enhanced diffusion of molecular catalysts is due to convection

doi.org/10.26434/chemrxiv.8259317.v2

Enhanced Diffusion of Molecular Catalysts Is Due to ConvectionThomas MacDonald, William S. Price, R. Dean Astumian, Jonathon Beves

Submitted date: 14/06/2019 • Posted date: 14/06/2019Licence: CC BY-NC-ND 4.0Citation information: MacDonald, Thomas; Price, William S.; Astumian, R. Dean; Beves, Jonathon (2019):Enhanced Diffusion of Molecular Catalysts Is Due to Convection. ChemRxiv. Preprint.

Intriguing reports of enhanced diffusion in enzymes and molecular catalysts have spurred significant interestin experimental and theoretical investigations of this phenomenon, with mechanistic understanding the subjectof ongoing and lively debate. Here we use time-resolved diffusion NMR methods to measure the diffusioncoefficients of small molecule species involved in chemical reactions with high temporal resolution. We showthe enhanced diffusion of small molecules cannot be explained by reaction velocity, and that apparentmeasurements of enhanced diffusion by small molecules appear to be caused by bulk fluid flow processessuch as convection.

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1

Supporting Information for

Enhanced diffusion of molecular catalysts

is due to convection

Thomas MacDonald, William S. Price, R. Dean Astumian and Jonathon E. Beves*

All experimental data used in this publication is publicly available from ChemRxiv: https://dx.doi.org/10.26434/chemrxiv.8259317

https://dx.doi.org/10.26434/chemrxiv.8259317

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Table of Contents

General Experimental ....................................................................................................................................... 4 S1.

Synthesis ................................................................................................................................................................ 5 S2. Grubbs metathesis[3] ............................................................................................................................................... 5 S2.1 Palladium-catalysed intramolecular quinolinone formation .................................................................................. 5 S2.2 Synthesis of substrate S1 for palladium-catalysed intramolecular cyclisation ........................................................ 6 S2.3

Acquisition and processing of time-resolved diffusion experiments .............................................. 6 S3. Moving-average processing of diffusion data ......................................................................................................... 6 S3.1

NMR Experimental data ................................................................................................................................... 6 S4. Static and dynamic T1 measurements ..................................................................................................................... 6 S4.1

Use of Cr(acac)3 to shorten T1 ......................................................................................................................... 7 S4.1.1.

NMR Reaction data ............................................................................................................................................. 9 S5. Representative NMR Stack plots ............................................................................................................................. 9 S5.1

Processed diffusion and concentration data for Grubbs ring-closing metathesis reaction .. 10 S6. Diffusion and concentration plots for Grubbs-catalysed ring-closing metathesis ................................................ 10 S6.1

Agreement of static diffusion values with literature ..................................................................................... 11 S6.1.1. Enhanced diffusion of Grubbs ring-closing metathesis................................................................................. 11 S6.1.2.

Additional Grubbs RCM experiment: 100 mM DDM ............................................................................................ 13 S6.2 Convection studies: influence of stimulated-echo delay Δ on measured diffusion coefficients........................... 14 S6.3

Δ = 25 ms....................................................................................................................................................... 14 S6.3.1. Δ = 50 ms....................................................................................................................................................... 15 S6.3.2. Δ = 100 ms..................................................................................................................................................... 16 S6.3.3. Relative and absolute changes in measured diffusion .................................................................................. 17 S6.3.4.

Discussion of the effect of changing ∆ on measured diffusion coefficients ................................................. 18 S6.3.5.

Processed diffusion and concentration data for palladium-catalysed intramolecular S7.cyclisation ........................................................................................................................................................... 20

Diffusion and concentration plots for palladium-catalysed intramolecular cyclisation ........................................ 20 S7.1 Enhanced diffusion of palladium-catalysed quinolinone formation ............................................................. 21 S7.1.1.

Convection studies: influence of stimulated-echo delay Δ on measured diffusion coefficients........................... 22 S7.2 Δ = 25 ms....................................................................................................................................................... 22 S7.2.1. Δ = 50 ms....................................................................................................................................................... 23 S7.2.2. Δ = 100 ms..................................................................................................................................................... 24 S7.2.3.

Discussion of the effect of changing ∆ on measured diffusion coefficients ................................................. 25 S7.2.4.

Influence of sample geometry on measured diffusion ....................................................................... 26 S8. The use of a fixed volume Shigemi NMR tube ...................................................................................................... 26 S8.1 The use of a thinner NMR tube suppresses diffusion changes ............................................................................. 27 S8.2

Processing methods with Python ............................................................................................................... 29 S9. General comments on processing methods ......................................................................................................... 29 S9.1 Python code for global moving-fit diffusion processing across multiple peaks .................................................... 29 S9.2

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Example data processing schema ......................................................................................................................... 33 S9.3 Data averaging methods ....................................................................................................................................... 35 S9.4 Processing schema for Pd-catalysed arylation data .............................................................................................. 39 S9.5

Additional References ................................................................................................................................. 41 S10.

4

General Experimental S1.

Reagents were purchased from Combi-Blocks or Sigma-Aldrich and used as received. Deuterated NMR solvents were purchased from Cambridge Isotope Laboratories and used as received unless otherwise noted. NMR experiments were conducted using Bruker Avance III 400, 500, or 600 MHz instruments. Pulsed gradient stimulated echo (PGSTE) NMR diffusion experiments were conducted using Bruker TCI or BBFO probes fitted with standard high-resolution gradient coils capable of gradient pulses up to ~50 G cm-1. Diffusion experiments used the Bruker diffSe or diffSte spin-echo or stimulated-echo pulse sequences, with a spoiler gradient in the recycle delay followed by a 1.5 s recovery used to destroy residual magnetization. Typical parameters for Grubbs metathesis and palladium-catalysed cyclisation diffusion experiments with respective D coefficients of 1 – 2 and 0.5 – 1 × 10-9 m2 s-1, were Δ = 50 ms and δ = 1.2 ms or 1.8 ms, respectively. Gradient pulses were sine-shaped and ranged in amplitude from 0 – 50 g cm-1. Spoiler gradient pulses with 1.5 s spoiler recovery delays were used for fast acquisition of diffusion data.

Figure S1. Pulsed-gradient stimulated echo (PGSTE) sequence used for all diffusion experiments. A spoiler-recovery sequence[1] consisting of two

mismatched gradient pulses of +33% and -90% gmax was used to destroy residual magnetization between experiments, allowing faster repetition

rates.[2] During acquisition, gradient length δ and echo delay Δ were held constant while gradient intensity g was varied according to a

predetermined list of random gradients.

Random gradient lists were prepared from lists of random decimal fractions over [0,1] (taken from https://www.random.org/decimal-fractions/) which were then scaled to make gradient lists from 5 – 50 G cm-1. These lists are used for the a long random-gradient diffusion experiments below. Spectra were automatically phased (“Regions Analysis” for per-spectrum phasing) and baseline-corrected (standard routine) with MestReNova software 12.0, with peak integrals and methanol CH3/OH chemical peak shifts obtained using the built-in data analysis routines and exported as csv data for further processing.

https://www.random.org/decimal-fractions/

5

Synthesis S2.

Grubbs metathesis[3] S2.1

Cr(acac)3 (3.50 mg, 10 µmol) was dissolved in 500 µL C6D6 to make a 20 mM stock solution, then diluted in C6D6 to 1 mM before use. Grubbs’ 2nd-generation catalyst (1.27 mg, 1.5 µmol) was dissolved in 500 µL of stock solution (1 mM Cr(acac)3 in C6D6) and transferred to a standard 5mm NMR tube with optional CH3OH capillary,[2] inserted into the NMR instrument, and used to lock, tune and match, and shim the instrument. After a single-scan 1H NMR experiment to check lineshape and instrument function, a long random-gradient diffusion experiment was made ready. The sample was removed from the NMR instrument and diethyl diallyl malonate (1, 24 µL, 100 µmol) added to give 200 mM solution substrate in the reaction mixture. The sample was then returned to the instrument and the diffusion experiment started as quickly as possible (2 – 5 minutes from mixing).

Palladium-catalysed intramolecular quinolinone formation S2.2

Palladium acetate dissolved in trifluoroacetic acid to make a 60 mM stock solution (13.6 mg/mL). Alkyne 3 (22 mg, 100 µmol) dissolved in 500 µL 3:1 trifluoroacetic acid:CD2Cl2 to make a 200 mM solution and transferred to a standard 5 mm NMR tube, inserted into NMR instrument, and used to lock, tune and match, and shim the instrument. After a single-scan 1H NMR experiment to check lineshape and instrument function, a long random-gradient diffusion experiment was prepared. The sample was then removed from the NMR instrument and Pd(OAc)2 in TFA (25 µL of 60 mM stock solution, 1.5 µmol Pd(OAc)2) added to give 3 mM solution of catalyst in the reaction mixture. Sample returned to the instrument and diffusion experiment started as quickly as possible.

