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Journal Pre-proof The Centenary of the Stern-Volmer Equation of Fluorescence Quenching: From the single line plot to the SV quenching map Marcelo H. Gehlen

PII:

S1389-5567(19)30136-4

DOI:

https://doi.org/10.1016/j.jphotochemrev.2019.100338

Reference:

JPR 100338

To appear in: Reviews

Journal of Photochemistry & Photobiology, C: Photochemistry

Received Date:

19 September 2019

Revised Date:

2 December 2019

Accepted Date:

4 December 2019

Please cite this article as: Gehlen MH, The Centenary of the Stern-Volmer Equation of Fluorescence Quenching: From the single line plot to the SV quenching map, Journal of Photochemistry and amp; Photobiology, C: Photochemistry Reviews (2019), doi: https://doi.org/10.1016/j.jphotochemrev.2019.100338

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The Centenary of the Stern-Volmer Equation of Fluorescence Quenching: From the single line plot to the SV quenching map

Marcelo H. Gehlen Department of Physical Chemistry, Institute of Chemistry of São Carlos, University of São Paulo, 13566-590 – São Carlos – SP – Brazil

Dedicated to Professor Frans C. De Schryver and to Professor Miguel G. Neumann, on the

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occasion of 80th birthday.

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MH Gehlen: [emailprotected]

Abstract:

In the year of 2019, we celebrate the centenary of the publication of the remarkable paper by Otto Stern and Max Volmer concerning the kinetics analysis of fluorescence quenching. Their

achievement changed enormously many fields of science with great impact in the studies of electronic spectroscopy and kinetics of organic, inorganic and biological compounds in condensed phase. The development of molecular photochemistry was in great part based on the

use of the Stern-Volmer (SV) approach to investigate bimolecular interaction in the electronic excited-state. This paper reviews and summarizes the assumptions behind the Stern-Volmer equation and the extensions of the theory to other important situations. Discussions about the use

of the SV approach to investigate probe and quencher distribution, association, diffusion and reaction at the molecular level obtained from advanced fluorescence microscopy methods are

also included.

Keywords: kinetics; excited-states; diffusion; quenching; fluorescence microscopy.

CONTENTS

1. Introduction 2. The classical Stern-Volmer model in hom*ogeneous phase 3. Transient quenching effects due to molecular diffusion 4. Fluorescence quenching and generalization of the SV equation in small domains 5. Static and dynamic quenching in bulk and in small domains 6. Energy migration and superquenching 7. Negative deviations of the SV equation, aggregation induced emission, and new analytical

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tools based on SV formalism 8. Microscopic analysis of the fluorescence quenching with FLIM methods

9. Fluorescence quenching analysis in small domains with the phasor method

10. Photo-antibunching, FCS and other single-molecule approaches to bimolecular quenching

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dynamics

11. Topographic quenching methods and applications in nanomaterial research

1. Introduction

12. Concluding remarks

One hundred years have passed since Otto Stern and Max Volmer proposed in a seminal paper

in 1919 the theory and equation relating the change in fluorescence quantum yield and fluorescence lifetime as a function of added quencher, a molecular species capable to deactivate the electronic excited-state of the fluorophore or luminophore back to its electronic ground state

[1]. O. Stern and M. Volmer were recognized as great scientists belonging to the emeritus group of founders of the experimental atomic physics [2] and modern physical chemistry [3],

respectively. The Nobel prize in Physics in 1943 was awarded to Otto Stern for his fundamental contributions in atomic physics. Max Volmer became renowned by his impressive research in electrochemistry where he co-developed the Butler-Volmer equation, a fundamental relationship in electrochemical kinetics. The SV theory and equation were a remarkable achievement in a period of Science where molecules and their electronic excited states were entities not fully understood or well defined. It has in photophysics and photochemistry a comparable prestige as the Michaelis-Menten equation (published six years earlier, in 1913) has in biochemistry. From the point of view of chemical 2

kinetics, SV equation makes a simple and powerful bridge between steady-state irradiation experiments with the dynamical properties of the excited fluorophore and its diffusional motion and interaction with the quencher species. In the early times of the SV equation, the measurement of a fluorescence lifetime was an enterprise or something practically impossible due to the absence of optical and electronic instrumentations with the necessary time-resolution capacity for optimal fluorescence decay measurements. Thus, photo-stationary measurements with determination of the Stern-Volmer constant KSV was the central issue for many years. The measurements of the emission spectra and the calculation of the relative quantum yield or emission intensity upon addition of the quencher species were typical routine experiments in the

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past photochemical research laboratories. Several fundamental photochemical systems were then studied initially in photo-stationary condition before of being illuminated by time or frequency resolved fluorescence methods. It was only with the development of pulsed and modulated light sources such as gas spark lamps (usually hydrogen) and later on with the advent of visible light lasers and solid-state fast electronics, that the measurement of fluorescence decay and precise

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determination of fluorescence lifetime became possible in advanced spectroscopic laboratories around the world [4–9]. Thus, the study of the photophysics and photochemistry of organic,

inorganic and biological compounds in hom*ogeneous solvent phase entered in a “new and excited” period with great scientific novelties over several decades. Details of the time evolution

of important molecular processes in electronic excited state such as electronic energy transfer, excimer and exciplex dynamics, photo-induced charge (electron and proton) transfer were extensively investigated [7–10]. These processes in excited states were explored in their

bimolecular scope and therefore were a good test of several theories of diffusion-controlled reaction involving the excited fluorophore and the added quencher in regular solvent solution as well as in micro heterogeneous systems. A step further embraced the studies in model compounds

where the fluorophore and the quencher were part of the same molecular framework allowing to investigate the fluorescence quenching process as a function of molecular distance and

orientation between donor and acceptor in photo-induced energy and electron transfer intramolecular processes [11,12]. Reviewing the enormous amount of scientific papers published with the application of the SternVolmer approach is beyond the scope of this article. Therefore, the central focus of this contribution is to highlight some important aspect of the Stern-Volmer equation discussing the fluorescence quenching theory in special situations such as the diffusion-controlled bimolecular quenching reactions and fluorescence quenching in confined space or small domains. Advanced use of the SV analysis in fluorescence microscopy where probe and quencher interactions are 3

monitored in a nanoscopic region of the system is also included as a modern aspect in photophysics and photochemistry with space and time resolution [13, 14]. The situation where a single pair of probe fluorophore and quencher is observed by the use of fluorescence microscopy techniques is discussed in the framework of single-molecule spectroscopy [15, 16]. Fluorescence instrumentation and data analysis are unfortunately not covered in this short review but these experimental aspects may be found in some of the references cited. We have not included a discussion of SV expression related to reactive quenching with photo-product formation because it is usually dependent of the type of the excited-state reaction mechanism taking place. 2. The classical Stern-Volmer model

