Electric Field‐Controlled Synthesis and Characterisation of Single Metal–Organic‐Framework (MOF) Nanoparticles

Abstract Achieving control over the size distribution of metal–organic‐framework (MOF) nanoparticles is key to biomedical applications and seeding techniques. Electrochemical control over the nanoparticle synthesis of the MOF, HKUST‐1, is achieved using a nanopipette injection method to locally mix Cu2+ salt precursor and benzene‐1,3,5‐tricarboxylate (BTC3−) ligand reagents, to form MOF nanocrystals, and collect and characterise them on a TEM grid. In situ analysis of the size and translocation frequency of HKUST‐1 nanoparticles is demonstrated, using the nanopipette to detect resistive pulses as nanoparticles form. Complementary modelling of mass transport in the electric field, enables particle size to be estimated and explains the feasibility of particular reaction conditions, including inhibitory effects of excess BTC3−. These new methods should be applicable to a variety of MOFs, and scaling up synthesis possible via arrays of nanoscale reaction centres, for example using nanopore membranes.


S1. Experimental Methods
Single-barrelled quartz nanopipettes were used as reaction centres for the precipitation of HKUST-1 and as a Coulter counter for particle analysis. A two-electrode system was employed with an Ag/AgCl wire quasi-reference counter electrode (QRCE) placed into both the nanopipette and the bath, and with the end of the nanopipette being positioned over a TEM grid (Carbon film on Gold 300 mesh, EM Resolutions) in some experiments (see main text). Aqueous solutions were made up using 18.2 MΩ cm water (Purite Select), and all other solvents and chemicals used were purchased from Sigma Aldrich. The nanopipettes were filled with solutions as described in the main text. For all injection and resistive pulse experiments, a bias of -1V was applied to the QRCE in the nanopipette relative to the bath, and the nanopipette was lowered into the droplet and left for a period of ~ 10 minutes. This potential was selected following CV measurements, where the potential was scanned in a cyclic waveform and the current measured, as described in the main text. Raman spectroscopy was conducted using a Raman microscope (Horiba LabRam HR Evolution) fitted with a charged couple device (CCD) detector and a 488 nm OPSS laser. A 50× objective was employed for all measurements. Pulled nanopipettes were characterized to determine the inner radius and overall probe geometry by scanning transmission electron microscopy (STEM) using a Zeiss Gemini 500 SEM. TEM analysis was carried out on a doubly corrected ARM200F microscope operating at 200 kV. Annular dark-field STEM (ADF-STEM) images were obtained using a JEOL annular field detector at a probe current of ~23 pA with a convergence semi-angle of ∼25 mrad.
When employed as the bath, methanol solutions of H3BTC were found to be sufficiently conductive even in the absence of supporting electrolyte (as based on the observation that currents, typical of nanopipette experiments, could be measured). Ionisation data for weak acids in non-aqueous solvents are rare, with no data found for H3BTC dissociation in MeOH. However , it is often found that the shift of the pKa from the non-aqueous to the aqueous value (the medium effect) is approximately constant for groups of closely related acids, with aromatic acids having a medium effect of around 5 in MeOH. [1] Extrapolating to H3BTC (pKa1,2,3 = 3.12, 3.89, 4.70) [2] predicts a pKa1 in MeOH of 8. A 40 mM solution would therefore be expected to contain 0.6 μM H2BTCand the same amount of cationic species (considering only pKa1 as an approximation, for simplicity). A coarse simulation of the current, based on the model in section 5 but considering only the ion fluxes and electric field, in a system of pure MeOH with 100 mM Cu(NO3)2 at the nanopipette boundary and 0.6 μM H + and H2BTCat the bath boundary, predicted 0.1 nA at -1 V (see Figure S14, section S7). This is lower than observed experimentally, but of the correct order given the rough nature of the calculation.

S2. STEM Analysis of Nanopipettes
Pipettes used in this study were characterised using STEM, which has been shown to allow accurate determination of their inner and outer diameters. [3] The inner diameter was typically ~30 nm ( Figure S1A).
When 30 nm diameter nanopipettes, filled with 100 mM aqueous Cu(AcO)2, were immersed in methanol solutions of H3BTC, no current was observed throughout voltage sweeps between -1 and +1 V. Absence of current persisted when 200 nm diameter nanopipettes were used in 50 mM H3BTC in methanol. STEM characterisation of these pipettes shows the formation of globular regions inside the tip consistent with solid precipitate (Figure S1 B,C). Further chemical analysis of this small region inside the nanopipette was not possible.

