Liquid-liquid phase separation in mixed organic/inorganic single aqueous aerosol

Direct measurements of the phase separation relative humidity (RH) and morphology of aerosol particles consisting of liquid organic and aqueous inorganic domains are presented. Single droplets of mixed phase composition are captured in a gradient-force optical trap and the evolving size, refractive index (RI) and morphology characterised by cavity enhanced Raman spectroscopy. Starting at a RH above the phase separation RH, the trapped particle is dried to lower RH and the transition to a phase separated structure inferred from distinct changes in the spectroscopic fingerprint. In particular, the phase separation RHs of droplets composed of aqueous solutions of polyethylene glycol (PEG-400)/ammonium sulfate and a mixture of C6-di-acids/ammonium sulfate are probed, inferring the RH from the RI of the droplet immediately prior to phase separation. The observed phase separation RHs occur at marginally higher RH (at most 4%) than reported in previous measurements made from studies of particles deposited on hydrophobic surfaces by brightfield imaging. Clear evidence for the formation of phase separated droplets of core-shell morphology is observed, although partially engulfed structures can also be inferred to form. Transitions between the different spectroscopic signatures of phase separation suggest that fluctuations in morphology can occur. For droplets that are repeatedly cycled through the phase separation RH, the water activity at phase separation is found to be remarkably reproducible (within ±0.0013) and is the same for the 1-phase to 2-phase transition and the 2-phase to 1-phase transition. By contrast, larger


