Quantifying surface tension of metastable aerosols via electrodeformation

Abstract

Accurate surface tension measurements are key to understanding and predicting the behavior of atmospheric aerosols, particularly their formation, growth, and phase transitions. In Earth’s atmosphere, aerosols often exist in metastable states, such as being supercooled or supersaturated. Standard tensiometry instruments face challenges in accessing these states due to the large sample volumes they require and rapid phase changes near surfaces. We present an instrument that uses a strong electric field, nearing the dielectric strength of air, to deform aerosol microdroplets and measure surface tension in a contact-free, humidity-controlled environment. A dual-beam optical trap holds single microdroplets between two electrodes and excites Raman scattering. When a high voltage is applied, droplet deformations reach tens of nanometers. These small shape changes are precisely measured through the splitting of morphology-dependent resonances, seen as sharp peaks in Raman spectra. Our measurements cover water activities where droplets are supersaturated, a region with limited previous data, and show good agreement with existing data where comparisons are possible. Unlike prior levitation-based methods, this approach measures surface tension in systems with viscosities over 10² Pa s without relying on dynamic processes.

Atmospheric aerosols are often in metastable states. Here, the authors present a non-contact method for measuring the surface tension in single microdroplets using electrodeformation and Raman scattering, which enables precise measurement of such states.

Introduction

Atmospheric aerosols impact Earth’s climate by scattering solar radiation and acting as cloud condensation nuclei. Surface tension, a physical property of a liquid’s surface that causes it to minimize surface area due to cohesive intermolecular forces, is key in aerosol processes, influencing cloud droplet formation^1,2 and affecting cloud albedo^3–5 and precipitation⁶. Thermodynamically, the surface tension of a droplet is defined as the partial derivative of the droplet’s Gibbs energy (or, alternatively, internal energy) with respect to a change in surface area. Despite its importance, accurately measuring and predicting the surface tension of aerosols remains challenging⁷. This is due to their varied chemical compositions and the complex nature of their interactions in the atmosphere. Furthermore, aerosols often exist in metastable states, such as being supercooled or supersaturated with respect to the formation of a crystalline phase (alongside a liquid phase)⁸. The physical properties of these states are not well characterized, primarily due to the difficulties in experimentally accessing them. Deviations in aerosol surface tension from that of pure water can greatly affect the formation and size of cloud droplets (e.g., the effect of organic components on aerosol surface tension can cause changes in cloud droplet number concentration by as much as 40%)^4,9. Additionally, studies indicate that incorporating surface tension effects in models can alter indirect radiative effects by nearly 1 W m^−2 4, a significant value for climate predictions. Overall, understanding aerosol surface tension is key to improving climate models and assessing mitigation strategies, as it remains a major uncertainty in evaluating aerosol impacts^10,11.

The presence of metastable states, such as those found in aerosols^12,13, are widespread in our atmosphere. For instance, so-called freezing fog is not uncommon in cold and moist climates, particularly in mountainous or coastal areas, and is composed of supercooled water droplets that are in a metastable equilibrium with respect to ice. These droplets will freeze upon contact with a surface, leading to the formation of rime ice. Freezing rain originates from a similar process and is certainly one instance of non-equilibrium thermodynamics that most residents in temperate regions are aware of, as severe ice storms are often some of the most costly natural disasters. However, not all examples of metastability in the atmosphere directly impact our lives in such an overt and destructive manner. In subsaturated air, the interplay between the solute effect (Raoult’s law) and surface tension can stabilize aerosol particles in an aqueous phase, allowing the concentration of dissolved species to exceed the bulk solubility limit^12–16, leading to supersaturation and significantly enhancing chemical reactivity¹⁷. More broadly, there are now many known examples of laboratory-generated and atmospheric aerosol particles that exist in a range of condensed phase states (e.g., liquid, highly viscous semi-solid, amorphous solid), even under conditions where these states are less thermodynamically favorable, i.e., metastable, compared to a crystalline state^18,19. These phase states impact processes such as light scattering²⁰, water uptake and loss²¹, cloud droplet activation²², mass transfer kinetics²³, and chemical reactivity²⁴. However, despite their importance in atmospheric aerosols²⁵, measurements of the physical and chemical properties of particles in these non-equilibrium states remain limited. The major reason for this is because metastable states are challenging to examine using methods that rely on bulk solutions with milliliter-scale volumes. For instance, standard laboratory experiments often necessitate the use of a container, like a cuvette, to hold a sample during analysis. As illustrated by the behavior of supercooled water, a rapid phase change, such as freezing, can be triggered by heterogeneous nucleation on surfaces. Additionally, investigating transient processes such as water uptake and loss in larger sample volumes leads to prolonged timescales, making experiments less feasible. To effectively study metastable states, an ideal approach would involve contactless confinement and analysis of particles at much smaller scales, specifically at nano-, pico-, and femtoliter volumes.