S3. TEM Images Following Local Injection Setup
The TEM images below (and in Figure 1B of the main text) were taken following the deposition of HKUST-1 crystals onto the surface of a TEM grid. The end of the nanopipette was ~1 cm above the TEM grid, and the MeOH solvent was left to evaporate, ensuring even coverage of HKUST-1 crystals across the entire grid. Images from various locations on the TEM grid can be seen below, as well as higher resolution images of individual truncated octahedral crystals, showing that even the smallest crystals have a well-defined truncated octahedral shape. Figure S2: TEM images of various crystals after local injection. Carboxylic acid groups References [4][5][6][7] Figure S3: Raman spectra of a different region of the TEM grid to that shown in the main text, showing characteristic peaks of both HKUST-1 and H3BTC residue.

S5. Data Analysis
Some variations in baseline current and resistive impulse shape during current-time runs were accounted for by automatically separating the data into regions of similar baseline (as determined from the modal current value). The separation algorithm compared a region of data in a given window, splitting the windowed data into two halves and comparing the difference in the modal value and standard deviation, and then splitting the data into four quarters and comparing the difference in modal values between quarters 1 and 2, and 3 and 4. If the differences were less than 5 pA, 20%, and 2 pA, respectively, the region was extracted. If the conditions were not met, the window was shrunk by 25% and the test repeated. If the window was shrunk to a minimum value (0.5 s) without satisfying the conditions, that region was skipped, and the process restarted 0.5 s further along the data. The window was initially set to the entire data set. This enabled a constant local baseline to be determined and subsequent automated analysis of impulses based on a local absolute 'on' threshold (15 pA decrease in current magnitude from the modal value of the section) and 'off' threshold (a subsequent increase in current to 7.5 pA below the modal value of section). The use of absolute (rather than percentage) changes simplified the analysis program and was justified based on the corresponding small percentage change, making it relatively insensitive to changes in the baseline current (for example, a 15 pA threshold for a 1500 pA baseline corresponds to a 1% threshold, while for a 1300 pA baseline it is similar at 1.15%; and these example baseline changes are extreme compared to those in the experiments analysed). Occasionally, the baseline current was far below the value expected, based on simulations of the ion flow, suggesting blockage of the nanopipette. Such data were excluded from the analysis (see examples below). A minimum region size of 0.5 s was used and sections of data failing to meet the criteria were excluded from the analysis (indicated by the absence of an indicated baseline in Figures S2, S3, S5 and S7).      As in Figure S4, the lower current magnitude observed in the experiment compared to the value observed in other transients and the simulated current suggests a blockage has occurred in the nanopipette, precluding further resistive impulse analysis on the extracted regions.

S12
The distribution of data in a typical region with impulses shows some deviation from a symmetric Normal distribution. This effect can be visualised by mirroring data from the right hand side of the histogram maximum, and shows that the number of data points below the 15 pA threshold exceeds that expected solely from normally distributed baseline noise. The exclusion of these data will lead to an overestimate of the mean impulse current and thus an overestimate of the mean particle size. Figure S10: Visualisation of systematic error introduced by the 15 pA threshold. Histogram (black) shows all data points in this region and deviates from the symmetric distribution generated by mirroring data to the right of the histogram maximum (red). The population a currents greater than the threshold (blue vertical line) but above the mirrored data are likely to be impulses which are excluded from the analysis.

S6. Description of Finite-Element Simulations
To understand the relationship between the magnitude of the resistive pulse and the nanoparticle size and to evaluate the plausibility that formed nanoparticles would exit the nanopipette, we performed numerical modelling. The finite-element model developed described the mixing of the solvents, the electric fields, the fluid flows, and the transport of the solutes due to diffusion, electromigration and electro-osmosis. The conditions of the model were taken from the experiments which they described, with the geometry of the pipette taken from STEM images.
The coupled equations describing mass transport, flow and electric field were solved for a steady state using the axisymmetric geometry shown in Figure S11, in which the axis of the pipette is the axis of symmetry. Also shown in the figure are the boundary conditions for the equations and the mesh used.
Below we describe the details of the numerical modelling, which is based on the single solvent model of White and Bund. [8] We start describing the general model, before detailing the modifications used to understand the current response and the likelihood particle ejection form the pipette. In all cases, the model was solved using the commercial finite element package COMSOL Multiphysics v5.5.
Figure S11: Geometry and boundary conditions used for FEM simulations. Detail of the tip region is shown below. ρq is (surface/space) charge density, n the wall normal vector, F the volume force responsible for electro-osmosis and E the electric field. The dashed red line indicates the symmetry axis.

