Effects of Cascading Optical Processes: Part I: Impacts on Quantification of Sample Scattering Extinction, Intensity, and Depolarization

Abstract

Light scattering is a universal matter property that is especially prominent in nanoscale or larger materials. However, the effects of scattering-based cascading optical processes on experimental quantification of sample absorption, scattering, and emission intensities, as well as scattering and emission depolarization, have not been adequately addressed. Using a series of polystyrene nanoparticles (PSNPs) of different sizes as model analytes, we present a computational and experimental study on the effects of cascading light scattering on experimental quantification of NP scattering activities (scattering cross-section or molar coefficient), intensity, and depolarization. Part II and Part III of this series of companion articles explore the effects of cascading optical processes on sample absorption and fluorescence measurements, respectively. A general theoretical model is developed on how forward scattered light complicates the general applicability of Beer's law to the experimental UV−vis spectrum of scattering samples. The correlation between the scattering intensity and PSNP concentration is highly complicated with no robust linearity even when the scatterers' concentration is very low. Such complexity arises from the combination of concentration-dependence of light scattering depolarization and the scattering inner filter effects (IFEs). Scattering depolarization increases with the PSNP scattering extinction (thereby, its concentration) but can never reach unity (isotropic) due to the polarization dependence of the scattering IFE. The insights from this study are important for understanding the strengths and limitations of various scattering-based techniques for material characterization including nanoparticle quantification. They are also foundational for quantitative mechanistic understanding on the effects of light scattering on sample absorption and fluorescence measurements.

Effects of Cascading Optical Processes: Part II: Impacts on Experimental Quantification of Sample Absorption and Scattering Properties

“…Equation is derived based on a similar theoretical consideration for developing the mathematical equation for correlating the sample experimental and theoretical extinction for scattering-only samples . Substitution of eq into eq leads to eq , where the logarithm terms (the second term in eq ) are identical to the equation for correlating experimental scattering extinction with the sample theoretical scattering extinction. E UV ( λ ) = prefix− log nobreak0em.25em⁡ I 0 ( λ ) 10 − E normalT ( λ ) false) + ( λ ) 0.25em I fS ( λ ) 10 − A ( λ ) I 0 ( λ ) E normalT ( λ ) = ε normalS ( λ ) l C normalS + ε normalA ( λ ) l C normalA = S ( λ )…”

“…A (λ) and S (λ) are the sample absorbance and scattering extinctions. E UV , UL ( λ ) = min ( S UL false( λ false) SER false( λ false) , A UL false( λ false) ) Equation shows that the experimental UV–vis spectrum can be approximated as the sample theoretical extinction spectrum for calculating the analyte concentration or extinction coefficient only when forward scattered light is insignificant in comparison to I 0 (λ) 10 –S(λ) . In other words, the scattering extinction of turbid samples must be below S UL (λ), the upper limit of scattering extinction for scattering-only samples . Therefore, the upper limit of the Beer’s-law-abiding experimental UV–vis extinction ( E UV,UL (λ)) of the samples that contain both light absorbers and scatterers can be predicted using eq , where A UL (λ) is the upper LDR limit of the UV–vis instrument that is quantified using a pure light absorber.…”

“…In other words, no isotropic light scattering can be achieved regardless of the degree of multiple scattering that occurs within the sample. Mechanistically, this phenomenon is caused by the polarization dependence of the scattering IFE …”

“…Such information is important for ensuring the reliability of using UV–vis spectra for experimental quantification of molar extinction coefficient of materials and for chemical quantifications. It is also relevant, considering the fact, that interference from forward scattered light can cause the measured UV–vis extinction to deviate from Beer’s law, even when the measured UV–vis intensity is within the instrument LDR …”

“…Intrinsic scattering depolarization is a fundamental material property, and it depends on the scatterers’ size, shape, and electronic structures. − However, experimental quantification of intrinsic scattering depolarization of scatterers is challenging. Sample scattering depolarization increases with increasing sample scatterers’ concentration due to increasing multiplicative scattering. , However, the impact of light absorption on sample scattering depolarization is unclear. Resolving this issue is necessary for reliable interpretation of sample scattering depolarization spectra and for understanding the impact of light absorption and scattering on the fluorescence depolarization.…”