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Synthesis of substrate 3 for palladium-catalysed intramolecular cyclisation S2.3

Tetrolic acid (500 mg, 5.95 mmol, 1 eq) and 3,5-dimethoxyaniline (1.0 g, 6.6 mmol, 1.1 eq) combined in 5 mL DMF. Diisopropylethylamine (DIPEA; 1.9 g, 2.7 mL, 15 mmol, 2.5 eq) added, and reaction mixture cooled to 0 °C with stirring. Propylphosphonic anhydride (5.6 mL 50 wt% solution in DMF; 2.8 g, 8.8 mmol, 1.5 eq) added dropwise with stirring, and reaction mixture left to stir overnight. The reaction mixture was diluted with ethyl acetate (100 mL) and washed with NaHCO3 solution (3 x 25 mL), water (1 x 25 mL), brine (1 x 25 mL), and dried over MgSO4 before concentration under reduced pressure to give a brown solid. Recrystallization from hot toluene/hexanes gave the pure 3 as a white amorphous solid in 65% yield. 1H NMR spectra (CDCl3) were in accordance with those previously reported.[4]

Acquisition and processing of time-resolved diffusion S3.

experiments

Diffusion NMR experiments were performed using lists of 200-1000 random gradients with 5 – 50 G cm-1 amplitude. See previous work for details.[2]

Moving-average processing of diffusion data S3.1

Time-resolved diffusion data were continuously acquisition using experiments set up with gradient lists, typically

containing 300 – 1000 gradient points. All time-resolved diffusion data were processed as previously described[2] by

using a moving-average approach to solve the Stejskal-Tanner equation:

𝐼𝐼 = 𝐼𝐼0 exp �−𝐷𝐷(𝑔𝑔𝑔𝑔𝑔𝑔)2 �Δ − 𝛿𝛿3�� = exp (−𝑏𝑏𝐷𝐷)

where 𝐼𝐼0 is the unattenuated intensity of the NMR echo signal, 𝐷𝐷 is the diffusion coefficient of the chemical species, 𝑔𝑔 is the gyromagnetic ratio, 𝑔𝑔 is the strength of the gradient pulse used, and 𝑔𝑔 and Δ are respectively the length of the gradient pulses and the delay between gradient pulses. I0 the echo intensity in the absence of gradient pulses.

NMR Experimental data S4.

Static and dynamic T1 measurements S4.1

Preliminary experiments following changes in diffusion during ring-closing metathesis showed anomalous changes in measured concentration, most notably showing the measure intensity of the residual solvent signal reducing by half over the course of the experiment. It was suspected that this effect might be caused by the combination of fast 5s repetition rates used for NMR experiments and changes in T1 longitudinal relaxation rates over the experiment, perhaps due to some sort of ‘self-sparging’ of the reaction mixture by generated C2H4 gas. This was confirmed through use of a time-dependent inversion-recovery experiment applying the same concepts of continuous acquisition and moving-fit processing as used in our diffusion experiments.

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O

O O

O

ab

cd

e

O

O O

O

ab

x

y

Grubbs catalyst

C6D6

Figure S2. Changes in concentration (top) and T1 longitudinal relaxation times (bottom) of NMR signals during Grubbs metathesis. Relaxation times

can be seen to increase significantly over the course of the experiment, perhaps driven by a ‘self-sparging’ effect where generated ethylene removes

paramagnetic dissolved oxygen from the system. Concentrations have been normalized by spin multiplicities and scaled to the ethyl peaks as an

internal 200 mM standard.

Figure S3. Expansion showing T1 longitudinal relaxation times of species other than benzene-d5 and ethylene over the three-hour period used for all

following diffusion experiments. T1 relaxation times can be seen to increase over this time, and all times are comparable to or longer than the 5 s

repetition rate preferable for fast time-dependent diffusion monitoring.

Use of Cr(acac)3 to shorten T1 S4.1.1.

As the long and changing T1 relaxation times demonstrated in Figure S2 and Figure S3 would interfere with quantitative NMR measurements of concentration, a relaxation agent was used to achieve acceptable relaxation over short repetition rates and retain quantitative information. Chromium(III) acetylacetonate is a paramagnetic species soluble in nonpolar organic solvents and capable of dramatically shortening T1 relaxation times.[5] 1 mM of Cr(acac)3

was used as an additive for all Grubbs metathesis reactions to allow the acquisition of near-quantitative data despite short fast experimental repetition times. A 1 mM concentration of Cr(acac)3 was chosen after T1 measurements of 200 mM DDM in C6D6 with 0.1, 1, and 10 mM dissolved Cr(acac)3 showed favorable relaxation times of 1-2 s at this concentration (Table S1).

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Table S1. T1 relaxation times of benzene and DDM with varying concentrations of paramagnetic Cr(acac)3. In the presence of 1 mM relaxation agent,

relaxation was found to occur with ideal T1 times of 1 – 2 s. This corresponds to approximately 92 to >99% signal recovery over a 5 s repetition rate

for standard diffusion experiments, with 5 – 2.5% signal loss over the Δ = 50 ms stimulated-echo delay. See below for proton labelling. Conditions:

200 mM DDM in C6D6, 500 MHz.

O

O O

O

ab

cd

e

T1 / seconds

[Cr(acac)3] (mM)

C6D5H d e b c a

10 0.27 0.30 0.26 0.23 0.31 0.26

1 2.00 1.72 1.34 1.37 1.08 1.42

0.1 6.10 3.48 2.39 2.85 1.47 2.65

0 8.82 4.24 2.77 3.48 1.60 3.12

0* 26.5 6.86 3.81 5.06 1.86 4.37

* sparged with argon

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NMR Reaction data S5.

Representative NMR Stack plots S5.1

Figure S4. Stacked NMR spectra of representative random-gradient diffusion experiment following Grubbs ring-closing metathesis (500 MHz, C6D6,

270 random gradient slices; 10 x decimation for clarity).

Figure S5 Stacked NMR spectra of representative random-gradient diffusion experiment following palladium-catalyzed quinolinone formation

reaction (400 MHz, 3:1 TFA:CD2Cl2, 203 random gradient slices; 10 x decimation for clarity).

0.00.51.01.52.02.53.03.54.04.55.05.56.06.57.07.5f1 (ppm)

3.54.04.55.05.56.06.57.07.58.08.59.09.510.010.511.011.512.012.513.013.514.0f1 (ppm)

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Processed diffusion and concentration data for Grubbs S6.

ring-closing metathesis reaction

Diffusion and concentration plots for Grubbs-catalysed ring-closing S6.1metathesis

Figure S6. Concentration and diffusion changes for all chemical species during Grubbs metathesis (200 mM DDM, 3 mM Grubbs catalyst, C6D6; 1H,

500 MHz, δ = 1.3 ms, Δ = 50 ms). Red lines and shaded areas represent measured diffusion coefficients and associated error; blue lines and shaded

areas represent measured concentrations and associated error. Red dashed lines show measured diffusion coefficients on reaction completion.

Concentrations calibrated from the ethyl protons as an internal standard at assumed 200 mM concentration.

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Agreement of static diffusion values with literature S6.1.1.

The self-diffusion coefficient of 14C-labelled benzene at 298 K has been measured[6] as 2.17 × 10-9 m2 s-1, which is in acceptable agreement with the at-equilibrium diffusion coefficient of 2.03 × 10-9 m2 s-1

measured for benzene-d5 in the absence of chemical reaction in this work. The at-rest diffusion coefficients for the other chemical species were measured as follows (500 MHz, 500 µL solution in C6D6, Δ = 50 ms, δ = 1.3 ms, ns = 8). Table S2. At-rest diffusion coefficients measured by NMR (500 MHz, 500 µL solution in C6D6, Δ = 50 ms, δ = 1.3 ms, ns = 8).

Species D / 10-9 m2 s-1

Benzenea 2.03 DDMa 1.08 Reaction productb 1.16 Grubbs’ catalystb 0.65 Dissolved ethyleneb 3.46

a 200 mM DDM in C6D6, without catalyst added. b Measured in reaction mixture long (>10 h) after reaction completion. c Measured for 3 mM solution of Grubbs catalyst in C6D6 (no DDM or reaction product).

Enhanced diffusion of Grubbs ring-closing metathesis S6.1.2.

Figure S7. Diffusion measurements of species present during Grubbs-catalyzed ring-closing metathesis (200 mM DDM, 3 mM Grubbs catalyst, C6D6; 1H, 500 MHz, δ = 1.3 ms, Δ = 50 ms). Data averaged across 8 separate experiments, with experimental error shown by shaded areas. Top: changes in

concentration over time; bottom: changes in diffusion over time (horizontal lines indicate final diffusion values on reaction completion).

