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Quantification of the Depolarization and Anisotropy of Fluorophore Stokes-Shifted Fluorescence, On-Resonance Fluorescence, and Rayleigh Scattering Kumudu Siriwardana,† Buddhini C. N. Vithanage,† Shengli Zou,‡ and Dongmao Zhang*,† †

Department of Chemistry, Mississippi State University, Mississippi State, Mississippi 39762, United States Department of Chemistry, University of Central Florida, Orlando, Florida 32816, United States

‡

S Supporting Information *

ABSTRACT: Fluorophores are important but optically complicated photonic materials as they are simultaneous photon absorbers, emitters, and scatterers. Existing studies on fluorophore optical properties have been focused almost exclusively on its photon absorption and Stokes-shifted fluorescence (SSF) with scant information on the fluorophore photon scattering and on-resonance fluorescence (ORF). Presented herein is a unified theoretical framework and experimental approach for quantification of the fluorophore SSF, ORF, and scattering depolarization and anisotropy using a combination of fluorophore UV−vis, fluorescence emission, and resonance synchronous spectroscopic spectral measurements. A mathematical model for calculating fluorophore ORF and scattering cross sections has been developed that uses polystyrene nanoparticles as the external reference. The fluorophore scattering cross section is ∼10-fold smaller than its ORF counterparts for all the six model fluorophores, but more than 6 orders of magnitude larger than the water scattering cross section. Another finding is that the fluorophore ORF has a depolarization close to 1, while its Rayleigh scattering has zero depolarization. This enables the experimental separation of the fluorophore ORF and photon scattering features in the fluorophore resonance synchronous spectra. In addition to opening a new avenue for material characterization, the methods and insights derived from this study should be important for developing new analytical methods that exploit the fluorophore ORF and photon scattering properties. method.16 With this method, we have quantified for the first time the ORF emission cross sections and quantum yields for a series of molecular and quantum dot fluorophores.17 While the R2S2 spectroscopic technique provides a convenient way for experimental correction of the sample inner filter effect (IFE) imposed by the fluorophore photon absorption on the combined fluorophore photon scattering and ORF contribution to experimental resonance synchronous spectrum (RS2), separation of the fluorophore ORF and photon scattering contribution to the IFE-corrected R2S2 spectrum is, however, challenging. It was performed through a spectral subtraction method on theoretical predication that the peak shape of the ORF is equivalent to the multiplication spectrum of the fluorophore UV−vis and SSF spectra.17 This method is, in theory, reliable only for the samples in which the fluorophore photon scattering and ORF occur in the different R2S2 wavelength region. Over- and undersubtraction can occur for the samples that have overlapping ORF and scattering features. We demonstrated herein a polarized resonance synchronous spectroscopic (PRS2) method that enables first experimental quantification of the fluorophore ORF and light scattering

F

luorescent chemicals are a class of photonic materials that have been used in displays, optical spectroscopy, forensic analysis, and diagnosis. Fluorophores are optically complicated materials as they are invariably simultaneous photon absorbers, scatters, and emitters that can emit photons with energy identical to, and lower than, the absorbed photons. Existing research on the fluorophore optical properties has focused predominantly on its photon absorption and the Stokes-shifted fluorescence (SSF) in which emitted photons have longer wavelengths than that of the excitation photon. There are many SSF-based analytical methods that are based on SSF intensities,1−7 lifetimes,8−11 and anisotropies.12−14 There is scant information on fluorophore photon scattering and onresonance fluorescence (ORF) in which the scattered or the emitted photons have the same wavelength as the excitation photons. This is in spite of the fact that molecular ORF has been depicted in the standard Jablonski energy level diagram for decades,15 and photon scattering is a universal material property because all materials have nonzero polarizability. Understanding the photon scattering properties of fluorescent materials is especially important because of the fluorophore ORF can be readily be mistaken as its photon scattering, and vice versa. The technique breakthrough leading to the first experimental detection of the fluorophore ORF is the recent development of the ratiometric resonance synchronous spectroscopic (R2S2) © 2017 American Chemical Society

Received: March 12, 2017 Accepted: May 15, 2017 Published: May 15, 2017 6686

DOI: 10.1021/acs.analchem.7b00907 Anal. Chem. 2017, 89, 6686−6694

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Analytical Chemistry

Figure 1. (A) Scheme of the instrument configuration of the spectrofluorometer. (B and C) Graphic representation of the notations of the spectra acquired with different the excitation and detection polarization combinations in the polarized fluorescence and resonance synchronous spectroscopic measurements.