I. Introduction
Aerosol particles are an important atmospheric constituent, influencing atmospheric chemistry, 1,2 air quality and global climate. [3][4][5][6][7] Their impact is highly dependent on their properties, including particle size, phase and morphology. 3,8,9 However, the dependence of these properties on particle composition and environmental conditions, specifically relative humidity (RH) and temperature, remains poorly understood leading to uncertainties in the magnitudes of the impacts of aerosols on climate and chemistry. Tropospheric aerosol is complex in composition containing organic matter (both primary and secondary with a large range of O:C ratios), inorganic salts (mainly ammonium, sulfate and nitrate in the accumulation mode particle size range 10 ) and water. These components can be internally mixed and, depending on the composition of the aerosol and the ambient conditions, may be one liquid phase, two liquid phases, an amorphous glassy state, a solid crystalline state or indeed a mixture of these states. 11 The phase of an aerosol particle is dependent on the immediate history of exposure to changing temperature and RH. 11 As ambient conditions change, an aerosol particle may go through some or all of the possible phases in a relatively short time, the timescale dependent on the equilibration time for gas-particle partitioning of water and other components. Timescales for equilibration can be of the order of seconds to minutes for high volatility components in liquid particles through to hours or days for components of lower volatility in solid or glassy aerosol. 12,13 An understanding of the conditions and timescales under which phase transitions occur is needed if our understanding of the behaviour of aerosols in the atmosphere is to be developed. The deliquescence and efflorescence phase behaviour of atmospheric aerosol is relatively well understood, 14-21 and there is an increasing awareness and understanding of the behaviour of "glassy" aerosol [22][23][24][25] and the conditions under which it is formed. Until recently, however, there has been little consideration of the phase separation of a homogeneous liquid particle into two liquid phases consisting of a predominantly hydrophilic domain containing inorganic solutes and a hydrophobic domain containing water insoluble organic components.
Studies of liquid-liquid phase separation (LLPS) in mixed organic/inorganic particles are relatively sparse but some broad conclusions can be drawn from the available data. Laboratory measurements on complex organic/ammonium sulfate (AS) mixtures with up to 10 organic components 15,26,27 have shown that LLPS always occurs if the O:C ratio is <0.56. In the intermediate range 0.56 < O:C < 0.8, the occurrence of LLPS is dependent on the specific functional groups forming the organic component 15,26 and the organic-to-sulfate mass ratio. 14 Recently, Song et al. 28 29 Ambient aerosol samples collected on substrates have also been investigated. Aerosol collected in Atlanta, 30 heavily influenced by both anthropogenic and biogenic emissions with an O:C ratio of ~0.5, showed LLPS. Aerosol sampled in the Amazon, 31 a region dominated by biogenic emissions, also exhibited LLPS over a range of O:C ratios consistent with the work of Song et al. 26 The morphology adopted by particles containing immiscible liquid domains after phase separation remains poorly understood. The arrangement of the phases adopted may be core-shell or partially engulfed, or may even contain small domains of one phase dispersed throughout the second. Reid and coworkers have provided a framework for predicting the morphology of liquid-liquid phase separated particles, with the formation of a core-shell or partially engulfed structure dependent not only on surface and interfacial tensions of the hydrophilic and hydrophobic phase domains but also the relative phase volumes. [32][33][34][35] The morphology of a particle affects a wide range of physical, chemical and optical properties and, thus, morphology can influence the effect of aerosols on the chemistry of the atmosphere and climate. 36 In atmospheric chemistry, the heterogeneous reactions of gas-phase species (such as ozone or N2O5) on the surface of aerosol particles play an important role in the removal of species that affect the oxidative balance of the atmosphere. The efficiency of these reactions in contributing to the removal of gas-phase species is likely dependent on the morphology of the particle and the chemical identity of the liquid phase exposed directly to the gas phase. For example, the hydrolysis of N2O5 on the surface of an aerosol will be inhibited by a partially engulfed particle as compared to a homogeneous aerosol particle due to the lower aqueous surface area. Indeed, if a core-shell morphology is adopted then the reaction may be effectively suppressed if the droplet is coated in an organic shell. 37 Recent work has shown that the reaction can still occur when the particle adopts a core-shell morphology albeit with a much reduced uptake coefficient. 38 Then, the exact decrease in reaction rate is determined by the hygroscopicity and viscosity of the organic shell. The morphology of a particle can also affect the hygroscopicity of the particle and the accessibility of sites for ice nucleation with the existence of an organicrich lens or shell at the surface of a particle affecting the kinetics of gas-particle partitioning of water. 39,40 Reid et al. 32 assessed the compositional dependence of the surface and interfacial tensions of the aqueous and organic phase volumes forming a particle for a large number of organic components, considering also the influence of the salting-out of organic components from the aqueous phase domain and the consequent influence on morphology. Their survey was limited to 65 organic components with an O:C ratio ranging from 0 to 0.6, with 90 % having ratios less than 0.25 and only one compound with a ratio >0.5. For these systems, they concluded that partially engulfed structures should predominate. Bertram et al. 14 and Ciobanu et al. 41 have concluded that core-shell morphologies are adopted for aerosol containing organic components with an O:C ratio <0.7 from measurements made on particles deposited on hydrophobic cover slips and using brightfield imaging microscopy. Notably, Bertram et al. 14 studied the phase behaviour of mixed solutions with AS and 18 organic components, but with 15 components having O:C ratios of >0.5 and the lowest having an O:C ratio of 0.29. Ciobanu et al. 41 studied the ternary poly(ethylene glycol)-400/ammonium sulfate/water system alone with the organic component having an O:C ratio of 0.56. The potential influence of the substrate on the particle phase behaviour and morphology is unclear, although assumed to be negligible. The Atlanta samples reported by You et al. 30 (O:C ~ 0.5) also suggested core-shell morphology when LLPS was observed. Song et al. 28 considered 33 components with O:C ratios ranging from 0.29 to 1.33 and observed the formation of both partially engulfed and core-shell morphologies for mixtures of dicarboxylic acids (di-acids) and AS. Indeed, for a mixture of C6 and C7 di-acids with AS (OIR of 0.67), phase separation to a core-shell morphology was observed at an RH of 83.5 % followed by a change to a partially-engulfed structure as the RH was lowered below 80 %. A similar transition in morphology was observed for droplets containing AS and a mixture of C6di-acids (OIR of 1:1 and 1:2), with the transition occurring at progressively lower RH as the OIR was reduced.
For mixtures of C7 di-acids and AS (OIR of 2:1) and C5/C6/C7 di-acids and AS (OIR of 1:1), spinodal decomposition was observed and led directly to partially engulfed structures. A comparison of these studies suggests that phase separated aerosol formed from hydrophobic and hydrophilic phase domains are likely to form partially engulfed structures if the organic components forming the hydrophobic phase are of low O:C ratio with an increasing trend towards core-shell with increasing O:C. However, the differences in energies between different morphologies are often only slight and switching between configurations may occur. 32 Direct observations of liquid-liquid phase separated particles in the aerosol phase rather than of sampled particles deposited on substrates have been limited. Measurements using aerosol optical tweezers have reported the direct formation of partially engulfed morphology structures on LLPS, albeit from studies with particles containing decane, octanol or oleic acid with O:C <0.1, i.e. lower than for the imaging microscopy studies. 32,35,42,43 Song et al. 28 have reported the formation of a core-shell morphologies for droplets of polyethylene glycol (PEG)/AS/water droplets levitated in an electrodynamic balance (EDB) when elastic light scattering measurements were compared to Mie calculations for homogeneous and core-shell configurations.
In this paper we present studies of liquid-liquid phase separation in single aerosol droplets trapped using optical tweezers. In particular, we focus on two model systems for which data are available from particles deposited on surfaces, specifically PEG-400/AS and a mixture of C6-di-acids/AS, a mixture of equal amounts (by mass) of 2-methylglutaric acid, 3-methylglutaric acid and 2,2-dimethyl succinic acid. For the former system, bulk phase studies have also been performed that allow the calculation of spreading coefficients. 28 The main aim of this work is to determine if the phase separation behaviour and compositional dependence of the separation RH of levitated droplets are consistent with the measurements reported from particles deposited on substrates.
Further, the sensitivity of the cavity enhanced Raman spectroscopy technique to the refractive index and morphology of optically tweezed droplets will be used to gain insight into the morphology of liquid-liquid phase separated aerosol particles.

