Understanding dynamic voltammetry in a dissolving microdroplet

Droplet evaporation and dissolution phenomena are pervasive in both natural and artificial systems, playing crucial roles in various applications. Understanding the intricate processes involved in the evaporation and dissolution of sessile droplets is of paramount importance for applications such as inkjet printing, surface coating, and nanoparticle deposition, etc. In this study, we present a demonstration of electrochemical investigation of the dissolution behaviour in sub-nL droplets down to sub-pL volume. Droplets on an electrode have been studied for decades in the field of electrochemistry to understand the phase transfer of ions at the oil–water interface, accelerated reaction rates in microdroplets, etc. However, the impact of microdroplet dissolution on the redox activity of confined molecules within the droplet has not been explored previously. As a proof-of-principle, we examine the dissolution kinetics of 1,2-dichloroethane droplets (DCE) spiked with 155 μM decamethylferrocene within an aqueous phase on an ultramicroelectrode (r = 6.3 μm). The aqueous phase serves as an infinite sink, enabling the dissolution of DCE droplets while also facilitating convenient electrical contact with the reference/counter electrode (Ag/AgCl 1 M KCl). Through comprehensive voltammetric analysis, we unravel the impact of droplet dissolution on electrochemical response as the droplet reaches minuscule volumes. We validate our experimental findings by finite element modelling, which shows deviations from the experimental results as the droplet accesses negligible volumes, suggesting the presence of complex dissolution modes.


Sl. no
and (Cp*) 2 Fe (III) as a function of time during the entire simulation.

S23
Electronic Supplementary Material (ESI) for Analyst.This journal is © The Royal Society of Chemistry 2024

Experimental Section
All aqueous solutions were prepared in ultra-pure water (18.20 MΩ.cm) from a GenPure water purification system (Millipore).1,2-dichloroethane (DCE) was obtained from Sigma Aldrich (Ward-Hill, MA).Decamethyl Ferrocene (Cp*) 2 Fe (II) ) was obtained from Aldrich (St. Louis, MO).To prepare the aqueous continuous phase, we used 10 mM of sodium perchlorate (Sigma Aldrich) in ultra-pure water, and the droplet contained varying concentrations of (Cp*) 2 Fe (II) in DCE.All reagents were of analytical grade and were used without purification.Glassware was thoroughly cleaned before experimentation with mQ water, acetone (99.9%,Sigma-Aldrich, Ward-Hill, MA), and finally with the respective solvent of interest for that solution.Gold (12.5 µm diameter) working electrodes were obtained from CH Instruments (Austin, TX).The Ag/AgCl, 1 M KCl aqueous reference electrode was purchased from CH Instruments (Austin, TX) and was used as the counter/reference electrode.The working electrodes were polished before use with 0.3 μm alumina powder suspension (Electron Microscopy Sciences, Hatfield, PA) on micro-cloth polishing pads (Buehler, Lake Bluff, IL) in water, followed by dipping them in piranha solution (a mixture of concentrated sulfuric acid with hydrogen peroxide in a ratio of 3:1).The lab-made electrochemical cell was built out of Teflon and cleaned in Piranha solution to remove any trace impurities.The microinjection experiments were performed using a micro-injector (FemtoJet 4i Eppendorf) and microinjection capillart tips of an orifice diameter of 10 um (Eppendorf Femtotips).The position of the microinjector was controlled using an XYZ micropositioning system (InjectMan 4) and monitored using an optical microscope (mini-2.5X\500 FL-Optem Fusion lens system).The optical microscope was equipped with a high-resolution sCMOS camera (C15440 Orca Fusion BT, from Hamamatsu, Japan).All electrochemical experiments were performed using on a CHI 6284E potentiostat (CH Instruments, Austin, TX).The reference electrode was placed in a compartment containing 1 M KCl (Fisher Bioreagents, Fair Lawn, NJ) and connected to the cell containing the continuous phase by a salt bridge.The salt bridge was made by filling a glass tube with 3% agarose (99.9%,Sigma-Aldrich, Ward-Hill, MA) containing 1 M potassium chloride (Fischer Bioreagents, Fair Lawn, NJ).The reference electrode served as both the reference and counter electrode.

