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Diffusion Assisted Bimolecular Electron Injection to CdS Quantum Dots: Existence of Different Regimes in Time Dependent Sink Term of Collins Kimball Model Aparna Bhowmik, Harveen Kaur, Somnath Koley, Subhra Jana, and Subhadip Ghosh J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11169 • Publication Date (Web): 25 Feb 2016 Downloaded from http://pubs.acs.org on March 1, 2016

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The Journal of Physical Chemistry

Diffusion Assisted Bimolecular Electron Injection to CdS Quantum Dots: Existence of Different Regimes in Time Dependent Sink Term of Collins Kimball Model Aparna Bhowmik,a, ϯ Harveen Kaur,a, ϯ Somnath Koley,a Subhra Janab and Subhadip Ghosha, * a.

School of Chemical Sciences, National Institute of Science Education and Research, Bhubaneswar 751 005, India. S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata, West Bengal 700098, India KEYWORDS: Collins Kimball Model, Bimolecular electron transfer, electron injection in Quantum Dot, Time dependent electron transfer sink, Nonadiabatic electron transfer reaction b.

ABSTRACT: Excited state lifetime and steady state fluorescence of a series of CdS quantum dots (QDs) with different sizes in toluene were quenched by electron donor molecule N-methyl aniline (NMA). Static quenching Collins Kimball (SQCK) diffusion model enabled convincing fittings to the steady-state and time-resolved data using nearly a same set of parameters, only after considering the presence of inherent quencher sites statistically distributed over the quantum dot surface. Electron injection rate shows strong chemical driving force dependency. QD with largest dimension (~5.4 nm) used in this study exhibits a slightly higher chemical driving force (∆G0=0.80 eV) of electron transfer as compared to that (-∆G0=0.79 eV) obtained for the smallest size QD (~3.8 nm). However, such a small change in driving force causes nearly ~3 times acceleration of the ET rate coefficient (k0 = 8.30×109 M-1S-1) within the larger size QD as compared to that (k0 = 2.74×109 M-1S-1) observed in smaller size QD. The time evolution of the sink term obtained from the Collins Kimball fitting of ET kinetics shows different regimes of the kinetics (static and non-stationary).

■ INTRODUCTION

Electron transfer is a fundamental process in biology and chemistry.1-16 Photo induced electron transfer (ET) in solution is of convenient category to study diffusion assisted bimolecular reaction in solution phase for a number of reasons: (1) reaction can be photo initiated, (2) relatively simple excited state process and (3) temporal profile of fluorescence intensity can be exploited as a probe to study the kinetics.3-6 A diffusion controlled bimolecular ET process involves three distinct quenching regimes:3-6 (1) at early time of the ET, kinetics is dominated by the reactant pairs those are already standing at proximal distance; no diffusion is required for ET to take place in this regime. This regime is called “static”. (2) At a relatively longer time, ET occurs between the reactant pairs residing at a little longer separation than the encounter distance and requires diffusion of reactant molecules to attain the encounter distance before ET to take place. This non-stationary state continues as long as equilibrium is established between the rates at which reactant pairs are disappearing through ET and the diffusion rate at which the encounter complexes are being formed.3-4, 7 (3) After sufficiently long time, reaction occurs between the reactant pairs those are separated by a long distance. In this regime ET is stationary in nature and maintaining an equilibrium

with the diffusion rate.3-4,7 The ET in this regime is controlled by the mass transportation rate rather than a kinetically controlled process. Therefore, a complete fitting function of a bimolecular ET reaction should consider all these three regimes. In a seminal work, Fleming and his coworkers studied the ET kinetics of rhodamine B-ferrocyanide reactant couple in solution phase.4 They found Collins Kimball model is unable to reconcile the time resolved and steady state data using a same set of fitting parameters. However when they added a position dependent ET rate coefficient to the Collins Kimball model they obtained a fast ET time of 27.5 ps.3 The sink term in their study considered all the three regimes of a position dependent bimolecular ET process. Following the work by Fleming and his co-workers, Shannon et al tested and articulated SQCK model to explain a bimolecular ET process from donors aniline (AN) and N,N-dimethylaniline (DMA) to the excited state coumarin-1 (C1) molecule as an acceptor.4 They observed DMA experiences a higher ET rate (kET ~15.2 ×109 M-1S-1) as compared to AN (kET~ 8.77×109 M-1S-1). Their observation is incongruent to the fact that latter (AN-C1 couple) has a lower activation barrier in the ET reaction. However, a detailed analysis showed a faster ET rate in DMA-C1 as compared to AN-C1 is may be due to a ~2 times higher value of electron coupling matrix parameter

