Akiko Sasaki

Julien Trébosc

Hiroki Nagashima

Jean-Paul Amoureux

Practical considerations on the use of low RF-fields and cosine modulation in highresolution NMR of I = 3/2 spin quadrupolar nuclei in solids

 Cl and 23 Na) nuclei at a moderate magnetic field (B0 = 14.1 T), we show the superior use of these experiments, especially for samples with large CQ values and/or low-gamma nuclei. Compared to all other existing sequences, the coslp-MQMAS method with initial WURST signal enhancement is the most robust, efficient and resolved high-resolution 2D method for spin 3/2 nuclei. Furthermore, using { 23 Na}-1 H spin systems, we demonstrate the sensitivity advantage of the WURST coslp-MQ-HETCOR acquisition upon 1 H detection and fast MAS conditions.

I.

Introduction

Nuclei with spin I > 1/2, are subject to quadrupolar interactions that cause an anisotropic broadening of the NMR resonances in solids. For half-integer spin quadrupolar nuclei (I = 3/2, 5/2, 7/2 and 9/2), this broadening is proportional to the magnitude of the quadrupolar interaction, which can be described with the CQ = e 2 qQ value. All transitions are affected by the large quadrupolar interactions, except the one-quantum central-transition (1Q-CT), between the  ½ energy levels, which is only broadened by the much smaller second-order quadrupolar contribution. However, Magic-Angle Spinning (MAS) does not fully refocus this residual anisotropic broadening, and hence to obtain isotropic spectra of half-integer quadrupolar nuclei, high-resolution two-dimensional (2D) methods, such as MQMAS (multiple-quantum MAS) 1 and STMAS (satellite-transition MAS), 2 are required. Owing to the ease in its experimental set up, MQMAS has been widely used as a routine method, whereas STMAS is technically more challenging due to the practical requirements such as the precise control of the spinning frequency and the accurate setting of the spinning axis to the magic angle. 3,4 Up to now, the low sensitivity of MQMAS, which originates from the use of 'forbidden' multiple-quantum coherences, is often a limiting factor in many practical applications. On the other hand, STMAS is more sensitive than MQMAS, but more challenging. Globally, MQMAS and STMAS are two complementary techniques, because the comparison of their isotropic dimensions allows to detect the presence of s motions around the quadrupolar nucleus of interest. 5,6 During the last decade, higher spinning rates have become more accessible on an everyday basis. Fast MAS experiments are highly promising in solid-state NMR investigations of half-integer spin quadrupolar nuclei, especially for samples with large CQ sites or multiple sites with a considerable chemical shift difference. For example, we have recently reported such investigations on (i) MQMAS/STMAS detections of a large range of CQ sites under moderate to fast MAS conditions, 7 and (ii) 1 H-detected MQ/ST-HETCOR (hetero-nuclear correlation) experiments, where the improved 1 H resolution under fast MAS was shown to be highly advantageous for the overall 2D sensitivity. 8,9 In MQ-based experiments (i.e. MQMAS and MQ-HETCOR), the MQ excitation/conversion efficiency is presently limited, especially under fast MAS. 10 This is because for the optimum MQ excitation/conversion, the conventional hard-pulses require a large RF-field that depends on the CQ values. Such large RFs are not always practically attainable for all nuclei, especially in the case of low-gamma nuclei, or when moderate or large diameter probes are used. In the following, this conventional sequence using two hard-pulses for the MQ excitation/conversion will be named hp-MQMAS. There exists a large variety of well-established experimental approaches to increase the sensitivity of MQMAS experiments (RIACT, 11 FAM, 12,13 DFS, 14 FASTER, 15 HS, 16 RAPT, 17 and CPMG-MQMAS 18 ), although they often require a time-consuming optimization process of multiple parameters.

Very recently, Hung and Gan presented two novel variations for the MQ excitation/conversion pulses of I = 3/2 nuclei, namely lp-MQMAS (low-power or long-pulse MQMAS) 19 and coslp-MQMAS (cosine lp-MQMAS), 20 based on their previous lp-STMAS approach developed to excite the innermost STs with low RF requirement. 21 Both lp-and coslp-MQMAS sequences utilize two identical one rotor period (R) pulses to transfer the magnetization between the 1Q-CT and the 3Q coherences. In lp-MQMAS, the one R pulses are conventional rectangular ones, with the same offset frequency irradiating one satellite transition. In coslp-MQMAS, their magnitudes are cosine modulated, which is equivalent to a double frequency irradiation of the two satellite transitions. 20 Both lp-and coslp-MQMAS experiments start with a 1Q-CT → 3Q transfer, and hence they benefit from any existing signal enhancement scheme for 1Q-CT signals, which can be applied prior to the first R-pulse. Among them, the WURST (wideband, uniform rate, smooth truncation) pulse was chosen as the simplest one to set up. 19,20 It has been experimentally shown that the lp-MQMAS sequence results in a small amount of broadening along the isotropic dimension, which is the inevitable consequence of the application of long pulses on ST coherences. 20 It was consequently claimed that coslp-MQMAS is superior to lp-MQMAS because: (i) its isotropic linewidth is not broadened, and its efficiency is (ii) about 30% higher, and (iii) less dependent on the CQ value. 20 The lp-and coslp-MQMAS experiments have initially been developed under slow spinning, R = 10-16 kHz. 19,20 Since then, one article showed up, in which the coslp-MQMAS approach was used to acquire 1 H/ 13 C/ 17 O 3D isotropic HETCOR spectra at B0 = 18.8 T with R = 90 kHz. 22 In these studies, the optimum conditions for the lp-and coslp-MQMAS variables were mostly reported as 'experimentally optimized' on the given sample.

