Single-Molecule Fluorescence Spectroscopy of Perylene Diimide

Feb 13, 2017 - Supramolecular complexation of γ-cyclodextrin (γ-CD) with N,N′-bis(2,6-dimethylphenyl)perylene-3,4,9,10-tetracarboxylic diimide (DM...
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Single-Molecule Fluorescence Spectroscopy of Perylene Diimide Dyes in a γ‑Cyclodextrin Film: Manifestation of Photoinduced H‑Atom Transfer via Higher Triplet (n, π*) Excited States Masaaki Mitsui,*,† Hiroki Fukui,‡ Ryoya Takahashi,‡ Yasushi Takakura,† and Toshinari Mizukami† †

Department of Chemistry, College of Science, Rikkyo University, 3-34-1, Nishiikebukuro, Toshima-ku, Tokyo 171-8501, Japan Department of Chemistry, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka 422-8529, Japan

‡

S Supporting Information *

ABSTRACT: Supramolecular complexation of γ-cyclodextrin (γ-CD) with N,N′-bis(2,6-dimethylphenyl)perylene-3,4,9,10-tetracarboxylic diimide (DMP-PDI) or N,N′-bis(2,6-dioctyl)perylene-3,4,9,10-tetracarboxylic diimide (C8-PDI) dye in an aqueous solution and in a γ-CD solid film were investigated via ensemble and single-molecule fluorescence spectroscopy. These two perylene diimide derivatives possess almost the same electronic structure but have different terminal functional groups. This structural difference leads to formation of an inclusion complex of γ-CD with DMP-PDI but not with C8-PDI in aqueous solution. In a γCD solid film, the distributions of the wavelengths of emission maximum (λmaxem) are strikingly different between these two dyes; a much narrower and blue-shifted λmaxem distribution was observed for C8PDI relative to DMP-PDI. This difference is attributed to the fact that the C8-PDI molecules are bound at the γ-CD/glass interface as a result of spin-coating of the sample solution, whereas the DMP-PDI molecules form 1:1 and 1:2 inclusion complexes with conformational heterogeneities in the film. In comparison to the case for C8-PDI, more frequent on−off blinking events were observed for DMP-PDI. The blinking statistics of DMP-PDI in the γ-CD film exhibit both single-exponential and nonexponential (i.e., dispersive) kinetics, revealed by robust statistical analysis. Energetic consideration with the aid of theoretical calculations suggests that the underlying photophysics most probably involves hydrogen atom transfer (HAT) between the DMP-PDI guest and γ-CD host via higher excited (n, π*) triplet states. The hypothesis of HAT in the inclusion complex reasonably explains the experimental results; however, a charge transfer hypothesis cannot explain the results. The dispersive kinetics is attributable to the effect of thermal fluctuation in the forward and backward HAT reactions.

1. INTRODUCTION

on photochemical and photophysical properties of guest molecules in aqueous solution.2,3 Consequently, it has been revealed that the reduced polarity and restricted space provided by the CD cavity markedly influence the photophysical/ photochemical dynamics of guest molecules.2,3 The photochemical reaction of guest molecules encapsulated in CDs has long been studied by numerous different analytical methods. In particular, the photoinduced hydrogen atom transfer (HAT) or H atom abstraction between a guest molecule and a CD host in liquid and solid phases has been observed when aromatic ketones (e.g., benzophenone and xanthone) were used as the encapsulated guest.4−9 The HAT reaction in supramolecular host−guest complexes has been preponderantly investigated using ensemble spectroscopic techniques such as transient absorption spectroscopy,4,5 timeresolved electron paramagnetic resonance,6−9 and nuclear magnetic resonance.9 Due to the exponential dependence of

Cyclodextrins (CDs) are a family of cyclic oligosaccharides formed by 6 (α), 7 (β), or 8 (γ) α-1,4-linked D-glucopyranoside units and are named α-, β-, and γ-CD (Figure 1a), respectively.1 They possess a hydrophobic cavity capable of forming inclusion complexes with a wide variety of guest molecules via noncovalent bonds. Considerable experimental and theoretical efforts have been devoted to elucidate the encapsulation effects

