Maider Ormaza
email: ormaza@ipcms.unistra.fr

Nicolas Bachellier

Marisa N Faraggi

Benjamin Verlhac

Paula Abufager

Philippe Ohresser

Loïc Joly

Michelangelo Romeo

Fabrice Scheurer

Marie-Laure Bocquet

Nicolás Lorente

Laurent Limot
email: limot@ipcms.unistra.fr

Efficient spin-flip excitation of a nickelocene molecule

Keywords: metallocene, spin-flip, magnetic anisotropy, tip functionalization, inelastic electron tunneling spectroscopy, X-ray magnetic circular dichroism, density functional theory

Recent advances in addressing and controlling the spin states of a surface-supported object -atom or molecule-have further accredited the prospect of quantum computing [START_REF] Gatteschi | Molecular Nanomagnets[END_REF][START_REF] Leuenberger | [END_REF][3] and of an ultimate data-storage capacity. 4 Information encoding requires that the object must possess stable magnetic states, in particular magnetic anisotropy to yield distinct spin-dependent states in the absence of a magnetic field together with long magnetic relaxation times. [5][6][7][8] Scanning probe techniques have shown that inelastic electron tunneling spectroscopy (IETS) within the junction of a scanning tunneling microscope (STM) is a good starting point to study the stability of these spin states. STM-IETS allows for an all-electrical characterization of these states by promoting and detecting spin-flip excitations within the object of interest. [9][10][11][12][13][14] It can also provide an electrical control over these states, 15 simplifying the information readout process. As spin excitations need however to be preserved from scattering events with itinerant electrons, single objects are usually placed on non-metallic surfaces such as thin-insulating layers 7,8,16,17 or superconductors. 18 is preserved in different environments and we explain the remarkably efficient spin-flip mechanism it exhibits. The chemical structure of nickelocene consists in a Ni atom sandwiched between two cyclopentadienyl rings (C 5 H 5 , Cp hereafter), endowing nickelocene with an electronic structure (a 1g ) 2 (e 2g ) 4 (e 1g ) 2 of spin S = 1 in the gas phase (Fig. 1a). 19 We prove that the molecular spin does not change upon adsorption on a metallic surface. In particular, by attaching a nickelocene to the tip apex of a STM, we show that two spin-flip excitations can be sequentially triggered, resulting in a large enhancement of the inelastic signal as illustrated by the IETS acquired above a surface-supported Nc. This unique situation can be achieved due to the chemical stability, the presence of magnetic anisotropy, the full preservation of the Nc spin on the tip apex, or more generally in a metallic environment, and the extremely efficient spin-flip excitation of this molecule.

To benchmark the electronic and magnetic properties of a Nc-terminated tip, we investigated first the nickelocene adsorption on a Cu(100) surface using a metal tip. The ring-shaped pattern visible in Fig. 1b indicates that individual nickelocene molecules bind to the surface through a Cp ring, while the other Cp ring is exposed to vacuum (see Methods for experimental details in the sample preparation). In particular, the Cp ring is centered on a hollow position of Cu(100) most likely adopting the D 5h symmetry (eclipsed configuration). 20 Figure 1c presents the differential conductance (dI/dV ) versus bias (V ) spectrum of an isolated Nc molecule by positioning the tip above the Cp ring, together with its numerical derivative. As shown, the dI/dV is small near zero bias (Fig. 1c) with symmetric steps (5±1) times higher in conductance at an energy of |3.2±0.1| meV (the uncertainty translates the tip-dependency observed). Since the vibrational excitations of nickelocene adsorbed on the surface can be a priori discarded in this energy range, 21 the differential conductance steps reveal the occurrence of spin-flip excitations within the molecule. In view of the spin 1 character predicted upon adsorption on Cu(100), 20 these excitations occur between the ground state (S=1, M =0) and the doubly-degenerated (S=1, M =±1) excited states of the (red circle) off-normal incidence under a 6.5 T field as a function of temperature. The dashed lines correspond to simulations (see supplementary material) for a S = 1 system with a magnetic anisotropy of D = 3.2 meV; the simulations are scaled to the data by a factor 0.8. Note that the magnetic field is parallel to the X-ray beam.

molecule. The threshold energy observed in IETS corresponds then to a direct measurement of the longitudinal magnetic anisotropy energy, D (see Supporting Information).

To further characterize the magnetic origin of the excitation, we performed X-ray magnetic circular dichroism (XMCD) measurements in a magnetic field of 6.5 T on a collection of individual Nc molecules on Cu(100) (see Methods and fig. S1). The top panel of Fig. 2a shows X-ray adsorption spectra (XAS) recorded at the L 2,3 edges of Ni for left and right circularly polarized light. The panel below presents the difference between them, the so-called XMCD spectrum. Having a clear dichroic signal is already an indication of the magnetic character of nickelocene on Cu(100). Figure 2b shows the evolution of the signal maximum at the Ni L 3 edge as a function of the temperature for grazing (red dots, θ = 60 • ) and normal (black dots, θ = 0 • ) incidence of the applied magnetic field. At low temperature, the signal shows a clear angular dependence revealing the existence of an easy magnetization direction, more specifically of an easy plane perpendicular to the molecular axis. For the sake of comparison, we have simulated in Fig. 2b the magnetization of a S = 1 system under an external field of 6.5 T and possessing a magnetic anisotropy of D = 3.2 meV as determined by STM (see details of the simulation in the Supporting Information). Based on the XMCD results, we can assert that D is positive, implying that M = 0 corresponds to the ground state of nickelocene and the M = ±1 to the excited state.

The magnetic properties of isolated nickelocene turn out to be robust against external perturbations, possibly owing this behavior to the cyclic π* orbital of the Cp rings sandwiching the Ni atom. This differentiates Nc from other systems reported so far 4,8,10,22 in which the local environment is a crucial factor determining the magnetic anisotropy and/or the spin. At higher coverages, for example, where Nc molecules self-assemble following a T-shaped geometry (Fig. 3b) typical for metallocenes, 20,23 no difference was observed in the IETS spectra of upstanding molecules within the layer (Fig. 3a). We have checked the impact of the surface symmetry by changing to Cu(111), also resulting in no difference for isolated or self-assembled nickelocene (Fig. 3a). Supporting these findings, we note that the spin 1 character and magnetic anisotropy are consistent with existing macroscopic measurements of Nc powder samples and crystallites 24,25 or matrix embedded samples 26 where D ranges from 3.17 meV to 4.16 meV; recent theoretical calculations for gas-phase Nc also predict D to be close to 5 meV. 27 In the following, we exploit such robustness to produce a portable source for spin-flip excitations by attaching a single nickelocene to the tip apex of the STM.