 Bond Number Calculation (B o )
In fluid mechanics, B o is a dimensionless number measuring the importance of gravitational forces compared to the surface tension: 1 Where, is the difference in the density of the two phases (kg/m 3 ), is the gravitational the affect to gravitational force is negligible in our system.

Figure. S4
Experimental data (red) and noise filtered data (purple) using Savitzky-Golay filter for the purple voltammogram shown in Fig. 3 (h).The experiments were conducted without the presence of a Faraday cage, which likely contributed to the observed noise in the system.

 Measurement of Contact Angle
An emulsion comprising 1,2 dichloroethane droplets dispersed within a continuous water phase was prepared using a horn sonicator and subsequently transferred into a glass cuvette.The emulsion was allowed to settle, enabling the oil droplets to descend freely onto the underlying glass substrate.Subsequently, side-view optical micrographs at the bottom of the cuvette were captured, as shown in Fig. S5.
 Geometrical description of a droplet on a substrate.
A droplet sitting on top of a flat substrate is depicted in Fig. S6.Under our experimental conditions gravity is much weaker than surface tension and thus the droplet adopts a spherical curvature.In 2-D the surface of the droplet can be described by the equation of a circle (considering y-axis as the rotational axis of symmetry), which in reality is a sphere in 3-D.

° (𝑥 -𝑥
where, R, and are the radius of the sphere and the coordinates of the center of the sphere,  0  0 respectively.Since the droplet does not translate along the x axis, a value of is used at all time.
0 = 0 The intersection between the sphere and the plane is a disk having a radius .This quantity will be   referred as the contact radius of the droplet.Therefore, in 3-D the sessile droplet resembles a spherical cap.
The angle corresponds to the angle between the tangent of the sphere at y = 0 and the substrate.This  angle is referred as the contact angle between the droplet and the substrate.These two quantities can be used to derive all the other geometric parameters of this system.We provide below relations between these two quantities and other parameters used in the simulation.
Volume of the droplet (V): Height of the droplet (h): Position of the center of the circle (x 0 , y 0 ) Radius of the circle (R):  Rate of dissolution of a sessile droplet under diffusion limited condition The rate-limiting process varies depending on the specific conditions, encompassing factors such as vapor transport, phase transition at the droplet's free surface, heat transfer within the droplet, heat conduction through the substrate, or their combination.Among these scenarios, the diffusion-limited model is extensively studied for situations where the diffusive transport of vapor from the droplet into the atmosphere governs the evaporation process. 35][6] Evaporation of a droplet occurs due to a negative concentration gradient of its constituents, which diffuses from the droplet interface towards the surrounding medium.Initially, Epstein and Plesset described this for free spherical air bubble in water. 7This solution was adapted for sessile droplets, considering the modified geometry and boundary conditions, particularly the absence of flux through the substrate, giving the solution for evaporation of sessile droplets.In 2005, Popov et al. extended this formulation to evaporating sessile droplets in air.The rate of volume change for such droplets is given by: 8 is the diffusion coefficient of the molecules constituting the droplet phase (DCE in our case) in the  bulk phase (water in our case).is the density of the dissolving phase (the DCE droplet) defined here  in units of volume per unit of mass.M is the molecular weight of the molecules constituting the droplet phase.
is the concentration at the interface between the droplet and the bulk phase.It is taken as the maximum concentration of DCE that can be dissolved in water (i.e., the concentration at saturation). is the concentration far from the interface.Since the cell is opened and DCE in water can evaporate this value is kept at zero at all time.Finally, the function in Eq. 7 is given by This function accounts for the substrate hindering the diffusion of DCE into water.When a spherical droplet is considered (i.e., in absence of a substrate) the term in Eq. [7] is equal to 1.