Received: November 11, 2016 Revised: February 6, 2017 Published: February 13, 2017

Figure 1. Molecular structures of (a) γ-CD, (b) DMP-PDI, and (c) C8-PDI. © XXXX American Chemical Society

A

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were prepared by spin-coating (1500 rpm) one drop of a prepared aqueous solution onto a thoroughly cleaned cover glass (Matsunami). As a result, DMP-PDI (C8-PDI) molecules were dispersed in a γ-CD thin film with a thickness of 200−300 nm, as measured by atomic force microscopy (AFM, SPM9700, Shimadzu). To remove THF and water from the γ-CD film, the sample-coated coverslips were heated to 80 °C for 90 min under reduced pressure. This temperature can remove residual water from the γ-CD film under atmospheric pressure.19 The sample slip was set on an O-ring and that acted as the top of a small vacuum chamber. During SMFS measurements, the sample was evacuated and flushed continuously with Ar gas to further remove residual water and oxygen from the γ-CD film. 2.2. Single-Molecule Fluorescence Spectroscopy. SMFS experiments were performed with a home-built laser scanning optical microscope, which is thoroughly described in ref 20. Briefly, the excitation light source was a 488 nm unpolarized continuous wave provided by an air-cooled Ar+laser (177G, Spectra Physics) or a 478 nm picosecond (ps)pulsed diode laser (PiL048X, Advanced Laser Diode System). The beam passed through a Glan-Thompson polarizer and a λ/ 4 plate, which were used to shift the beam polarization to circular. The resultant circular polarized beam was directed by a dichroic mirror (DM, Semrock) to the back aperture of an oilimmersion objective lens (100×, NA 1.4, Olympus), which focuses the beam to a diffraction-limited spot size (∼210 nm fwhm), providing light intensities in the range 0.5−1 kW/cm2. Fluorescence photons from the excited molecule were collected through the same objective, and then passed through the DM and long-pass and notch filters to block the scattered laser light. The fluorescence was then split by a 50:50 unpolarized beam splitter. Half of the detected fluorescence signal was sent to a polychromator (SpectraPro 2300i) coupled to a liquidnitrogen-cooled CCD camera (Spec-10:100B/LN, Roper Scientific). The other half was focused onto a pinhole (75 μm diameter) to reject the out-of-focus background. The signal was further split by a polarizing beamsplitter and directed onto two avalanche photodiodes (APDs). This setup allows the simultaneous detection of the parallel (I∥) and perpendicular (I⊥) components of the fluorescence signal, from which the polarization is calculated as P = (I∥ − GI⊥)/(I∥ + GI⊥). Here the factor G corrects for the sensitivity difference between the two APDs. The fluorescence intensity and spectral traces (3 s per spectrum) were acquired until a photobleaching event occurred. If not otherwise mentioned, SMFS measurements were carried out at room temperature (22 °C). Lowtemperature measurements at −10 °C were also implemented by continuously flushing a sample substrate with Ar gas cooled by liquid nitrogen. The substrate temperature was controlled by adjusting the flow rate of cold Ar gas and monitored using a thermocouple. A (10 × 10) μm2 fluorescence image of the sample was acquired by raster scanning of the laser focal spot (Figure S1). From the image, the coverage density was confirmed as approximately 0.5 molecules per μm2. Data were acquired with SymPhoTime v5.2.4 software (PicoQuant). 2.3. Blinking Analysis. When the blinking trajectories were analyzed, the “on” and “off” levels were differentiated by a socalled histogram method. To determine the dwell times in the “on” and “off” levels, the unbiased threshold level (Ith) was determined from the equation (Ith − Ioff)/ Ioff = (Ion − Ith)/ Ion where Ion and Ioff are the mean intensity levels of the “on”