anisotropy and for accurate quantification of the fluorophore ORF and light scattering cross sections. To this aim, we developed a unified theoretical framework for experimental quantification of the fluorophore SSF, ORF, and photon scattering depolarization spectra (PfX(λ)) and anisotropy spectra (rXf (λ)) that are defined with the generalized eqs 1 and 2, respectively. The subscript “f” refers to the fluorophore, and the superscript “X” can be “SSF”, “ORF”, or “sca” in these equations for the fluorophore SSF, ORF, and scattering depolarization and anisotropy, respectively.

PfX(λ) = rfX(λ) =

PfX(λ) =

the excitation polarization is kept vertically polarized (V, along the Z-axis), but the detection polarization is either vertically (V) or horizontally polarized (H, along the X-axis) (Figure 1). Whenever possible, we use V and H to represent the photon polarizations because they are the most popular notations in chemistry literatures. However, X, Y, Z are used when it is necessary to differentiate the H-polarized excitation and detection photons. Mathematically, the solution and solvent polarized SSF spectra can be expressed with eqs 4−7. The solvent is assumed to be optically transparent for the sake of sample IFE consideration.

X σf,VH (λ ) X σf,VV (λ )

(1)

SSF,obsd SSF Raman ISolution,VV (λ) = I0(λ x )B V (λ)K (λ)(Cf σf,VV (λ) + Csolvσsolv,VV (λ))

1 − PfX(λ) 1+

× 10−(A x (λ)d x + A m(λ)dm)/ dUV

2PfX(λ)

(2)

SSF,obsd SSF Raman ISolution,VH (λ) = I0(λ x )BH (λ)K (λ)(Cf σf,VH (λ) + Csolvσsolv,VH (λ))

X G(λ)If,VH (λ )

× 10−(A x (λ)d x + A m(λ)dm)/ dUV

X If,VV (λ )

(3)

The definition (eq 1) in this work for the depolarization calculation is different from the equation (eq 3) used in literature for the SSF and light scattering depolarization.18−20 Another popular way of describing SSF depolarization is to define the SSF polarization as R X =

X X IVV (λ) − G(λ)IVH (λ) 21,22 . X X IVV (λ) + G(λ)IVH (λ)

(4)

(5)

SSF,obsd Raman ISolv,VV (λ) = I0(λ x )B V (λ)K (λ)Csolvσsolv,VV (λ)

(6)

SSF,obsd Raman ISolv,VH (λ) = I0(λ x )BH (λ)K (λ)Csolvσsolv,VH (λ)

(7)

The exponent terms in eq 4 and eq 5 describe the degree of the sample IFE induced by the fluorophore photon absorption at the excitation (Ax) and emission (Am) wavelength. dx and dm are the effective excitation and emission path lengths in the fluorescence detection. These two parameters are related to the instrument configuration but independent of the excitation and detection wavelengths. Experimental determination and validation of the dx and dm value can be readily achieved by measurement and correction of the sample IFE on solvent Raman signal (Supporting Information, Figure S1).23 dUV is the path length of the UV−vis cuvette used for the Ax and Am quantification. Cf and Csolv are fluorophore and solvent concentrations, respectively. I0(λx) is the normalized polarized excitation intensity which is achieved by dividing the acquired spectral intensity by the photon intensity measured by the reference detector (Figure 1). BV(λ) and BH(λ) describe the detectionpolarization bias of the instrument response when the detection polarization is vertical and horizontal, respectively. K(λ) defines the combined effects of the detector quantum yield, the

We

use the depolarization, not the polarization to discuss the fluorophore SSF, ORF, and scattering anisotropy, considering the fact that these optical processes only reduce (depolarize), rather than enhance, the polarization of the polarized excitation light. We will demonstrate later in this work that eq 1 and eq 3 are equivalent under conditions that the sample IFE and the solvent Raman/Rayleigh scattering contributions to the solution polarized fluorescence emission or RS2 used in eq 3 are reliably corrected.

