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Quantification of Material Fluorescence and Light Scattering Cross-sections using Ratiometric BandwidthVaried Polarized Resonance Synchronous Spectroscopy Joanna Xiuzhu Xu, Juan Hu, and Dongmao Zhang Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b00847 • Publication Date (Web): 14 May 2018 Downloaded from http://pubs.acs.org on May 14, 2018

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Analytical Chemistry

Quantification of Material Fluorescence and Light Scattering Cross-sections using Ratiometric Bandwidth-Varied Polarized Resonance Synchronous Spectroscopy Joanna Xiuzhu Xu†, Juan Hu, # and Dongmao Zhang†,*

†

Department of Chemistry, Mississippi State University, Mississippi State, Mississippi, 39762, United States

#

Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60604, United States

Corresponding author: Email: [email protected]

*

Fax: 662-325-1618

1 ACS Paragon Plus Environment

Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT Presented herein is the ratiometric bandwidth-varied polarized resonance synchronous spectroscopy (BVPRS2) method for quantification of material optical activity spectrum. These include the sample light absorption and scattering cross-section spectrum, the scattering depolarization spectrum, and the fluorescence emission cross-section and depolarization spectrum in the wavelength region where the sample both absorbs and emits. This ratiometric BVPRS2 spectroscopic method is a self-contained technique, capable of quantitatively decoupling material fluorescence and light scattering signal contribution to its ratiometric BVPRS2 spectra through the linear curve-fitting of the ratiometric BVPRS2 signal as a function of the wavelength bandwidth used in the PRS2 measurements. Example applications of this new spectroscopic method are demonstrated with materials that can be approximated as pure scatterers, simultaneous photon absorbers/ emitters, simultaneous photon absorbers/scatterers, and finally simultaneous photon absorbers/scatterers/ emitters. Since the only instruments needed for this ratiometric BVPRS2 techniques are the conventional UV-vis spectrophotometer and spectrofluorometer, this work should open doors for routine decomposition of material UV-vis extinction spectrum into its absorption and scattering component spectra. The methodology and insights provided in this work should be of broad significance to all chemical research that involves photon/matter interactions.

KEYWORDS: Fluorescence, Scattering, Depolarization, Aggregation, Cross Section.


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INTRODUCTION Light/matter interactions are the most fascinating phenomena in nature that have been remaining as central research topics since the inception of modern science.1-10 Applications exploiting light/matter interactions encompass essentially every imaginable scientific discipline that ranges from molecular sciences to space exploration.11-18 Depending on their optical properties in the UVvis wavelength region, all materials can be divided into the following five categories: 1) approximate pure light absorbers with no significant light scattering and emission;19 2) pure light scatterers with no significant light absorption and emission20; 3) simultaneous light absorbers and scatterers with no significant photon emission, such as metal nanoparticles21-24 4) simultaneous light absorbers and emitters with no significant photon scattering25; all the way to 5) simultaneous light absorbers, scatterers, and emitters, including synthetic fluorescent nanoparticles26 and supramolecules27. Many emerging functional materials, especially nanoscale photonic materials are highly optically complicated because they can simultaneously absorb, scatter, and emit light in the same wavelength regions.28-31 Reliable determination of the material photon extinction, absorption, scattering, and emission activities is critical for material characterizations, designs, and applications. While quantifying material UV-vis extinction cross-sections is straightforward with conventional UV-vis spectrophotometers, deducing its light scattering, absorption, and emission cross-sections can be very challenging for optically complicated materials. One common practice in literature is to equate material UV-vis extinction spectrum as its absorption spectrum.32-35 This approximation is applicable for small molecular chromophores and fluorophores dispersed in



diluted solutions, but can be highly problematic for chromophore and fluorophore aggregates, nanoparticle chromophores and fluorophores, and materials deposited on the solid supports. The most popular methods for evaluating material light scattering and fluorescence activity are integration-sphere-36,37 and spectrofluorometer -based38,39 approaches. The accuracy of both techniques can be problematic because of a host of instrument- and sample-specific issues. As an example, excitation photons are usually plane polarized in conventional spectroscopic measurements, but the scattered and emitted fluorescence photons can be globally polarized in X, Y, and Z directions. The relative intensity of the scattered and emitted photons with X, Y, and Z polarization directions depends on the sample light scattering and fluorescence emission depolarizations. Apparently, no detector is capable of collecting photons with all different polarization directions with the same efficiency. Furthermore, the fraction of the photons reaching the detector depends not only on the instrument geometry, the degree of the sample light scattering and fluorescence depolarization, but also its polarization bias in instrument optical throughput.40 The latter is because the performance of many optical elements is polarization dependent.41 These effects must be taken into account in the determination of the material light scattering and fluorescence cross-sections.42 We have recently developed a polarized resonance synchronous spectroscopy (PRS2) method and demonstrated that both fluorophore photon scattering and fluorescence emission can contribute to the resonance synchronous spectroscopic (RS2) signal obtained with fluorescent samples. However, beguiled by the fact that the PRS2 spectra were acquired under resonance condition in which the excitation and detection wavelength were kept identical during the entire spectral acquisition, we have attributed the fluorescence signal observed in PRS2 spectrum


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exclusively to fluorophore on-resonance fluorescence (ORF), the possible Stokes’-shifted fluorescence (SSF) contribution to the PRS2 spectra was totally ignored. Demonstrated herein is a ratiometric bandwidth-varied PRS2 (BVPRS2) method that provides conclusive evidence that ORF and SSF emission both contribute to the fluorescence signal observed in the PRS2 spectrum. As such, the fluorophore ORF cross-sections evaluated in the earlier PRS2 works should be referred to as the fluorescence cross-sections comprising both ORF and SSF contributions. Theoretical consideration and experimental measurements revealed that the light scattering contribution to the ratiometric BVPRS2 spectra is totally independent of the wavelength bandwidth, but the fluorescence contribution increases linearly with the wavelength bandwidth. Such difference provides a convenient way for one to differentiate and separate the material light scattering and fluorescence emission in its ratiometric BVPRS2 spectrum. This is in contrast to the initial PRS2 spectroscopic technique that can only separate the light scattering and fluorescence signal when the material light scattering depolarization is zero. THEORETICAL CONSIDERATION 𝑃𝑅𝑆2 (𝜆, 𝑊) 𝐼𝑓,𝑉𝑉