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(‫׀‬v‫ )׀‬in the former couple.4 In a remarkable work by Tachiya and his co-workers studied fluorescence quenching reaction using different donor-acceptor pairs in tetrahydrofuran (THF) within a framework of Collins-Kimball approximations. They observed reaction radius R increases with increasing chemical driving force of their ET reaction.5 Most of the experimental verifications of Collins-Kimball model including the above studies show a clear ambiguity between the theoretical predictions with experimental observations. The major drawback of classic Collins Kimball model is its intrinsic assumption of a single reaction distance; reaction occurs at a single donor-toacceptor distance and rate falls to zero at any other separations. This is clearly an unrealistic assumption. Therefore without incorporating sink term describing a position dependent ET rate [k(r)] into the diffusion equation, classic Collins Kimball model alone can’t take the wealth of a distance dependent nonadiabatic ET kinetics taking place in most of the real systems.2--5 Burshtein recently overcame this unrealistic boundary condition of Collins Kimball model by developing Differential Encounter Theory (DET), which has ability of using a position dependent ET rate coefficient within the diffusion equaton.6 The numerical solution of the encounter theory using a set of an appropriate physical parameters within a framework of requisite distance dependence provides the exert form of a bimolecular ET kinetics taking place in solution either at a nonadiabatic or an adiabatic limit. In a recent work, Vauthey and his coworkers studied ET in imidazolium-based roomtemperature ionic liquids (RTIL) as medium using differential encounter theory (DET). DET, using the inter-reactant distance and reactant pair distribution function as fitting parameters, successfully reproduces the “static”, “nonstationary” and “stationary” regimes of the kinetics of ET from DMA to 3-cyanoperylene in RTIL.7 Recently Maroncelli and his co-workers studied electron transfer reaction between electron donor DMA to the excited state electron acceptor molecule 9,10-dicyanoanthracene in various ionic liquid solvents. They compared their results in ionic liquids with conventional solvents.8 Data were analysed using a model similar to DET, that comprises of a time-dependent reaction rate coefficient k(t), pair distribution function ρ(r,t) and w(r), accounting the potential of mean force between donor and acceptor. A nice congruent between the experimental data and fitting model was observed and a strong distance dependence of ET was another remarkable observation in this study.8 In a seminal work by Kumbhakar et al showed a bimolecular electron transfer from DMA to

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different coumarin derivatives in a highly viscous ionic liquid medium is better appreciated by using a two-dimensional ET description (instead of conventional Marcus ET model used in the recent studies). Combining an extremely slow relaxing solvent coordinate with a fast intranuclear coordinate using Sumi-Marcus two dimensional ET model, they observed appearance of Marcus inverted region at an exergonicity of -0.5 eV.9 They conclusively ruled out the possibility of any interference from the diffusion process into the ET kinetics they observed by obtaining the time-resolved components from ultrafast (~1-10 ps) region only. In the ultrafast region diffusion of reactant molecules is negligible. All the studies discussed above have invested significant amount of efforts to distinguish the role of diffusing in a bimolecular ET process which is found to be much challenging in most of the cases especially when someone tries to extract the ET component from overall kinetics. However, in a rather simpler approach using transient absorption spectroscopy, Sen and his co-workers showed ET kinetics obtained by monitoring of a transient component (appears due to ET process) is free from any diffusion characteristic of the medium.10 Demanding of clean energy requires developing of next generation semiconductor based devices, where QDs are used as building blocks.1, 14-16 Foremost use of QD in devices is as a light absorbing element.1 After absorbing light, exciton is generated within the QD*. Consequently the charge carriers on QD* is separated through an ultrafast electron transfer from QD* to the adjacent composite layer. An ideal composite layer strongly opposes the recombination of charge carriers through back electron transfer, by fast removal of oppositely charged carriers and collected to the respective electrodes. Recent studies have shown QD not only be used as an electron donor, also can act as a potential electron acceptor in many cases like light emitting diodes (LEDs).1 The details understanding of the ET process, where QD works as an electron acceptor will help us of rational designing of the next generation devices. In this study we explore bimolecular ET process from an organic dye to various size CdS QDs. Using an advanced level fitting model we observed bimolecular ET process in solution is associated with different regimes. A classic SternVolmer (S-V) fitting only considers the stationary regime of the ET kinetics assuming electron transfer rate is strictly a time independent parameter which is not true in our case.