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Figure S8. Changes in measured diffusion coefficients of species present during Grubbs-catalyzed ring-closing metathesis (200 mM DDM, 3 mM

Grubbs catalyst, C6D6; 1H, 500 MHz, δ = 1.3 ms, Δ = 50 ms). Top: relative changes in measured diffusion compared to static diffusion coefficients.

Bottom: absolute changes in measured diffusion.

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Additional Grubbs RCM experiment: 100 mM DDM S6.2


500 MHz, δ = 1.3 ms, Δ = 50 ms). Red lines and shaded areas represent measured diffusion coefficients and associated error; blue lines and shaded

areas represent measured concentrations and associated error. Red dashed lines show measured diffusion coefficients on reaction completion.

Concentrations calibrated from the ethyl protons as an internal standard at assumed 100 mM concentration.

14

Convection studies: influence of stimulated-echo delay Δ on measured S6.3diffusion coefficients

Diffusion measurements via pulsed-gradient stimulated echo NMR involve the application of two gradient pulses of length δ separated by a diffusion measurement timescale Δ.

Δ = 25 ms S6.3.1.


500 MHz, δ = 3.0 ms, Δ = 25 ms), averaged from three independent experiments. Red lines and shaded areas represent measured diffusion

coefficients and associated error; blue lines and shaded areas represent measured concentrations and associated error. Red dashed lines show

measured diffusion coefficients on reaction completion. Concentrations calibrated from the ethyl protons as an internal standard at assumed 200

mM concentration.

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Δ = 50 ms S6.3.2.

Figure S11. Duplicate of Figure S6. Concentration and diffusion changes for all chemical species during Grubbs metathesis (200 mM DDM, 3 mM

Grubbs catalyst, C6D6; 1H, 500 MHz, δ = 1.3 ms, Δ = 50 ms), averaged from eight independent experiments. Red lines and shaded areas represent

measured diffusion coefficients and associated error; blue lines and shaded areas represent measured concentrations and associated error. Red

dashed lines show measured diffusion coefficients on reaction completion. Concentrations calibrated from the ethyl protons as an internal standard

at assumed 200 mM concentration.

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Δ = 100 ms S6.3.3.


500 MHz, δ = 1.0 ms, Δ = 100 ms), averaged from three independent experiments. Red lines and shaded areas represent measured diffusion

coefficients and associated error; blue lines and shaded areas represent measured concentrations and associated error. Red dashed lines show

measured diffusion coefficients on reaction completion. Concentrations calibrated from the ethyl protons as an internal standard at assumed 200

mM concentration.

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Relative and absolute changes in measured diffusion S6.3.4.

Figure S13. Relative and absolute changes in measured diffusion coefficients during Grubbs metathesis (200 mM DDM, 3 mM Grubbs catalyst, C6D6; 1H, 500 MHz, δ = 3.0 ms, Δ = 25 ms).

Figure S14. Relative and absolute changes in measured diffusion coefficients during Grubbs metathesis (200 mM DDM, 3 mM Grubbs catalyst, C6D6; 1H, 500 MHz, δ = 1.0 ms, Δ = 100 ms).

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Discussion of the effect of changing ∆ on measured diffusion coefficients S6.3.5.

As shown in figures Figure S8, Figure S13, and Figure S14, increases in measured diffusion coefficients over the course of the ring-closing metathesis reaction vary significantly depending on the stimulated-echo delay Δ. This behavior is inconsistent with purely diffusive motion, where the measured diffusion coefficient D is obtained independently of the echo delay Δ. A positive correlation between measured D and echo delay time Δ is indicative of bulk fluid motion, most commonly convection.[7] As can be seen in Figure S15, the measured diffusion coefficient of Grubbs’ catalyst at t = 30 minutes (approximately where D is highest) varies linearly with increasing Δ. An extrapolation of this trend to Δ = 0 gives an implied D of 0.65 ± 0.04 x 10-10 in the absence of convection, equal to the diffusion coefficient of 6.5 × 10-10 m2 s-1 measured for Grubbs’ catalyst in C6D6 (S6.1.1). This indicates that measured ‘enhanced diffusion’ of this reaction is a bulk transport phenomenon, and that the rate of molecular self-diffusion does not increase during this reaction.

Figure S15. Influence of Δ on measured increase in diffusion. Left: the increase in measured diffusion coefficient at t = 30 minutes (close to the point

of maximum enhancement) can be seen to increase linearly with increasing diffusion experiment Δ parameter. Extrapolating<Hedin, 2000,

7548-7550> this fit to Δ = 0 gives a diffusion coefficient of approximately 6.5 ± 0.4 x 10-10 m2 s-1 in the absence of convection, the same value

measured for Grubbs’ catalyst in C6D6 (S6.1.1). This behavior is characteristic of convection but not of enhanced diffusion. For diffusive processes,

measured D is obtained independently of Δ. Right: absolute enhancement in the measured diffusion coefficient of Grubbs’ catalyst divided by the

value of Δ (eg 𝐷𝐷−𝐷𝐷0Δ

) plotted over time shows good agreement between curves at all times, again consistent with Δ-dependent bulk motion and

inconsistent with Δ-independent diffusion.

The exact mechanism by which this reaction generates a density gradient in the reaction mixture and drive convection is undetermined. Two potential influences are:

a) The generation of ethylene gas during ring-closing metathesis. This could drive convection either through bubble formation (a phenomenon familiar to anyone who has ever enjoyed a pint of stout[9]), or with a gradient in dissolved ethylene concentration formed by losses at the air-liquid interface.

b) Convection driven by temperature gradients, where enthalpically-driven internal heating or cooling of the reaction mixture creates a temperature gradient to the (assumed constant) temperature of the tube surface.

To investigate the possibility of temperature gradients, two experiments were performed with a flame-sealed methanol capillary present in the reaction mixture (Figure S16). No changes in temperature were observed within the accuracy of the measurement (approx. 0.1 K).

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Figure S16. Top: Internal temperatures of two Grubbs metathesis reaction mixtures (top) measured over time with a sealed methanol capillary,[2]

show no detectable temperature changes during the reaction (to within approximately 0.1 K). Bottom: corresponding diffusion-time profile.

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Processed diffusion and concentration data for S7.

palladium-catalysed intramolecular cyclisation

At-rest diffusion coefficients of chemical species under reaction conditions (before addition of Pd(OAc)2 or long after reaction completion) were measured as follows (500 MHz, 500 µL solution, Δ = 50 ms, δ = 1.8 ms, ns = 8). Table S3. The at-rest diffusion measured by NMR (500 MHz, 500 µL solution in C6D6, Δ = 50 ms, δ = 1.8 ms, ns = 8).

Species D / 10-9 m2 s-1

Trifluoroacetic acid (OH proton)a 1.5 CDHCl2

a 3.2

Alkyne 3a 0.7 Quinolinone 4b 0.7

a 200 mM in 3:1 TFA:CD2Cl2, without catalyst added. b Measured in reaction mixture long (>10 h) after reaction completion.

Diffusion and concentration plots for palladium-catalysed intramolecular S7.1cyclisation

Figure S17. Concentration and diffusion changes for all chemical species during palladium-catalyzed intramolecular cyclisation (200 mM substrate, 3

mM Pd(OAc)2, 3:1 TFA:CD2Cl2; 1H, 500 MHz, δ = 1.8 ms, Δ = 50 ms). Red lines and shaded areas represent measured diffusion coefficients and

associated error; blue lines and shaded areas represent measured concentrations and associated error. Concentrations calibrated from the sum of

starting material and product at assumed 200 mM concentration.

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Enhanced diffusion of palladium-catalysed quinolinone formation S7.1.1.

Figure S18. Diffusion coefficients measured during palladium-catalyzed arylation reaction, averaged over six experiments with calculated errors

shown as shaded channels. As the reaction runs to completion, the concentration of starting material becomes insufficient for diffusion

measurements (visible as a sharp increase in error from approximately t = 80 min).

Figure S19. Changes in diffusion coefficients (Top: relative; bottom: absolute) measured during palladium-catalyzed arylation reaction. As the

reaction runs to completion, the concentration of starting material becomes insufficient for diffusion measurements (visible as a sharp increase in

error from approximately t = 80 min).

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Convection studies: influence of stimulated-echo delay Δ on measured S7.2diffusion coefficients

Δ = 25 ms S7.2.1.

Figure S20. Concentration and diffusion changes for all chemical species during palladium-catalysed intramolecular cyclisation (200 mM substrate, 3




23

Δ = 50 ms S7.2.2.