In this study, we take a more general view and aim to establish the appropriate use and setup of these methods for potential applications in materials science. We focus on practical considerations of lp-and coslp-MQ-based experiments for I = 3/2 under moderate and fast MAS conditions, discussing the pros and cons of each approach. We also verify by both experiments and simulations, the versatility of the WURST sensitivity enhancement for the second-order broadened 1Q-CT lineshape. Additionally, we briefly compare the experimental setup of the z-filter and full-echo versions of WURST lp-and coslp-MQMAS experiments. Finally, we demonstrate the highly advantageous use of the WURST coslp-MQ-HETCOR approach over the ST-HETCOR counterpart, for the ease of experimental setup and the increased sensitivity, using { 23 Na}-1 H systems (NaH2PO4 and Na2HPO4) at R = 62.5 kHz.

II. Methods

All experiments were performed using a Bruker Avance NEO spectrometer with a B0 = 14.1 T wide-bore magnet at a Larmor frequency of 196.37 ( 87 Rb), 183.06 ( 71 Ga), 58.81 ( 35 Cl) and 158.75 ( 23 Na) MHz, equipped with HX MAS probes using either  = 3.2 mm rotors at R = 16-20 kHz or  = 1.3 mm at R = 62.5 kHz. Maximum RF fields of 1 = 83 ( 87 Rb) and 42 ( 35 Cl) kHz were attained with  = 3.2 mm, and 1 = 125 ( 87 Rb), 167 ( 71 Ga) and 137 ( 23 Na) kHz with  = 1.3 mm. Powder samples (RbNO3, Rb2SO4, -Ga2O3, L-histidine.HCl.H2O, NaH2PO4, Na2HPO4) were packed as purchased.

The MQMAS and STMAS pulse sequences used in this study are shown in Figs. 1 andS1, for split-t1 full-echo and z-filter acquisition, respectively, and in Fig. S2 for {I = 3/2}-1 H MQ/ST-HETCOR experiments. For the ease of data handling, most experiments were performed with the split-t1 full-echo approach that does not require any extra shearing processing. 23 The recycling delays and echo-times for full-echo experiments (Fig. 1) were {RD (s), echo (ms)} = {0.5, 4} for Rb2SO4, {1.5, 0.2} for - Ga2O3, {1, 2.5} for L-histidine.HCl.H2O, {0.25, 8} for RbNO3 and {1, 6} for NaH2PO4 and Na2HPO4. The TopSpin pulse programs for WURST lp/coslp-MQMAS and -MQ-HETCOR experiments are provided in the Supplementary Information.

STMAS-based high-resolution experiments require a stringent technical set up, such as an accurate magic angle setting (e.g. 54.736  0.002) and a very stable spinning frequency (e.g. 1 part in 10 4 ), to acquire the isotropic spectra with little anisotropic bradening. 3,4 In this study, the magic angle was set on the sample of interest prior to the acquisition of STMAS and ST-HETCOR spectra, using the split-t1 full-echo DQF-STMAS pulse sequences. 24 The spinning stability was maintained by a MAS III unit within 10 Hz at R = 16, 20 or 62.5 kHz. Chemical shift scales, shown in ppm, were referenced using the sample of interest itself as a secondary reference, and all 2D spectra were referenced according to the unified representation. 25 Further experimental details are given in the figure captions.

All simulations were performed using the SIMPSON simulation programs. 26 The input variables were the magnetic field (B0 = 14.1 T), the nucleus of interest, the spinning frequency (R), the RF-field (1) and the quadrupolar coupling constant (CQ). The quadrupolar interaction with Q = 0 was taken into account up to the second-order, without scalar or dipolar coupling. To calculate the efficiency of the methods, coherences were selected to emulate the STMAS and MQMAS sequences without any delay, except for the rotor-synchronized STMAS experiment (t1min = R -p1/2 -p4 -p2/2). The efficiency was defined with respect to the signal observed after a CT-selective 90° pulse. For the WURST simulations, the sequence consisted of the WURST pulse followed by a CTselective 90 pulse. The powder averaging parameters (i.e. crystal file and number of -angles) and the t maximum time step over which the Hamiltonian is considered time-independent were tested for convergence, and a combination of ZCW54  10 -angles, 27- 29 with t = 0.1 s was sufficient for the given range of CQ values used in this study. Since both the real and imaginary parts of the signal were found to be significant, its magnitude ((Re 2 + Im 2 )) is plotted as the signal intensity. Further simulation details are given in the figure captions.

III. Results and discussion

We first briefly summarize a few essential points to remember upon practical consideration of lp-and coslp-MQMAS experiments, based on the theoretical treatment and experimental demonstrations given in the previous studies. [19][20][21] (i) For the MQ excitation/conversion, a one-rotor pulse creates an inversion between the 1Q-CT and 3Q coherences. (ii) The two identical one R pulses need to be symmetrically applied for excitation and conversion to cancel the anisotropic dephasings related to long pulses. 19,20 (iii) In lp-MQMAS, the irradiation offset frequency of the R-pulses, irr, should be applied within the ST manifold, which means far off-resonance from the CT signal, 19 whereas in coslp-MQMAS, the R cosine irradiation is applied near the CT signal, and ideally on the center-band position of the 1Q-STs. 20 (iv) The optimum RF requirement (1,opt) is higher by 2 in coslp-than lp-MQMAS, and is dependent on both the CQ value and the spinning frequency (R), namely, 1,opt  (CQR/12) for lp-MQMAS and (CQR/6) for coslp-MQMAS. 20 (v) Spinning fluctuations may cause an additional line broadening and a t1-noise along the isotropic dimension of lp-MQMAS, while coslp-MQMAS is robust to such spinning instabilities. 20 (vi) Both z-filter and full-echo acquisitions are plausible in lp-or coslp-MQMAS. 19 (vii) When the full-echo acquisition is employed, the phase modulation of the signal may cause confusion during the optimization process, but this problem can be circumvented by displaying the spectra in the magnitude mode. 19 These practically important points to the successful acquisition of lp-and coslp-MQMAS signals are thoroughly illustrated in the following, using 87 Rb and 71 Ga having moderate and large CQ sites respectively, and using 35 Cl (0 = 58.81 MHz at 14.1 T) as a low-gamma nucleus, with the aid of both experiments and simulations. We should remind here that such isotropic 2D acquisition of half-integer quadrupolar nuclei may intrinsically take several hours or days. We have recently established the eligibility of Non-Uniform Sampling (NUS) schemes in MQMAS/STMAS and MQ/ST-HETCOR acquisitions, which can be conveniently employed to reduce the total experiment time of such long 2D experiments. 9 Where plausible, the applicability of 50% NUS acquisition in the indirect dimension is demonstrated, to reduce the total experiment time (Texp) by a factor of 2.

