Field-Controlled Charge Separation in a Conductive Matrix at the Single-Molecule Level: Toward Controlling Single-Molecule Fluorescence Intermittency.

The fluorescence intermittency or "blinking" of single molecules of ATTO647N (ATTO) in the conductive matrix polyvinylcarbazole (PVK) is described in the presence of an external applied electric field. It is shown that due to the energy distribution of the highest occupied molecular orbital (HOMO) level of PVK, which is energetically close to the HOMO of ATTO, sporadic electron transfer occurs. As a result, the on/off dynamics of blinking can be influenced by the electric field. This field will, depending on the respective position and orientation of the dye/polymer system with respect to those of the electrodes, either enhance or suppress electron transfer from PVK to ATTO as well as the back electron transfer from reduced ATTO to PVK. After the charge-transfer step, the applied field will pull the hole in PVK away from the dye, increasing the overall time the dye resides in a dark state.

Introduction

The fluorescence of a bulk sample containing many fluorophores shows, in the absence of bleaching, a constant fluorescence intensity upon continuous illumination. In contrast, the fluorescence intensity of individual molecules with time is nearly always fluctuating, a phenomenon called blinking or fluorescence intermittency.[1−6] Hence, the fluorescence intensity of an individual molecule measured as a function of time alternates between the so-called on and off states over a wide range of time scales (from microseconds to milliseconds and longer). This blinking can be attributed to diverse processes like intersystem crossing to a nonemissive triplet state,[3,7,8] spectral diffusion,[9,10] conformational changes,[11−13] molecular reorientation,[14,15] and inter- or intra-molecular charge transfer.[16−23] Blinking has been observed for virtually any emitting material, including quantum dots,[4,24,25] conjugated polymers,[26−28] organic dyes,[3,7,29,30] fluorescent proteins,[31−35] and recently also perovskite nanocrystals.[36−38] Whereas the shorter off times in the micro- and milli-second ranges are usually attributed to intersystem crossing to the triplet manifold, the longer off times are attributed to charge transfer (usually electrons, but eventually also proton transfer in the case of fluorescent proteins) from or to the surroundings.[1,5,21] It was noticed, first for quantum dots and later also for dyes, that the distribution of these on and off times for a single particle/molecule (or the average distributions of several single emitters) follows so-called inversed power laws, pτ ∼ τ–μ, that span time scales of several orders of magnitude.[3,4,39,40] For the exponents, μ values between 1.5 and 2.2 are generally found, although larger values have also been reported.[39] It was shown that the off exponents are highly dependent on the dielectric constant of the medium, in contrast to the on exponents, which show an exponential cutoff with increasing dielectric constant. These dependencies suggest that a photoejected charge is self-trapped in the surroundings. The current model to explain these power laws, presented by Orrit et al.,[5,39] proposes a four-level system, in which a charge transfer to the surroundings occurs with the formation of charge-separated radical ions. As long as no back charge transfer leading to recombination takes place, the molecule will remain in a dark state. For rhodamine 6G in poly(vinylalcohol), electron paramagnetic resonance experiments confirmed the existence of the radical anion of the dye in the dye/matrix system.[5] Summarizing, trapping and detrapping processes linked to charge transfer are at the core of blinking over long time scales. We postulate that when this model is valid the use of a conductive polymer matrix enables the fate of the photogenerated charges to be influenced by applying an external electric field.

Several studies on the blinking dynamics under the influence of an electric field have been performed. Most of these studies focused on single conjugated polymer chains embedded in an inert matrix. De Schryver reported fluorescence quenching in the presence of an electric field due to (photo)injected polarons.[27] Scheblykin reported on the fluorescence quenching of single polymer poly [2-methoxy, 5-(2′-ethyl-hexyloxy)-p-phenylene-vinylene] (MEH-PPV) molecules. This quenching in the presence of an electric field was attributed to the formation of long-living charge-separated species due to charge transfer either between different segments of the same polymer chain or with the involvement of impurities.[41] In a follow-up study, it was shown that the electric field influences not only the equilibrium between the neutral and charged chains but also the movement of the charge on the polymer chain with respect to the orientation of the field.[42] Barbara et al. revealed a great deal on the mechanism of polaron-induced quenching in device-like configurations of single polymer chains.[43,44] Chen et al. probed the electric-field induced polarization and relaxation dynamics of a PMMA matrix by monitoring the fluorescence intensity response of single squarine dyes embedded into the matrix in their study.[45]

