Direct imaging of changes in aerosol particle viscosity upon hydration and chemical aging

We report quantitative, real-time, online observations of microscopic viscosity changes in aerosol particles of atmospherically relevant composition, using fluorescence lifetime imaging (FLIM) of viscosity.

Kinetic Modelling of aerosol surface and bulk chemistry. The kinetic multi-layer model for aerosol surface and bulk chemistry (KM-SUB) 1 has been used to model the temporal evolution of viscosity during oleic acid ozonolysis. KM-SUB treats the following processes explicitly: gas-phase diffusion, adsorption and desorption, surface-bulk exchange, bulk diffusion, and chemical reactions at the surface and in the bulk. In this study, the model adopts the following chemical mechanism of oleic acid ozonolysis 2 In R1, oleic acid reacts with ozone (O 3 ) to form either nonanal (NN) or another not further distinguished C 9 compound (C9, a lumped surrogate of azelaic acid, nonanoic acid, 9-oxo-nonanoic acid) and a Criegee intermediate (CI). The branching ratio between NN and C9 is described by the stoichiometric coefficient c. The highly volatile nonanal is assumed to evaporate instantaneously once it reaches the particle surface. The reactive CI is lost by first-order decay to C9 (R2) or by recombination with another CI (R3). The CI initialises the oligomerisation reaction by formation of a reactive dimer (R4) that undergoes further oligomerisation with CI (R5-R7). Oligomerisation is treated as occurring with a uniform oligomerisation rate constant k BR,4 until the pentamer level. Higher oligomers have been neglected since these are assumed to form in insignificant amounts 4 . The viscosity of the organic mixture ν mix has been calculated using an Arrhenius approach, Equation 5 5 .
where x i and ν i are the pure components' mass fraction and viscosity, respectively. The viscosity of oleic acid is 0.083 Pa.s 6 , which can be converted to a bulk diffusion coefficient using the Stokes-Einstein equation. The viscosity and the bulk diffusion coefficient of monomeric compounds (NN, CI, C9) are assumed to be the same as of oleic acid and have been fixed to these values during the optimisation. The viscosity of the pure oligomer compounds has been approximated to scale in a power law relationship with chain length. The scaling factor f visc was used as a fitting parameter since no experimental data is available for the products in this study (ν trimer = ν dimer (M trimer /M dimer )^f visc , ν tetramer = ν dimer (M tetramer /M dimer )^f visc , etc.).
O 3 reacts with oleic acid while diffusing into the particle, creating a steep gradient from particle surface to bulk. This scenario is often referred to as the classical reacto-diffusive case e.g. Hanson et al. 1994 7 . The sub-surface bulk layer resolution of the kinetic model is adjusted to be 1/3 of the reacto-diffusive length, which is the distance an ozone molecule travels on average before reacting with an oleic acid molecule. In total, particles have been described with 30 layers in this study.
Bulk diffusion of oleic acid occurs sufficiently fast in the liquid aerosol particles so that no concentration gradient is observed 1 . Bulk diffusion coefficients of compounds below the dimer level have thus been lumped to a value of D b,monomer = 1.00×10 -7 cm 2 s -1 that ensures perfect mixing. The diffusion coefficient of the oligomeric species, D b,oligomer , has been used as a fitting parameter to preserve the possibility of diffusive limitation to the reaction rate. Surface reaction rates k SLR are assumed to scale linearly with a factor of f SLR to their respective bulk reaction rate constants k BR (k SLR = f SLR k BR ).
The numerical values of the kinetic parameters required for KM-SUB are summarised in Fig. S9. They have been obtained by a global optimization method that combines a uniformly-sampled Monte-Carlo search with a Genetic Algorithm (MCGA). This MCGA method first samples a large number of randomly generated kinetic parameter sets and evaluates their (least squares) deviation to multiple experimental data sets. Data sets with highest correlation are picked and then further optimized using a genetic algorithm. The experimental data sets to which the model has been optimised were viscosity data (this study), degradation of oleic acid concentration data 8 and oligomer ratios 4 . These data sets cover a wide range of particle size and ozone concentration, a necessary condition to restrain the kinetic regime of the reaction system 9 . It can be seen that KM-SUB reproduces all the experimental results very well with a single set of kinetic parameters, as shown in Table S1.
The oleic acid -ozone reaction mechanism has been investigated extensively in the past (e.g. ref 2,3 ), but too complex mechanisms would leave to much freedom to the kinetic model. The model mechanism is hence kept as simple yet compliant with the current literature as possible (Eqs. R1-R7).
As a result, the kinetic parameters of the model have to be seen as effective parameters of simplified processes and their numerical value should not be over interpreted. The range of the kinetic input parameters however was constantly monitored and cross-checked with literature estimates if available and we find no unrealistic kinetic parameters. Rate constants were determined to be in the range of 1×10 -18 to 2×10 -16 cm 3 s -1 ; diffusion coefficients did not fall below 1×10 -9 cm 2 s -1 , still corresponding to a liquid solution. Henry's law coefficient lies within a factor of 1.5 with what has been estimated before in the literature 10 .
During the model building process, the chemical mechanism had to be iterated several times until a good agreement with the experimental data could be obtained. The initial reaction of oleic acid and ozone is well-described by a near-surface bulk reaction producing Criegee intermediates. The model reproduces oleic acid decay data fully (ref 8 , Fig. S9). Criegee intermediates play a central role as they function as building blocks for the oligomers, which are responsible for the viscosity increase.
This general idea is compliant with the observed product distribution showing a gradual decrease in the abundance of oligomers with increasing length (Fig. 4e). The model fitting determines the relative rates of CI oligomerization vs. CI removal that leads to such a distribution. The fact that higher order oligomers affect the viscosity much stronger than lower order oligomers, a result returned from the model fitting, explains the time delay between oleic acid consumption and increase in viscosity that leads to the s-shape in the measured viscosity data versus time. A mechanism where reactive intermediates are added subsequently to existing oligomers is further backed up by the fact that the final viscosity is mostly independent of particle size and oxidant concentration: this can only be understood when the processes leading to oligomerization are all pseudo-first order i.e. one reactant (here: oligomers) being available in excess over another very reactive compound (here: Criegee intermediate).       size dependent response, (Fig 3c main text). Importantly, two negative controls were completed to test the imaging protocol and molecular rotor. We confirmed that without ozone exposure the droplet viscosity did not change (purple dotted line, a-c) and that squalane aerosols (unreactive to ozone) with BODIPY-C 10 under ozone also showed no change to viscosity (turquois star black outline,    Movie S1. Visualising the diffusion fronts during hydration of oxidised myrcene aerosol (impactor collection method) by FLIM. The timescale of the movie is 0 -23h. A selection of stills of the movie is shown in Fig. 2, main text.
Movie S2. Visualising the development of heterogeneity in oleic acid droplet (69.4 m diameter) during its exposure to 377 ppm of ozone for 1000 sec. The lifetime distribution in a droplet is visualised against a rainbow colour hue of 1 ns width (same increment), such that the increasing spread in colours indicates increasing heterogeneity. Note, the centre point of each 'colour hue' shifts with time as shown in the histogram of Fig. 4b, main text. A selection of stills from the movie is shown in Fig. 4b, main text.