III.1 87 Rb of Rb2SO4 at R = 20 and 62.5 kHz

In Fig. 2, the 87 Rb isotropic projections of the STMAS and MQMAS high-resolution 2D spectra of Rb2SO4 are shown at R = 20 and 62.5 kHz, with or without WURST enhancement for the MQMAS experiments using R pulses. There are two rubidium species in this compound, Rb1 and Rb2, with (CQ, Q) = (2.5 MHz, 0.9) and (5.3 MHz, 0.1), respectively. 30,31

III.1.a WURST optimization

For spin 3/2 nuclei, the transfer of population related to the WURST pulse scales up by a factor of 2-3 the populations of the 1/2 Zeeman levels. As a result, the advantage of WURST coslp-MQMAS is apparent as its intensity is 1.5-2.0 times higher than that of STMAS for the same experimental time. Among the existing 1Q-CT signal enhancement schemes, the practical advantage of WURST is that its optimum conditions are robust with respect to its length (WURST), its offset frequency (off) and the RF field amplitude (1,WURST), and the WURST sweep range is set to the spinning frequency (i.e. sweep = R). This robustness is experimentally demonstrated in Fig. S3, where a series of 1D 87 Rb full-echo WURST coslp-MQMAS spectra of Rb2SO4 is shown at R = 20 and 62.5 kHz for a range of WURST, off and 1,WURST values. It must be noted the WURST optimization can be more easily obtained with a 90° CT-selective pulse, instead of the MQMAS here. The WURST signal intensity is on a plateau around the optimum conditions of each parameter (WURST = 1-5 ms, off = 200-500 kHz, and 1,WURST = 10-20 kHz). This experimental observation is verified by the simulations presented in Fig. S4. Except in Fig. S3, we have always used WURST = 1 ms. Both our experiments and simulations confirm that WURST is efficient, robust and simple to set up for the 1Q-CT enhancement, which is a prerequisite to increase the sensitivity of subsequent lp-and coslp-MQMAS acquisition.

III.1.b lp-and coslp-MQMAS optimization

We then move on to illustrate the optimum conditions for the lp-and coslp-MQMAS variables of the R-pulses: RF-field (1) and frequency of either the rectangular pulses for lp-MQMAS (irr), or the cosine modulations for coslp-MQMAS (cos). We show in Fig. 3, an experimental 87 Rb signal intensity profile of these parameters at R = 20 kHz using Rb2SO4. As proposed in the previous studies, this optimization profile is shown in the magnitude mode. 19 With coslp-MQMAS, the optimum RF field is higher than with lp-MQMAS (1,opt  75 and 40 kHz) and slightly more robust to RF inhomogeneity (second line in Fig. 3).

For a given sample, the last parameter to be optimized is the frequency of either the irradiation, irr, for lp-MQMAS or the cosine modulation, cos, for coslp-MQMAS (first line in Fig. 3). They both are on a plateau in the same range of irr  cos  200-350 kHz, similar to that observed for the WURST pulse (Fig. S4). These experimental observations have been verified using the simulations shown in Fig. S5.

With the coslp-MQMAS sequence, it has been recommended to fix the carrier frequency (irr) of the cosine modulation of the R-pulses onto the center-band position of the 1Q-STs. 20 To verify this point, we show in Fig. S6 the 87 Rb 1D spectra recorded at R = 20 kHz with various irr values and one observes that the sequence is robust with respect to this parameter. However, simulations (not shown) suggest that as CQ increases, there is a decrease in signal as the pulse offset from the ST increases. This point has been confirmed with the optimization of the 71 Ga experiments (section III.2).

Having established the optimum conditions for the lp-and coslp-MQMAS variables, we can now safely compare the efficiency of such novel methods versus the conventional approaches. Fig. 4 summarizes the simulated 87 Rb signal intensity of STMAS and MQMAS spectra at R = 20 and 62.5 kHz, with respect to CQ and the RF-field (1) of the MQ excitation and conversion pulses. In good agreement with the 2D experimental results (Fig. 2), WURST coslp-MQMAS shows the highest sensitivity, especially for large CQ values.

