Theory
2.4 Aerosol Mixing State and Volatility
an Aitken, an accumulation and a coarse mode with median diameters of 0.05, 0.2 and 2 µm and a common GSD = 2. Further shown are the corresponding surface and volume size distributions. It is apparent that, while the particle number concentration is dominated by the small Aitken and accumulation mode particles, the surface and especially the volume size distribution are governed by the coarse particles. This demonstrates that it is crucial to choose the appropriate moment size distribution when studying a particular aerosol feature. However, due to their direct relationship, the whole information given by the different moment distributions is already contained in the lognormal parameters of a single moment size distribution. For instance, for a N-modal distribution all information is included in the 3N parameters determining the NSD, i.e. the set ofnmode,CMDandGSDof the individual modes. From this NSD parameter set (or the parameter set of any other moment distribution) the moments of all other distributions can be directly calculated. Inserting Eq. (2.3.5) into Eq. (2.3.3) yields the q-th moment of the k-th moment distribution
Mqk =CMDqkexp (qlnGSD)2 2
!
=CMDqexp
kq+ q2 2
!
(lnGSD)2
!
The mean particle diameter for the volume size distribution, for instance, results from k = 3 and q = 1. This study concentrates on particle NSD. Yet, by means of the previous formulae the NSD results presented later on (cf. Tab. B.5.1 to B.5.3) can easily be converted into higher order distributions.
It should be mentioned that in practice the NSD and the other moment size distri-butions are often plotted not only on a logarithmic abscissa but also on a logarithmic ordinate to reveal all details of the distributions. The area under such a curve no longer represents the integral quantity, such as particle number concentration, but the logarithm thereof. Moreover, to guarantee comparability between size distributions that are measured under different pressure and temperature conditions, concentra-tions are regularly expressed in reference to standard temperature and pressure (STP) conditions. Any concentration size distribution recorded at pressure p and tempera-ture T, determining the aerosol parcel volume V, is converted to STP conditions by multiplication with the factor
fST P = V
VST P = pST P p
T
TST P (2.3.6)
with the standard pressure pST P, temperature TST P and corresponding parcel volume VST P. In physics, pST P and TST P are usually defined as 1013.25 hPa and 273.15 K.
Accordingly, a STP size distribution corresponds to the size distribution that would be measured upon bringing the aerosol parcel to these reference conditions (assuming an ideal gas).
Figure 2.4.1: Transmission electron microscopy images of different aerosol particle mixing states. The upper and lower row show particles before and after electron bombardment (heating), respectively. Images (a) and (b) display a rather pure non-refractory sulfate particle. Images (c) and (d) present an internal mixture of sulfate and refractory soot, where the soot is embedded within a sulfate coating. Images (e) and (f) show another internal mixture of these components, this time in form of a coagulation product. Adopted from Kandler et al. (2011).
the situation is more complex and several particulate components are present. How different components/materials are distributed among the particles is described by the aerosol mixing state. One extreme case is a completely externally mixed aerosol where individual particles are made up of one single component only. An example would be an aerosol with particles that are either pure ammonium sulfate or pure mineral dust.
The other extreme is an entirely internally mixed aerosol in which all components are equally distributed among the particles. Sticking to the previous example, this would mean that all particles carry the same (volumetric) amount of mineral dust and ammonium sulfate. Internal mixtures can arise from coalescence or coagulation of particles, heterogeneous condensation of vapor molecules onto particles and chemical reactions at the particle surface. Figure 2.4.1 shows exemplary transmission electron microscopy images for possible mixing states, i.e. a pure sulfate particle and two examples for internal mixtures of soot and sulfate, one where the soot is coated, i.e.
situated in the particle core with a sulfate shell, and another where the particle is a coagulation product of these two components.
It is evident that the mixing state can have important implications. Assuming again a two-component mixture between hygroscopic ammonium sulfate and hardly hygroscopic mineral dust and recalling Sect. 2.1, an external mixture would imply dif-ferences in the CCN ability of equally sized particles. This means that at certain sizes the ammonium sulfate particles would activate into droplets at a given water vapor su-persaturation while mineral dust particles of the same size would remain non-activated.
