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Tracing Single Electrons in a Disordered Polymer Film at Room Temperature Kevin Wilma, Abey Issac, Zhijian Chen, Frank Würthner, Richard Hildner, and Jürgen Köhler J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b00446 • Publication Date (Web): 01 Apr 2016 Downloaded from http://pubs.acs.org on April 2, 2016

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The Journal of Physical Chemistry Letters

Tracing Single Electrons in a Disordered Polymer Film at Room Temperature ⊥

⊥

Kevin Wilmaa, , Abey Issaca,†, , Zhijian Chenb,‡, Frank Würthnerb, Richard Hildnera, and Jürgen Köhlera,*

a

Experimental Physics IV and Bayreuth Institute for Macromolecular Research (BIMF), University of Bayreuth, 95440 Bayreuth, Germany b Institut für Organische Chemie and Center for Nanosystems Chemistry, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany

*

Corresponding authors: [email protected]

⊥

†

these authors contributed equally to this work

Current address: Department of Physics, Sultan Qaboos University 123 Muscat (Oman)

‡

Current address: School of Chemical Engineering and Technology, and Collaborative Innovation Center of Chemical Science and Chemical Engineering (Tianjin) Tianjin University 300072 Tianjin (China)

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K. Wilma et al. Tracing single electrons in a polymer film.

Abstract The transport of charges lies at the heart of essentially all modern (opto-) electronic devices. Although inorganic semiconductors built the basis for current technologies, organic materials have become increasingly important in recent years. However, organic matter is often highly disordered, which directly impacts on the charge carrier dynamics. To understand, and optimize device performance, detailed knowledge of the transport mechanisms of charge carriers in disordered matter is therefore of crucial importance. Here we report on the observation of the motion of single electrons within a disordered polymer film at room temperature, using single organic chromophores as probe molecules. The migration of a single electron gives rise to a varying electric field in its vicinity, which is registered via a shift of the emission spectra (Stark shift) of a chromophore. The spectral shifts allow us to determine the electron mobility, and reveal for each nanoenvironment a distinct number of different possible electron transfer pathways within the rugged energy landscape of the disordered polymer matrix.

TOC Graphic

Key Words Single Molecule Spectroscopy, Electron Transport, Rugged Energy Landscape, Single Electron Mobility, Disordered Organic Matter

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Manuscript Text An important prerequisite for exploiting organic matter for optoelectronic applications is to develop a basic understanding of the transport mechanisms of charge carriers in materials that are commonly considered as disordered. In contrast to classical semiconductors or metals most organic systems like semiconducting polymers are often non-crystalline. When moving through the material, the electrons experience a rather rugged energy landscape, which refers to the potential energy hypersurface featuring a large number of minima, maxima and saddle points 1,2. To reveal the key parameters that determine the charge transport efficiency in such materials it is of crucial interest to follow the transport pathway of a single electron through such a potential. Unfortunately this is impossible in conventional experiments conducted on ensembles of electrons, because those provide only averaged information and details about the individual pathways are lost. The Orrit group demonstrated that (ensembles of) electrons can be traced at cryogenic temperatures in anthracene crystals doped with dibenzoterrylene molecules by exploiting the sensitivity of these probe molecules to the presence of close-by charges

3,4

. The trapping and

detrapping of charges was monitored by the spectral shift (Stark shift) of the electronic absorptions of the probe molecules, which is induced by the varying electric field of moving electrons in its local nanoenvironment. Here we extend this approach in a proof-of-principle experiment to study the transport of a single electron in a non-ordered material at room temperature. We use perylene bisimide (PBI) molecules as probe molecules that are embedded in the disordered host material polystyrene (PS). This choice is motivated as follows: PBI derivatives are known as strong emitters

5–7

, which

allows to record photoluminescence (PL) spectra from individual molecules with sufficient signalto-noise ratio within some ten milliseconds. Moreover PBIs form stable radical anions

8,9

by

capture of an electron from the host. PS represents an electrically insulating material, hence it slows down the mobility of the electrons to a time scale such that their migration becomes experimentally accessible by single-molecule spectroscopy. To identify events where a single electron approaches a single PBI molecule we exploit the phenomenon of fluorescence intermittency or blinking. Blinking has become a hallmark of single particle detection