It should be noted here that, 2D rotor-synchronized acquisition (t1 = R), ST-based experiments such as STMAS or ST-HETCOR take a twice-longer time than the analogous MQMAS or MQ-HETCOR to achieve the same resolution. This is because the isotropic spectral width (SWiso) is twice larger in ST-based experiments than in their MQ-based counterparts. When the expected isotropic peaks lie within a narrow chemical shift range, an optimized rotor synchronization can be conveniently employed in STbased experiments to reduce the total 2D experimental time, Texp, 9 by incrementing the t1 value by a multiple of the rotor period and scaling down the spectral width. This has been illustrated in Fig. 2, where the STMAS acquisition was performed with t1 = R and also 2R, then reducing SWiso and Texp by a factor of 2, making it comparable to the MQMAS counterpart. The Sensitivity (S = SNR/√Texp in min -1/2 ) of the 2D 87 Rb isotropic peaks is indicated in Fig. 2 for all variations. Our comparison of the Sensitivity values confirms that WURST coslp-MQMAS is indeed the method of choice for the best sensitivity and resolution for a given spectrometer time, without the need for the so-called STMAS specifications. As example, at R = 62.5 kHz, for the two 87 Rb species we observe S = 8.8/4.8 and 11.3/9.3 min -1/2 with STMAS and WURST coslp-MQMAS, respectively (Fig. 2). Whatever the analyzed nucleus and the spinning frequency, we have always observed (i) a WURST gain of ca. Having thoroughly established the experimental variables and hence the expected optimum conditions for the R-based approaches using Rb2SO4, we now demonstrate that one of the main power of WURST coslp-MQMAS lies in the efficient detection of species with large CQ values.

Ga2O3 samples have been employed in several solid-state 71 Ga NMR investigations, mostly under MAS, [32][33][34][35][36][37] and 2D WURST lpand coslp-MQMAS spectra of -Ga2O3 were demonstrated at very high magnetic fields (B0 = 19.6-20.0 T) with R = 14 kHz. 19,20 Our as-purchased Ga2O3 sample was found to be a pure -Ga2O3 form with two Ga sites with (CQ (MHz), Q) = (8.3, 0.1) and (11, 0.9). 32,34 In this study, we demonstrate the feasibility of acquiring high-resolution 71 Ga 2D spectra of such large CQ sites with a moderate Fig. 5 shows a comparison of the 1D (t1 = 0) STMAS and MQMAS 71 Ga spectra of -Ga2O3 at R = 62.5 kHz. As expected, the conventional hp-MQMAS fails for such large CQ sites, while the WURST coslp-MQMAS signal intensity is higher than that of STMAS. In Fig. S8a, we compare the simulated 71 Ga signal intensity of STMAS and MQMAS methods with respect to CQ and 1 of the excitation/conversion pulses. The poor sensitivity of hp-MQMAS is confirmed, except for small values of CQ  1 MHz. One also observes the sensitivity advantage of WURST coslp-MQMAS over STMAS, especially for large CQ values. This is also the case in Fig. 6a, which compares the isotropic projections of 71 Ga 2D spectra of -Ga2O3 at R = 62.5 kHz. The WURST coslp-MQMAS signal intensity is similar to that of STMAS, without the stringent requirements e.g. the prior need for the accurate adjustment of the spinning axis to the magic angle.

We should note here that, in Fig. 6a, the larger CQ site (Ga2) should appear at 280 ppm in the isotropic dimension but that it is aliased and appears at about 100 ppm. For compounds with large chemical shift differences, increasing SWiso may be helpful upon spectral interpretation. This can be achieved either by physically increasing R or by decreasing the t1 increment with MQMAS methods (e.g., t1 = 8 instead of 16 s at R = 62.5 kHz), although the latter option inevitably increases Texp. This loss in time can be compensated by the appropriate use of a Non-Uniform Sampling (NUS). We have previously demonstrated the simplicity and robustness of a NUSbi-exp method with simultaneous exponential decreasing sampling density and increasing sampling delay, and we have established that 32-50% NUS can be safely employed in the acquisition of isotropic spectra of halfinteger quadrupolar nuclei. 9 As shown in Fig. 6b, the identical isotropic information on Ga1 and Ga2 is obtained in only half of the time taken to record the conventional, non-NUS spectrum. We should emphasize here that NUSbi-exp acquisition is particularly useful under fast MAS (e.g. R = 62.5 kHz), where an intrinsically large number of t1 increments are required to achieve the expected resolution in the isotropic spectrum of half-integer quadrupolar nuclei.

III.3 35 Cl of L-histidine.HCl.H2O at R = 20 kHz

L-histidine.HCl.H2O has been widely employed in 35 Cl NMR investigations (e.g. MAS, 38,39 DNP-CPMAS, 40 CPMG 41 ), and recent studies are mostly concerned with the demonstration of 1 H- 35 Cl correlation approaches, such as D-HMQC, [42][43][44][45][46] D-RINEPT, 47 D- RESPDOR, 48 and T-HMQC. 49,50 Despite its high natural abundance (75.8%), its low gyromagnetic ratio and hence Larmor frequency (58.81 MHz at 14.1 T) limit the accessible range of RF-field. With our  = 3.2 mm MAS probe, a maximum RF-field of only 40 kHz was achievable. This hinders the acquisition of conventional hp-MQMAS signals, which requires a high RF-field for efficient MQ excitation/conversion. This is experimentally demonstrated in Fig. 7, where we compare the 1D 35 Cl (CQ = 1.8 MHz, Q = 0.66) 39 STMAS, hp-MQMAS and WURST coslp-MQMAS spectra of L-histidine.HCl.H2O at R = 20 kHz. While the conventional hp-MQMAS resulted in only noise, the WURST coslp-MQMAS signal was larger than that of STMAS. It should be reminded again that the WURST pulse gives an enhancement factor of 2-3 under optimum conditions (Fig. S7b).

It must be noted that in this case the WURST lp-and coslp-MQMAS sensitivities were similar (Fig. S9). This is because 1 was limited to 40 kHz with our 3.2 mm probe, whereas the simulations shown in Fig. S8b point out that with CQ = 1.8 MHz, the optimum RF-fields are ca. 35 and 50 kHz for and coslp-MQMAS, respectively. Moreover, one observes in Fig. S9 that coslp-MQMAS leads to a narrower isotropic resonance (55 % 75 Hz) than lp-MQMAS. Last, as already demonstrated with -Ga2O3 (Fig. 6), 50% NUS can be safely employed for 2D isotropic acquisition, which doubles the sensitivity (Fig. S9).