Single-particle levitation, achievable through methods like optical trapping^8,26,27, the electrodynamic balance (EDB)^8,28–30, or acoustic trapping^31,32, has been shown to enable the direct study of phase states commonly found in atmospheric aerosols. For the specific case of measuring surface tension, several contactless, single-particle techniques based on analyzing the normal modes of droplet shape oscillations have been developed. Holographic optical tweezers have been demonstrated to measure surface tension by observing oscillations in elastic light scattering intensity as two droplets coalesce^9,33–35. The frequency of these oscillations corresponds to the normal modes of the resulting droplet, which are related to droplet size and surface tension. However, this technique has limitations: it permits only a single measurement per droplet pair, and viscous forces can damp oscillations during coalescence³³, which restricts its applicability to many systems of atmospheric interest (e.g., the surface tension cannot be measured if the droplet viscosity is greater than 10⁻² Pa s)⁹. Utilizing quasi-elastic light scattering, contactless surface tension measurements have been performed using both optical tweezers³⁶ and an EDB³⁷ as the trapping platform. However, this technique has the same limitations due to viscous damping as the holographic optical tweezers. Surface tension measurements with an EDB have also been shown to be possible through phase analysis of the oscillations of a charged droplet driven by an external electric field³⁸. Finally, acoustic levitation has been utilized for temperature-dependent surface tension measurements of single, millimeter-sized, supercooled water droplets³⁹.

Atomic force microscopy (AFM) has been used to directly measure the surface tension of atmospherically relevant droplets⁴⁰, including model systems containing inorganic salts and dicarboxylic acids^41–43, saccharides⁴², as well as actual field samples of sea spray aerosol⁴⁴. In comparison to the techniques listed above, AFM is unique in that it can access submicron droplet sizes and measure surface tension in droplets with viscosities up to 10² Pa s. However, AFM is not a surface-free method; it involves placing the droplet on a substrate and making further contact using a nanoneedle (the AFM tip). The concern of crystallization due to heterogeneous nucleation that may occur during the measurement process, as well as the potential bias from the substrate itself, will always be present. Nonetheless, AFM has demonstrated the ability to probe supersaturated states in nano-sized droplets.

We have previously reported the use of optical deformation in a dual-beam trap to measure the surface tension of single aerosol particles⁴⁵. This technique relies on the sensitivity of morphology-dependent resonances (MDRs) to nanometer-scale deformations of microdroplets. MDRs are optical resonances that occur when electromagnetic waves are confined within a microdroplet, leading to constructive interference and resonant enhancement of certain wavelengths. These resonances can appear as sharp peaks in both elastic and inelastic light scattering spectra, and they are highly sensitive to changes in droplet shape, size, and refractive index²⁷. Although an all-optical technique is inherently appealing, in this instance, the analysis of measurements with such an instrument is, in fact, very complicated. Challenges include the concurrent heating that occurs as the beam power is varied during the measurement process, and the strong non-linear dependence of deformation on beam power due to the trapping laser exciting MDRs. Furthermore, the careful alignment of the counter-propagating beams is also necessary for accurate surface tension measurements and can be tedious⁴⁶.

In this study, we apply a uniform electric field to exert stress on droplets, causing them to stretch. This phenomenon, often referred to as electrodeformation, allows us to directly measure the surface tension. In our experiments, we achieve these measurements on single droplets by optically trapping them between two closely spaced electrodes, as shown in Fig. 1a–c. For aqueous droplets in air, the surface tension is typically on the order of tens of mN m⁻¹. As a result, the deformation of a micron-sized droplet will be only a few nanometers, even as the electric field strength between two electrodes approaches the dielectric strength of air and causes dielectric breakdown. Therefore, deformation cannot be measured with optical imaging. Instead, we use MDR splitting, which occurs when a spherical droplet transforms into a prolate spheroid under the stress of the electric field. The electrodes and the droplet are contained within an relative humidity (RH)-controlled cell, allowing us to analyze how surface tension varies with water activity (fractional RH).