HAT on the reaction distance (r) with a large exponential decay factor of β (i.e., β = 25−40 Å−1),10,11 HAT is extremely sensitive to r and occurs over an extremely narrow distance range. In CD complexes, guest molecules are loosely bound inside the CD cavity via noncovalent host−guest interactions.5 Therefore, the HAT reaction rate within the complex may be affected by thermal (or structural) fluctuation, even in rigid environments. Such fluctuation effects on the reaction can be probed by time variations of fluorescence multiparameters and blinking statistics, obtained by a single-molecule fluorescence spectroscopy (SMFS) technique. To the best of our knowledge, there are no SMFS investigations on HAT in supramolecular host−guest complexes, because HAT occurs via the low-lying (n, π*) excited states of guest molecules (e.g., aromatic carbonyl compounds), which are usually nonfluorescent or very weakly fluorescent.12 Herein, we report an SMFS study of two perylene diimide (PDI) derivatives, hereafter termed DMP-PDI (Figure 1b) and C8-PDI (Figure 1c), in a γ-CD solid film. The PDI dyes were adopted as guest fluorophores in this study because (i) PDI possesses four carbonyl groups and thereby has the (n, π*) excited states, existing as higher excited states, (ii) the molecular size of PDI allows for encapsulation by γ-CD,13 but the formation of a γ-CD inclusion complex was observed for DMP-PDI, not for C8-PDI in aqueous solution, (iii) PDI outperforms other types of fluorescence dyes at the singlemolecule level in terms of brightness and survival time,14,15 and (iv) the blinking statistics of DMP-PDI has been recently well established.16,17 Therefore, the fluorescence characteristics and blinking dynamics of DMP-PDI and C8-PDI dyes in a γ-CD solid film were investigated by SMFS. The single-molecule blinking statistics were analyzed using a combination of the maximum likelihood estimator (MLE) with the Kolmogorov− Smirnov (KS) test, hereafter termed the MLE-KS method.18 On the basis of experimental and theoretical results, we discuss whether HAT between DMP-PDI and γ-CD is responsible for the blinking observed in this system.

2. EXPERIMENTAL AND DATA ANALYSIS 2.1. Sample Preparation. The following reagents were used in this study: N,N′-bis(2,6-dimethylphenyl)perylene3,4,9,10-tetracarboxylic diimide (DMP-PDI, ≥ 90%, SigmaAldrich), N,N′-bis(2,6-dioctyl)perylene-3,4,9,10-tetracarboxylic diimide (C8-PDI, 98%, Sigma-Aldrich), α- and γ-CDs (Wako), toluene (spectroscopic grade, Wako), cyclohexane (spectroscopic grade, Wako), tetrahydrofuran (THF) (spectroscopic grade, Wako), ethanol (spectroscopic grade, Wako), and dimethylformamide (DMF) (Wako). Ultrapure water with a conductivity of 18.2 MΩ cm (MILLPORE) was used throughout the experiment. Ensemble absorption spectra of DMP-PDI in cyclohexane, THF, and water containing γ-CD were recorded on a UV-1650PC spectrometer (Shimadzu), whereas fluorescence spectra were obtained with a RF-5300PC fluorometer (Shimadzu). The concentrations of DMP-PDI or C8-PDI are low enough to avoid aggregation in aqueous solution (∼10−6 M). Samples of varying CD concentrations were prepared by addition of different volumes of a CD stock solution (10 mM). A sample solution of DMP-PDI (or C8-PDI) was prepared by adding a trace amount of THF solution of DMP-PDI (C8PDI) (10−7 M) to γ-CD aqueous solution (10−2 M). To remove aggregates, the solution thus prepared was filtered through a membrane filter. Samples for SMFS experiments B

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Table 1. Wavelengths of Absorption and Emission Maxima and Fluorescence Lifetimes of DMP-PDI and C8-PDI in Various Environments, Together with Static Dielectric Constants (εs) of Solvents DMP-PDI