II.a Bulk Measurements of Refractive Index and Phase Separation
To interpret the single particle measurements presented later, it is important to first fully characterise the compositional dependence of the refractive indices of the mixed component solutions studied. Measurements of the refractive indices (RIs) of the mixed organic/inorganic (either PEG/AS or di-acids/AS) aqueous solutions were made as a function of mass fraction of solute for the same OIR (mass ratios) used in the aerosol optical tweezers measurements described later. Measurements were first carried out at sufficiently high dilution/large mass fraction of water that phase separation had not occurred and the solutions could be considered homogeneous. Where possible, measurements of the RIs of both organic and aqueous phases were recorded for the more concentrated solutions that exhibited liquid-liquid phase separation. For these measurements, solutions were made up in a separating funnel and the two phases separated for refractive index measurement. All measurements on bulk solutions were carried out with a digital refractometer (Misco #PA203, wavelength of 589 nm). The water activity of each solution composition was calculated using the Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model, 44 based on knowledge of the exact masses of each solute and water forming the mixture. For the phase separated solutions, the water activity is assumed to be the same as that for a homogeneous solution of the same composition calculated with AIOMFAC restricting the calculation to prevent phase separation. From the measured dependence of the refractive index (RI) on water activity, polynomial expressions were then used to describe the relationship between RI and water activity for each phase. These relationships between RI and water activity were then used to calculate the water activity of the single particles in the tweezers system at phase separation, with direct measurements of RI possible by this technique. Slightly different procedures were followed for the PEG:AS systems and the C6 acids:AS systems, as outlined below.
PEG:AS -For the PEG:AS system, a version of AIOMFAC optimised for the parameterisation of polyethylene glycols 45 was used to calculate the water activity of each solution for which the RI was measured. The RI as a function of calculated water activity for each composition studied is shown in Figure 1 and the coefficients of the polynomial relationships are given in Table 1. The RI as a function of water activity is reported for solutions with dry mass solute ratios of 9:1, 3:1, 1:1, 1:3 and 1:9 (corresponding to OIR of 9, 3, 1, 0.33 and 0.11). Liquidliquid phase separation is not observed for the bulk solutions in which the OIR is very high or very low. At intermediate OIR, phase separation is observed with the RI of the homogeneous solution just prior to phase separation tending to the RI of the dominant aqueous (inorganic rich) or PEG (organic rich) layer of the phase separated solution. For solutions with a 1:1 PEG:AS dry mass ratio (OIR = 1), there is a clear discontinuity between the refractive index of the single phase and both the aqueous and organic layers.
C6-di-acids:AS -For this system, in which the organic component is an equal mass mixture of 2-methylglutaric acid, 3-methylglutaric acid and 2,2-dimethylsuccinic acid, the standard web based AIOMFAC model 44 was used in the same way as for the PEG:AS system. However, the bulk solubility limit was reached at higher water activities than required for LLPS to occur due to the limited solubilities of these components. As a consequence, phase separation was not observed in the bulk measurements and the use of a polynomial relationship between the measured RI and calculated water activity would involve a large extrapolation to lower water activities to allow a direct estimation of the water activity at the SRH. To avoid this unconstrained extrapolation, the experimental RI were fitted to a variety of simple mixing rules derived from AIOMFAC data of solution properties as a function of water activity to allow a more robust and constrained calculation of the RI as a function of composition. The experimental data fitted best with the simple mass weighted mixing rule (shown in Figure 2 with fit coefficients in Table 2), and the relationship between RI and water activity using this mixing rule was used to calculate the water activity from the measured RI at phase separation.

II.b Single Particle Measurements.
The aerosol optical tweezers instrument coupled with Raman spectroscopy has been described in detail previously [46][47][48] and will only be summarized here. A gradient force optical trap is formed by focussing the light from a Nd:YVO4 frequency doubled laser (532 nm) through a 100 × objective (numerical aperture of 1.25), with the light passing from the objective through a layer of immersion oil and then through a glass cover slip before entering the trapping cell. This creates an optical trap ~40 µm above the microscope glass cover slip.
Aerosol is introduced into the cell using a medical nebuliser (Omron MicroAIR Pocket Nebuliser) and any aerosol droplet that passes through the focal volume becomes trapped. The back scattered Raman signal from the droplet is focussed onto the entrance slit of a spectrograph equipped with a 1200 grooves per mm diffraction grating and a CCD array of 1024 × 256 pixels. The spectroscopic time resolution is 1 s. From the unique fingerprint of stimulated Raman scattering occurring at wavelengths commensurate with whispering gallery modes (WGMs), the refractive index and radius of the droplet can be derived with a high degree of accuracy by comparing the observed WGM positions to the predicted positions from Mie scattering calculations. 49 In most experiments presented here, no active RH control was imposed and the trapped particles were allowed to dry as the RH declined to that of the ambient air. For some experiments, a slow (30 sccm) flow of dry nitrogen was passed through the cell to dry the trapped particle. Typical rates of RH change were 4 % in 1000 s and no dependence of the RH at phase separation on the rate of RH change was observed. Instead of measuring the RH using a capacitance probe, the water activity was inferred from the refractive index retrieved from the Raman measurement using the relationships between n and aw obtained from the bulk measurements described earlier. In previous work we have shown that this approach allows the RH to be determined with an accuracy of better than ±0.1 %, considerably more accurate that can be measured by a capacitance probe. 50 The temperature of the measurements was in the range 20 to 23 o C.