These studies were performed with either isolated conductive polymer chains or single dye molecules embedded in a nonconductive matrix, leading to deep qualitative insight and understanding. However, for example, for dye molecules embedded in an inert matrix, the nature and hence energy levels of the electron donors and (more likely) acceptors that interact with the dye creating an “off” state are not known. This makes it very difficult to discuss the blinking phenomenon and its electric-field dependence in a more quantitative manner. Using an already extensively investigated conductive matrix will allow for a semiquantitative analysis in the framework of Marcus theory and take into account bulk observable parameters, such as disorder, and the energy levels (highest occupied molecular orbital/highest occupied molecular orbital (HOMO/LUMO)) of the used polymer.

To test the aforementioned hypothesis of long-time-scale blinking, we used here a combination of dye ATTO647N (ATTO) and conductive polymer polyvinylcarbazole (PVK). Taking into account the excitation energy of ATTO[1,29] and the oxidation and reduction potentials of PVK[46] and ATTO, it is expected that “reductive” electron transfer (or hole transfer) is energetically possible by a small margin. In such a reductive electron transfer process, an electron from the HOMO of PVK will be transferred to the HOMO of an excited ATTO molecule. Although ATTO is surrounded by several carbazole moieties, just one of these will be more favorable for electron transfer than the others, considering the energy level, distance, and orientation with respect to the dye. After the electron transfer, the hole on PVK can either recombine in a nanosecond-to-microsecond time scale with the electron on ATTO or execute a “random walk” in the PVK matrix,[47] during which it can be trapped. In the latter case, this will result in a dark state that persists until back electron transfer occurs. It is important to understand that although PVK is considered a hole-conducting material this mobility is still as low as ∼10–5 cm2/V s at reasonable applied fields (∼300 kV/cm), so the extent of this random walk will be limited.

A conductive polymer cannot be accurately characterized by a single value for its HOMO and LUMO. To account for the observable charge mobilities, the disordered nature of these materials needs to be taken into account. According to the disorder model,[48] the carrier mobility in a disordered amorphous material, including polymers, is governed by “diagonal” and “off-diagonal” disorders. Diagonal disorder is related to the distribution of the energy levels of the charge-carrier transport sites. This distribution can be described by the density of states (DOS) of the carrier transport sites in the polymer (DOS) and will, in most cases, lead to a Pool–Frenkel type behavior, that is, increased charge mobility with increasing electric field. Off-diagonal disorder can be related to the distribution of intermolecular distances and orientations. These will lead to a distribution of the orbital overlap between neighboring molecules and hence of the interaction energies between the HOMO’s and the LUMO’s of neighboring transport sites (off-diagonal elements of the matrix elements of the Hamiltonian).

Because of the DOS at the energy level of the HOMO of PVK (see Figure ), one can expect that for only a small fraction of the ATTO–carbazole pairs electron transfer is thermodynamically favorable. When applying an external electric field, several hypothetic scenarios can be expected: (1) an electric field pointing from ATTO to PVK will make the electron transfer on average less endergonic by making the energy difference between the center of the DOS of ATTO and that of PVK smaller. This will increase the rate constant and hence the probability of electron transfer from PVK to the excited ATTO and result in shorter on times. Considering that the electron transfer can also be followed by very fast recombination not leading to an observable off period, one can expect that for this particular situation that the electric field will reduce the average intensity during an “on” period. (2) An electric field pointing from PVK to ATTO will make the electron transfer on average more endergonic by making the energy difference between the center of the DOS of ATTO and that of PVK larger. The probability of electron transfer from PVK to ATTO decreases resulting in longer on times. Considering that the electron transfer can also be followed by very fast recombination not leading to an off period, one can expect that for these systems the electric field will enhance the average intensity during an on period. (3) The electric field pointing from ATTO to PVK will keep the separated charges apart longer and promote hole transport in PVK. This effect will result in longer off times, whereas the on times remain constant. Hence, the on times will be directly related to the DOS and thus diagonal disorder. The off times on the other hand will be related to the general transport properties of the polymer, both off-diagonal and diagonal disorder.

