Acoustic levitation with polarising optical microscopy (AL-POM): water uptake in a nanostructured atmospheric aerosol proxy †

Laboratory studies on levitated particles of atmospheric aerosol proxies have provided signi ﬁ cant contributions to our understanding of aerosol processes. We present an experimental method combining acoustic levitation with polarising optical microscopy (AL-POM) to probe optically birefringent particles, such as the nanostructured surfactant atmospheric aerosol proxy studied here. Birefringent particles were subjected to a step increase in humidity. A decrease in birefringence was measured over time as a result of a nanostructure change, con ﬁ rmed by complementary synchrotron X-ray scattering. A multi-layer water uptake model was created and ﬁ tted to the experimental data, revealing a water di ﬀ usion coe ﬃ cient increase by ca. 5 – 6 orders of magnitude upon phase transition. This has implications for the timescale of water uptake in surfactant-containing aerosols and their atmospheric lifetimes. This experimental setup has strong potential to be used in conjunction with other levitation methods and in di ﬀ erent contexts concerning birefringent materials such as crystallisation.


Introduction
Atmospheric aerosols facilitate cloud droplet formation 9 and have a signicant impact on urban air quality. 10The organic fraction of atmospheric aerosols can include a diverse range of molecules from alkanes to harmful polycyclic aromatic hydrocarbons (PAHs).This organic composition varies over time and between environments. 11,12tty acids are organic surfactants commonly observed in cooking and marine aerosol emissions. 13,14Organic surfactant material affects cloud droplet nucleation by decreasing surface tension. 157][18] The diffusion of small molecules through these phases is known to vary considerably due to the variable viscosities of these phases, compared with the free fatty acid. 19Water uptake and diffusion through viscous particles has been an important topic of study due to the implications for cloud droplet nucleation. 1,4,20We have previously shown that unsaturated fatty acid self-assembly can decrease reactivity with ozone by ca. an order of magnitude and that this could lengthen the atmospheric chemical lifetime by days. 21,22urfactant molecule self-organisation and effects on water uptake in aerosols have much more general signicance in different medical and commercial contexts.Inhaled therapeutic aerosols may deliver surfactants as active ingredients (as in the treatment of infant respiratory distress syndrome) 23,24 or excipients, where they effect hygroscopicity. 25Hygroscopic growth and water uptake in inhaled drugs affects efficient delivery to the lungs. 26,27Hygroscopicity and deliquescence of industrial surfactants in cleaning products causes caking, leading to processing problems. 28Surfactants also effect efflorescence of salts within aerosols; in this way surfactant additives alter delivery of ionic active ingredients in agricultural sprays, 29 and lung surfactants in exhaled respiratory aerosols likely affect water uptake and salt efflorescence, which has been suggested as a mechanism for humidity-dependent viability of airborne pathogens. 30e present a new experimental approach to following water diffusion through LLC phases by coupling acoustic levitation with polarising optical microscopy (AL-POM).We followed the change from an optically birefringent (lamellar) to nonbirefringent (close-packed inverse micellar) phase during humidication in a controlled gas-phase environment.A multilayer water uptake model was created to reveal how water diffusivity changes during humidication, depending on the fatty acid molecular arrangement.