24

Δ = 100 ms S7.2.3.





25

Discussion of the effect of changing ∆ on measured diffusion coefficients S7.2.4.

Figure S23. Influence of Δ on measured increase in diffusion coefficient for cyclized product. Left: the increase in measured diffusion coefficient at t

= 40 minutes (close to the point of maximum enhancement) increases with increasing echo parameter Δ, and can be approximated by a linear fit.

Extrapolating this fit to Δ = 0 gives a diffusion coefficient of approximately 6.5 x 10-10 m2 s-1 in the absence of convection, the same value measured

for the reaction product at reaction completion.[8] This behavior is characteristic of convection but not of enhanced diffusion: for diffusive processes,

measured D is obtained independently of Δ (eg the line would be flat). Right: absolute increase in the measured diffusion coefficient of cyclized

product divided by the value of Δ (eg 𝐷𝐷−𝐷𝐷0Δ

). This plot shows good agreement between curves over time, again consistent with bulk motion and

inconsistent with diffusion.

As for Grubbs ring-closing metathesis, the measured diffusion coefficient for the Pd-catalyzed cyclisation reaction (Figure S23) increases proportionally to echo time Δ and is characteristic of convection or other directional motion. The absence of gaseous byproducts (compared to Grubbs RCM) shows that gas generation is not required for reaction-driven convection. An experiment conducted with an internal methanol capillary revealed a slight increase in sample temperature by 0.15 K during the reaction, perhaps sufficient to drive convection.

Figure S24. Top: Internal temperature changes during palladium-catalyzed cyclization, measured through use of a methanol capillary.[2] Internal

temperature of the reaction mixture is seen to increase by approximately 0.15 K during the reaction before returning to a stable 298.25 K. This

coincides with an increase in measured diffusion (bottom), suggesting that internal temperature gradients may be responsible for driving

convection.

26

Influence of sample geometry on measured diffusion S8.

The use of a fixed volume Shigemi NMR tube S8.1

As convection is known to depend substantially on sample geometry, diffusion behaviour was also investigated in a restricted volume Shigemi NMR tube. The palladium-catalysed arylation reaction was chosen as a model due to concerns regarding gas generation within the enclosed environment of a Shigemi tube, with results presented in Figure S25. A 100 ms Δ delay was used such that any bulk motion would be readily apparent, and while an increase in measured D was observed the increase was much less than that seen in the comparable experiment conducted with a standard 5 mm NMR tube (Figure S22). While the trifluoroacetic acid and starting material/product diffusion coefficients were previously observed to increase to approximately 2.0 and 1.1 × 10-9 m2 s-1 respectively, under the confines of a restricted volume Shigemi tube smaller increases in diffusion coefficients to 1.5 and 0.75 × 10-9 m2 s-1 were observed. This influence of sample geometry on observed diffusion coefficients is difficult to justify based on nano-scale dynamic coupling, but is consistent with convection.


mM Pd(OAc)2, 3:1 TFA:CD2Cl2; 1H, 500 MHz, δ = 1.1 ms, Δ = 100 ms) for 200 µL of reaction mixture in a 5 mm Shigemi NMR tube. Red lines and

shaded areas represent measured diffusion coefficients and associated error; blue lines and shaded areas represent measured concentrations and

associated error. Concentrations calibrated from the sum of starting material and product at assumed 200 mM concentration.

27

The use of a thinner NMR tube suppresses diffusion changes S8.2

Figure S26. Concentration and diffusion changes observed during reaction in a standard 5mm NMR tube (repeat of data shown in Figure S22). Axes

are scaled for consistency with data from the 3mm tube experiment give below (Figure S27).


mM Pd(OAc)2, 3:1 TFA:CD2Cl2; 1H, 500 MHz, δ = 1.1 ms, Δ = 100 ms) for 200 µL of reaction mixture in a 3 mm diameter NMR tube. Data are combined

from three separate experiments. Red lines and shaded areas represent measured diffusion coefficients and associated error; blue lines and shaded

areas represent measured concentrations and associated error. Concentrations calibrated from the sum of starting material and product at assumed

200 mM concentration.

28

The use of a 3 mm NMR tube for diffusion experiments leads to an almost entirely flat time-dependent measurement of diffusion (i.e. no observed enhancement in diffusion), even with a long echo delay of Δ = 100 ms. Comparing the results obtained using the 3 mm NMR tube (Figure S27) to those obtained using a 5 mm sample tube under otherwise identical conditions (Figure S26) the observed “enhanced diffusion” appears entirely dependent on sample geometry. This observation is incompatible with microscopic views of enhanced diffusion as driven by dynamic coupling or molecular interactions, but is entirely consistent with misinterpreted convection driven by temperature or other inhomogeneity across the bulk reaction solution.

29

Processing methods with Python S9.

General comments on processing methods S9.1

Scripts written in Python 3.7 for the processing of time-resolved diffusion NMR data, adapted from those published previously.[2] Integrals corresponding to a single species of interest (I1, I2, … In) were obtained using MestReNova, and saved as CSV.

The values for b (in s·m-2), where 𝐵𝐵𝑖𝑖 = (𝑔𝑔𝑔𝑔𝑔𝑔𝑖𝑖)2(Δ − 𝛿𝛿3) are obtained from the Bruker difflist file, which is generated

when running a diffusion experiment with the Bruker diff program in Topspin 3.5. Values for integrals and b were combined in a csv file with the following format:

b1 I1,1 I2,1 … In,1

b2 I1,2 I2,2 … In,2

b3 I1,3 I2,3 … In,3

⋮ ⋮ ⋮ ⋱ ⋮ bm I1,m I2,m … In,m

These csv files were processed to obtain time-dependent diffusion and concentration data with the moving nonlinear fit technique described in Section S3.1 , implemented using the Python numpy, pandas, and lmfit libraries for analysis and matplotlib for plotting.

Python code for global moving-fit diffusion processing across multiple S9.2peaks

Time-dependent moving fitting of diffusion data was conducted with the code shown in Script S1, run through iPython. Please see https://github.com/tscmacdonald/diffusion-fits/ for any updates. Script S1. Scripts used for moving-fit diffusion processing and gradient calibration from methanol.

'''Module for global fitting of (time-dependent) diffusion NMR data.

This module provides the following functions:

GlobalDiff(data)

Global nonlinear fitting of the S-T equation for an arbitrary number of gradients and chemical shift

environments.

Returns an lmfit parameters object containing fitted I0 intensities for all peaks, as well as a single

globally fitted D value.

MovingDiff(data,slicelength=10)

Global moving average fit for diffusion, using GlobalDiff to obtain a D value for each time point.

S

Takes as input a pandas dataframe with the first column containing B values, and subsequent columns

containing integrals for the peaks of interest.

Slicelength sets the number of experiments used for each D(time) point. Slicetime sets the time (in

https://github.com/tscmacdonald/diffusion-fits/

30

minutes) taken to acquire each gradient slice.

Returns (Dpoints, I0points,Derr,Ierr): four pandas dataframes, each with indices corresponding to time.

I0points and Ierr contain a column for each fitted NMR peak, while Dpoint and Der contain a single column

with globally fitted diffusion data.

For systems involving multiple chemical species, use SeparateMovingDiffusion to obtain individual

(non-globally fitted) diffusion coefficients.

Dpoints, I0points, Derr, and Ierr contain diffusion points, extrapolated intensities, and respective

errors for each from fitting.

MovingDiff_csv(fname,slicelength=10,slicetime=2/3)

A wrapper for MovingDiff to act on a similarly formatted .csv file.

SeparateMovingDiffusion(data,slicelength=10,slicetime=2/3)

Returns (Dpoints, I0points,Derr,Ierr): four pandas dataframes, each with indexes corresponding to time

and a column for each peak.

Dpoints, I0points, Derr, and Ierr contain diffusion points, extrapolated intensities, and respective

errors for each from fitting.

SeparateMovingDiffusion_csv(fname,slicelength=10,slicetime=2/3)

Generates a pair of pandas dataframes [D,I] containing calculation time-dependent diffusion

coefficients and unattenuated integrals.

Acts on a .csv file with the first column containing B-values, and each subsequent column containing

the corresponding integrals for a particular chemical shift.

MeOHTemp(dDelta)

Calculates temperature from methanol OH-CH3 chemical shift separation (in ppm)

MeOHDiff(dDelta)

Calculates expected diffusion coefficient from methanol OH-CH3 chemical shift separation (in ppm)

'''

def GlobalDiff(data):

'''Function to globally fit a single diffusion coefficient to data from a list of peaks

Input: a pandas dataframe consisting of:

B_0 I0_0 I1_0 ... In_0

B_1 I0_1 I1_1 ... In_1

...