■

THEORETICAL CONSIDERATION Fluorophore SSF Depolarization and Anisotropy. The theoretical discussion is on the basis of fluorescence detection geometry shown in Figure 1, which is also the most popular configuration in commercial spectrofluorometers. The polarized SSF emission and the RS2 spectra are obtained such that 6687

DOI: 10.1021/acs.analchem.7b00907 Anal. Chem. 2017, 89, 6686−6694

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polarization is horizontal (along Y-axis) but the detection polarization is vertical (Z-axis) and horizontal (X-axis), respectively. In this case, the number of the vertically and horizontally polarized fluorophore SSF photons and solvent Raman photons that can reach the sample detector must be the same crossing the entire wavelength region. This is because the degrees of the depolarization for Y-polarized excitation light to generate Z- and X-polarized SSF or Raman photons are the same. Therefore, the intensity difference between the SSF experimental ISSF Solution,HV(λ) and ISolution,HH(λ) spectra must be due entirely to the instrument bias.

excitation light beam size, and collection volumes on the Raman fluorescence signal. σRaman solv,VV(λ) and σsolv,VH(λ) are solvent Raman SSF SSF cross sections, and σf,VV(λ) and σf,VH(λ) are the fluorophore SSF cross sections evaluated at the indicated excitation and detection wavelengths and polarization geometries. As evident from eqs 4 and 5, the solution polarized emission spectrum in general contains both fluorophore SSF and solvent Raman signal. However, direct solvent background subtraction to remove Raman signal is problematic because solvent Raman signal in the fluorophore-containing solution is invariably lower than that in the solvent-alone sample due to the sample IFE imposed by the fluorophore photon absorption at the excitation wavelength and at Raman photon wavelength.23,24 Correcting the sample IFE using eqs 8 and 9 followed by simple mathematical manipulation, one can determine the fluorophore-specific polarized SSF signal with eq 10 and eq 11. SSF,corr SSF,obsd ISolution,VV (λ) = ISolution,VV (λ) × 10−(A x (λ)d x + A m(λ)dm)/ dUV

(8)

SSF,corr SSF,obsd ISolution,VH (λ) = ISolution,VH (λ) × 10−(A x (λ)d x + A m(λ)dm)/ dUV

(9)

G(λ) =

(10) =

SSF,corr ISolution,VH (λ)

SSF ISolv,VH (λ)

−

=

SSF I0(λ x )BH (λ)K (λ)Cf σf,VH (λ)

(11)

Dividing eq 11 by eq 10 with simple mathematical manipulation leads to eq 12 SSF If,VH (λ) SSF If,VV (λ)

=

SSF,corr SSF ISolution,VH (λ) − ISolv,VH (λ) SSF,corr SSF ISolution,VV (λ) − ISolv,VV (λ)

=

SSF BH (λ)σf,VH (λ) SSF B V (λ)σf,VV (λ)

(12)

The ratio between BV(λ) and BH(λ) is the G-factor spectrum (eq 13). Combining eqs 12 and 13 leads to eq 14 for the fluorophore SSF depolarization that is defined with eq 1. G(λ) =

SSF σf,VH (λ) SSF σf,VV (λ)

RS2

sca + Csolvσsolv,VV (λ))10−A(λ)deff

(13) = G(λ)

SSF If,VH (λ) SSF If,VV (λ)

= G(λ)

SSF,corr SSF ISolution,VH (λ) − ISolv,VH (λ)

RS2

sca + Csolvσsolv,VH (λ))10−A(λ)deff

Once the SSF depolarization is determined with eq 14, its SSF anisotropy is calculated using eq 15. This equation is derived on the basis of eq 2 that describes the relationship between the depolarization and anisotropy. (15)

Using polarized SSF emission spectra taken with the solvent control, one can also calculate the solvent Raman depolarization and anisotropy using eqs 16 and 17, respectively. Raman PSolv (λ) =

Raman rSolv (λ) =

Raman σSolv,VH (λ) Raman σSolv,VV (λ)

= G(λ)

SSF ISolv,VH (λ) SSF ISolv,VV (λ)

(16)

Raman 1 − PSolv (λ) Raman 1 + 2PSolv (λ)

(19)

/ dUV

(20)

PRS2 sca ORF If,VV (λ) = γ(λ)B V (λ)Cf σf,VV (λ) + γ(λ)B V (λ)Cf σf,VV (λ)

(21)

PRS2 sca ORF If,VH (λ) = γ(λ)BH (λ)Cf σf,VH (λ) + γ(λ)BH (λ)Cf σf,VH (λ)

(22)