Figure 1

(A) Structures of PVK and ATTO and (B) schematic representation of the HOMO levels of ATTO (5.6 eV) and PVK (center at 5.5 eV) in an electric field. The blue arrow indicates the influence of the applied electric field on the HOMO levels.

Methods

Device

Cover slides with a 20 nm patterned layer of indium tin oxide (ITO) and a 150 nm insulating layer of SiO2 (ECI Evaporated Coatings Inc.) were ultrasonically cleaned. A solution of 20 mg/mL of PVK in chlorobenzene with 10–9 M ATTO was spin cast under an inert atmosphere at 1000 rpm for 60 s on top of this substrate, and an aluminum layer of 150 nm was evaporated on top of this film. The film thickness was determined via the capacitance and amounted to 150 nm.

Confocal Microscopy

The excitation source was the 632.8 nm line of a continuous wave HeNe laser (Thorlabs HNL150R/HRS015). The fluorescence above 640 nm was split via an 80:20 beam splitter and directed, respectively, to an avalanche photodiode to measure the intensity trajectories and to a nitrogen-cooled charge-coupled device (CCD) (Princeton Instruments SPEC-10:100B/LN eXcelon CCD camera, SP 2356 spectrometer with 1-030-500 grating 300 g/mm @ 500 nm) to subsequently measure single-molecule (SM) spectra, to discriminate between emission of ATTO and that of impurities in the PVK matrix. The fluorescence was passed through appropriate filters to suppress the excitation beam.[49,50] Both the binning and threshold method[51] and second-order autocorrelation method[10,52] were used to analyze the blinking behavior of the samples. For the first method, we used a binning time of 1 ms. The threshold was determined as the lowest possible value for which the background signal did not result in any off times. As a control, several SMs of ATTO (20) were measured in a polystyrene matrix using the same device configuration. No influence of the electric field on the fluorescence intensity was observed (Figure S1).

Results and Discussion

The devices were placed on a confocal microscope with SM detection sensitivity. The fluorescence intensity of single ATTO molecules was measured in the absence of an applied bias voltage and while applying a bias of 20 V (E = 667 kV cm–1) over the device every 10 s for 5 s. SM emission spectra were measured to make sure that the intensity changes observed upon applying an electric field were not due to a Stark shift or to a conformational reorganization of the dye molecules. Both processes would lead to changes in the emission spectrum: a change in the features or shift of the position, respectively. The obtained traces (126 molecules measured in total) can be divided into four populations depending on how the fluorescence of the SMs responded to the application of the electric field. An example of a representative molecule of each population is shown in Figure . Population A comprises SMs for which the fluorescence intensity does not show a clear dependence on the electric field (41% of the measured molecules) (Figure A). Population B comprises SMs that showed a reduced intensity when the electric field is on (47%) (Figure B). Population C consists of molecules that showed the exact opposite behavior, that is, their fluorescence intensity is enhanced by the electric field (9%) (Figure C). SMs of which the emission was almost completely suppressed upon applying an electric field make up the fourth type of field-dependent behavior (3%) (Figure D) in population D.

Figure 2

Representative examples of the four types of field-dependent SM fluorescence traces obtained during repeated application of a 20 V potential across the device. Population A: the electric field has no effect on the fluorescence intensity, population B: the electric field reduced the fluorescence intensity, population C: the fluorescence intensity is enhanced by the electric field, and population D: the fluorescence intensity is almost completely suppressed by the electric field.