Similarly to previous works in which the STM tip was functionalized with atomic pointlike probe-particles [28][29][30][31][32][33][34][35] or larger organic molecules, 36,37 we can transfer a Nc to our monoatomic tip apex by approaching the tip to the target molecule at -1 mV and 50 pA. This condition corresponds to a molecule-tip distance of 1.3 Å closer than the usual distances in the tunneling conditions in which we acquire the spectrum (-30 mV and 100 pA) (Figs. 3c and3d). The tip functionalization is reversible, i.e., in the same way the molecule goes to the tip it can be released back to an atom on the surface (+1 mV), indicating that the molecule remains intact during the transfer process. Counter-images of the molecular tip acquired above a Cu atom (inset of Fig. 3d) confirm the presence of a nickelocene molecule. The half-moon shape that is observed can be easily assigned to a tilted Nc. 38 The nickelocene on the tip exhibits similar magnetic properties as previously seen for nickelocene on the surface (Figs. 3a and4a). IETS acquired with such a molecular tip above the bare surface reveals a larger magnetic anisotropy of D = (3.7 ± 0.3) meV and conductance steps up to (9±1) times higher compared to the elastic conductance alone. The large step height observed experimentally in the conductance reflects a highly efficient spin-flip excitation that can be explained using a multichannel T -matrix approach due to the interference of two spin-channels with different symmetries, an effect not seen in previous experiments where only one channel prevails (see Supporting Information). The conductance above the inelastic threshold can be almost one order of magnitude larger than the elastic conductance, with some dependence on the STM tip employed for the measurements.

The magnetic properties of the molecular tip are computed by fully-relaxing a single nickelocene atop a Cu atom adsorbed on Cu(100). In Figs. 3e-g, the spin density of Nc in Finally, to exemplify the effect of having a functionalized Nc tip we acquired IETS spectra above of a Nc molecule adsorbed on the surface using a molecular tip (see Fig. 4a-c). In this case, along with the conductance steps at ∆ = |3.4 ± 0.2| meV, a new set of prominent steps appears at |6.9 ± 0.4| meV, which are the signature of a double spin-excitation process sequentially involving the nickelocene on the tip and on the surface, or vice versa. These inelastic processes can be directly detected in the I(V ) curve shown in Fig. 4d. To explain the origin of these steps, we suppose first, for simplicity, that the molecules on the tip and on the surface have the same threshold energy ∆. When a tunneling electron has an energy below ∆ (region 1) only elastic tunneling processes can take place (Fig. 4e). Above that threshold but below 2∆ (region 2), one of the molecular spins, either the one on the tip or the one on the surface, can be excited (Fig. 4f). Above 2∆ (region 3) a tunneling electron has sufficient energy to excite inelastically both molecules (Fig. 4g). Taking now into account the slightly different threshold energies as evidenced above for Nc on the tip (3.7 meV) and on the surface (3.2 meV), we find that their sum nicely matches the threshold energy found for a double excitation. In principle, in region 2 two additional steps (at 3.2 meV and 3.7 meV) rather than one (3.4 meV) should be observed, but their detection is beyond our energy resolution.

The most prominent effect associated to the double spin excitation is the drastic enhancement of the conduction step height observed at 2∆ (a factor 43 with respect the elastic signal in the spectrum of Fig. 4b) that we explain as follows. Let us suppose that the conductance is proportional to the probability of taking one electron from one electrode (tip) into the other electrode (surface), in other words that the conductance is proportional to the T -matrix modulus squared (see Supporting Information). Since the T -matrix has now spin degrees of freedom in the tip and on the sample, we denote the new matrix elements as T n,m where n is the number of excitations of the tip and m the number of excitations of the sample. Then, the conductance will be proportional to

∑ n,m |T n,m | 2
, with a sum on the excitations since the channels are supposed independent. In this case, T 0,0 corresponds to the elastic transmission of an electron from the tip to the surface or vice versa (region 1). T 1,0 and T 0,1 correspond to the case in which there is only one inelastic event during the process, i.e., in the molecule on the tip, or on the surface. Finally, T 1,1 is related to the probability of an electron being transmitted inelastically between the electrodes exciting both molecules. Hence, if the applied bias is high enough to open the first excitation channel for the molecules on the tip and on the sample (region 3), we obtain that the conductance

is proportional to |T 0,0 | 2 + |T 1,0 | 2 + |T 0,1 | 2 + |T 1,1 | 2 .
The observed inelastic versus elastic ratios show tip dependency. Considering the maximum step height values we observed, we have for the Nc on the tip that (|T 1,0 | 2 + |T 0,0 | 2 )/|T 0,0 | 2 ≈ 9 and for the Nc on the surface

(|T 0,1 | 2 + |T 0,0 | 2 )/|T 0,0 | 2 ≈ 6.
Since the excitations of the molecule on the tip and on the sample are independent, the relative transmission probability of a double spin-flip excitation

to occur is approximately |T 1,0 | 2 |T 0,1 | 2 /|T 0,0 | 4 = |T 1,1 | 2 /|T 0,0 | 2 ≈ 8 • 5 = 40. The conductance is then in region 3, (|T 0,0 | 2 + |T 1,0 | 2 + |T 0,1 | 2 + |T 1,1 | 2 )/|T 0,0 | 2 =1+6+9+40
, this is 56 times higher than the elastic conductance alone (region 1).

To summarize, we have shown how the spin of a nickelocene molecule is preserved in different situations; isolated, self-assembled on a metallic surface or even in the tip apex.

The remarkably efficient inelastic spin-flip mechanism exhibited by the molecule has been explained using a T -matrix approach due to the interference effect of the two spin-channel symmetries. The tip-functionalization has been used to trigger a double molecular spin-flip excitation leading to an enhancement of the inelastic signal in spin-flip spectroscopy. On a more fundamental note, the portability of the spin-flip excitations, whether of nickelocene or eventually of other molecules, could serve as a spin-sensitive probe (with or without magnetic field) and thereby provide quantitative spin-dependent STM data.

Methods

Tip and sample preparation

The Cu(100) and Cu(111) samples were cleaned by repeated Ar + ion bombardment and annealing at 810 K. The nickelocene (Nc) molecules were deposited onto the copper surfaces by sublimating a nickelocene powder purchased from Sigma-Aldrich. Given the low vapor pressure of nickelocene, 40 the powder sublimation occurs at room temperature in vacuum.

The nickelocene powder was first purified for 5 hours at a pressure close to 10 -6 mbar; nickelocene deposition was carried out at room temperature in ultra-high vacuum through a gate valve onto the copper surfaces kept at temperatures ranging from 70 to 150 K. The pressure during deposition was 7•10 -10 mbar, while the deposition rate was 0.025 monolayer/min. The copper samples were subsequently cooled down to the working temperature.

