyelectrolytes with M w over one million in D 2 O  and G 128 = 1250, 1550, and 1500 G/cm in (a-c), respectively containing 0.1 to 1 M salts. This is particularly relevant to the study of sludge solutions. For example, the electrical conductivity of common sludge is approximately the same as that of 0.1 M NaCl aqueous solution (22 μS/m) [54]. Many studies have been conducted to elucidate the mechanism of sludge dehydration using polymer flocculants, although few have focused on the structure of these polymers [55,56]. We expect that the application of the DOSY-CONTIN method will provide information on the structure and mobility of polymer flocculants in stimulated sludge solutions.
Acknowledgements The Bruker AVANCE NEO 400 spectrometer with the Diff BBI probe was financially supported by the Polymer DOSY Consortium of Tokushima University.

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