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In the case of single exponential decay of the fluorophore with lifetime 0 in absence of added quencher Q and corresponding fluorescence quantum yield 0, the Stern-Volmer equation correlates the lifetime  and the corresponding quantum yield  upon addition of quencher at concentration [Q] by [1, 8, 9],

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∅0 𝜏0 = = 1 + 𝑘𝑞 𝜏0 [𝑄] ∅ 𝜏

(1)

In eq. 1, kq is the bimolecular rate constant of the fluorescence quenching process due to a shortrange interaction of species. If the fluorescence quantum yield remains proportional to the

integrated emission intensity upon addition of the quencher, then eq. 1 is usually replaced by the corresponding ratio of fluorescence intensities,

(2)

𝐼0 = 1 + 𝐾𝑆𝑉 [𝑄] 𝐼

where Ksv = kq0 is the Stern-Volmer constant that in a purely dynamic fluorescence quenching

process is the product of the bimolecular quenching rate constant and the fluorescence lifetime in absence of added quencher. The linear relationship between relative fluorescence intensity under low light excitation and quencher concentration allows easy graphical determination of

KSV. If the fluorescence lifetime 0 is known then the bimolecular quenching rate kq is determined from photo-stationary measurements using a simple steady-state fluorimeter. Although we have addressed the quenching problem in a deactivation without formation of photoproducts, the SV approach is also applicable in photoreactions or in photocatalytic processes where an electronic excited-state is depleted by reaction with the added quencher. In such situation, photoproducts must not absorb light at the excitation and detection wavelengths. It follows that the measured quantum yield (emission or photoproduct formation) may be related to SV type equation where

the KSV will depend on the steady-state condition of the underlying photochemical mechanism [17, 18]. The Stern-Volmer equation in fluorescence quenching is straightforward derived assuming the following processes involving the fluorophore or probe in the excited state F* surrounded by quenchers Q in a bimolecular deactivation process, 𝑘0 = 1⁄𝜏0

𝐹∗ → 𝑘𝑞

𝐹∗ + 𝑄 → 𝐹 + 𝑄

𝐹 + ℎ𝜈𝐹

(3)

(4)

The rate constant k0 contains the radiative (kf) and non-radiative (knr) decay rate components and

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in the standard SV model it is not affected by the presence of the quencher. The overall rate is a sum of the self-decay rate with the bimolecular quenching rate where the quencher concentration is considered constant (a pseudo-first order condition),

(5)

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𝑑𝐹 ∗ = −(𝑘0 + 𝑘𝑞 [𝑄])𝐹 ∗ 𝑑𝑡

Thus, the decay for  pulse excitation is exponential, and it is given by,

𝐹 ∗ (𝑡) = 𝐹 ∗ (0)𝑒𝑥𝑝[−(𝑘0 + 𝑘𝑞 [𝑄])𝑡]

(6)

decay function resulting in,

The corresponding emission intensity I is proportional to the time-integral of the fluorescence

∞

𝐼 = 𝑘𝑓 ∫ 𝐹 ∗ (𝑡) 𝑑𝑡 =

𝑘𝑓 𝐹 ∗ (0)

(𝑘0 + 𝑘𝑞 [𝑄])

(7)

which in absence of added quencher is reduced to 𝑘𝑓 𝐹 ∗ (0) 𝑘0

(8)

𝐼0 =

The fluorescence lifetime in the presence of the added quencher is  = (k0 + kq[Q])1 and, therefore, the ratio of lifetimes or intensities results in the SV equation. In a hom*ogeneous 3D solvent medium with diffusion-controlled irreversible quenching process, the quenching rate constant may be given by the classical expression 𝑘𝑞 = 𝑘𝑑 = 4𝜋𝐷𝑅𝑁𝐴 where D, R and NA stand for the mutual diffusion constant of probe and quencher, their encounter radial distance, and the Avogadro number, respectively. Usually R is of the order of the sum of molecular radii of F* and Q species. In the case where the quenching process may not occur at each approach of the species,

the stationary quenching rate becomes a function also of the rate of the activated quenching process (kact) and therefore 𝑘𝑞 = 𝑘𝑑 𝑘𝑎𝑐𝑡 (𝑘𝑑 + 𝑘𝑎𝑐𝑡 )−1

(9)

Departure or deviation from the linear Stern-Volmer law has been observed in many experimental systems since a long time ago, and it has been ascribed to the presence of diverse factors depending also on the type of underlying quenching mechanism [19–22]. Diffusion effects, reversible quenching in excimer and exciplex formation, distance-dependent activated quenching process, no single lifetime decay of the excited probe in the absence of added quencher, selfquenching, quencher concentration beyond the dilute regime and caging effects, confinement of

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species and partition in different molecular environments, chemical association prior excitation are some of the factors that may give a non-linear behavior or inequality of the ratio of lifetimes compared with the ratio of intensities as expressed by equations 1 and 2. Extensive efforts were devoted for improving the Stern-Volmer analysis beyond the classical linear form and important

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contributions in the generalization of the SV equation are presently known (vide infra). In order to simplify the analysis, we dedicate attention more to the immediate results of some of the main

factors that may produce a nonlinear SV behavior as they will be described in the next sections. More details of each theoretical model discussed here may be found in the references cited.