Inelastic electron tunneling spectroscopy (IETS)

The tunneling spectra were acquired with an ultra-high vacuum scanning tunneling microscope operated at 2.4 K at a base pressure below 10 -10 mbar. Electrochemically etched W tips were cleaned by Ar-ion sputtering and indented in vacuo into the pristine copper surfaces to ensure a flat electronic structure in the bias range of interest. The differential conductance, dI/dV , was measured by means of a lock-in amplifier using a modulation of 150 µV rms at 722 Hz. In order to precisely extract the threshold energy of the spin-flip excitation, we fitted the IETS spectra with the expression of Ref. 41 The d 2 I/dV 2 versus V spectra were obtained by numerically deriving the dI/dV spectra.

X-ray magnetic circular dichroism (XMCD)

The XMCD measurements were carried out at the DEIMOS beamline of synchrotron SOLEIL (Saint-Aubin, France) by using circularly polarized light at a temperature ranging from 3.4 to 85 K with a maximum magnetic field of 6.5 T. The samples were prepared following the same procedure used for the STM measurements, using a low coverage within the isolated molecule regime. In our XMCD measurements the applied static magnetic field is parallel to the photon beam direction (fig. S1), which impinges on the sample surface with an angle θ. The angle θ = 0 • defines the normal incidence, and θ = 60 • the grazing incidence. Since isolated nickelocene molecules adsorb with the molecular axis perpendicular to the surface, for simplicity we define the z-axis along the molecular axis. The magnetic field is then in the (x, z) plane.

DFT

Our calculations were done in the framework of Density Functional Theory (DFT) as implemented in the Vienna ab-initio Simulation Package (VASP) 42,43 using the projectoraugmented wave (PAW) 44 formalism. We adopted the exchange correlation functional with the spin-polarized generalized gradient approximation (GGA) 45 with the PBE 46 form. The wave plane expansion has a kinetic energy cut-off of 800 eV. Partial occupancies were determined by the Methfessel-Paxton scheme considering a smearing of 0.2 eV. The Cu(100) surface was modeled using a supercell built up of five Cu atomic layers and additional vacuum in the Z direction (19 Å), large enough to avoid residual interactions with periodic images.

The nickelocene molecule was placed in a 6 × 6 surface unit cell of Cu(100) with the longer axis perpendicular to the surface, i.e., in a vertical position. The adsorbed Cu atom was placed in a hollow adsorption site according to a previous geometric optimization. 20 The two topmost copper layers, the molecule and the adsorbed Cu atom were allowed to relax until the forces on the individual atoms were less than 0.01 eV Å-1 together with an electronic convergence criterion of 10 -7 eV Å-1 . All calculations were performed for the Γ k-point in the first Brillouin zone of the supercell.

To obtain the magnetic anisotropy energy (MAE) within the DFT framework we included the Spin Orbit Coupling (labelled SOC) as implemented in VASP by Kresse and Lebacq. [START_REF] Kresse | VASP manual[END_REF] The Magnetic Anisotropy Energy (labelled MAE) is defined as

M AE = E SOC || -E SOC ⊥ , ( 1
)
where E SOC || and E SOC ⊥ correspond to the energy obtained including the spin orbit interaction while considering the spin axis respectively parallel and perpendicular to the metallic surface.

Both energies were calculated from a previous relaxed magnetic ground state, with no further relaxation. According to the MAE sign one can distinguish two possible cases. When MAE is positive (negative), the E SOC ⊥ (E SOC

||

) is more stable yielding a magnetic easy axis along the perpendicular (parallel) direction with respect to the surface. As the order of magnitude of the MAE value is several times lower than the total energy of the system, the accuracy determining each energy value is crucial. For that reason different calculation parameters such as the energy cut-off, smearing width, and convergence thresholds were thoroughly checked in order to obtain a good compromise between precision and computational effort.

Figure 1 :Figure 2 :

 12 Figure 1: Spin-flip excitations of a single Nc molecule. (a) Energy diagram of the zero-field splitting for Nc. The ground state is S=1, M =0 and the degenerate excited states correspond to S=1, M =±1. (b) STM topography (14.5 × 14.5 nm 2 , -15 mV, 20 pA) of Nc molecules adsorbed on a Cu(100) surface. Inset: Nc structure calculated by DFT. White, grey and green atoms correspond to H, C and Ni atoms. (c) Differential conductance spectrum and its derivative measured at 2.4 K acquired at 50 pA and -15 mV. The spectrum was measured by means of a lock-in amplifier using a modulation of 150 µV rms at 722 Hz. The d 2 I/dV 2 versus V spectrum was obtained by numerically differentiating the dI/dV spectrum.

Figure 3 :

 3 Figure 3: Nc molecule in different environments. (a) Second derivative of the differential conductance measured for three different environments: isolated Nc adsorbed on Cu(111) (in blue), Nc within the molecular self-assembled monolayer on Cu(100) (in green) and Nc adsorbed on the tip (in red). The spectra were taken with different feedback parameters and overlaid to highlight the different bias thresholds. (b) STM topography of the self-assembled Nc molecules forming a compact arrangement on Cu(100). Images (c) before and (d) after the transfer of Nc to the tip. The protrusion on the left corresponds to a Cu atom. With the Nc-terminated tip, the Cu atom exhibits a molecular pattern as visible in the inset of panel (d). (e-g) Calculated spin density (majority spin in red, negligible minority spin) and total electron density (grey transparent) of gas phase Nc with MAE= -1.54 meV (e), adsorbed Nc on Cu(100) with MAE= -1.27 meV (f) and adsorbed Cu-Nc on Cu(100) with MAE= -1.49 meV (g). A negative MAE corresponds to an easy plane, in other words to a positive value of D. The isosurface of the spin (total electron) density is 0.02 (1.3) electron per Å3 . Vertical heights are given in Å. Image parameters: (b) 18 × 18 nm 2 , -20 mV, 20 pA, (c) and (d) 3.5 × 3.5 nm 2 (Inset of panel d: 1.5 × 1.5 nm 2 ).