II.c Fitting of WGMs in Raman Spectra to Homogeneous and Core-Shell Morphologies.
The WGMs in the Raman spectra of homogeneous spheres were fitted using a previously described algorithm. 49 For the Raman spectra of core-shell particles, WGMs were fitted using a similar algorithm that had the following modifications: (i) the resonance condition was that of two concentric spheres, and (ii) additional parameters were incorporated into the search space during the fitting. Fuller details of this will be described in a future publication.
Concerning the first difference, resonance combinations of particle size parameters (total radius and wavelength) and core and shell dimensions with independent RIs were identified by calculating the scattering coefficients for two concentric spheres over a wide range of trial solutions. 51 Resonances occur when a pole exists in the scattering coefficients and, as adopted previously, 49 the Newton-Raphson method was used to find the complex roots of the denominators of these coefficients. The main difficulty when employing a root-finding algorithm like the Newton-Raphson method is that suitable initial guesses are required. Here, guesses for the modes of interest were found by taking the resonances from a homogeneous sphere (calculated using the method in Preston and Reid 49 ) and using these as initial guesses for the resonances for fitting the WGMs to a core-shell particle with a very thin shell. Once resonances had been identified for the particle with a thin shell, they could then be used as the initial guesses for the resonances of a core-shell particle with progressively thicker shells. This process was repeated until resonances were found for all shell thicknesses of interest. The assumption of this procedure is that small changes to shell thickness will only result in small changes to resonant size parameters.
The second difference between the fitting procedure used here and that used previously is that the search grid for the core-shell particle contains at least four parameters (if nothing is known beforehand about the coreshell particle): the radius of the shell, the radius of the core, the refractive index of the shell and the refractive index of the core. Additionally, the inclusion of a linear dispersion term in both the refractive index of the core and shell may be needed if fits with higher accuracy are desired. 49 Therefore, in the absence of any prior information about the core-shell particle, it is necessary to generate and search a six-dimensional grid in order to find an accurate best fit. To reduce the computational demand, the linear dispersion term for both the core and the shell RIs was simply set to 15 nm -1 , a typical value from all of our previous work. 49 Additionally, for the fitted data presented in this publication, the RIs of the core and the shell at a fixed wavelength were chosen to be 1.385 and 1.400, the values at the water activities close to phase separation using the bulk data shown in Figure 1 for the PEG/AS system studied with an OIR of 0.33. By fixing the RIs with these values, it was then only necessary to search a two-dimensional grid which consisted of the radii of the two concentric spheres, allowing an approximate retrieval of the core radius and the shell thickness from the Raman spectra.

III.a Signatures of LLPS in Trapped Particles
It is first important to identify the possible signatures of liquid-liquid phase separation that arise when studying phase separation in optically tweezed aerosol droplets. The onset of liquid-liquid phase separation can be observed from the Raman spectra from the appearance of any one of three signatures, examples of which are shown in Figures 3-5. Briefly, the persistence of strong WGMs in the Raman fingerprint at phase separation accompanied by dramatic changes in their relative wavelengths provides a signature of phase separation to a morphology that retains spherical symmetry, but with a significant change in the radial profile in refractive index arising from the formation of a core-shell structure. Complete loss of the WGMs is consistent with a loss of spherical symmetry, a quenching of the high-quality WGMs of the previously spherical cavity and the formation of a partially engulfed structure. Finally, a dramatic increase in the error associated with fitting the WGM structure, although more ambiguous, indicates the departure of the droplet from an homogeneous sphere and the possible formation of multiple inclusions or small distortions from sphericity.  resulting from a breakdown in the assumption that the particle is homogeneous when fitting the WGM fingerprint. The apparent sharp changes in the radius and refractive index retrieved from the Raman spectrum are not real and indicate phase separation has occurred. Additionally, the persistence of strong WGMs indicates that the morphology of the droplet remains spherical following LLPS and is core-shell. In the measurements reported below, the fitted refractive index immediately prior to LLPS has been used to infer the RH at phase separation; once phase separation starts (taking only a few seconds), the size and RI retrieved from the fit are in error and cannot be used to infer the water activity at phase separation. For some of the experiments consistent with the formation of a core-shell morphology, the WGMs were compared with Mie simulations for droplets of core-shell morphology allowing estimations of the core size and shell.

Quenching of WGMs (QM):
In previous publications we have shown that LLPS can lead to the quenching of WGMs in the Raman spectrum, a consequence of the distortion in shape from a perfectly spherical resonator and the reduction of the high cavity quality factors usually associated with the WGMs for a droplet. 42, 43 We observe similar behaviour in a number of experiments in this study: as the particle diminishes in size, the WGMs became sporadic or even disappear completely, even though the particle remains trapped. An example of this behaviour is shown in Figure 4 for a PEG/AS particle: panel a shows two spectra, one taken before and another after phase separation. The wavelengths of the WGMs observed as a function of time are shown in panel b and the results of the fitting of the WGM fingerprint to a homogeneous droplet are shown in panel c.
As before, we conclude that the quenching of WGMs could be indicative of a distortion from sphericity due to phase separation and a morphology that is partially-engulfed in which a lens of one phase at the surface of the particle disrupts the formation of WGMs. Such spectra could also be consistent with the formation of inclusions of ammonium sulfate within the droplet that move close to the surface disrupting the modes. 52 This latter scenario can also explain why the intensity of the background spontaneous Raman OH band is considerably lower after the phase separation. In experiments that showed this behaviour, phase separation was deemed to occur at the last frame where the spectra could be reliably and successfully fit to a homogeneous particle. The fitted refractive index was used to infer the RH at phase separation. It should be noted that following the apparent phase separation, WGMs can periodically reappear in the Raman spectrum but with much lower intensity than for a homogeneous droplet (not shown in the Figure), as apparent in Figure 4b.