Fig. 1. Experimental setup for surface tension measurements of optically trapped microdroplets in an external electric field.

a Schematic of the instrument used to perform surface tension measurements on individual microdroplets. b Rendering of the trapping cell, including the two counter-propagating beams and the two electrodes that are connected to the high-voltage power supply. The inset in (b) is an image of an optically trapped microdroplet between two electrodes. c Shows an image at 10 × magnification of a microdroplet optically trapped between the two electrodes in the cell. Illustrations of a single optically trapped droplet (d) without an external electric field and (e) with an external electric field.

Using this instrument, we measure the surface tension as a function of water activity in micron-sized droplets. We examine aqueous solutions of sodium chloride and ammonium sulfate, the ions of which make up a major percentage of sea salt⁴⁷ and thus significantly contribute to the composition of atmospheric aerosols, particularly in the marine boundary layer. We also consider aqueous solutions of two dicarboxylic acids: glutaric acid and maleic acid, both of which have been used extensively in atmospheric chemistry research as surrogates for more complex organic aerosols^48–50. Additionally, we examine an aqueous mixture of glutaric acid and ammonium sulfate. Finally, we perform measurements on aqueous citric acid, which has been used as a model system for high-viscosity oxidized organic aerosol material^51–53. The majority of the measurements presented here are performed at RHs where the droplet is supersaturated, and there are often no previous measurements. Furthermore, in the case of citric acid, we measure the surface tension of droplets whose viscosity is predicted to be over 10³ Pa s.

Results

Electrodeformation of single aerosol particles

A single droplet was optically trapped between closely spaced electrodes within an RH-controlled cell, as depicted in Fig. 1b, c. A uniform electric field was then applied across the droplet. The study of how droplets, ranging from microns to millimeters in size, deform under the influence of external electric fields has been thoroughly explored through both theoretical and experimental investigations for liquid droplets dispersed within another liquid (e.g., an oil-oil emulsion), droplet streams, or a liquid droplet on a surface^54–63. The presence of an electric field generates stress at the boundary between immiscible media due to the discontinuity in electric field components at the interface. In the case of a spherical liquid droplet, a balance is established between the electric stress and the product of surface tension and curvature. This equilibrium results in the droplet being deformed from its original spherical shape.

In experiments performed here, the electric field between the electrodes causes the optically trapped droplet to deform into a prolate spheroid, stretching it in the direction of the electric field, as depicted in Fig. 1d, e. The deformation, D, is defined as

$$D=\frac{R_{\mathrm{p}}-R_{\mathrm{e}}}{R_{\mathrm{p}}+R_{\mathrm{e}}},$$ 1

where, R_e and R_p represent the semi-minor and semi-major radii of the deformed droplet, respectively. Deformations will be small: for a droplet with a radius of 5 μm being held in our setup, even at a voltage of 600 V, the semi-minor and semi-major radii will typically change by only  ≈10 nm and  ≈20 nm, respectively. Such changes are not observable using optical imaging. However, MDRs that appear in the Raman spectra of single microdroplets are sensitive to nanoscale deformations, which result in an observed splitting of MDR peaks (Fig. 2). This phenomenon can be utilized to accurately measure droplet deformation and is discussed in the next section along with the framework for its analysis. During a typical measurement, the voltage applied to the electrodes is increased in a stepwise manner over a period of about one minute (Fig. 3a). MDR splitting results in each MDR peak becoming a band containing two peaks at either edge (e.g., Fig. 2d, e). For each observed MDR, these peaks are tracked over time (Fig. 3b).

Fig. 2. Comparison of theoretical and experimental results for mode splitting in a deformed droplet.

a Measured Raman spectra of a single aqueous citric acid droplet at 0 V (undeformed) and 600 V (deformed). Compare two MDR peaks from (a) to both calculated Raman spectra and resonance positions from Eq. (4) for both the undeformed (b, c) and deformed (d, e) cases. Source data are provided as a Source Data file.

Fig. 3. Typical Raman spectra and analysis during the electrodeformation of an optically trapped droplet.

Here, an aqueous maleic acid droplet is held in a cell fixed at 72% RH and the undeformed radius, R_o, of the droplet is 4.266 μm. a The stepwise manner in which the applied voltage between the electrodes is changed. The maximum voltage of 600 V corresponds to an applied electric field strength of 2.7 × 10⁶ V m⁻¹. b Measured Raman spectra. c Difference between these two peaks in resulting MDR bands, Δλ, determined from the spectra in (b). d The corresponding semi-minor radius, R_e, and the semi-major radius, R_p, of the deformed droplet. Source data are provided as a Source Data file.