III.4 87 Rb of RbNO3 at R = 16 kHz

Since the one-rotor based MQMAS methods can be incorporated in both amplitude-modulated z-filter and phase-modulated full-echo pulse sequences, 19 one may envisage that, as with conventional hp-MQMAS, WURST coslp-MQMAS may be preferably employed with z-filter when the full-echo acquisition is not efficient, e.g. for materials that are either amorphous or with short T2' values.

We have used 87 Rb NMR of RbNO3 to analyse this point at R = 16 kHz. There are three different Rb species in RbNO3 with (CQ (MHz), Q) = (1.7, 0.6), (1.7, 0.2) and (2.0, 0.9), called respectively Rb1, Rb2 and Rb3. 4 The 1D (t1 = 0) spectra recorded with z-filter and full-echo acquisition of STMAS, hp-MQMAS, and WURST coslp-MQMAS are shown in Fig. S10, and in Fig. 8 we compare the corresponding isotropic projections of the 2D spectra. The STMAS and hp-MQMAS isotropic spectra are almost the same with zfilter and full-echo, whereas for WURST coslp-MQMAS, the full-echo signal is more sensitive than the STMAS counterpart, as expected, but the z-filter signal results in a decreased sensitivity. Furthermore, by considering the two left resonances (Rb2 and Rb3), we observe that STMAS is less resolved than WURST coslp-MQMAS, and it must be noted that these two peaks fully overlap with lp-MQMAS (not shown). These losses of resolution are related to spinning rate fluctuations and misadjusted magic angle.

We also realized that finding an optimum condition for the WURST coslp-MQMAS variables is more complicated for z-filter than for full-echo, due to the phase evolution. Indeed, when optimizing one particular parameter (1, cos or irr), a local maximum in intensity is easily obtained. However, the absolute maximum without phase distortion was found to be dependent on the combination of these 3 variables, requiring the optimization process to be performed in multiple dimensions. Additionally, a set of chosen parameters with a good-looking 1D spectrum (i.e. no phase distortion) occasionally resulted in some artefacts in the 2D spectrum, while sometimes an 'unphasable' spectrum in 1D resulted in a better-looking 2D spectrum. Further investigations on this phase issue are currently ongoing. In this last section, we demonstrate the advantageous use of the WURST coslp-MQMAS quadrupolar filter in the HETCOR experiments involving I = 3/2. Despite that HETCOR experiments between spin 1/2 nuclei have been routinely performed in solidstate NMR investigations, when a half-integer quadrupolar nucleus is correlated with another one, a structurally or chemically important information is often hindered by the quadrupolar broadening that causes a severe loss in resolution. This motivates the incorporation of a high-resolution MQMAS or STMAS quadrupolar filter in the HETCOR pulse sequences, leading to the development of MQ-HETCOR and ST-HETCOR experiments. Various population transfer schemes, to or from the half-integer quadrupolar nuclei, have been developed in the context of MQ/ST-HETCOR (e.g. MQ-CPMAS, [51][52][53][54][55][56][57] ST-CPMAS, 58 MQ-J-RINEPT, 57,59- 62 and MQ-D-RINEPT 60,[63][64][65] ). The SPAM (Soft-Pulse Added-Mixing) sensitivity enhancement scheme [66][67][68][69] has also been implemented in MQ/ST-HETCOR pulse sequences (i.e. MQ/ST-SPAM-HETCOR). Recently, we have made a comparison of CPMAS, D-RINEPT and PRESTO transfers in MQ/ST-HETCOR schemes upon 1 H detection under fast MAS conditions. 8,9 Although CPMAS may be found efficient for relatively small CQ sites, D-RINEPT should be generally recommended for a wider range of CQ sites.

Very recently, the increased sensitivity of WURST coslp-MQMAS was shown to contribute to the successful acquisition of 3D isotropic 1 H/ 13 C/ 17 O (I = 5/2) HETCOR spectra at B0 = 18.8 T and R = 90 kHz. 22 In our present study, we focus on I = 3/2 nuclei and employ { 23 Na}-1 H spin systems to demonstrate the feasibility of the WURST coslp-MQ-HETCOR 2D experiments and their preferential use for the ease of experimental setup and better sensitivity.

The MQ/ST-HETCOR pulse sequences used in this study are summarized in Fig. S2. We employed two Na salts, NaH2PO4 (CQ = 1.6, 2.4 MHz) and Na2HPO4 (CQ = 1.4, 2.3, 3.7 MHz). 70 As a prerequisite to HETCOR acquisition, we analyzed first the sensitivity of the quadrupolar filters under the fast MAS conditions required for 1 H detection. Indeed, during the last decade, following the development of fast spinning probes, 1 H detection has become frequently used owing to the increased 1 H resolution under fast MAS. In Fig. S11 we compare the 23 Na isotropic projections of STMAS, hp-MQMAS and WURST coslp-MQMAS at R = 62.5 kHz, with z-filter and full-echo acquisition. In consistence with the 87 Rb observations of RbNO3 (Fig. 8), the full-echo WURST coslp-MQMAS signals are more sensitive and resolved than the STMAS ones, but the z-filter signals resulted in a slight loss of sensitivity. It should be remembered here that, although two symmetrical pathways are simultaneously detected in MQ-HETCOR (like with z-filter MQMAS), the actual selected coherences are equivalent to the one used in the fullecho acquisition (See Figs. 1d, S1c andS2d).