Modelling Transport, Flow, and Electric Fields
Solvent mixing was calculated using the 'Transport of Concentrated Species' module. The mole-fraction dependent density and diffusion coefficients were taken from experimental values, which were interpolated to give a continuous function. [9][10][11][12][13][14] Fick's first law of binary diffusion was assumed for the solvent mixing where the mass flux of solvent i relative to the mass averaged velocity, ji, is given by equation S1, with ρ the mixture density, Di the diffusion coefficient of i, ωi the mass fraction of i, Mn the mean molar mass of the mixture (calculated by S2, where Mi is the molar mass of solvent i) and jc,I the mixture diffusion correction factor (to maintain the net diffusive mass flux at zero, calculated by equation S3 where xk is the mole fraction of component k). [15] Mass conservation is provided by equation S4, where u is the solution velocity.
The flux of the solute species i = Cu 2+ , NO3and BTC, ji, were calculated from the Nernst-Planck equation (eq. S5) utilising the 'Transport of Diluted Species' module.
The charge on the solute is given by zi, ci is the local concentration, and F, R and T the Faraday constant, molar gas constant, and temperature (298 K), respectively. V is the electric potential and u the solvent velocity. Diffusion coefficients were varied based on the local solvent ratio ( Figure S16). These were interpolated from reported experimental conductivities of MeOH/DMSO mixtures, except for H3BTC, which was estimated based on the Wilke-Chang correlation, using local values for the mean molar mass, density and viscosity at temperature T. [9][10][11][12][13][14] The electric potential was calculated by solving Poisson's equation (eq. S6) using the 'Electrostatics' module. It contained the space charge associated with local imbalance of Cu 2+ and NO3and used local values for permittivity, ϵ, based on the local solvent ratio and interpolated literature values, [9][10][11][12][13][14] where ε0 is the permittivity of free space.
Given the Reynolds number (Re ~ 10 -5 << 1) we used creeping flow (S7) to simulate electroosmotic flow based on the volume force arising from the space charge.
In this equation, p is the pressure and μ is the dynamic viscosity.

Evaluating the Resistive Pulse Response
The effect on the current of a nanoparticle moving through the nanopipette was simulated by introducing a spherical void into the nanopipette tip ( Figure S12). For simplicity, we assumed the particle had no surface charge. Simulations were carried out for a range of void diameters. The current was determined by the integration of the ionic fluxes passing through the top boundary of the pipette.
The current of an open pipette was used to calculate the percentage blockage from the presence of a particle. A calibration plot of normalised current as a function of particle diameter is presented in Figure 4 (inset) in main text. Note, while the axisymmetric simulation restricts us the simulating a particle coaxial with the pipette, simulations of resistive pulses in uniform media have shown that the current varies by only ~15% as the lateral position of the particle is varied. [16] This introduces only relatively minor uncertainties in calculating the nanoparticle diameter.

Evaluating the Likelihood of Particle Escape
To assess the plausibility that a nucleated nanoparticle would exit the nanopipette, we solved the Fokker-Planck equation, which describes the time-varying likelihood (probability density) of finding a particle at a particular position, as a function of time. Such an approach has previously been used to calculate capture efficiencies and distributions of translocation times in nanopore systems. [17,18] We use the flows calculated as described above. The initial condition is that there is 100% likelihood of finding the particle in the small region representing where the nanoparticle forms. This approach is analogous to releasing a cloud of tracer particles of point size, which possess the diffusion characteristics of the particle (calculated from the Stokes-Einstein equation), and watching where they are transported to.
Integrating the flux of the probability distribution function (PDF) over the aperture of the nanopipette calculates the rate with which the particles leave the pipette. When this is integrated over time, it gives the fraction of particles anticipated to be released.
The probability density as a function of time for two release locations is shown in Figure S13.
We can see that initially, the nanoparticle is almost certainly to be found where it is released. However, due to Brownian motion, the region within which one expects to find the particle broadens with increasing time. This distribution skews to the interior of the nanopipette due to the electroosmotic flow. However, the non-zero probability density at the pipette orifice (d = 0 nm) is indicative that a certain fraction of the time a particle formed close to the orifice will escape. Figure S13: Evolution of probability density function (PDF) taken along the axis of the nanopipette. This function describes the likelihood of finding a particle at different positions within the nanopipette as a function of time. PDF evolution shown for particles released at two positions.

