Multiangle Light-Scattering Measurements of Refractive Index of Submicron Atmospheric Particles

Figures & data

FIG. 1 Photograph of the DAWN-A optical assembly showing the argon-ion laser, light-scattering chamber, and fiber-optic detectors. Azimuthal (φ) and polar (θ) angular coordinate directions are indicated by arrows.

FIG. 2 Schematic diagram of the flow system used for generation and sampling of calibration particles.

FIG. 3 RH-dependent refractive index of sulfuric acid and ammonium sulfate derived from partial molar refractions at λ = 488 nm.

TABLE 1 Cauchy dispersion parameters, values of n calculated from the Cauchy formula

	Cauchy dispersion n = a + b/λ^2		n calculated from Cauchy dispersion
Species	a	b (μ m^2)	λ = 0.488 μ m	λ = 0.5893 μ m
DOS	1.4371*	3.8772 e-3	1.4534	1.4483
DOP	1.4677*	5.7789 e-1	1.4920	1.4843
PSL	1.5683†	10.087 e-3	1.6107	1.5973
*Derived from Abbé refractometer measurements.
†Kerker (1969).

FIG. 4 Responses to six different 0.3-μ m calibration particles vs. Lorenz-Mie theoretical dimensionless irradiances calculated for polar angles θ = 55° and 75°.

FIG. 5 Example of the χ²-best-fit inference of the real component of refractive index shown for a 0.3-μ m ammonium sulfate droplet. Scattering diagrams calculated with Lorenz-Mie theory are shown for the expected refractive index (broken line) and the inverted refractive index (solid line).

TABLE 2 Errors in inferred refractive indices (inferred-expected) for calibration particles. For the values shown, shape distinction was not applied to the measurements prior to their inversion

Material	Wet H2 SO4	Wet (NH4)2 SO4	Dry H2 SO4	DOS	DOP			Solid (NH4)2SO4	Solid NaCl
RH	69–72	69–73	8–9					7–9	5–6
Expected n	1.376 to 1.378	1.411 to 1.415	1.421 to 1.423	1.453	1.492	Droplet	Droplet	1.531	1.553
D p (μ m)	Δ n	Δ n	Δ n	Δ n	Δ n	Average Δ n	St. Dev. Δ n	Δ n	Δ n
0.2	−0.008	+0.024	+0.024	−0.011	−0.007	+0.004	0.018	−0.033	−0.070
0.3	−0.016	+0.009	+0.036	−0.002	−0.018	+0.002	0.022	−0.015	−0.065
0.4	−0.004	+0.019	+0.027	−0.004	−0.008	+0.006	0.016	−0.030	−0.064
0.5	−0.010	+0.005	+0.018	−0.002	−0.022	−0.002	0.015	−0.037	−0.065
0.6	−0.024	+0.015	+0.025	−0.004	−0.009	+0.001	0.019	−0.054	−0.153
0.7	−0.009	+0.005	+0.015	+0.002	−0.007	+0.001	0.010	−0.069	−0.107
0.8		−0.001		+0.004	−0.008	−0.002	0.006	−0.066	−0.106
Average	−0.012	+0.011	+0.024	−0.003	−0.011	+0.001	0.015	−0.043	−0.090

Table 3 Errors in inferred refractive indices (inferred-expected) for light-absorbing DPS particles measured during the SEAVS field study. The values shown are for selected spherical subfractions to which laboratory/field “hybrid” calibrations were applied. The expected real part of the refractive index is n = 1.449

Known k	0.002	0.005	0.010
D p (μ m)	Δ n	Δ n	Δ n	Average	St. Dev.
0.2	+0.024	+0.010	−0.016	+0.006	0.020
0.3	+0.006	−0.005	−0.013	−0.004	0.010
0.4	−0.015	−0.012	−0.014	−0.013	0.002
0.5	+0.008	−0.008	−0.020	−0.006	0.014
0.6	−0.010	+0.014	+0.006	+0.004	0.012
Average	0.003	0.000	−0.011	−.003	0.012

FIG. 6 Sensitivity of angular scattering to the real and imaginary components of the complex refractive index, illustrated with scattering diagrams calculated for a matrix of refractive indices defined by real values n = 1.40 and 1.45 and imaginary values k = 0.000 and 0.010.

FIG. 7 Inference of size-dependent atmospheric particle refractive index from χ²-best-fits of Mie theory to calibrated responses. Angular scattering patterns are compared for wet and dry samples for D _p = 0.2 μ m (a), 0.3 μ m (b), 0.4 μ m (c), and 0.5 μ m (d).

FIG. 8 Inference of atmospheric particle refractive from a χ²-best-fit of Mie theory to calibrated response for D _p = 0.8 μ m. The angular scattering pattern for the inferred value (solid line) is compared to patterns calculated for water (dotted line) and crystalline ammonium sulfate (dashed line).

TABLE 4 Species properties assumed for refractive index modeling. Refractive index real and imaginary components n and k are specified for a wavelength of λ = 488 nm

Species	Mass CCF*	Density (g/cm^3)	n	k
OC	2.1	1.4	1.46	0.0
EC	1.0	1.9	1.93	0.66
SO4	1.12–1.376	1.77–1.84	1.47–1.54	0.0
H2O	1.0	1.0	1.337	0.0
*The component conversion factor (CCF) is the multiplicative factor that converts OC to organics or sulfate to a salt of ammonium and sulfate.

