J. Phys. Chem. A 2010, 114, 7077–7084
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Influence of Uncertainties in the Diameter and Refractive Index of Calibration Polystyrene Beads on the Retrieval of Aerosol Optical Properties Using Cavity Ring Down Spectroscopy Rachael E. H. Miles, Svemir Rudic´, Andrew J. Orr-Ewing, and Jonathan P. Reid* School of Chemistry, UniVersity of Bristol, Bristol BS8 1TS, United Kingdom ReceiVed: April 11, 2010; ReVised Manuscript ReceiVed: June 2, 2010
We consider the impact of uncertainties in the refractive index and size of polystyrene beads on the retrieved optical properties of aerosol particles by aerosol cavity ring down spectroscopy (A-CRDS). Polystyrene beads are frequently used to verify and calibrate light extinction measurements by cavity ring down instruments. Any uncertainties in either the polymer particle size or the refractive index can contribute to systematic errors in properties retrieved for any subsequent measurements on other aerosol types. We demonstrate that the tolerances on bead size reported by the manufacturers can lead to a range in the real part of the refractive index of the polymer beads retrieved from A-CRDS measurements of as large as 2.9%. Further, we show that the current uncertainty in the refractive index of polystyrene beads in the visible part of the electromagnetic spectrum limits the accuracy with which the real part of the refractive index of other aerosol types can be retrieved to uncertainties of -0.5% and +0.3% at a minimum. This error should be included in any subsequent retrieval of aerosol optical properties from aerosol cavity ring down instruments that are dependent on polystyrene bead calibration. It is expected that such calibrations could lead to significantly larger uncertainties if the complex part of the refractive index is to be retrieved. I. Introduction Direct climate forcing by atmospheric aerosol is known to lead to a net negative radiative forcing; however, uncertainties in the magnitude of this effect prevent accurate modeling of future climate change.1 The radiative forcing effects of aerosol are determined by their optical properties, which depend not only on the physical characteristics of the aerosol (size, shape, etc.), but also on the wavelength-dependent refractive index of the particle medium. The measurement of aerosol optical properties to retrieve refractive index information is critical to understanding and predicting perturbations in the radiative balance of the atmosphere. In recent years, the use of aerosol cavity ring down spectroscopy (A-CRDS) to measure optical properties has become increasingly popular due to its high sensitivity and ability to measure absolute extinction by aerosol particles. A wide variety of field2-7 and laboratory-based8-17 studies have been undertaken, using both pulsed8,11-14,16-22 and cw-laser systems.10,15,23-26 The optical properties of a range of nonabsorbing, atmospherically relevant inorganic salts such as sodium chloride and ammonium sulfate,13,16,21,27 and organic compounds such as glutaric acid,13,14 have been measured, in addition to absorbing aerosol containing nigrosin dye,14,16 humic like substances,19 and soot.8,28 As well as single component aerosol, the optical properties of internal and external mixtures of both nonabsorbing and absorbing aerosol media have been investigated. Rudich and co-workers,13 Garland et al.,11 Freedman et al.,27 and Beaver et al.9 have all studied extinction by internally mixed aerosol composed of nonabsorbing components or mixtures of nonabsorbing and absorbing components. Experimental data have been compared to predictions from various optical mixing rules. Radney et al. have studied the optical properties of an external * Corresponding author. E-mail:
[email protected].
mixture of absorbing nigrosin dye and ammonium sulfate aerosol.16 Khalizov et al.8 and Xue and co-workers17 have used A-CRDS to study the influence of nonabsorbing coatings on the optical properties of freshly generated soot particles. Measurements of extinction by different particle morphologies, such as core-shell aerosol, have also been made. Lack et al. used a photoacoustic absorption spectrometer in addition to an A-CRDS instrument to study the enhancement in extinction and absorption seen when absorbing polystyrene spheres were coated with oleic acid.18 Rudich and co-workers studied the optical properties of core-shell particles composed of an absorbing nigrosin core with a nonabsorbing shell of solid glutaric acid or liquid diethyl-hexyl-sebacate.14 Both authors retrieved values of particle refractive index from measurements on single component aerosol and compared the optical extinction of the mixed component aerosol to predictions from core-shell Mie theory. Despite the capability of determining absolute values of particle refractive index by aerosol cavity ring down, the capacity of any new instrument to accurately extract aerosol optical properties must first be assessed through validation experiments on aerosol with known optical properties. Any difference between the experimentally measured and theoretically predicted light extinction necessitates the estimation of a calibration factor that must be included in the analysis of data from samples with unknown optical properties. Monodisperse polystyrene spheres are commonly used as aerosol analogues and have been widely used in A-CRDS validation experiments.2,8,10,12,13,15,16,18,19,21,24-26,29 As such, any uncertainty in the size of the polystyrene spheres or their refractive index will have implications for instrument testing and thus the accuracy of optical parameters retrieved for other aerosol systems. Here, we present the results of validation experiments using polystyrene spheres on a new aerosol cavity ring down instrument, highlighting the effect that an inherent uncertainty in the diameter of such particles has on the refractive index retrieved from the experimental data. Further, we present the
10.1021/jp103246t 2010 American Chemical Society Published on Web 06/15/2010
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Miles et al.