B_m I0_m I1_m ... In_m

where B is the list of B-parameters for all experiments, and each column In_ contains the integrals

measured for a single peak.

The function returns a single lmfit Parameters object.

'''

import numpy as np

import pandas as pd

from lmfit import minimize, Parameters, report_fit

def STExp(B,I0,D):

I0,B,D = np.asarray(I0), np.asarray(B), np.asarray(D)

return I0*np.exp(-B*D)

def STExp_dataset(B,params,i):

I0 = params['I0_%i' % (i+1)].value

31

D = params['D_%i' % (i+1)].value

return STExp(B,I0,D)

def objective(params,B,data):

dataT = np.array(data.T[1:])

ndata, nx = dataT.shape

resid = 0.0*dataT[:]

#Residual per data set:

for i in range(ndata):

resid[i,:] = dataT[i,:] - STExp_dataset(B,params,i)

#Flatten to a 1d array:

return resid.flatten()

B = data.iloc[:,0]

dataT = np.array(data.T[1:])

fit_params = Parameters()

I0guesses = data.max()[1:]

for iy, y in enumerate(dataT):

fit_params.add('D_%i' % (iy+1), value = 1e-9, min = 1e-12, max = 1e-8)

fit_params.add('I0_%i' % (iy+1), value = I0guesses[iy], min = 1, max = 100*I0guesses[iy]) #Give

each I0 parameter a unique guessed I0

for iy in range(2,len(dataT)+1):

fit_params['D_%i' % iy].expr='D_1'

return minimize(objective,fit_params,args=(B,data))

def MovingDiff(data,slicelength=10,slicetime=2/3):

'''Fitting for time-dependent diffusion + concentration data.

Input: pandas dataframe formatted as

B_0 I0_0 I1_0 ... In_0

B_1 I0_1 I1_1 ... In_1

...

B_m I0_m I1_m ... In_m

'''

import numpy as np

import pandas as pd

from tqdm import tqdm_notebook as tqdm

from lmfit import minimize, Parameters, report_fit

npoints = data.shape[0]-slicelength

ipoints = np.arange(0,npoints)

tpoints = ipoints*slicetime+slicetime*slicelength/2

cols = data.columns[1:]

D = pd.DataFrame(index = tpoints,columns = [cols[0]])

Derr = pd.DataFrame(index = tpoints,columns = [cols[0]])

I0 = pd.DataFrame(index = tpoints,columns = cols)

I0err = pd.DataFrame(index = tpoints,columns = cols)

32

for i in tqdm(range(npoints),desc='Progress:',position=1,leave=False):

params = GlobalDiff(data.iloc[i:i+slicelength])

I0slice,I0errslice = [],[]

for Ival in range(0,len(cols)):

ParamName = 'I0_{}'.format(Ival+1)

#I0.insert(params.params[ParamName].value,index=i,col)

I0slice.append(params.params[ParamName].value)

I0errslice.append(params.params[ParamName].stderr)

D.loc[tpoints[i],cols[0]] = params.params['D_1'].value

Derr.loc[tpoints[i],cols[0]] = params.params['D_1'].stderr

I0.loc[tpoints[i],cols] = I0slice

I0err.loc[tpoints[i],cols] = I0errslice

return D,I0,Derr,I0err

def MovingDiff_csv(fname,slicelength=10,slicetime=2/3):

'''A simple wrapper of MovingDiff() to act on .csv files'''

import pandas as pd

return MovingDiff(pd.read_csv(fname),slicelength,slicetime)

def SeparateMovingDiffusion(data,slicelength=10,slicetime=2/3):

'''Moving average diffusion processing for multiple separate chemical species.

Acts on a pandas dataframe containing a list of B-values in teh first column, and corresponding peak

integrals in subsequent columns.

Returns a pair of pandas dataframes [D,I] containing the calculated diffusion coefficients

and concentrations for each peak present in the input array. '''

import pandas as pd

import numpy as np


npoints = data.shape[0]-slicelength

ipoints = np.arange(0,npoints)

tpoints = ipoints*slicetime+slicetime*slicelength/2

D = pd.DataFrame(index = tpoints,columns=data.columns[1:])

I = pd.DataFrame(index = tpoints,columns=data.columns[1:])

Derr = pd.DataFrame(index = tpoints,columns=data.columns[1:])

Ierr = pd.DataFrame(index = tpoints,columns=data.columns[1:])

for peak in tqdm(data.columns[1:],desc='Peak-by-peak progress',position=2):

td,ti,tderr,tierr =

MovingDiff(pd.concat([data.iloc[:,0],data[peak]],axis=1),slicelength=slicelength,slicetime=slicetime

)

D[peak] = td

I[peak] = ti

Derr[peak] = tderr

Ierr[peak] = tierr

return D, I, Derr, Ierr

def SeparateMovingDiffusion_csv(fname,slicelength=10,slicetime=2/3):

33

'''A wrapper of SeparateMovingDiffusion to act on .csv files'''

import pandas as pd

return SeparateMovingDiffusion(pd.read_csv(fname),slicelength=slicelength,slicetime=slicetime)

def MeOHTemp(dDelta):

'''Converts a methanol CH3-OH chemical shift separation (in ppm) to a temperature (in K).

See J. Magn. Reson. 1982, 46, 319-321'''

return 409-36.54*dDelta-21.85*dDelta**2

def MeOHDiff(dDelta):

'''Calculates the expected self-diffusion coefficient of methanol for a given OH-CH3 peak chemical

shift separation. See MacDonald et al, ChemPhysChem 2019, 20, 926–9'''

import numpy as np

return 5.124e-7 * np.exp((-1601)/(MeOHTemp(dDelta)))

Example data processing schema S9.3

NMR peak integrals obtained from MNova were saved as CSV files and processed with the following schema. First, integral data was processed to obtain time-dependent diffusion datasets: Script S2. Code used to process all NMR integral data using the functions defined in Script S1 and correct time indices to synchronize all

experimental data.

'''Processing of NMR integral data for Grubbs metathesis to obtain time-dependent diffusion information.

Outputs ‘grubbs’ as a tuple, with each tuple item made up of a tuple containing diffusion and concentration

data as generate by SeparateMovingDiffusion() function shown above.'''

import os


path = '5. NMR data\Grubbs Integrals' #Set path to directory containing all CSV files

grubbs = ()

for entry in tqdm(os.scandir(path)):

data = SeparateMovingDiffusion_csv(entry,slicelength=10,slicetime=2/3) #Moving-fit processing of

every file in directory. Here, diffusion fits are conducted over a slice of 10 gradients (slicelength=10),

each of which was acquired in 40 s (slicetime=2/3 minutes).

for item in data:

item.name=entry.name[:-4] #Set the name of each dataset to the name of the corresponding .csv file

grubbs += (data,)

from scipy.optimize import curve_fit

def expkin(t,delt,I,k):

return I*(1-np.exp(-k*(t-delt)))

#Reset all indices to start from 0

for data in grubbs:

for j in range(len(data)):

data[j].index = data[j].index - data[j].index[0]

#Fit exponential kinetics to datasets, and add offsets to time indices such that product concentration

34

is 0 at t = 0

fig,ax = plt.subplots(2,1,figsize=(12,15),sharex=True)

for data in grubbs:

offsets = []

for curve in data[1].columns:

if np.average(data[1][curve].iloc[-5:])/np.average(data[1][curve].iloc[:5])>1.2:

popt,pcov =

curve_fit(expkin,np.array(data[1].index,dtype=float),np.array(data[1][curve],dtype=float),p0=[1,max(

data[1][curve]),1])

corrfactor = data[1][curve][45:50].mean(axis=0)

ax[0].plot(data[1].index,data[1][curve]/corrfactor,label=curve)

ax[0].plot(data[1].index,expkin(data[1].index,popt[0],popt[1]/corrfactor,popt[2])) #Plot

uncorrected data and fit curves for each dataset

ax[1].plot(data[1].index-popt[0],expkin(data[1].index-popt[0],0,popt[1]/corrfactor,popt[2]))

ax[1].plot(data[1].index-popt[0],data[1][curve]/corrfactor,label=curve) #Plot corrected data

and fit curves for each dataset

offsets.append(popt[0])

offset = np.median(offsets)

for j in range(len(data)):

data[j].index = data[j].index-offset #Add offset to indices of each dataset

ax[0].set_xlim(0,180)

ax[0].set_ylim(0,None)

plt.show() #Show all plots

35

Data averaging methods S9.4

Data over multiple datasets were combined using a moving average approach and time-corrected to account for delays between mixing compounds and the beginning of NMR acquisitions (code snippets above and Figure S28).