The recorded traces can be analyzed with either the binning and thresholding (B&T) technique or the autocorrelation method. However, because of the limited number of observations per cycle of the applied electric field, the B&T method was deemed less suitable when quantitative data analysis per cycle was aimed for. Nevertheless, when combining the obtained on (or off) times (obtained with the B&T method) of several individual molecules, a clear power-law was observed for both the on and off times (data not shown, see Supporting Information, Figures S2 and S3). To analyze and compare the on and off times of each electric-field cycle, we opted for the autocorrelation method. For each cycle (period of 0 V and period of 20 V), the second-order autocorrelation functions of the intensity are calculated. This was also done for the pure PVK matrix to ensure that no unexpected correlations showed up. This second-order autocorrelation function (g(2)) is constructed using the following equationI(t) is the fluorescence intensity measured in the integration interval centered at time t. These autocorrelation functions are fitted to a single exponential with decay time τac and amplitude A. This allows one to calculate the average on (τon) and off times (τoff) using the following equationsIt has been shown that for molecules undergoing intersystem crossing these on and off times are related to triplet dynamics.[3,7,8,52−54] Likewise, when electron or hole transfer is possible between the excited dye and the matrix, the off times can be related to the rate constant of charge recombination, krec.The on times will be a function of the rate constant for excitation, the probability for excited-state electron transfer and the probability for geminate ion pair separationket is the rate constant for forward electron transfer, whereas kfluor, kisc, and kic are the rate constants for fluorescence, intersystem crossing, and internal conversion of the ATTO dye. kexc is the rate constant for excitation. The latter should be related to the excitation intensity and ground-state absorption cross section of ATTO. φsep is the probability that a hole generated on a carbazole next to an ATTO molecule will escape recombination. Holes that fail to do so will recombine with the electron on the dye molecule on a nanosecond time scale and hence will not be able to create a dark state with a lifetime of micro- or milli-seconds. A simplified picture of the electron dynamics is given in Scheme .

Scheme 1

Jablonski Diagram for Photoinduced Electron Transfer from Carbazole to ATTO*

After the photoinduced electron transfer, the probability for the electron on the ATTO molecule to hop to other dye molecules is extremely low as they are present at SM concentration. This electron can also not be injected in the LUMO of the carbazole moieties as the energy of the LUMO of carbazole (2.2 eV) is much higher than that of ATTO. However, the hole created on a carbazole in contact with ATTO can start to hop to neighboring carbazoles with rate constant kdiss and will execute a random walk on the carbazole moieties[47,55] in the field of the net negative charge on the ATTO (due to the negative charge of the ATTO counterion).

Eventually, the hole ends up on a carbazole in contact with the reduced ATTO (with rate constant k–diss) where recombination with the electron on ATTO can occur with rate constant kbet and kbet′ (see Scheme ). If the time dependence of kdiss and k–diss(56−58) is neglected, then φsep will be given byIn this framework krec will be given byket, kbet, kbet′, kdis, and k–diss will all depend on the applied electric field. According to the classical Marcus theory,[59−63] the rate constant for (back) electron transfer can be given bywhere κET is the electronic transmission factor (∼1 for adiabatic ET, ≪1 for nonadiabatic ET), h is the Planck constant, kB is the Boltzmann constant, T is the temperature, ΔG° is the standard Gibbs free energy change (in electronvolts), and λ is the reorganization energy (in electronvolts). For reductive electron transfer, ΔGet° is given by the Rehm–Weller equation[64,65]E° (0.74 eV vs ferrocene[46,66]) is the oxidation potential of the PVK film, as determined by cyclic voltammetry, E° (−1.25 eV vs ferrocene) is the reduction potential of ATTO as determined by cyclic voltammetry (see Figure S4), and ΔE00 is the excitation energy (1.96 eV) of ATTO (0–0 absorption in film). In this way, a value of +0.03 eV is obtained for ΔGet°. In the same way, ΔGbet° and ΔGb′et° are given byandΔET is the triplet energy of ATTO, E° of PVK and E° of ATTO were determined in solution where, due to the rapid motion of the solvent molecules, all carbazole and ATTO moieties have an identical time-averaged environment. The redox processes we are interested in, however, occur in a rigid and largely amorphous and disordered polymer matrix. This means that all carbazole and ATTO moieties have a different local environment characterized by different van der Waals, dipole–dipole, ion–dipole, and π−π interactions.[48,67−71] As in a film, conformational changes are slow compared to the excited-state decay time; the oxidation potential (or the position of the HOMO level) of the carbazole molecules and the reduction potential (or the position of the LUMO level) of the ATTO moieties will be given by a distribution function. Hence, rather than being characterized by a single value, the values of ΔGet° will also be given by a distribution and different molecules of ATTO will experience a different value of ΔGet°. In a first approximation, this distribution can be considered as a Gaussian distribution of the DOS.[48,67,70] Besides the factors mentioned above, the energy of HOMO of carbazole will be governed by the overlap of neighboring carbazole moieties, which depends on the conformation of the chain segments linking neighboring carbazole moieties.[72−74]