𝜆+

= 𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝑉 (𝜆, 𝑊)𝐶𝑓 ∫

𝑊 2

𝑊 𝜆− 2

𝜆+

∫ 𝜆𝑥

𝑊 2 𝑊 𝜆− 2

+ 𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝑉 (𝜆, 𝑊)𝐶𝑓 ∫ 𝑊 2 𝑊 𝜆− 2

𝑃𝑅𝑆2 (𝜆, 𝑊) = 𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝐻 (𝜆, 𝑊)𝐶𝑓 ∫ 𝐼𝑓,𝑉𝐻

𝜆+

𝜆+

∫𝜆

𝑥

𝑊 2

𝜆+

𝑊 2

𝐹 (𝜆𝑥 , 𝜆𝑚 )𝑑𝜆𝑚 𝑑𝜆𝑥 𝜎𝑓,𝑉𝑉

𝑆𝑐𝑎 (𝜆𝑥 )𝑑𝜆𝑥 𝜎𝑓,𝑉𝑉

(1)

𝐹 (𝜆𝑥 , 𝜆𝑚 )𝑑𝜆𝑚 𝑑𝜆𝑥 𝜎𝑓,𝑉𝐻 𝑊 2 𝑊 𝜆− 2

+𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝐻 (𝜆, 𝑊)𝐶𝑓 ∫

𝜆+

𝑆𝑐𝑎 (𝜆𝑥 )𝑑𝜆𝑥 𝜎𝑓,𝑉𝐻

(2)

For generality, a theoretical model of the ratiometric BVPRS2 method is developed for the most optically complex model materials that are simultaneously photon absorbers, scatterers, fluorescent emitters in the probed wavelength region. Mathematically, the BVPRS2 spectra 5 ACS Paragon Plus Environment


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detected with excitation and detection polarization combinations of “VV” and “VH” can be represented using Eqs. 1 and 2, respectively. “V” and “H” represents the light polarization vertical or horizontal to plane defined by the excitation lamp, cell sample, and detector of the spectrofluorometer used for the BVPRS2 measurements. Eq. 1 and 2 are derived similarly as that for Eq. 21 and Eq. 22, respectively in the initial PRS2 publication.20 𝐶𝑓 is the fluorophore concentration.

𝑃𝑅𝑆2 𝑃𝑅𝑆2 (𝜆, 𝑊) , 𝐼𝑜 (𝜆, 𝑊) , 𝐾(𝜆, 𝑊) , 𝐵𝑉 (𝜆, 𝑊) ,and The variables 𝐼𝑓,𝑉𝑉 (𝜆, 𝑊) , 𝐼𝑓,𝑉𝐻

𝑃𝑅𝑆2 𝑃𝑅𝑆2 𝐵𝐻 (𝜆, 𝑊) are all defined similarly as 𝐼𝑓,𝑉𝑉 (𝜆) , 𝐼𝑓,𝑉𝐻 (𝜆) , 𝐼𝑜 (𝜆) , 𝐾(𝜆) , 𝐵𝑉 (𝜆) ,and 𝐵𝐻 (𝜆) ,

respectively, in the initial PRS2 work.20 The inclusion of wavelength bandwidth parameter W in the variables in Eqs. 1 and 2 is to reflect the fact that the values of these variables can depend on the wavelength bandwidth used in the resonance photon excitation and detection. 𝐹 𝐹 𝜎𝑓,𝑉𝑉 (𝜆𝑥 , 𝜆𝑚 ) and 𝜎𝑓,𝑉𝐻 (𝜆𝑥 , 𝜆𝑚 ) refer to the fluorophore fluorescence (F) cross-sections at

the exact excitation wavelength of 𝜆𝑥 and exact detection wavelength of 𝜆𝑚 under the excitation and detection polarization combinations of “VV” and “VH”, respectively. This is contrast to the 𝑂𝑅𝐹 𝑂𝑅𝐹 notations 𝜎𝑓,𝑉𝑉 (𝜆) and 𝜎𝑓,𝑉𝐻 (𝜆) used in the initial PRS2 work.20 Replacing the superscript “ORF”

with “F” is to reflect the fact that both SSF and ORF contribute to the detected PRS2 signal. The using of the two wavelength variables 𝜆𝑥 and 𝜆𝑚 in the fluorescence cross-section terms 𝐹 𝐹 𝜎𝑓,𝑉𝑉 (𝜆𝑥 , 𝜆𝑚 ) and 𝜎𝑓,𝑉𝐻 (𝜆𝑥 , 𝜆𝑚 ) indicates that the wavelength of the emitted photons can be

different from the incident photons even at the resonance excitation and detection conditions. This is true in all practical experimental conditions since all measurements are conducted with a finite (not infinitely small) wavelength bandwidth. The 𝑊 2 𝑊 𝜆− 2

∫

𝜆+

𝜆+

∫𝜆

𝑥

𝑊 2

double

integrals

𝑊 2 𝑊 𝜆− 2

∫

𝜆+

𝜆+

∫𝜆

𝑥

𝑊 2

𝐹 (𝜆𝑥 , 𝜆𝑚 )𝑑𝜆𝑚 𝑑𝜆𝑥 𝜎𝑓,𝑉𝑉

and

𝐹 (𝜆𝑥 , 𝜆𝑚 )𝑑𝜆𝑚 𝑑𝜆𝑥 in Eqs. 1 and 2 described the integrated fluorescence cross𝜎𝑓,𝑉𝐻