Figure S28. Time correction of data from Grubbs metathesis, plotted by the code snippet above. Top plot: delays between starting the reaction and

beginning NMR acquisition lead to nonzero concentrations of product (brown, red) and ethylene (lavender) at t = 0. This is corrected by fitting

changing concentrations to a first-order exponential of the form 𝐼𝐼0 �1− exp �− 𝑘𝑘𝑡𝑡−𝛿𝛿𝑡𝑡

��, then adding the time offset 𝑔𝑔𝛿𝛿 to all datasets such that

concentrations can be extrapolated to 0 at t = 0 (bottom plot).

Figure S29. Concentration (top) and diffusion coefficient (bottom) data for all peaks from 8 separate ring-closing metathesis reactions, plotted on

the same axes. Datapoints are colour-coded by NMR peak. Diffusion plots from top (highest D) to bottom (lowest D) correspond to ethylene,

benzene, starting material and product (overlapping), and Grubbs’ 2nd-generation catalyst. Plot generated with Script S3.

36

Script S3. Code used to generate Figure S29, taking data processed with Script S1 and Script S2.

peaks = range(grubbs[0][0].shape[1])

fig,ax = plt.subplots(2,1,figsize=(8,6),sharex=False)

malpha = 0.1

for data in grubbs:

for i in peaks:

color = 'C{}'.format(np.mod(i,10))

ax[0].plot(data[1].iloc[:,i]/data[1].iloc[:20,-1].mean(),color+'o',alpha=malpha)

ax[1].plot(data[0].iloc[:,i]*1e9,color+'o',alpha=malpha)

for i in peaks:

col = 'C{}'.format(np.mod(i,10))

patches.append(mpatches.Patch(color=col,label=datasets[0][0].columns[i]))



ax[1].set_ylim(0,5)

ax[0].set_ylabel('Normalised intensity')

ax[1].set_ylabel('D (m$^2$ s$^{-1}$ x $10^{-9}$)')

ax[1].set_xlabel('Time (minutes)')

plt.tight_layout()

plt.savefig('SI-allgrubbsdata-all.png',dpi=300)

plt.savefig('SI-allgrubbsdata-all.pdf')

plt.show()

After separate processing of each peak of each datasets, results were combined to produce time-dependent diffusion and concentration curves for each molecular species, averaged over all peaks and all datasets. Script S4. Moving-average combination of all Grubbs datasets to produce per-species diffusion and concentration data.

import pandas as pd

def MovingAverage(data,window,step):

centre = window/2

time,val,err = [],[],[]

while max(data.index) > centre:

vals = data.loc[centre-window/2:centre+window/2].values.flatten()

time.append(centre)

val.append(np.nanmean(vals))

err.append(np.nanstd(vals))

centre += step

output = np.vstack([val,err])

DFout = pd.DataFrame(np.transpose(output),index=time,columns=['Mean','Error'])

DFout.name = data.name

return DFout

datasets = tm91

peaks = [[0],[1,4],[2,6],[3],[5,10],[8,9]]

37

multiplicities = [[1],[2,4],[2,4],[4],[4,6],[3,3]]

grubbslabels = ['Benzene-$d_5$','DDM','Cyclopentene product','Ethylene','Ethyl (S.M and

product)',"Grubbs' Catalyst"]

grubbsdata = ([],[])

for i in range(len(peaks)):

Dconcat = pd.DataFrame()

Iconcat = pd.DataFrame()

for data in datasets:

#First, use the ethyl signals as an internal standard fixed at 200 mM to get quantitative data

for the peak

datanorm =

200*((data[1].iloc[:,peaks[i]]/multiplicities[i])/((data[1].iloc[:,peaks[4]]/multiplicities[4]).mean

(axis=1).mean(axis=0))).mean(axis=1)

#Then conccatenate the normalised data for all datasets to give a single pandas dataframe for the

peak

Iconcat = pd.concat([Iconcat,datanorm],axis=1)

Dconcat = pd.concat([Dconcat,data[0].iloc[:,peaks[i]]],axis=1)

#Give the dataframe a name attribute for the peak

Dconcat.name=grubbslabels[i]

Iconcat.name=grubbslabels[i]

#Moving-average processing. Here, generate a point every 0.25 minute using a 5-minute averaging window.

grubbsdata[1].append(MovingAverage(Iconcat,5,0.25))

grubbsdata[0].append(MovingAverage(Dconcat,5,0.25))

#Output: grubbsdata tuple containing diffusion data as tuple in grubbsdata[0] and concentration data as

tuple in grubbsdata[1].

#Diffusion and concentration tuples each contain a dataframe for each chemical species.

With combined data generated using Script S4 above, results can be plotted and analyzed further. For example, the per-species subplots shown Figure S6 can be generated using the following code: Script S5. Plotting of data processed through Script S1, Script S2, and Script S4 to generate graphs shown in Figure S6.

#Plotting limits for diffusion are set here:

Dlims = ((2,3),(1.2,2.2),(1.2,2.2),(3.5,6.5),(1.2,2.2),(0.6,1.6))

#Now make plots for each peak grouping.

fig,ax = plt.subplots(3,2,figsize=(8,9),sharex=True)

cf = 1.14 #Correction factor for diffusion coefficients (eg gcc)

endtime = 180

ax2 = []

ax = ax.flatten()

for axs in ax.reshape(-1):

# Hide the right and top spines

axs.spines['right'].set_visible(False)

38

axs.spines['top'].set_visible(False)

# Only show ticks on the left and bottom spines

axs.yaxis.set_ticks_position('left')

axs.xaxis.set_ticks_position('bottom')

axs.set_xlabel('Time / min')

for i in range(len(grubbsdata[0])):

ax[i].fill_between(x=grubbsdata[0][i].index,y1=(grubbsdata[0][i].Mean-grubbsdata[0][i].Error)*cf*1e9

,y2=(grubbsdata[0][i].Mean+grubbsdata[0][i].Error)*cf*1e9,color='r',alpha=0.3,linewidth=0.0)

ax[i].plot(grubbsdata[0][i].index,grubbsdata[0][i].Mean*cf*1e9,'r-',label=grubbslabels[i])

#ax[i].errorbar(x=grubbsdata[i].index,y=grubbsdata[i].Mean*cf*1e9,yerr=grubbsdata[i].Error*cf*1e9,fm

t='k.',label=grubbslabels[i])

finalval = grubbsdata[0][i].Mean.loc[endtime-5:endtime+5].mean(axis=0)*cf

ax[i].axhline(y=finalval*1e9,color='r',linestyle='--')

ax[i].set_ylabel('D / m$^2$ s$^{-1}$ x $10^{9}$',color='red')

ax[i].set_ylim(Dlims[i])

ax2.append(ax[i].twinx())

ax2[i].fill_between(x=grubbsdata[1][i].index,y1=(grubbsdata[1][i].Mean-grubbsdata[1][i].Error),y2=(g

rubbsdata[1][i].Mean+grubbsdata[1][i].Error),color='b',alpha=0.3,linewidth=0.0)

ax2[i].plot(grubbsdata[1][i].index,grubbsdata[1][i].Mean,'b-',label=grubbslabels[i])

ax2[i].set_ylabel('Approx. concentration / mM',color='blue')

ax[i].set_title(grubbslabels[i])

ax[0].set_xlim(0,endtime)

#Export plots as PNG and PDF files

plt.tight_layout()

fname = 'grubbs-allsubplots-SI'

plt.savefig(fname+'.png',dpi=300)

plt.savefig(fname+'.pdf')

plt.show()

39

Processing schema for Pd-catalysed arylation data S9.5

Processing of the palladium-catalysed data largely proceeded as above, but with minor alterations to deal with the presence of two experiments conducted with 20 s gradient slice times (instead of the 40 s used elsewhere). Script S6. Moving-average processing of all .csv files in a given folder.

import os

import re

path = "5. NMR data\Pd Integrals" #Set path to folder containing integrals here

pdarylation = ()

for entry in tqdm(os.scandir(path)):

slicetime = int(re.findall(r'\.(\d*)\D*\.csv$',entry.name)[0]) #Use regular expression to get

experiment slice time from end of CSV filename

data = SeparateMovingDiffusion_csv(entry,slicelength=10,slicetime=slicetime/60)

for item in data:

item.name=re.findall(r'^(\S*?)\.',entry.name)[0]

pdarylation += (data,)

As the arylation reaction did not follow first-order exponential kinetics, start time offsets could not be calculated from exponential fits as shown in Script S2 and Figure S28 for the Grubbs RCM reaction. Instead, all experiments were offset such that the crossover point where product concentration equals starting material concentration occurred at the same time. Script S7. Correction of time indices for Pd-catalysed arylation time-dependent concentration and diffusion data to compensate for variable delays in

starting the experiment.