2


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■ RESULTS AND DISCUSSION

Dimensions of CdS QDs were determined from the transmission electron microscopy (TEM) and fluorescence correlation spectroscopy (FCS) measurements which were found to be ~3.8 nm, ~4.5 nm and ~5.4 nm for CdS440, CdS460 and CdS480, respectively (see experimental section and Figures S1 and S2 in SI). NMA and oleic acid capped QD both are hydrophobic in nature. In a hydrophobic medium like toluene both are highly soluble and ET is expected to be collisional in nature. ET from single quantum state NMA (HOMO-level) to the valence band of a photo excited QD* (type II band alignment, Figure 1) causes significant quenching of the steady-state emission and excited state QD lifetime (Figures S3 and S4 in SI). Excitation (λex) at 375 nm used in this study selectively excites only the acceptor molecules (QD) within a QD and NMA mixture. Thus the possibility of ET from LUMO level of NMA to the conductance band of QD is convincingly ruled out. ET is also not possible to an energetically much higher state (-4.7 eV vs. SCE) LUMO of an unexcited NMA from the conductance band of QD*. A second possibility of quenching is elucidated by the probable energy transfer from QD* to NMA, which is not possible here due to the absence of spectral overlapping between the donor’s emission and acceptor’s absorption (Figure 1). Steady-state S-V plot was obtained by plotting the steady-state fluorescence intensity ratios of QD* in the absence (I0) and presence (Ic) of quencher molecule (NMA) as a function of quencher concentration up to 0.147 M (Figure 2). Two striking features are revealed from the S-V plots in Figure 2: (1) the slope of the curve increases with increasing the QD particle size; indicating the overall ET rate increases within the larger size QD. (2) All the three curves in Figure 2 are straight at low quencher concentrations, however, significantly bent with an upward curvature at high NMA concentrations. Overall curvature nature is more prominent within the larger size particles (i.e., CdS480); indicating the mixing of quasi-static states (originated at the initial time of the kinetics and higher quencher concentrations) with the transient and stationary states of ET.7 A classical S-V equation only considers the stationary regime of ET kinetics assuming a linear dependency of fluorescence quenching of QD* with increasing the quencher concentration. Thus a special treatment of SQCK diffusion model is employed in this study that considers all the three distinct regimes of a bimolecular ET process.2-4

Figure 1. (a) Absorption spectra of NMA (black solid line), CdS440 (3.8 nm, blue dotted line), CdS460 (4.5 nm, green dotted line) and CdS480 (5.4 nm, red dotted line). Corresponding emission spectra of the QDs are shown in solid lines (same colours with absorption spectra). NMA is non fluorescent. (b) Energy band alignment diagram of QD-NMA pairs used in this study (see table S1 and SI).

A valid fitting model should fit both the steady-state and time-resolved data using a same set of fitting parameters, provided no ultrafast component is overlooked in time-resolved study. The functional form of time resolved fluorescence intensity [I(t)] of QD* in the presence of NMA is obtained from the time integration of differential equation of the survival probability [∫dS(t)/dt = ∫{-1/τ0 - ck(t)}S(t)] of QD* in presence of NMA as,3-4, 7 t

I ( t ) = I (0) exp( − t / τ 0 − c ∫ k ( t ') dt ')

(1)

0

Where S(t) be the survival probability of QD* when the excited state depopulation of QD* is taking place

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simultaneously by ET as well as natural lifetime decay processes. τ0 is the excited state lifetime of QD in the absence of NMA (natural lifetime). k(t) be the time dependent ET rate coefficient (or sink term), and c is the bulk NMA concentration. Unravelling of the ET kinetics from the overall excited state lifetime decay was strategically made by constructing a survival probability function [Sq(t)] of QD* in the presence of NMA, whose decay describes the ET process only as (Figure 3).3-4

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fluorescence intensity of QD* (IC) in the presence of NMA. Which was used for constructing a fitting equation of steady state S-V plot as follows,3-4

(

)

 1 + R / Dτ 0  I0    = 1 + 4π RDτ 0 k 0   I k + 4π RD + 4π R 2 D / τ 0  C  CK  0

  c + ....  

