Light and matter interactions such as light absorption, scattering, and emission are among the most fascinating phenomena in nature.
Optical spectroscopic techniques including UV-vis, fluorescence, and light scattering are among the most taught techniques in STEM education.
Moreover, these techniques are widely used measurement techniques in essentially every area of scientific inquiries and technological developments. [1][2][3][4][5][6] The broad availability of commercial optical spectroscopic instruments have made the acquisition of UV-Vis, fluorescence, and scattering intensity spectra trivial. However, the reliable interpretation of experimental data can be challenging, especially for samples where two or more cascading optical processes can be triggered by individual incident photons. 7- 11 Examples of cascading optical events include the re-scattering or absorption of scattered light, emission triggered by light absorption, and so on. Samples that exhibit such cascading optical events are ubiquitous in biological, chemical, environmental, and materials research. Indeed, optical spectroscopic measurements performed with samples that contain pure scatterers, simultaneous absorbers and scatterers, simultaneous absorbers and emitters, and finally simultaneous absorbers, scatterers, and emitters can all be complicated by such cascading optical processes. [11][12][13] In Part I of the three companion articles, we investigated the effects of light scattering on experimental quantification of sample scattering extinction, intensity, and depolarization. The first key learning is the interference of the forward scattered light on the UV-vis spectral acquisition, 14 which can compromise the general applicability of Beer's law for experimental quantification of scatterers' concentration or molar scattering coefficient. The second key finding is that the cascading light scattering complicates the correlation between scattering intensity and the scatterers' concentration. The scattering intensity initially increases with increasing scatterer concentration. However, when the scatterer's concentration is higher than a certain threshold, increasing its concentration further reduces the sample scattering intensity due to scattering inner filter effect (IFE). The third key learning is that scattering depolarization monotonically increases with scatterers' concentration. However, the maximum achievable scattering depolarization remains less than unity even when the sample optical density is very high (e.g., >15). 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. 14 The present work (Part II) is an extension of Part I and focuses on the effects of the cascading optical processes on optical spectroscopic measurement of solutions that contain both absorbers and scatterers, but not emitters. Samples that contain light absorbers, scatterers, and emitters will be discussed in Part III of the companion works. There are four major goals in this study. The first is to establish a general guideline for predicting the linear dynamic range (LDR)
for the UV-vis spectra obtained with samples containing absorbers and scatterers. Such information is important for ensuring the reliability of using UV-vis spectra for experimental quantification of materials' molar extinction coefficient 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. 14 Second, we wish to determine the effects of light absorption on the sample scattering depolarization (or interchangeably scattering anisotropy). Intrinsic scattering depolarization is a fundamental material property, and it depends on the scatterers' size, shape, and electronic structures. [15][16][17][18][19][20][21][22] However, experimental quantification of scatterers' intrinsic scattering depolarization is challenging. Sample scattering depolarization increases with increasing sample scatterers' concentration due to increasing multiplicative scattering. 14,15 However, 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. The latter will be studied in Part III of these companion articles.
Third, we wish to quantify the effects of scattering on the light absorption by chromophores in turbid samples. Conventional UV-vis spectral measurements allow one to quantify the light attenuation along its optical path from the excitation source to the detector. However, it provides no insight into the interplay of light absorption and scattering in the sample, such as the absorption of the scattered photons or the total number of photons absorbed by the sample. Quantifying the actual light absorbed by samples is important for photoactivated nanomaterial applications, including photocatalysis 23,24 , displays 25,26 , photothermal therapy, 27,28 and photodynamic therapy. 29,30 It is the total number of the absorbed photons that is responsible for photocatalyzed reactions, the temperature increase in the photothermal effects, and the singlet oxygen generation in photodynamic therapy. Therefore, it is critical to quantify the total light absorbed to determine the quantum efficiency in these applications.
Fourth, we wish to further examine the validity of the recent ISARS method for quantifying materials absorption and scattering extinction contribution to their UV-vis extinction spectrum.