Figure 4 :

 4 Figure 4: Double spin-flip excitation. (a) dI/dV spectrum of a Nc-terminated tip above Cu(100). Panel (b) and (c) show the dI/dV spectrum of a Nc molecule measured with a Nc-terminated tip and its derivative. Three tunneling regimes are highlighted (see text) indicated by regions 1, 2 and 3. To record the spectra the feedback loop was opened at 100 pA and -40 mV. Note that the different elastic background observed in (a) and (b) is due to a larger tip-surface distance in (b). Panel (d) presents the I(V ) curve showing the opening of the inelastic channels. Panels (e) to (g) present a sketch of the different tunneling mechanisms: (e) there is only elastic tunneling of electrons; (f) the spin of just one of the molecules is excited. In this case the excitation of the molecule on the tip from M = 0 to M = +1 is shown, (g) both molecules undergo spin-flip excitations.

Funding

This work has been supported by the Agence Nationale de la Recherche (Grant No. ANR-13-BS10-0016, ANR-11-LABX-0058 NIE, ANR-10-LABX-0026 CSC). Experiments were performed on the DEIMOS beamline 48 at SOLEIL Synchrotron, France (proposal number 20150309). We are grateful to the SOLEIL staff for smoothly running the facility. We thank the national computational center IDRIS, CINES and TGCC (Grant -[x2015087364]) for CPU time.

Supporting Information Available

Additional information regarding the XMCD measurements and the T -matrix calculation.

This material is available free of charge via the Internet at http://pubs.acs.org/.


Ruel Cedeno

Romain Grossier

Mehdi Lagaize

David Nerini

Nadine Candoni

Adrian Flood

Stéphane Veesler

For Table of Contents Use Only Nucleation in Sessile Saline Microdroplets: Induction Time Measurement via Deliquescence-Recrystallization Cycling

Keywords: nucleation, induction time, sessile droplets, contraction, evaporation, image processing, optical microscopy

With the aim of quantifying nucleation kinetics, a method for induction time measurement on sessile microdroplets has been developed based on deliquescence-efflorescence cycle and image analysis.

Nucleation in Sessile Saline Microdroplets: Induction Time Measurement via Deliquescence-Recrystallization Cycling

Ruel Cedeno 1,2 , Romain Grossier 1 *, Mehdi Lagaize 1 , David Nerini 3 , Nadine Candoni 1 , Adrian Flood 2 *, Stéphane Veesler 1 *

Introduction

Nucleation in solutions has been a subject of numerous investigations due to its significance in material synthesis 1 , pharmaceutical purification 2 , and biomineralization 3 . In general, nucleation is the step that determines how long we must wait before the appearance of a stable crystal cluster in a supersaturated solution. 4 This "waiting time", referred to as induction time, is a function of the nucleation rate and the system size. Most induction time measurements are carried out at constant supersaturation for the sake of "simplicity" of data interpretation and modeling 4 . However, in reality, most nucleation processes occur at varying supersaturation, either by cooling, antisolvent, or evaporative crystallization 5 . Thus, a thorough understanding of the nucleation kinetics of such systems is important. In this context, due to the stochastic nature of nucleation, dropletbased microfluidic systems have been widely used as experimental tool as they permit numerous independent experiments using very small quantities of material. Moreover, their small sizes promote homogeneity in temperature and composition. Despite these advantages, there remain some drawbacks in the use of droplet-based microfluidics in the context of nucleation studies. First, since induction time scales inversely with the system size due to kinetic confinement effect, high supersaturation level must be achieved in order to observe nucleation events in small volumes within reasonable time scales. Consequently, in constant supersaturation experiments, not all of the microdroplets (denoted as µDs) will nucleate, thereby reducing the statistical quality of the data (data is censored). Another issue is that the time for a critical cluster to grow to detectable size depends on the instrument sensitivity, which can also affect the robustness of the measurements 6 . Regarding these limitations, evolving supersaturation experiments where the solvent is allowed to evaporate seem promising 7 : µDs rapidly reach high supersaturations where growth time to detectable size is negligible, and every µD will give rise to a nucleation event (uncensored data). Thus, in our previous work, we have developed an experimental setup allowing facile generation of monodisperse arrays of nanoliter to femtoliter droplets immersed in an oil film, which can serve as evaporative microcrystallizers 8,9 . We have also shown that a simple and efficient digital-image processing method based on the standard deviation of the grey-level pixels of a single µD and its immediate vicinity (σ) is useful in probing the microdroplet dynamics, particularly the onset of nucleation. 9, 10 Interestingly, we have observed that in these experiments, microdroplets can interact with each other via water diffusion dynamics, i.e. when one µD nucleates, water can diffuse to its closest neighbors. Unfortunately, these interactions would complicate the analysis of induction times obtained from µD arrays. In this contribution, we develop a new approach to measure induction time in sessile arrays of microdroplets using deliquescence-recrystallization cycles. With the help of our in-house developed microdroplet generation system with humidity control module, we show that by controlling the relative humidity, the interfering diffusion-mediated interactions between microdroplets can be eliminated. Then, by using appropriate statistical tests, we show that our measurement method is robust and reproducible. Finally, our evaporative nucleation experiments on 60pL and 4pL microdroplets (at equilibrium) confirm the confinement effect 11 where smaller systems reach higher supersaturations.

Experimental Section

I.Production of microdroplets with microinjectors (Fig. 1a). We employed a mechanically controlled micropipette to generate arrays of monodisperse aqueous NaCl sessile microdroplets (1.7 M) on the surface of a poly(methyl methacrylate) (PMMA)-coated glass slide immersed in a 0.4mm-thick layer of polydimethylsiloxane (PDMS) oil (10 cSt). A detailed description of this procedure has been presented previously 8 while the details of the chemical products and equipment used are shown in the Supplementary Information (SI) 1 and 2.

II. %RH control system.

A home-made, 3D printed (Formlabs printer, PMMA resin) %RH controller module (Fig. 1b), allows us to control the %RH of an air flow on the oil surface, while still having physical access to µDs (not a closed box, but an open-to-air design). Humid air is obtained through consecutive bubbling of a dry airflow: first in hot-water, then in room-temperature water. A liquid trap ends the process to remove undesired water droplets generated by the bubbling process and conveyed in tubing. Mixing humidair with dry-air allows fine control of %RH, from a maximum humidity condition (95% RH) to a dry condition (10% RH). The flow is then distributed uniformly above the oil layer. Calibration and stability of %RH were conducted with a %RH sensor (Sensirion SHT85) plugged onto a RaspberryPi3, and a home-made Python3 script to record %RH measurements (see SI3).

III. (𝜎,t) measurements. The dynamics of each individual µD is followed through an already developed image-processing technique.