C8-PDI

solvent

εs

λmax /nm

λmax /nm

τf/ns

λmax /nm

λmaxem/nm

τf/ns

cyclohexane toluene THF ethanol DMF γ-CD/water water γ-CD film

2.02 2.38 7.52 25.3 38.3 50−70a 80.1

516 526 522 524 527 535 NAb NA

520 535 535 536 537 546 550 543c (9.9)e 536d (9.7)e

4.1 3.7f 4.0 4.2 4.1 4.6 4.0 5.2g

516 527 521 NA 526 NA NA NA

519 537 534 533 535 NA NA 531c (2.4)e

4.0 4.1 4.3 4.3 4.2 NA NA 6.5h

abs

em

abs

a

Taken from ref 1. bNot available. Note that C8-PDI has extremely low solubility in ethanol and water; therefore, it was impossible to measure the absorption spectrum. cAverage value of λmaxem obtained for unannealed samples. dAverage value of λmaxem obtained for annealed samples (Figure S3). e Values in parentheses indicate fwhm of λmaxem distributions. fTaken from ref 15. gAverage fluorescence lifetime of 78 molecules. hAverage fluorescence lifetime of 47 molecules.

(above the Ith) and “off” (below the Ith) states, respectively.21 Although the on and off durations are sensitive to Ith,22−25 the high S/B ratios of the trajectories observed in the present system (S/B ∼ 10 at 10 ms bin-time) ensure reliable on/off event durations in the histogram method and allow us to always set the threshold above the noise (see, for example, Figure 4d). Such a threshold does not influence the resultant on-time/offtime distribution.24,25 The cumulative distribution function (CDF) was calculated from the experimental data as follows: CDF(t )data

1 = N

∑ Nt

computed using the best-fit parameters and compared with the empirical CDF. Finally, the goodness-of-fit (p-value) between the fitted and empirical PDFs was evaluated by the two-sample KS test, which determines the probability that the two CDFs share the same PDF. The p-value is calculated as follows:26 p = 1 − PKS[( Ne + 0.12 + 0.11/ Ne )D]

where PKS is given by PKS(z) =

i

(1)

i=1

−α α − 1⎛ t ⎞ ⎟ ⎜ tmin ⎝ tmin ⎠

(2)

2 μ⎤ ⎞ ⎥⎦ ⎟ ⎠

A−1 ⎛ t ⎞A A ⎛⎜ t ⎞⎟ exp⎜ − ⎟ ⎝ τ⎠ τ ⎝τ⎠

j=1

(6)

(7)

3. RESULTS 3.1. Ensemble Spectroscopy. Although DMP-PDI has extremely low solubility in water, the fluorescence spectrum of DMP-PDI in water was very weakly observed at λmaxem = 550 nm, which is red-shifted by 15−30 nm, compared to the λmaxem values in nonpolar and polar organic solvents (e.g., λmaxem = 520 and 535 nm in cyclohexane and THF, respectively; see Table 1). As shown in Figure 2a, gradual addition of γ-CD to an aqueous solution of DMP-PDI leads to remarkable enhancement of the fluorescence intensity and a gradual blue shift from 550 to 546 nm (inset in Figure 2a) when the concentration of γ-CD is increased from 10−4 to 10−2 M. These spectral variations indicate the formation of a DMP-PDI−γ-CD complex in aqueous solution. Such fluorescence enhancement

(3)

where the parameters μ and σ represent the geometric mean and standard deviation of the variable’s natural logarithm, respectively, and (iii) the Weibull function P(t ) =

⎛ (2j − 1)2 π 2 ⎞ ⎟ 8z 2 ⎠ ⎝

We also define the reduced data density Ne = N1N2/(N1 + N2), which represents the difference in the number of data points between the two CDFs. The probability that data match a presumed model function is increased as the p-value approaches unity. If p = 0, the experimental data and the model are fundamentally different. However, the accuracy of the p-value itself worsens as the number of data points decreases, as ∼1/(2 N1 )18 Herein, single-molecule data with N1 < 20 were excluded from the analysis. In judging the goodness-of-fit using p-values, we concomitantly considered the accuracy of the p-value, depending on the number of points in a data set.