The 1 H and 23 Na 1D projections of { 23 Na}-1 H MQ/ST-HETCOR spectra of NaH2PO4 and Na2HPO4 at R = 62.5 kHz are shown in Figs. S12 and9, respectively, using STMAS, hp-, hpspam-and WURST coslp-MQMAS quadrupolar filters. In addition, in Fig. S13, we show the experimental WURST lp/coslp-MQ-HETCOR signal intensity profiles with respect to the three variables: 1, irr and cos. As observed in the context of MQMAS (Fig. S11), the WURST coslp-MQ-HETCOR quadrupolar filter is more sensitive than STMAS, and this is consequently reflected in the isotropic comparisons of { 23 Na}-1 H MQ/ST-HETCOR spectra. Moreover, we have previously reported that, in ST-HETCOR spectra with I = 3/2, the presence of artefacts (denoted with asterisks (*) in the isotropic projection in Fig. 9) is inevitable. 9 This is not the case with MQ-HETCOR spectra. Furthermore, despite the higher accessible RF-field with small rotors, the hp-MQMAS excitation/conversion efficiency is known to decrease at high spinning rates. 10 The WURST coslp-MQMAS approach does not suffer from this limitation, even at ultra-fast MAS that is necessary for the improved resolution upon 1 H detection in the direct dimension.

Although we have chosen these two Na-H model samples with small to moderate CQ values (1.6-3.7 MHz) for the comparative demonstration of MQ/ST-HETCOR variants at B0 = 14.1 T in a reasonable amount of spectrometer time, one may take advantage of the high sensitivity of WURST coslp-MQ-HETCOR and apply it to large CQ samples. It must be noted that, even at high-spinning rates, the 1 H resolution can still be enhanced using homonuclear decoupling schemes. [71][72][73] Following the recent development of two new sequences with two one-rotor pulses for the efficient MQ excitation/conversion of I = 3/2, namely lp-and coslp-MQMAS, we have performed a thorough examination on their variables in the context of MQMAS and MQ-HETCOR experiments, with the aid of simulations and experiments at a moderate magnetic field (B0 = 14.1 T).

IV. Conclusions

We employed a range of nuclei and samples with either moderate CQ values and Larmor frequencies ( 87 RbNO3, 87 Rb2SO4, 23 NaH2PO4, and 23 Na2HPO4), large CQ values (-71 Ga2O3), or low Larmor frequency (L-histidine.H 35 Cl.H2O), to show the feasibility of lp-and coslp-MQMAS-based experiments under both slow and fast MAS conditions (R = 16/20-62.5 kHz).

In both lp-and coslp-MQMAS-based acquisitions, a 1Q-CT initial signal enhancement provides a gain of 2-3 in sensitivity. We have shown that the WURST scheme with sweep = R, is robust and easy to set up with respect to its three variables (i.e. WURST = 1-5 ms, off = 200-500 kHz and 1,WURST = 10-20 kHz).

For the best robustness, sensitivity and resolution, WURST coslp-MQMAS is the method of choice irrespective of the nuclei, the CQ values or spinning frequencies. This sequence is easy to set up experimentally as it does not require any stringent STMAS specification (perfect magic-angle and stable spinning frequency) to keep the best resolution. To decrease the experimental time this sequence can be used with a bi-exponential NUS sampling and a CPMG recycling of the signal.

It should be remembered that the one-rotor pulses serve as inversion pulses between the 1Q-CT and 3Q coherences, and they are compatible with both z-filter and full-echo acquisition, like the conventional MQMAS experiment. However, in z-filter WURST coslp-MQMAS experiments, we observed several issues such as phase complexities, a slight loss of sensitivity and a presence of 2D artefacts. Further investigations on these problems need to be performed.

For I = 3/2 nuclei, there exist only two 1Q-STs and one 3Q coherences. For higher spin values, the presence of other 1Q-STs and 3Q coherences introduces further complexities to the theoretical treatment, as the 1Q-CT  3Q transfers become less confined, causing coherence leakage during the selective inversion of the inner STs, resulting in a lower efficiency for the MQ excitation/conversion. 19,20 At the time of writing, similar investigations to this study are under progress for I > 3/2 systems and will be reported elsewhere. We hope that our thorough investigations on each variable of WURST coslp-MQMAS and coslp-MQ-HETCOR will serve as a reference point to an efficient set up of these experiments and contribute to increase the number of such successful demonstrations of these experiments in materials science in the near future.

Fig. 1 .

 1 Fig.1. Pulse sequences and coherence transfer pathways used in this study for split-t1 full-echo acquisition of (a) hp-MQMAS, (b) DQF-STMAS, (c) WURST lp-MQMAS and (d) WURST coslp-MQMAS experiments, where {RMQ, RST} = {7/9, 8/9} for I = 3/2 nuclei.

Fig. 2 .

 2 Fig.2. Isotropic projections of 2D 87 Rb DQF-STMAS, hp-, lp-and coslp-MQMAS full-echo spectra of Rb2SO4 at R = 20 (a) and 62.5 (b) kHz, with or without the WURST enhancement for lp-and coslp-MQMAS. The Texp values are indicated on the left sides and the Sensitivities (in min -1/2 ) are given in the square brackets for the two Rb sites. NS = 192. WURST-80: 1,WURST = 19, off = +200 kHz. lp-MQMAS: 1 = 45, irr = +250 kHz. coslp-MQMAS: 1 = 75, irr = +1, cos = 250 kHz. (a) 1,CT = 10 kHz. hp-MQMAS & STMAS: 1 = 83 kHz; {p1, p2, p4} s = {7.0, 2.0, 25} MQ, {2.5, 1.2, 25} ST. t1{MQ, ST} = {50, 50/100} s, Nt1 {MQ, ST} = {64, 128/64}. At R = 20 kHz, SWiso is not large enough and hence the SNR and the Sensitivity values are only estimates. (b) 1,CT = 20 kHz. hp-MQMAS & STMAS: 1 = 125 kHz; {p1, p2, p4} s = {3.0, 1.0, 12} MQ, {1.5, 0.6, 12} ST. t1{MQ, ST} = {16, 16/32} s, Nt1 {MQ, ST} = {192, 384/192}.