3. Transient quenching effect in hom*ogeneous phase

The non-exponential decay of the excited probe in diffusion-limited or in a distance dependent quenching process would result in a time-dependent rate kq(t) in eq. 4. The quenching

shows a dynamic disorder of the system at short times following the definition given by Zwanzig [23]. Such transient effect on the fluorescence decay occurs usually in a picosecond time scale

but if solvent viscosity is high or excited probe-quencher distance coupling is large, it may be extended over a longer time regime of nanoseconds. The relative fluorescence intensity on the

other hand departs from a linear dependency on [Q] and it may be expressed as ∞ 𝐼 = 𝑘0 ∫ 𝑒𝑥𝑝[−(𝑘0 𝑡 + [𝑄]𝜑(𝑡))]𝑑𝑡 𝐼0 0

(10)

where

𝑡

𝜑(𝑡) = ∫ 𝑘𝑞 (𝑡′)𝑑𝑡′

(11)

When the quenching is fully diffusion-controlled (kact >> kd), the time-dependent rate in the Smoluchowsky model is given as kq(t) = kd (1 + R(Dt)1/2) [24, 25]. 6

In general, the analytical expression of the SV relation may be obtained only in limiting cases of a time-dependent quenching rate (t) and it will ultimately result in an extra power term of [Q], which in a polynomial approximation may be represented by [26] 𝐼0 ≅ 1 + 𝑎[𝑄] + 𝑏[𝑄]𝜈 𝐼

(12)

The diffusion transient usually gives an upward curvature on the SV plot with quencher concentration thus indicating that  > 1. In 3D diffusion within the Smoluchowski approximation and also in the model of stationary random array of sinks developed by Felderhof and Deutch, the condition of  = 3/2 appears [26 – 29]. The corresponding values a, b in those two classical

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diffusion models applied to fluorescence quenching are not equivalent even considering that effective quenching distance R given the sum of the molecular radii of F* and Q would correspond to the quenching sink radius (see parameters definition and simulated results in figure 1). Although the use of the expression above may be appealing due to easy polynomial fitting,

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the direct extraction of the molecular parameter R from it is not recommended unless as a first guess for more advanced treatment of the fluorescence quenching using complete and more

elaborated models combining both time-resolved and stationary experimental data in a global analysis approach [30, 31]. Another form to describe nonlinear SV plots with quencher concentration is to take into account the effect of proximity of species in bimolecular quenching.

The onset of nonlinear SV behavior has also some dependency with solvent viscosity as early demonstrated by Wagner and Kochevar [32]. When the quencher concentration increases in a hom*ogeneous solvent medium, there may be some close distance excited probe-quencher pairs

not forming a stable bimolecular complex but subjected to a very fast deactivation leading to a static quenching effect. This effect has been called as the sphere-of-action which was postulated

several decades ago by Frank and Wawilow [33]. In such a simple case, the linear SV without diffusion transient is multiplied by exp(VqNA[Q]) where Vq is the quenching sphere volume per

molecule which accounts in a very phenomenological form for the static quenching effect. However, similar exponential term can also be derived as a particular limit of the SV equation with diffusion quenching model in the radiation boundary condition (Collins-Kimball diffusion model) [20, 21, 34]. In that particular limit, the steady-state SV equation may have a similar expression as that of sphere of action model corresponding to [35] 𝐼0 ≅ (1 + 𝐾𝑆𝑉 [𝑄])𝑒𝑥𝑝(𝑉̃ 𝑁𝐴 [𝑄]) 𝐼

(13)

in which 𝑉̃ is related to the effective volume that a single fluorophore encompasses in its random walk steps during the excited state survival time τ, 𝑉̃ = 4𝜋𝑅̅ 2 √𝐷𝜏

(14)

𝑅̅ = 𝑅𝑘𝑎𝑐𝑡 /(𝑘𝑎𝑐𝑡 + 𝑘𝑑 ) is the effective radius corresponding to a fraction of encounter radial distance R and τ is the asymptotic decay time in the presence of added quencher, i.e. 1/𝜏 = (𝑘0 + 4𝜋𝑅̅ 𝐷𝑁𝐴 [𝑄]). Although the exponential term of the sphere-of-action or of the effective volume of diffusion may be somewhat similar, the meaning is different. In the former the exponential term arises from a statistical equilibrium probability of having a quencher near a promptly excited probe but in the latter, it is related to the diffusion spread during the fluorescence

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transient event. The exponential expansion of the sphere-of-action results in SV equation with linear [Q] and quadratic form [Q]2 while effective volume of diffusion will produce a linear plus rational forms with [Q]1/2 and [Q]3/2. In order to give to the reader a flavor about these four simple descriptions in the modulation of the SV plot we have simulated those models under their

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restricted approximations using common parameters (0, D and the effective quenching radius of

each particular model) as displayed in Figure 1.

Smo

Sink

I0 / I

Sph

the SV equation may be expressed by, ∞

〈𝑞〉𝑥 I0 = 𝑒𝑥𝑝[〈𝑞〉] (∑ (1 + 𝑥𝑘𝑞 /𝑘0 )−1 (1 + 𝑥𝐾)−1 ) I 𝑥!

−1

(34)

𝑥=0

In the treatment used, it is considered that the static quenching modifies the initial condition for the dynamic quenching. However, the two quenching contributions cannot be separated in eq. 34 as occurs in both eq. 32 and 33, showing an apparent inconsistency of the proposed model. As a recommendation, relative fluorescence intensity data should not be used as the only observable 16

to get information regarding the model parameters involved in the fluorescence quenching process because in general correlations between quenching rate constant and FQ complexation constant may be present. Thus, time-resolved fluorescence quenching measurements combined with electronic absorption and emission spectral data in a global analysis approach should be used for a more consistent determination of the intrinsic parameters specially when probe and quencher association may be taken place. Nevertheless, the average number of quenchers per micelle should keep at moderate values to validate the quencher distribution assumed as a Poisson law. On the other hand, probe and quencher association should be verified independently by using complementary technique (such as electronic absorption and/or NMR spectroscopy techniques)

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given the signature of the presence of FQ complex [84]. Fluorescence quenching with larger static contribution may occur when a molecular probe in excited state has a strong coupling at short distance with a metal nanoparticle (NP) acting as an effective quencher species [85]. In this case the initial addition of NP causes a preferential

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location of the probe near the NP surface or adsorbed on it, and as a consequence the relative intensity becomes governed by the corresponding static quenching component. Dynamic

quenching may be present through very fast decay components.