10–15

and refers to a random, reversible switching of the photoluminescence

intensity between emitting (on) and non-emitting (off) periods

16


. For organic dyes it was found


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that the reversible formation of a radical, e.g. by capture of one electron from the host, represents the dominant mechanism for blinking

17

. Hence, we search for those blinking events that are

accompanied by a change of the spectral position of the PL as depicted schematically in Fig. 1, because these can be associated with the movement of a single electron towards the probe molecule. We study two PBI derivatives in the following referred to as PBI 1 and PBI 2, see Fig. S.1, Supporting Information (SI), embedded in PS. To record blinking events and at the same time spectral shifts induced by the electric field of an approaching electron, we measure typically 2000 PL spectra from each single PBI molecule with a short exposure time of 30 ms. The total PL intensity trajectory is retrieved from such data by spectral integration of each PL spectrum, and the spectral shifts as a function of time are obtained by fitting a Gaussian function to the purely electronic transition, which yields the energy of the peak intensity of each PL spectrum νpeak (see methods, SI). A representative PL intensity trajectory of a single PBI 1 molecule is shown in Fig. 2(a) (top). A pronounced blinking behaviour, i.e. a change of the PL intensity between a high level (on state) and a low level (off state), is clearly observed. During the on state the PL intensity varies between several levels (e.g. at 22 s and 27 s), which is caused by matrix-induced changes of the absorption cross-section and/or the PL quantum efficiency 18. Finally, this trajectory is terminated after about 31 s by an irreversible photobleaching event, that results in a charged photoproduct

19

. The

corresponding trajectory of the peak emission energy, shown in Fig. 2(a) (bottom), is essentially constant. Yet, the striking observation is that immediately before photobleaching ν peak is shifted by about 1000 cm-1 to the blue, i.e. to higher energies, as shown in Fig. 2(b). A second example recorded from a different PBI 1 molecule, Fig. 2(c), (d), features a blinking event that is accompanied by a spectral shift of ~ 160 cm-1 at about 42.5 s. Interestingly, this spectral shift is reversible when the molecule returns to the high-intensity level and the on state is restored, see Fig. 2(d). At the end of the off period both the fluorescence intensity and the peak emission energy are shifted back to the same level/spectral position as observed prior to the blinking event. Since variations of electronic transition energies may also be caused by conformational variations of the surrounding PS host 20 or of the phenoxy-groups at the bay positions of PBI 1 21–24 as well as by twisting of the perylene core

25

, we performed two control experiments. First, for


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about 50 % of all investigated molecules we recorded simultaneously with the PL spectra also the fluorescence lifetime (see SI, Fig. S.2 for an example). However, since the lifetime did not change while the emission spectra feature a shift we can exclude both twisting of the perylene core and substantial variations of the local PS matrix as origin for the spectral shifts immediately before or after a blinking event. Second, we used PBI 2 as probe molecule that lacks these substituents at the bay positions, cf. Fig. S.1, SI. An example for the variation of the PL intensity as well as the spectral peak shift in a PBI 2 molecule as a function of time is provided in Fig. S.3 in the SI. For PBI 2 we found similar spectral shifts associated with blinking events as for PBI 1, which excludes conformational fluctuations of the PBI substituents as origin for the observed spectral shifts. In total we were able to identify 25 (27) blue (red) shifts in the trajectories of 46 PBI 1 molecules, and 11 (14) blue (red) shifts for 20 PBI 2 molecules. Since these spectral shifts occur immediately before (or after) a blinking event, we associate these with the capture (release) of an electron from (to) the surrounding polystyrene matrix (see SI, section 5 for a justification). In other words, we ascribe these spectral shifts to an electric field effect (Stark effect) that is induced by the electric field of a moving electron in the vicinity of the probe molecule 26,27. The origin of these “free” electrons in polystyrene is probably related to the synthesis and purification process