In a Region-Of-Interest (ROI), centered on each µD and its immediate vicinity as shown in Fig 2, we extract, for each time step (image), a single scalar value: the standard-deviation 𝜎 of ROI-pixels' greylevels. This is a post-processing technique: images of the whole µDsarray are acquired at a desired frequency until the end of the experiment, then we process the image-stack with ImageJ (FIJI). First, we extract each µDs edges on first images, and plot a ROI around each one. We then propagate 𝜎 measurement in each ROI through the whole image-stack to obtain the (𝜎,t)-curves which reflects the spatial and temporal dynamics of each µD. (𝜎,t)-curves are then processed with home-made Python3 scripts (available on request). IV. Experimentation timeline. The experiments can be divided into 3 consecutive steps. Step 0 -this step is dedicated to obtaining an array of sessile crystals. A µD array is generated (Fig. 1c), following a previously developed method. %RH is here not controlled, and just need to be lower than %RHeq, so that µDs will contract (water diffuses to the oil and above-oil atmosphere) until nucleation and growth of a unique crystal in each µD. This step ends when an array of fully-dried crystals is obtained. Step 1 -the %RH above the oil layer is increased so that %RH > %RHeq (the %RH corresponding to the equilibrium water partial vapor pressure above a saturated solution). Crystals will then, until complete dissolution, absorb water through the oil-layer. Step 1 ends after every crystal has been completely dissolved and the size of the resulting µDs seems constant.

Step 2 -the %RH above the oil layer is decreased so that %RH < %RHeq. Water then selectively diffuses from µDs, through the oil to the above-oil atmosphere; this contraction ultimately leads to nucleation and growth of a single crystal in each µD. Step 2 ends when we recover the initial conditions of step 1: an array of fully dried sessile crystals. Cycling -The sequence Step 1 and Step 2 can then be repeated at will.

Results and Discussion

The dynamical behavior of the generated µDs depends on the relative humidity %RH above the oil in comparison with the equilibrium %RHeq above the saturated solution (for NaCl in water, %RHeq=75% at 25°C). Generally, if %RH > %RHeq, the crystal would absorb moisture leading to deliquescence, dissolution, and dilution. If %RH < %RHeq, water would evaporate from the µD leading to an increase in salt concentration until nucleation. By controlling the prevailing %RH, we demonstrate the use of our image analysis protocol to track the dissolution and nucleation of µDs through (𝜎,t)-curves. I. Analysis of (𝜎,t)-curves. Figure 2 presents the typical time evolution during a nucleation experiment of 𝜎 measured for each ROI, i.e., for each µD. The analysis of (𝜎,t)-curves show characteristic points which are useful data points giving information on the dynamics of each µD, on both dissolution (deliquescence of the crystal), contraction and nucleation (See the video in SI for the whole process). Their sequence and characteristics are discussed hereafter: t0 -tDISS. Dissolution time (tDISS) is the first encountered characteristic point, appearing as a local minimum on the curve. From t0 (at time t=0) to tDISS, the crystal is dissolving through water absorption, and tDISS is the ultimate point of this process, when the crystal was last seen before total dissolution. It is noted that, on the path to tDISS, the signal can present large and erratic oscillations, due to small movements of the crystal (jiggling) along the process leading to its total dissolution. tDISS -tSHIFT. This is the µD dilution step, where, after the crystal completely dissolves, we allow µDs to continue to absorb water, thereby decreasing their NaCl concentration: µDs are undersaturated. At some time (tSHIFT), when µDs do not visually evolve anymore, we shift %RH above the oil-layer, from above %RHeq to a lower value, here from 95% to 10%RH. tSHIFT -tMATCH. From the time we shift %RH, each µD will contract by selective diffusion of water through the oil-layer to the controlled atmosphere. Initially, the µDs have a refractive index lower than the oil one, but as contraction occurs, their refractive will increase, and will at some time (tMATCH) match the oil refractive index: at this point µDs optically disappear. tMATCH -tNUC. The refractive index increases, linked to the increase in NaCl concentration, until crystal nucleation. Therefore, sigma will gradually re-increase after tMATCH and crystal nucleation will appear as a large instantaneous (<1s) jump in sigma values at tNUC. The growth of the single nucleated crystal will continue to occur as long as the contraction of the µD continues, until no more water is available: we recover the initial state, a dry sessile crystal. II. Estimating tSAT. For experiments with evolving supersaturation, the time at which the microdroplet becomes saturated (tSAT) must be subtracted from the nucleation time tNUC to calculate the induction time. 12 Otherwise, the measured induction time would depend on the arbitrary initial concentration. In principle, tSAT can be estimated by computing the evaporation rate as a function of %RH and system geometry 13 but this could introduce another layer of uncertainty. Alternatively, we can extract tSAT from (𝜎,t)-curves by making two assumptions. First, we consider that during the dissolution step of the crystal (t0 to tDISS), the solution is in equilibrium with the crystal 14 , i.e at saturation concentration. Second, we consider that along the expansion stages (tDISS to tSHIFT) and contraction stages (tSHIFT to tMATCH), the µD shape have the same symmetric evolution, i.e. its shape follows the same smooth reversible path. Given that 𝜎 is a function of only shape and refractive index (so NaCl concentration), we can use the value of σ at tDISS (where µD is saturated) as reference to find tSAT during the contraction stages (Figure 2). Thus, the µDs are assumed to be at saturation when their σ is equal to that of tDISS. This is a direct consequence of our symmetric shape path hypothesis.

III. Eliminating interactions via %RH control.

When the droplet contraction is done at %RH close to the %RHeq, the µDs can interact with each other via water diffusion dynamics. This was previously reported and explained in a previous paper. 10 To summarize, when a microdroplet nucleates, it suddenly increases the chemical potential of water inside the microdroplet. As a result, water diffuses from the nucleated microdroplet to its closest neighbors and thereby decreases their solute concentration. This is shown in Figure 3, where selected (𝜎,t)-curves show clear oscillations, typical of nucleation induced µD-to-µD interactions. This data was obtained in contracting µDs at 55% RH (room conditions, without using the %RH module). Unfortunately, these interactions would make it impossible to consider each µD as an independent micro-crystallizer. To perform experiments in conditions where one can rule-out any possibility of µD-to-µD interactions, the %RH must be lowered such that the driving force for diffusion towards the atmosphere is high enough to prevent diffusion to neighboring µDs. For this purpose, we developed two versions of an air-flow dispatcher module (v1 and v2, see SI3). If the interactions are fully eliminated, there should be no oscillations in the σ-curve prior to nucleation in contrast to Figure 3. Although both designs were able to eliminate such oscillations, the v2 module design provides a much better spatial homogeneity of hygrometric conditions as revealed by the statistical-momentums analysis of tDISS distributions (see SI3). This led us to choose the v2 design for the experiments conducted and analyzed here. Figure 3. (𝜎,t) curves for 4 neighboring µDs, under conditions (room conditions at 55%RH, without using %RH module) which promote µD-to-µD interactions, which appear as oscillations in the 𝜎 signal. While a µD nucleates a crystal at time 'h', water is released to other neighboring µDs, thus diluting them. Their associated 𝜎 temporarily decreases before µD contraction re-occurs, thereby re-increasing their associated 𝜎. Amplitude and time shift of the interactions are driven by both µD and nucleating-µD parameters such as size, supersaturation, and also by their separation distance. The spatial arrangement of µDs, named by their nucleation time, are the following: i, k, j, h. It is notable that these interactions are unobservable on images while looking at µD diameter changes under optical resolution.

