Supporting Information for
Blinking statistics correlated with nanoparticle number
Siying Wang,1 Claudia Querner,1 Michael D. Fischbein,1 Lauren Willis,1
Dmitry Novikov2, Catherine H. Crouch3 and Marija Drndic1*
1
Department of Physics and Astronomy, University of Pennsylvania, 209 S 33rd, Philadelphia, PA 19104, USA;
2
Department of Physics, Yale University, New Haven, CT 06520, USA;
3
Department of Physics and Astronomy, Swarthmore College, 500 College Avenue, Swarthmore, PA 19081, USA
*
e-mails: [email protected]
1 Experimental details on nanorods’ synthesis and characterization
CdSe/ZnSe/ZnS core/double shell semiconductor nanorods (NRs) are prepared in a two-step
procedure.
First, CdSe core NRs having a diameter of 5.8 nm and a length of 34 nm are synthesized using a
multiple injection method.[1] In detail, 45.1 mg of cadmium oxide (CdO, Aldrich, 99%) have been
placed with 140.9 mg of decylphosphonic acid (DPA, Alfa Aesar, 99%) and 5.5 g of tri noctylphosphine oxide (TOPO, Aldrich, 90%) under nitrogen atmosphere and were heated to 300°C for
approximately 2 hours until the initially red-brown suspension turned colorless. Independently, a
solution of 563 mg of selenium powder (Se, Aldrich, 99.99%) was dissolved in 7 mL of tri noctylphosphine (TOP, Aldrich, 99%). The TOPSe solution was injected slowly into the Cd-precursor
solution in aliquots of 0.1 mL (5 times, 2 min waiting between each injection), 0.2 mL (5 times, every
3 min), and finally 0.4 mL (10 times, every 5 min). The intial injection temperature was 295°C, which
was gradually reduced via 280°C (during the 0.2 mL injections) to 270°C (for the 0.4 mL injections).
The reaction was stopped after 80 min by removing the heating source and the growth solution was
allowed to cool to 60°C, when 20 mL of methanol were added to precipitate the NRs. After
centrifugation and washing additionally with methanol (3 times), the NRs were dispersed in toluene for
optical characterization (Figure S1a).
The absorption spectrum (USB-2000 spectrometer, Ocean Optics) is characterized by an excitonic
peak at 640 nm. Concentration dependent absorption measurements allowed to determine an
absorption cross-section at 488 nm of 4.22·10-14 cm2.[2] The emission (USB-4000FL spectrometer,
Ocean Optics, excitation: 470 nm LED, 35 µW) of these NRs is centered at 665 nm with a full-width at
half maximum (FWHM) of 38 nm, i.e., this sample exhibits a Stokes shift of 15 nm. Comparing the
area of the emission peak to the one of an aqueous solution of rhodamine 6G adjusted to an identical
optical density at the excition wavelength allows to estimate a fluorescence quantum yield of 0.3%.
These NRs were further characterized by high-resolution transmission electron microscopy (HRTEM, JEOL 2010F) after deposition on holey carbon grids from a dilute solution. From the TEM
images (cf., Figure S1a inset) we determined a NR size of 5.8×34 nm, i.e., the aspect ratio is ~5.9.
1
Figure S1. a) Absorption and emission spectra of CdSe core NRs recorded in toluene. The inset shows a TEM image (the
scale bar is 50 nm) of this sample. b) Absorption and emission spectra of CdSe/ZnSe core/shell NRs (circles, dark blue and
red) and of CdSe/ZnSe/ZnS core/double shell NRs (triangles, light blue and orange). For comparison reasons, the emission
of the core NRs is indicated as dashed line.
Subsequently, the CdSe core NRs were capped with a thin intermediate ZnSe shell and a thicker
ZnS outer shell to prepare the CdSe/ZnSe/ZnS core/double shell system.[3] In particular, 4.4·10-9 mol
of the CdSe core rods have been mixed with 5.0 g of TOPO and 3 g of hexadecylamine (HDA,
Aldrich, 90%). Solutions of 0.08 M TOPSe (6.4 mg Se in 1 mL TOP) and 50 mg of zinc stearate
(ZnSt, Aldrich, 99%) in 1 mL of dioctylamine (DOA, Aldrich, 99%) are prepared and mixed together.
These quantities should correspond to the formation of 1 monolayer (ML) of ZnSe. At 225°C, this
solution is slowly injected over a period of 10 min. The reaction mixture is allowed to stir for another
15 min.
To half to the above reaction mixture, still at 225°C, a total of 7 mg bis-(trimethylsilyl)-sulfur
((TMS)2S, Aldrich, 99%) and 125 mg of ZnSt in 6 mL DOA are injected over a period of 30 min.
These quantities should lead to the growth of 5 ML of ZnS. The reaction mixture is allowed to
continue stirring for 10 min after complete injection and finally to cool. Purification is carried out by
precipitating the sample in methanol.
The absorption and emission spectra of the core/shell(s) systems are summarized in Figure S1b.