 Calculating diffusion coefficient of DCE in water for CCA and CCR modes Part A: CCA Mode of Dissolution
As discussed previously, the contact angle ( ) remains constant during CCA mode.Differentiating Eq.

𝜃 𝑐
S3 with the constraint of a constant , and plugging in the value of , into Eq.S7 yields: .() } . 1 Therefore, a plot of vs. has a constant slope: Using the value of from the fit, the value of for DCE in water can be calculated.From the fit shown in Fig. 3 (e) in the main text, the value of was found to be -2.4 cm 2 /s, which gives a value of for DCE in water as 4.5 x 10 -6 cm 2 /s.

Part A: CCR Mode of Dissolution
For the CCR mode of dissolution, remains constant and decreases.Similar to the last case, differentiating Eq.S3 with the constraint of a constant , and plugging in the value of , into Eq.S7 yields: We define as to obtain the more compact formula: A plot of vs. is has a constant slope: Using the value of from the fit, the value of for DCE in water can be calculated.From the fit shown below, Fig. S7, the value of was found to be -3.8 cm 2 /s, which gives a value of for DCE    in water as 3 x 10 -6 cm 2 /s.

 Derivation of the Mesh Velocity Part A: CCR Mode of Dissolution
The circle defining the boundary between the droplet and the bulk phase can be expressed as a function of the contact angle and the contact radius by combining Eqs.S4 and S5 to obtain: The derivative of the Eq.S11 with respect to time is Note that there are no time derivatives for as it is a constant during CCR mode of dissolution.For the point , Eq. S12 can be written as: The problem of deriving the rest of points is the parameterizations of the circumference of the circle. 9e can define a scaling variable such that it goes from 0 to 1 and is independent of The expression y , .
for is given as: Using Eq.S13 and S14, we can write an expression for for all other points on the circumference of the circle.Differentiating Eq.S13 and substituting in Eq.S14 we get: Now that we have the expression for all the velocity along the y axis, we can substitute Eq. [15] back into Eq.S12 to calculate the velocity along the x axis, which yields the following: Eq. S15 and S16 describe the x and y components of velocity of the droplet boundary during the CCR mode of dissolution of the droplet.

Part B: CCA Mode of Dissolution
To derive equation for the velocity of the droplet boundary along the x and y axis, a similar approach as part A can be taken.Eq.S11 can be written in terms of the radius of the circle . () This equation of circle described above can be differentiated w.r.t time to give the following expression: Note that is a constant during CCR mode of dissolution.For the point , Eq. S18 can be written as: Defining a scaling variable like the previous case, we can represent the velocity of all of the points y along the y axis as the following: Using Eq.S20 and S21, we can write an expression for for all other on the circumference of (/) the circle.Differentiating Eq.S21 and substituting Eq.S20 we obtain: Now that we have the expression for all the velocity along the y axis (Eq.S22), we can substitute Eq.S22 into Eq.S18 to calculate the velocity along the x axis, which yields the following: To further simplify Eq.S23, we can substitute results from Eq. S17 to derive the following expression: Eq. S21 and S24, can accurately describe the velocity of the droplet boundary during the CCA mode of dissolution of the droplet.