6. Energy migration and super-quenching

Energy migration is the mobility of the exciton from one probe to a neighboring one via excited state coupling though space or among chromophores in a chain as in the case of

conjugated polymers. In solution, the energy migration is usually a fast process and it may be investigated though time resolved fluorescence depolarization. Such mechanism enlarges the range of fluorescence quenching probability and gives rise to what has been called by Whitten as

the super-quenching effect [86, 87]. The relation between fluorescence intensity in absence and presence of added quencher may have linear or non-linear behavior but a substantial change in

slope occurs at very low concentration or density of the added quencher as low as mol/L. Therefore, the apparent quenching rate constant kq is much higher than diffusion-controlled rate constant kd. The super-quenching of the fluorescence of conjugated polymers and polyelectrolytes have been used as a tool in biosensing for enzyme activity assays, detection of proteins and DNA [88]. Similar enhanced quenching process has been found in emissive quantum dots QD upon addition of particular quencher species that bound to its surface. Although the mechanism of exciton diffusion and trapping in QD may be different than that in conjugated polymer systems the effect is similar, means an effective quenching process even at low number 17

or density of quenchers on the QD surface [85]. In special systems where the long polymer chain creates a segmentation of small clusters as in the case of hemi-micelles of surfactant molecules supported in a long chain polyelectrolyte, energy transfer or migration between chromophores sharing neighboring compartments may occur as long as the coupling distance is of the order of the average distance between compartments. This effect is also present in micellar solution at high concentration where inter-micellar energy migration or long-range energy transfer becomes an operative process. Note that in such cases the species may be considered practically immobile with respect to diffusion or exchange to neighboring compartments or micelles. This kinetics may be analyzed in the scope of the model of Tachiya and Barzykin of electronic energy transfer in

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concentrated micellar solution [89]. In the case where Förster critical radius R0 of the donoracceptor pair (or probe-quencher pair) is larger than the diameter of the micro-domains, the relative fluorescence intensity may follow a simple expression [90] 𝐼0 = 𝑒 〈𝑞〉 (1 + 𝛽〈𝑞〉) 𝐼

(35)

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 is a function of micelle number density m and of the donor lifetime 0 ∞

𝜌𝑚 𝛽= ∫ ∅(𝑡)𝑒 −𝑡⁄𝜏0 𝑑𝑡 𝜏0 0

(36)

(t) depends on the average survival probability of the excited donor in a given micelle interacting with a single acceptor located in a neighboring micelle (via long range dipole-dipole coupling).

(t) is a function of the micelle pair radial distribution function [89]. Eq. 35 was applied in the

analysis of FRET among dyes with large R0 dispersed in micelles as illustrated in the plot of relative intensity divided by the factor exp[q] given in figure 4. The parameter  appeared as a

non-linear function of micelle density as one can see from its plot against micelle concentration

given in figure 5.

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Figure 4. Relative fluorescence intensity from the quenching of (a) acridine by Nile Blue, (b) 9aminoacridine by Nile Blue, in SDS aqueous micelles as a function of the average number of acceptors dyes per micelle. SDS surfactant concentration: 20 mM (■), 30 mM (●), 40 mM (▲), 50 mM (▼), 60 mM (♦) (reproduced from ref. 90 with permission of Elsevier Science B.V.).

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Figure 5. Plot of  as a function of micellar concentration for acridine/Nile blue (■) and 9aminoacridine/Nile blue (●) donor-acceptor dye pair. Förster critical radius of the donoracceptor dye pairs are 68 ± 6 Å and 36 ± 4 Å, respectively. (reproduced from ref. 90 with permission of Elsevier Science B.V.).

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7. Negative deviation of the SV equation, aggregation induced emission, and new analytical tools based on SV formalism.

The presence of a downward curvature of the SV plot may occur due to different factors such as the presence of inaccessible fluorophores, the formation of excited-state conformers or

tautomers, the effects of metal-enhanced fluorescence and fluorophore undergoing aggregationinduced emission. The effect of inaccessible population of fluorophore can be rationalized by rescaling the relative intensity plot in a modified SV equation [91 - 93],

𝐼0 1 1 = + 𝐼0 − 𝐼 𝑓 𝑓𝐾𝑆𝑉 [𝑄]

(37)

where f is the fraction of accessible fluorophore by the quencher species at concentration [Q]. This has been a classical model used in the interpretation of some results of fluorescence quenching in protein solution [9]. One should note that fluorescence decay in the presence of

added quencher is bi-exponential with two components 0 and 0(1−kq0[Q])−1 with amplitudes proportionally to 1−f and f, respectively. Although the fluorophore may stay in two different molecular environments, it is assumed that its lifetime is roughly constant keeping close to the value of 0. If the fluorophore has a distribution in n of different environments, the SV relation including the sphere of effective quenching model should be rewritten as [8] 𝑛

𝐼 𝑓𝑖 = ∑ 𝐼0 (1 + 𝐾𝑆𝑉,𝑖 [𝑄])𝑒𝑥𝑝[𝑉𝑞,𝑖 𝑁𝐴 [𝑄]] 𝑖=1

(38)

where fi stands for the fractional contribution of the ith species to the total fluorescence intensity. On the other hand, ‘extended’ SV equations have been derived and applied to study the fluorescence quenching of one or more fluorophores by a series of different quenchers [94, 95]. In such applications, the SV formalism is the theoretical basis of the very interesting analytical tools for macro and microanalysis of different chemical samples [95]. Recently, the SV formalism has been applied in a continuous-flow platform for fluorescence quenching studies [96] as well as in microfluidic devices owing to mapping the gradient of quencher species by fluorescence quenching imaging [97]. The effect of metal NP in fluorescence is dual because it can improve the emission quantum yield

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of the chromophore due to plasmon-coupled emission effect or may quench its excited state depending of the degree of coupling dictated by the relative distance and orientation between the species involved [98]. This important topic in fluorescence has been named as radiative decay engineering and it has been explored by Lakowicz, Geddes and co-workers in biophysical and

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biomedical applications [99, 100].