IV. Small and Big-Droplets (SD and BD) experiments.

To study the effect of confinement on nucleation, we performed experiments involving small droplets SD (4 pL) and big droplets BD (60 pL). First, we generated lines of monodisperse aqueous NaCl sessile microdroplets (1.7 M). Big µDs (total number of imaged µDs: 191, in 5 lines: 38, 36, 39, 39 and 39 µDs) were generated first. µDs are left free to contract (Step 0), at room conditions (55% RH), until we obtain lines of totally dried sessile crystals. Then, as the %RH above the oil is increased to 95%RH (Step 1), we start image acquisitions at a 1Hz rate for BD and 4Hz rate for SD. Following this experiment, we generated smaller µDs (total number of imaged µDs: 170, in 3 lines: 56,56 and 58 µDs), and conducted the same experiment, except that for these small µDs we cycle them twice through Step 1 / Step 2. Images of representative lines of small and large µDs are provided on Figure 4.

Datasets. S(t) is the cumulative probability that nucleation has not occurred as a function of time t, and is called the survival function.

In experiments presented here, the time evolution of the fraction of droplets in which nucleation has not occurred is considered a good estimator of the underlying S(t). Each µDs line is treated as an ensemble (with associated S(t)), and constitute a dataset. We consider datasets relative to the µDs sizes they are associated to: BD datasets (Big µDs) and SD datasets (Small µDs). These datasets are in fact different uncensored (every generated µD give rise to a detected crystal) samplings of the nucleation times survival function, if existing. Costs and benefits of increasing supersaturation. For experimentations conducted at constant supersaturation, there are two major drawbacks, sources of uncertainties in interpreting obtained nucleation data: tGROWTH and data censoring. tGROWTH is the time to grow from the critical size (the nucleation event in itself) to a detectable size, and needs additional hypothesis to be modeled. Data censoring is the fact that not every experiment (supersaturated µDs in our case) will lead to a nucleation event, because nucleation rates may span over a large bandwidth, so that there's missing information. Here, conducted experiments provide access to uncensored data: every single µD leads to a detectable nucleation event, due to constantly increasing supersaturation. For tGROWTH, we also benefit from the supersaturation constantly increasing, combined with a kinetic confinement effect 15 , as the probability to nucleate scales with the inverse of the volume, µDs reach high supersaturations before nucleation occurs. As a consequence of these high supersaturations, growth from critical cluster to detectable size is fast enough to be ignored: in less than a second, where experiment span over hundreds to thousands, a large crystal is detected. These benefits in experimentations translate in a cost relative to the increased complexity to model nucleation in this evolving supersaturation framework.

Checking for heterogeneities and memory effect.

A common source of uncertainties in nucleation experiments are heterogeneities, impurities, and their impact on measured nucleation rates (see the discussion on thermal and quenched disorder in reference 4 ). The cycling can be viewed as an interesting approach 16 to detect a subset (some µDs in the experiments) where nucleation is mainly due to heterogeneities, which translates in a population of µDs that "statistically always" nucleates first. For SD datasets, that's what Figure 5 is about: with two cycles, we can compare the nucleation ranks of every µD from a cycle to the following. If a population of µDs present heterogeneities leading to faster nucleation rates exist, it could appear as a pattern, for first ranks: they would statistically nucleate faster than other µDs, so in lower rank positions in both cycles. Figure 5 does not show any kind of patterning, the distribution of ranks spread homogeneously in the whole available space. Moreover, it also indicates lack of historical contamination or memory effect from a cycle to the following, that is, nucleation is independent of previous cycle behavior. Nevertheless, further analyses and larger a number of cycles would be needed to confirm this and will be the subject of another study. Distribution of characteristic time points. Due to the stochastic nature of nucleation, a distribution of times tNUC is expected. But we also see, in Figure 6, that contraction characteristic time points tSAT and tMATCH also distribute: despite optimization in hygrometric conditions, µDs dynamics still show individual characteristics. Such discrepancies can find their source in varying local conditions such as, without being an exhaustive list, surface roughness or chemistry on which µDs rely, local water concentration in oil, small differences or variations in imposed above-oil %RH. Also, small differences in initial diameter, lower than the resolution of our optical system, cannot be ruled out. However, we see in Figure 6 the astonishing similarity of the diverse characteristic time points distributions, in terms of both shape and scale. All µDs lines, whatever the cycle for SDs, shows such resemblance (see SI4). Ultimately, these distributions of tSAT and tMATCH will be reflected in nucleation time tNUC distributions. Also, for the case of SDs, which experienced two deliquescence/nucleation cycles, Figure 6 shows a Cycle-to-Cycle times location shift in distributions of times tMATCH and tNUC, similar for every SD lines. It seems that, statistically, µDs are slower to reach tMATCH and tNUC during cycle 2 as compared to cycle 1: µDs contract slower in cycle 2.

Dimensionless Induction Time  (DIT).

To compare µDs and associated tNUC, we have to take into account differences that may only arise from their individual behavior (discrepancies in contracting dynamics), and also from their "cycle" behavior (the location shift shown from cycle 1 to cycle 2 for both tMATCH and tNUC distributions). For this purpose, we non-dimensionalized individual induction times tNUC relative to tSAT and tMATCH. The individual µDs times to nucleation tNUC are converted to a dimensionless induction time, as specified by equation 1, here:

τ = t NUC -t SAT t MATCH -t SAT (1)
Figure 7. Survival function (sf) semi logarithmic plot of Dimensionless Induction Times (DITs) of every µD line in the full dataset of big droplets (BD) and small droplets (SD). Among SD datasets we discriminate Cycle 1 (SD Cycle1) from Cycle 2 (SD Cycle2). Best fits from a Weibull sf are here provided as guide to the eye, calculated for the full pooling of all BD datasets (BD fit.), and for a subset (all pooled but line 3 in cycle 1) of the full pooling of SD datasets (SD fit.). Associated respective Weibull shape parameters are reported as 𝑘 𝐵𝐷 𝑊𝑒𝑖𝑏𝑢𝑙𝑙 and 𝑘 𝑆𝐷 𝑊𝑒𝑖𝑏𝑢𝑙𝑙 .