In the framework of the model developed for charge transport in amorphous materials,[48,67,70] the width of the Gaussian distribution of the HOMO level can be determined from the field and temperature dependence of the hole mobility, which was determined using the “Time of Flight” method (TOF)[75,76] (see Figures S5 and S6). In this way, a value of 129 meV was obtained for the standard deviation associated with the Gaussian distribution of DOS of the HOMO level (see Figure S6 and Table S1). This value is comparable with results reported in the literature.[77] As described in the Introduction, applying an electric field can change the energy difference between the ATTO HOMO and the PVK HOMO. Hence, also the difference E° – E° – ΔE00 will be altered by −E⃗ * r⃗, where E⃗ is the applied field and r⃗, a vector with the origin in the center of the ATTO molecule and oriented to that of the carbazole unit responsible for the electron transfer. This vector product is illustrated in Figure for populations B and C. This figure also serves as a summary of the general observations and given explanations related to these populations. Assuming a homogeneous field (667 kV cm–1) and an average distance of 0.5 nm between the center of the molecules involved, this difference spans a range from 0.033 to −0.033 eV, depending on the orientation of the vector r⃗ relative to E⃗. Hence, the electric field will increase or decrease ΔGet° by a value between 0 and 0.033 eV. As the absolute value of ΔGet° will always be small compared to λ (typically 0.4–2 eV), ΔGet≠ will be changed by values between 0.0165 and −0.0165 eV. This will increase or decrease the rate constant for the electron transfer between PVK and the excited ATTO by a factor between 1 and 1.9. Therefore, the quenching (through electron transfer) will be enhanced for some ATTO molecules and prohibited for others. Furthermore, after the initial charge-separation step, the hole injected into the carbazole will start diffusing over the PVK moieties in the field of the counterion of ATTO and, due to this field, eventually recombine with the electron in the LUMO of the ATTO molecule. Depending on the relative orientation of the ATTO and the carbazole moiety with respect to the applied field, the applied field can enhance or hinder the diffusion of the hole toward the reduced ATTO molecule, speeding up or slowing down the regeneration of a fluorescent ATTO molecule. With this framework laid out, we will now step-by-step consider each population of molecules.

Figure 4

Schematic illustration of the proposed orientation of the applied electric field, E⃗, vs the direction of photoinduced electron transfer, r⃗, for the different types of fluorescence intensity trajectories B and C. The black line in C represents the off-diagonal disorder, which prevents hole hopping.

Population A

These are the individual ATTO molecules where the electric field does not affect the fluorescence intensity (Figure A). There is no observable influence of the electric field on the blinking dynamics as well; both on and off times remain constant through out the entire trace. Therefore, there is no evidence of electron transfer (ket ≪ kisc + kf + kic) followed by hole hopping (kdiss ≪ k–diss) taking place and the system can be described by a simple three level system where blinking is, for example, caused by intersystem crossing to the triplet manifold. Typical off times are several 100 μs, which corresponds to triplet associated off times reported in literature.[4] Indeed, for most ATTO–PVK pairs the initial ΔGet≠ will be unsuitable for efficient electron transfer. The possible increase in ΔGet≠ due to the electric field (max 0.0165 eV) will not compensate this for all molecules and depending on the vector −E⃗ * r⃗ even further impair this process. Although an orientation of the ATTO–PVK pair perpendicular to the electric field would also result in a ket that is independent of this electric field, an effect on the hole hopping (kdiss) is nevertheless expected as this will usually be in the direction of the field. Therefore, it is more reasonable to conclude that for this class of molecules no electron transfer takes place. Indeed, Scheblykin et al. demonstrated a low enhancement factor for charge separation due to an electric field for isolated MEH-PPV molecules in a nonconducting polymer. Even close to a hole-conducting layer, Barbara et al. observed no signs of efficient exciton dissociation for most molecules.

