Photonic mode density effects on single-molecule fluorescence blinking

We investigated the influence of the photonic mode density (PMD) on the triplet dynamics of individual chromophores on a dielectric interface by comparing their response in the presence and absence of a nearby gold film. Lifetimes of the excited singlet state were evaluated in order to measure directly the PMD at the molecule's position. Triplet state lifetimes were simultaneously determined by statistical analysis of the detection time of the fluorescence photons. The observed singlet decay rates are in agreement with the predicted PMD for molecules with different orientations. The triplet decay rate varies in a fashion correlated to the singlet decay rate. These results show that PMD engineering can lead to an important suppression of the fluorescence blinking, introducing a novel physical mechanism to enhance fluorescence intensity in PMD-enhancing systems such as plasmonic devices.


Introduction
The rate of spontaneous photon emission by an excited molecule can be modified by changing the density of possible electromagnetic decay channels, i.e., the photonic mode density (PMD) [1]- [3] at the emitter position. In particular, a nearby metallic object supporting plasmonic excitations can produce noticeable changes in the PMD. Together with the increased optical excitation in a locally enhanced electric field, modifications of the PMD leading to a faster de-excitation have been identified as responsible for the enhanced fluorescence signal close to metal structures. This approach to obtain stronger fluorescence signals promises significant progress for experimental schemes where weak fluorescence signals need to be retrieved with high signal-to-noise ratios such as single molecule methods [4,5], fluorescence correlation spectroscopy [5,6] and biosensors [7,8]. Following first experiments in front of a metallic mirror [9]- [11], recent progress in nanofabrication technologies envisaged the investigation of more sophisticated geometries showing drastic modifications of the PMD [6,12,13]. Recently, a number of investigations addressed the quantitative analysis of fluorescence in PMD modifying environments [14]- [16]. So far, the PMD effects on the fluorescence have been analysed in the framework of a modified singlet decay. Enhancements of phosphorescence signals from emitters in the vicinity of metals were recently reported too [17,18], showing that the PMD can also modify the dynamics of the triplet state. In the present paper, these two concepts are brought together. We show that the dynamics of the singlet and the triplet states can be modified simultaneously by the PMD and that a faster triplet decay contributes noticeably to an enhanced fluorescence signal.
Fluorescence emission of single emitters is typically intermittent (blinking). Excursions to the long-lived triplet state leads to fluorescence blinking for all organic chromophores [19,20]. Other blinking mechanisms such as conformational changes [21,22] and radical formation [23] are known as well for particular molecules. Triplet blinking can be understood with the help of figure 1(a) which depicts a simplified picture of the molecular fluorescence process in terms of a three-state model [4]. A molecule initially in the ground singlet state S0 is excited upon photon absorption to the singlet excited state S1 with a rate k 12 . From S1, the molecule returns to S0 with a total rate k 21 composed of a radiative decay k 21,r and an intramolecular non-radiative relaxation k i 21,nr ; based on previous studies [24,25], we will consider k i 21,nr as negligible. Efficient fluorophores perform many cycles like this in the singlet subspace while fluorescence photons are emitted. Although suppressed by spin selection rules, singlet ↔ triplet transitions (inter-system crossing, ISC) still occur and interrupt the fluorescence emission. An excited molecule has a finite probability (k 23 ) of undergoing ISC to a lower energy, long-lived triplet state (T1) from which the molecule decays back to S0 with a rate k 31 ; this latter step may involve photon emission (phosphorescence). If the triplet lifetime is long enough (small k 31 ) triplet blinking can be directly observed in the fluorescence emission of single molecules as a binary switch between successive bright (on) periods where fluorescence photons are detected and dark (off ) periods where only background photons are detected ( figure 1(b)). The fluorescence intensity of the on state as well as the mean duration of the on-and off-period length are readily derived from the transitions in the three-level system. The on-and off-periods are thus exponentially distributed [20,26] 2 and their average times τ on and τ off are given by τ on = (k 21 + k 23 )/(k 12 k 23 ) and τ off = 1/k 31 . Although ISC does not usually affect the overall fluorescence quantum yield due to the low absorption of T1 at the frequency of the S0 → S1 excitation, it limits the maximum achievable fluorescence intensity [20]. A reduction of the triplet lifetime of organic fluorophores, with a corresponding increase in brightness, was demonstrated by the presence of molecular oxygen which quenches T1 and returns the molecules to S0 up to 100 times faster [26,27]. However, oxygen is undesired as it is also responsible for most photodegradation processes.
Although most pronounced PMD enhancements are observed on irregular metal structures such as silver island films [3] or sharp metallic tips or junctions [6,12,13], we used planar systems which are better suited for a quantitative study of the underlying physical effects because they can be prepared with high accuracy and can be fully modelled [2,9,10,25].