Increase in fitting error (IFE):
In a final class of experiment, WGMs continue to be observed with no significant increase in mode offset identified. However, the fitting error (the discrepancy between the measured wavelengths of the peaks and those calculated from Mie theory) is observed to increase by orders of magnitude.
An example of this is shown in Figure 5: panel a shows spectra of the PEG/AS system (OIR = 3.0) recorded before and after the phase separation, panel b shows the fitting error as a function of time, and panel c the retrieved radius and refractive index of the droplet. Such observations can only be consistent with a breakdown in the assumption that the droplet is homogeneous, leading to inconsistency between the wavelengths of WGMs observed in the measurement and the predictions for a homogeneous droplet of any refractive index.
Thus, an observation of IFE was assumed to indicate that the droplet was no longer homogeneous; indeed, it is most likely that the morphology is consistent with the presence of small inclusions of the aqueous phase moving around within the organic phase (similar to the QM case), but inclusions of a size that are unable to fully quench the high quality factor WGMs. The lowering of the quality of the WGMs leads to marginal increases in their linewidths, a degradation in the determination of the resonant line centres and an increase in the associated errors in the fitting. For accurate fits to an homogeneous droplet, the fitting error corresponds to an average error of ~0.01 nm/peak across all WGMs in the spectrum, reflecting the enhanced accuracy achieved from fitting the dispersed lineshapes (~0.04 nm/pixel) to a Gaussian when determining the line centres. Frame to frame fluctuations in the error become much larger after phase separation occurs, with some frames fitting by chance remarkably well and some showing large errors and a broadening in the retrieved droplet sizes and RIs from the fitting. Again, phase separation is deemed to occur at the last frame at which the pattern of WGMs is well represented by Mie simulations assuming homogeneity in composition. The average refractive index of the 10 frames preceding this is then used to determine the phase separation water activity. This assignment is not as robust as the previous two signatures of phase separation. Such behaviour is consistent with previous observations of the elastic scattering measured from phase separated droplets, in which distinct departures in elastic scattering from that expected for a homogeneous sphere were observed, but without a clear assignment in morphology possible. 28

III.b Compositional Dependence of the SRH
Using the signatures of phase separation described in the previous section, we report the observed phase separation humidities for PEG/AS mixtures inferred from the aerosol optical tweezers measurements in Figure   6. The bounded area indicates the range and uncertainty of phase separation RHs reported by Ciobanu et al. 41 for this system. In Table 3 we report the phase separation RHs and identify the signature of phase separation for each droplet studied. It is apparent that the single particle data show phase separations at relative humidities between ~86 and ~94 %, broadly consistent with, but marginally higher than, previous studies. It is, perhaps, surprising that the SRH from levitated droplets is marginally higher in some cases than the SRH of ~85% to ~91% reported for single particles deposited on cover slips. Bulk and single particle measurements were performed in the temperature range from 293 -298 K. Although SRH depends on temperature, the dependency is minor in this limited temperature range and within the uncertainties of RH measurements. Also, in principle, the retrieval of the SRH is extremely accurate in the optical tweezers measurements given the accuracy with which the refractive index of the droplet just prior to phase separation can be determined. However, the estimated SRH does depend on the relationship of refractive index/mass fraction of solute to the water activity and this is dependent on the accuracy of the thermodynamic relationship provided by bulk phase data with measurement accuracies typically of ±0.3 % RH. 21,41 Some of our bulk phase measurements of RI show liquidliquid phase separation at RHs in between our optical tweezers measurements and the previously published values, reflecting the pronounced dependencies on environmental parameters and composition that exist. The low variability in the refractive indices at phase separation (and, thus, the precision on the SRH determinations) must reflect the intrinsic variability in the separation relative humidities of different droplets and compositions rather than resulting from the more typical random error in measurement of the gas phase RH typical of most measurements. We will return to this point when we describe the reproducibility of the SRH recorded for the same droplet on repeated drying and humidifying cycles and, thus, repeated phase separation cycles. We first present a brief summary of the results for each composition.

1:1 PEG-400:AS by mass (OIR=1):
For single particles of this composition, phase separation occurred at relative humidities between 90.9 and 92.8%, slightly higher than the data presented by Ciobanu et al. 41 for particles deposited on cover slips and bulk data. In Figure 6 single particle data are presented for 11 particles, 5 of which showed a clear increase in mode offset (CMO) and 6 of which showed phase separation by a break down in the homogeneous particle fitting (IFE) as described in the section III.a.

1:3 PEG:AS by mass (OIR=0.33):
Liquid-liquid phase separation was observed to occur between 92.6 and 93.8% relative humidity, higher than the range indicated in the work of Ciobanu et al. 41 Data are presented in Figure 6 for 10 particles, two of which showed a marked increase in mode offset (CMO behaviour) and 8 showed a breakdown in the fit and sporadic WGMs (QM behaviour).

3:1 PEG:AS by mass (OIR=3):
Liquid-liquid phase separation was observed to occur between relative humidities of 86.4 and 91.5%, in excellent agreement with the Ciobanu 41 data, although our measurements for this composition exhibit a larger range of variability in phase separation RH than for other compositions. In Figure 6, data are presented for 9 single particles only one of which showed a mode offset increase (CMO).
Of the remainder, 6 showed QM behaviour and the remaining two particles showed IFE behaviour.

1:9 PEG:AS by mass (OIR=0.11):
Phase separation was observed to occur between 88.6 and 89.8% RH, again in excellent agreement with previous work on particles deposited on substrates and with bulk measurements that showed LLPS at 88.4 % RH. 41 Data are presented in Figure 6 for 12 single particles, 9 of which show CMO behaviour, one of which shows QM behaviour and two IFE behaviour.