28

, see also SI (section 5). In a disordered

polymeric host an electron experiences a rugged energy landscape rather than a smooth potential as for example in crystalline environments. Accordingly, the electron has to cross over and/or tunnel through many barriers that feature a wide distribution of widths and depths, see Fig. 1. This results in a rather slow, stepwise change of the spatial position of the electron, which can be monitored via a stepwise change of the transition energy of the chromophore. For both types of PBI derivatives we find concordantly that about 25% of the blinking events are accompanied by a shift of the spectral peak position. The absence of spectral shifts for the remaining blinking and bleaching events may be explained by i) blinking due to a photochemical reaction with oxygen 29,30, ii) spectral shifts that occur on timescales too fast to be resolved experimentally, and iii) the fact that PBI is a centrosymmetric molecule that a priori does not possess a permanent electric dipole moment. Hence, observing a Stark shift is restricted to molecules with reduced symmetry due to embedding in PS, which is found for ca. 25 % of all investigated PBIs. Such symmetry breaking was observed previously for PBI derivatives 31,32, giving rise to a difference between the permanent electric dipole moments in the electronic groundACS Paragon Plus 5 Environment


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state and the first electronically excited-state of up to ∆µ = 3 Debye

32

. Since the mutual

orientation of (the change of) the permanent dipole moment and the electric field induced by the approaching electron are random, both the magnitude and the sign of the observed Stark shift vary statistically, as demonstrated by the observation of roughly an equal number of blue and red shifts in our data. Our data allow gaining insights into charge carrier pathways on the nanoscale in disordered materials. From the maximum spectral peak shift ∆ν max we can determine the minimum distance

rmin between the electron and the probe molecule immediately before a blinking event occurs. Generally, a chromophore at a distance r from an electron is exposed to an electric field

E=

qe , where qe denotes the elementary charge, and εrε0 the dielectric constant of the 4πεr ε 0r 2

host material. For simplicity we restrict ourselves to a linear Stark effect. Then the electronic transition energy of the chromophore is shifted by ∆ν =

∆µ⋅ f⋅ E , where f refers to the dielectric hc

screening, h to Planck’s constant, and c to the speed of light. For the relation between the observed spectral shift ∆ν and the distance r between the electron and the center of mass of the probe molecule this yields

r=

∆µf qe . 4πεr ε 0hc∆ν

(1)

Replacing ∆ν by the maximum spectral shift ∆ν max in (1), we find rmin . For a quantitative analysis, we fitted the observed shifts of the spectral peak position νpeak with an exponential function νpeak (t ) = ν0 + νA ⋅ e

±

(t −t 0 ) τ

. We note that the choice of an exponential function for the

fitting was purely for pragmatic reasons, other time dependencies, such as power laws, would of course be consistent with the data points as well. However, the exponential function allows us to extract several parameters in a simple way: The characteristic time constant τ of the exponential provides a measure for the time scale of the electron to approach/leave the probe molecule. ν0 (t0) denotes a spectral (temporal) offset and νA is the amplitude of the exponential part. The + (-) sign applies for a spectral blue (red) shift. The maximum spectral shift ∆νmax = νmax − ν0 is then obtained as the magnitude of the difference between the initial spectral peak position ν0 and the experimentally observed peak position immediately prior to or after the off period νmax , see also ACS Paragon Plus 6 Environment

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Fig. 2(b) bottom. For the two examples in Fig. 2 the results of the fits are summarized in Table 1. The distributions of ∆ν max for 52 (25) spectral shifts of PBI 1 (PBI 2) are presented in Fig. 3 (a), (b) both featuring a pronounced maximum at 75 cm-1. Nevertheless, for PBI 2 the distribution appears narrower with respect to that of PBI 1. Using eq. (1), εr = 2.5 and f = 0.6 for PS

