Optical Characterization of the Properties of Media Containing Nanoscale Nonuniformities

Transcription

1 Optical Characterization of the Properties of Media Containing Nanoscale Nonuniformities Gordon T. Mitchell, Anatol M. Brodsky, and Lloyd W. Burgess Center for Process Analytical Chemistry Department of Chemistry University of Washington Seattle, WA, USA

2 Outline Introduction Optical Analysis of Heterogeneous Media Grating Light Reflection Spectroscopy (GLRS) Optical Low-Coherence Reflectometry (OLCR) Conclusion

3 Introduction Many systems of commercial and scientific interest are highly heterogeneous.

4 Introduction The heterogeneous properties of such systems makes analysis challenging: Highly concentrated Wide range of sizes, broad PSD Strongly absorbing and/or scattering Undergo dynamic changes Need for in situ real time process sensors suitable to these kinds of applications along with adequate theoretical descriptions of properties of samples of interest.

5 Outline Introduction Optical Analysis of Heterogeneous Media Grating Light Reflection Spectroscopy (GLRS) Optical Low-Coherence Reflectometry (OLCR) Conclusion

6 Optical Analysis of Heterogeneous Media Optical methods are preferred for these types of analyses for their speed and non-invasive nature. However, we must deal with the phenomenon of light scattering. Csca 4π = 2 k β ( ) Im A The scattering cross-section of a particle depends on the complex scattering amplitude function, A β. β

7 Optical Analysis of Heterogeneous Media The exact form of A β is complicated, and depends non-trivially on the morphology and dielectric properties of the particle, and the wavelength and polarization state of the incident light.

8 Optical Analysis of Heterogeneous Media Simplified expressions for A β () exist for limiting cases: Rayleigh interval Resonance interval Fraunhofer interval (R/λ < 1) (R/λ ~ 1) (R/λ > >1) ( ) Re A β Im A β 3 3 Rβ 1 = ε 2 p εm 2 λ 2+ ε 3 4 R β ( ) = ( εp εm) 4 3 λεm m 2 y 1 e Aβ ixr y e 2 y 2 y ( ) = β + + ( 1) ( εp εm) y = 2ix ω x = 2πRβ c ε m ( ) Re A = β ( ) Im A β = S β λ Knowing the form of A β (), we can predict the angle, intensity, and polarization of the scattered light as well as the complex dielectric function of the system. c ε ω = 2π β nmω β ( ) N A( ) By measuring ε, we can gain information about the physical properties of the scatterers. 2 β

9 Outline Introduction Optical Analysis of Heterogeneous Media Grating Light Reflection Spectroscopy (GLRS) Optical Low-Coherence Reflectometry (OLCR) Conclusion

10 Grating Light Reflection Spectroscopy Critical wavelength depends on Re ε (i.e. refractive index of sample) Ω m = Reε sinθ + λm Λ 2

11 Grating Light Reflection Spectroscopy Imε Reε I 2 mcr mcr = const. ξ Ω + Ω + 2 ( Imε ) 2 Sharpness of transition depends on Im ε (i.e. scattering and absorbance of sample) For convenience in visualization and data manipulation, we often take derivatives of the spectral data. Re ε and Im ε track independently.

12 GLRS Instrumentation

13 GLRS Response to Random Scatterers The observed dielectric function of randomly-distributed spheres is given by: ( ) = n ( ) = n ( ) + ( ) ε ω ω ω κ ω m c κ ω = 2π β nmω β ( ) N A( ) In the Rayleigh limit, we can directly relate κ to particle radius, R, size distribution width Δ, dielectric contrast γ, and concentration of scatterers, ρ. by: ρ 1 c R c Δ c ω Reκ = sin y cos y+ sin y 2 R cos y 2nm 4γ ω 2γ ω 4 ω c ρ R c R c 1 c Δ c ω Imκ = sin y ( 1 cos y) + 1 cos y+ 2 R sin y 2nm 2 ω 2γ ω 4Δ ω 4 ω c 2 β We have studied model systems of polystyrene nanospheres with R < 1 nm and ρ from 1 1%. G.T. Mitchell, A.M. Brodsky, and L.W. Burgess, Optical Analysis of Nanoscale Nonuniformities using Grating Light Reflection Spectroscopy, J. Opt. Soc. Am., in press, June 29.

14 GLRS Response to Random Scatterers Determination of PSD from GLRS data Observed Predicted With some knowledge of the system (γ, ρ ), direct solution of the inverse solution (i.e. obtaining particle properties from spectral data) is theoretically possible using curve-fitting software, but complete deconvolution of parameters is difficult.

15 Outline Introduction Optical Analysis of Heterogeneous Media Grating Light Reflection Spectroscopy (GLRS) Optical Low-Coherence Reflectometry (OLCR) Conclusion

16 Optical Low Coherence Reflectometry Response to structured materials

17 OLCR Instrumentation Optiphase All-Fiber Autocorrelator INST-1 Illumination source: 131 nm SLED Sweep range: ~ 5 mm Scan speed: ~1 Hz

18 OLCR Biomedical Imaging Left ankle Right ankle?

19 OLCR Response to Random Scatterers Randomly-distributed nonhomogeneity produce an exponential decay as photons are incoherently scattered as they travel into the sample. ( ) ( α l = + ) log S-S log 1 C e β c ρ ( ) 2 cos y 1 1 ω n y siny 2 α = R y y y y c 3ρ 1 1 cosy sin y β = + ω Rn 2 2 y y Results are for monodisperse particles, but valid over resonance interval. A. M. Brodsky, G. T. Mitchell, S. L. Ziegler, and L. W. Burgess, "Coherence Loss in Light Backscattering by Random Media with Nanoscale Nonuniformities," Phys. Rev. E 75, 4665 (27).

20 OLCR Response to Random Scatterers Particle sizes range from 2 nm 2 μm span from Rayleigh to Fraunhofer limit Coherent Backscatter Signal (log S Intensity log So ) (db) Coherent Backscatter Signal (log Intensity S log So (db) ) Particle Radius (nm) λ(mm) 3 Photon Dwell Distance (mm) λ(mm) Particle Radius (nm) Photon Dwell Distance (mm) 1% 1%

21 OLCR Response to Random Scatterers Observed vs. Predicted α values Coincident maxima indicated single scattering events even at 1% solids. Correspondence with theory is good, but solving the inverse problem in the resonance interval is difficult due to nonmonotonic response.

22 Outline Introduction Optical Analysis of Heterogeneous Media Grating Light Reflection Spectroscopy (GLRS) Optical Low-Coherence Reflectometry (OLCR) Conclusion

23 Addendum GLRS and OLCR are also well-adapted to monitoring dynamic processes with qualitative or multivariate data analysis. Attrition milling of active pharmaceutical ingredient monitored with GLRS Second Derivative of Reflected Intensity 2 1 x 1-4 Largest Particle Samples -1 39,27 25,5-2 3, Smallest Particle Samples Wavelength (nm) Agglomeration of polystyrene particles monitored with OLCR

24 Conclusion GLRS and OLCR are versatile optical methods capable of interrogating highly scattering samples in real-time. We have developed theoretical relationships between the physical properties of nanoparticles and observed optical response. GLRS and OLCR can be used to characterize numerous other dynamic and static processes.

25 Acknowledgements Dr. Anatol Brodsky Dr. Lloyd Burgess Dr. Summer Zeigler DOE CPAC