(4)

The above expression is based on the assumption that ET reaction can takes place only at an encounter distance R and sharply falls to zero at any other separations. This is clearly an unrealistic assumption t that could not explain the upper curvature of the S q (t ) = S (0) exp( − c ∫ k (t ') dt ') = S (t ) / exp( −t / τ 0 ) (2) steady state S-V plot at higher quencher concentration 0 (Figure 2). Equation 4 predicts only a linear The rate coefficient k(t) in the above equation was dependency of QD* fluorescence intensity with the constructed using Collins Kimball boundary quencher concentrations. Therefore, in this work we conditions; assuming the quenching rate of a relaxed this assumption by considering bimolecular bimolecular reaction is proportional to the probability intrinsic ET can take place in other separations (r) that a QD* molecule finds one NMA molecule at a also, as long as r falls within the range a≤ r ≤R. Where distance between R and R+δr (δr→0).2-4 R is the a is the physical contact distance of QD and NMA in reaction radius or encounter distance. The time QD-NMA complex.2-4 Reaction at r>R is purely dependent rate coefficient is constructed using Collins diffusion assisted. At r=a, reaction is kinetically Kimball model as,3-4 controlled and at a< r R) reaction is purely diffusive in nature; Collins Kimball diffusion rate equation (equation 3) could nicely explains this regime. However, considering these two phenomena inadequately fitted our time resolved data. On further modification to equation 7 (and eventually to equation 8), we considered another non-radiative decay channel that can cause excited state depopulation of QD*, and originated from the presence of intrinsic “defect sites” (act as a quencher) statistically distributed over the quantum dot surface.18 This assumption led to a conclusive fitting to both steady-state (Figure 2) and time-resolved data (Figure 3) using a same set of fitting parameters; except a slight variation in R values obtained from steady-state and lifetime fittings (Table 1). Following Tachiya’s formula of Poisson type distribution of the quencher sites, we introduced a depopulation channel in equation 7 that accounts the defect induced quenching process along with ET as,18-

(7)

kD=kCK Above equation, elucidating the excited state depopulation kinetics of QD* in the presence of NMA, providing a theoretical expression of Sq(t) when normalised with the excited state lifetime profile of QD* in absence of quencher as,3-4    τ  t Sq (t ) = I (t) / I(0)exp(− t/ τ 0 ) = exp −cυ 1 − q kSQ (t )  − c∫ kD (t ')dt ' (8)  υ  0  

This equation was used to fit the experimental Sq(t) curves in Figure 3, however, provided inadequate fittings.

19

 t  t   τq  t  I (t) = I(0)exp − − cυ 1− kSQ (t) − c∫ kD (t ')dt ' − m1− exp −  τ υ    0  0  τd 

(9)

Where m is the average number of defect sites per QD and τd is the defect induced quenching time.18 Figure 4 shows the static, non-stationary and stationary regimes of electron transfer rates for all the three QD-NMA pairs using best fitting parameters. The average number of defect sites per QD was found to increase from ~1.05 (CdS440) to ~1.53 (CdS480) as QD size is increased from 3.8 to 5.4 nm (Table S2). This fact rationalizing the descending trend of QDs’ average lifetimes in the absence of NMA from ~5.34 ns to ~4.16 ns as QD size is increased from ~3.8 nm to ~5.4 nm (Tables S1 and S2). More quencher sites in larger dimension QD (CdS480) drives the defect induced quenching to a relatively faster time (τd~1.1 ns) as compared to that (τd ~1.4 ns) obtained in a smaller size QD (CdS440) (Table S2). In this study, we obtained ~3 times faster ET rate (k0 ~8.3×109 M-1S-1) from larger size QD (CdS480) as compared to that (k0 ~2.74×109 M-1S-1) obtained from a smaller size QD (CdS440); nicely correlating with their chemical driving forces (larger QD has slightly higher -∆G value, Table 1). This observation is indicating that our ET kinetics appear in the normal regime of the Marcus nonadiabatic ET model as (after applying Fermi’s golden rule),21-22

Figure 3. Time evolution of experimentally measured survival probability due to ET process only [Sq(t) in equation 2] for (A) CdS440, and (B) CdS480 at various quencher concentrations. Red lines represent the SQCK fittings. Fitted with Equation 9 [kD(t) from Eq. 3 and Eq. 5 for k0 in kD(t)].