Preparation of the fatty acid aerosol proxy
Oleic acid (Sigma-Aldrich, 90% purity) and sodium oleate (Sigma-Aldrich, 99% purity) were dissolved as 10 wt% solutions in methanol, with gentle heating at ∼50 °C until fully dissolved.Equal volumes of each solution were mixed to afford a 1 : 1 wt ratio solution of oleic acid and sodium oleate.This mixture was used throughout this study and is analogous to the mixture used for kinetic experiments on this proxy system. 21oustic levitation-polarising optical microscopy (AL-POM) Acoustic levitation 2,5-8 of the fatty acid aerosol proxy was achieved by injecting ∼20 mL of the proxy solution into the node of a modied commercial acoustic levitator (tec5, Oberursel, Germany) and allowing the solvent to evaporate, leaving behind the levitated sample.Multiple droplets can be levitated simultaneously. We asumed that the droplets were in thermal equilibrium with the surrounding atmosphere.This levitator has a xed transducer frequency (100 kHz) and variable HF power (0.65-5 W).A concave reector was positioned above the transducer and the transducer-reector distance (typically 20-30 mm) was adjusted with a micrometre screw.The levitator was contained in a bespoke 3-D-printed chamber with ports to allow gas ow and viewing windows for optical and X-ray experiments (Fig. 1).
A cross-polarised optical system was established by attaching two light polarising lters on two opposing viewing windows of the levitation chamber.These lters were aligned in order to extinguish the light passing through both lters.An LED lamp was used as the light source.Only birefringent material placed between these lters would allow light to pass through, allowing detection of a birefringent levitated particle (see images in Fig. 1).A macroscope with a digital camera attached (Leica MC190 HD) was used to take images of the levitated particles from the side opposite to the incoming light.One image was taken every minute.A magnication of ×3.2 was used and the working distance was ∼100 mm.Particle size was determined by measuring the diameter of the particle in pixels, a graticule was used to calibrate the particle size in physical units (mm).Particles were 165-260 mm in diameter.Particles tended to disintegrate into this diameter range aer injection.The detailed image analysis procedure is described in the ESI.† For higher resolution visualisation, droplets were imaged with a horizontal tube microscope comprising a long working distance innity corrected objective (Mitutoyo 5X Plan Apo), tube lens (Mitutoyo MT-1) and CMOS camera (Basler ACA1920-155uc) yielding a resolution of 1.2 mm per pixel.A single-colour cold visible mounted green LED (530 nm Thorlabs M530L4) tted with a collimation adapter (Thorlabs COP1-A) was used to illuminate the droplets.Cross-polarised imaging was achieved by mounting two dichroic lm polarisers (Thorlabs LPVISE100-A); one mounted between the LED and the LED collimator and the other between the tube lens and the camera.The axes of the polarisers were oriented orthogonally to one another which, in the absence of a birefringent sample, yielded minimum light transmission.
Humidity was controlled using a bespoke Raspberry Pi (RPi) mini-computer system.This system controlled an air pump which pumped air through a glass humidier.A humidity sensor (DHT22) was placed inside the levitation chamber and read by an Arduino mini-computer, which fed into the RPi humidity control soware.For all experiments the starting relative humidity (RH) was ∼50%.The levitation chamber was humidied to 90% RH for each experiment.The accuracy of the humidity sensor was 2-5% RH between 0-100% RH, as quoted by the manufacturer.

Acoustic levitation small-angle X-ray scattering (SAXS)
Small-angle X-ray scattering (SAXS) probes samples on the nanoscale to reveal how molecules aggregate together. 31The nanostructured sample is illuminated by X-rays, some of which are scattered.Plots of scattered intensity vs. q (momentum transferrelated to scattering angle) allow for determination of which (if any) arrangement is present in a sample by identifying Bragg scattering peak positions. 32AXS measurements were carried out on levitated particles on the I22 beamline at the Diamond Light Source synchrotron X-ray facility. 33Levitated particles were exposed to X-rays of 12.4 keV energy in 1 s frames using a Pilatus P3-2M detector.The size of the X-ray beam used was ∼22 mm × 19 mm.We assume that any droplet temperature rise associated with X-ray irradiation is negligible due to the small beam in comparison to the droplet and the short exposure time.

Multi-layer water uptake model
We have devised a multi-layer approach to spatially and temporally resolve the uptake and diffusion of water through a self-assembled particle, incorporating changes in diffusivity caused by water content-dependent phase changes.This modelling approach is similar to those which resolve aerosol and surface and bulk chemistry [34][35][36][37][38] and ones which consider water uptake into viscous particles. 4,20,39The multi-layer model is described in detail in the ESI †.
Water diffusion was treated as composition-dependent and is related to the mole fraction of lamellar phase in layer I (f lam,i ) by a Vignes-type relationship: 40 Where D b,w,lam and D b,w,mic are the diffusivities of water in the lamellar phase and close-packed inverse micellar phase, respectively.
We could not directly determine D o w in these phases with this experiment, though there have been NMR-based diffusion measurements on similar systems. 41We use this literature value of D o w in order to place the model results in a physically meaningful context (see later).
The model parameters were optimised using a differential evolution algorithm available in the SciPy package in Python. 42,43The initial population of parameter sets were sampled using a latin hypercube, which ensures the initial population evenly covers the available parameter space.The resulting population was evolved in parallel over 20 cpu cores.This approach to global optimisation is similar to that of Berkemeier et al., who used an initial Monte Carlo sampling method. 44The number of model layers was adjusted to maintain the same spatial resolution for each particle (i.e.200 layers for the 220 mm diameter particle; 236 layers for the 260 mm particle).