Usually normal fluorophores or dyes may form dimeric species causing auto-quenching if its

concentration is increased or solubility of the chromophore is someway reduced in the solvent medium. However, when a weak fluorophore undergoes self-aggregation that precludes an intrinsic intramolecular rotation or charge transfer to a non-fluorescent or dark state, its

fluorescence quantum yield may increase substantially. In this particular case, the addition of any compound or changing the experimental condition in order to cause self-aggregation of the

chromophore will act as an anti-quenching species or process and therefore, it will give a fluorescence intensity higher than the initial one causing a strong negative deviation of SV equation. This molecular behavior has been called aggregation induced emission (AIE) and it has

been explored in many fields including chemical sensing [101, 102]. Unfortunately, there is not

simple or general equation rationalizing the AIE effect.

8. Microscopic analysis of the bimolecular fluorescence quenching with FLIM methods In the previous section of bimolecular fluorescence quenching we considered that the

sample is irradiated in a large volume thus exciting randomly several molecules which always provides an ensemble average measurement over fluorophore populations. When time and space resolution is achieved as in the case of fluorescence microscopy of a system having low concentration of fluorophore, local fluctuations of the emission signal play an important role. This is an essential feature of fluorescence microscopy with time and space resolution allowing 21

determination of molecular properties that may be hidden in ensemble average measurements. In the last two decades, advanced fluorescence microscopy techniques have provided new and relevant tools to study chemical and biological systems at molecular level. Fluorescence Lifetime Imaging (FLIM) and Single Molecule Fluorescence Spectroscopy (SMFS) became powerful strategies to investigate the structure, mobility and reactivity with space and time resolution [15, 16, 103, 104]. Quantification of the fluorescence quenching at microscopic or nanoscopic level with the Stern-Volmer analysis is a complex task because in general the fluorescence relaxation at a given position r of the sample space (it defines a small volume or spot due to finite optical resolution) may not be exponential in absence as well as in the presence of added or an intrinsic

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quencher. Also, if the number of fluorophores is too low, decay transients may not be easily recorded to a desired amplitude due to low signal, blinking and bleaching effects of the fluorophore. In the most favorable conditions, however, the decays are roughly exponentials and are measured by FLIM so that the SV analysis at a given region r of the sampled space may read, (39)

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𝜏0 ( ) = 1 + 〈𝑘𝑞 𝜏0 〉𝑟 [𝑄]𝑟 = 1 + 〈𝐾𝑆𝑉 〉𝑟 [𝑄]𝑟 𝜏 𝑟

where [𝑄]𝑟 is the local concentration or density of the quencher species at equilibrium, 〈𝐾𝑆𝑉 〉𝑟 is

the SV constant and τ0 and τ stand for the decay times in absence and presence of quencher in r, respectively. Using the equation above we are neglecting diffusion transients or any other non-

linear effect such as those discussed previously. These decay time values may be recovered from the FLIM analysis in two separated experiments being the first one in the absence of added quencher and the second one in the presence of the added quencher. This simplified treatment

will generate a Stern-Volmer map (SVmap) represented by eq. 39. The relative quencher density or concentration at different microscopic parts of the sample may be estimated only in the case

where KSV is considered barely independent of position in the sample. Such assumption has been used to evaluate oxygen and other quenchers concentrations (or its relative concentration) such as halides (I and Cl) by fluorescence quenching using FLIM analysis [105 - 108]. In most of

the cases of FLIM analysis, however, the goal is to estimate from the change in fluorescence lifetime the relative concentration of an intrinsic quencher or the local condition such as pH because these parameters modulate the range of fluorescence lifetimes observed at a given position of the sample. Thus, FLIM measurements of pH and quencher local density are relatively easy as long as only relative concentration changes are concerned but absolute measurements are far more difficult requiring calibration protocols [104]. When the observed decay is multiexponential, FLIM data is related to the average decay time and the image analysis is basically qualitative although it can provide significant information. On the other hand, 22

fluorescence intensity measurements usually generate smooth images with different pattern when compared with FLIM because concentration of the fluorophore may change with position in heterogeneous samples. Nevertheless, the average number of fluorophores in a small irradiated volume can be estimated from photon-counting histogram (PCH) or Fluorescence intensity distribution analysis (FIDA) and, therefore, information about the fluorophore concentration may be extracted from the results [108, 109]. An interesting alternative to FLIM methods to evaluate the quencher concentration is the use of ratiometric methods based on a combination of fluorophore and phosphor compounds bound to the same molecular framework or nanoparticle. This particular strategy provides an efficient method to evaluate the local concentration or partial

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pressure of oxygen using a previously calibrated SV type relationship [110]. When the size of the sampled region becomes very small (for instance when using stimulated emission depletion (STED) techniques) there may be a discrete number of quencher and fluorophore molecules inside the core of the high resolution optical fluorescent spot observed at

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a given time [111]. The study of bimolecular fluorescence quenching process in such a very small volume down to attoL should require a stochastic description of the fluorescence quenching in a similar way used in small domain quenching kinetics. When this very small sampled region has

no defined borderlines that critically confine the species, the rates of entrance and exit of species become fast and similar to the quenching rate inside because they are diffusion processes that

may be classified in reactive and non-reactive trajectories. Under this condition (exchange rates are comparable to quenching rate) and using the general theory of fluorescence quenching in small domains, the solution of the integral equation (eq. 23) converges to an exponential

relaxation at point r given by,

𝑓(𝑡)𝑟 = 𝑒𝑥𝑝 [−(𝑘0 + 〈𝑞〉𝑘𝑞 )𝑟 𝑡]

(40)

Thus, the average decay in -pulse excitation or the relaxation function in the analysis of the fluctuations in CW irradiation is controlled by the average number of quenchers molecules q =

[Q] r / Vr around the excited state. The first-order quenching rate inside the small volume Vr is related with the second-order quenching rate constant of the classical SV equation by kq(2) = kq(1)/Vr. Thus, the ratio of lifetimes in a very small region again reduces to a SVmap represented by eq. 39 as long as diffusion transients are neglected and quencher concentration is substantially low. Moreover, excitation light power should be moderate so that fluorophore population is not driven to saturation.

