Paul Devlin 4
Department of Chemistry University of British Columbia Vancouver, British Columbia, Canada
Chemical Sciences Division Lawrence Berkeley National Laboratory Berkeley, California
Physikalische Chemie Freie Universitọt Berlin Berlin, Germany
Department of Physics and Astronomy University of Iowa
U.S Army Research Laboratory Adelphi, Maryland
Center for Global and Regional Environmental Research
University of Iowa Iowa City, Iowa
Department of Physics and Astronomy University of Iowa
School of Chemistry University of Bristol Bristol, United Kingdom
Physikalische ChemieFreie Universitọt BerlinBerlin, Germany
Department of Chemical and Biomolecular
Hong Kong University of Science and
Institute for Meteorology and Climate
Gwangju Institute of Science and
Gwangju, Republic of Korea and
Department of Chemistry University of Antwerp (Campus Drie Eiken), Universiteitsplein, Wilrijk-Antwerpen, Belgium
Department of Chemistry University of British Columbia Vancouver, British Columbia, Canada
School of Chemistry University of Bristol Bristol, United Kingdom
Department of Environmental Sciences Weizmann Institute
Physikalische Chemie Freie Universitọt Berlin Berlin, Germany
Karlsruhe Institute of Technology Institute for Meteorology and Climate Research
Hermann-von-Helmholtz-Platz Eggenstein-Leopoldshafen, Germany
Department of Physics Kansas State University Manhattan, Kansas
Astrophysical Institute and University Observatory
Friedrich-Schiller-University JenaSchillergọòchen, Jena, Germany
Centre for Atmospheric and Instrumentation
University of Antwerp (Campus Drie Eiken)
Institute for Meteorology and Climate Research
Physikalische Chemie Freie Universitọt Berlin Berlin, Germany
Chemical Sciences Division Lawrence Berkeley National Laboratory Berkeley, California
University of Geneva—GAP- Biophotonics
Rue de l’Ecole de Medecine Geneva, Switzerland
Department of Chemistry University of Antwerp (Campus Drie Eiken) Universiteitsplein, Wilrijk-Antwerpen, Belgium
Department of ChemistryUniversity of IowaIowa City, Iowa
1 Infrared Spectroscopy of Aerosol Particles
Thomas Leisner and Robert Wagner
Mid-infrared extinction spectroscopy is a crucial technique for analyzing the microphysical properties of aerosols, including their size, shape, and phase, and is applicable in both laboratory and remote sensing contexts The extinction of an infrared beam results from the combined effects of light absorption and scattering by aerosol particles, with absorption being predominant for particles smaller than approximately 200 nm This method leverages the unique absorption bands of organic and inorganic functional groups in aerosol particles, facilitating effective chemical characterization Notable applications include tracking the chemical changes of secondary organic aerosol in smog chambers and differentiating various polar stratospheric cloud particles through satellite infrared data Additionally, infrared spectroscopy is particularly effective in studying the deliquescent and efflorescent behaviors of aerosols, as it can detect phase transitions by monitoring the broad liquid water absorption band around 3300 cm−1.
1.2.1 Particle Sizes Small Compared to the Wavelength (Rayleigh Regime) 5
1.2.1.1 General Equations and Comparison with
1.2.1.3 Derivation of Optical Constants from the Absorption Spectra of
1.2.2 Infrared Extinction Spectra of Wavelength-Sized Particles (Mie Regime) 10
1.2.2.1 Dependence of the Spectral Habitus on the Particle Size 10
1.3.1 Typical Infrared Spectral Habitus of Large Cloud Particles 17
1.3.2 Solution Ambiguity of the Size Distribution Retrieval for
References 22 also a common experimental tool in studies on the ice-freezing behavior of supercooled aqueous solution droplets 10−14
In the realm of small particles, Rayleigh theory indicates that the absorption spectrum is primarily influenced by the particle volume rather than the aerosol size distribution However, for particles with diameters under approximately 20 nm, notable size-dependent phenomena can emerge, especially in cases involving equivalent molecules and vibrational bands with significant molecular transition dipoles These size-dependent spectral characteristics can be effectively modeled using the quantum-mechanical vibrational exciton model, which accounts for resonant transition dipole coupling among the molecules within the aerosol particle As illustrated by the asymmetric stretching mode of CO2, the modulation of intermolecular interactions by particle boundaries becomes crucial for diameters below 20 nm, leading to distinct fine structures in the absorption spectrum for each particle size within this range.