33

,

distributions of rmin (see Fig. 3(c), (d)) for both PBI derivatives are calculated from the corresponding distributions of ∆ν max . We find that rmin is widely spread between 0.4 and 2.3 nm for PBI 1, and between 0.7 and 2.2 nm for PBI 2, indicating the existence of many different electron transfer pathways within the disordered polystyrene host. The mean value for both distributions of rmin is 1.4 nm, which represents an average over many charge transfer pathways through the host matrix. Additionally we obtain information about the dynamics of the transfer process from each fit of the peak emission trajectory. The distributions of the characteristic time constants τ for PBI 1 and PBI 2 are shown in Fig. 3(c), (f). Both distributions of τ have a pronounced maximum at 75 ms. Interestingly, we find that for each individual probe molecule the characteristics of the spectral shifts ( ∆ν max , τ and rmin ) are unique suggesting a specific charge transfer pathway towards/away from each PBI molecule within its particular nanoenvironment. This is demonstrated by the fit parameters obtained for the second molecule (Fig. 2(d)). The extracted values for ∆ν max , τ and rmin for the blue shift prior to the blinking event and the red shift afterwards agree within experimental accuracy (see Tab. 1). In the SI (see Fig. S.4) we provide an example where two events that are separated by about 8 s in time feature very similar values for the above mentioned parameters despite the rich blinking dynamics observed during this time interval. This is another strong indication for the existence of specific electron transfer pathways with well-defined spatial and temporal characteristics. An important parameter to characterize these preferential pathways is the electron mobility. If we postulate a three dimensional diffusion process for the migration of electrons in polystyrene, we can associate the spatial separation between the electron and the probe molecule with the mean square displacement (∆r) = 6Dτlag . Here D denotes the diffusion coefficient and 2

τ lag the typical time constant of the diffusion process. The diffusion coefficient is connected with the charge carrier mobility ξ through the Einstein-Smoluchowski equation ACS Paragon Plus 7 Environment

34

ξ=

D qe . Here kB kBT


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denotes the Boltzmann constant and T the temperature. Calculating (∆r)2 for two distinct spectral shifts from (∆r ) =  rmin  2

∆µ f q e  1 1 − r 1  = − e  4πε r ε 0 hc  ∆ν max ∆ν 1 e  2

νmax divided by 2.718, see Fig. 2 (b), finally yields ξ =

2

  , where ∆ν corresponds to 1e  

2 (∆r ) q e

6τlagk B T

for the charge carrier mobility.

Using a value of 3 Debye for ∆µ, and associating the measured time constants τ with the lag time

τlag we obtain the distributions for the charge carrier mobility displayed in Fig. 3 (g), (h) for both PBI derivatives. The mobility is in the order of 10-12 cm2/Vs and independent of the type of the probe molecule. This very small electron mobility is characteristic for an insulating material and testifies that we indeed determine a property of the polystyrene host material, i.e. the migration of a single electron through the host. The wide distributions of both the electron mobility and minimum distances demonstrate that distinctly different electron transfer pathways exist within the disordered polymer. We have performed experiments using an electrically insulating material as matrix in order to slow down the electron transport processes to a timescale that is experimentally accessible by single-molecule spectroscopy. Yet, increasing the time resolution

35

may allow to apply our

approach also for studying charge transport in technologically more relevant (disordered) organic semiconductor systems, such as films of conjugated polymers. In device applications this material class is characterized by a complex nano- to microstructure that may vary from entirely amorphous to highly crystalline within the same film. Owing to this complexity, a general picture for the charge transport in these organic semiconductors is still not available 36, yet it is required to ultimately improve device performance. Thepresent results may open the possibility to connect e.g. local nanostructure in conjugated polymer films with charge carrier mobility and to reveal the possible charge transfer pathways within those structures.


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Figures

FIG. 1. (a) Sketch of the rugged energy landscape (thick grey line) experienced by an electron (orange dot) in the vicinity of a probe molecule in a disordered polymeric host (thin grey lines). Confocal excitation (green) results in photoluminescence of a single probe molecule (red wavy arrow) (b) An approaching electron gives rise to formation of radical anions of the probe molecule, that leads to a transition from a bright photoluminescent state into a dark state, i.e. a digital 'on' – 'off' behaviour of its photoluminescence intensity (black trace). At the same time the electric field of the electron causes a spectral shift (Stark shift) of the peak emission wavelength (red circles).



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FIG. 2. (a) Top: Fluorescence intensity (black line) of a single PBI 1 molecule as a function of time. Bottom: Simultaneously recorded energy of the peak of the emission (red circles). (b) Expanded view of the time interval from 28.5 s - 33 s of the data presented in a. The grey line corresponds to an exponential fit of the data. For more details see text. (c) Top: Fluorescence intensity (black line) of another single PBI 1 molecule as a function of time. Bottom: Simultaneously recorded energy of the peak of the emission (red circles). (d) Expanded view of the time interval from 40 s - 44 s of the data presented in (c).