Once the deformation is determined from measured MDR splitting, surface tension is found by treating aqueous droplets as leaky dielectrics suspended in a medium with a much lower conductivity (i.e., air). The electric capillary number, Ca_E, is a dimensionless number used to characterize the relative effect of electric stress (the applied electric field strength, E) to the capillary forces (the surface tension γ of the liquid droplet). It is defined as⁵⁹

$${\mathrm{Ca}}_E=\frac{{\epsilon }_{\mathrm{m}}{\epsilon }_0{R}_{\mathrm{o}}{E}^2}{\gamma },$$ 2

where ε₀ is the permittivity of free space, ε_m is the relative permittivity of the surrounding medium, and R_o is the characteristic length scale, in this case the radius of the undeformed droplet. For an aqueous droplet in air within an electric field, an approximate relationship between Ca_E and D, which is accurate for small deformations, is D = (9/16)Ca_E⁵⁹. With Eq. (2), this yields

$$D=\frac{9}{16}\frac{{\epsilon }_{\mathrm{m}}{\epsilon }_0{R}_{\mathrm{o}}{E}^2}{\gamma }.$$ 3

Therefore, if E, R_o, and D are known, then γ can be determined using Eq. (3).

Cavity-enhanced Raman spectroscopy of single particles

The MDRs of the trapped droplet are characterized by two sets of orthogonal polarizations, transverse electric, ${\mathrm{TE}}_{lm}^{\nu }$, and transverse magnetic, ${\mathrm{TM}}_{lm}^{\nu }$, where l is the mode number, m the azimuthal mode number ( − l ≤ m ≤ l), and ν the mode order. In the case of a spherical cavity, the 2l + 1 azimuthal states are degenerate due to the spherical symmetry, so the modes can be labeled ${\mathrm{TE}}_l^{\nu }$ and ${\mathrm{TM}}_l^{\nu }$. When exposed to a uniform electric field, the droplet is deformed into a prolate spheroid whose major axis is parallel to along the electric field lines. This deformation lifts the azimuthal degeneracy of the MDRs, and, due to the symmetry of the spheroid, the MDRs split into l + 1 azimuthal states. For D ≪ 1, which will be valid here, perturbation theory⁶⁴ shows that the resulting l + 1 modes, with wavelengths λ_lm, can be related to the degenerate mode in the spherical cavity, ${\lambda }_l^{\mathrm{Mie}}$, by

$$\frac{1}{{\lambda }_{lm}}=\frac{1}{{\lambda }_l^{\mathrm{Mie}}}\left[1-\frac{D}{3}\left(1-\frac{3m^2}{l\left(l+1\right)}\right)\right].$$ 4

Figure 2 a shows an example of measured MDR peaks in Raman spectra for an undeformed (0 V) and deformed droplet (600 V, corresponding to an applied electric field strength of 2.7 × 10⁶ V m⁻¹). In Fig. 2b–e, the measured intensity of the ${\mathrm{TM}}_{42}^1$ and ${\mathrm{TE}}_{42}^1$ modes are compared to simulated spectra at 0 and 600 V. This was done using a classical electromagnetic model of Raman scattering⁶⁵, summarized in the Suppl. Note 1. In Fig. 2b, c, the measured peaks are well approximated by the single Lorentzian owing to the degeneracy of the azimuthal states. In In Fig. 2d, e, the model shows that the change in the lineshapes, resulting from the loss of degeneracy, agree well with the measured lineshapes. MDR wavelengths from Eq. (4) are indicated by tick marks here; when examined along with the Raman scattering simulations, the calculations confirm that the two dominant modes in the measurements correspond to m = 0 and m = l.

Surface tension measurements

Figure 3 shows a typical single droplet electrodeformation experiment performed at a fixed RH. The voltage between the two electrodes is increased in a stepwise manner from 0 to 600 V over a period of just over a minute (Fig. 3a). Raman spectra from the optically trapped droplet, held between the two electrodes, are collected during this time (Fig. 3b). As the voltage rises, individual MDR peaks in the Raman spectra split. As discussed in the previous section, the resulting bands are dominated by two peaks associated with the m = 0 and m = l modes of a prolate spheroid. For each MDR, the difference between these two peaks, Δλ, is taken from the Raman spectra (Fig. 3c) and used to determine the major and minor axes of the deformed droplet through Eq. (4) (Fig. 3d). Fitting Eq. (3) with these measurements allows the surface tension to be found as it is now the only unknown parameter. The procedure can be repeated at different RHs to determine how the surface tension varies with water activity and associated concentrations of a solute.