9. Fluorescence quenching analysis in small domains with the phasor method The question whether the decay in the absence and in the presence of added quencher observed at position r is roughly exponential may be investigated with the Phasor method [112 – 117]. The Fourier transform of the fluorescence decay signal (with a modulation light source or short-pulse excitation at an optimal frequency w) collected at position r originates a Phasor or polar plot in the complex plane with real G(w) and imaginary S(w) Fourier components at a given position r given by

𝑖

𝑆𝑟 (𝑤) = ∑ 𝑖

𝑓𝑖 (1 + 𝑤 2 𝜏𝑖2 )

(41)

𝑓𝑖 𝑤𝜏𝑖 (1 + 𝑤 2 𝜏𝑖2 )

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𝐺𝑟 (𝑤) = ∑

(42)

fi stands for the fractional contribution of the i-component expressed by 𝛼 𝑖 𝜏𝑖 ∑𝑖 𝛼𝑖 𝜏𝑖

-p

𝑓𝑖 =

(43)

where αi and τi are the pre-exponential factor and corresponding decay time of the fluorescence

decay f(t) for -function excitation. In the case of single-exponential decay, such vector with components (G,S) belongs to semicircle of center at (½, 0) and radius ½. Short lifetime is then

close to the point (1,0) while the phasor corresponding to a long decay time approaches to the coordinate (0,0). Considering that the fluorescence quenching reduces the decay time according

to SV equation, the corresponding phasor will move in a clockwise direction along the semicircle upon addition of the quencher as long as the process remains roughly single exponential. This linear SV quenching effect in the phasor plot has been observed in some fluorescence microscopy

studies, and it has also been used as a calibration method in advanced wide-field FLIM in the frequency domain measurements [117]. In the general case of multi-exponential fluorescence

decay with irreversible quenching (no other excited state is formed from the prompt excited state), the phasor points will fall below the semicircle and each one will be a linear combination of the components with distinct decay time. In principle we can apply the phasor analysis in fluorescence quenching in micro-domains using the decay function given by eq. 15 but representing it in a multi-exponential form, ∞

𝑓(𝑡) = ∑ 𝛼𝑖 𝑒 −𝑡⁄𝜏𝑖

(44)

𝑖=0

where 𝛼𝑖 =

〈𝑞〉𝑖 −〈𝑞〉 𝑒 𝑖!

;

𝜏𝑖 = (𝑘0 + 𝑖𝑘𝑞 )

−1

(45)

In figure 6 we have plotted the simulated phasor diagram of fluorescence quenching as a function of q in these two extreme situations of immobile species (multiexponential decay given by eq. 45) and highly mobile species when the decay converges to a single exponential (eq. 40).

55 ns

45 ns

38 ns 33 ns 29 ns 26 ns

71 ns

0.4

100 ns

S 0.3

0.2

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11 ns

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0.5

0.0 0.2

0.4

0.6

0.8

1.0

0.0

0.1

Figure 6. Phasor plot of the quenching kinetics in confined space in two limiting conditions under numerical simulation. ■ fast probe and quencher migration given exponential decay (eq. 40), ▲ immobile species with multiexponential decay (eq. 44). Parameters used in the simulation: fluorescence lifetime 0 = 100 ns, first-order quenching rate kq = 0.02 ns-1, frequency w = 0.02 ns-1, quencher average occupancy q from 0 – 4 molecules per confinement.

10. Fluorescence correlation spectroscopy, photo-antibunching, and other single molecule approaches in bimolecular quenching dynamics

FLIM by laser pulse excitation combined with time-correlated single-photon counting (TCSPC) is a suitable method to investigate the fluorescence quenching process with good time and space resolution. On the other hand, analysis of single-molecule (SM) fluorescence photon counting time-series is an ultrasensitive method that provides very unique and complementary information of molecular processes involved in the fluorescence quenching in a given position of the sample. SM fluorescence time-series can be obtained with constant light irradiation of a very small confocal region aligned to a point detector or by photon counting over pixels of an EMCCD or CMOS camera in wide-field high resolution usually under TIRF microscopy. This advanced 25

fluorescence research area is nowadays broad and embraces several different topics going from SM FRET and SM PET dynamics in proteins and macromolecules to intermittency of luminescence of single quantum dots [15, 16]. Here we keep attention to the quenching of fluorescence by molecular association investigated by fluorescence correlation spectroscopy (FCS). The autocorrelation function of the fluorescence signal of a sample of low concentration of fluorophore (typically less than 10−9 mol/L) observed at a small volume defined by the laser focus in a confocal microscope is affected by several factors including the diffusion of the fluorophore in and out of the observed confocal region. The slow part that is ascribed to fluctuations due to diffusion of the fluorophore has an autocorrelation function FD(τ) for one-

𝐹𝐷 (𝜏) =

1 (1 + 𝜏⁄𝜏𝐷 )−1 (1 + 𝜏⁄𝜎𝜏𝐷 )−1⁄2 𝑁

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photon excitation single-focus FCS given by [16] (46)

where τD is molecular diffusion time related with the translational diffusion coefficient of the fluorophore, and N is the average number of fluorophore molecules in the effective volume

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observed by the laser confocal microscope configuration, and σ = (z0 / w0)2 is the square ratio between axial and radial coordinates of the sample volume at which the intensity profile decreases

to 1/e2. The translational diffusion coefficient D of the fluorophore is related by τD = w02 / 4D, and using a standard fluorophore with a well know D, the spatial coordinates of the FCS

instrument setup are then calibrated [16].