S17
The Fokker-Planck approach approximates a particle as a point, which does not influence the solution of equations S1-S7. It is apparent that a particle of similar size to the pipette diameter will influence the flow and the solute and solvent distribution and thus the results of these simulations should be taken as qualitative in nature. These results show that is likely that some finite fraction of particles formed near the orifice escape the pipette, while particles formed further up the pipette are unlikely to exit the aperture. The simulation of a single translocations of finite sized particle of has previously been demonstrated; [16] however, to perform such a simulations on a large enough number of particles to determine statistics is unfeasible.

S7. Results of Finite-Element Simulations
The model developed above was primarily used for the analysis of the concentration profiles and electric field distribution in the DMSO/MeOH system. However, the same geometry was also used to provide a coarse estimation of the current flow and electric field distribution in the H2O/MeOH injection experiments, as described in section S1. A solution with a dielectric constant equivalent to methanol (ε = 33) was assumed. The potential at the nanopipette boundary was set to -1 V, concentrations were fixed at 100 mM of M 2+ , 200 mM Xions and 0 mM H + and 0 mM H2BTC -. The bath potential was set to 0 V and concentrations were fixed at 0 mM of M 2+ , 0 mM Xions and 0.6 μM H + and 0.6 μM H2BTC -. Diffusion coefficients were all equivalent at 10 -5 cm 2 s -1 . Space charge was included but flow was not considered. The results suggest that the potential drop and resulting electric field will exist at the nanopipette/bath boundary and into the bath. This will limit the ingress of deprotonated H2BTCinto the pipette, preventing precipitation inside which would block the nanopipette and prevent further delivery of Cu 2+ into the bath. The relatively weak field inside the pipette will also hold Cu 2+ less strongly inside the nanopipette, contributing to its release into the bath. Conversely, a positive applied potential would pull H2BTCtowards the nanopipette tip, enhancing the likelihood of precipitation inside the nanopipette orifice, blocking the current.  Figure S16 Variation in diffusion coefficients, D, for Cu 2+ and NO3 -, as a function of DMSO mole fraction, χ. Diffusion coefficients are weighted averages based on experimental conductivities reported in the two pure solvents. [12][13][14] Figure S17: Effect of applied nanopipette voltage on the concentrations of Cu 2+ and NO3near the tip end, as measured along the central axis of the nanopipette. The full, accurate nanopipette geometry was used. 2D plots of the Cu 2+ concentration at -1 V, -0.1 V and +0.1 V are shown in the main text ( Figure 3A).

Electroosmotic flow
Electroosmotic flow is generated when an electric field exerts a force on a volume of solution possessing a non-zero net charge. It is described quantitatively by the final term on the right hand side of equation S7. If we consider the application of a -1 V bias, as was used in experiments, the electric field ( Figure S15, solid lines) is directed into the nanopipette and is largest at approximately 100 nm inside the pipette. The net charge is initially positive inside the aperture of the pipette, before becoming negative further inside the pipette, as can be seen in the black curve in Figure S18. These indicate that the electroosmotic volume force is upward nearer to the tip and downward farther inside. The resulting electro-osmotic flow shown in Figure S20 is directed from the bath as into the nanopipette indicating that the upward force is dominant.
Interestingly, the mechanism by which the space charge forms differs from that reported for glass nanopipettes filled with aqueous electrolytes, in which electroosmotic flow is also observed. In this system, a positive space charge in the double-layer balances that of the deprotonated silanol groups, creating an electroosmotic force. In this work we did not include charge on the nanopipette walls in this model ( Figure S11), as surface ionisation behaviour in the solvents used in this work is not well defined. Instead, the charge separation arises from differences in the relative ion transport of the two species (Cu 2+ /NO 3-) in different solvents ( Figure S16) leading to an accumulation/depletion in the region just inside the pipette (Fig S18).
In the present system, the relatively low concentration of species and the limited region of high velocity means that the magnitude of the convective flux is much lower than that due to diffusion or migration, such that the concentration profiles remain similar in the absence of simulated electroosmosis.