9:1: PEG:AS (OIR=9):
For these organic rich droplets, LLPS was observed over a much larger RH range than the other compositions extending from 88.3 to 93.0% RH. However, of the 5 particles for which data are presented in Figure 6, none of these particles exhibited CMO behaviour and only one exhibited QM behaviour.
The remaining droplets were determined to have phase separated through an observed increase in the fitting error (IFE, the least robust indicator of phase separation) and as such these data should be treated with caution.
We shall return to the reasons for the apparent dominance of this form of phase separation indicator below.
Given that the data for droplets of the 9:1 PEG:AS solution are the least reliable, agreement of the SRH between this study and the previous bulk phase measurements and studies of droplets on coverslips is within 4 % with an enhanced asymmetry with inorganic rich solutions showing an higher SRH, particularly the 1:3 PEG:AS solution. There is no systematic dependence of the SRH on the signature of LLPS. Again, it should be stressed that the narrow range (high precision) of SRHs reported indicate a true level of variability droplet to droplet.

III.c Comparison of Reproducibility in SRH for Different Particles and the Same Particle
As can be seen from Table 3, the variability in separation relative humidity between different particles of the same composition is generally within 2-3% RH for sulfate rich particles and within ~5% for PEG rich particles.
The high degree of precision with which the refractive index at phase separation is inferred from the refractive index indicates that the range of values observed over numerous droplets reflects the real variability in composition at phase separation from droplet to droplet rather than uncertainty in an experimental variable such as RH. To support this conclusion, a single particle was repeatedly passed through the phase transition on a number of RH cycles, repeatedly switching between a homogeneous single phase droplet and a droplet with LLPS. If it is correct that the tweezers measurements are sufficiently precise to distinguish between the small (but real) differences in phase separation RH between different particles, it would be expected that the same particle should show a smaller degree of variation in SRH than is observed between the particles shown in Figure 6 and Table 3. Figure 7 reports the results from the repeated cycling of the same 1:3 PEG:AS (OIR=0.33) particle through the phase separation RH, both through drying and humidifying cycles. It is immediately apparent from the mode offset data (CMO) that phase separation and re-merging to one phase occur on repeated cycles and this is supported by the error in the spectral fitting (IFE), which shows excellent correlation with the CMO signature. A breakdown in the assumption of homogeneity in refractive index is indicated by both the CMO and IFE signatures. It should also be noticed that the noise in the time series of radius and refractive index also increases upon phase separation for the same reason and that the apparent change in radius and refractive index when separation occurs is simply an artefact of the breakdown of this assumption.
The exact times at which phase separation and the return to one phase occur are not possible to define; instead phase transitions occur over narrow periods in time. In identifying these periods, we note the following. Firstly, before the first clear discontinuity in slope and increase in error, mode offset and radius at ~2500 s (Figure 7), the error increases and the mode offset cannot be calculated from ~1700 s. This is a consequence of a diminution of mode intensities to a point where first order TM modes are no longer sufficiently intense and sharp to determine a mode offset, but the persistence of first and second order TE modes ensures that fitting can be achieved, albeit with larger errors. This is possibly a consequence of some initial phase separation with formation of very small inclusions that partially quench modes; however, it is not possible to convincingly identify this point as the time of phase separation. Instead, all four signatures (radius, RI, error and mode offset) show consistent and sudden changes at ~2500 s and we report this point as being the time at which liquidliquid phase separation occurs. On humidifying, the error and mode offset never return to the consistently low values seen at the very beginning of the experiment, suggesting that a completely homogeneous phase is never fully re-established but small inclusions may persist. Similar abrupt changes occur on subsequent drying cycles at ~5230 and ~7300 s and we report the droplet sizes, RIs and RHs at these times in Table 4. Given the very slow rate at which the RH is changing, uncertainties are small but we report ranges for each of these quantities based on the time period between which the error first increases above 1×10 -2 nm to when it increases above 2×10 -2 nm, typically a period of 50 s. Although a rather arbitrary choice, our purpose here is to look at the reproducibility in the behaviour of the droplet from one cycle to the next. This error also corresponds approximately to an increase in the average error in reproducing the resonant wavelengths in the Raman spectrum from less than one pixel on the CCD on average to more than 1. At times after these, fitting to an homogeneous Mie calculation leads to clear errors in representing the light scattering from the droplet. The same change in error, decreasing from 2×10 -2 to 1×10 -2 nm, is used to define the time period over which the two phases merge to form a droplet formed predominantly from one phase.
Some trends in the radii, RIs and water activities are clear in Table 4. The ranges of radii, RIs and water activities are consistent with each other for either phase separation or the return to one phase. Differences in the initial and final water activities reported are within a range of ±0.1 % and ±0.5 % RH, respectively, for phase separation. While the first point in the range is fairly well-defined, the final point is less defined. For the return to one phase, the two measurements of the final water activity (now the most well-defined) are in perfect agreement while the initial water activities differ by only 0.3 % RH. Most clearly, the water activities at which the error in the fitting crosses the 0.01 nm threshold agree to with a standard deviation of ±0.13 % RH across all five transitions. From these measurements, the variability of composition/SRH determined for repeated measurements on the same particle is much smaller than the variability between particles. Although the data reported here are for a single particle, the one for which we have the most comprehensive set of data, similar behaviour has been observed for numerous droplets. This supports our conclusion that each particle shows a distinct (and slightly different) SRH but that there is considerable variability between particles. The reasons for variability between particles at the same composition are not clear as they are prepared by nebulising the same bulk solution. In addition, no obvious correlation could be found between SRH and particle radius, rate of drying or length of experiment.