Population D

The class of molecules belonging to trace D in Figure , the molecules where the fluorescence is completely quenched, is the opposite extreme case. Here, it is intuitive to assume that the electric field enhances both the electron transfer step (ket ≫ kisc + kf) and the hole hopping. The hole hops away from the ATTO molecule under the influence of the applied electric field and most likely becomes trapped, leaving behind a dark ATTO radical. Although the fluorescence intensity is almost completely suppressed when the electric field is on, some fluorescence spikes occasionally occur. When the fluorescence is completely quenched, no autocorrelation functions can be analyzed, yet for the spikes it remains possible to obtain and analyze the autocorrelation function. For the specific trace in Figure D, the duration of the on times remained constant when comparing these spikes to the situation where the electric field is off. Hence, the electron transfer step itself is not influenced, but the field is strong enough to prevent the hole to recombine with a reduced ATTO molecule most of the time. Holes most likely end up in a deep trap being somewhere in the vicinity. Occasionally, the hole escapes this trap and has a chance of recombining. This will be described more in detail in section Subclass B3.

Population B

Next, the intermediate situation, where the electric field suppresses the fluorescence intensity of the ATTO dye (Figure B) is considered. The autocorrelation traces for trace B are depicted in Figure , and the corresponding calculated on and off times are shown in Table (subclass B1). When comparing the on and off times without and with electric field, the molecules that show a reduced intensity upon applying an electric field can be divided into three subclasses (B1, B2, and B3).

Figure 3

Second-order autocorrelation traces of trace B (Figure ).

Table 1

Representative On and Off Times of Several Molecules for the Subclasses in Population B

subclasses of population B	on time (ms) 0 V/20 V	off time (ms) 0 V/20 V
B1 (46%)	22.20/22.36	4.44/12.63
	21.11/21.91	4.05/13.18
	22.35/22.09	4.29/11.77
	23.40/23.96	4.25/12.75
	23.65/23.48	3.83/10.80
B2 (28%)	2.15/30.21	0.03/5.42
	39.39/65.22	0.03/4.90
	14.81/58.80	0.22/7.40
	22.53/88.40	0.41/7.07
	11.52/104.9	0.44/6.61
B3 (26%)	14.40/12.70	7.20/9.39
	15.10/11.42	7.48/9.55
	15.52/11.81	6.74/9.62

Subclass B1

The majority of the molecules show on times that remain more or less constant, whereas the off times increase significantly (Table , subclass B1). This means that the product of ketφsep does not change much, whereas krec is decreased. As generally the effect of the applied field on kdiss or k–diss is larger than that on ket or kbet, the observation that τon does not change significantly, whereas τoff is increased suggests that the decrease of k–diss by the applied field is much larger than the increase of kdiss. This is no surprise as, initially, the electron and hole are still close together and kdiss will correspond to a transfer between two neighboring carbazole units. On the other hand, the recombination process will involve holes that have moved in a random way in several steps. If an electric field is applied, then they will preferentially move in the direction of the field. Hence, the process described by k–diss will correspond to a large number of hops (compared to kdiss), most of them opposite to the applied electric field. Therefore, k–diss will be suppressed by an applied field. The back electron transfer step kbet is very exergonic and will most often correspond to an electron transfer opposite to the applied field. Applying an electric field will make ΔGbet° less negative and will enhance kbet as ΔGbet° is in the Marcus inverted region.[62] Both the decrease of k–diss and increase of kbet will lead to a decrease of krec and an increase of τoff. This means that the applied electric field reduces the probability that the hole recombines with the electron in ATTO. Furthermore, the observation that for the largest group of molecules τon does not change upon the application of an electric field means that for this group also the efficiency of electron transfer, , and hence ΔGet° does not change when an electric field is applied. This means that the orientation of the vector r⃗ is close to perpendicular to the applied field for the ATTO–PVK pair most favorable for electron transfer (Figure , subclass B1). The probability that the angle between the vector r⃗ and the applied field is between θ and θ + dθ is given by sin θ dθ. The probability that this angle is between π/4 and 3π/4 is 2–1/2 ≈ 0.7, whereas the probability that this angle is between 0 and π/4 or between 3π/4 and π is 1 – 2–1/2 ≈ 0.3. This means that for most molecules θ is relatively close to π/2 and hence ΔGet° and ket will not be influenced to a large extent by the applied field. This allows us to conclude that the observed field dependence of τon and τof is compatible with a model where charge transfer and the formation of a long-lived charge-separated state, which is stabilized by the applied field, are responsible for the off times.