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sections when the excitation and detection wavelengths both center at the same wavelength of  𝜆+

and with an identical bandwidth of W. The inner integrals ∫𝜆 𝑥 𝜆+

∫𝜆

𝑥

𝑊 2

𝑊 2

𝐹 (𝜆𝑥 , 𝜆𝑚 )𝑑𝜆𝑚 and 𝜎𝑓,𝑉𝑉

𝐹 (𝜆𝑥 , 𝜆𝑚 )𝑑𝜆𝑚 refer to the emitted fluorescence cross-sections are integrated from the 𝜎𝑓,𝑉𝐻

excitation wavelength of 𝑥 to  + 𝑊/2, the upper limit of the collected wavelength region. The 𝑊 2 𝑊 𝜆− 2

outer integral in∫

𝜆+

𝜆+

∫𝜆

𝑊 2

𝑥

𝑊 2 𝑊 𝜆− 2

𝐹 (𝜆𝑥 , 𝜆𝑚 )𝑑𝜆𝑚 𝑑𝜆𝑥 and ∫ 𝜎𝑓,𝑉𝑉

𝜆+

𝜆+

∫𝜆

𝑥

𝑊 2

𝐹 (𝜆𝑥 , 𝜆𝑚 )𝑑𝜆𝑚 𝑑𝜆𝑥 reflects the 𝜎𝑓,𝑉𝐻

fact that excitation wavelength varies from  − 𝑊/2 to  + 𝑊/2. 𝑊 2 𝑊 𝜆− 2

The integrals ∫

𝜆+

𝑊 2 𝑊 𝜆− 2

𝑆𝑐𝑎 (𝜆𝑥 )𝑑𝜆𝑥 and ∫ 𝜎𝑓,𝑉𝑉

𝜆+

𝑆𝑐𝑎 (𝜆𝑥 )𝑑𝜆𝑥 associated with the light scattering 𝜎𝑓,𝑉𝐻

terms in Eqs.1 and 2 describe the fluorophore integrated light scattering cross-sections in the excitation and collection wavelength region from  − 𝑊/2 to  + 𝑊/2. Since the detection wavelength bandwidth W in practical PRS2 measurements is very small in comparison to the bandwidth of typical light scattering and fluorescence peaks, one can 𝐹 approximate the material fluorescence and light scattering cross-section 𝜎𝑓,𝑉𝑉 (𝜆𝑥 , 𝜆𝑚 ) , 𝐹 𝑆𝑐𝑎 𝑆𝑐𝑎 (𝜆𝑥 ) and 𝜎𝑓,𝑉𝐻 (𝜆𝑥 ) in the wavelength region from  − 𝑊/2 to  + 𝑊/2 as 𝜎𝑓,𝑉𝐻 (𝜆𝑥 , 𝜆𝑚 ) , 𝜎𝑓,𝑉𝑉 𝐹 𝐹 𝑆𝑐𝑎 𝑆𝑐𝑎 (𝜆) and 𝜎𝑓,𝑉𝐻 (𝜆) respectively. Under this condition, Eqs. 1 constants of 𝜎𝑓,𝑉𝑉 (𝜆) , 𝜎𝑓,𝑉𝐻 (𝜆) , 𝜎𝑓,𝑉𝑉

and 2 are then converted into Eqs. 3 and 4 with simple mathematical manipulations (Supporting Information). 𝑃𝑅𝑆2 (𝜆, 𝑊) = 𝐼𝑓,𝑉𝑉

𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝑉 (𝜆, 𝑊)𝐶𝑓 𝜎𝐹𝑓,𝑉𝑉 (𝜆)

2

𝑊2

+𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝑉 (𝜆, 𝑊)𝐶𝑓 𝜎𝑆𝑐𝑎 𝑓,𝑉𝑉 (𝜆)𝑊

𝑃𝑅𝑆2 (𝜆, 𝑊) = 𝐼𝑓,𝑉𝐻

𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝐻 (𝜆, 𝑊)𝐶𝑓 𝜎𝐹𝑓,𝑉𝐻 (𝜆)

2 7

ACS Paragon Plus Environment

𝑊2

(3)


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+𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝐻 (𝜆, 𝑊)𝐶𝑓 𝜎𝑆𝑐𝑎 𝑓,𝑉𝐻 (𝜆)𝑊

(4)

Experimental determination of the values of the instrument related parameters such as 𝐵𝑉 (𝜆, 𝑊), 𝐵𝐻 (𝜆, 𝑊), 𝐾(𝜆, 𝑊) and 𝐼𝑜 (𝜆, 𝑊) is impossible. This precludes the possibility for direct

experimental quantification of the fluorophore polarized light scattering and fluorescence crosssections using the PRS2 spectra measured with fluorophores alone. Fruitfully, these instrumentrelated parameters can be eliminated ratiometrically by using pure light scatterers such as polystyrene nanoparticle (PSNP) as the external reference. The PSNP light scattering crosssection can be readily quantified using conventional UV-vis measurement. Mathematically, The PSNP BVPRS2 can be expressed with Eq. 5. This equation is obtained from Eq. 3 by treating 𝐹 (𝜆) = 0). Dividing Eq. 3 by PSNP as a fluorophore with fluorescence cross-section of 0 (𝜎𝑃𝑆𝑁𝑃

E.5, and Eq. 4 by Eq. 6 leads to Eq. 7 and Eq. 8, respectively. 𝑃𝑅𝑆2 (𝜆, 𝑊) = 𝐼𝑜 (𝜆, 𝑊)𝐾(𝜆, 𝑊)𝐵𝑉 (𝜆, 𝑊)𝐶𝑃𝑆𝑁𝑃 𝜎𝑆𝑐𝑎 𝐼𝑃𝑆𝑁𝑃,𝑉𝑉 𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆) 𝑃𝑅𝑆2 𝐼𝑓,𝑉𝑉 (𝜆,𝑊) 𝑃𝑅𝑆2 𝐼𝑃𝑆𝑁𝑃,𝑉𝑉

= 2𝐶 (𝜆,𝑊)

𝑃𝑅𝑆2 𝐼𝑓,𝑉𝐻 (𝜆,𝑊) 𝑃𝑅𝑆2 𝐼𝑃𝑆𝑁𝑃,𝑉𝑉

𝐶𝑓

𝑃𝑆𝑁𝑃

= 2𝐶 (𝜆,𝑊)

𝐶𝑓

𝑃𝑆𝑁𝑃

𝐹 𝜎𝑓.𝑉𝑉 (𝜆) 𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

𝑊+

𝐶𝑓

𝑆𝑐𝑎 𝐶𝑃𝑆𝑁𝑃 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

𝐹 𝐵𝐻 (𝜆,𝑊)𝜎𝑓.𝑉𝐻 (𝜆) 𝑆𝑐𝑎 𝐵𝑉 (𝜆,𝑊)𝜎𝑃𝑆𝑁𝑃,𝑉𝑉

𝑆𝑐𝑎 𝜎𝑓,𝑉𝑉 (𝜆)