α>1

⎛ 1 ⎡ ln t − 1 exp⎜ − ⎢ 2π σt ⎝ 2⎣ σ

∞

∑ exp⎜−

D = max ti ≥ tmin|CDF(ti)fit − CDF(ti)data |

where the parameters α and tmin represent the power-law exponent and the onset time for power-law behavior, respectively, (ii) the log-normal function P(t ) =

2π z

and D is the maximum distance between the CDFs determined from the empirical data and the hypothetical PDF model:

where Nti is the number of on/off events with the duration of ti ≤ t, and N is the total number of events in the range tmin ≤ ti ≤ t. Because blinking events are most probable at tmin, the complementary CDF (cCDF), defined as 1 − CDF, was used. The blinking data (i.e., on-/off-time durations) were analyzed by an MLE-KS method developed by Reid and co-workers.18 First, the blinking data were fitted by several heavy-tailed probability density functions (PDFs): namely, (i) the powerlaw function P(t ) =

(5)

(4)

where A (A > 1 means that the probability of a molecule leaving a particular emissive state increases with time, whereas A < 1 is the opposite case) and τ correspond to the parameters of this function. The best-fit parameters to each PDF were determined by an MLE algorithm. The corresponding CDFs were then C

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3.2. Single-Molecule Spectroscopy. As shown in Figure 3a and Figure S3, the average values of λmaxem, i.e., ⟨λmaxem⟩,

Figure 3. (a) and (b) Wavelengths of emission maximum (λmaxem). (c) and (d) Fluorescence lifetimes (τf), obtained for DMP-PDI (a, c) and C8-PDI molecules (b, d) in unannealed γ-CD samples, along with fitted Gaussian functions (solid lines). Insets in parts a and b display typical single-molecule fluorescence spectra, and arrows indicate the λmaxem and τf values of the 1:2 DMP-PDI−γ-CD complex in aqueous solution. Note that the data of parts a and b were obtained using a 488 nm continuous wave (cw)-excitation laser, whereas the data of c and d were obtained using a 478 nm ps-pulsed laser. All the fluorescence lifetimes were obtained from single exponential fits of fluorescence decay profiles.

Figure 2. (a) Fluorescence spectra of DMP-PDI in the presence of varying concentration of γ-CD (1.0 × 10−4 to 1.0 × 10−2 M) in aqueous solutions. The inset shows corresponding wavelengths of fluorescence maxima (λmaxem) plotted against the γ-CD concentration. Absorption spectrum of DMP-PDI at [γ-CD] = 1.0 × 10−2 M (dash line). (b) Proposed structures for 1:1 (left) and 1:2 (right) DMPPDI−γ-CD inclusion complexes in aqueous solution. The structure of the 1:1 complex (also shown in Figure S12a) was obtained by performing the geometry optimization and vibrational frequency analysis at the PM3 semiempirical calculation, whereas the 1:2 complex structure was deduced from the optimized structure of the 1:1 complex.

obtained from data for 263 single molecules, are 543 nm (unannealed samples) and 536 nm (annealed samples), which are blue-shifted by 3 and 10 nm relative to that of the 1:2 DMP-PDI−γ-CD complex in aqueous solution, respectively. The 7 nm blue shift from an untreated sample relative to a treated sample suggests that most of the water molecules were removed from the γ-CD film by the thermal annealing treatment, and thereby the stabilization effect upon the hydration is likely almost lost. As can be seen in Figure 3c, the average value of the fluorescence lifetime, i.e., ⟨τf⟩, of DMPPDI in the solid γ-CD samples also agrees well with that of DMP-PDI in γ-CD aqueous solution. The similar values of ⟨λmaxem⟩ and ⟨τf⟩ between liquid and solid phases suggest that the 1:1 and/or 1:2 inclusion complexes also formed in the solid film. Compared to the case for DMP-PDI, a significantly sharper and blue-shifted distribution of λmaxem (average value of 531 nm) was observed for C8-PDI single-molecules (Figure 3b). Because this feature was similar to that of the sample where the C8-PDI molecules were physisorbed on glass (Figure S5c), they probably bind at the γ-CD/glass interface during spin coating of the sample solution (Figure S5). As depicted in Figure 3d, the ⟨τf⟩ value of C8-PDI (6.5 ns) becomes slightly longer than that of DMP-PDI (5.2 ns), suggesting that the γCD/glass interface provides different environmental parameters (e.g., refractive index, polarity, and rigidity) for C8-PDI. Accordingly, we infer that the C8-PDI molecules do not form the inclusion complex in a γ-CD film. The broad distributions of λmaxem and τf of DMP-PDI suggests that 1:1 and 1:2 inclusion complexes of DMP-PDI−γ-CD have various inclusion modes; there is inhomogeneity in the conformation of the inclusion complexes because of a sufficiently large cavity size of γ-CD for DMP-PDI.5,27