 Calculation of Junction Potential ( w/o ) ∆𝜙
Junction potential at the oil|water interface occurs as a result of the difference of solubility of the ion between the two immiscible liquids.The electrical potential difference across the interface, w/o , is ∆ calculated using: 10 The first term on the right side is the standard potential difference of ion transfer for ClO 4 -from water to DCE.The second term on the right depends on the ratio of ClO 4 -in both phases.This equation assumes that only ClO 4 -will partition between DCE and water (i.e.Na + partitioning is neglected).This is a good approximation considering that < . 11,12Maintaining electro-neutrality inside the DCE droplet imposes that .Since we assumed that ClO 4 -is the only anion that can be present in DCE then, for each being oxidized to there has to be one ClO 4 -entering the droplet and This process is depicted in Fig. S8.
The total potential loss between the working electrode and the reference electrode is the summation of all the potential loss along the electrical path.In addition to the potential loss at the DCE|water interface we should consider potential loss at the salt bridge and the frit of the reference, for example.These last two sources of potential loss are assumed to be constant as the composition of the solution at each of these interfaces is not changing.Hence, the total potential loss becomes: where cste corresponds to constant sources of potential loss (salt bridge and frite of the reference electrode).The value of [ClO 4 -] water is 10 mM and constant with time as the aqueous phase acts as an infinite reservoir of perchlorate ions.[ClO 4 -] DCE is assumed to be equal to [(Cp*) 2 Fe (III) ].The w/o vs. ∆ time curve in the main file was adjusted for a potential of 19 mV, which is attributed to the junction potential loss at the salt bridge-water interface.

 Numerical Simulation
This section describes the overarching design of the simulation and provides explanation about the choice of the boundaries, important parameters to consider and how was tested the simulation.A full COMSOL report is provided in a separate file in SI.
Simulations were performed using a Finite Element Method with a commercial software, COMSOL Multiphysics 6.0.A 2D axial symmetry was used with a time-dependent solver.Simulations were run on a PC equipped with an intel Xeon processor, 64-bit operating system, x64-based processor and 32 GBs of RAM.A typical simulation takes about 45 min which lead to approximately 11 seconds of simulation per second of experiment.A sequence of 44 voltammograms represents 242 s under our experimental conditions.
The goal of the simulations is to predict the electrochemical response of the (Cp*) 2 Fe (III) , /(Cp*) 2 Fe (II) , contained in a droplet during the dissolution of this latter.More precisely, the simulation solves for the diffusion of the redox molecules within the droplet in presence of a UME biased with a ramp of potential.The dissolution of the droplet is accounted in the simulation by deforming the mesh with an Arbitrary Lagrangian-Eulerian (ALE) method.The rate of deformation of the mesh is an adjustable parameter of the simulation.To ease the adjustment of the simulation on the experiment, the simulation was cut into 5 separate time segments (called "Study" in COMSOL) with the "n+1" study starting from the final solution of the "n" study.

Geometry & Mesh Deformation
The meshed geometry used for the simulation is shown in Fig. S9.Only the volume inside the droplet is simulated.The electrode sits at the bottom of the droplet.A small volume surrounding the electrode is finely mesh to capture precisely the gradients of concentration.Meshing is critical to avoid significantly distorted elements.The initial mesh is designed to follow the deformation, like a conformal mapping.An automatic remeshing node was used in the solver to prevent very large distortions.The initial mesh was optimized by manually increasing the number of elements in the mesh.A number of 3,500 elements was chosen.Since gravitational forces are weak in comparison to surface tension the droplet is assumed to adopt a spherical curvature at all time.The simulation reflects this shape by using the equation of circle to draw the initial droplet and subsequently using specific rates equations for the mesh deformation that ensure the conservation of the curvature.Two cases were considered, constant contact angle (CCA) and constant contact radius (CCR).The equations for both cases are given in Table S1.A node "Prescribed Mesh Velocity" in the ALE module was used to apply a deformation on the mesh.The derivation of the rate equations is given on Pg. no S13-14.Table S1.Rate equations for the « r » and « z » velocity components of the mesh at the water|DCE interface.
The dissolution of the droplet can alternate between these two modes in the so-called "stick & slip" mode.The transition between CCA and CCR mode is determined in the simulation by adding a conditional statement in the mesh velocity node.If the contact radius is larger than 1.25 times the radius of the electrode (i.e., 8 µm) then, the dissolution follows a CCA mode.Otherwise, mesh displacement obeys a CCR mode.This reflects our experimental observations.The contact line between the droplet and the glass is pinned when reaching the gold/glass boundary.A value of 1.25 (and not 1) is used to avoid the disappearance of a boundary (the glass sheath) during the simulation.