Many variables have been discussed in the preceding section on the fluorophore SSF. Only the new parameters are defined here. A(λ) is the fluorophore UV−vis absorbance. σsca solv,VV(λ) sca and σsca solv,VH(λ) are solvent scattering cross sections, σf,VV(λ) and σsca f,VH(λ) are the fluorophore scattering cross sections, and ORF σORF f,VV (λ), and σf,VH (λ) are the fluorophore ORF cross sections, all evaluated at the specified wavelength and with the indicated excitation and detection polarization combinations. Notably, the as-obtained solution PRS2 spectra at any wavelength contain collective contributions from both solvent and fluorophore PRS2 signal, and they both are modified by the sample IFE. One must correct the sample IFE before subtraction removal of solvent PRS2 spectral contribution in order to obtain the fluorophore-specific PRS2 spectral features defined with eqs 21 and 22. Mathematically, the solvent PRS2 spectra are expressed with eqs 23 and 24.

1 − PfSSF(λ) 1 + 2PfSSF(λ)

/ dUV

PRS2,obsd sca ORF ISolution,VH (λ) = I0(λ)K (λ)BH (λ)(Cf σf,VH (λ) + Cf σf,VH (λ)

SSF,corr SSF ISolution,VV (λ) − ISolv,VV (λ)

(14)

rfSSF(λ) =

(18)

PRS2,obsd sca ORF ISolution,VV (λ) = I0(λ)K (λ)B V (λ)(Cf σf,VV (λ) + Cf σf,VV (λ)

B V (λ) BH (λ)

PfSSF(λ) =

SSF ISolution,HH (λ)

Fluorophore ORF and Light Scattering Depolarization and Anisotropy. Identification of the fluorophore ORF and light scattering features and quantification of their depolarization and anisotropy require combined UV−vis, polarized SSF, and PRS2 measurements. To ensure the generality in discussion, we assume the fluorophore in the solution is a simultaneous photon scatterer, absorber, and emitter. In this case the detected solution PRS2 spectra IPRS2,obsd Solution,VV(λ) and IPRS2,obsd Solution,VH(λ) can be expressed with eqs 19 and 20, respectively. These two equations can be justified on the basis of the recent work on the R2S2 method.16 The exponent terms in these equations are for the sample IFE induced by the sample photon absorption that attenuates the number of photons reaching the sample detector. dRS2 eff is the effective path length for correcting the sample IFE in the RS2 measurements.16,25 dRS2 eff is the sum of dx and dm, the effective excitation and emission path lengths discussed in the preceding subsection for correcting the sample IFE in SSF measurements as the excitation and the detection wavelengths are the same in RS2 spectral acquisition.

SSF SSF,corr SSF SSF If,VV (λ) = ISolution,VV (λ) − ISolv,VV (λ) = I0(λ x )B V (λ)K (λ)Cf σf,VV (λ)

SSF If,VH (λ)

SSF ISolution,HV (λ)

(17)

The G-factor spectrum defined with eq 13 can be readily SSF determined using eq 18 where ISSF Solution,HV(λ) and ISolution,HH(λ) are the fluorophore polarized fluorescence SSF spectra taken with the excitation and detection polarization depicted in Figure 1. In these spectral acquisitions, the excitation

PRS2 sca Isolv,VV (λ) = I0(λ)K (λ)B V (λ)Csolvσsolv,VV (λ )

6688

(23)

DOI: 10.1021/acs.analchem.7b00907 Anal. Chem. 2017, 89, 6686−6694

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Analytical Chemistry PRS2 sca Isolv,VH (λ) = I0(λ)K (λ)BH (λ)Csolvσsolv,VH (λ )

spectra into its photon scattering and ORF component spectra can be readily achieved using the methods outlined in the preceding sections. It is, however, impossible to determine the fluorophore ORF and scattering cross sections using these component spectra alone. Besides the fluorophore ORF and light scattering cross sections, there are multiple instrument parameters that can affect the detected fluorophore ORF and light scattering intensity as shown in eqs 31 to 34.