fig,ax = plt.subplots(2,1,figsize=(8,4))

toffsets = np.zeros(len(pdarylation))

j=0

def sigmoid(t,I,k,t0): #Reaction appears to follow sigmoidal kinetics, so use that for curve-fitting

t = np.array(t,dtype='float64')

return I*(1 - 2/(1+np.exp(-k*(t-t0))))

for data in pdarylation:

for dset in data:

dset.index = dset.index - dset.index[0] #Reset all indices to begin at t = 0

#Calculate scalefactor to normalise all concentrations against sum of SM + P:

scalefactor =

((data[1].iloc[:,peaks[2]]/multiplicities[2]).mean(axis=1).mean(axis=0))+(data[1].iloc[:,peaks[1]]/m

ultiplicities[1]).mean(axis=1).mean(axis=0)

#Calculate [SM] - [P]

line =

((data[1].iloc[:,peaks[1]]/multiplicities[1]).mean(axis=1)-(data[1].iloc[:,peaks[2]]/multiplicities[

2]).mean(axis=1))/scalefactor

popt,pcov = curve_fit(sigmoid,data[1].index.values,line,p0=[1,1e-2,30]) #Fit sigmoidal curve to [SM]

- [P] curve

toffsets[j] = popt[2]

j+=1

40

j = 0

for data in pdarylation:

scalefactor =

((data[1].iloc[:,peaks[2]]/multiplicities[2]).mean(axis=1).mean(axis=0))+(data[1].iloc[:,peaks[1]]/m

ultiplicities[1]).mean(axis=1).mean(axis=0)

line =

((data[1].iloc[:,peaks[1]]/multiplicities[1]).mean(axis=1)-(data[1].iloc[:,peaks[2]]/multiplicities[

2]).mean(axis=1))/scalefactor

tmax = max(toffsets) #Get the maximum offset time. This is added to all offset times such that all

reactions are only plotted for positive times (t > 0)

x1 = data[1].index.values #Uncorrected times

x2 = data[1].index.values-toffsets[j]+tmax #Corrected times

xes = np.arange(0,100)

ax[0].plot(x1,line,label='Dataset {}'.format(j+1)) #Plot uncorrected data

ax[0].plot(xes,sigmoid(xes,popt[0],popt[1],popt[2])) #Plot fitted curves against uncorrected data

ax[1].plot(x2,line,label=j) #Plot corrected data

ax[1].plot(xes,sigmoid(xes,popt[0],popt[1],tmax)) #Plot fitted curves against corrected data

j +=1

ax[0].legend()

for axs in ax.reshape(-1): #Set up axis limits and labels

axs.set_ylim(-1,1)

axs.set_xlim(0,100)

axs.axhline(y=0,color='k')

axs.set_xlabel('Time / min')

axs.set_ylabel('[SM] - [P] / a.u.')

plt.tight_layout()

plt.show()

Figure S30. Time calibration of Grubbs metathesis data. Each experimental

41

Figure S31. All concentration (top) and diffusion (bottom) points measured across all six Pd-catalyzed arylation reactions plotted simultaneously.

Note: the TFA-OH peak is approximate 30 x more concentrated than the starting material and product peaks, and so has been excluded from the

concentration plot.

Additional References S10.

[1] T. Stait-Gardner, P. G. Anil Kumar, W. S. Price, Chem. Phys. Lett. 2008, 462, 331-336. [2] T. S. C. MacDonald, W. S. Price, J. E. Beves, ChemPhysChem 2019, 20, 926-930. [3] K. K. Dey, F. Y. Pong, J. Breffke, R. Pavlick, E. Hatzakis, C. Pacheco, A. Sen, Angew. Chem. Int. Ed. 2016, 55,

1113-1117. [4] T. Vacala, L. P. Bejcek, C. G. Williams, A. C. Williamson, P. A. Vadola, J. Org. Chem. 2017, 82, 2558-2569. [5] O. A. Gansow, A. R. Burke, G. N. L. Mar, J. Chem. Soc., Chem. Commun. 1972, 456-457. [6] A. F. Collings, R. Mills, Trans. Faraday Soc. 1970, 66, 2761-2766; D. R. Falcone, D. C. Douglass, D. W.

McCall, J. Phys. Chem. 1967, 71, 2754-2755. [7] W. S. Price, NMR Studies of Translational Motion Principles and Applications, Cambridge University Press,

Cambridge, 2009; I. Swan, M. Reid, P. Howe, M. Connell, M. Nilsson, M. Moore, G. Morris, J. Magn. Reson. 2015, 252, 120-129.

[8] N. Hedin, T. Y. Yu, I. Furó, Langmuir 2000, 16, 7548-7550. [9] E. S. Benilov, C. P. Cummins, W. T. Lee, Am. J. Phys. 2013, 81, 88-91.

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Enhanced diffusion of molecular catalysts is due to convection Thomas S. C. MacDonald,[a] William S. Price,[b] R. Dean Astumian[c] and Jonathon E. Beves*[a] Abstract: Intriguing reports of enhanced diffusion in enzymes and molecular catalysts have spurred significant interest in experimental and theoretical investigations of this phenomenon, with mechanistic understanding the subject of ongoing and lively debate. Here we use time-resolved diffusion NMR methods to measure the diffusion coefficients of small molecule species involved in chemical reactions with high temporal resolution. We show the enhanced diffusion of small molecules cannot be explained by reaction velocity, and that apparent measurements of enhanced diffusion by small molecules appear to be caused by bulk fluid flow processes such as convection.

Synthetic nanoscopic and molecular scale[1] machines, motors, and devices have undergone significant advances in recent years. Small objects have been designed to undergo powered translational motion in solution,[2] with nano-rods,[3] tubes[4] and Janus particles[5] powered by catalytic decomposition of hydrogen peroxide or ultrasound[6] among the best known examples. Natural enzymes have also been shown to undergo chemotactic[7] or anti-chemotactic[7j] behavior moving across substrate concentration gradients. Despite broad differences between fluid dynamics in macroscopic high Reynolds number regimes and in microscopic low-Reynolds regimes being well understood,[8] the underlying mechanism of this motion remains unclear. The short rotational correlation times of small molecules in solution would appear to rule out ballistic motion, suggesting that active propulsion of small molecules (if possible) would be observed as an increased diffusion coefficient rather than as a linear velocity. This increase in diffusion coefficient is referred to as enhanced diffusion.[7a] There have been multiple reports of enhanced diffusion in active enzymes,[7a-e, 7g, 7h] with measurements generally performed used optical techniques such as fluorescence correlation spectroscopy (FCS).[7d, 9] These results have been subject to recent questions regarding the possible dissociation of enzymes at the low substrate concentrations needed for FCS,[9e] and some experiments using dynamic light scattering[10] (DLS) or diffusion NMR[11] have been unable to replicate the microscopy results. The theoretical framework surrounding the observed enhanced diffusion remains an open question with multiple proposed models[7d, 7h, 12] drawing links between enhanced diffusion and reaction rates, binding-unbinding rates, and reaction thermodynamics, and conclusions ranging from new possibilities in targeted molecular

transport[12d] to skepticism of enhanced diffusion in sub-nanometer objects.[13] While proposed models focus on enhanced diffusion in enzymes, their findings should in principle also be applicable to small molecules. A single example of enhanced diffusion of a small molecular catalyst has been reported, using 2nd generation Grubbs catalyst to drive an intramolecular ring-closing reaction (Scheme 1).[14] Herein we use recently developed time-resolved diffusion NMR techniques[15] to study two mechanistically distinct metal-catalyzed intramolecular ring-closing reactions, beginning with the previously reported example shown in Scheme 1.

O

O O

OO

O O

OGrubbs' 2nd-gen

C6D6, rt, 3 hC2H4

+

1 2

Scheme 1. Ring-closing metathesis (RCM) of diethyl diallyl malonate (DDM, 1) using Grubbs 2nd generation catalyst. The ring closing of 1 is reversible, but the reaction is driven to completion by the loss of ethylene gas.

These techniques allow simultaneous measurement of concentration and diffusion coefficients for all species in solution over time scales of minutes and give access to more finely resolved time-dependent information. Internal sample temperatures were monitored from inside the NMR sample using a methanol capillary, eliminating the possibility of observed changes in diffusion being the result of sample temperature variations. The self-diffusion[16] data obtained (Figure 1) is in reasonable agreement with that previously reported at low time resolution,[17] except now we can reveal data about the early stages of the reaction. The results are not as expected. As shown in Figure 2b, the measured diffusion coefficients for each species are higher in the early stages of the reaction than at the end, consistent with that reported previously.[14b] However, the higher time resolution of our data reveals that the rate of

Figure 1. Time-dependent diffusion measurements of benzene during Grubbs metathesis, measured by us (line and shaded area showing mean and error over eight experiments) and as previously reported[14b] (black diamonds). Enhanced diffusion has been presented as following reaction kinetics, described by an exponential function (solid red line). We find enhanced diffusion to follow more complex profile of rising and falling that cannot be adequately explained by single-order exponential kinetics (red dashed line). See SI-3 to SI-5 for details of NMR experiments.