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FIG. 3. (a), (b) Distribution of the maximum shift of the peak emission for PBI 1 (a) and PBI 2 (b). The inset in a shows the full range of observed shifts, for a better comparison with the data for PBI 2 the main figure is restricted to a maximum of 700 cm-1. (c), (d) Minimum distances rmin between probe molecule and electron immediately before the blinking events for PBI 1 (c) and PBI 2 (d). (e),(f) Distribution of the time constants from the exponential fit of the spectral shifts for PBI 1 (e) and PBI 2 (f). (g), (h) Distribution of the charge carrier mobility ξ for PBI 1 (g) and PBI 2 (h) in polystyrene.



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Parameter

Molecule 1

Molecule 2

blue shift / capture

blue shift / capture

red shift / release

τ

(0.148 ± 0.025) s

(0.096 ± 0.025) s

(0.098 ± 0.025) s

∆ν max

(1070 ± 15) cm -1

(138 ± 15) cm -1

(160 ± 15) cm -1

∆ν 1

(210 ± 15) cm -1

(30 ± 15) cm -1

(38 ± 15) cm -1

(0.52 ± 0.15) nm

(1.45 ± 0.15) nm

(1.35 ± 0.15) nm

e

rmin

TAB. 1. Parameters extracted from the fit of the data shown in Fig. 2(b), (d). For molecule 2 the left (right) column refers to the data before (after) the blinking event. determined by the temporal and spectral resolution of the experiment.


The accuracy is

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Acknowledgement

A.I. would like to thank the elite study program "Macromolecular Science" in the framework of the "Elite Netzwerk Bayern" for financing his position. K.W., R.H., and J.K. thankfully acknowledge financial support by the Deutsche Forschungsgemeinschaft (GRK1640, HI1508/3). J.K. and F.W. acknowledge financial support by the State of Bavaria for the Collaborative Research Network “Solar Technologies go Hybrid”.

Supporting Information

Experimental details, control experiments, and detailed information about single electrons in polystyrene. This information can be found on the internet at http://pubs.acs.org.



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Page 16 of 19

aPage 17 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31


Intensity

Peak emission energy

b

ACS Paragon Plus Environment

Time

(a.u.)

Norm. intensity

Page 18 of 19

0.2 0.0

peak

16800

(cm-1)

16900

17400

16800 16700 16600

16200 5

10

15

20

25

30

35

40

45

20

25

30

35

Time (s)

0.2 17400

Δ

ACS

16200

max

Δ 1/e Paragon

0

55

60

0.2 0.0 16800

16700 Plus Environment

28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0

Time (s)

50

16900

max

peak

16800

45

0.4

(a.u.)

Norm. intensity

d 0.6

40

Time (s)

(cm-1)

Norm. intensity

(a.u.) (cm-1)

peak

Norm. intensity

peak

0.6 0.2

(a.u.)

1 2 3 4 5 6 b7 8 9 10 11 12 13 14 15 16

c 0.6 The Journal of Physical Chemistry Letters 0.4

1.0

(cm-1)

a

16600

41.0

41.5

42.0

42.5

Time (s)

43.0

43.5

44.0

500

Δ

1000

1500

2000

max

5

200

Δ

max

400 600 ( cm-1 )

Occurrence

d PBI 2

10

PBI 2

5

f

ACS Paragon Plus 0

24

e

PBI 1

0.5 1.0 1.5 2.0 2.5 3.0 rmin (nm)

16 12 8 4

10 8 6 4 Environment 2 0 0.0 0.2 0.4

τ (s)

25 20

0.8

PBI 1

15 10 5

h

PBI 2

0.6

g Occurrence

0

PBI 1

20 Journal of Physical Chemistry Letters

Occurrence

0

10The

Occurrence

PBI 1

4

Occurrence

2 310 48 6 54 62 700 8

8

Occurrence

Occurrence

Occurrence

8 6 4 12

b

c

12

10 Page 19 of 19

Occurrence

a 12

20

PBI 2

15 10 5

0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 -12 ξ (10 cm²/Vs)

Tracing Single Electrons in a Disordered Polymer ... - ACS Publications

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