results of a review of polystyrene refractive indices reported in the literature, which suggests that the true value of the polystyrene refractive index is still in dispute. The consequences of these uncertainties in the calibrant aerosol should be accounted for when reporting the retrieved optical properties of aerosol of unknown refractive index. II. Experimental Section Aerosol optical properties are commonly given with reference to the size parameter, x, the dimensionless ratio of the particle circumference, πd, to the wavelength of the illuminating radiation, λ.
x)
πd λ
(1)
Through measurements of optical extinction for particles of varying diameter at constant illumination wavelength, the size parameter dependence of the extinction efficiency, Qext, can be determined experimentally. For spherical particles (and to a first approximation for nonspherical particles), such data can be compared to predictions from Mie theory and the refractive index retrieved for the aerosol medium at the wavelength of interest.13,14,19,24,30,31 In a previous publication, we retrieved the polystyrene refractive index over the wavelength range 540-570 nm through measurement of Qext as a function of size parameter, where the particle diameter was kept the same and the illumination wavelength varied.30 In this work, optical extinction measurements are performed at a constant illumination wavelength of 560 nm using monodisperse polystyrene beads with mean diameters of 240, 299, 349, 404, 453, 498, 596, and 707 nm (3000 Series, Nanosphere Size Standards, Thermo Scientific, previously sold by Duke Scientific), corresponding to a range in size parameter from 1.346 to 3.966. The experimental setup for studying 5% for the smallest particles studied by A-CRDS. Indeed, extinction data recorded from the low size limit are often weighted most heavily in the retrieval of refractive index data from A-CRDS measurements due to the higher degree of precision in the measurements: the lower optical cross-section allows measurements to be performed at higher number concentrations leading to the most precise determinations of the extinction efficiency. The variability in the theoretical estimate of the extinction efficiency arising from the uncertainty associated with the bead diameter and refractive index can lead to systematic errors in the calculation of the merit function for recovering the optimal fit from eq 4 and, thus, in the accuracy of the retrieved optical properties. The dominant contribution to this systematic error would be the uncertainty in the refractive index of the polymer beads, provided that the bead sizes used are not all at the lower or upper end of the quoted bead
Retrieval of Aerosol Optical Properties Using CRDS
J. Phys. Chem. A, Vol. 114, No. 26, 2010 7083 In summary, in any A-CRD measurement that is based on retrieving optical constants for an aerosol based on a prior polymer bead calibration, it is essential that raw extinction values for the unknown aerosol be corrected to provide both upper and lower extinction values based on the accepted lower and upper values of the refractive index of the polymer beads used for calibration. This is particularly important if the aerosol is both scattering and absorbing, and the extinction measurements are being used to retrieve both the real and the imaginary parts of the complex refractive index. If the uncertainty in the refractive index of the polymer beads is not accounted for by obtaining upper and lower limits on the calibration factor, the imaginary part of the refractive index may be artificially lower or higher than its true value as it compensates for the inaccuracies incurred in the estimation of the correction factor from the calibration. IV. Conclusions
Figure 8. (a) Sensitivity of calculated extinction efficiency to the tolerance on the bead size and the reported refractive index treatments. The benchmark refractive index is taken to be that of Matheson.37 Percentage differences in extinction efficiency when compared to that calculated from the benchmark refractive index are shown by filled symbols (nr ) 1.5860 at 560 nm, Ma38) and open symbols (nr ) 1.6005 at 560 nm, Bateman41). The upper and lower tolerances on the bead size (from Table 1) are shown by circles and squares, respectively. (b) Illustration of the error incurred in the refractive index fitting for sodium chloride aerosol once the systematic error in a polymer bead calibration is accounted for. The horizontal bars denote the upper, best, and lower estimates of the extinction efficiencies of the sodium chloride aerosol based on a simulated correction of raw extinction data using a polymer bead calibration (for particle sizes of 240, 349, 453, and 596 nm). The solid and dashed black lines show the impact of the upper, best, and lower estimates of the extinction efficiencies on the refractive index fit.