During the electrodeformation experiment shown in Fig. 3, the droplet is subjected to a uniform electric field of up to 2.7 × 10⁶ V m⁻¹. Any heating caused by the electric field appears to be negligible, as the droplet volume remains constant throughout the measurement (e.g., no shrinking due to heating as the voltage is increased). This is in contrast to our previous optical deformation experiments⁴⁵, where electromagnetic heating through absorption at optical wavelengths caused significant size changes as the beam power was varied during the measurement. We also observed that optical deformation was negligible compared to electrodeformation in our experiments, as the measured surface tension was not affected by varying the trapping beam power (i.e., from 100 to 500 mW).

Figure 4 shows surface tension measurements for six aqueous systems determined using electrodeformation. Vertical lines in each panel indicate the water activities at which reported solubility limits occur^66,67. Below these values (or, on the concentration scale, above these values), the solution becomes supersaturated. Most supersaturated measurements can only be compared to literature values near the solubility limit because crystallization below this point limits bulk methods. Conversely, accurate measurement of RH in our trapping cell are challenging above water activities of 0.85 due to limitations of the capacitance sensors employed. However, for aqueous sodium chloride, aqueous citric acid and the aqueous glutaric acid and ammonium sulfate mixture, the solubility limit occurs at a lower water activity, and our measurements show good agreement with bulk techniques^9,68–71 where water activity overlap occurs. For the other three systems, our values trend towards those from bulk measurements^{9,68,70,72–74} at high water activities. For aqueous sodium chloride, existing surface tension measurements from holographic optical tweezers⁹ agree well with our measurements in the supersaturated regime. Additionally, AFM has been used to measure the surface tension of both supersaturated aqueous glutaric acid and maleic acid⁴², though these measurements were conducted at higher water activities than ours. Overall, Fig. 4 shows that surface tension measurements at water activities significantly lower than previously possible are achievable with single droplet electrodeformation.

Fig. 4. Surface tension measurements for various aqueous systems.

a Sodium chloride, (b) citric acid, (c) ammonium sulfate, (d) glutaric acid, (e) maleic acid, and (f) ammonium sulfate and glutaric acid (1:1 molar ratio). Measurements from other sources are also included^9,42,68–74. Gray vertical dashed lines indicate reported solubility limits^66,67. In (a–e), the Connors-Wright surface tension equation^80,97 was used to fit either bulk data alone (dotted lines) or both bulk data and the measurements taken in this study (dashed lines). Predictions from a thermodynamic model⁸³ are shown in all panels (solid lines). The concentration and mole fraction scales in (f) refer to either glutaric acid or ammonium sulfate individually, rather than to their combined amounts. For results from this study, error bars represent standard errors from four independent experiments. Source data are provided as a Source Data file.

Discussion

The results in Fig. 4 demonstrate that aerosol electrodeformation enables surface tension measurements of solute concentrations previously inaccessible by both bulk techniques and other single-particle methods, such as AFM and holographic optical tweezers. This ability to study highly supersaturated systems is shown across all six aqueous systems; for instance, measurements at concentrations more than double the solubility limit are possible for maleic acid. Such measurements were not possible with previous methods due to constraints like viscous damping or solubility limitations. This capability to access metastable states not only improves our general understanding of physicochemical phenomena but also has important atmospheric implications. Several large-scale atmospheric models account for aerosols in metastable states by incorporating the metastable branch within their thermodynamic frameworks. For example, the global aerosol climate model GLOMAP treats all inorganic aerosols as aqueous, implying an assumption of the metastable state⁷⁵. The Community Multiscale Air Quality (CMAQ) model explicitly performs inorganic thermodynamic equilibrium modeling using the metastable branch assumption⁷⁶. Similarly, the Weather Research and Forecasting Model coupled with Chemistry (WRF-Chem) determines whether aerosols are on the metastable or stable branch based on air mass history¹³. The GEOS-Chem 3-D chemical transport model employs the ISORROPIA II solver, which considers both the metastable and stable aerosol branches⁷⁷, and its latest version uses the Heterogeneous Parallel (HETP) solver for metastable branch computations⁷⁸. Moreover, a detailed overview in ref. ⁷⁹ indicates that many regional and global atmospheric chemistry models account for, or even assume, a metastable aqueous aerosol state by default in their water uptake and gas-particle partitioning assumptions. Therefore, our capability to access metastable states experimentally enables data-backed improvements of the aerosol representations in such atmospheric models.