Fig. 3 .

 3 Fig.3. Experimental 87 Rb signal intensity profiles of WURST lp-and coslp-MQMAS variables of Rb2SO4 at R = 20 kHz, with respect to the RF-field (1) and the frequencies of either the irradiation (irr) or the cosine modulation (cos). NS = 48, Texp = 24 s each. WURST-80: 1,WURST = 20, off = +200 kHz.

  2.5, confirmed by the simulations shown in Figs.S4 and S7, and a smaller (ii) sensitivity and (iii) isotropic resolution of the lp-MQMAS methods as compared to the coslp-MQMAS ones. Therefore, in the following figures of the main text, for the one R based MQMAS methods we will only present the results recorded with WURST coslp-MQMAS. III.2 71 Ga of -Ga2O3 (CQ = 8.3, 11.0 MHz) at R = 62.5 kHz

Fig. 4 .

 4 Fig.4. Simulated 87 Rb signal intensity of DQF-STMAS, hp-, WURST lp-and WURST coslp-MQMAS at R = 20 and 62.5 kHz, with respect to CQ and the RF-field (1) of the MQ excitation and conversion pulses. For R = 20/62.5 kHz, we have respectively observed: hp-MQMAS & STMAS, {p1, p2, p3, p4} s = {6.0, 2.0, 12.5, 25} MQ, {1.6/1.2, 1.6/1.2, 12.5/6.25, 25/12.5} ST with 1,CT (p3, p4) = {10/20} kHz; WURST lp-MQMAS: irr = +360/500 kHz; WURST coslp-MQMAS: cos = 250/375 kHz. The intensity of WURST lp-and coslp-MQMAS was scaled up by a factor of 2.5 to take into account the WURST enhancement.

Fig. 5 .

 5 Fig.5. A comparison of 1D (t1 = 0) 71 Ga DQF-STMAS, hp-MQMAS and WURST coslp-MQMAS spectra of -Ga2O3 at R = 62.5 kHz. NS = 384, Texp = 9.5 min each. hp-MQMAS & DQF-STMAS: 1 = 167 & 20 kHz. {p1, p2, p4} s = {3.0, 1.0, 12} MQ, {1.0, 0.6, 12} ST. WURST coslp-MQMAS: 1 = 143, irr = +10, cos = 300 kHz. WURST-80: 1,WURST = 25, off = +500 kHz.

Fig. 6 .

 6 Fig.6. A comparison of isotropic projections of 71 Ga DQF-STMAS and WURST coslp-MQMAS spectra of -Ga2O3 at R = 62.5 kHz with (a) conventional and (b) 50% NUS acquisition. NS = 384, Nt1 {MQ, ST}: (Conventional/NUS 50%) = {32/16, 64/32}. Further experimental details are given in Fig.5 caption.

III. 5 {

 5 23 Na}-1 H NMR of NaH2PO4 and Na2HPO4 at R = 62.5 kHz

Fig. 7 .

 7 Fig.7. Comparison of 1D (t1 = 0) 35 Cl (a) hp-MQMAS, (b) DQF-STMAS, and (c) WURST coslp-MQMAS spectra of L-histidine.HCl.H2O at R = 20 kHz. NS = 192, Texp = 3.2 min each. hp-MQMAS & STMAS: 1 = 40 & 10 kHz. {p1, p2, p4} s = {4.5, 4.5, 25} MQ, and {4.0, 2.0, 25} ST. WURST coslp-MQMAS: 1 = 40, irr = +3, cos = 250 kHz. WURST-80: 1,WURST = 20, off = +300 kHz. The relative intensities with respect to WURST coslp-MQMAS are given in the curly brackets.

Fig. 8 .

 8 Fig.8. Isotropic projections of 2D 87 Rb DQF-STMAS, hp-MQMAS and WURST coslp-MQMAS spectra of RbNO3 at R = 16 kHz, with (a) z-filter and (b) fullecho acquisition. Texp = 1.4-1.6 h each. Further experimental details are given in Fig.S10 caption.

Fig. 9 .

 9 Fig.9. Comparison of isotropic projections of { 23 Na}-1 H MQ/ST-HETCOR spectra of (a-d) NaH2PO4 and (e-h) Na2HPO4 at R = 62.5 kHz, using the DQ-STMAS (b,f) or the hp-(d,h), hp-spam-(c,g) and WURST coslp-MQMAS (a,e) quadrupolar filters and a CPMAS transfer of magnetization. In ST-HETCOR spectra (b,f), the positions of artefacts are denoted by an asterisk (*). t1{MQ, ST} s = {64, 128} (a-d), {32, 64} (e-h), Texp (h) = 0.7-1.0 (a-d), 1.8-2.7 (e-h). Further experimental details are given in Fig.S12 caption.

Acknowledgements

The authors would like to thank Dr. Sebastian Wegner (Bruker BioSpin GmbH) for the help with the implementation of the pulse sequences on TopSpin software.

Conflicts of interest

There are no conflicts to declare.


Walid Ijassi
email: walid.ijassi@grenoble-inp.fr

Damien Evrard

Peggy Zwolinski

Summary of "Identifying Value Chain Variables and Attributes for Urban Factories and Proposal of a Model to Support Eco-designers in their Characterization"

Keywords: urban factory, characterization, value chain model, eco-design

This summary presents results from the paper "Identifying Value Chain Variables and Attributes for Urban Factories and Proposal of a Model to Support Eco-designers in their Characterization" which has been submitted to Sustainable Futures and is still in the review process. In this summary, a new model has been developed to allow designers to determine relevant parameters to consider when designing value chains for urban factories. This has been conducted through a systematic literature review on value creation of urban factories, which has resulted in identifying variables and attributes for each value chain activity.

