A new method for estimating the extinction efficiency of polystyrene microsphere by micro-FTIR spectroscopy

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 181 (2017) 249–253

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A new method for estimating the extinction efficiency of polystyrene microsphere by micro-FTIR spectroscopy Shu-Feng Pang ⁎, Jing Wang, Yun Zhang, Chun-Bo Leng, Yun-Hong Zhang ⁎ The Institute of Chemical Physics, School of Chemistry and Chemical Engineering, Beijing Institute of Technology, Beijing 100081, China

a r t i c l e

i n f o

Article history: Received 16 December 2016 Received in revised form 23 March 2017 Accepted 28 March 2017 Available online 30 March 2017 Keywords: Micro-FTIR Microsphere Extinction efficiency (Qext) Aperture Mie scattering

a b s t r a c t The IR spectra of a single, isolated polystyrene sphere with diameter of 4.46 μm under different aperture sizes have been measured by Micro-FTIR spectrometer and the scattering signal can be seen obviously. Based on Mie scattering theory, a feasible method has been proposed to estimate the extinction efficiency (Qext) of microsphere. Qext from Mid-IR spectroscopy is consistent well with that derived from MiePlot software. It shows that the extinction efficiency of microsphere with the size of the Mid-IR range (2.5 μm–25 μm), which exhibits weak IR absorption, can be obtained by using the present method based on recorded Micro-FTIR spectra. © 2017 Elsevier B.V. All rights reserved.

1. Introduction The impact of aerosols on the Earth's climate and air quality is important, yet there remained a major uncertainty in climate change models as reported in the Intergovernmental Panel on Climate Change (IPCC) report [1]. These large uncertainties are due to inadequate knowledge of aerosol optical properties and their large spatial and temporal variation. The radiative properties of aerosols directly acting on climate by scattering and absorption, which give rise to a “cooling effect” on the climate, [2] are controlled by their optical and physical features [3–5]. The sum of the scattering and absorbing efficiency is the extinction efficiency (Qext), which is often used to describe the light attenuation in the course of propagation. A variety of instruments have been used to study aerosol optical properties in laboratory measurements. Cavity ring down spectroscopy (CRDS) is an important new contender for making highly sensitive measurement of absolute extinction by an aerosol sample without prior instrument calibration. The Qext at 532 nm was examined using continuous wave CRDS with high sensitivity and repetition [6]. But by using CRDS technique, only aerosol extinction can be detected for the sphere in the range of nanometer size up to a micron [7,8]. Polar and integrating nephelometers also are applied to measure the particle scattering cross-section [9,10]. whereas, these suffer from truncation errors due to instrumental geometry which generally limits the angular viewing range from ~ 7° to ~ 170° [11]. Such errors become more

⁎ Corresponding authors. E-mail addresses: [email protected] (S.-F. Pang), [email protected] (Y.-H. Zhang).

http://dx.doi.org/10.1016/j.saa.2017.03.063 1386-1425/© 2017 Elsevier B.V. All rights reserved.

pronounced as the particle size parameter increases. How to gain Qext of the aerosols with the size of microns is under study. In recent years, micro-infrared spectroscopy has been used to study the biological and biomedical sample, because it is sensitive enough to allows the acquisition of spectral data from objects as small as fractions of human cells, and of small regions of microtome tissue sections [12, 13]. In studies of human cells and tissue by Micro-FTIR, several researches have demonstrated the Mie scattering from infrared spectra of biological cells [14,15]. The existence of scattering signals may affect seriously the identification of characteristic peaks, leading to possible errors in spectral analysis. However, for the small particles, the scattering signals also can be used to evaluate extinction effect. In 2010, Davis et al. reported a complete but complicated solution [16,17]. 2013, Dijk et al. provided a seminal algorithm for retrieving the scatter extinction from experimental micro-infrared spectra of PMMA spheres, [18] however, the algorithm is computationally expensive. In present paper, a simpler approach was proposed to extract the scattering efficiency from IR transmission spectra of a single polystyrene microsphere with known size by mathematical conversion. The polystyrene sphere is selected as the studied object because that the absorption, scattering cross sections are known by the Mie theory and refractive index of polystyrene has been reported [19]. 2. Experimental Approach The polystyrene sphere suspension is purchased from the Corporation of Weike in Wuhan. Before measurement, drops of suspension are added into 10 mL distilled water to get mono-dispersed microspheres. In the experiment, a drop of polystyrene suspension is first