Subclass B2

A second category of molecules with reduced intensity in the presence of the electric field shows both longer off times and longer on times (Table , subclass B2). One should note that these molecules are characterized by off times that, in the absence of an applied field, are much smaller than those of subclasses B1 and B3. The effect of the applied field on the on and off times implies that the electric field on one hand again keeps the charges separated longer due to a decrease in k–diss and hence of krec but, on the other hand, also delays the electron transfer step ket. Here, the PVK moiety close to the dye will most likely be located on the ITO side of the device and hence the energy difference between the HOMO of ATTO and that of PVK (ΔGet°) will become larger (less negative or more positive) by −E⃗ * r⃗. Here, r⃗ is now more or less opposite to the electric field (θ close to π, Figure , subclass B2). For this geometry, the first step in the dissociation of the electron hole pairs by hopping of the holes over the carbazole moieties (kdiss) cannot be in the direction of the applied field as this would bring the hole back on ATTO (kbet or k′bet) and hence will not be enhanced effectively by the applied field. Both effects will have as consequence that the product is decreased and therefore τon is increased. On the other hand, once the hole escapes initial recombination, it can travel a significant distance in the direction of the field, allowing it to reach a position from which k–diss will be depressed strongly by the electric field, leading to an increase in τoff. This later effect seems to dominate. In its absence (for instance when using a nonconductive polymer), one would expect an increase in the fluorescence intensity when the electric field is on due to the observed increase in τon.

Subclass B3

The third category of reduced intensity molecules also show longer off times but shorter on times (Table , subclass B3) in the presence of the electric field. In contrast to previous subclasses, the increase of the off times and also the decrease of the on times are quite modest. Here, we infer that ket and/or φsep are increased. PVK moieties located at the aluminum side of an ATTO possess a decreased relative energy difference between their HOMO and that of ATTO (ΔGet° becomes more negative or less positive) by (E⃗ * r⃗) (Figure , subclass B3) upon applying the electric field. The resulting increased probability of electron transfer ket reduces the on times. Furthermore, in contrast to the previous case, the first step in the dissociation of the electron hole pair by hopping of the holes over the carbazole moieties (kdiss) is now possible in the direction of the field and hence kdiss can be enhanced by the applied field. Both factors will increase the product and hence reduce τon. On the other hand, the electric field once again leads to a decrease in k–diss and krec and therefore to shorter off times.

Population C

Only a few molecules showed intensity traces where the electric field enhances the fluorescence. Surprisingly, the autocorrelation functions reveal that for every molecule that shows enhanced fluorescence when the electric field is applied, the off time decreases significantly, whereas only a minor change (increase or decrease) in τon is observed. One possible way to explain this is by assuming that k–diss increases significantly in the presence of the electric field, whereas kdiss is possibly decreased. The latter factor will only play a significant role when kdiss is not small compared to kbet + k’bet. To understand this behavior, some specific aspects of charge-carrier transport in amorphous materials have to be considered.

As described in the Introduction, off-diagonal disorder can be related to the orbital overlap between neighboring molecules. This overlap is proportional with exp(−αL), where L is the distance between hopping sites and α is an attenuation factor of the wavefunction. Because of the variation with L, some indirect paths characterized by a favorable overlap, but involving steps against the direction of the applied field, can be faster at low/zero field than the direct paths containing only steps in the direction of the applied field. At larger fields, this effect will saturate and become compensated by the effects of the tilting of the DOS caused by the applied field (Pool–Frenkel behavior).[48] The subsequent saturation of the hole mobility at low fields has been observed for PVK.[48]