The absorption of all three samples is very similar and the main difference consists in a increasing
absorption at higher energies (i.e., at smaller wavelengths) with increasing shell thickness. The width
of the emission peak remains unchanged upon shell growth and is slightly red-shifted (with increasing
shell(s) thickness) compared to the core NRs. The fluorescence quantum yield increases significantly
during the shell growth: from 0.3% for the CdSe core sample to 1.7% for the CdSe/ZnSe core/shell
NRs and 1.6% for the CdSe/ZnSe/ZnScore/double shell NRs. These values are obtained for the
extensively purified samples. One can however note that for samples taken at intermediate stages of
the shell growth, recorded in solutions containing still excess surface ligands such as HDA or DOA,
fluorescence quantum yields of up to 14% for the core/shell NRs and 6.1% in the case of the
core/double shell NRs have been measured.
2
2 Statistical analyses of intensity trajectories
2.1 Background correction and definition of threshold
In contrast to mica, silicon nitride (Si3N4) membrane devices show a slight background
fluorescence signal that is not homogenous throughout the whole substrate. Consequently, in this
study, each fluorescent segment was corrected with respect to a dark segment in its vicinity. Moreover,
the background can evolve slightly over time for very long fluorescence movies. To account for these
changes, we fit the background signal with a fourth-order polynomial that is subtracted from the
fluorescence segment (Figure S2a). To set the threshold level, we previously added the width of the
background noise plus one standard deviation to the minimum of the fluorescence intensity time trace.2
Figure S2b shows the intensity time-trace of an individual NR (corrected according to Figure S2a)
and the different threshold levels that were tested. Here, m dark is the mean, and σ dark is the standard
deviation of the intensity vs. time of a nearby dark region, ∆I dark and min(dark) are the width and the
minimum value of the background signal, and min(intensity) is the minimum value of fluorescence
intensity vs. time.
Table 1 summarizes the blinking parameters for the individual NRs and small clusters presented in
the main paper. In conclusion, all results reported in this paper were determined using a threshold of
m dark + 7σ dark chosen to lie above the signal from the dark regions. Setting the threshold higher or
lower by σdark does not change the on-/off-time probability densities significantly (Table S1).
Figure S2. (a) Background signal with a polynomial fit. (b) Intensity trajectory of an individual NR. Different lines (color)
are the different threshold levels tested.
Table S1. List of blinking parameters of NR clusters from Figures 2,4 for different threshold levels (see also Figure S2).
Threshold
Individual NR (from Figure 2)
lin
α off
log
α off
Individual NR (from Figure 4a)
α on
τ /s
lin
α off
log
α off
Two NRs (from Figure 4b)
α on
τ /s
lin
α off
log
α off
Three NRs (from Figure 4c)
α on
τ con / s
lin
α off
log
α off
α on
τ /s
mdark + 8 σdark
min(intensity)+ ∆Idark
+ σdark
min(intensity) + ∆Idark
1.44
1.19
1.23
1.56
1.11
2.43
1.32
2.25
1.27
2.72
1.29
1.92
1.10
1.52
1.24
1.88
1.49
1.32
1.23
1.57
1.16
3.10
1.34
2.29
1.22
1.70
1.32
2.05
1.04
1.61
1.28
2.04
1.42
1.30
1.23
1.57
1.06
3.52
1.40
2.47
1.25
2.13
1.35
2.02
1.14
2.13
1.31
2.18
mdark + 7 σdark
1.46
1.35
1.22
1.57
1.1
2.96
1.36
2.33
1.29
1.80
1.33
2.05
1.03
1.22
1.26
1.95
mdark + 6 σdark
min(intensity) + (mdark
+ 4σdark - min(dark))
min(intensity) + (mdark
+ 3σdark-min(dark))
1.44
1.40
1.24
1.58
1.03
3.50
1.41
2.48
1.26
2.29
1.37
2.07
1.11
1.83
1.28
2.06
1.62
2.37
1.23
1.66
1.00
3.36
1.42
2.49
1.27
2.54
1.31
1.92
1.18
2.31
1.31
2.21
1.86
3.9
1.20
1.78
1.05
4.72
1.45
2.50
1.18
3.46
1.35
2.06
1.07
2.86
1.39
2.30
on
c
on
c
3
on
c
lin
log of individual NRs and small
Figure S3-A. Histogram of the blinking parameters(a) α on , (b) τ con , (c) α off
and (d) α off
clusters up to 15NRs, shown for m dark + 6σ dark .
lin
log of individual NRs and small
Figure S3-B. Histogram of the blinking parameters(a) α on , (b) τ con , (c) α off
and (d) α off
clusters up to 15NRs, shown for m dark + 7σ dark .
4
lin
log of individual NRs and small
Figure S3-C. Histogram of the blinking parameters(a) α on , (b) τ con , (c) α off
and (d) α off
clusters up to 15NRs, shown for m dark + 8σ dark .