Experimental
Two sample architectures were employed. In samples I, chromophores were placed on top of a dielectric layer. In samples II, the same dielectric layer was used as a spacer to place the chromophores at a controlled distance from a thin gold film. Figure 2(a) shows a schematic of the two sample architectures and corresponding single molecule fluorescence confocal micrographs; the fluorescence blinking can be directly observed. The thicknesses of the gold film and the dielectric spacer layer were 44 and 30 nm, respectively in order to achieve optimum single molecule detection [24,25]. The dielectric spacer was composed of alternating layers of poly(allylamine) (PAH) and poly(styrenesulfonate) (PSS). On the samples with the gold film, the polyelectrolyte layers were prepared following a published method [25]. The samples without the gold film were prepared using the same procedure to deposit 2.5 PSS/PAH bilayers on optically transparent glass substrates, which were previously functionalized with 3-aminopropyltriethoxysilane (3-APTES) (See supporting information). On both types of samples, fluorescent 1, 1 , 3, 3, 3 , 3 -hexamethylindicarbocyanine iodide (DiIC1(5), molecular probes) molecules were deposited electrostatically on the negatively charged surface of the multilayer terminated with PSS by immersing the samples in a 10 −10 M, Milli-Q water solution. The immersion time (10-30 s) was adjusted to obtain well-separated chromophores. The polyelectrolytes were chosen as dielectric spacer because they can be prepared with controlled thickness and allow the chromophores at their interface to adopt all possible orientations [25]. DiI chromophores were chosen because they exhibit clear and well investigated triplet blinking [26,27]. They have a long triplet lifetime of 10-50 ms in the dry state and absence of oxygen. Both conditions were fulfilled in our experiment by attaching the dye to a solid matrix and performing the experiments under a continuous flow of dry nitrogen.
On a home-built confocal microscope, a region of the samples was imaged in epi-illumination through the glass slide, a single molecule was moved into the focus and its fluorescence emission was recorded as a function of time. A laser-diode (Hamamatsu PLP10-063/C) was used for pulsed excitation (100 ps FWHM, 100 MHz rep. rate) at 633 nm through a 1.4 NA oil-immersion objective. Annular illumination was used for samples II in order to optimize the signal to background ratio [25]. Fluorescence photons were collected by the same objective, separated from the excitation light by suitable dichroic and notch filters and their arrival times were recorded by means of an avalanche photo-diode (Perkin-Elmer SPCM-AQR-13) and a time correlated single photon counting module (Becker&Hickl SPC-630). For each detected photon two times were recorded independently: the time elapsed since the last excitation pulse (micro-time) and the time elapsed since the beginning of the measurement (macro-time), with a resolution of 7 ps and 50 ns, respectively. The excited singlet state decay k 21 was obtained by a single-exponential fit to a histogram of the micro-times (see supporting information). The overall system response was limited to approximately 0.6 ns (see supporting information). The macro-times provide information about the intensity fluctuations and thus about the fluorescence blinking. The τ off can be obtained in two ways. Firstly, the off-periods can be directly measured by placing a suitable intensity threshold in an intensity histogram of the fluorescence emission ( figure 1(b)). Alternatively, τ off can be obtained from an exponential fit to the fluorescence intensity autocorrelation [19]. The latter method, although less intuitive, turns out to be more reliable, especially at low signal to background conditions (see supporting information) and was thus used in the further analysis.

PMD distribution in the samples
Changes in the PMD affect all transitions coupled to the electromagnetic field. A nearby metallic object can modify k 21,r and introduces additional electromagnetic non-radiative channels k em 21,nr . This effect is well understood and can be fully modelled by considering point oscillating electric dipoles interacting classically with the electromagnetic field [2,14,15]. In the following, an analysis of the variations of k 21 is presented which gives direct access to the PMD experienced by the individual molecules. This information is a prerequisite for the analysis of the PMDinduced variations of the triplet dynamics that is shown later.
For chromophores near a plane interface, k 21 depends on the polar angle φ between the dipole moment of the molecule and the surface normal and can be calculated from the limiting cases of molecules parallel (φ = π/2) and perpendicular (φ = 0) to the interfaces k 21 and k ⊥ 21 are determined by the dielectric properties of the layered system [24]. Due to the very short immersion times used in the sample preparation, the chromophores cannot diffuse inside the polymer [28] and are placed at the interface. In point-dipole theory, k 21 varies continuously across the interface whereas k ⊥ 21 takes two different values at each side of the interface according to the dielectric contrast with the subscripts N 2 and pol referring to an infinitely small displacement to the nitrogen and polymer side, respectively. On a molecular level, the chromophores have a finite size and the polymer surface has a certain structure leading to different radiative decay rates for molecules that probe more one or the other side of the interface. Thus a distribution of k 21 due to molecular orientation and local environment may be anticipated. The experimental distributions of k 21 obtained from approximately 100 molecules in each type of samples are displayed in figure 2(b) together with calculated distributions.Arrows indicate the theoretical decay rates for parallel and perpendicular dipoles at each side of the interface [24]. These calculated rates need to be adjusted to the experimental ones by one common scaling factor for all calculated rates [25]; i.e., a reference is needed. We assign the most frequent value of k 21 in samples I to parallel molecules because those are the statistically most probable and the most effectively detected molecules. The adequacy of this choice is supported by the very good agreement between the calculated and experimentally detected extreme values of k 21 for molecules in samples I and the maximum detected k 21 for molecules in samples II. We know from previous studies that in samples II, parallel molecules and molecules probing more 6 Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT the polymer side of the interface are not detectable in this scheme [25]; i.e., for samples II, the minimum observed k 21 is expected to be larger than the minimum calculated k 21 (k 21 ). An accurate calculation of the distributions of k 21 is not possible since that would imply knowing the polymer/N 2 composition of the local environment of each molecule. Only as a reference, calculated distributions corresponding to randomly oriented molecules, half of them placed in N 2 and half in the polymer are shown in figure 2(b). In comparison, the experimental distributions of k 21 are poorer in molecules with extreme lifetimes, an effect that is expected if the environment of the molecules is neither purely polymer nor N 2 but some average. In summary, the variation of the PMD has been quantified by means of k 21 for both samples and its distribution can be fully explained by the different location and orientation of the molecules with respect to the interface and, in samples II, to the nearby gold film.