𝑊+ (𝜆)

𝐵 (𝜆,𝑊)

𝐺(𝜆, 𝑊) = 𝐵𝑉 (𝜆,𝑊) 𝐻

𝐶𝑓

𝑆𝑐𝑎 𝐵𝐻 (𝜆,𝑊)𝜎𝑓,𝑉𝐻 (𝜆)

𝑆𝑐𝑎 (𝜆) 𝐶𝑃𝑆𝑁𝑃 𝐵𝑉 (𝜆,𝑊)𝜎𝑃𝑆𝑁𝑃,𝑉𝑉

(5) (6)

(7) (8)

The ratio between 𝐵𝑉 (𝜆, 𝑊) and 𝐵𝐻 (𝜆, 𝑊) is the G-factor spectrum 𝐺(𝜆, 𝑊) (Eq. 8) that quantifies the instrument bias on the polarization of the detected photons.20 It is trivial to demonstrate that the G-factor spectrum 𝐺(𝜆, 𝑊) can be experimentally determined by using Eq. 9, 𝑃𝑅𝑆2 ( 𝑃𝑅𝑆2 ( where 𝐼𝐻𝑉 , 𝑤) and 𝐼𝐻𝐻 , 𝑤) are material PRS2 spectra obtained with combination of

excitation and detection polarization of “HV” and “HH”, respectively (Figure S1, Supporting information). Any materials with nonzero scattering and/or fluorescence depolarizations can be used for G-factor spectrum acquisition. 8 ACS Paragon Plus Environment

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𝐼 𝑃𝑅𝑆2 (,𝑊)

𝐺(, 𝑊) = 𝐼𝐻𝑉 𝑃𝑅𝑆2 (,𝑊)

(9)

𝐻𝐻

Multiplying both size of Eq. (7) with 𝐺(𝜆, 𝑊)defined by Eq. 8 leads to Eq. 10. 𝐼 𝑃𝑅𝑆2 (𝜆,𝑊)

𝑓,𝑉𝐻 𝐺(, 𝑊) 𝐼𝑃𝑅𝑆2

𝑃𝑆𝑁𝑃,𝑉𝑉

𝑃𝑅𝑆2 𝐼𝑓,𝑉𝑉 (𝜆,𝑊) 𝑃𝑅𝑆2 𝐼𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆,𝑊)

= 2𝐶 (𝜆,𝑊)

𝑃𝑆𝑁𝑃


𝑆𝑐𝑎 𝜎𝑓,𝑉𝐻 (𝜆)

𝐶𝑓


𝑓,𝑉𝐻 and 𝐺(, 𝑊) 𝐼𝑃𝑅𝑆2 (𝜆,𝑊)

𝑃𝑆𝑁𝑃,𝑉𝑉 (,𝑊)

𝑃𝑅𝑆2 and 𝑅𝑉𝐻 (, 𝑊), respectively.

𝑃𝑅𝑆2 to as the sample ratiometric BVPRS2 spectra 𝑅𝑉𝑉 (, 𝑊)

In this case, Eqs. 6 and 10 are rewritten as Eqs. 11 and 12,

respectively where the slope ( 2𝐶

𝐶𝑓

𝑃𝑆𝑁𝑃

𝐹 𝜎𝑓.𝑉𝑉 (𝜆) 𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉

) and intercept ( 𝐶 (𝜆)

𝐶𝑓

𝑃𝑆𝑁𝑃

𝑆𝑐𝑎 𝜎𝑓,𝑉𝑉 (𝜆) 𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

𝐹 𝜎𝑓.𝑉𝐻 (𝜆) 𝑆𝑐𝑎 𝑃𝑆𝑁𝑃 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

denoted as 𝑆𝑉𝑉 (𝜆) and 𝑏𝑉𝑉 (𝜆) , respectively, and the slope ( 2𝐶 (𝐶

𝐶𝑓

𝑃𝑆𝑁𝑃

𝑆𝑐𝑎 𝜎𝑓,𝑉𝐻 (𝜆)

(10)

𝑆𝑐𝑎 𝐶𝑃𝑆𝑁𝑃 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

(Eq. 10). For discussion simplicity, we will refer hereafter

𝑃𝑆𝑁𝑃,𝑉𝑉 (,𝑊)

𝑃𝑅𝑆2 𝐼𝑃𝑆𝑁𝑃,𝑉𝑉

𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉

𝑊+ (𝜆)

is linearly dependent on the wavelength bandwidth W (Eq. 6), so is the

𝑓,𝑉𝐻 quantity of 𝐺(, 𝑊) 𝐼𝑃𝑅𝑆2 𝑃𝑅𝑆2 𝐼𝑓,𝑉𝑉 (𝜆,𝑊)

𝐹 𝜎𝑓.𝑉𝐻 (𝜆)

𝐶𝑓

𝐶𝑓

) in Eq. 6 are

) and intercept

) in Eq. 10 as 𝑆𝑉𝐻 (𝜆) and 𝑏𝑉𝐻 (𝜆). The ratio between the slopes gives rise the

𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

fluorophore fluorescence depolarization spectrum (Eq. 13), while that between the intercepts is the fluorophore light scattering depolarization spectrum (Eq.14). 𝑃𝑅𝑆2 ( 𝑅𝑉𝑉 , 𝑤) = 𝑆𝑉𝑉 ()W + 𝑏𝑉𝑉 ()

(11)

𝑃𝑅𝑆2 ( , 𝑤) = 𝑆𝑉𝐻 ()W + 𝑏𝑉𝐻 () 𝑅𝑉𝐻

(12)

𝑃𝑓𝐹 (𝜆) =

𝐹 𝜎𝑓,𝑉𝐻 (𝜆) 𝐹 𝜎𝑓,𝑉𝑉 (𝜆)

𝑃𝑓𝑆𝑐𝑎 (𝜆) =

=

𝑆𝑐𝑎 𝜎𝑓,𝑉𝐻 (𝜆) 𝑆𝑐𝑎 (𝜆) 𝜎𝑓,𝑉𝑉

𝑆𝑉𝐻 () 𝑆𝑉𝑉 ()