was not observed when the concentration of α-CD was increased, instead of γ-CD. This indicates that the cavity size of α-CD is not sufficient for producing the inclusion complex. For the C8-PDI dye, fluorescence enhancement was not observed upon the γ-CD addition, indicating no complex formation of C8-PDI with γ-CD in water. A small blue shift (+4 nm) in the fluorescence spectrum from that of free DMP-PDI in water suggests that complexation of DMP-PDI with γ-CD affords only partial protection to the dye, with the dye being largely solvent-accessible (i.e., imperfect solvent shielding). In this supramolecular complex, therefore, the 2,6-dimethylphenyl groups and dicarboxylicimide moieties at the both ends of DMP-PDI are probably docked inside the γ-CD cavity and the π-conjugated perylene framework is exposed to solvent, as shown in Figure 2b. The formation of a 1:2 DMP-PDI−γ-CD complex at higher γ-CD concentrations (>1 mM) is demonstrated by analysis of the Benesi−Hildebrand plots shown in Figure S2. The association constants were determined to be 294 M−1 for the 1:1 complex and 2.1 × 104 M−2 for the 1:2 complex; therefore, the formation ratio between the 1:1 and 1:2 complexes is 29:71 in aqueous solution. This result ensures that most of DMP-PDI molecules exist as the 1:1 or 1:2 complexes in a γ-CD film, though it is difficult to estimate their relative abundance in the solid film. As seen in Table 1, the fluorescence lifetime of DMP-PDI is not so sensitive to the complexation (i.e., a slight increment from 4.0 to 4.6 ns). Therefore, it appears that the fluorescence lifetime cannot serve as a useful parameter to distinguish encapsulated and nonencapsulated DMP-PDI in a γ-CD film. D

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The Journal of Physical Chemistry A Parts a−c of Figure 4 show typical fluorescence intensity, polarization, and λmaxem time traces, respectively, obtained for a

and the average value is 5.2 ns (Table 1), slightly longer than the fluorescence lifetimes of DMP-PDI in water (4.0 ns) and the 1:2 DMP-PDI−γ-CD complex in aqueous solution (4.6 ns). No fluorescence quenching upon complexation indicates that the underlying process of blinking is quite rare event. 3.3. Blinking Statistics. To understand the underlying photophysics of blinking, the cCDFs of the on-time and offtime durations were obtained using the histogram method. Our recent SMFS study on the DMP-PDI/PMMA system demonstrated that the on-time/off-time distributions obtained at a bin time larger than 10 ms do not comprise the contribution of ISC in DMP-PDI (i.e., triplet blinking).16 Thus, we hereafter analyze the 10 ms bin-time distributions, which provide an accurate analysis of the underlying process causing fluorescence intermittency. Parts a and b of Figure 5a and b exemplify the singlemolecule cCDFs of on-time and off-time, respectively, together

Figure 4. Typical time evolutions of (a) fluorescence intensity, (b) polarization, (c) wavelengths of emission maximum (λmaxem), obtained from the fluorescence spectra, one of which is shown in (c) as an inset, and (d) the intensity histogram. The data was obtained using a 488 nm cw-excitation laser.