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deposited onto a ZnSe substrate with 2 mm thickness and then is allowed to evaporate for several minutes. Thus, some dried and isolated polystyrene spheres with the diameter of 4.46 μm, measured by microscope, can be achieved. The infrared spectra are recorded by Nicolet IN10 Micro-FTIR spectrometer equipped with a liquid-nitrogen-cooled Mercury-CadmiumTelluride (MCT) detector. A pictorial representation of experimental optical path of Micro-FTIR is shown in Fig. 1. The parallel incident beam is reflected by Reflector 1 to two concave semi-spherical mirrors (objectives) to form tapered beam, and the θ1 = 10.17, θ2 = 43.67, coning angle θ2-θ1 = 33.5°. When the tapered beam irradiates to a single polystyrene sphere, the transmission and scattering light both reach the condensers. After they are reflected by Reflector 2, the parallel beam is then focused onto the MCT detector. In the measurement, the size of aperture was adjusted from 10 × 10 μm2 to 200 × 200 μm2 gradually in steps of 10 × 10 μm2, where only a single polystyrene sphere was probed. For each aperture size, a sample spectrum and a corresponding background spectrum on a blank ZnSe substrate were acquired by 64 scans with spectral resolution of 8 cm.

3. Results and Discussion 3.1. The FTIR Spectra of a Single Polystyrene Microsphere Fig. 2 shows the FTIR spectra of polystyrene microsphere with different aperture sizes of 60 × 60 μm2, 100 × 100 μm2, 140 × 140 μm2 and 180 × 180 μm2. The four curves all exhibit regular ripple shape, sloped baseline and local maximum. The regular ripple shape and sloped baseline imply the scattering effect, which comes from the complex interactions of scattered and incident rays, and the local maximum may be due to interference of the incident and diffracted light at the particle-medium interface [20]. In the whole mid-IR range, the characteristic bands from sample are very weak except the two discernable bands at 1488 cm− 1 and 1444 cm−1, which are assigned to C_C stretching mode. These characteristic peaks will not affect the analysis of extinct efficiency of the present polystyrene.

Fig. 2. The transmission IR spectra of 4.46 μm diameter single polystyrene microsphere on ZnSe substrate with the various aperture sizes.

3.2. The Preliminary Building of Approximation Model for Extinction Efficiency From FTIR Spectra Consider a spherical particle illuminated by parallel beam with wavenumber of λ, the transmission beam is weaker than incident beam because of the particle attenuates incident beam by both scattering and absorption, and the sum of the two processes is referred to as extinction. So the particle attenuates incident beam can be expressed: Eext ¼ Einc −Etrans

ð1Þ

where Eext, Einc and Etrans represents extinction energy, incident energy and transmission energy, respectively. When the aperture area is S, the Eext is: Eext ¼ ðI0 −IÞ  S

ð2Þ

where the I0 and I (W·m−2) represent incident and transmission energy density, respectively. In addition, the Eext can also be calculated by the extinction cross section, Cext (m2) and the incident energy density I0 (W·m−2) [21]: Eext ¼ I0  Cext

ð3Þ

Relating the Eqs. (2) to (3) can give the following equation: ðI 0 −IÞ  S ¼ I0  C ext

ð4Þ

The extinction cross section, Cext, can be given by the extinction efficiency Qext multiplying the particle geometrical cross section, which is πr2for spheric particle. C ext ¼ πr 2  Q ext

ð5Þ

It is well known that the transmittance, T, is followed as: T¼

I I0

ð6Þ

T can be gained by the FTIR spectrum. Combination of the Eqs. (5) and (6) with Eq. (4) can get the extinction efficiency, Qext, which can be expressed as: Fig. 1. Schematic diagram of transmission mode for Micro-FTIR spectrometer. The sample was illuminated by a conical shell beam with a range of angles from 10.17°to 43.67°.

Q ext ¼

ð1−T Þ S πr 2

ð7Þ

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Thus the experimental extinction spectrum can be obtained from transmission spectra by using the Eq. (7). Fig. 3 shows the extinction spectra (solid line) corresponding to that in Fig. 2, which show the extinction efficiency dependent upon the aperture size.