The ISARS method first quantifies the total fraction of the incident photons absorbed by the sample placed inside integrating sphere and subsequently uses a developed mathematical model by parameterizing ISARS intensity spectra to convert the ISARS-based absorbance to the sample conventional double-beam UV-vis absorbance. 10 The effectiveness of the ISARS methods have been validated with optically transparent chromophores and fluorophores, but not with samples that contain both scatterers and absorbers. If sample scattering has a significant impact on total light absorption, the mathematical model developed for converting the ISARS-based absorbance to the double-beam absorbance can be problematic. Fruitfully, we find that while scattering invariably reduces the light absorption along the optical path length used in conventional UV-vis measurements, its impacts on the total light absorption by the sample is negligibly small under the data acquisition conditions used in this work (vide infra). The TEM images of plain PSNP have been shown before, 14 while that of dPSNPs are shown in the supporting information (Figure S1). KMnO4 was obtained from Sigma-Aldrich and used as received. Nanopure water (18.2 MΩ cm -1 , Thermo Scientific) was used for all sample preparations.
A Shimadzu UV-2600i spectrophotometer with an ISR 2600 integrating-sphere accessory (Duisburg, Germany) was used for all UV-vis and integrating-sphere UV-vis (ISUV) spectra.
Resonance synchronous (RS) and linearly polarized resonance synchronous (LPRS) spectra were obtained using a FluoroMax-4 spectrofluorometer (Horiba Jobin Yvon, Edison, NJ) equipped with excitation and emission linear polarizers. A K-Sphere Petite integrating-sphere (Horiba PTI) with an internal diameter of 80 mm was used for ISARS spectral acquisition. All spectrofluorometer-based spectra were acquired with an integration time of 0.3 s and a bandwidth of 2 nm for both excitation and emission monochromators. The spectral intensity is the ratio between the signal from the sample detector and reference detector (S1/R1). All spectroscopic measurements are performed with a solution volume of 3 mL contained in a 1-cm square fluorescence cuvette.
Gold and silver nanoparticles. Gold nanoparticles (AuNPs) of three different sizes (35±2.4 nm; 54±4.4 nm; 91±8.6 nm) were synthesized using an established stepwise method. 31 Colloidal silver nanoparticle (AgNPs) of three different sizes (38±2.5 nm; 59±4.1 nm; 84±7.5 nm) were also synthesized based on a published protocol. 32 The synthesis procedures, TEM images, and particle size analysis are shown in the Supporting Information (Figures S2 andS3). The theoretical total extinction, absorption extinction, and scattering extinction spectra of the AuNPs and AgNPs were determined using a free, online Mie theory calculator from nanoComposix. 33 Computational simulation. The details of the computational model used is based on electrodynamics theory and the Monte Carlo method, which is discussed in a previous work. 14 The instrumental parameters (cuvette size, solution height and volume, detector collection angle) used in the simulations were close to the experimental parameters. Particle size and incident wavelength were taken from the experiment. We also include the absorption of the nanoparticle, which was treated as zero when modeling polystyrene nanoparticles as pure scatterers. The scattering spectra were collected along directions perpendicular to the incident light direction using a collection angle of 2 degrees.
Sample characterization. Two representative types of samples that contain both light absorbers and scatterers are employed in this study. The first is a mixture of light absorbers and scatterers prepared by mixing carboxylate polystyrene nanoparticles (PSNPs), which are approximately pure scatterers with no significant absorption, 34,35 and KMnO4, a small molecular chromophore that is approximately a pure light absorber. 36 For convenience, we refer to the samples containing both KMnO4 and PSNP as PSNP/KMnO4 solutions. Since those samples are used for probing the interplay between the sample absorptions and scattering, it is important to exclude the possibility of significant physiochemical interactions between KMnO4 and PSNP to ensure the reliability of the spectral interpretation. [37][38][39][40] There are strong optical interactions between the KMnO4 and as-obtained PSNPs. The UV-vis spectrum of KMnO4 mixed with as-obtained PSNPs deviates significantly from the mathematically additive spectrum of KMnO4 and carboxylated PSNPs (Figure S4). Dialysis is effective to eliminate such spectral difference for samples prepared with PSNP100, PSNP200, and PSNP380, as evident from the excellent agreement between the experimental UV-vis spectrum of PSNP/KMnO4 solutions and the mathematic summation of UV-vis spectra of PSNP and KMnO4 controls (Figure 1A), but not that with PSNP50 (Figure S4). As a result, the KMnO4 mixed with dialyzed PSNP100, PSNP200, and PSNP380 are used as the PSNP/KMnO4 solutions in subsequent studies.