(24)

Defining the sample-IFE-corrected solution PRS2 spectra with eqs 25 and 26 and with simple mathematical manipulation, one can obtain the fluorophore-specific PRS2 spectra as shown with eqs 27 and 28. RS2

PRS2,corr PRS2,obsd ISolution,VV = ISolution,VV 10 A(λ)deff

/ dUV

RS2

PRS2,corr PRS2,obsd ISolution,VH = ISolution,VH 10 A(λ)deff

/ dUV

(25) (26)

PRS2 PRS2,corr PRS2 If,VV (λ) = ISolution,VV (λ) − Isolv,VV (λ )

(27)

PRS2 PRS2,corr PRS2 If,VH (λ) = ISolution,VH (λ) − Isolv,VH (λ )

(28)

σfsca(λ) =

σfORF(λ) =

The fluorophore-specific PRS2 spectra are composed of fluorophore photon scattering and ORF spectral features (eqs 21 and 22). Mathematical decomposition of the fluorophore PRS2 spectra to their photon scattering and ORF component spectra are shown in eqs 31−36. PRS2 sca ORF If,VV (λ) = If,VV (λ) + If,VV (λ )

(29)

PRS2 sca ORF If,VH (λ) = If,VH (λ) + If,VH (λ )

(30)

(31)

sca sca If,VH (λ) = I0(λ)K (λ)BH (λ)Cf σf,VH (λ )

(32)

ORF ORF If,VV (λ) = I0(λ)K (λ)B V (λ)Cf σf,VV (λ )

(33)

ORF ORF If,VH (λ) = I0(λ)K (λ)BH (λ)Cf σf,VH (λ )

(34)

Fruitfully, one can readily experimentally decompose the fluorophore photon scattering and ORF component spectra by taking advantage of the two experimental observations that will be demonstrated in the Results and Discussion section. The first is that fluorophore photon scattering has negligible depolarization (σsca f,VH(λ) = 0). As a result, one can simplify eq 22 and eq 32 into eqs 35 and 36, respectively. The second observation is that the fluorophore SSF depolarization is independent of the degree of the Stokes shift in the SSF spectrum. This enables one to approximate the ORF depolarization to be the same as the SSF depolarization and calculate the fluorophore polarized ORF spectrum IORF f,VV (λ) using the experimental spectra of IPRS2 (λ) by eq 37. f,VH PRS2 ORF If,VH (λ) = If,VH (λ )

(35)

sca If,VH (λ ) = 0

(36)

ORF (λ ) = If,VV

ORF If,VH ( λ ) G (λ )

PfSSF(λ)

=

MATERIALS AND METHODS Reagents and Equipment. All chemicals were purchased from Sigma-Aldrich and used as received. CdTe-core quantum dots with peak emission wavelength of 570 and 610 nm are abbreviated as QD570 and QD610, respectively. The molecular fluorophores used in this work include eosin Y, acridine orange hemi(zinc chloride) salt (AOH), quinine sulfate, fluorescein isothiocyanate (FITC), rhodamine-6G (R6G), cresyl violet perchlorate (CVP), anthracene (ANT), tryptophan, harmane, harmine, and 9,10-diphenylanthracence (DPA). UV−vis spectra were acquired using Thermo Scientific Evolution 300 UV−vis spectrophotometer. The PRS2 and SSF spectra were acquired using a Horiba FluoroMax-4 spectrofluorometer. Detailed spectral acquisition procedures including the excitation and emission wavelengths with each of the used fluorophores are shown in the Supporting Information (Table S1). All the resonance synchronous spectra shown in this work are cuvette-background-subtracted before further data processing. These background spectra were obtained with the empty cuvette under conditions identical to that used for sample spectrum (Supporting Information, Figure S2).

(37)

Combining eq 37 with eq 29 leads to eq 38 for experimental determination of the fluorophore polarized photon scattering spectrum. sca PRS2 If,VV (λ) = If,VV (λ ) −

PRS2 If,VH ( λ ) G (λ )

PfSSF(λ)

(40)

■

PRS2 If,VH ( λ ) G (λ )

PfSSF(λ)

ORF (1 + 2PfORF(λ)) C PSNPIf,VV (λ) sca σPSNP(λ) sca sca (1 + 2PPSNP (λ)) Cf IPSNP,VV (λ )

(39)