=

𝑏𝑉𝐻 () 𝑏𝑉𝑉 ()


(13)

(14)


𝐹 𝜎𝑓,𝑉𝑉 (𝜆)

Using the relationship between 𝜎𝑆𝑐𝑎

𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

𝜎𝑓𝑆𝑐𝑎 (𝜆) 𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃 (𝜆)

and

Page 10 of 26

𝜎𝑓𝐹 (𝜆)

(Eq. 15), and

𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃 (𝜆)

𝑆𝑐𝑎 𝜎𝑓,𝑉𝑉 (𝜆) 𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

and

(Eq. 16) established in the earlier work,20 Eq. 17 and Eq. 18 are developed for

calculating the fluorophore fluorescence cross-section 𝜎𝑓𝐹 (𝜆), and light scattering cross-section 𝜎𝑓𝑆𝑐𝑎 (𝜆) . 𝜎𝑓𝐹 (𝜆) and 𝜎𝑓𝑆𝑐𝑎 (𝜆) the fluorophore fluorescence and light scattering cross-sections under plane polarized light for excitation but with hypothetical 3-dimensional global detection of all lights that are polarized in X, Y, and Z directions. 𝜎𝑓𝑆𝑐𝑎 (𝜆) 𝑆𝑐𝑎 (𝜆) 𝜎𝑃𝑆𝑁𝑃

=

𝜎𝑓𝐹 (𝜆) 𝑆𝑐𝑎 𝜎𝑃𝑆𝑁𝑃

𝜎𝑓𝐹 (𝜆) =

(1+2𝑃𝑓𝑆𝑐𝑎 (𝜆))

𝑆𝑐𝑎 𝜎𝑓,𝑉𝑉 (𝜆)

𝑆𝑐𝑎 (𝜆)) 𝜎 𝑆𝑐𝑎 (1+2𝑃𝑃𝑆𝑁𝑃 𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

(1+2𝑃𝑓𝐹 (𝜆))

= (1+2𝑃𝑆𝑐𝑎 (𝜆)

𝐹 𝜎𝑓,𝑉𝑉 (𝜆)

𝑆𝑐𝑎 𝑃𝑆𝑁𝑃 (𝜆)) 𝜎𝑃𝑆𝑁𝑃,𝑉𝑉 (𝜆)

2𝐶𝑃𝑆𝑁𝑃 (1+2𝑃𝑓𝐹 (𝜆))𝑆𝑉𝑉 (𝜆)

𝜎𝑓𝑆𝑐𝑎 (𝜆) =

𝑆𝑐𝑎 (𝜆)) 𝐶𝑓 (1+2𝑃𝑃𝑆𝑁𝑃


𝐶𝑃𝑆𝑁𝑃 (1+2𝑃𝑓𝑆𝑐𝑎 (𝜆))𝑏𝑉𝑉 (𝜆) 𝑆𝑐𝑎 (𝜆)) 𝐶𝑓 (1+2𝑃𝑃𝑆𝑁𝑃


(15)

(16)

(17)

(18)

In theory the slopes (𝑆𝑉𝑉 () or 𝑆𝑉𝐻 ()) of the linear regression equation of ratiometric 𝑃𝑅𝑆2 ( 𝑃𝑅𝑆2 ( BVPRS2 signal (𝑅𝑉𝑉 , 𝑤) or 𝑅𝑉𝐻 , 𝑤)) as a function of wavelength bandwidth (W) should

be strictly zero for non-fluorescent samples (Eq. 6). Conversely, the intercepts (𝑏𝑉𝑉 () or 𝑏𝑉𝐻 ()) of the linear equation modeling the ratiometric BVPRS2 signal as a function of wavelength bandwidth should be zero for samples with no significant light scattering signal (Eq. 6). In practices however, because of measurement errors there are finite nonzero slopes for samples thatare fluorescence inactive, and nonzero intercepts for samples that have no significant light scattering.

It is therefore important to define the threshold 𝑆𝑡 (𝜆) and 𝑏𝑡 (𝜆) values for

determining the statistical significance of the slopes and intercepts obtained by the linear curvefitting. Eqs. 19 and 20 are derived in analogy to the signal threshold for one to determine the 10 ACS Paragon Plus Environment

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̅̅̅̅̅̅̅̅̅ limit of quantification (LOQ) for an analytical method. 𝑆 𝐹𝐵 () and 𝐹𝐵 () are the mean and standard derivation of the slopes ( 𝑆𝑉𝑉 () )of the linear regression equation modeling the experimental ratiometric BVPRS2 signal as a function of wavelength bandwidth for non̅̅̅̅̅̅̅̅̅ fluorescent controls. These samples can be viewed as the fluorescence-blank (FB). 𝑏 𝑆𝐵 () and 𝑆𝐵 () are the mean and standard derivation of the intercepts (𝑏𝑉𝑉 ()) of the linear regression equation modeling ratiometric BVPRS2 signal as a function of wavelength bandwidth for fluorophores that have negligible light scattering signal. Those samples serve as light scattering blanks (SB). Only the experimental slopes and intercepts of the sample that are larger than the corresponding threshold values will be used directly for the fluorescence and light scattering depolarization calculations. Otherwise, these values will be set to zero, indicating the sample fluorescence or light scattering intensity is below the LOQ of this ratiometric BVPRS2 method. ̅̅̅̅̅̅̅̅̅ 𝑆𝑡 () = 𝑆 𝐹𝐵 () + 3𝐹𝐵 ()

(19)

̅̅̅̅̅̅̅̅̅ 𝑏𝑡 () = 𝑏 𝑆𝐵 () + 3𝑆𝐵 ()

(20)