Semi-empirical surface tension models find use in many areas of fundamental and applied research. Many of these models explicitly incorporate the surface tension of pure solutes as a parameter⁸⁰. Those that do not still implicitly account for it, provided their aim is to accurately determine surface tension at high solute concentrations. In the atmosphere, many aqueous particles are highly concentrated systems that exist in subsaturated environments (RH < 100%) where metastable states are ubiquitous²⁵. For the systems in Fig. 4d, e, bulk measurements are limited to solute mole fractions between 0 and 0.2, whereas the methodology used here extends this range up to 0.8. As evidenced by the best fits to the Connors-Wright surface tension equation shown in Fig. 4, extrapolating beyond the solubility limit from bulk measurements leads to inaccurate predictions of the surface tension at supersaturated concentrations. Although not shown here, other commonly used semi-empirical surface tension models, such as the Szyszkowski-Langmuir equation, result in comparable inaccuracies. Therefore, in addition to expanding the range of experimentally available data, the measurements presented here highlight the importance of supersaturated measurements in obtaining accurate parameters for widely used semi-empirical surface tension models. This also includes systems with more than two components, such as the aqueous organic-inorganic system shown in Fig. 4f. These systems are common in the atmosphere but remain an enormous challenge for semi-empirical surface tension models⁸¹.

First-principle models for surface tension prediction, such as those based on thermodynamics^82,83 or statistical mechanics^84,85, obviously also require accurate measurements for validation. In this context, the availability of direct surface tension measurements over a wide concentration range is very useful to constrain adjustable parameters in predictive thermodynamic models more reliably and to identify systems over a range of compound classes that may aid in the development of improved models. In Fig. 4, a current thermodynamic model for size-dependent surface tension⁸³ is compared across all of the measurements from this study. The comparison shows good agreement with the measurements for aqueous glutaric acid and citric acid, while indicating notable discrepancies with the other four systems. In the latter cases, the model–measurement deviations allow us to identify and understand inaccuracies in the chosen thermodynamic model, specifically the assumed pure-component surface tension values of the solute and inaccuracies in the predicted water content for a set bulk water activity.

High viscosity, submicron-sized particles or phases thereof are a significant part of atmospheric aerosol, especially at lower tropospheric temperatures and lower RH. The transition from a liquid to a semi-solid occurs at viscosities around 10² Pa s, and all three measurements of aqueous organic compounds exceed this threshold⁸⁶. In the case of aqueous citric acid, surface tension measurements were made at viscosities exceeding 10³ Pa s. This is several orders of magnitude larger than the operational limits of other single-particle levitation techniques, which are limited to  < 10⁻² Pa s⁹. Above this limit, viscous forces begin to dampen oscillations. Furthermore, this viscosity is also greater than the upper limit for AFM techniques, which is 10² Pa s⁴⁰, where viscous forces start to significantly influence the measured retention force. Therefore, our citric acid data likely represent the first surface tension measurements on semisolid aerosol particles. We can also qualitatively confirm the non-liquid phase state of the particle by bringing it into contact with the electrode post-measurement (Supplementary Fig. 1). Upon doing so, the particle retains its shape and does not break apart and spread in the manner characteristic of liquid (low-viscosity) particles. Finally, surface tension measurements of higher viscosity droplets are possible, although the viscous relaxation time of the droplet must be shorter than the longest feasible experimental duration. In practice, this duration is likely a few hours, which places an upper limit on the droplet viscosity of 10⁷ Pa s for a droplet with a radius of a few micrometers and a surface tension on the order of tens of mN m⁻¹.

Methods

Optical trapping and manipulation of single aerosol particles

A dual-beam optical trap is used to suspend a single aqueous droplet in a RH-controlled cell. The diagram in Fig. 1a illustrates the experimental setup. Polarized light emitted by a λ = 532 nm OPSL laser (Verdi G5, Coherent Inc., US) undergoes beam separation as it passes through a beam displacer (Calcite crystal, 4 mm beam separation, THORLABS, US), dividing it into two beams with orthogonal polarizations of equal power. Subsequently, a knife-edge right-angle prism mirror (Ag coated, THORLABS, US) directs one beam to the right and the other to the left. These beams are expanded using a beam expanding system comprising two lenses with focal distances of 15 and 25 cm, respectively, to ensure the necessary overfilling of the back aperture of the objective lens. Two long-working distance objective lenses (50 × , NA = 0.42, Plan Apo NIR B, Mitutoyo, Japan) ultimately capture and focus these beams into a single point within the trapping cell.