tolerances, which leads to the unlikely but significant uncertainty identified in Figure 7. If the calibration of an A-CRDS instrument is performed using polystyrene beads, assuming the Matheson and Saunderson treatment of refractive index and the nominal bead diameter, extinction efficiencies recorded on an unknown aerosol sample and corrected by a polymer bead calibration could be in error by as much as -3% to +2%. An example of the error incurred in the retrieved value of the refractive index from a set of measurements is shown in Figure 8b. In this example, we consider a dry sodium chloride aerosol sample of refractive index nr ) 1.544. Once again, the refractive index of the polymer beads used for the instrument calibration is taken to be in the interval set by the Ma et al.38 and Bateman et al.41 parametrizations. The systematic uncertainty in the polystyrene refractive index leads to systematic under- or overestimates in the extinction efficiency recorded from the sodium chloride aerosol. The ensuing errors associated with retrieval of the refractive index of the sodium chloride aerosol are shown in Figure 8b, +0.004 . At with the determined value estimated to be nr ) 1.544-0.007 + 0.3% and -0.5%, these errors are larger than or comparable to the error reported in many A-CRDS measurements, which range from ∼0.2%19 to ∼0.7%,24 both measured for ammonium sulfate.
The performance of A-CRD instruments is often verified by using monodisperse polymer beads as an aerosol sample. However, we suggest that care must be taken in interpreting such extinction measurements and it is essential to consider the inherent uncertainties in bead size and refractive index, particularly if they are being used to perform a calibration of instrumental parameters for correction of subsequent measurements. Values of the refractive index at λ ) 560 nm reported in the literature vary from 1.586 to 1.630, a range of ∼2.7%. This can lead to uncertainties in the theoretical estimate of the extinction efficiency and can have the consequence of introducing systematic errors into the calibration of A-CRDS. In turn, this leads to systematic errors in the retrieval of optical constants from subsequent aerosol samples, which can be in the range -0.5 to +0.3%. We have also shown that uncertainties in bead diameter of only (6 nm, arising from the tolerances associated with the TEM calibration of the polystyrene spheres with NIST SRM, can lead to significant errors in the polystyrene refractive index retrieved from experimental measurements. A-CRD spectroscopy remains a particularly sensitive and robust approach for examining the optical properties of aerosol. However, it is important to be aware of the errors incurred even in retrieving the refractive index of a supposedly well-characterized sample, polystyrene spheres, when the accuracy of measurements on aerosol of less well-known composition, homogeneity, and mixing state is to be assessed. Acknowledgment. This study was funded by NERC grant NE/C512537/1. S.R. and R.E.H.M. are grateful to the NERC and EPSRC for postdoctoral and studentship funding, respectively. A.J.O.-E. thanks the Royal Society and Wolfson Foundation for a Research Merit Award. and J.P.R. acknowledges the EPSRC for Leadership Fellowship funding. We thank Miss Jin Kim for helpful discussions. References and Notes (1) Forster, P.; Ramaswamy, V.; Artaxo, P.; Berntsen, T.; Betts, R.; Fahey, D. W.; Haywood, J.; Lean, J.; Lowe, D. C.; Myhre, G.; Nganga, J.; Prinn, R.; Raga, G.; Schulz, M.; Van Dorland, R. Changes in Atmospheric Constituents and in Radiative Forcing. In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the IntergoVernmental Panel on Climate Change; Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., Miller, H. L., Eds.; Cambridge University Press: New York, 2007. (2) Strawa, A. W.; Elleman, R.; Hallar, A. G.; Covert, D.; Ricci, K.; Provencal, R.; Owano, T. W.; Jonsson, H. H.; Schmid, B.; Luu, A. P.; Bokarius, K.; Andrews, E. J. Geophys. Res. 2006, 111, D05S03.
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