2.2 Fitting methods of probability densities for on- and off-times
From the intensity time-traces I(t) of the fluorescent segments, we determined the probability
densities for off- and on-events of duration toff and ton, respectively, using a weighted method to
estimate the true probability of rare events.4
N t off ( on )
1
a+b
average
with ∆t off
,
⋅ average
P t off ( on ) =
( on ) =
total
2
N off ( on ) ∆t off ( on )
(
(
)
(
)
)
total
where N t off (on ) is the number of off (on) events of duration t off (on ) , N off
( on ) is the total number of off
average
(on) events, observed from that fluorescent segment, and ∆t off
( on ) is related to the duration of the
measurement frames, i.e., 100 ms. In the case of common event durations, a and b (time differences to
the next longest and next shortest observed event) equal this frame duration and consequently
average
average
∆t off
( on ) = 100 ms. However, in the case of rare events, a or b exceed 100 ms and ∆t off ( on ) increases.
In our previous paper,2 we discussed how different fitting approaches influence the off-time powerlaw exponents.
The probability densities are commonly plotted on a log10-log10 scale as they largely follow a
power-law behavior. However, there is a more or less pronounced deviation from that behavior at long
times. When fitting the data on a linear scale with a power-law, the short events dominate in the fitting.
5
The power-law exponent ~ 1.3 (Figure S4a) is relatively robust with respect to changes of samples,
environment or laser intensity. However, a linear fit to the log10-log10 plot accounts better for the long
log
time data, leading to an increase in the exponent, α off
~ 1.7, in the case of individual NRs and ~ 2.0
for small ensembles (Table 1).
The on-time probability densities deviate from the power-law and are described by a “truncated
power-law”, a combination of a power-law and an exponential,
on
−αon −t on / τ c
P(t on ) ∝ t on
e
,
where the truncation time, τ con , describes the transition between the two regimes. We previously
used a fitting method where both the on-time exponent, α on , and the truncation time, τ con , where left
unconstrained.2 However, a two-step fitting method, where first, α on is determined with respect to the
first four points (i.e., for on-times, ton < 1 s) and second, where τ con is allowed to vary while keeping
α on constant, was found to be more appropriate: the fitting parameters show higher consistency within
one sample and the associated errors are smaller. Figure S4b compares the two fitting methods for the
probability density of an individual NR.
lin
Figure S4. a) Off-time probability density of an individual NR, fitted by a power-law (red line, α off
= 1.30) or fitted by a
log = 1.69). b) On-time probability density of an individual NR, fitted by a truncated
line to the log-log data (blue line, α off
power-law where both parameters are unconstrained (blue line, α on = 1.20, τ con = 1.43 s) and fitted by a sequential fitting
method, where first αon is determined by fitting the first four points, followed by the truncated power-law fitting (red line,
α on = 1.18, τ con = 1.36 s). For this particular NR trace, both fitting methods yield consistent results. However, in many
cases, the first method underestimates the truncation time.
6
Figure S5. Off-time (a) and on-time (b) probability densities of an individual NR whose intensity trajectory is shown in
Figure 4a of the main paper, including the corresponding fits of the probability densities.
7
3 Dependence of blinking parameters on NR angle relative to the laser polarization
direction
Figure S6. Blinking parameters of individual NRs on silicon nitride substrates as a function of NR angle relative to the
laser polarization direction.
8
4 Additional examples of intensity trajectories
Figure S7. Intensity trajectory and intensity histogram (b) of an individual NR shown in (a), oriented at ~41° relative to the
laser polarization direction. Off- and on-time probability densities and related fits are shown in (c).
Figure S8. (a) Intensity trajectories of two parallel NRs oriented at ~ 15° relative to the laser polarization direction. (b)
Intensity trajectory of the same two NRs when the laser polarization was rotated by 90°, i.e., the NRs are oriented at ~ 75°
relative to the laser polarization direction (b). (c) Example of three parallel NRs oriented ~ 70° relative to the laser
polarization showing a faint fluorescence signal.
9
Figure S9. Additional examples of very long intensity trajectories shown in black for N = 1 (top three panels) and for N = 2
(bottom panel). The corresponding background signals are shown in grey.
10
5 Auto-Correlation Function Analysis
The autocorrelation function is defined as
g (2 ) (τ ) =
I (t ) ⋅ I (t + τ )
I (t )
2
where I(t) is the fluorescence intensity at time t, and τ is the lag time.
Figure S10 shows the autocorrelation functions of the fluorescence intensity trajectories of
individual NRs and small NR clusters up to 15 NRs. We find that the autocorrelation functions of NR
clusters fall within the broad family of curves for single NRs and that no clear distinction can be made
in terms of slope or magnitude.
Figure S10. Autocorrelation functions of individual NRs (black curves) and small NR clusters (shown in color).
References:
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3
Reiss, P.; Carayon, S.; Bleuse, J.; Pron, A. Synth. Met. 2003, 139, 649.
4
Kuno, M.; Fromm, D.P.; Hamann, H.F.; Gallagher, A.; Nesbitt, D.J. J. Chem. Phys. 2001, 115, 1028.
2
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