The trapping cell is shown in Fig. 1b. Its body is constructed from polyethylene terephthalate (PET), a durable dielectric material with low electrical conductivity and resistance to all chemicals used in this study. The RH within the cell is regulated by two inlets, which facilitate the flow of RH-controlled air across the cell. A third inlet enables the introduction of aerosols (discussed below). The cell also contains two collinear electrodes (AMTOVL) whose tips face each other. These electrodes are used to apply a strong electric field in order to deform trapped droplets. The electrodes, composed of nickel-plated copper, are first precisely sharpened and then polished using a fine-grade (3 μm) diamond polishing pad (Sigma Aldrich) on a rotating stage. This polishing procedure is described in detail in the Supplementary information. Tip diameters are approximately 280 μm. In the cell, the electrodes are positioned to ensure the shared focal point of two optical beams falls within the small gap between their tips, allowing the trapped droplet to be held between them. To generate a strong electric field between the electrodes, it is necessary that their separation be as small as possible without interfering with the optical trap. Here, the tip-to-tip separation is maintained at approximately 220 μm. The electrodes are connected to a variable high-voltage source (HP 6516A) of up to 600 V. Figure 1c shows an image of a droplet trapped between the electrodes. The operation of the electrodes to apply an electric field to trapped droplets is described in the Results section.

After the electrodes and trapping beams are properly positioned and aligned, droplets are introduced into the cell with an aerosol generated from aqueous solutions using a medical nebulizer (VIOS – aerosol delivery system with PARI LC Sprint, Mexico). The aerosol plume was directed into the cell via tubing that was attached to the nozzle of the nebulizer. A single droplet was then trapped at the shared focal point of the two trapping beams. The radii of trapped droplets are typically between 3 and 6 μm. The laser beam power was set around 300 mW during trapping and subsequent measurements (accounting for reflective losses prior to reaching the droplet). Across multiple experiments and during nebulization associated with the trapping process, it is likely that droplets came into contact with the electrode tips. Although this contact could potentially alter the electric field within a few micrometers of the electrode surface, the surface tension values retrieved in all experiments remained within the same uncertainty range across all measurements, indicating that the applied electric field at the optical trap location was unaffected. Another concern with the single droplet electrodeformation method is that the measured surface tension may be reduced due to surface charging, with the effect being proportional to the square of the applied voltage⁸⁷. However, since no size changes were observed during voltage increases (e.g., Fig. 3), no surface tension reduction could have occurred, indicating that the applied electric field and/or the charge density on the trapped droplet are likely too small for this effect to be significant.

The nebulized aqueous solutions each contained a single solute: sodium chloride (99%, ACP Chemicals, Canada), ammonium sulfate (≥99%, Sigma-Aldrich, France), citric acid (100%, Fisher Chemicals, US), glutaric acid (99%, Acros Organics, China), or maleic acid (99%, Acros Organics, Spain). All solutions were prepared with deionised water and were saturated, a condition chosen because it resulted in larger droplets being trapped. The RH and temperature were monitored by a sensor (SHT75x, Sensirion) positioned  ≈5 mm from the trapped droplet. For the measurements in Fig. 4, the temperature was 298 K for panels (a), (b), (d), and (e), and 295 K for panels (c) and (f). In panel (f), the solubility limit and bulk surface tension values for an aqueous solution of ammonium sulfate and glutaric acid (in a 1:1 molar ratio) were measured in our lab, with the latter determined using the pendant drop method.

An illumination system projects blue light onto the optically held droplet, while an imaging system captures a microscopic image of the droplet, as shown in the inset of Fig. 1. The trapped droplet scatters both elastic and inelastic (Raman) light. Raman scattering from the droplet was collected using one of the objectives that focuses the trapping laser. The scattered light, containing polarization components of both transverse electric (TE) and transverse magnetic (TM) modes, was then passed through a long-pass dichroic mirror (DMLP550R, THORLABS, US) and then directed towards and coupled into a spectrometer (IsoPlane SCT-320, Teledyne Princeton Instruments, US). The optically trapped microdroplet supports strong MDRs and these appear as narrow peaks in the measured Raman spectra, i.e., cavity-enhanced Raman scattering (CERS). By analyzing the measured MDR peak positions with the MRFIT code^88,89, we can determine the size (±1 nm) and refractive index (±0.0005) of the optically trapped microdroplet.