DMP-PDI−γ-CD complex embedded in a γ-CD solid thin film. The intensity time trace exhibits frequent on−off blinking events over a wide temporal range (tens of milliseconds to as long as tens of seconds). Similar frequent blinking events were also observed for a large number of the DMP-PDI−γ-CD complexes examined (58% of 263 molecules). In contrast, such species were significantly reduced in C8-PDI (17% of 280 molecules), which does not form an inclusion complex in a γCD film, as mentioned before. Therefore, formation of the inclusion complex (i.e., the penetration of the carbonyl groups of PDI into the γ-CD cavity) may correlate with the frequency of the blinking events. However, the abundance of the DMPPDI−γ-CD complex showing frequent blinking events is relatively low (i.e., 58%), possibly suggesting the existence of nonencapsulated DMP-PDI molecules in the film. Before and after each off-time event in Figure 4a, the polarization values and shapes of the fluorescence spectra remained almost intact. The fluorescence spectra closely resemble the ensemble spectra of DMP-PDI in γ-CD/water, indicating that the fluorescence signal is indeed attributable to an immobile DMP-PDI−γ-CD single complex. Remarkably, the frequency of on−off blinking does not change regardless of whether the samples were annealed, whereas the value of ⟨λmaxem⟩ for nonannealed samples is red-shifted by 7 nm compared to values of the annealed samples (Figure S3). This result indicates that residual water molecules do not participate in the underlying photophysics of blinking; therefore, the blinking is probably caused by the reaction between a DMPPDI guest and a γ-CD host in the inclusion complex. The fluorescence lifetimes of single DMP-PDI−γ-CD complexes in the γ-CD film are distributed in the range 2−10 ns (Figure 3c)

Figure 5. Single-molecule cCDFs of (a) on-time and (b) off-time, fitted to single-exponential (solid lines), log-normal (dashed lines), and Weibull (dotted lines) functions. Note that the fitting curves of single-exponential and Weibull functions are completely overlapped in panel a.

with the fitting curves obtained from MLE-KS analysis. This entire part of the curve was fit well to a single exponential function of the form exp(−ton/off/τon/off) with τon = 0.70 s (p = 0.99) for on-time and τoff = 1.37 s (p = 1.0) for off-time. Because the CDF of the Weibull distribution with A = 1 coincides with that of the single exponential distribution, their fitting curves are completely overlapped in Figure 5a. Seventyfour percent of the on-time cCDFs (113/152 molecules) and 47% of the off-time cCDFs (72/152 molecules) were best reproduced by a single-exponential function, whereas the cCDFs of the remaining molecules were reproduced by nonexponential functions, such as Weibull and/or log-normal functions (Figure S6). Note that when the Weibull or lognormal function best reproduced the data, the p-values of the E

DOI: 10.1021/acs.jpca.6b11353 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Weibull and log-normal functions were almost comparable within the accuracy of the p-value. Due to the limited number of blinking events in single-molecule data (typically 20−100 events), the accuracy of the p-value is rather low (i.e., 0.05− 0.1); thus, we cannot determine which function is the best model function. The distributions of τon and τoff obtained by the fittings of data from 152 single molecules are presented in Figure 6, and their average values are given in Table 2. The

absorption occurs under excitation by 488 nm laser light (2.54 eV) owing to its large overlap with the S0 → S1 absorption.17 Hence, formation of the long-lived off-state was found to occur from the higher excited triplet Tn states in DMP-PDI. Because the intrinsically very small S1 → T1 ISC yield of DMP-PDI (∼10−4) significantly limits the formation of the long-lived offstate, the fluorescence (S1) lifetime of DMP-PDI is not shortened in γ-CD/water (4.6 ns) or a γ-CD film (5.2 ns), compared to that of DMP-PDI in water (4.0 ns). Accordingly, we consider that the underlying process in a γ-CD film also takes place from the Tn states of DMP-PDI, whereas the photoinduced reaction responsible for blinking cannot be immediately assigned to charge transfer between DMP-PDI and γ-CD.

Figure 6. Histograms of (a) on-time and (b) off-time obtained from 152 DMP-PDI molecules. The mean values (assuming Poisson distributions) are 0.24 and 3.7 s, respectively.