[a] Mr T. S. C. MacDonald, Dr Jonathon E. Beves School of Chemistry UNSW Sydney Sydney, NSW 2052 (Australia) E-mail: [email protected]

[b] Prof. W. S. Price Nanoscale Group School of Science and Health Western Sydney University Penrith, NSW 2751 (Australia)

[c] Prof. R. D. Astumian Department of Physics University of Maine Orono, Maine 04469-5709 (USA)

Supporting information for this article is given via a link at the end of the document.

Figure 2. Measured concentrations (a) and diffusion coefficients (b) of species present in the reaction shown in Scheme 1 over time (SI-6). By plotting relative increases in measured diffusion coefficients (c) Grubbs’ catalyst appear to show greater enhancement than the other molecular species, but we believe this to be coincidental as absolute changes in measured diffusion coefficients (d) are uniform for all chemical species. Each line and associated uncertainties (shaded areas) are from the combined results of eight separate experiments; see SI-3 to SI-5 for data, SI-6 for processing. Horizontal lines indicate the measured final diffusion coefficients of each species on reaction completion. All data presented in this study use 200 mM DDM in benzene-d6 and 3 mM Grubbs 2nd generation catalyst in the presence of 1 mM Cr(acac)3 as a paramagnetic relaxation agent[18] (see SI-4) to allow quantitative kinetics.

diffusion for all species does not reach a maximum until approximately 25 min into the reaction. This delayed increase in measured diffusion indicates that, in contrast to theoretical explanations,[19] the degree of diffusion enhancement is not directly proportional to the strictly decreasing reaction velocity or to the rate of catalyst binding/unbinding events. Figure 2c shows the enhanced diffusion for all chemical species present relative to their final diffusion coefficients, D0. The maximum relative enhanced diffusion of each species is in agreement with that reported under the same conditions.[14b][20] The large relative increase in D seen for the active catalyst compared to the low relative increase observed for the unreactive benzene solvent has been viewed as supportive of enhanced diffusion being driven by the active catalyst, but we believe that this ordering is coincidental. By comparing the absolute increase in diffusion of each species (Figure 2d; SI-6.1) it is clear each species has an identical profile over the reaction. For example, at the point of maximum measured diffusion (25 min) each species has a diffusion coefficient approximately 0.7 × 10-9 m2s-1 greater than that at the end of the reaction.[21] This additive increase to measured diffusion is suggestive of directional bulk transport such as convection, rather than increased diffusive motion. In the presence of bulk transport, the seemingly high relative diffusion enhancement of the Grubbs catalyst relative to other species present is a consequence of its low thermodynamic diffusion coefficient (i.e. its large size).

To investigate a possible link between enhanced diffusion and gas generation and whether enhanced diffusion could be similarly observed for other catalyzed reactions, we selected a known[22] palladium-catalyzed intramolecular cyclisation reaction that does not generate any form of by-product (Scheme 2). This reaction has favorable kinetics for NMR monitoring over a few hours and the mechanism of palladium-mediated C-C bond formations are well known.[23]

O

OHN O

O

OHN O

Pd(OAc)2

TFA/CH2Cl2

rt, 1.5 h

3 4

Scheme 2. Model synthesis of a quinolinone 4 via room-temperature palladium-catalyzed intramolecular ring closure of alkyne 3. Unlike the Grubbs metathesis, this ring closure generates no chemical by-product. All data presented here involved the reaction of 4 (200 mM) and Pd(OAc)2 (3 mM) in 1:3 TFA:CD2Cl2.

The data obtained for the diffusion of the starting material, the product, and trifluoroacetic acid (TFA)[24] are shown in Figure 3. Similar to the ring-closing metathesis reaction, an initial increase in measured diffusion reaching a maximum at 30-40 min is followed by a gradual decrease to a stable value matching that of the isolated species in solution (SI-7). Again, the absolute increase in diffusion coefficients (Figure 3b, SI-7.1) are in good agreement for all species, suggesting the measured increases in diffusion coefficients are caused by bulk transport.

Figure 3. Diffusion enhancement of palladium-catalyzed intramolecular arylation shown in Scheme 2. Data are averaged from six independent experiments, with standard errors shown as shaded areas. a) Relative changes in diffusion of TFA protons and reaction product 4; b) Absolute changes in diffusion of the same species. Note: diffusion-time curves for 3 have been truncated at t = 75 min due to low concentration making diffusion measurements difficult beyond this point. See SI-7 for details.

Convection can be dramatically reduced by using narrow NMR tubes.[25] Figure 4 shows data for the same Pd-catalyzed cyclization reaction where the standard 5 mm NMR tube has been replaced with a narrower 3 mm NMR tube (SI-8.2; see SI-8.1 for additional data using a Shigemi restricted-volume NMR tube). No increase in diffusion was observed over the reaction. The measured increase in D for experiments in standard tubes was also found to vary systematically with the diffusion measurement timescale (Δ) (see SI-6.3; SI-7.2), inconsistent with enhanced diffusion, but as expected for convection.[25]

Figure 4. No increase in measured D is observed when the Pd-catalysed cyclization reaction shown in Scheme 2 is conducted in a narrow 3 mm NMR tube. Lines show measured diffusion coefficients for starting material and reaction products averaged over three experiments, Δ = 100 ms, see SI-8.2 for details.

From several key observations we have shown that the only reported example of enhanced diffusion driven by a small molecule catalyst is likely caused by convection. Measured diffusion coefficients are seen to increase early in reactions in contrast to the strictly decreasing reaction velocity, inconsistent with rapidly established microscopic interactions but consistent with slower convection currents. Measured diffusion coefficients were found to increase by the same absolute value for all species in the reaction mixture and vary linearly with Δ. Finally, no increase in diffusion was observed for reactions conducted in a narrow NMR tube. Although no detectable temperature change were found for the Grubbs reaction (ΔT < 0.1 K, see SI-6.3.5), the formation of a gaseous product may be a contributing factor. For the second cyclisation reaction a small 0.15 K temperature change does correlate with changes in measured diffusion (see SI-7.2.4) and may offer a possible origin for convection. These findings provide experimental evidence that challenge the concept of enhanced diffusion in molecular systems and may also have implications for enzymatic systems.

Keywords: diffusion • molecular motors • non-equilibrium • diffusion NMR • chemotaxis

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[16] Self-diffusion and mutual diffusion are not strictly identical except at infinite dilution. For a detailed explanation, see S. A. Willis, T. Stait-Gardner, A. S. Virk, R. Masuda, M. Zubkov, G. Zheng, W. S. Price, in Modern NMR Techniques for Synthetic Chemistry, 1st ed. (Ed.: J. Fisher), CRC Press, Boca Raton, 2014, pp. 125-175.

[17] The previous report of diffusion enhancement during this reaction by Dey et al appears to have used non-calibrated gradients during the NMR experiment leading to incorrect measured absolute diffusion coefficients. For example, the quoted diffusion coefficient for benzene of 2.68 x 10-10 m2 s-1 is not in agreement with accepted literature values of 2.21 x 10-10 m2 s-1 (Trans. Faraday Soc., 1970, 66, 2761-2766). As miscalibrated gradient pulses distort measured diffusion coefficients by a constant scaling factor, it is still possible to compare relative D/D0 values as shown here.

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[20] Values for ethylene were not previously reported. [21] The diffusion coefficients of each of species were also measured in the

absence of the catalyst, or in the case of the Grubbs catalyst in the absence of the substrate for comparison. Values are in agreement with those found at the end of the reaction, see SI-6.1.1 for details.

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[24] Values for TFA are for the broad exchangable proton signal, and will include a significant contribution from water.

[25] a) N. Hedin, T. Y. Yu, I. Furó, Langmuir 2000, 16, 7548-7550; b) T. M. Barbosa, R. Rittner, C. F. Tormena, G. A. Morris, M. Nilsson, RSC Adv. 2016, 6, 95173-95176.

Entry for the Table of Contents COMMUNICATION

Active catalysts go with the flow: the potential of active enzymes or catalysts acting as propulsive nano-motors to drive enhanced diffusion has drawn great interest. A detailed NMR study of two metal catalysts found this behavior to actually be bulk convective flow, raising questions of the generality of this phenomenon.

Thomas S. C. MacDonald, William S. Price, R. Dean Astumian and Jonathon E. Beves*

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Enhanced diffusion of molecular catalysts is due to bulk convection

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