Fruitfully, the fluorophore ORF and light scattering cross sections can be quantified using a ratiometric PRS2 method that employs pure photon scatterers such as polystyrene nanoparticles (PSNPs) as the external references. Detailed derivation of the eq 39 and eq 40 for the calculation of the fluorophore photo scattering and ORF cross-section spectra is shown in the Supporting Information. Isca PSNP,VV(λ) is the PSNP polarized spectrum acquired with “VV” excitation and detection polarization combination. Experimentally, this spectrum is obtained by subtracting the solvent PRS2 spectrum IPRS2 Solv,VV(λ) from the PSNP-containing solution PRS2 spectrum sca IPRS2 Solution,VV(λ). σPSNP(λ) is the PSNP cross section measured with the conventional UV−vis measurement and evaluated by taking into account all the scattered photons, regardless of their ORF (λ) are polarization and propagation directions. σsca f (λ) and σf the fluorophore light scattering and ORF cross sections that are evaluated in analogy to the PSNP light scattering cross section sca σsca PSNP(λ). PPSNP(λ) is the PSNP light scattering depolarization. Since all the right-hand parameters in eqs 39 and 40 are measurable, these two equations enable the experimental quantification of the fluorophore light scattering and ORF cross sections by using the polarized RS2 measurements.

In which sca sca If,VV (λ) = I0(λ)K (λ)B V (λ)Cf σf,VV (λ )

sca (1 + 2Pfsca(λ)) C PSNPIf,VV(λ) sca σPSNP(λ) sca sca (1 + 2PPSNP(λ)) Cf IPSNP,VV(λ)

(38)

Determination of Fluorophore Light Scattering and ORF Cross Sections. Decomposition of the fluorophore PRS2 6689

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SSF Figure 2. First row: the as-acquired (black) ISSF HV (λ) and (red) IHH(λ) spectra for the specified calibration fluorophore. Second row: the G(λ) value using the spectral show in the first row. Only the spectral features between the two dash lines are used for the G-factor calculation.

■

for all the validation fluorophore samples (Supporting Information, Figure S3). The G-factor spectrum determined in Figure 3 is highly reproducible. Similar G-factor spectrum was acquired during the entire approximately 2 month experimental period, reflecting the robustness of the instrument. Fluorophore SSF and Solvent Raman Depolarization and Anisotropy. Figure 4 shows experimental data obtained with QD610 for the fluorophore SSF and the solvent Raman depolarization and anisotropy quantification. The UV−vis spectrum (Figure 4A) is taken to correct the sample IFE in the as-acquired QD610 SSF spectra (Figure 4B). The effective excitation and emission path lengths used for correcting the sample IFE are 0.618 and 0.523 cm, which are determined on the literature procedure (Supporting Information, Figure S1).16,25 The peaks in the solvent polarized SSF spectra in Figure 4C are the solvent Raman features. The fluorophorespecific SSF spectra in Figure 4E are obtained by subtracting the solvent SSF spectra in Figure 4C from the IFE-corrected solution SSF spectra in Figure 4D. Using the procedures described in the Theoretical Consideration section and the Gfactor spectrum evaluated in the preceding section, we quantified both the solvent Raman and fluorophore SSF depolarization and anisotropy. The solvent Raman depolarization and anisotropy are 0.23 and 0.52, respectively, which are compared to their respective counterparts of 0.98 and 0.007 for QD610 SSF. This indicates that solvent Raman is highly polarized and anisotropic, but the fluorophore SSF is almost completely depolarized and entirely isotropic. Following the same procedure used for QD610 in Figure 4, we determined the depolarization and anisotropy (Table 1) for a series of water-soluble fluorophores (Supporting Information, Figure S4). The most notable observation from the data shown in Figure 4 and Figure S4 (Supporting Information) is that the fluorophore SSF depolarization and anisotropy are independent of their emission wavelength. This indicates that the internal conversions responsible for the Stokes shift in the SSF measurements have no significant effect on the SSF depolarization. Another evidence of the independence of the fluorophore SSF depolarization from the degree of Stokes shift comes from the polarized excitation spectra obtained with FITC. The depolarization measurement at the emission