Our constructed fitting function (equation 8) essentially considers two fundamentally different ET

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k

E T

  π =   2 h k T λ S B  

1/2

V

2

 ∆ G *  exp  −  k BT  

CdS480-NMA reactant couples; a complete congruent with the sequence of their ET rates. In a recent work by Vauthey and his co-workers have shown that two fluorescent dye molecules with same intrinsic ET rates against a quencher molecule can possibly give two different apparent ET rates when there is a significant difference among the excited-state lifetimes (τ0) of the dye molecules.24 A short-lived dye can survive mostly in static regime where ET rate is high (at initial time of the ET kinetics, Figure 4). Whereas, for a long lived dye ET is mainly controlled by slow mass transportation rate at longer time rather than a fast kinetically controlled process. In our case also similar trend was observed: CdS440 (τ0= 5.34 ns, k0=2.74×109 M-1S-1), CdS460 (τ0= 4.61 ns, k0=4.31×109 M-1S-1) and CdS480 (τ0= 4.16 ns, k0=8.3×109 M-1S-1). However, by studying ET in neat NMA (quencher as solvent) we confirmed that the trend of ET rates (k0) obtained from SQCK fittings is not due to a fudge factor obtained from dissimilar lifetimes among the QD particles. In neat NMA, where excited state lifetime (τqneat, Table 1) of QD* is solely determined by the intrinsic ET rate (diffusion independent), we observed a similar trend of τqneat with static quenching time (τq, Table 1) obtained from SQCK fitting of QD-NMA pair in toluene.25-27 This observation also rules out the possibility of a more local concentration of NMA around a bigger size QD in toluene to become a probable reason of getting higher ET rate as compared to the smaller size QD in toluene. In this study, same ET rate was reproduced from steady state and time resolved fittings of experimental data using a same set of fitting parameters. This can only be possible when no ultrafast ET component is overlooked. ET rates observed from all the three QD-NMA pairs in this study are significantly lower than the diffusion controlled limit (~1.1×1010 M-1S-1) of any bimolecular process in toluene. Therefore, the ET rates reported in this study are truly kinetically controlled rather than a diffusion limited process.

(10)

V in the above equation is representing the electronic coupling parameter between reactant and product states. ∆G* [=(∆G0+λS)2/4λS] and λS are the activation energy of electron transfer and solvent reorganisation energy, respectively. ∆G0 be the equilibrium free energy change between product and reactant states and which was obtained using the recipe provided by Brus.20 A detail of this calculation has been provided in supporting information. We studied the temperature response of ET rates from all the three QDs in toluene using an Arrhenius type plot of Marcus non-adiabatic ET equation (Equation 10). Table 1: SQCK fitting parameters of time resolved [Sq(t)] and steady-state S-V plots of QD-NMA pairs [using equations 6-9 with kD(t) from equation 3 & k0 from equation 5]. ∆G was calculated from ref 20 (see SI). τqneat is the QD* lifetime in neat NMA. Rtr(Rss) is the reaction radius (R) obtained from time-resolved (steady-state) SQCK fitting. Unit of R and a is nm. CdS a

Rtr(Rss) τq(ns) τneatq(ns) k0(M-1S-1) ∆G(eV)

440 2.21 2.23(2.29) 0.70 460 2.56 2.57(2.62) 0.45 480 3.00 3.02(3.06) 0.25

0.53

2.74×109

-0.790

0.45

4.31×10

9

-0.795

8.30×10

9

-0.800

0.37

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A plot of ln(kET√T) as a function of inverse of temperature (K-1) provided a nearly linear curve from all the three QD-NMA pairs (see SI, Table S3 and Figures S5 and S6). From the slope of the fitted line (assuming a linear dependency), we obtained a slightly lesser activation barrier for CdS480 (~6.54 kJ/mole) as compared to CdS460 (~6.73 kJ/mole) or CdS440 (~6.93 kJ/mole) [see SI, Table S3]. This observation nicely correlates with the sequence of their ET rates. Using the relation ∆G*=(∆G0+λS)2/4λS and known values of activation energy (∆G*) and free energy change (∆G0) we also calculated the solvent reorganization energy (λS), which was found to be ~0.44 eV for all the cases. However this value for toluene is much higher than that one can expect from any dielectric solvation model.23 A large value of λS may arises due to an artifact of our analysis that presumes the ET from NMA to the QD is purely nonadiabatic. On further analysis, we also calculated electronic coupling matrix element ‫׀‬v‫ ׀‬from the preexponential factor of Equation 10 and values for ∆G*, λS and kET determined earlier (Table S4). ‫׀‬v‫ ׀‬values were found to be 10.5 cm-1, 12.5 cm-1 and 16.5 cm-1, respectively for CdS440-NMA, CdS460-NMA and