EXPERIMENTAL SECTION BVPRS2 Measurements. The information of materials, equipment, and 𝐺(, 𝑊) determination (Figure S2) is provided in supporting information . All BVPRS2 spectra are conducted with a nominal wavelength bandwidth systematically varying from 1 nm to 2 nm with a step value of 0.2 nm. The exact wavelength bandwidth, estimated on the basis of PSNP light scattering is (Figure S3, Supporting information), 0.98 nm, 1.1 nm, 1.2 nm, 1.4 nm, 1.5 nm, and 1.6 nm , respectively. The excitation wavelenghth and bandwidths are kept identical to their respective detection counterparts in all spectral acquisitions. For discussion simplicity, we refer to all used analytes as fluorophores. The fluorophore-specific BVPRS2 spectra were obtained by subtracting cuvette- and solvent-background BVPRS2 spectra from the as-acquired BVPRS2 spectra of the sample 11 ACS Paragon Plus Environment


solutions. For samples with photon extinction higher than 0.05, the sample inner filter effect in the as-acquired solution spectra were corrected before the background subtraction. The BVPRS2 spectra shown in the main text were analyte-specific spectra where the interference from sample inner-filter-effect and solvent- and cuvette-background signals are corrected with procedure shown before,20 while the as-acquired sample BVPRS2 spectra, PSNP BVPRS2 spectra, and the cuvette/solvent background BVPRS2 spectra were shown in the supporting information. Linear Regression. The linear curve-fitting is performed through a software package developed specifically for this work. The input includes the calibrated wavelength bandwidth used in the BVPRS2 spectral acquisition, instrument G-factor spectrum, the fluorophore and PSNP BVPRS2 spectra obtained with varying wavelength bandwidths, and the threshold values for the intercept (𝑏𝑡 () = 0.014) and slope (𝑆𝑡 () = 0.12) obtained with the scattering and fluorescence-blanks (Figure S4, Supporting Information).

RESULTS AND DISCUSSION Quantification of light scattering and fluorescence cross-sections: The effectiveness of the ratiometric BVPRS2 quantification of the material light scattering and fluorescence depolarizations and cross-sections were demonstrated with a series of materials with increasing optical complexities. Figures 1 and 2 show the experimental data acquired with silicone oil that is a pure light scatterer, nanoparticle AuNR550 that is simultaneously a light absorber and scatterer, and diluted molecular fluorophore R6G (~5 µM) that is simultaneously a light absorber and emitter. Figures 3 and 4 are the data acquired with QD570/PSNP (a mixture of quantum dots QD570 and polystyrene nanoparticales) that contains simultaneous photon absorbers, scatterers, and fluorescence emitters.


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The data in Figure 1 provides conclusive evidence that one can readily differentiate the material light scattering and fluorescence on the basis of its ratiometric BVPRS2 spectra. This is consistent with the prediction in the theoretical consideration section. Evidently, ratiometric BVPRS2 spectra of silicone oil and AuNPs are totally independent of the wavelength bandwidth crossing the entire spectral wavelength region. The slope of their ratiometric BVPRS2 spectra as a function of wavelength bandwidth is zero (below the LOQ) crossing the entire spectrum. In contrast, the R6G ratiometric BVPRS2 signals increases linearly with the wavelength bandwidth

Figure 1 Experimental data obtained with (1st row) pure silicone oil, (2nd row) gold nanorod AuNR550 (3.4310-11M), and (3rd row) R6G (4.92 M). Plots (A), (E), and (I) in the 1st colum are the sample BVPRS2 spectra obtained with excitation and detection polarization combination of “VV”. Plots (B), (F), and (J) in the 2nd column are the sample BVPRS2 spectra obtained with excitation and detection polarization combination of “VH” . Plots (C), (G), and (K) are the sample ratiometric BVPRS2 spectra obtained with excitation and detection polarization combination of “VV”. Plots (D), (H), and (L) are the sample ratiometric BVPRS2 spectra obtained with excitation and detection polarization combination of “VH”. The insets in column 3 and 4 are the spectral intensity change as a function of the wavelength bandwidth at an example wavelength marked with a dash line. The as-acquired solution BVPRS2 spectra, solvent and cuvette background BVPRS2 spectra were shown in Figures S6-S8 in Supporting information.



in the wavelength region where R6G are fluorescence-active under the resonance excitation and detection condition (Figure 1(K-L)), but the intercepts of its ratiometric BVPRS2 VV intensity as a function of wavelength bandwidth are below the instrument LOD.

Figure 2 (A) and (B) light scattering depolarization spectra for silicone oil and gold nanorod, respectively, and (C) fluorescence depolarization spectrum of R6G. The solid line in (C) is for guiding view. (D) and (E) light scattering cross-section spectra for silicone oil and gold nanorod, respectively, and (F) fluorescence cross-section spectrum of R6G.


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The silicone oil and AuNPs light scattering and the R6G fluorescence depolarization spectra (Figure 2(A-C)) were calculated using the Eqs. 13 and 14, respectively, while their light scattering and fluorescence cross-section spectra (Figure 2(D-F)) were determined using Eqs. 17 and 18, respectively. The intercepts and the slopes needed for the depolarization and cross-section spectra were obtained by linearly curve fitting of the experimental ratiometric BVPRS2 spectra as

Figure 3 Experimental data obtained with (left) the QD570 (7.) and (right) QD570/PSNP ([QD570]=7.PSNP=3.1510-12M). (A) and (B) are the sample UV-vis extinction, (C) and (D) are the SSF spectrum of the specified samples. (E) and (F) are the ratiometric BVPRS2 spectra obtained with excitation and detection polarization combination of “VV” for the indicated samples. (G) and (H) are the sample ratiometric BVPRS2 spectra obtained with excitation and detection polarization combination of “VH”. The insets in the plots shown in 3rd and 4th row are ratiometric BVPRS2 spectral intensity as a function of the wavelength bandwidth for the wavelength marked with dashed line. The as-acquired QD570/PSNP and QD570 solution BVPRS2 spectra were shown in Figure S9 in Supporting information. 15 ACS Paragon Plus Environment


a function of the wavelength bandwidth (Figure 1, column 3 and column 4) according to Eqs. 11 and 12. The fluorescence depolarizations of AuNR550 and silicone oil are not defined since it is 𝑃𝑅𝑆2 not fluorescence active, i.e, the slope in the linear regression of 𝑅𝑉𝑉 (, 𝑊) as the function of W