In contrast, in an internal mixture all particles would exhibit the same hygroscopicity, so that particles of equal size would all activate at the same supersaturation. Mixtures also affect the optical properties of particles via the refractive index. Erlick (2006) compares refractive indices for two-component mixtures predicted by various mixing
rules and demonstrates that obtaining a representative refractive index can be compli-cated even for such simple scenarios. However, when the shape and spatial distribution of the different materials within a particle are unknown, a simple linear volume mixing rule often provides sufficiently good estimates (Erlick, 2006; Michel Flores et al., 2012).
In the majority of cases, aerosols are neither strictly externally nor internally mixed but have an intermediate mixing state, which means that both pure components and particle mixtures of various degrees are present. The mixing state can further be size-dependent since, as mentioned in Sect. 2.3, aerosols regularly feature distinct size modes arising from different sources and particles from the individual modes are not necessarily blending. For example, the measurements of Kandler et al. (2009) in North-west Africa (see Fig. 1.3.2) show a joint occurrence of internal and external mixtures of dust and sulfate, and a pronounced size-dependence of particle composition. The mix-ing state might also be a function of aerosol lifetime. If particle coagulation/coalescence rates are low and no vapor is present that could induce heterogeneous processes, the aerosol mixing state can stay rather constant with time. On the other hand, the oppo-site might be the case when reactive particles and vapors are present. In consequence, information on the size-dependent aerosol mixing state provides important insights into the physiochemical particle properties and their evolution.
One way to assess the aerosol mixing state is to measure the so-called volatility of the particles, i.e. their stability upon exposure to high temperatures. When an aerosol is heated to a certain temperature particle components that are non-refractory will pass over into the gaseous phase by evaporation/sublimation. For a completely internally mixed aerosol containing a non-refractory (volatile) particle component this would cause a uniform relative shrinkage of all particles. The total particle number is conserved in this case but the size distribution shifts towards smaller diameters. An externally mixed aerosol, on the other hand, would lose its volatile particles connoting a reduction in total particle number to the refractory fraction. Particle volatility information can be gained either by microscopic techniques or by a combination of size distribution measurements using heating methods. The former is demonstrated in Fig. 2.4.1. Here, single particle images before and after heating are compared with each other to derive a refractory particle volume fraction rf that is defined by the initial and remnant particle volumesVi and Vr as
rf = Vr
Vi (2.4.1)
Vi and Vr are usually estimated from the projected area equivalent diameters. For single-component particlesrf is either 0 (refractory, volatile) or 1 (refractory, non-volatile), while it is in between these limits for particle mixtures. The other way to determine the aerosol mixing state in terms of particle volatility is to compare the NSD before and after exposure to high temperature, i.e. the total NSDF (D) and the NSD of the refractory remainderFr(D). From these size distributions a size-dependent volatile particle fraction vf (D) can be defined as
vf (D) = 1− Fr(D)
F(D) (2.4.2)
To obtainFr(D), the aerosol particle population is commonly passed through a heated tube previous to the measurement (see Sect. 3.2.1). Although vf (D) ≤ 1 for most
Figure 2.5.1: Illustration of mechanisms occurring during aerosol sampling and trans-port that lead to a distortion of aerosol measurements. Adopted from von der Weiden et al. (2009).
realistic scenarios, the volatile fraction can theoretically also exceed unity since the loss of particles with diameterD by shrinkage or complete vaporization is counteracted by the gain of shrunken particles with larger initial diameters.
Certainly, particle volatility can only provide indirect information about the im-portant intrinsic particle properties, such as particle hygroscopicity. Nevertheless, es-pecially in combination with additional information on the aerosol’s chemical compo-sition, the mixing state with respect to volatility proofs to be a useful measurand (e.g.
Brooks et al., 2007).