The second type of samples used in this study are nanoparticles that are simultaneous light absorbers and scatterers with no significant emission activities. The model analytes include dPSNPs and plasmonic gold and silver nanoparticles (AuNPs and AgNPs, respectively). Unlike the plain PSNPs that are pure light scatterers in the probed wavelength region, dPSNPs contain light-absorbing dyes (vide infra) impregnated inside the polymer matrix. Experimental confirmation of the dye impregnation came from the total absence of the UV-vis feature in the spectrum obtained with the filtrate of the dPSNPs (Figure 1B). Fluorescence measurements confirm that dPSNPs have no significant fluorescence activities (Figure S5).
UV-vis extinction. Part I showed that forward scattered light interferes with the UV-vis spectral measurement, making the experimental scattering extinction spectrum deviate from Beer's law even when the sample theoretical extinction is within the instrument LDR. Theoretically, interference of forward scattered light is a general phenomenon in the UV-vis measurement for scatterer-containing samples. Eq. 1 correlates the sample experimental UV-vis extinction spectra 𝐸𝐸 𝑈𝑈𝑈𝑈 (λ) of solutions containing both absorbers and scatterers and its theoretical counterparts 𝐸𝐸 𝑇𝑇 (λ), is defined by Eq. 2. Eq. 1 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. 14 Substitution of Eq. 2 into Eq. 1 leads to Eq. 3, where the logarithm terms (the second term in Eq. 3) are identical to the equation for correlating experimental scattering extinction with the sample theoretical scattering extinction.
𝐼𝐼 0 (λ)
(1)
𝐼𝐼 0 (λ), 𝐼𝐼 𝑓𝑓𝑆𝑆 (λ), and η(λ) has been defined before. 14 𝐼𝐼 0 (λ) is the intensity of the incident light. 𝐼𝐼 𝑓𝑓𝑆𝑆 (λ) is the forward scattered light without considering the absorption inner filter effect on scattered light, where η(λ) is the fraction of forward scattered light reaching the detector. ε 𝑆𝑆 (λ) and ε 𝐴𝐴 (λ) is the sample scattering and scattering absorption, respectively. 𝐶𝐶 𝐴𝐴 and 𝐶𝐶 𝑆𝑆 are the concentration of the absorbers and scatterers, respectively. They are identical for analytes that are simultaneous light absorbers and scatterers. 𝐴𝐴(λ) and 𝑆𝑆(λ) are the sample absorbance and scattering extinctions.
Eq. 3 shows that the experimental UV-vis spectrum can be approximated as sample theoretical extinction spectrum for calculating the analyte concentration or extinction coefficient only when forward scattered light is insignificant in comparison to 𝐼𝐼 0 (λ)10 -𝑆𝑆(λ) . In other words, the scattering extinction of turbid samples must be below 𝑆𝑆 𝑈𝑈𝑈𝑈 (λ), the upper limit of scattering extinction for scattering-only samples. 14 Therefore, the upper limit of the Beer's-law-abiding experimental UV-vis extinction (𝐸𝐸 𝑈𝑈𝑈𝑈,𝑈𝑈𝑈𝑈 (λ)) of the samples that contain both light absorbers and scatterers can be predicted using Eq. 4, where the 𝐴𝐴 𝑈𝑈𝑈𝑈 (λ) is the upper LDR limit of the UV-vis instrument that is quantified using a pure light absorber. 𝑆𝑆𝐸𝐸𝑆𝑆(λ) is the sample scattering extinction vs. total extinction ratio at the excitation wavelength.