is zero. Conversely, the light scattering cross-sections and depolarizations of R6G are unquantifiable because its light scattering intensity is below the detetion limits. The difference between light scattering and fluorescence in the wavelength bandwidth dependence of their BVPRS2 feature provides a convenient way for separating the material light scattering and fluorescence present in the BVPRS2 spectra obtained with samples that are simultaneous photon absorbers, scatters, and emitters. These samples can be relatively large fluorescent nanoparticles, mixtures of fluorophores with light scattering particles, as well as aggregated molecular fluorophores. Figure 3, 4 show the experimental data acquired with the QD570, and QD570/PSNP mixture prepared by spiking PSNP into QD570 solution. The extinction and SSF spectra of QD570 are highly similar to their respective counterparts of QD570/PSNP mixture (Figure 3A and 3B, and Figure 3C and Figure 3D). This is expected because PSNP concentration is very low and their UV-vis extinction and SSF intensity is negligibly small in comparison to that of QD570. However, situation is more complicated in the comparison of the ratiometric BVPRS2 of QD570 spectra with those for QD570/PSNP. While the ratiometric BVPRS2 VH spectra of these two samples acquired with excitation and detection polarization of “VH” are highly similar, their BVPRS2 VV spectra are remarkably different. The reason for such a drastical difference is that PSNP has near zero light scattering depolarizations, resulting inPSNP light scattering only observable only in the BVPRS2 VV spectra of QD570/PSNP. The light scattering and fluorescence cross-section and depolarization spectra of QD570 and QD570/PSNP are quantified on the basis of the slopes and intercepts obtained by linearly


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fitting the sample ratiometric BVPRS2 intensity as a function of the wavelength bandwidth. As expected from the experimental data shown in Figure 4, the UV-vis extinction and fluorescence cross-sections, and fluorescence deploarization of QD570 are statistically the same as their respective counterparts of QD570/PSNP mixture. The light scattering cross-section spectra of the PSNPs from the QD570/PSNP mixtures calculated on the basis of PSNP concentration is the same as that calculated with the pure PSNPs. These results demonstrate the effectiveness of this ratiometric BVPRS2 for quantitative separation of the material photon scattering and fluorescence emission and quantification of their depolarization and cross-section spectra for the most optically complicated samples that contain photon absorbers, scatterers, and fluorescence emitters. Comparing and constrasting the data obtained with ratiometric BVPRS2 spectra and those with the intial PRS2 method is revealing. For light scattering, the depolarization and cross-sections obtained with both methods are statistically identical as they are independent of bandwidth,

Figure 4 (A) Extinction cross-section spectra of the QD570 and QD570/PSNP, (B) Light scatttering depolarization, (C) Fluorescence depolarizations. The solid line is for guiding view. (D) Light scattering cross-section, (E) fluorescence cross-sections. (F) the absorption cross-section spectra of (black) QD570 and (red) QD570/PSNP 17 ACS Paragon Plus Environment


demonstrated by the data of non-emitter AuNR550 published in the previous work.43 For fluorescent materials, however, the ratiometric BVPRS2 can be much more reliable and informative. First, the initial PRS2 can separate the material light scattering and fluorescence only for samples only with zero light scattering depolarizations,20 while the ratiometric BVPRS2 technique quantiatively separates the light scattering and fluorescence signal regardless of the light scattering depolarizations. Second, the initial PRS2 calculates the fluorophore depolarizations and fluorescence cross-sections under the assumption that its fluorescence depolarizations under the resonance excitation and detection conditions are identical as those of the fluorophore SSF depolarization. In contrast, the ratiometric BVPRS2 is a self-contained method, capable of directly quantifying the fluorophore fluorescence depolarization without SSF measurements. This, on one hand, eliminates the necessity of SSF measurement in the PRS2 spectral data analysis. On the other hand, it enables for the first time experimental comparison of the fluoropore fluorescence depolarizations under Stokes-shifted and resonance excitation and detection conditions. Indeed, the R6G and QD570 fluorescence depolarizations detected under resonance excitation and detection conditions are the same as their respectively counterparts determined with the SSF measurements (Figure S5, Supporting information). While 𝑓𝐹 () determined using this ratiometric BVPRS2 method can be viewed as fluorophore wavelength-specific fluorescence cross-section that is independent of wavelength bandwidth, the one determined with the intial PRS2 technique20 should be viewed as the bandwidth-dependent fluorescence cross-section 𝐹𝑃𝑅𝑆2 (, 𝑊). It is simple to establish Eq. 21 that describs the relationship between the wavelength-specific fluorescence cross-section 𝑓𝐹 () and bandwith-dependent fluorescence cross-section 𝐹𝑃𝑅𝑆2 (, 𝑊) (Supporting information). Using


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this relationship, one can readily convert the bandwidth-dependent fluorescence cross-sections determined in the earlier work into their wavelength-specific fluoresence cross-sections.

𝐹𝑃𝑅𝑆2 (, 𝑊) = 𝑊 𝑓𝐹 ()/2

(21)

With its ability to quantify the material light scattering and fluorescence cross-sections, this ratiometric BVPRS2 method opens a door for a series of applications that are impossible or difficult to perform before. One such example is the determination of the effect of fluorophore aggregation on the interplay of its photon absorption, scattering, and emission (Figure 5 and 6). In this work, we used the ratiometric BVPRS2 to quantify the effect of FITC sample aggregation on its optical properties. Earlier work demonstrated that the FITC aggregates in water even at concentration as low as 10 µM. 44 However, quantification of the effect of fluorophore aggregation on its light scattering and fluroescence depolarizations and cross-sections has not been possible.