Physics
The diffusion of the species (Cp*) 2 Fe (III) and (Cp*) 2 Fe (II) inside the droplet during the course of the voltammetric experiment is simulated by solving the second Fick's law: Eq. S27 Eq.S19 V z Eq.S25 Eq.S18 where D i , and C i are the diffusion coefficients and concentrations of the species "i", respectively.Briefly, a flux boundary is used at the surface of the electrode to reflect the consumption/production of the species upon exchange of an electron.The Butler-Volmer law for current-potential is used to set the flux.The flux is controlled by the difference of potential between a reference (taken here as the potential of the solution far away from the electrode) and the surface of the electrode.This potential difference is expressed as the sum of three terms: Where, the potential ramp applied at the electrode, , the potential loss in solution, , and the    junction potential at the oil/water interface.The first term is the applied potential ramp shown in Fig. 3 (f) in the main text.The potential loss in solution (aka ohmic drop) is defined as the product of the current passing through the electrode, i, and the resistance, R, of the solution: Where, R 0 , C ox,ini and C ox are the initial resistance of the solution, the initial concentration of (Cp*) 2 Fe (III) and the concentration of (Cp*) 2 Fe (III) , respectively.Since water contains 10 mM of supporting electrolyte but the DCE droplet does not have any added salt we assume that most of the resistance originates from the droplet.The resistance is proportional (in first approximation) to the concentration of ions and thus the resistance of the droplet will vary as a function of concentration of (Cp*) 2 Fe (III) .The initial resistance was found by adjusting the first CVs in Fig. 3

(g).
A value of 100 MΩ was determined.The value of is set as 20% ,  of the initial concentration of ferrocenyl species.irst, we simulated cyclic voltammograms in two limiting cases, "bulk-like" condition and "thin layerlike" condition.These two simulations are given in Fig. S10 (a In Fig. S9 (b), the current on the y axis was normalized with respect to the value of the peak current for thin-layer voltammetry given by the following equation: 10

Validation of the model
In Eqs.S31 and S32, denoted the no of electrons, is the Faraday's constant, C is the concentration of the redox species (155 uM Cred), is the scan rate, is the diffusion coefficient, is the universal gas    constant, is the radius of the electrode (6.3 um), is the temperature (298 K) and is the volume of    the solution.For, Fig. S10 (b), the droplet volume was calculated using Eq.S3 with and droplet radius of .The product of in Eq. 32 was found to be x moles.The FWHM thin-layer electrochemistry.A good agreement is observed.It was observed that in the absence of any ion-transfer across the oil-water interface, the simulation struggled to conserve the mass of ferrocenyl molecules.We attribute this to systematic errors made by the simulation during the droplet dissolution process.To address this, a compensation for mass loss function was introduced in the form of an interpolation function, with values manually determined to ensure the conservation of overall mass within the droplet.This was implemented before introducing any partitioning kinetics across the oilwater interface.Further details on the mass loss function can be found in the COMSOL report.Then, we ensured that mass is being conserved (in absence of our first order kinetic of ion transfer).Fig. S11 shows the number of moles of species (normalized with respect to the initial amount) during the entire simulation.In order to enforce mass conservation, we used a manually parametrized function that accounts for systematic errors made while adjusting the movement of the water|DCE boundary and the flux of species at that same boundary.These errors are kept below at all times.A Lagrange ± 2 % multiplier approach was also tested to maintain mass conservation.However, due to the prohibitive increase of simulation time (about 10X) we favored manual parametrization that would take about one day to perform and then could be used for all the simulations.