Experimental validation of Eq. 4 for predicting the upper LDR limit of the sample UV-vis extinction are performed with three series of PSNP380/KMnO4 solutions with different scatteringto-extinction ratios (Figure 2). While the LDR range of the UV-vis spectra obtained with the conventional UV-vis and the ISUV for KMnO4, an approximately pure molecular absorber, are the same, the upper LDR limit of UV-vis spectra obtained with the conventional UV-vis method is far higher than that using the ISUV method for the scattering samples. This result is not surprising because the IS collects all forward scattered light and is thereby much more sensitive than conventional UV-vis to the interference of light scattering in UV-vis spectral measurements.
The excellent agreement between the conventional UV-vis and the ISUV spectra of KMnO4 confirms that KMnO4 is predominantly a light absorber with no significant scattering contribution to its UV-vis spectrum.
The instrument upper LDR limit of the spectrophotometer for a pure absorber is ~4 (Figure 2C), which is quantified using KMnO4 at the excitation wavelength of 320 nm. The upper LDR limit at 320 nm for PSNP380, a pure scatterer, is 1.8 (Figure 2I). The upper LDR limit of the experimental extinction of the PSNP380/KMnO4 mixtures with a SER at 320 nm of 0.75 and 0.85 are ~2.4 (Figure 2) and ~2.2 (Figure S6), respectively, which agree with that predicted using Eq.
Apparently, the experimental UV-vis spectrum is equivalent to the sample theoretical extinction only when the measured extinction intensity is within the LDR defined with Eq. 4. In this case, one can use Beer's law to calculate the analyte extinction coefficient and/or concentration, and the sample UV-vis extinction spectrum is the sum of its absorption extinction and scattering extinction spectrum. The latter has significant implication for quantitative separation of scattering and absorption extinction contribution to the sample UV-vis extinction spectrum (vide infra).
Effect of light absorption on scattering intensity. The impact of light absorption on the scattering intensity was investigated by comparing the PSNP scattering intensities between a series of PSNP/KMnO4 and their respective PSNP controls (Figure 3). All PSNP/KMnO4 solutions have the same KMnO4 concentration but differ in the PSNP concentration.
The scattering intensity of the KMnO4-containing PSNP solutions are invariably lower than that of their respective PSNP controls in the wavelength region where KMnO4 absorbs (Figure 3(A-B) and 3(D-E)). The higher the KMnO4 absorbance is at the probed wavelength, the higher the scattering intensity ratio between the PSNP control and its corresponding PSNP/KMnO4 solution (Figure 3C). Critically, these intensity ratios are totally independent of the PSNP concentrations and depend only on the KMnO4 concentration (Figure 3C). The logarithm spectra (Figure 3F) of these intensity ratio spectra are remarkably similar to the UV-vis absorbance spectrum of KMnO4 (Figure S7).
Mechanistically, KMnO4-induced scattering intensity reduction occurs due to KMnO4 absorption of the incident and scattered light, which is known as the absorption inner filter effect (IFE). Earlier works have demonstrated that absorption IFE on scattering intensity can be modelled with Eq. 5, where 𝐼𝐼 𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑎𝑎𝑠𝑠 (λ) and 𝐼𝐼 𝑠𝑠𝑠𝑠𝑠𝑠 0 (λ) are the scattering intensity of the sample with and without light absorbers, respectively. 34 𝐴𝐴(λ) is the double-beam absorption extinction of the absorber-containing sample measured with a cuvette pathlength of 𝑑𝑑 𝑑𝑑𝑎𝑎 (λ), which is 1-cm in most UV-vis measurements, including the ones in this work. 𝑑𝑑 𝑒𝑒𝑓𝑓𝑓𝑓 (λ) is the effective absorption pathlength of photons along the optical excitation and detection paths employed in the scattering intensity detection. For simplicity, we refer to 𝑑𝑑 𝑒𝑒𝑓𝑓𝑓𝑓 (λ) as the effective absorption pathlength.