For particle diameters exceeding 200 nm, scattering effects in infrared extinction spectra become evident, resulting in slanted baselines in nonabsorbing spectral regions and distortion of absorption bands Unlike the Rayleigh limit, scattering is size-sensitive and can be utilized to determine aerosol size distributions through a least-squares minimization of measured and calculated infrared spectra Classical scattering theories, including Mie theory for spherical particles and T-matrix or discrete dipole approximation for nonspherical particles, are commonly employed for these calculations The effectiveness of this method depends on precise frequency-dependent optical constants, specifically the real (n) and imaginary (k) components of the complex refractive index Recent research has focused on enhancing the database of optical constants for relevant aerosol particles, with significant attention given to the temperature-dependent infrared refractive indices of various substances, including the H2SO4/H2O/HNO3 system, supercooled water, and ice.
Spherical particles allow for accurate retrieval of bi- or multimodal aerosol size distributions from infrared extinction spectra However, important aerosol constituents like sodium chloride, ammonium sulfate, mineral dust, and ice crystals often exhibit irregular shapes, complicating spectral analysis due to size and shape ambiguities This ambiguity can hinder the precise determination of aerosol particle size and shape, necessitating prior information or independent measurements for accurate characterization Additionally, particle shape significantly impacts the scattering contributions of larger aerosols and alters the absorption band spectra in the Rayleigh limit For specific optical constants, shape-dependent resonances can cause the spectrum of small particles to diverge from the bulk absorption spectrum, highlighting the critical role of particle shape in spectral sensitivity.
This article provides a concise overview of how size and shape influence the infrared extinction spectra of aerosol particles, using classical continuum models It discusses methods for deriving optical constants from the extinction spectra of airborne particles while highlighting the uncertainties related to retrieving size distributions for nonspherical particles Additionally, it presents selected applications of aerosol infrared spectroscopy for determining particle properties and analyzing multiphase aerosol processes, based on measurements conducted in the AIDA large aerosol and cloud chamber at the Karlsruhe Institute of Technology.
1.2.1 P article S izeS S mall c omPared to the W avelength (r ayleigh r egime )
1.2.1.1 General equations and comparison with Bulk Absorption Measurements
For infrared optical depth measurements on airborne particles, the Lambert–Beer equation can be written under the single scattering criterion in discrete form as τ( ) ( )
The optical depth τ( )ν j at a specific wave number ν j is connected to the optical path length l, the number concentration n(D i ) of particles within a designated size bin D i of width ΔD, and the size-bin averaged extinction cross-section C ext( , D i ν j ).
The extinction cross-section C ext is the sum of the absorption cross-section C abs and the scattering cross-section C sca:
In the Rayleigh approximation, the absorption cross-section of a small sphere for transmission measurements in air (refractive index of the medium ≈ 1) is written as
The volume of a sphere with diameter D is represented by V(D), while the complex refractive index of the particle is denoted as N(ν) = n(ν) + ik(ν) Equation 1.4 is based on the assumptions that x = πDν ≈ j 1 and that x N| (ν) | ≈ 1 Additionally, if the scattering contribution to extinction is negligible, Equation 1.1 simplifies to τ = π.
The recorded optical depth is determined solely by the total particle-volume concentration (V_tot), independent of the aerosol number size distribution (n(D_i)) This means that different size distributions with the same overall particle-volume concentration produce identical infrared absorption spectra Additionally, when comparing this with the absorption spectrum of the same substance in the bulk phase, it is noted that for transmission measurements of a thin film with thickness d, the optical depth is directly proportional to the imaginary part of the complex refractive index.