As the off-diagonal disorder in PVK is relatively large,[60] one can expect, despite the fact that this process is supposed to be activationless,[78] to have a large distribution in the rate constants for hopping between neighboring carbazoles where the hole jumps to a site lower in energy. For hopping toward sites with higher energy, this distribution will come on top of the distribution of the Boltzmann factors. It was shown from the saturation of the charge-carrier mobility at low fields that in systems with significant nondiagonal disorder the most advantageous pathway involves states where the hole has to move in the opposite direction to the applied field. Therefore, it is possible that the hole of the initial electron hole pair hops in a direction opposite to the applied field when it starts its random walk and gets trapped in a poorly connected and/or deep lying transport site in a direction opposite to that of the applied field. In Figure C, this trap and the off-diagonal disorder is represented by the black line. In this case, the applied field will tilt the DOS and enhance the escape of the carrier from the trap by the Poole−Frenkel effect.[79] This will lead to an increase of k–diss and a consequent reduction of τoff upon increasing the applied field. When the applied field has little or no influence on τon while τoff is decreased, it will enhance the fluorescence intensity. Although, in general, one would expect that the fluorescence enhancement is mainly due to a decreased rate of electron transfer, in our system the effect of the field on hole hopping dominates the former and thus reduces the fluorescence intensity for most observed molecules (populations B and D as discussed earlier). In the specific case of population C, the fluorescence enhancement finds its origin in the prevention of hole hopping due to the presence of off-diagonal disorder.

Barbara et al.[44] provided an alternative explanation for the enhancement of the fluorescence by an applied field. In the system studied by Barbara et al., the off times correspond to triplet excitons that are more easily quenched by holes (leading again to an on-state) injected by the field than singlet excitons. However, in our device, no holes generated by injection from the electrode as noninjecting contacts are used. Furthermore, as PVK is not excited, no holes can be created by field-assisted exciton dissociation of PVK. Because of the very low concentration of ATTO used (singe molecule conditions), the small number of holes created by quenching of ATTO will not be able to influence the triplet decay time of ATTO.

Conclusions

The generally accepted model of blinking being caused by the formation of a radical ion through charge transfer can be applied to understand the blinking in the system ATTO/PVK. The redox potentials of both ATTO and PVK are such that they allow sporadic photoinduced electron transfer from PVK to the excited state of ATTO, leaving a hole, which can execute a random walk in the PVK matrix, in the HOMO of PVK. As PVK is a disordered material, one can expect that the energy of the HOMO follows a distribution, the width of which is related to the diagonal disorder, which can be represented by a DOS. The position of the HOMO of PVK in this distribution versus that of ATTO dictates the ease of the charge transfer step and hence is responsible for the distribution of the observed on times. The conductive properties and/or traps in PVK are responsible for the off times. The effect of an applied electric field on the on times will depend on the direction of the electron transfer versus that of the applied field. The field dependence of the off times will be related to the diagonal and nondiagonal disorder between the transport sites in PVK. The observed changes in on and off times when an electric field is applied can be related via a simplified kinetic scheme to a combination of the Marcus formalism[49−53] for electron transfer and the model developed for the hopping of charge carriers in a Gaussian DOS.[57−60] For the combination of ATTO and a PVK matrix, and for cases where a clear response to the electric field is observed, the majority of the molecules show a reduced fluorescence intensity when the electric field is applied. In general, this reduction is due to longer off times when an electric field is applied, corresponding to a decrease of k–diss, an increase of kdiss, and hence a decrease of krec. The on times reveal information about the electron transfer step and the probability of immediate recombination versus dissociation of the electron hole pair. Increasing the duration of on times when an electric field is applied suggests a delay in the electron transfer step caused by a change in ΔGet° by −E⃗ * r⃗, which gives information about the orientation of the ATTO/PVK pair with respect to the electric field. Some molecules show an increased intensity when an electric field is applied. Intuitively, one would explain this observation by a reduction of the rate of the electron transfer step, which should increase τon. Blinking analysis reveals however that a decrease of the off times is the main reason for this behavior. Positions with high nondiagonal disorder will effectively lead to an increased k–diss upon increasing the applied field, which will lead to an increase of the fluorescence intensity. Our study provides in-depth insight into the fundamental concept of fluorescence intermittency caused by charge transfer to the environment. This understanding and the used concept has the potential to unravel mechanistic losses in photovoltaic devices by means of inducing controlled blinking. Alternatively, electric field induced blinking can be used for super-resolution techniques, such as PALM and STORM.