The effective absorption pathlengths 𝑑𝑑 𝑒𝑒𝑓𝑓𝑓𝑓 (λ) in the PSNP/KMnO4 solutions are the same (1.04±0.03 cm) and are close to 1-cm, as expected from the 1-cm square cuvette used in the scattering intensity measurement. Since the excitation and detection are centered at the middle of the cuvette, one would expect an effective pathlength of 1-cm (0.5 cm for excitation and 0.5 cm for detection) for a perfectly aligned instrument under conditions that light scattering doesn't change the photon pathlengths. The fact that the effective pathlengths for the IFE correction are essentially independent of the sample scattering extinction indicates (Figure 3F) light scattering has no significant impact on the sample effective absorption pathlength or the total light absorption. Absorption on scattering depolarization. Light absorption reduces the sample scatterer depolarization, which is concluded on both experimental measurements (Figure 4) and computational modeling (Figure S8). The experimental samples used for studying the impact of light absorption on the sample scattering depolarization are a series of PSNP/ KMnO4 solutions comprising of PSNPs at a constant concentration and KMnO4 of varying concentrations (Figure 4). The sample scattering depolarization is calculated by dividing the sample LPRS VH spectra by the LPRS VV spectra and then multiplying the results by the instrument G-factor spectrum determined with a reported method. 34 This G-factor spectrum is to correct instrument bias in quantification of light with different polarizations. "VV" and "VH" refers to the combinations of the polarization directions of the excitation linear polarizer (the first letter) and the detector polarizer (the second letter). "V" represents that the light is polarized perpendicular to the instrument plane defined by the light source, sample chamber, and the detector, while "H" indicates that the light is polarized parallel to the instrument plane.
Both LPRS VV and VH intensities decrease with increasing KMnO4 concentration in the wavelength region where KMnO4 absorbs, which is consistent with the absorption inner filter effect discussed in the preceding section (Figure 3). The observation that scattering depolarization decreases with increasing KMnO4 concentration indicates that light absorption attenuates the LPRS VH signal more effectively than LPRS VV intensity. Mechanistically, this phenomenon is due to the combination in the difference of the path lengths of the V and H polarized light, and the interconversion between the V and H polarized lights, as well as the polarization dependence of the scattering IFE. 14 Since the intensity of V and H polarized light changes during each light scattering process, experimental determination of the average optical path length of the V and H polarized light is currently impossible. Apparently, the polarized light that has a longer effective path length will have higher signal attenuation.
It has been well documented that light scattering enhances sample scattering and depolarization. 13,21,22 However, the impact of light absorption on scattering or fluorescence depolarization has, to our knowledge, not been reported. The finding that absorption reduces sample scattering depolarization further highlights the complexity of the cascading optical processes and their impacts on spectroscopic measurements for samples containing both scatterers and absorbers. This finding also raises questions about the potential interference of light absorption on fluorescence anisotropy measurements, a question that will be addressed in part III of this series of companion articles.
Scattering has no effect on the measured sample absorption extinction if the sample experimental extinction is below the upper LDR limit defined with (Eq. 4). This conclusion is drawn based on the additivity of the sample scattering extinction spectrum and the absorption extinction spectrum (Figure 1A). However, experimental quantification of the impact of scattering on the intensity of the absorbed light in the conventional with Eq. 6, Eq. 8, and Eq. 9 as a function of the extinction intensity for samples with an AER = 0.5. (B) (black squares) The double-beam absorption extinction calculated using Eq. 8 and (red dots) the simulated actual light absorption extinction calculated using Eq. 10. The solid line is present to guide the view. Data for the AER from 0.1 to 0.9 with increments of 0.1 are shown in Figures S8 andS9.
UV-vis measurement is challenging. One may be tempted to use Eq. 6 and Eq.7, both derived from Eq. 2, for evaluating the absorbed 𝐼𝐼 𝑠𝑠𝑎𝑎𝑠𝑠 (λ) and scattered light 𝐼𝐼 𝑠𝑠𝑠𝑠𝑠𝑠 (λ), respectively. However, this approach invariably leads to overestimated scattering intensity and underestimated absorption intensities for samples that both absorb and scatter at the probed wavelength (𝑆𝑆(λ) > 0 and 𝐴𝐴(λ) > 0). This is because these equations fail to consider the absorption of the scattered light.
The latter increases the absorbed photon intensity and reduces the scattering intensity predicted with Eq. 6 and Eq. 7, respectively.