RESULTS AND DISCUSSION Determination of the G(λ). Figure 2 shows the polarized SSF SSF (λ) and IHV (λ) obtained with a set of SSF spectra IHH calibration fluorophores for G(λ) quantification. Evidently, SSF the experimental ISSF HH(λ) and IHV (λ) intensity can be markedly different. Such intensity difference is due exclusively to the difference of the instrument response in detecting the horizontal (x-axis) and vertical (z-axis) polarized light. SSF Otherwise, the ISSF HH(λ) and IHV (λ) should be the same since the degrees of the depolarization for the horizontally polarized excitation (y-axis) photons to emit photon with polarization along the x- and z-axes are the same. SSF The ratios between ISSF HV (λ) versus IHH(λ) obtained with the calibration fluorophores give the value of G(λ) shown in the second row in Figure 2. It is noted that individual fluorophore allows G(λ) determination for a relatively narrow wavelength region where the fluorophores are fluorescence-active. Obtaining the G-factor spectrum crossing the entire spectral region requires polarized SSF measurement with multiple fluorophores that emit in different wavelength regions. Figure 3 shows the G-factor spectrum from 300 to 650 nm obtained with fluorophores shown in Figure 2. Evidently, the G(λ) factor is strongly wavelength-dependent. The G(λ)-factor spectrum was independently validated with a series of fluorophores that are different from the fluorophores used for G(λ)-factor determination (Supporting Information, SSF,obsd (λ) spectrum overlaps Figure S3). The solution ISolution,HV perfectly with the multiplication spectra of G(λ)ISSF,obsd Solution,HH(λ)

Figure 3. G(λ) factor spectrum obtained by combining the G(λ) values obtained with the calibration fluorophores shown in Figure 2. 6690

DOI: 10.1021/acs.analchem.7b00907 Anal. Chem. 2017, 89, 6686−6694

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Figure 4. Experimental data obtained with fluorophore QD610 in water. (A) The UV−vis spectrum obtained with a 1 cm cuvette. (B) As-acquired SSF SSF SSF (black) ISSF Solution,VH(λ) and (red) ISolution,VV(λ) spectra of the solution. (C) Solvent (black) Isolv,VH(λ) and (red) Isolv,VV(λ) spectra. (D) The IFESSF,corr SSF,corr corrected solution spectrum (black) ISSF,corr Solution,VH(λ) and (red) ISolution,VV(λ) spectra. (E) The IFE and solvent Raman corrected (black) If,VH (λ) and SSF,corr (red) If,VV (λ) spectra. (F) QD SSF (black) depolarization and (red) anisotropy at the sample region the fluorophore are fluorescence-active.

Table 1. Experimental Results Obtained with the Model Fluorophores P λext max λORF max −16 ORF σext cm2 f (λmax ) × 10 −20 ORF σsca (λ ) × 10 cm2 f max −19 ORF σORF (λ ) × 10 cm2 f max −3 ext Γ(λmax) × 10 −3 Γ(λORF max ) (×10 ) −2 Q(λORF ) (×10 ) max

R6G

FITC

AOH

eosin Y

QD570

QD610

0.96 526 539 0.88 7.62 29.5 0.57 0.87 3.36

0.89 476 501 0.25 0.742 2.44 0.099 0.29 0.96

0.96 491 511 0.26 0.548 1.29 0.036 0.21 0.39

0.89 518 530 1.86 4.8 13.44 0.086 0.46 1.9

0.97 533 556 1.24 6.81 26.2 0.28 0.55 2.1

0.98 565 586 1.24 26.3 21.8 1.2 2.1 1.7

PRS2 Figure 5. Experimental data obtained with fluorophore QD610 in water. (A) As-acquired (black) IPRS2 solution,VH(λ) and (red) Isolution,VV(λ). (B) AsPRS2 sca (λ) and (red) I (λ). (C) The PSNP scattering spectra (black) I (λ) and (red) Isca acquired solvent PRS2 spectrum (black) IPRS2 Solv,VH Solv,VV PSNP,VH PSNP,VV(λ). corr,PRS2 corr,PRS2 (D) The sample-IFE-corrected solution PRS2 spectra (black) Isolution,VH(λ) and (red) Isolution,VV(λ). (E) Fluorophore-specific polarized PRS2 spectra PRS2 PRS2 (black) IPRS2 f,VH (λ)G(λ)/P(λ) and (red) If,VV (λ). (F) Comparison of the fluorophore (blue) multiplication spectrum If,VH (λ)G(λ)/P(λ) with (red) PRS2 sca PRS2 PRS2 If,VV (λ). (G) The If,VV(λ) spectrum obtained by subtracting If,VV (λ) with If,VH (λ)G(λ)/P(λ). (H) (red) fluorophore polarized ORF and (black) photon scattering cross-section spectra calculated using the polarized PSNP as the external reference. The experimental data obtained with other model fluorophores are shown in the Supporting Information.

wavelength of 540 nm remains the same (0.89 ± 0.03) when the excitation wavelength varies from 450 to 520 nm. The fact that the SSF depolarization values are