■ SUMMERY The functional form of the sink term [kCK(t)] of SQCK model within a non-adiabatic limit of requisite distance dependence has nicely reproduced the ET kinetics and its regimes from time-resolved and steady-state fittings of experimental data using nearly a same set of fitting parameters. Faster ET kinetics associated with larger size QD as compared to the smaller size QD is elucidated by the lower activation barrier and higher electronic coupling between

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reactant and product states in the bigger size QD. The basic understanding of ET kinetics in semiconductor nanocrystals would help researchers the rational designing of next generation semiconductor based devices. In this regard present work is a significant contribution towards the exploring of better usages of semiconductor nanocrystals as an electron scavenger in optoelectronics devices. It may be noteworthy that the reaction radius (R) is a sensitive fitting parameter in SQCK model.3-5 Even a small difference in R values obtained from the steady state and time resolved data (Table 1) is indicating the SQCK model is to some extent inaccurate and this model may not be regarded as a perfect fitting model for studying a bimolecular ET process.

■ AUTHOR INFORMATION Corresponding Author *Subhadip Ghosh School of Chemical Sciences National Institute of Science Education and Research Bhubaneswar 751 005 (India) E-mail: [email protected]

■ AUTHOR CONTRIBUTIONS ϯ

Both the authors contributed equally.

■ ACKNOWLEDGMENT Subhadip Ghosh thanks Ramanujan fellowship grant (SR/S2/RJN-36/2012), DST, India for the support to carry out this work. AB thanks CSIR for research grant and fellowship.

■ REFERENCES 1. Kamat, P. V. Boosting the Efficiency of Quantum Dot Sensitized Solar Cells through Modulation of Interfacial Charge Transfer. Acc. Chem. Res. 2012, 45, 1906–1915.

2. Litniewski, M.; Gorecki, J. Molecular Dynamics Tests of the Smoluchowski–Collins–Kimball. Phys. Chem. Chem. Phys. 2004, 6, 72-83. 3. Eads, D. D.; Dismer B. G.; Fleming, G. R. A Subpicosecond, Subnanosecond and Steadystate Study of Diffusion Influenced Fluorescence Quenching. J. Chem. Phys. 1990, 93, 1136-1148. 4. Shannon, C. F.; Eads, D. D. Diffusion‐Controlled Electron Transfer Reactions: Subpicosecond Fluorescence Measurements of Coumarin 1 Quenched by Aniline and N, N‐dimethylaniline. J. Chem. Phys. 1995, 103, 5208-5223. 5. Murata, S.; Nishimura, M.; Matsuzaki, S. Y.; Tachiya, M. Transient Effect in Fluorescence Quenching Induced by Electron Transfer. I. Analysis by the Collins Kimball Model of Diffusion-Controlled Reactions. Chem. Phys. Lett. 1994, 219, 200-206. 6. Burshtein, A. I. Non-Markovian Theories of Transfer Reactions in Luminescence and Chemiluminescence and Photo- and Electrochemistry. Adv. Chem. Phys. 2004, 129, 105. 7. Koch, M.; Rosspeintner, A.; Angulo, G.; Vauthey, E. Bimolecular Photoinduced Electron Transfer in Imidazolium-Based Room-Temperature Ionic Liquids is not Faster than in Conventional Solvents. J. Am. Chem. Soc. 2012, 134, 3729-3736.

Figure 4. Time evolution of the rate coefficient of electron transfer from NMA to three different size QDs (obtained from SQCK fittings). The insets show the same plots in log scale (time axis): static (red line) and nonstationary (green line) regimes are clearly visible within the plot.

■ ASSOCIATED CONTENT Supporting Information. Experimental section, calculations of electronic band positions of QDs and NMA, free energy calculations of QD-NMA pairs, TEM images, FCS curves, fluorescence quenching curves (steady state and lifetime) and decay of survival probability functions of QD-NMA pairs at different temperatures. are available in supporting information. “This material is available free of charge via the Internet at http://pubs.acs.org.”

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Diffusion Assisted Bimolecular Electron Injection to ... - ACS Publications

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