There is no current experimental method for quantifying the intensity of absorbed or scattered light by a sample used in conventional UV-vis measurements, without perturbing light/matter interactions. However, the data shown in Figure 3 provides indirect evidence that addition of scatterers to absorbing samples have no significant impact on the total absorbed photons by the light absorbers. Otherwise, the sample absorption IFE imposed by KMnO4 on the scattering intensity will also depend on the PSNP concentration, but not on the KMnO4 concentration alone. This empirical observation is supported by the computational simulation performed for a series of analytes that are simultaneous light absorbers and scatters with absorption-to-extinction ratios (AER) varying from 0.1 to 0.9. The simulated sample extinction varies from 0.01 to 7, covering essentially all possible LDR range currently achievable with a modern UV-vis spectrophotometer. The simulated total light absorption was compared to that calculated using Eq. 6, Eq. 8, and Eq. 9 (Figure 5A, and Figure S9). Eq. 8 quantifies the fraction of the excitation light absorbed by setting 𝑆𝑆(λ) = 0 in Eq. 6, while Eq. 9 quantifies the absorbed light in case one mistakes the experimental UV-vis spectrum as absorbance spectrum.
The modelled fraction of excitation light absorbed is significantly higher than that predicted with Eq. 6. This is expected because Eq. 6 considers only the light absorption along the optical path from the excitation source to the UV-vis detector, but not the absorption of the scattered light. On the other hand, the modelled light absorption is lower than that shown by Eq. 9, which is also expected because not all the scattered light can be absorbed. Fruitfully, the modelled total light absorption is close to that predicted with Eq. 8 across the entire simulated sample extinction range (Figure 5A and The simulation of the absorbed light also enables determination of the actual absorption sample extinction 𝐴𝐴 𝑡𝑡𝑡𝑡𝑡𝑡𝑠𝑠𝑡𝑡 (λ) defined with Eq. 10 and shown in Figure 5B, where 𝐼𝐼 𝑠𝑠𝑎𝑎𝑠𝑠,𝑡𝑡𝑡𝑡𝑡𝑡𝑠𝑠𝑡𝑡 (λ) is the intensity of total simulated light absorption, including the ones scattered before absorption.
The differences between 𝐴𝐴 𝑠𝑠𝑠𝑠𝑡𝑡𝑎𝑎𝑠𝑠𝑡𝑡 (λ) and the UV-vis double-beam absorption extinction calculated with Eq. 8 are less than 10% for all the modelled samples (Figure 5B, Figure S10), which is negligible for most practical applications.
𝐼𝐼 0 (λ) (10) Implication to ISARS quantification. ISARS is a recently developed method for quantification of materials double beam absorption and scattering extinction contribution to the sample UV-vis extinction spectrum. 10 The key working principle underlying the ISARS method is that ISARS quantifies the total light absorption of the samples placed inside the integrating sphere. By including the effective stepwise absorption path length after each diffuse reflection by the integrating sphere, a mathematical model is developed for correcting the interference due to the multipath absorption caused by the IS diffuse reflection. 10 However, this stepwise absorption path length is quantified empirically through curve-fitting the experimental ISARS-based absorbance and double-beam absorbance for a series of optically transparent samples. While this ISARS method has been validated with optically transparent samples, its utility to samples that contain both scatterers and absorbers has not been examined.
Herein, we provide an empirical validation to the ISARS method for experimental quantification of absorption and scattering extinction contribution to the UV-vis extinction spectra of three types of nanoparticles that are simultaneous absorbers and scatters, but with no significant fluorescence activities. The data obtained with dPSNPs are shown in Figure 6 and in S14). The double-beam UV-vis absorbance and scattering extinctions derived from the ISARS all exhibit excellent linearity with the nanoparticle concentration when the sample UV-vis extinction is within its LDR (Figure 6(D,H,I); Figure S13(F) and S14 (F)). Critically, the equation used for conversion of the sample ISARS-based absorbance to its double-beam absorbance is the one derived earlier with the optically transparent samples. 10 The linearity observed with these nanoparticle samples indicates that the effective stepwise light absorption path length inside the integrating sphere in the ISARS measurements is independent of sample scattering extinctions.