FCS measurements and its corresponding log plot of the lag time τ allows the separation of the

fast and slow processes. Let’s now to suppose that the fluorophore may form a complex with a quencher in ground state similar as that represented by bimolecular association reaction given in eq. 31. Keeping the quencher concentration low, the dynamic fluorescence quenching will have

a minor effect but some small fraction of complex FQ may still be formed. Its formation and dissociation dynamics during residence time of the species inside the confocal volume leads to

fluctuations in the fluorescence signal that will generates a multiplicative term in the autocorrelation function with an extra exponential contribution so that [16], 𝐹(𝜏) = 𝐹𝐷 (𝜏) [1 +

1−𝑝 𝑒𝑥𝑝(− 𝜏⁄𝜏𝑐 )] 𝑝

(47)

where p is the fraction of free fluorophore. The relaxation time of the association process τc = (k− + k+q)−1 is a function of k+ and k−, the bimolecular association rate constant forming the FQ species and its first-order dissociation rate constant, respectively. Thus, a plot of the inverse of relaxation time τc against quencher concentration q resembles the SV method. It should be noted 26

that from macroscopic fluorescence quenching using eq. 32 one recovers only the value of equilibrium Ka = k+/ k− but FCS as a microscopic SM technique based on fluctuations can provide the rate constants of association and dissociation separately. Interestingly, analysis of singlemolecule fluorescence time-series in terms of the on/off states will also provide the rate constants of formation and dissociation processes at a molecular level as demonstrated by Kiel and collaborators in the study of metal-binding ligand kinetics [118, 119]. The ACF is also modulated by the photophysics of the fluorophore forming a dark or triplet electronic state producing a similar exponential relaxation as that ascribed to probe and quencher association. The effect of triplet state kinetics in the ACF may be in principle reduced when working at low laser irradiance

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and having an excited state with low yield of intersystem crossing. To overcome the size limitation of confocal FCS, STED FCS has been addressed as an advanced nanoscopic approach in 2D and 3D fluorescence microscopy with length-scale of tens of nanometers or attoliters of sample observation [111]. This high spatial resolution of STED – FCS opens new doors for studying molecular quenching interaction at SM level. On the other hand, situations where the

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change in brightness of the fluorophore occurs as a result of its association or binding to a molecular site close to or bound to an optical glass surface, the use of excitation by evanescent

light field provides an increase in z resolution. This approach has been called total internal reflection fluorescence correlation spectroscopy (TIR-FCS) [120]. The ACF expression with TIR

excitation is more sophisticated than that in 3D space but the FQ association dynamics will appear in a similar exponential form as discussed above.

Conventional FCS measurements, where the lag time scans from sub-microseconds to

milliseconds, are not critically affected by the dynamic quenching specially at the very dilute regime of quencher concentration. However, increasing the quencher up to mM concentration

will display FCS correlations at the nanosecond time regime and will modulated the so-called photon antibunching effect. Photon antibunching reflects the fact that at SM level, re-excitation of the fluorophore should be preceded by its relaxation to electronic ground-state (the re-

excitation cycle is controlled by the Rabi frequency) [121]. As a single molecule cannot emit more than a single photon per excitation cycle, the ACF will have a steep decrease towards times shorter than the inverse of the Rabi frequency. Thus, the antibunching curves becomes a function of the added quencher concentration. This new strategy has been developed by Sharma, Enderlein and Kumbhakar to investigate dynamic quenching and interaction of species in solution [122, 123]. Combining nanosecond FCS with traditional time-resolved and stationary quenching measurements, they have been able to show that such unified analysis provides rate constants as well as equilibrium constants of association or binding of species. The interaction of tryptophan 27

with the fluorescent dye Atto-655 was analyzed with nanosecond FCS [123]. Photon antibunching revealed static and dynamic quenching contributions. A typical result is illustrated

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in figure 7.

Figure 7. FCS data with photon antibunching effect of the dye Atto-655 in the absence and presence of added tryptophan involving static and dynamic fluorescence quenching monitored at the single-molecule level. (Reprinted with permission from A. Sharma, J. Enderlein, M. Kumbhakar, J. Phys. Chem. Lett. 8 (2017) 5821 – 5826, Copyright  2017, American Chemical Society). It is clear that SM fluorescence correlation spectroscopy (FCS) at nanosecond time range is modulated by the fluorescence quenching kinetics. The quenching rate may be described properly

in terms of the average number of q quencher in the observed small volume as previously discussed, since that local viscosity is not large enough to introduce persistent diffusional

transient in the nanosecond time domain. But here some complications may arise due to the fact that re-excitation of recently quenched fluorophore-quencher pair could be significant if the

excitation photon flux in the small volume is not controlled to a moderate level. More sophisticate extensions of standard FCS technique have been worked out. They have included multi-color excitation and detection, two-photon excitation and fluorescence lifetime correlation spectroscopy [16]. If the goal is to analyze an extended region of the sample by fast scanning or using EMCCD or CMOS camera with the cost of less time resolution, fluorescence fluctuation image (FFI) may be the choice [124]. Such methods are today very important in the study of cellular processes at molecular level. The possibility of using such advanced method in microscopic analysis of fluorescence quenching process by added species is an open field. 28

11. Topographic quenching methods and applications in nanomaterial research As a final topic of fluorescence quenching process in imaging we would like to comment its use in what may be called as topographic quenching methods. Different strategies may be explored in material science and we discuss briefly some of them. Suppose that one has a very thin layer containing a fluorophore highly dispersed on it so that its fluorescence map or SM fluorescence signals may be mapped with good precision. Thus, a nanoscopic quencher such as the graphene oxide 2D nano-sheet deposited over the surface will quench by energy transfer the fluorophores under it and will provide a high-resolution contour map of the GO particle that may

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appear as a shadow or dark area. This interesting approach was called fluorescence quenching microscopy (FQM) by Huang and collaborators [125, 126]. More recently, such method has been upgraded with high space resolution and it has been called as quenched stochastic optical reconstruction microscopy (qSTORM) by Waigh and Lu [127]. Figure 8 illustrates such

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interesting approach of topographic quenching microscopy using FQM method.