Introduction

Factories have been subject to delocalization from urban areas for various reasons such as their environmental impacts exceeding restrictions set inside the urban area [START_REF] Herrmann | Urban production: State of the art and future trends for urban factories[END_REF]. The new wave of cleaner production technologies, circular economy and sustainable business models have enabled their relocalization inside urban areas [START_REF] Meyer | Increasing resilience of material supply by decentral urban factories and secondary raw materials[END_REF]- [START_REF] Sajadieh | A Conceptual Definition and Future Directions of Urban Smart Factory for Sustainable Manufacturing[END_REF].This concept has been referred to as urban factories [START_REF] Kreuz | Urban factories-interdisciplinary perspectives on resource efficiency[END_REF], [START_REF] Juraschek | Urban Factories: Ecotones as Analogy for Sustainable Value Creation in Cities[END_REF]. Urban factories have been defined as factories located inside an urban environment whose characteristics are utilized in the value creation [START_REF] Herrmann | Urban production: State of the art and future trends for urban factories[END_REF], [START_REF] Juraschek | Urban Factories and Their Potential Contribution to the Sustainable Development of Cities[END_REF]. Eco-designing value chains for urban factories can be extremely challenging due to the multitude of variables related to production factors, the urban environment, and their interactions [START_REF] Koop | Integrated water resources management in cities in the world: Global solutions[END_REF]. Urban environments characteristics for example vary from one urban area to another due to many differences such as governance, infrastructure, size, and culture [START_REF] Mcfarlane | Cities within cities: intra-urban comparison of infrastructure in Mumbai, Delhi and Cape Town[END_REF]. To start this design, an explorative step of the value chain is needed to describe and conduct a diagnosis of the current situation. This will then be compared with other successful local urban factories. To date, many studies have explored the concept, but no study has covered all relevant activities of the value chain. From a benchmarking perspective, a model is needed to provide a structure for analysis to eco-designers in order to result in sustainable value chain architectures relevant to the local context. Covering this gap represents the main purpose of the paper associated to the present summary, which is led by the following research questions: How to model value chains for urban factories throughout all value creation activities?

Methodology

To design a framework that allows the modeling of value chains for urban factories throughout all their value creation activities, two main steps have been used. First, the identification and analysis of relevant case studies that presents various models of value chains for urban factories. Then, the mapping of the analysis results on Porter's value chain model. To overcome the lack of studies in the literature where the term 'urban factory' has been cited, other case studies have been considered. These represent value chains with similar patterns as the definitions presented in the typology [START_REF] Ijassi | Characterizing urban factories by their value chain: a first step towards more sustainability in production[END_REF]. To identify such case studies, a systematic literature review has been conducted using the Preferred Reporting Items for Systematic Reviews and Meta-analysis (PRISMA) guidelines [START_REF] Selçuk | A Guide for Systematic Reviews: PRISMA[END_REF]. An initial screening of results has been conducted on titles and abstracts to identify potential case studies that fall under one of the urban factory definitions. Finally, full texts have been screened to keep only studies with a presentation or a description of at least a value chain activity. To make sure all activities are included in the scope of the study, Porter's value chain model has been used as it includes "the full range of activities which are required to bring a product or service from conception, through the different phases of production" [START_REF] Kaplinsky | A handbook for value chain research. Prepared for the IDRC[END_REF]. Based on results of the systematic literature review, each value chain activity has been described or presented explicitly with various attributes. Semantic similarities of the extracted attributes have allowed the definition of relative instances using meanings of words and their intuitive relatedness such as defining the instance 'beverage' for the two attributes 'coffee' and 'tea' [START_REF] Harispe | Semantic Similarity from Natural Language and Ontology Analysis[END_REF]. The resulting instances have been projected on Porter's value chain model.

Result: proposal of a value chain model for urban factories

In order to describe and characterize value chains in the context of urban factories, each instance has been projected in the box relating to the value adding activity it presents. This has led to the creation of the model presented in Fig. 1. All value chain activities are identified by integers ranging from 1 to 4 for secondary activities, and 5 to 9 for primary activities. Each activity box includes the all associated instances with each an identification number that starts with the same number of the activity it represents, followed by a point, then a positive integer ranging from 1 to the total number instances. For example, with a total of 4 instances identified for infrastructure activities which are identified by number 1, the possible identification numbers for these instances are 1.1 to 1.4. To determine the orders, the number of mentions in the literature has been used to sort instances inside the same activity box by giving the smallest identification numbers to the most mentioned instances in the literature. To better support the use of this model and to maintain a standard form intended for data analysis purposes, the types of instances have been included using a code put between brackets following the name of each instance. For example, transportation distances in inbound and outbound logistics are followed by the code RN which indicated the attribution of a real number for these two instances. Other codes are explicated in the lower part of Fig. 1. This has been mainly done to avoid having irregularity issues such as affecting continuous attributes to a discrete instance, or categorical attributes to a numeric instance.

Conclusion

To model value chains for urban factories throughout all value creation activities, Porter's model has been used as a foundation to build the model proposed in this summary. Firstly, an extensive systematic literature review has been conducted and the results have been analyzed for each value chain activity. Identified characteristics have been grouped according to their semantic similarity into instances for which they represent attributes. All resulting instances have been mapped in Fig. 1 to represent the proposed model.

The proposed model can be used by eco-designers to identify adapted attributes based on value chains architectures and patterns resulting from analyzing models of successful urban factories. In addition to setting a logical context, the model provides designers with a standard structure to collect data on existing urban factories and have a homogeneous dataset.