Identication of surfactant arrangements at low and high humidity
In order to conrm which molecular arrangements were present at room (∼50% RH) and high (∼90% RH) humidity, samples were levitated and SAXS patterns were taken at a synchrotron X-ray source. 33Fig. 2a shows the 2-D scattering pattern from the top edge of a levitated particle ∼3 min aer levitation at room humidity.This scattering pattern corresponds to the lamellar phase.This lamellar phase is highly oriented due to the lack of a diffuse scattering ring for each lamellar Bragg peak (see ESI † for a scattering pattern from a randomly oriented lamellar phase showing diffuse scattering rings).This kind of surface orientation has been observed previously in levitated droplets of LLC phases 3 and in nanometre-scale lms of this system. 45iffusion is highly anisotropic in the lamellar phase. 46,47If lamellar bilayers are highly aligned parallel to the droplet surface (as observed here), water uptake is likely to be affected.This justies the explicit separation of water uptake into the lamellar and inverse micellar phase in the surface layer of the model (see ESI †).
At high humidity, we observed the ordered inverse micellar phase with Fd3m symmetry aer ∼10 min (Fig. 2b).The close- packed inverse micelles present in this phase have varying sizes and restricted water mobility. 41,48he close-packed inverse micellar phase is isotropic and is not observable by POM.This is in agreement with the levitation-POM humidity experiment where an optically anisotropic (lamellar) phase is transformed into an optically isotropic phase (close-packed inverse micellar) (compare typical images in Fig. 1).

Following water uptake during humidication
We levitated two particles of 220 and 260 mm diameter simultaneously and followed their respective water uptakes with the levitation-POM experiment.A single set of optimised model parameters t reasonably well with these data (Fig. 3a).A separate model optimisation using the data from a 190 mm particle returned optimised parameters which were similar to those obtained by the simultaneous particle optimisation (Fig. 3b and c).This set of parameters t well to both the 190 and 165 mm particles, which were levitated in separate experiments.Optimised model parameters are presented in the ESI.† The water uptake model did not account for any intermediate phases that could have formed when transitioning from the anhydrous lamellar to the close-packed inverse micellar phase.It is possible that a disordered (rather than close-packed) inverse micellar phase forms as an intermediate phase. 49This has been observed in experiments on a crystalline form of this proxy. 50The less viscous nature of the disordered inverse micellar phase, which is also non-birefringent, could account for some of the difference between the model ts and experimental data.
The diffusion coefficient of water in the oleic acid-sodium oleate close-packed inverse micellar phase has been experimentally determined to be 2.4 × 10 −8 cm 2 s −1 . 41We used this to convert model diffusion coefficients to physically meaningful values.The water diffusion coefficient in the lamellar phase was determined from the model t as 7.0 × 10 −14 cm 2 s −1 .This puts water diffusivity in these observed phases in the semi-solid regime. 51This value was obtained from the set of model parameters tting to the 220 and 260 mm diameter particles (Fig. 3a), which were levitated simultaneously and had the most experimental measurements to t to.
Water diffusion through the anhydrous lamellar phase is ca.5-6 orders of magnitude slower than in the close-packed inverse micellar phase, demonstrating the sensitivity of water diffusion to particle nanostructure and viscosity.Note that the lamellar phase studied here is anhydrous and not a lyotropic system (i.e. it is without a solvent).Without water acting as a plasticiser, anhydrous lamellar bilayers are more restricted in their movement, increasing their rigidity and viscosity. 52The spacing between fatty acid chains in this lamellar phase has been measured to be 0.441 nm. 21This is within double the molecular diameter of water (ca.0.27 nm). 53The steric restriction imposed by the spacing between fatty acid alkyl chains helps explain why water diffusion through the anhydrous lamellar phase is so much slower than in the close-packed inverse micellar phase.
A steep water diffusion gradient is established within the particle during humidication (Fig. 4a).As more water is taken up, the lamellar phase transitions to the close-packed inverse micellar phase, affecting D w via the Vignes-type relationship described earlier.
Particle water activity (a w ) and lamellar phase mole fraction (f lam ) follow a similar trend, highlighting the link between water content, phase transition and water diffusivity (Fig. 4b and c).Acoustic levitation does not allow us to directly determine the mass or volume of water in this case.Time-resolved size information is sacriced in AL-POM due to the loss of particle brightness during humidity induced phase transitions.This is because we used the brightness of a particle as a way of identifying the particle and determining particle diameter against the dark background.
Data collected by AL-POM could be used to follow chemical reactions which destroy the birefringent phases being probed.38]54 AL-POM only probes birefringent phases, therefore it is specic and could be used for chemical kinetics in a similar way to the use of SAXS as a tool to measure reaction kinetics of specic self- organised structures. 21Application of a kinetic multi-layer model to those kinetic data could then provide insights into the real-world impact of a particular phenomenon (e.g.how surfactant self-organisation impacts the chemical lifetime of atmospheric aerosol constituents). 22