Figure 8. FQM image of GO sheets on a glass substrate with a 30 nm thick fluorescein/PVP coating (scale bar = 50 m). Reprinted with permission from J. Kim, L. J. Cote, F. Kim, J. Huang, J. Am. Chem. Soc. 132 (2010) 260 – 267, Copyright  2010, American Chemical Society. 12. Concluding remarks In this short review of the historical development and applications of the bimolecular SV equation, we described the evolution of the fluorescence quenching studies in solution. We escaped from giving extensive number of practical examples or long mathematical deductions of 29

the underlying theoretical models of quenching kinetics. These points may be fulfilled from the indicated references and their cross referencing inside. Finally, in this review we have focused on the bimolecular quenching in a phenomenological description without discussion in great details the quenching mechanism behind it. Thus, we did not include a comprehensive discussion on fluorescence quenching by long-range coupling mechanism such as Förster resonance energy transfer (FRET) or short-range by photo-induced electron transfer (PET). FRET and PET are nowadays some of the most explored quenching mechanisms in SM fluorescence microscopy because they provide a sensitive tool for studying distance dependent process in the nanometer and Å range specially when the species are chemically bound to the same molecular framework

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or nano-structure. However, we have included discussions about the use of ns autocorrelation function and SM time-series analysis as advanced methods to recovery bimolecular quenching rate constants and association at the single molecule level in a small volume. We have also addressed the new topic here called high-resolution topographic fluorescence quenching as a new tool for material science investigations. Much of the understanding of such advanced fields could

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not be achieved without knowing the SV kinetics in its simple as well as in more elaborated

situations as discussed in this short review.

Acknowledgements

The author thanks Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP 2018/22159-5) and Brazilian Research Council (CNPq 303997/2017-6) for financial support.

Part of this review was elaborated during my sabbatical period at University of Colorado – Boulder and the assistance received is gratefully acknowledged. We are indebted with numerous collaborators who over the years have inspired and contributed to our research in molecular

fluorescence.

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Biography: Marcelo Henrique Gehlen received his Doctoral degree in physical chemistry from University of São Paulo in 1993. In 1990 – 1992 he was an International Research Fellow at K. U. Leuven working with Professor Frans C. De Schryver in the Chemistry Department. He became full Professor at University of São Paulo in 2009 and was appointed twice as Head of Physical Chemistry Department – IQSC – USP. In 2019 he stayed as visiting Professor at University of Colorado - Boulder. His main research interest is focus on reaction kinetics in small domains

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with time and space resolution.

The centenary of the Stern-Volmer equation of fluorescence quenching: From the single line plot to the SV quenching map - PDF Free Download (2024)

FAQs

What is the equation for fluorescence quenching Stern-Volmer? ›

1 is usually replaced by the corresponding ratio of fluorescence intensities,(2) I 0 I = 1 + K S V Q where K_sv = k_qτ₀ is the Stern-Volmer constant that in a purely dynamic fluorescence quenching process is the product of the bimolecular quenching rate constant and the fluorescence lifetime in absence of added quencher.

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How do you calculate KSV from Stern Volmer equation? ›

The slope of the Stern-Volmer plot is the Stern-Volmer constant Ksv, which is product of the quenching rate constant and the radiative life-time, i.e., Ksv = Kq . t0 where, Ksv = Stern Volmer constant, Kq = quenching rate constant, t0 = radiative life-time.

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How to do Stern-Volmer plot? ›

A plot of F₀/F versus the quencher concentration, [Q], is linear (Stern-Volmer plot) with an intercept of 1 and a slope equal to the Stern-Volmer quenching constant, K_SV, if only dynamic quenching occurs. When the plot is found to be linear, the Stern-Volmer constant is calculated from the slope of the plot.

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What is the Stern-Volmer plot for dynamic quenching? ›

The Stern-Volmer plot is used to analyse how the fluorescence intensity or the fluorescence lifetime of an emitter is affected by the quencher's concentration. The plot is an important tool to characterise the different types of luminescence quenching (dynamic or static) in a bimolecular system.

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What is the history of the Stern Volmer equation? ›

Proposed in 1919 by Otto Stern and Max Volmer, the Stern–Volmer model quantitatively described the decrease in the fluorescence intensity of emitters in the presence of quenchers, molecules that are capable of bringing the excited emitters back to ground states.

How do you calculate fluorescence quenching efficiency? ›

Quenching efficiency was determined by dividing the fluorescence intensity of the hybrid by the fluorescence intensity of the fluorophore-labeled oligodeoxyribonucleotide, multiplying the result by 100 and then subtracting the result from 100.

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What is Stern-Volmer luminescence quenching analysis? ›

Emission quenching (also called Stern–Volmer) studies consist of measuring emission intensity fluctuations of the photocatalyst excited state in the presence of a quencher.

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What is the Y intercept of the Stern-Volmer plot? ›

The y-axis is the ratio of the unquenched fluorescence intensity divided by the quenched fluorescence intensity. The x-axis is the quencher concentration. The y-intercept is 1. The slope is the Stern-Volmer constant.

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What does a linear Stern-Volmer plot mean? ›

Stern-Volmer plot for quenching systems showing linear relationship (red curve); upward deviation relationship (blue curve); and downward deviation (green curve). A linear relationship is most associated with dynamic quenching, where the quenching is mainly due to collisions between the emitter and quencher molecules.

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What is the importance of Stern-Volmer constant? ›

The Stern-Volmer constant K SV informs us about the availability of the quencher to the excited fluorophore and its increase points to the reduction of the distance between the ligand and macromolecule [51] .

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Why is fluorescence quenching important? ›

This quenching results in the non-radiative transformation in the ground state such as charge or energy transfer. This method is the strongest signal transduction process that has been used significantly in different areas due to their high sensitivity, selectivity and easy working.

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What is the equation for dynamic quenching? ›

F0 F =1+ kqτ0[Q] =1+ KD[Q] Page 2 Copyright © 1999 – 2010 by Mark Brandt, Ph.D. 32 where τ0 is the lifetime of the fluorescent state in the absence of the quenching agent. If the quenching is not known to be due to dynamic quenching, KD is replaced by KSV.

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What is the equation for fluorescence? ›

The fluorescence intensity is proportional to the excited state population, and will decay exponentially following the formula I(t) = I0 exp(-t/τ), where I(t) is the intensity at time t, I0 is the initial intensity and τ is the lifetime that is the inverse of the total decay rate (τ = 1/ktot).

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What is the equation for fluorescence correlation spectroscopy? ›

For classic FCS, W(r) is approximated by a Gaussian, W ( r ) = exp [ − ( 2 ( x 2 + y 2 + ( z a ) 2 ) / s 2 ) ] , where s is the laser waist and r₀ is the position of the center of the laser beam and the autocorrelation function becomes G ( τ ) = G ( 0 ) [ ( 1 + τ τ d ) ( 1 + a − 2 ( τ τ d ) ) 1 2 ] – 1 , in which a is ...