3 Figure S2 :S4 4 Figure S3 : 6 Figure S4 :9
Optical micrograph showing the size of the Au disk UME S3 Experimental and simulated voltammogram of 155 M (Cp*) 2 Fe (II/III) in  DCE.Cyclic voltammetry of 1 mM (Cp*) 2 Fe (II/III) in bulk DCE phase with 10 mM tertbutyl ammonium perchlorate.Experimental data and noise filtered data using Savitzky-Golay filter for the purple voltammogram shown in Fig. 3 (h) Geometrical Description of Droplet (Figure S6) S9 Rate of dissolution of a sessile droplet under diffusion limited condition S10 10 Calculating diffusion coefficient of DCE in water for CCA and CCR modes, rate of decrease of contact angle vs. K ( ) (red points) (Figure S7)  Potential (∆ϕ w/o ), Partitioning of perchlorate ions across the oil-water interface during the oxidation and the reduction (Figure S8) Lifetime of Droplet, Figure S9: Meshed geometry for the simulation, Figure S10: Simulated voltammograms for "bulk-like" condition and thinlayer-like" condition, Figure S11: Total number of moles of (Cp*) 2 Fe

Figure S1 . 3 Figure S2 .
Figure S1.Optical micrograph showing the size of the Au disk UME used.The diameter of the exposed disc was found to be 12.6 µm which corresponds to a radius of µm.6.3

Figure S3 :
Figure S3: Cyclic voltammetry of 1 mM (Cp*) 2 Fe (II/III) in bulk DCE phase with 10 mM tertbutyl ammonium perchlorate.The cyclic voltammograms were obtained at 0.2 V/s with a 12.3 diameter Au disk UME as the working electrode, and  a Ag/AgCl (1 M KCl) reference served as the reference as well as the counter.The Ag/AgCl 1 M aqueous reference electrode used in the experiments were separated from the cell by a salt bridge.The E 1/2 value was found to be -0.1 V vs. Ag/AgCl (1 M KCl) reference.

Figure S5 .
Figure S5.(a) Contact angle measurement for 1,2 dichloroethane droplets on a glass substrate surrounded by a bulk water phase.The contact angle was measured to be 149 ± 4 (b)Table of measured contact angles for five different droplets, the standard °deviation

Figure S6 .
Figure S6.Geometry of a droplet on a substrate.The y axis is a rotational axis of symmetry for the droplet.

Figure S8 .
Figure S8.Partitioning of perchlorate ions across the oil-water interface during the oxidation and the reduction of (Cp*) 2 Fe(II)   and (Cp*) 2 Fe(III)  , respectively.For the sake of clarity (Cp*) 2 Fe (III) is denoted as Cp* + and (Cp*) 2 Fe (II) is denoted as Cp*.

Figure S9 .
Figure S9.Meshed geometry for the simulation.The scale bar is 20 m.

Figure S10 .
Figure S10.(a) Simulated voltammograms for "bulk-like" condition using a droplet of radius and a contact angle of 51  (b) Simulated voltammograms for "thin-layer-like" condition using a droplet of radius and a contact angle of 149°8  .60°F ) and (b), respectively.For both, Fig. S9 (a) and (b), a scan rate of a formal potential of -was used.In Fig. S9 (a), the current 20 / 40  on the y axis was normalized with respect to the steady state current given by the following equation: 10   = 4 [31]

Figure S11 .
Figure S11.Total number of moles of (Cp*) 2 Fe(II)  and (Cp*) 2 Fe(III)  normalized with respect to the initial total amount, ~83 fmol as a function of time during the entire simulation.

Figure S12 .
Figure S12.In-situ observation of droplet size dynamics correlated with cyclic voltammetry measurements over time for 1 mM of (Cp*) 2 Fe (II ) droplets within a bulk aqueous phase devoid of salts.The cyclic voltammetry measurements were continuously performed as the droplets underwent shrinkage.Panel (a) illustrates voltammograms recorded in different colors, denoted as 1 to 4, corresponding to distinct droplet sizes.Panel (b) showcases color-coded optical micrographs captured at points 1 to 4, corresponding to the voltammograms in panel (a).Panel (c) provides a schematic depiction of the ion partitioning mechanism across the oil-water boundary.The voltammograms presented above were processed using an adjacent weighted averaging technique, employing a window size of 19 points and applying a periodic boundary condition.