## Abstract

The apparent “boosted mobility” observed by Wang et al. (Reports, 31 July 2020, p. 537) is the result of a known artifact. When signal intensities are changing during a nuclear magnetic resonance (NMR) diffusion measurement for reasons other than diffusion, the use of monotonically increasing gradient amplitudes produces erroneous diffusion coefficients. We show that no boosted molecular mobility is observed when shuffled gradient amplitudes are applied.

In their report (1), Wang et al. use diffusion nuclear magnetic resonance (NMR) (2) to show that several chemical species, including solvents, experience higher self-diffusivities during chemical reactions. The authors assign this increased diffusion to transduction from chemical into mechanical energy (1). Similar claims of enhanced self-diffusion have been reported with enzymatic reactions, but some of the experimental evidence has recently been questioned (38). Additionally, diffusion enhancement during Grubbs metathesis (9) was shown to be caused by convection artifacts in diffusion NMR measurements (10). Wang et al. avoided convection artifacts but did not fully account for non–diffusion-based changes in signal intensity during the reaction. This oversight is apparent from the inconsistency in reported diffusion values of the reactant propargyl alcohol. The 1H NMR signal of the alkyne and methylene protons of the same molecule are reported to have diffusion coefficients that differ by almost 30% [6.62 × 10–10 m2 s–1 and 8.55 × 10–10 m2 s–1, respectively, in table S4 of (1)]. Below we show the source of this inconsistency.

As two independent laboratories, we have reproduced the copper-catalyzed click chemistry reaction as presented in figure 1 of (1), because this reaction showed the largest diffusion changes and has the most data supplied. We used very similar diffusion NMR parameters. In (1) the signal intensities changed substantially during the diffusion measurements (e.g., over 5 min for 16 gradient values) for reasons other than diffusion. A known artifact (11) arises when signal intensity changes occur during the diffusion measurement, which leads to a systematic error in the regression of the Stejskal-Tanner equation (2):

$I=I0exp[−b(g)D]$

(1)where I and I0 are the echo intensity with and without gradient pulses, respectively; b is the diffusion weighting factor, which is a function of the gradient pulse strength g; and D is the diffusion coefficient. Typically, NMR diffusion measurements are performed using a series of monotonically increasing g values. However, if I0 is also a function of time t, then changes in g will correlate with changes in I0. This can result in excellent data fits of the model in Eq. 1, but with incorrect D values (11), as seen in (1). Faster changes in I0 or longer measurements will result in data fits with greater deviations from actual diffusion coefficients (Fig. 1, dashed red line). This effect is reversed when decreasing gradients are used (Fig. 1, dotted blue line). In the presence of a dynamic signal intensity change, shuffled gradient amplitudes (1113) should be used to estimate the real diffusion coefficient (Fig. 1, solid green line).

When a monotonically increasing gradient order is used, we also observe apparent diffusion enhancement (Fig. 2, A and B, red), which decays over time, as reported in (1). However, the opposite effectslower diffusionis observed when the gradients are ordered in decreasing strength (Fig. 2, A and B, blue), or for the product where the concentration is increasing (Fig. 2C). Thus, the reported diffusion enhancement must be an artifact, as the true diffusion coefficient cannot depend on the order of the applied gradients. Changes in concentration due to the ongoing reaction (1) cannot account for the observed apparent diffusion change in Fig. 2, A and B. The intensity I0 is not only a function of concentration, but also depends on spin relaxation (14). We find that the spin-lattice relaxation constant T1 changes for all species, including the solvent, as a result of the changing concentration of paramagnetic Cu(II) ions. For example, T1 for azidoacetic acid increases from ~50 ms to more than 2 s within the first 20 min of the reaction (determined by inversion recovery experiments). This drastic T1 increase leads to the I0 change, which has been misinterpreted as faster diffusion in (1). The artifact vanishes when a shuffled gradient order is used (Fig. 2, green), as was previously shown to be required for time-resolved diffusion NMR measurements of dynamic systems (1113). Additionally, the alkyne and methylene protons have the same diffusion coefficients, as expected, when using shuffled gradients (Fig. 2D). Changing T1 values also affect the determination of reaction rates, because the integrated intensities are not proportional to concentration throughout the experiment. We observe an almost constant apparent reaction rate (20 to 30 μM s–1) over the first 150 min, similar to that reported in (1).

We demonstrate that there is no enhanced or “boosted” diffusion during the click reaction in (1), shown here for the reactants azidoacetic acid and propargyl alcohol, the product, and the residual solvent HDO. Changes in signal intensities unrelated to diffusive attenuation are the source of the artifact, which results in apparent changes in measured diffusion coefficients. Because Wang et al. state that they used increasing gradients for all diffusion NMR measurements, the artifact presented here applies also to the remaining reactions of (1).

## References

1. W. S. Price, NMR Studies of Translational Motion (Cambridge Univ. Press, 2009).

Acknowledgments: Funding: Supported by Australian Research Council grant FT170100094 (J.E.B.).