III.d Morphology of Liquid-Liquid Phase Separated Particles
Ciobanu et al. 41 identified the initial process by which phase separation occurs from the imaging of particles at the onset of phase separation in their microscope images of particles deposited on surfaces. Their data indicate that phase separation occurred by the formation of aqueous inclusions for particles with a high OIR of 8:1 to 2:1. In particles with low OIR (1:2 to 1:8), phase separation occurred by growth of a second organicrich phase from the particles rim. At intermediate OIR, phase separation developed by the formation of schlieren which eventually coalesced into aqueous inclusions. These observations seem to imply that particles rich in sulfate should separate into core-shell particles (the formation of an organic rich layer from the surface).
Conversely, as the proportion of the organic component in the droplet increases, the tendency to separate through the formation of inclusions within the droplet was observed.
From Table 3 it is clear that the very sulfate rich particles (OIR=0.11) show predominantly CMO behaviour, consistent with the formation of a thin shell at the surface of the particle. In particles with a very low mass fraction of sulfate (OIR of 3 and higher), the results show the particles are more likely to show QM or IFE behaviour on separation, consistent with the formation of inclusions within the droplet moving around and quenching the appearance of WGMs or with the formation of a partially engulfed structure. At the intermediate OIRs studied in this work, the data seem to be fairly evenly split between CMO and QM type behaviour, possibly indicating some degree of competition between these two mechanisms with a stochastic element determining which is the initiating factor. The data on levitated single particles in this study, therefore, seem to broadly validate the observations of Ciobanu et al. 41 for the very aqueous rich and organic-rich particles, but with some ambiguities arising in the particles of intermediate OIR. In this study, all of the particles that lost sufficient water to reach the SRH showed LLPS, as did those observed by Song et al. 28 for particles of the same compositions.
For particles which show CMO behaviour, we have investigated the plausibility of fitting the WGM fingerprints to a core-shell structure rather than a homogeneous droplet, potentially allowing a determination of the refractive index and radius of the core as well as the refractive index of the shell and the shell thickness.
Fitting of all four parameters independently is computationally expensive. Instead, the refractive indices of the core and shell are fixed at values representative of the expected values at the water activity corresponding to the SRH, as discussed in Section II.c. Then, the radius of the core and thickness of the shell are varied to obtain a best-fit for the observed WGM fingerprint. Results for core-shell fitting are shown in Figure 8 for a particle (PEG:AS 1:3; OIR=0.33) which started as a homogeneous particle, phase separated into a core-shell morphology at a time of 878 s and then reformed a homogeneous particle again at a time of 38783 s. As the Figure shows, the shell develops and increases in thickness to 100 nm before decreasing again and disappearing as the particle returns to one phase. The film thickness is ~2.5% of the particle radius at a maximum, corresponding to a volume ratio of the aqueous AS core to total droplet volume, V(AS)/V(tot), of 0.93.
The ratio V(AS)/V(tot) that would be expected from thermodynamic predictions can be calculated using AIOMFAC to calculate the compositions of PEG/water and AS/water phases at a range of RHs close to the SRH observed for particles of this composition. The results of these calculations, as well as the experimental data from the core-shell fitting, are shown in Figure 8b. It is apparent that the volume ratio derived from the Raman spectra is close to that calculated using AIOMFAC at 94% RH (the SRH observed in the tweezers system) shown by the middle line in Figure 8b. The upper line (AIOMFAC calculation for 96% RH) and lower line (AIOMFAC calculation for 92% RH) are shown to give an idea of the sensitivity of these calculations to RH. The slight underestimation in the calculation by ~1.5 % may be due to incomplete phase separation, i.e. that none of the organic component remains in the aqueous phase. The estimation, based on AIOMFAC calculations, assumes that complete phase separation occurs. This may not be a good assumption close to the onset of phase separation and may account for the discrepancy: close to separation, a significant proportion of the PEG may still reside in the core aqueous phase. We should also note that we have assumed particular values for the RIs of the aqueous and organic phases to perform the core-shell fitting, potentially introducing some error into the radii of the core and shell.

IV. Phase Behaviour and Morphology for Mixed C6-di-acids/AS Particles
In this system, the organic component is a mixture containing equal amounts (by mass) of 2-methylglutaric acid, 3-methylglutaric acid and 2,2-dimethylsuccinic acid. These organic components formed one of the mixtures of complex composition chosen by Song et al. 15 to better reflect the complexity observed in atmospheric aerosol and to have similar O:C ratios to compounds observed in ambient aged secondary organic aerosol. Song et al. 15 observed significantly lower SRHs than observed for the aqueous PEG-400/AS system, and found that both core-shell and partially engulfed morphologies could form upon LLPS. This system therefore allows a second direct comparison between droplets deposited on coverslips and optically trapped droplets under dryer conditions with a morphology dependent on RH.