Figure 5 Experimental data obtained with (Top) the fresh FITC in water (4.8510-5M), (bottom) FITC in ethanol (4.8510-5M). (A) and (E) in the 1st column are the FITC UV-vis extinction spectru. (B) and (F) in the 2nd column are the FITC SSF. (C) and (G) int eh 3rd column are the sample ratiometric BVPRS2 spectra obtained with excitation and detection polarization combination of “VV”. (D) and (H) in the 4th column are the sample ratiometric BVPRS2 spectra obtained with excitation and detection polarization combination of “VH. The insets are ratiometric BVPRS2 spectral intensity as a function of the wavelength bandwidth for the wavelength marked with dashed line. The as-acquired solution BVPRS2 spectra, solvent and cuvette background BVPRS2 spectra were shown in Figure S10 in supporting information. 19 ACS Paragon Plus Environment


Apparently the PRS2 method is most sensitive to detection of the fluorophore aggregation. This is evident from the fact that UV-vis and SSF spectra of FITC in water are much more similar to their respective counterparts for FITC in ethanol (Figure 5(A, E) and Figure 5(B, F)), which their ratiometric BVPRS2 spectra are drastically different (Figure 5(C, G) and Figure 5(D, H)). FITC is simultaneously a light absorber scatter, and fluorescence emitter in water, but predominantly a photon absorber and emitter in ethanol. This FITC photon absorption and fluorescence emission is deduced from their SSF activity (Figures 5B and 5F), while the light scattering of the FITC in water is deduced from the its ratiometric BVPRS2 VV spectra (Figure 5C). The fact that the ratiometric BVPRS2 intensity FITC in water remains as a nonzero constant as a function of wavelength bandwidth indicates that its BVPRS2 signal is dominated by light scattering with no significant fluorescence crossing the entire wavelength region. In contrast, the ratiometric BVPRS2 of FITC in ethanol is dominated by the FITC fluorescence with no detectable light scattering.This is because the intercepts are all neligibly small in the linear equations obtained by curve-fitting the ratiometric BVPRS2 intensity as a function of its wavelength bandwidth (Figure 5H). On the basis of the slopes and the intercepts obtained by linearly fitting the ratiometric BVPRS2 intensities (Figure 5 and supporting information), one can readily calculate the light scattering cross-section and depolarization spectra for FITC in water, and the fluorescence crosssection (Figure 6E) and depolarization spectra (Figure 6C) for FITC in ethanol in the wavelength region that FITC both absorbs and emits. The light scattering cross-section spectrum (Figure 6D) of FITC in water is to our knowledge the first experimental quantification of the light scattering activity of fluorophore aggregates. The wavelength dependence of light scattering cross-section of aggregated FITC in water differs tremendously from that of small solvent light scattering


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Figure 6 (A) Extinction cross-section spectra of the FITC (B) Light scatttering depolarization of FITC in water, (C) Fluorescence depolarization spectrum. The solid line is for guiding few. (D) Light scattering cross-section and the scattering to extinction ratio spectra for FITC in water, (E) fluorescence cross-section of FITC in ethanol. (F) FITC absorption cross-section spectra. molecules and nanoparticles such as PSNPs. The light scattering cross-section of those solvent molecules all empirically follow the Rayleigh scattering model, i.e, the light scattering crosssection is linearly proportional to the reciprocal of the fourth power of the wavelength (𝜆−4 ). However, the maximum light scattering cross-section are from ~450 nm to 520 nm in the probed wavelength region (Figure 6D). More importantly, the light scattering to extinction (SER) ratio, the measure of light scattering contribution to the total photon extinction observed in the UV-vis spectrum increases monotonically (within the measurement errors) from less than 1% at 400 nm to more than 80% at 520 nm (Figure 6D). Since the FITC UV-vis extinction cross-section spectra (Figure 6A) are known from the conventional UV-vis measurements, one can deduce the FITC absorption spectra (Figure 6F) by subtracting the FITC light scattering cross-section spectrum from its extinction cross-section spectrum.



Although light scattering cross-section spectra of FITC in water provides conclusive evidence that the light scattering by aggregated fluorophores can deviate drastially from the Rayleigh scattering, detailed understanding the wavelength dependence of the FITC light scattering proves to be difficult. Presumably, its light scattering activity depends critically on the size and shape of FITC aggregates in water. Unfortuantely, however, attempt to experimentally evaluate the size and shape distribution has not been successful. Nonetheless, the ability for us to experimentally quantify photon absorption, scattering, and fluorescence activity of the aggregated fluorophores represents a critical step forward to developing a mechanistic understanding of the effect of fluorophore aggregation on its optical properties.

CONCLUSIONS Using the ratiometric BVPRS2 spectroscopic method developed in this work, we demonstrated that fluorophore light scattering, SSF emission, and ORF emission can all contribute to the fluorophore resonance light scattering spectra. By using BVPRS2 spectra of PSNP as the external reference, one can conveniently differentiate and separate fluorophore light scattering and fluorescence signals in the measured ratiometric BVPRS2 spectra based on their difference on the wavelength bandwidth dependence. This enables the calculation of the fluorophore light scattering and fluorescence depolarization as well as their cross-section spectra. The ratiometric BVPRS2 study performed with FITC in water demonstrated that aggregation can drastically changes the interplay of fluorophore photon absorption, scattering, and fluorescence under the resonance excitation and detection conditions. The ratiometric BVPRS2 method is a self-contained technique globally applicable to materials that can be as complicated as simultaneous photon absorbers, scatterers, and absorbers. Since the only instruments needed for this ratiometric BVPRS2


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techniques are the conventional UV-vis spectrophotometer and spectrofluorometer, this work should open doors for routine decomposition of material UV-vis extinction spectrum into its absorption and scattering component spectra. The methodology and insights provided in this work should be of broad significance to all chemical research that involves photon/matter interactions.

ASSOCIATED CONTENT Supporting Information. Derivations of equations 3 and 4 in the main text. Mathematical justification of G-factor quantification with equation 9 and 21. Materials and Equipment. Quantification of 𝐺(𝜆, 𝑊) spectra. Experimental evaluation of the wavelength bandwidth as a function of nominal instrument wavelength bandwidth. Determination of threshold slope 𝑆𝑡 (𝜆) and intercept 𝑏𝑡 (𝜆) . R6G and QD570 fluorescence depolarization determined with the SSF measurements. As-acquired BVPRS2 spectra of silicone oil, AuNR550-solution, R6G-solution, QD570/PSNP solution, QD570 solution, FITC in water and in EtOH, cuvette background, solvent, and PSNP. Multiplication spectra of UV-vis extinction spectrum and SSF spectrum for FITC in water and ethanol. http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] Tel: (662) 325-6752 ACKNOWLEDGMENT This work was supported by NSF funds (CHE 1151057) and (EPS-0903787) provided to D.Z.



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Quantification of Material Fluorescence and Light ... - ACS Publications

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