Figure 7. Proposed photophysical kinetic scheme of DMP-PDI in a γCD solid film. The S0−T1 transition energy was taken from ref 30. The vertical transition energies of T14−T17 were obtained from the TDDFT calculation. The RP-state energy was simply estimated by subtracting the sum of the total energies of DMP-PDI and γ-CD from the sum of total energies of the HAT product radicals of DMP-PDI and γ-CD, which were obtained at the B3LYP/6-31G(d,p) level (see Table S1).

single exponential kinetics of a large number of single DMPPDI−γ-CD complexes examined indicates that the rate constant for the underlying process does not vary with time and occurs at a constant reaction distance. Conversely, the nonexponential kinetics (i.e., 26% for on-time and 53% for offtime) is presumably due to the fluctuation in reaction distance during measurements. For C8-PDI, the numbers of blinking events in single-molecule data (N1 < 20) were not enough to conduct the analysis. Instead, the ensemble cCDFs of on-time and off-time were analyzed, but none of the model functions reproduce the distributions (Figure S7).

Assuming the kinetic scheme shown in Figure 7, the formation rate constant of the off-state (koff) is the reciprocal of the average on-time (τon): 1 koff = = 1k 01ΦISC3k1nτTΦoff τon (8)

4. DISCUSSION According to past SMFS studies on PDI derivatives in polymer matrixes,16,17,28,29 the long off-time periods of the second order in blinking arise by a charge transfer process between PDI and its host matrix. As reported for a PDI derivative, the T1 → Tn

where 1k01 and 3k1n stand for the excitation rates from S0 to S1 and from T1 to Tn, respectively. Φoff is the formation yield of the long-lived off-state produced from the Tn states. The 1k01 and 3k1n values at the excitation wavelength of λ = 488 nm were calculated as follows:

Table 2. Ensemble-Averaged ISC Yield, Triplet Lifetime, On-Time, Off-Time, and the Formation Yield of Long-Lived Off-State of Single DMP-PDI Molecules Embedded in γ-CD Film at Room Temperature (Determined by SMFS under Continuous Wave (cw) Excitation at 488 nm) DMP-PDI/γ-CD

ΦISC

τT/μs

⟨τon⟩/s

⟨τoff⟩/s

Φoff

1.1 × 10−4 a

120a

0.24 (152)b 1.33a

3.7 (152)b 61.8a

1.9 × 10−3 c (152)b 1.5 × 10−4 a

DMP-PDI/PMMA a

Taken from ref 16. bNumbers in parentheses indicate the number of molecules yielding an average value. cObtained using eq 8. F

DOI: 10.1021/acs.jpca.6b11353 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Table 3. Calculated Vertical Transition Energies to the Excited Triplet States of PDI with Their Contributing Excitations (%), Associated Wavelengths, and Characters energy a

b

k

transition

1 14

H(π) → L(π*) H−13(n) → L(π*) (65%) H−14(n) → L+1(π*) (18%) H−13(n) → L+1(π*) (18%) H−14(n) → L(π*) (65%) H(π) → L(π*)+1 (55%) H−9(π) → L(π*) (44%) H−12(π) → L(π*)+1 (43%) H(π) → L+2(π*) (50%)

15 16 17

exp

character

eV

nm

eV

π−π* n−π*

1.24 3.41

998 364

1.21c

n−π*

3.42

363

π−π*

3.46

358

∼3.59d

π−π*

3.57

347

∼3.59d

a

k = number of excited triplet state according to the TD-DFT calculations: TD-B3LYP/6-31G(d,p)//B3LYP/6-31G(d,p). bH = highest occupied molecular orbital; L = lowest unoccupied molecular orbital. Symbols in parentheses indicate orbital characters. All the associated molecular orbitals shown in Figure S8. cValue taken from ref 30. dValue estimated from refs 17 and 30. 1/3

k ij =

ln(10)ελPex NAhc /λ

T15, which are very closely located to the T16(π, π*) and T17(π, π*) states. The vertical transition energies from S0 to T16(π, π*) and to T17(π, π*) are 3.46 and 3.57 eV, respectively, which show excellent agreement with the sum of the experimental S0− T1 and T1−Tn transition energies (i.e., 3.59 eV).17,30 The energy proximity between the π, π* and n, π* states (