TABLE 5 Properties used for modeling refractive index of dry (∼ 0% RH) ammoniated sulfate. Properties of ammonium bisulfate and letovicite were determined from interpolation of sulfuric acid and ammonium sulfate properties, where the ammonium-to-sulfate molar ratio, B, is the dependent variable. Values of R and n are for λ = 488 nm unless indicated otherwise

Sulfate Species	B	M	CCF	ρ	V	R	n (Eq. 11)	n Lit.
Sulfuric acid	0.0	98.072	1.021	1.841	53.271	13.621	1.425	1.443 ^a
Ammonium bisulfate	1.0	115.11	1.198	1.805	63.773	18.571	1.494	1.473 ^b
Letovicite	1.5	123.62	1.287	1.787	69.177	21.045	1.520	1.523 ^c
ammonium sulfate	2.0	132.14	1.376	1.769	74.698	23.520	1.542	1.531 ^c

FIG. 9 Study-average dry Δ n values resulting from variation of dry OC n. The size-average of these values is minimized for OC n = 1.45 (average Δ n = −0.0003 among the sizes shown).

TABLE 6 Size-dependent, study-averaged real refractive indices n measured at RH = 4–10% (dry) and results from comparison with modeled values. Assumed properties for dry organics are ρ = 1.4 and n = 1.46

D p , μ m	x	Meas. Dry n (RH = 4–10%)	k T	Δ n T	R T
0.2	1.3	1.488 ± .018	.0170	.007	0.52
0.3	1.9	1.496 ± .018	.0173	−.001	0.67
0.4	2.6	1.497 ± .021	.0085	.002	0.62
0.5	3.2	1.493 ± .017	.0084	.003	0.46
Ave., 0.2–0.5 μ m	1.494 ± .018		.003	0.57
n: Average and standard deviation of the real part of the complex refractive index inferred from DAWN-A measurements.
k: Average of the imaginary component values assumed for Mie-theory inversions of the real component values.
Δ n: Average of (modeled n - measured n).
T: Subscript denoting estimation of water content from TDMA measurements.
R: Coefficient of correlation between modeled and measured values of n.
x: Dimensionless size parameter (x = πD p /λ; Eq. 2a).

TABLE 7 Size-dependent, study-averaged real refractive indices measured at RH = 44–76% (wet) and results from comparison with modeled values. Assumed properties for dry organics are ρ = 1.4 and n = 1.46

D p , μ m	x	Meas. Wet n (RH = 44–76%)	k I + O	Δ n I + O	R I + O	Δ n I	R I	Δ n T	R T
0.2	1.3	1.406 ± .023	.0091	.016	0.34	.033	0.16	.035	0.23
0.3	1.9	1.425 ± .018	.0095	−.002	0.59	.014	0.64	.017	0.26
0.4	2.6	1.406 ± .027	.0043	.014	0.58	.023	0.59	.042	0.29
0.5	3.2	1.424 ± .018	.0044	−.004	0.58	.004	0.63	.024	0.27
0.6	3.9	1.404 ± .023	.0027	.011	0.42	.014	0.52	.041	0.19
0.7	4.5	1.398 ± .015	.0017	.013	0.73	.014	0.72	.041	0.81
0.8	5.2	1.417 ± .016	.0018	−.013	0.75	−.012	0.76	.016	0.95
Ave., 0.2–0.5 μ m		1.415 ± .022		.006	0.52	.018	0.50	.030	0.26
n: Average and standard deviation of the real part of the complex refractive index inferred from DAWN-A measurements.
k: Average of the imaginary component values assumed for Mie-theory inversions of the real component values.
Δ n: Average of (modeled n - measured n).
I: Subscript denoting the use of water content estimates for the inorganic fraction (ammoniated sulfate) using the ZSR method.
I+O: Subscript denoting the use of the sum of water content estimates for organic and inorganic fractions.
T: Subscript denoting estimation of water content from TDMA measurements.
R: Coefficient of correlation between modeled and measured values of n.
x: Dimensionless size parameter (x = πD p /λ; Eq. 2a).

FIG. 10 Comparison of modeled refractive indices with atmospheric refractive indices measured by the DAWN-A during SEAVS for D _p = 0.3 μ m. Two estimates of water content are compared for wet indices: thermodynamically predicted water associated with supersaturated ammoniated sulfates (I; inorganic contribution), and the sum of the inorganic contribution and water content associated with organics (I+O).

FIG. 11 Time-series comparisons of modeled refractive indices with atmospheric refractive indices measured by the DAWN-A during SEAVS for D _p = 0.3 μ m. For wet indices, modeled water content includes contributions from both inorganic and organic aerosol fractions (I+O).

Merwin , H. E. 1930 . “ Refractivity of Birefringent Crystals ” . In International Critical Tables of Numerical Data Physics, Chemistry and Technology , Edited by: Washburn , E. W. , West , C. J. , Dorsey , N. E. and Ring , M. D. 16 New York : McGraw-Hill .

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