The optical depth ratio for small particles and thin films is proportional to n(ν) / ((νj nνj² - k(νj)² + 2)² + (nνj k(νj)²)²) In spectral regimes with weak absorption bands (k < 0.3), the proportionality factor simplifies to n(ν) / ((νj nνj² + 2)²), assuming n(ν)νj ≫ k(νj) in the relevant wave number range As n(νj) shows only minor dispersion features, the small-particle absorption spectrum closely resembles that of the bulk phase, as illustrated in panels a and b of Figure 1.1, using aqueous sulfuric acid (25 wt% H₂SO₄) as an example.
FIGure 1.1 Panel a: Small-particle absorption spectrum of aqueous sulfuric acid with 25 wt% H2SO4
The absorption spectrum of crystalline ammonium sulfate spheres is analyzed, revealing significant differences between small-particle and bulk absorption features Utilizing Equation 1.5 with parameters V_tot = 1000 μm³/cm³ and l = 100 m, and based on optical constants from Earle et al at 298 K, the small-particle absorption spectrum shows enhanced intensity and a shift to higher wave numbers, particularly in the intense v₃ (SO₄²⁻) absorption band at 1100 cm⁻¹ This shift indicates that the spectral characteristics, including band intensity and peak position, deviate from the corresponding bulk absorption, suggesting that certain spectral regimes may meet the resonance condition inherent in Equation 1.5 Comparisons with the thin-film absorption spectrum calculated using Equation 1.6 further illustrate these phenomena, highlighting the complex interactions within the absorption spectra of small spheres.
The spectral characteristics of intense small-particle absorption bands are significantly influenced by particle shape, particularly in needle- and disk-like spheroids, which are two subcategories of ellipsoidal particles For a comprehensive analysis of shape effects, readers are encouraged to consult the textbook by Bohren and Huffman In the context of ellipsoidal particles, it is essential to incorporate the geometrical factor L into the formula for calculating the absorption cross-section.
The particle diameter \( D_V \) represents the diameter of a sphere with the same volume as a nonspherical particle For ellipsoids, each of the three principal axes has a distinct geometrical factor \( L \) (denoted as \( L_1, L_2, \) and \( L_3 \)), and the average absorption cross-section for randomly oriented ellipsoids is calculated as the arithmetic mean of these factors In the case of a sphere where \( L_1 = L_2 = L_3 = \frac{1}{3} \), the absorption equation simplifies accordingly For needle- and disk-like spheroids, two distinct geometrical factors emerge, leading to the potential observation of two resonances, in contrast to the single absorption band seen in spheres The intensity and spectral splitting of these bands depend on the spectral variation of the refractive index \( n \) and extinction coefficient \( k \) over the relevant wave number range For instance, the absorption spectra of crystalline ammonium sulfate needles and disks demonstrate band splitting, with a common mode at 1090 cm\(^{-1}\) for both shapes, while the disk-like shape exhibits increased intensity due to its contribution to the averaged cross-section Additionally, the needle absorption band at 1120 cm\(^{-1}\) and the shoulder at 1140 cm\(^{-1}\) for disks correspond to resonances for \( L = 0.5 \).
The needle-like shape of the two bands results in increased intensity, attributed to the doubled weight of the L = 0.5 principal cross-section and a more favorable resonance condition in comparison to the geometrical factor L = 1.
Recent studies, including those by Sigurbjửrnsson et al., have successfully utilized the quantum-mechanical vibrational exciton model to analyze the shape effects in the infrared absorption spectra of Rayleigh-sized particles, specifically with radii ranging from 10 to 100 nm These studies indicate that significant shape effects are observed primarily in intense vibrational bands characterized by high molecular transition dipoles This observation suggests that strong resonant intermolecular transition dipole coupling serves as the microscopic basis for the shape effects seen in small-particle absorption spectra The resulting exciton coupling facilitates the delocalization of excitation energy across the entire particle, contributing to the shape sensitivity of the absorption bands.
In addition to crystalline ammonium sulfate, significant aerosol components such as mineral dust exhibit notable shape-dependent infrared absorption bands in specific spectral regions Mineral dust containing silicates is particularly characterized by a distinct Si–O stretch resonance near a certain wavelength.
1050 cm −1 ), 31 nitric acid dihydrate (in the nitrate absorption regime between 1500 and 1000 cm −1 ), 32 and ammonia aerosols (ν2 N–H bending mode at 1060 cm −1 ) 33