DITs seem similar. DITs semi logarithmic plots of their survival function are reported on Figure 7. At first sight, such nucleation dimensionless time allows comparison of µDs with individual contraction dynamics, which first benefit, for the SDs case, is to make cycle-tocycle tNUC location shifts vanish: there is no evidence of a location shift (see SI5), from cycle 1 to cycle 2, so that nucleation times as reported through the use of DITs compare well. It seems, to the eye, that lines in BD datasets and SD datasets can, respectively, be fully pooled to be treated as representative of a unique experiment, thereby increasing the statistically representation. This will be addressed hereafter in the "Datasets pooling" section. Also evident on Figure 7, for both BD and SD datasets, the log(sf) of their respective DITs do not follow a purely exponential decay, which would appear as a straight line on the plot: lowest values of DITs draw a plateau. This plateau is both typical of experimentation inaccuracies (tGROWTH, heterogeneities), and of compressed exponential decays. As a reason for this plateau, we can here eliminate inaccuracies that arise from a shift between nucleation and detection of the crystal as growth is almost instantaneous to a visible and consequent size: growth time does not pollute these measurements. Also, as shown on Figure 5, the lack of patterns (at least for SDs, the only µDs that underwent two cycles) in their cycle-to-cycle ranks do not promote evidence of a µD population (which nucleates first) subject to a higher nucleation rate due to nucleation promoting heterogeneities. In doing so, this plateau seems to have an existence independently of experimentations inaccuracies, and will be treated as such, promoting datasets fittings (addressed hereafter in a specific part) with the help of a typical stretch/compressed distribution: the Weibull distribution, which shape parameter k discriminate between stretching (k<1) and compression (k>1) of an exponential decay. Weibull survival function, in its standardized form, can be written as follows (eq.2), with k being the shape parameter:

𝑆(𝑡) = exp(-𝑡 𝑘 ) (2)
Datasets pooling. Up to now, we implicitly considered a µD line as the scale of the sampling of the nucleation times distribution, each line forming a dataset, and kept comparing line-to-line similarities.

There is high temptation to pool all datasets toward a "superdataset" that could be treated as a whole, but the problem would be to justify such data pooling. Such authorization for datasets pooling could rely on the use of a non-parametric statistical test: the "ksample Anderson-Darling test" (kADt). 17 The kADt tests the null hypothesis "H0: the k-samples are drawn from the same population" versus the alternative hypothesis "H1: the k-samples are drawn from different populations". In other words, do here presented DITs associated to each µD lines could be considered as samples representative of the same distribution, i.e., could we model these samples with the same distribution function, and pool datasets? For the 5 BD datasets (see SI6), with a 5% significance level, kADt fails to reject the null hypothesis H0: the 5 µD lines and associated DITs distributions can be modeled with the same distribution function, and we pool datasets in BDSUP superdataset. Regarding (see SI6) the 6 SD datasets (considering each cycle -3 lines each -as independent sampling as lines could be), the kADt reject null hypothesis H0: the 6 datasets cannot be considered to be drawn from the same distribution. We then test every combination of 5 among 6 lines with kADt, and one SD dataset seems to be the source of the null hypothesis rejection: line 3 in cycle 1. In removing this dataset, kADt cannot reject the null hypothesis H0 anymore, and we can then construct a SD superdataset SDSUP constituted of 5 pooled SD datasets: lines 1 and 2 in cycle 1, and every 3 lines in cycle 2. Datasets Fittings. Complementary to the analysis of Survival function (sf) semi logarithmic plots of Dimensionless Induction Times (DITs) presented on Figure 7, the contracting process (where, as volume decreases, supersaturation increases, imposing also nucleation rate to do so upon nucleation of a crystal) encompassed by µDs also justify the modeling of DITs with a Weibull distribution function, which would correspond to a compressed exponential function of class III as suggested by Sear. 4 A fitting procedure was applied to newly constructed SDSUP and BDSUP datasets, and results are presented on Figure 8. It is to note that sensitivity of fittings algorithm to both outliers and initial fitting guesses was addressed in two steps: we first fit "roughly", with guessed outliers removed, then we re-incorporate 98% of the full dataset to refine fit. R 2 and mean squared errors were calculated on the full dataset. Despite such precautions, as seen on Figure 8, there is departure of the fit from data at distribution tail (highest DITs). This is not an artefact, tail is not well fitted, but using semi logarithmic scale here does not render justice to quality of fittings, as measured with both R 2 and mean squared errors (see SI7). Moreover, Figure 8 confirms confinement effects where the induction time shifts due to system (µD) size: the smaller the system, the longer the induction time. Supersaturations at nucleation times. To translate DITs in supersaturations, one need a contraction model: how µDs volume evolves with time. An exact and precise model is complex and out of the scope of this paper, and will be the object of specific studies later on. But from previous works, and for the sake of simplicity, we can choose a linear evolution of volume with time, which allow (see SI8)

to calculate supersaturations NUC from DITs and supersaturation MATCH at matching time tMATCH, following equation here:

𝛽 𝑁𝑈𝐶 = 1 1 - × (1 - 1 𝛽 𝑀𝐴𝑇𝐶𝐻 )
In Figure 9, we report calculated supersaturation distributions for both BDsup and SDsup superdatasets, with corresponding Weibull function best fits for both. For BDSUP, nucleation occurs at a mean supersaturation of 1.61 and 95% spans from 1.58 to 1.65. For SDSUP, nucleation occurs at a mean supersaturation of 1.85 and 95% spans from 1.74 to 2. There is high correspondence with supersaturation values already reported in literature, for comparable system sizes [18][19][20] (3)

Conclusions

In this communication, we present a microdroplet generation system with humidity control module and a novel approach for measuring and analyzing induction times in lines of saline sessile microdroplets undergoing a deliquescence/recrystallization cycling process. With the help of a recently developed image analysis protocol, we first assert microdroplets act independently: there is no microdroplet-to-microdroplet interactions. Second, using a dimensionless time, dynamics of microdroplets along deliquescence/recrystallization cycles are specified, allowing to obtain precise estimation of the nucleation induction times survival function S(t), for every microdroplet lines. Considered as samples of the underlying (unknown) nucleation probability density function, line datasets that satisfies a k-sample Anderson-Darling test are pooled, and resultant superdatasets are fitted with a Weibull function. Moreover, evaporation experiments on 60pL and 4pL microdroplets, at saturation confirm confinement effect that smaller systems reach higher supersaturations. Both the experimental method and the data-treatment procedure seems promising for the study of fundamental aspects of nucleation kinetics, confinement effects in particular, and is adaptable to other salts, pharmaceuticals, or biological crystals of interest.