Atmospheric implications
The D w range derived from our model (∼10 −14 -10 −8 cm 2 s −1 ) is similar to measurements of D w in water-sucrose mixtures (∼10 −13 -10 −6 cm 2 s −1 ), placing this nanostructured proxy system in a similar water diffusion regime.
There is a strong dependence of D w on molecular arrangement, with D w increasing by ca.5-6 orders of magnitude upon the lamellar-to-ordered inverse micellar phase transition.We thus have direct evidence that water diffusion is affected by molecular arrangement, similar to the effect that nanostructure formation has on the oxidation reactivity of the same proxy system. 216][57] We have shown here that the diffusivity of water though a nanostructured surfactant aerosol proxy is impacted by the arrangement of these surfactant molecules, which itself is determined by the amount of water in the system.
With AL-POM, it is also possible to determine whether humidity-induced phase transitions are between amorphous or crystalline phases, which are oen optically birefringent if the crystal structure is anisotropic.This is of importance when considering the interaction of aerosol particles with water vapour. 58he AL-POM experimental setup is possible in a standard chemistry laboratory and could be coupled with other forms of levitation such as an electro-dynamic balance (EDB).Coupled with the improved optics, optical textures can be distinguished in a levitated birefringent particle with the increased resolution.We demonstrated this by watching a non-birefringent methanolic solution of oleic acid-sodium oleate-fructose (1 : 1 : 1 wt) evaporate to form a birefringent phase (Fig. 5).There is therefore the possibility to identify phase separation between birefringent and non-birefringent domains within levitated droplets.0][61] Even if no high-quality camera is available, the phase transition observed during this study is still observable with a standard computer webcam (as demonstrated in the ESI section S5 †).

Conclusions
This work has shown that a comparably facile laboratory-based setup (AL-POM) consisting of polarising lters, an acoustic levitator, a camera and a light source can return physically meaningful results provided the sample environment can be controlled.LLC phase transitions have previously been followed in acoustically levitated droplets when coupled with X-ray scattering techniques, providing a more detailed insight into the nanostructure of the particle. 3,16,50However, this requires rather specialist instrumentation and access to a synchrotron light source.
The simple composition-dependent parameterisation of water diffusivity, along with the inclusion and parameterisation of phase transition boundaries in the model, means that the model could be applied to more complex systems such as the inverse micellar (non-birefringent)-hydrated lamellar (birefringent)-inverse cubic (non-birefringent) phase transitions observed for the phytantriol-glycerol system. 62With prior knowledge of the diffusion coefficient of water through at least one of these phases, predictions could be made regarding the diffusivity of water through such phases.AL-POM could be applicable to studies concerning atmospheric and respiratory aerosol, drug delivery, and cosmetics.

Fig. 1
Fig. 1 Schematic representation of the AL-POM setup with typical images of a levitated sample during a humidity experiment, illustrating a reduction and then the disappearance of the particle birefringence.

Fig. 2
Fig. 2 2-D SAXS patterns from a levitated oleic acid-sodium oleate particle.(a) The edge of the particle at the beginning of the experiment (low RH), showing a highly oriented lamellar phase.(b) The centre of the same particle at high humidity (90% RH), showing the Fd3m close-packed inverse micellar phase.(c) The edge of the same particle at 90% RH showing some orientation of the Fd3m phase.

Fig. 3
Fig. 3 Plots of the normalised amount of lamellar phase ([Lam]/[Lam] 0 ) vs. time with corresponding model fits (solid lines) for each particle diameter.(a) An experiment where two particles were levitated simultaneously.(b) and (c) Two particles levitated separatelythe optimised model fits for these two experiments returned slightly different parameters to the ones optimised in panel (a).

Fig. 4
Fig. 4 Model outputs for a 110 mm radius particle exposed to 90% RH.(a) Evolution of the water diffusion coefficient (D w ) throughout the humidifying particle.(b) Evolution of the mole fraction of lamellar phase (f lam ) throughout the particle.(c) Evolution of water activity (a w ) throughout the particle.

Fig. 5
Fig. 5 Cross-polarised images of acoustically levitated droplets of oleic acid-sodium oleate-fructose (1 : 1 : 1 wt) evaporating from a 10 wt% methanolic solution.(a) The start of the experiment where the initial droplet is a solution of oleic acid-sodium oleate-fructose in methanol.(b)The end of the experiment where methanol has mostly evaporated from the droplet to leave a birefringent phase.