19
The SRH estimated from measurements made with this system are reported in Figure 9. The signifier of phase separation (as defined in section III.b) is identified in each case. Also shown are the data points from Song et al. 15 and a shaded area indicating the range of compositions and separation humidities for aerosol richer in the inorganic component presented in the same paper. It is immediately apparent that the data presented for this work show phase separation at higher relative humidities than those reported by Song et al. 15 This may be due to inaccuracies in the mass mixing rule used to calculate the water activity from the refractive index at phase separation in this work. The variability of the relative humidity at phase separation (~5-6% RH) between particles is comparable to that in the PEG:AS system, again indicating a small but real difference in the behaviour of individual particles of the same composition.
Over the narrow composition range shown in Figure 9 our work indicates a slightly higher number of particles that show CMO type behaviour (9 particles) (indicative of core-shell morphology) than QM type behaviour (5 particles) (indicative of partially engulfed morphology or inclusions within the particle) although both compositions show both types of behaviour. For this system, Song et al. 15 observed the formation of aqueous ammonium sulfate inclusions, some of which merged over time, with the more major inclusions moving towards the droplet edge, behaviour that would be consistent with the eventual observation of a QM signature.

IV. Conclusions
Data is presented showing how the relative humidity at which liquid-liquid phase separation occurs varies with composition for single levitated particles containing PEG-400/ammonium sulfate/water and a mixture of C6di-acids/ammonium sulfate/water. In the PEG/AS system the observed SRH in the optical tweezers is in general agreement (albeit slightly higher for some compositions) with the data of Ciobanu et al. 41 who observed liquid-liquid phase separation in droplets of the same compositions deposited on hydrophobic substrates, indicating the substrate does not have an appreciable effect on the relative humidity at which separation occurs for this system. For the di-acid system, the phase separation relative humidities derived from this work are higher than those presented by Song et al. 15 , again inferred from measurements on substrates.
The morphology of the particles has also been investigated using characteristic changes in the Raman spectra of the droplets to infer phase changes of the particle. In the PEG system, at high AS content the droplets predominantly form core-shell particles; at high PEG content it appears the spectra are more consistent with a morphology consisting of small inclusions of an aqueous phase dispersed in the organic phase or partially engulfed structure. However, in all cases, a mixture of indicators is observed for phase separation and the indicators fluctuate over time, suggesting that the morphology may not be constant and that different morphologies may be adopted depending on exact volume ratios, RH and composition. This is consistent with simulations from an early framework developed to predict the morphology in which the energy differences between different structures can be very small. 33 Our measurements suggest a distinction between two mechanisms of LLPS at the onset of phase separation with CMO type behaviour at low OIR indicating the formation of a thin organic shell at the surface and QM type behaviour indicating the formation of aqueous inclusions which may go on to form an aqueous core. These findings are in agreement with Ciobanu et al. 41 and Song et al. 15 For particles exhibiting core-shell morphology we have retrieved the shell thickness from the wavelengths of the WGMs in the Raman spectra, results that compare well with estimates of the expected film thickness using AIOMFAC to estimate the water associated with ammonium sulfate and PEG-400 and, thus, the volume ratio of the two phases. The experimental data marginally underestimate the film thickness, but this may be due to the incomplete partitioning of PEG from the aqueous AS core into the shell over the finite timescale of the measurement. For the C6 di-acid system, our results imply that over the narrow composition range studied core-shell, satellite inclusions and partially engulfed morphologies are possible. This is again in broad agreement with the work of Song et al. 15 who showed that after phase separation partial coalescence led to the formation of a major inner inclusion together with satellite inclusions. At a lower RH, the major inner inclusion tended to move from the core to the edge of the particle leading to a partially engulfed configuration. 15 Table 1. Polynomial coefficients for relationship between refractive index (n in equation) and water activity aw for PEG/AS solutions of specified OIR, in form aw = a n 2 + b n + c derived from experimental data in the temperature range 20 to 23 o C for single phase mixtures prior to phase separation.    Figure 1. Bulk refractometer data showing refractive index at a wavelength of 589 nm as a function of water activity for the PEG:AS system (green pointssingle phase; blue pointsorganic phase; red pointsinorganic phase; black linesfits). Water activities calculated using AIOMFAC as detailed in the text.    and refractive index (blue). When the droplet has separated into two phases, the reported radii and refractive indices retrieved from homogeneous fits to the spectra should not be taken as correct. (b) Time dependence of mode offset (green) and error (black). The size, RI and water activity at each phase separation is reported in Table 4. Figure 8. (a) Total radius of droplet (red) and radius of core (grey) for a particle with OIR = 0.33. Black vertical lines mark start and end of LLPS. Prior to 878 s and liquid-liquid phase separation, the WGM fingerprint is accurately represented by fits to a homogeneous spherical droplet; fitting to a core-shell structure need not be considered. After this time, the droplet phase separates into a core-shell structure with an aqueous inorganic core assumed to have a refractive index of 1.385 and an organic shell of refractive index 1.392. After 38783 s, the WGM fingerprint once again is consistent with a homogeneous droplet without phase separation.

Tables
(b) From the radius of the core and the total droplet size, the volume fraction of the inner aqueous phase can be calculated and compared with the overall volume of the droplet. This volume fraction is consistent with expectations of the volume ratio of the aqueous inorganic and organic phases calculated from AIOMFAC (black horizontal line) based on phase separation at a relative humidity of 94 %, as inferred from the refractive index at phase separation determined from the homogeneous fitting prior to the signature of phase separation.
The upper and lower blue lines indicate the volume ratios that would be expected from AIOMFAC if the phase separation occurred at SRHs of 96 % or 92 %, respectively.