PMD influence on the triplet decay
With this information in hand, we proceed to investigate the effect of the PMD on k 31 . In figure 3, the distributions of k 21 and k 31 obtained from molecules in samples I and II are shown together with a scatter plot of k 31 versus k 21 . The distributions of k 31 in samples I and II differ significantly. Molecules in samples II have both an increased average k 31 and large k 31 values exceeding 200 s −1 that are not observed in the absence of the gold film. The student's t-test [29] was employed to quantify the statistical relevance of this difference. The obtained t value (t = 3.25) indicates that the probability to obtain the difference in experimental distributions by chance without a true difference between the two configurations amounts to 0.14%.
In spite of some statistical scatter, a positive correlation between k 31 and k 21 can be observed in both data sets. The Pearson's linear correlation coefficient [29] R is used to quantify this observation. Correlation coefficients of R = 0.46 and 0.35 are obtained for the molecules in samples I and II, respectively. In order to test the significance of these correlations, the k 31 and k 21 data sets were randomly re-ordered and the R coefficients were calculated. The distribution of R values obtained from 10 5 random combinations of k 31 and k 21 is shown in the inset of figure 3. Probabilities of obtaining by chance R values equal or higher than the experimental ones are 0.006% and 0.035% for samples I and II (see supporting information), respectively, thus confirming the significance of the observed correlations.
The correlation between k 21 and k 31 can be explained by PMD variations for the individual molecules due to their local environment and orientation if k 31 depends in a similar fashion on the PMD as does k 21 . While some interaction with the surroundings on a molecular scale affecting both transitions could also produce such a positive correlation, this can be excluded as the reason for any difference between the molecules in samples I and II because they experience an identical chemical environment. Therefore, the significant difference between the distributions of k 31 in samples I and II must be assigned to a PMD-mediated enhancement due to the nearby gold film. This in turn supports the interpretation of the positive correlation between k 21 and k 31 in terms of similar PMD effects on the singlet and triplet de-excitations.
The noticeable effect of the PMD on k 31 is a sign of a T1 → S0 transition that occurs mainly radiatively and the positive correlation between k 21 and k 31 indicates that the transition dipoles associated with the T1 → S0 and S1 → S0 transitions have similar orientations. It is important to note that the PMD enhancements achieved in this planar geometry are modest in comparison to what can be achieved in more complex structures. Still, the enhanced k 31 is accompanied by a stronger fluorescence signal because it leads to a faster return to the singlet manifold, allowing the molecule to emit more fluorescence photons per time unit. As illustrative examples, a 1s trace and the photon-per-bin histogram of an average (A) and a strongly enhanced (B) molecule are shown also in figure 3 (an intermediate case is shown in figure 1(b)). Clearly, molecule B is a much brighter emitter than A because it spends much more time in the singlet subspace emitting fluorescence photons.

Conclusions
In conclusion, the influence of the PMD on the electronic transition rates involved in molecular fluorescence was investigated by studying simultaneously the emission blinking and excited state lifetime of individual molecules. The singlet de-excitation rate is affected in good agreement with theory. It was demonstrated that the triplet de-excitation is affected in a similar way by the PMD indicating that for the investigated system the T1 → S0 transition has a strong radiative component with a transition dipole moment of similar orientation to the S1 → S0. These findings complete the picture of the PMD-mediated fluorescence enhancement which has so far only been discussed for the singlet manifold. Firstly, an enhanced excitation (k 12 ) and singlet decay (k 21 ) at constant branching rate to the triplet (k 23 ) allows the dye to emit more photons before entering the triplet and secondly, the residence time in the triplet is reduced due to its enhanced decay (k 31 ). This new finding on the improvement of chromophore performance should encourage further the investigation of PMD enhancing structures such as plasmonic nano-objects to obtain single super-emitters.