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is the calculated results. It is obvious that the theoretical Qext is independent to the aperture size, which is different from the experimental Qext (solid line) dependent upon the aperture size. The inconsistent suggests that the above preliminary model is imperfect to assess the extinction efficiency and need to be calibrated.

3.3. The Calculation of Theoretical Qext and Estimation of Preliminary Model 3.4. Calibration of Preliminary Model for Extinction Efficiency The theoretical Qext can be calculated based on classical light scattering theory [22]. According to the Mie scattering theory, the extinction of a particle depends on the chemical composition, shape, size, orientation, the number and refractive index of particles, the surrounding medium, the polarization state and the frequency of incident beam [23]. So it is necessary to know these parameters for calculating the Qext. Herein, we consider extinction by a single polystyrene spherical particle in air and illuminated by IR beam. The refractive index of air was taken as 1. When an incident beam is lighting on a single spherical polystyrene particle, the interaction between incident radiation and polystyrene can be expressed as a function of the material refractive index m, [24] which is commonly represented by the complex notation defined as: m ¼ n−ki

ð8Þ

In the notation of complex refractive index, the real part of the refraction index (n) is closely related to optical scattering, which can be decided by an inverse method. In this method, n can be expressed as: n¼Aþ

B λ2

þ

C λ4

The above approximation model is based on the assumption that the single spherical particle is illuminated by a parallel beam and that scattered radiation at all directions can reach the detector. However, in present micro-FTIR technique, only the cone beam with the 33.5° angle can be collected by the detector (shown in Fig. 1). The cone beam intensity interacted with the particle is different from that of parallel beam at each aperture size. So the fraction of scattering light, f, and the light intensity coefficient P will be used to calibrate the disagreement in Fig. 3. At first, the accurate extinction coefficient is determined corresponding to the present 33.5° cone channel. When the IR beam lights a single particle, there are different incident angles α among the conical shell beam (inset of in Fig. 4), so the near forward scattered light through angles from 0° to α and from 0° to 33.5 − α can be collected by detector. If A0 expresses the scattered light intensity over all angles, A1 and A2 are the intensity in a particular direction from 0 to α and 0 to 33.5−α, respectively. Then the fraction of the scattered light, f, can be gained by the following description:

ð9Þ

For polystyrene with λ in units micrometer, the parameters are A = 1.5725, B = 0.0031080, and C = 0.00034779. In present experiment, the wavelength in Mid-infrared region is from 2.5 to 25 μm, so the value approximate to 1.57 can be obtained from this formula [19]. While the imaginary part (k) characterizes absorption effect and always been affected by n. In Fig. 2, the absorption intensity in IR spectra is weak, so the value of imaginary part of complex refractive index is small enough to be neglected. So the refractive index m is taken as 1.57 in calculating Qext. After the m has been provided, the Qext of the polystyrene can be calculated from MiePlot software. This software is based on the BHMIE code published in Appendix A of the book “Absorption and Scattering of Light by Small Particles” [23] by using the Mie scattering algorithm. The calculations of the impulse response of a spherical particle are based on the work of Heinrich Bech and Alfred Leder [25,26]. The dash line in Fig. 3

Fig. 3. The experimental extinction spectra based on approximate mode and calculated extinction spectra by Mieplot software.

f ¼

A 1 þ A2 A0

ð10Þ

To gain the A1, A2 and A0 in the Eq. (8), the distribution of the scattering with the angle is necessary. Herein, the incident wavelength of 4 μm, which is close to the diameter of a particle. By Mieplot software, the scattering intensity as a function of the angular distributions can be obtained (shown in Fig. 4). The 0° angle represents forward scattering while the 180° angle is back scattering. It shows that scattering in near forward directions is much greater than that in near backward directions, which is consistent with the feature of Mie scattering. Integrating the area over 0° to 180°, 0° to α and 0° to 33.5− α, separately, giving the corresponding A0, A1 and A2. Because each incident angle is corresponding to a particular f value, so the average of all f should be obtained. In present mode, it is assumed that α change every 3° (Δα = 3°) in the conical shell, so the ten different f values can be obtained. The average

Fig. 4. The angular distributions of scattered light based on the Mie scattering theory. The incident wavelength is 4 μm, the diameter and refractive index of the particle is 4.46 μm and 1.57, respectively. The inset is an illustration of the light in present work.