Otherwise, the derived double-beam absorption extinction should depend on both the sample concentration and its scattering extinction, causing nonlinear dependence between absorption extinction and sample concentration.
The normalized absorption extinction spectra derived from the ISARS measurement for the dPSNPs of all three different sizes are in good agreement (Figure S12), which further validates the ISARS method. These dPSNPs contain the same dye molecules. Therefore, the shapes of the absorption extinction spectra of the dPSNP of different sizes should be approximately the same as observed. If scattering indeed changes the effective stepwise absorption path length in the ISARS method, the shapes of the ISARS-derived double-beam absorbance spectra of these dPSNPs must differ significantly because the dPSNP of three different sizes differ significantly in their scattering features.
The ISARS-derived double-beam absorbance and scattering spectra for the plasmonic AuNPs and AgNPs are all in reasonable agreement with the theoretical spectra based on Mie theory calculations (Figure S2 andS3). 33 The relatively small difference between the experimental and computed spectra is due likely to the fact that the theoretical spectra are calculated with the assumption that the nanoparticles are perfectly spherical with a uniform size; however, the synthesized AuNPs and AgNPs all have a relatively small, but finite size and shape distribution as shown with the TEM images.
It is critical to note that the linearity of the ISARS-derived double-beam absorbance doesn't guarantee the validity of the double-beam scattering extinction quantified using Eq. 2. To ensure the validity of the scattering extinction spectrum derived from the ISARS method, one must also ensure that the experimental UV-vis extinction must be equivalent to the sample theoretical extinction, i.e., the interference due to the forward scattered light is insignificant, as discussed earlier in this work. Otherwise, the ISARS measurement will provide an underestimated doublebeam scattering extinction even when the deduced double-beam absorption extinction is accurate.
Such an effect is evident from the dPSNP of three different sizes (Figure 6). The double-beam absorption extinction derived from the ISARS measurement maintains excellent linearity with the dPSNP concentration. In contrast, the sample UV-vis extinction spectra and the deduced doublebeam scattering extinction begin deviating from their linear dependence on the dPSNP concentration when the sample experiment UV-vis extinction is higher than 2.5 and 2.2 for dPSNPs having a diameter of 510 nm and 1.1 µm, respectively (Figure 6D, 6H, 6I). These data indicates that for applications where only sample light absorption is of interest, a single sample ISARS quantification of the sample double-beam absorbance can be adequate. However, for applications where sample scattering extinction is needed, one should ensure the experimental UVvis extinction spectrum is within the sample LDR. The recommended approach for such applications is through serial dilution, as demonstrated herein with dPSNP (Figure 6) and the plasmonic AuNPs and AgNPs (Figures S13-S14).
The present work systematically investigated the impact of the cascading optical processes on experimental quantification of absorption and scattering properties of samples that contain absorbers and scatterers, but no emitters. A generalized mathematical equation was developed for predicting the upper LDR limit for the sample UV-vis spectral acquisition. The sample experimental UV-vis extinction spectrum is equal to the sum of the absorption and scattering extinction spectrum when the forward scattering of the sample is small. While light absorption reduces not only the sample scattering intensity, and its scattering depolarization, the impact of scattering on the sample light absorption is much more complicated. Scattering invariably reduces the intensity of the light absorption along the linear optical path from the light source to the UVvis transmittance detector. However, the absorption of the scattered light can offset reduced light absorption along the linear optical path, making total light absorption by scatterer-containing samples comparable to that by the scatterer-free counterpart with the same absorption extinction.
The latter provides critical validation to ISARS quantification of the double-beam light absorption and scattering extinction for samples with no significant forward-light-scattering interference in their UV-vis extinction measurements. These insights are important for improving the optical spectroscopic application of samples that contain both absorbers and scatterers. It is noted that while the cascading optical process are inevitable in all light scattering samples, their impact on optical spectroscopic measurements depends not only on materials structure and composition, but also the instrument and measurement settings, including cuvette size. Nonetheless, whenever possible one should use diluted samples for experimental quantification of the optical properties of nanoscale or larger materials.