Measuring aerosol deformation

Deformation is determined by measuring the positions of the two peaks that appear on the sides of MDR band after an electric field is applied to a droplet. An example of this splitting is shown in Fig. 2. Where, at 0 V, there is no applied electric field, and the trapped droplet is assumed to be spherical. Each labeled MDR assumes a Lorentzian lineshape. At an applied electric field strength of 2.7 × 10⁶ V m⁻¹ (600 V), mode splitting causes the MDR lineshapes to distort from the typical Lorentzian, giving them two distinctive peaks instead of one. From (4), the leftmost peaks are attributed to modes with m = l, whereas the rightmost peaks correspond to modes with m = 0. At 0 V, MRFIT⁸⁹ can be used to determine the radius and refractive index of the trapped droplet as it is spherical. When the droplet is deformed into a spheroid (e.g., at 600 V in Fig. 2), the positions of the two observed peaks, λ_l0 for m = 0 and λ_ll for m = l, can be used with (4) to generate two equations with the two unknowns ${\lambda }_l^{\mathrm{Mie}}$ and D. For l ≫ 1, the solutions can be approximated as

$${\lambda }_l^{\mathrm{Mie}}=\frac{3{\lambda }_{ll}{\lambda }_{l0}}{{\lambda }_{l0}+2{\lambda }_{ll}}\mathrm{and}D=\frac{3\left({\lambda }_{l0}-{\lambda }_{ll}\right)}{{\lambda }_{l0}+2{\lambda }_{ll}}.$$ 5

The value for ${\lambda }_l^{\mathrm{Mie}}$, determined using this approach, can be fit using MRFIT to determine the undeformed radius, R_o, of the droplet, along with the refractive index.

Determining aerosol composition

The Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) thermodynamic model^90–93 was used to determine the composition of single droplets, as well as their viscosity, assuming equilibrium with the trapping cell’s RH. AIOMFAC can calculate water activity as a function of either the mole or mass fraction of solutes in an aqueous system. The composition that yields a water activity value corresponding to the surrounding RH, normalized to a fraction (RH/100%), is considered to be the equilibrium composition. Every system studied here is binary (a single solute + water) or has the ratio of solutes fixed by a known ratio. Therefore, the approach to determining the droplet composition involves solving a univariate root-finding problem with one variable, such as the mass fraction of the solute.

Many surface tension measurements in the literature are reported as a function of molar concentration. It is necessary to convert these measurements to a mass or mole fraction scale in order to compare them with the measurements taken here. For an aqueous solution with only a single solute, α, the relationship between mass fraction, w_α, and molar concentration c_α, is given by c_α = w_αρ/M_α, where ρ is the density of the solution and M_α is the molar mass of solute α. To determine ρ, tabulated aqueous density data was parameterized as a function of mass fraction, i.e., $\rho =a{w}_{\alpha }+b{w}_{\alpha }^2$, where a and b are parameters of best fit to the data. For inorganic solutes, data was taken from ref. ⁶⁷. For maleic acid and glutaric acid, data from ref. ⁹⁴ and ref. ⁹⁵ were used respectively. For citric acid, no fitting was necessary as the parameterization from ref. ⁵² was applied.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

V.S. and T.C.P. conceived the study and designed the experiments. T.C.P. supervised the study. V.S. conducted all experiments. V.S., B.V., and T.C.P. analyzed the measurements. J.M. and S.B.S. assisted with the design and operation of the electrode system. R.S. and A.Z. performed surface tension model calculations. V.S., B.V., and T.C.P. wrote the manuscript, with edits from A.Z. All authors read and approved the revised manuscript.

Peer review

Peer review information

Nature Communications thanks Alexei Tivanski and the other, anonymous, reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data that support the findings of this study are available from the corresponding authors upon request. Source data are provided with this paper.

Code availability

The MRFIT source code is available at https://web.meteo.mcgill.ca/~tpreston/code.html. AIOMFAC can be run online at http://www.aiomfac.caltech.edu, and the source code is available from Zenodo⁹⁶.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-54106-3.