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experimental smallest aperture is 10 μm × 10 μm, which is described as Smin), the conical incident beam can be viewed as the parallel light. The incident energy is defined as E0 corresponding to Smin, therefore, the energy of parallel light is in direct proportion to the aperture size: E2 ¼ E 0 

S Smin

ð11Þ

Based on the Eq. (11), The E2 can be calculated (shown in upper of Fig. 5). Comparing the energy of conical beam (E1), which are measured in experiment, the E1 is smaller than E2 and the discrepancy between E1 and E2 became larger with the aperture size S. A factor P is used to calibrate the derivation: P¼

Fig. 5. (a) Experimental energy and planar energy as a function of the aperture size. (b) The ratio P = E1/E2 dependent on the aperture sizes.

of the ten f values is 0.5092, which is relatively precise. So the actual extinct cross section in present conical shell beam is f·Cext. Next, the coefficient P needs to be determined. The energy of conical incident beam is different from that of parallel beam. It means that the incident energy irradiating on a polystyrene sphere E1 is different from that of planar wave E2. When the aperture is very small (the

E1 E2

ð12Þ

The P values at different aperture sizes have been shown at bottom of Fig. 5. The genuine intensity interacted with particle is I0 × P and transmitted is I × P. So the following equation can be obtained: P  ð1−T Þ  S ¼ f  πr 2  Q ext P  ð1−T Þ  S Q ext ¼ f  πr 2

ð13Þ

According to Eq. (13), the Qext values corresponding to different aperture sizes in Mid-IR range have been known, which are shown in Fig. 6.

Fig. 6. Comparison of the theoretical Qext (dashed curve) fitted with MiePlot software and the experimental Qext (full curve) modeled with Eq. (13) at different apertures.

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3.5. Estimation of Extinction Efficiency From Calibration Model Comparison of the extinction efficiency based on Eq. (11) from theoretical curves can estimate the experimental extinction efficiency and examine the validity of the calibration model. In Fig. 6a–d, the solid lines are the experimental Qext based on the calibration modes and the dash lines is theoretical value fitted by MiePlot software. The error bars are standard deviations rising from the ten times calculations of fraction f. Because the present particle has a diameter of 4.46 μm, which is close to the wavelength at 2500 cm− 1, so the theoretical value was fitted by the incident wave λ = 4 μm. It shows the excellent agreement between experimental and the theoretical value around 2500 cm−1. The theoretical Qext value at 2500 cm−1 is 4.5, which corresponds to the scattering maximum and not influenced by characteristic chemical absorption bands in present study. At other wavenumbers, there are differences between the experimental and theoretical Qext. The discrepancy may be attributed to derivation of the selected incident wavelength in MiePlot software. We calculated several values of f using different incident wavelength, which are 0.5676, 0.5405, 0.3731, 0.3038, 0.2531 corresponding to 2.5 μm, 3 μm, 6 μm, 8 μm, 10 μm, respectively. It means that the true f values corresponding to wavelength is different from the average f (0.5092). So the error of f value can explain the observed discrepancy. From the above analysis, the calibration model is validity for acquiring the true extinction efficiency Qext of spherical particles with the size of 2.5–25 μm. The data exhibits good agreement with that from CWCRDS, [6] which further confirmed the feasibility of the present method by Micro-FTIR technique.

[2]

[3] [4] [5] [6]

[7] [8]

[9]

[10]

[11]

[12] [13] [14]

4. Conclusion [15]

FTIR spectra of a single polystyrene microsphere under different aperture sizes have been measured, which are featured by the ripple structure, sloping baseline and local maximum. Combining the experimental condition with the Mie scattering theory, a new method for estimating the extinction efficiency (Qext) has been proposed. In present method, the fraction of the scattered light, f, the aperture size S and the light coefficient P have been considered. Qext calculated from the present method shows great consistence with the theoretical Qext from classical light scattering theory. The advantage of this method is that we can directly measure the extinction efficiencies of the micro-spheres at Mid-IR range, which plays the key role to climate. And the present method has the application potential to forecasting the extinction effects of the atmospheric aerosols. Acknowledgements We thank the National Natural Science Foundation of China (91644101, 21373026, 41175119, and 21473009) and thank Jonathan P. Reid very much for his advices.

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[19]

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