The modeling of evaporation and the use of a modified Poisson distribution which considers the time-dependence of the nucleation driving force 5 will be a subject of a future work.

Figure 1 .

 1 Figure 1. (a) Schematic diagram of the microdroplet generation system with humidity control module (b) picture of the confined microdroplet generation chamber that contains PMMA-coated glass plate immersed in PDMS oil (c) sessile microdroplets printed on the surface of the PMMA using a motorized microinjector.

Figure 2 .

 2 Figure 2. Typical (𝜎,t)-curve, during a full %RH cycle (deliquescence/recrystallization), associated to each Region-Of-Interest (ROI). An illustrative ROI is provided in the lower part of the graph to show typical evolution of µDs. Characteristic time points are reported on both %RH curve and (𝜎,t)-curve. %RH cycle (dotted orange) goes from step 1 (crystal deliquescence up to tDISS followed by µD dilution) to step 2 (µD contraction) at time tSHIFT. During contraction, µD is at saturation at time tSAT, optically disappear at time tMATCH, and crystals nucleate at time tNUC.

Figure 4 .

 4 Figure 4. Representative lines of small µDs and large µDs.

Figure 5 .

 5 Figure 5. µDs nucleation rank comparison in the two consecutive cycles for SD datasets. "Rank Cycle 1" is µD nucleation rank position in cyle 1 SD datasets, while "Rank Cycle 2" is the µD corressponding rank position it nucleates in cycle 2 SD datasets.

Figure 6 .

 6 Figure 6. Distributions (kernel density estimation of probability density function) of characteristic time points (tSAT, tMATCH and tNUC), for a typical dataset (here SD line 1 dataset), for both deliquesence/nucleation cycles (C1 for cycle 1, C2 for cycle 2). Plots are against a shifted time where the mean tSAT, respectively to the cycle, is taken as the origin of times.

Figure 8

 8 Figure 8 Survival function (sf) semi logarithmic plot of Dimensionless Induction Times (DITs) for both BDSUP and SDSUP datasets. Best fits with a Weibull function are shown as 'SDSUP fit.' and 'BDSUP fit.' With reported associated distribution shape parameters as 𝑘 𝐵𝐷 𝑊𝑒𝑖𝑏𝑢𝑙𝑙 and 𝑘 𝑆𝐷 𝑊𝑒𝑖𝑏𝑢𝑙𝑙 .

Figure 9 .

 9 Figure 9. Supersaturation histograms and best fits with a Weibull probability density function (pdf), in using a linear decrease of droplets volume with time model. SD and BD are the pooled data as determined by Anderson-Darling k-sample tests. 'SD fit.' and 'BD fit.' are, respectively, SD and BD Weibull pdf best fits. Median and mean times of each fits are reported on graph for both SDs and BDs fits.

Acknowledgement R. Cedeno acknowledges the financial support of Vidyasirimedhi Institute of Science and Technology (VISTEC) and the Eiffel Excellence Scholarship (N°P744524E) granted by the French Government. Distribution of sigma-curves characteristic points versus time Distribution of sigma-curves characteristic points versus time for BDs lines. Distribution of sigma-curves characteristic points versus time for SDs lines.

Supporting Information

SI2

Details of Instrumentation

To avoid microdroplet spreading and coalescence, we coated the glass cover slip with a hydrophobic PMMA resin. For this, glass coverslips (18-mm diameter, cleaned via plasma treatment) were spincoated at 4000 rpm for 1 min (SPIN 150, SPS) with PMMA which were then annealed for 10 min at 170C. The coverslips were then covered with a 0.8 mm thick layer of PDMS oil. The saline microdroplets were generated on the cover slip by a micropipette with an internal diameter of 0.5 um (Femtotip Eppendorf).

The micropipette is mechanically controlled by a home-made motorized micromanipulator consisting of 3 miniature translation stages (piezo electric, MS30 Mechonics) which allows displacement of the micropipette holder in three dimensions by steps of 16 nm. A series of 16-bit images were obtained using an optical microscope (Zeiss Axio Observer D1 equipped with an ANDOR neo sCMOS camera). Images were processed using FIJI software (Image J, NIH, USA) which calculates σ for each region containing microdroplets.

SI3 Humidification control and dispatching module

The humidification chamber (airflow module dispatcher) was custom fabricated via SLA 3D-printing (Formlabs, clear resin).

Improving Spatial Homogeneity

To choose airflow module dispatchers, we compared measured distributions of tDISS in both models (v1 and v2). With this v2 design, to assess asses the speed at which the humidity can be changed, we measured the %RH in the microdroplet generation chamber with "dry" air (directly obtained from compressed air pipelines) and our humid air.

Figure S1

Relative humidity vs time in the humidifier when RH is shifted from minimum to maximum value and vice versa. This suggests that our humidity control system can almost instantaneously change the RH of our microdroplet generation chamber (negligible lag period). We also show we can maintain a reasonably stable RH as needed.

SI5 Cycle-to-cycle nucleation times shift. Distribution, for SDs datasets, of dimensionless induction times, while cycle-aggregated.

There is no evidence of cycle shifting.

SI6 Anderson-Darling k-sample test for different aggregation subsets.

Anderson-Darling k-sample test tests for:

-"null hypothesis H0: samples data are drown from the same distribution" -"alternative hypothesis H1: samples data are drawn from different distributions". We fix risk to reject H0 despite true at a usual value of p-value=.05.

BD: Big Droplets datasets (line number) k=5

(1, 2, 3, 4, 5) -> 1.7277 / 0.0606 Ok The pooling of every BD datasets succeeds. SD: Small Droplets datasets (SD_cycle_line format, ex: SD23 is line 3 in cycle 2) K=6 ['SD11', 'SD12', 'SD13', 'SD21', 'SD22', 'SD23'] -> 2.5189 / 0.0212 X The pooling of every datasets fail. We can then try different combinations of 5 among 6 datasets. K=5

Ok ['SD12', 'SD13', 'SD21', 'SD22', 'SD23'] -> 2.7799 / 0.0162 X

There are combinations which succeed test, we choose the highest statistical significance (0.

2275).

SI7

SI8 Supersaturation Calculation from DITs Determination of Supersaturation Ratio at Refractive Index Matching

The refractive index of NaCl solution at ambient conditions is plotted against supersaturation ratio. The supersaturation ratio that corresponds to the refractive index of PDMS oil is the supersaturation ratio during refractive index matching (Sm). Data were taken from https://www.topac.com/Salinity_brix.html.