The exciton peak in the excitation–emission matrix (EEM) of colloidal quantum dots implicitly contains information about inhomogeneous broadening and the photoluminescence (PL) and photoluminescence excitation (PLE) spectra of individual particles in the vicinity of the absorption onset. A numerical procedure for extracting this information has been developed and applied to the EEMs of polydisperse InP/ZnS core/shell colloidal quantum dots and their supernatant solutions obtained by partial precipitation with a non-solvent. The inhomogeneous broadenings obtained in this way have been converted by the sizing curve into particle-size distributions. These distributions have been found to be in agreement with the size-selective precipitation theory proposed recently. The homogeneous PL and PLE line shapes obtained by analyzing the EEMs were found to satisfy the Kennard–Stepanov relation, which is the first more or less direct evidence of its validity for colloidal quantum dots.

1.
O.
Chen
,
J.
Zhao
,
V. P.
Chauhan
,
J.
Cui
,
C.
Wong
,
D. K.
Harris
,
H.
Wei
,
H.-S.
Han
,
D.
Fukumura
,
R. K.
Jain
, and
M. G.
Bawendi
, “
Compact high-quality CdSe–CdS core–shell nanocrystals with narrow emission linewidths and suppressed blinking
,”
Nat. Mater.
12
,
445
451
(
2013
).
2.
W. W.
Yu
,
J. C.
Falkner
,
B. S.
Shih
, and
V. L.
Colvin
, “
Preparation and characterization of monodisperse PbSe semiconductor nanocrystals in a noncoordinating solvent
,”
Chem. Mater.
16
,
3318
3322
(
2004
).
3.
S.
Hussain
,
N.
Won
,
J.
Nam
,
J.
Bang
,
H.
Chung
, and
S.
Kim
, “
One-pot fabrication of high-quality InP/ZnS (core/shell) quantum dots and their application to cellular imaging
,”
ChemPhysChem
10
,
1466
1470
(
2009
).
4.
M. P.
Hendricks
,
B. M.
Cossairt
, and
J. S.
Owen
, “
The importance of nanocrystal precursor conversion kinetics: Mechanism of the reaction between cadmium carboxylate and cadmium bis(diphenyldithiophosphinate)
,”
ACS Nano
6
,
10054
10062
(
2012
).
5.
S. A.
Tovstun
and
V. F.
Razumov
, “
Theoretical analysis of nonradiative energy transfer in nanoclusters of quasi-monodisperse colloidal quantum dots
,”
High Energy Chem.
49
,
352
360
(
2015
).
6.
L.
Qu
and
X.
Peng
, “
Control of photoluminescence properties of CdSe nanocrystals in growth
,”
J. Am. Chem. Soc.
124
,
2049
2055
(
2002
).
7.
L.
Li
and
P.
Reiss
, “
One-pot synthesis of highly luminescent InP/ZnS nanocrystals without precursor injection
,”
J. Am. Chem. Soc.
130
,
11588
11589
(
2008
).
8.
K.
De Nolf
,
R. K.
Capek
,
S.
Abe
,
M.
Sluydts
,
Y.
Jang
,
J. C.
Martins
,
S.
Cottenier
,
E.
Lifshitz
, and
Z.
Hens
, “
Controlling the size of hot injection made nanocrystals by manipulating the diffusion coefficient of the solute
,”
J. Am. Chem. Soc.
137
,
2495
2505
(
2015
).
9.
N.
Pradhan
,
D.
Reifsnyder
,
R.
Xie
,
J.
Aldana
, and
X.
Peng
, “
Surface ligand dynamics in growth of nanocrystals
,”
J. Am. Chem. Soc.
129
,
9500
9509
(
2007
).
10.
Y. P.
Rakovich
,
J. F.
Donegan
,
N.
Gaponik
, and
A. L.
Rogach
, “
Raman scattering and anti-Stokes emission from a single spherical microcavity with a CdTe quantum dot monolayer
,”
Appl. Phys. Lett.
83
,
2539
2541
(
2003
).
11.
A. L.
Washington
 II
and
G. F.
Strouse
, “
Selective microwave absorption by trioctyl phosphine selenide: Does it play a role in producing multiple sized quantum dots in a single reaction?
,”
Chem. Mater.
21
,
2770
2776
(
2009
).
12.
D.
Segets
,
J.
Gradl
,
R. K.
Taylor
,
V.
Vassilev
, and
W.
Peukert
, “
Analysis of optical absorbance spectra for the determination of ZnO nanoparticle size distribution, solubility, and surface energy
,”
ACS Nano
3
,
1703
1710
(
2009
).
13.
D.
Segets
,
J. M.
Lucas
,
R. N.
Klupp Taylor
,
M.
Scheele
,
H.
Zheng
,
A. P.
Alivisatos
, and
W.
Peukert
, “
Determination of the quantum dot band gap dependence on particle size from optical absorbance and transmission electron microscopy measurements
,”
ACS Nano
6
,
9021
9032
(
2012
).
14.
D.
Segets
, “
Analysis of particle size distributions of quantum dots: From theory to application
,”
KONA Powder Part. J.
33
,
48
62
(
2016
).
15.
S. B.
Brichkin
,
M. G.
Spirin
,
S. A.
Tovstun
,
V. Y.
Gak
,
E. G.
Mart’yanova
, and
V. F.
Razumov
, “
Colloidal quantum dots InP@ZnS: Inhomogeneous broadening and distribution of luminescence lifetimes
,”
High Energy Chem.
50
,
395
399
(
2016
).
16.
E. H.
Kennard
, “
On the thermodynamics of fluorescence
,”
Phys. Rev.
11
,
29
38
(
1918
).
17.
B. I.
Stepanov
, “
A universal relation between the absorption and luminescence spectra of complex molecules
,”
Sov. Phys. Dokl.
2
,
81
84
(
1957
).
18.
S. A.
Tovstun
and
V. F.
Razumov
, “
Method of separation of homogeneous and inhomogeneous broadenings of absorption and luminescence spectra of colloidal quantum dots
,”
High Energy Chem.
50
,
281
299
(
2016
).
19.
M. J.
Fernée
,
P.
Jensen
, and
H.
Rubinsztein-Dunlop
, “
Origin of the large homogeneous line widths obtained from strongly quantum confined PbS nanocrystals at room temperature
,”
J. Phys. Chem. C
111
,
4984
4989
(
2007
).
20.
D.
Mutavdžić
,
J.
Xu
,
G.
Thakur
,
R.
Triulzi
,
S.
Kasas
,
M.
Jeremić
,
R.
Leblanc
, and
K.
Radotić
, “
Determination of the size of quantum dots by fluorescence spectroscopy
,”
Analyst
136
,
2391
2396
(
2011
).
21.
O. V.
Prezhdo
, “
Multiple excitons and the electron–phonon bottleneck in semiconductor quantum dots: An ab initio perspective
,”
Chem. Phys. Lett.
460
,
1
9
(
2008
).
22.
A. J.
Nozik
, “
Multiple exciton generation in semiconductor quantum dots
,”
Chem. Phys. Lett.
457
,
3
11
(
2008
).
23.
M. D.
Peterson
,
L. C.
Cass
,
R. D.
Harris
,
K.
Edme
,
K.
Sung
, and
E. A.
Weiss
, “
The role of ligands in determining the exciton relaxation dynamics in semiconductor quantum dots
,”
Annu. Rev. Phys. Chem.
65
,
317
339
(
2014
).
24.
T.
Rajh
,
O. I.
Mićić
, and
A. J.
Nozik
, “
Synthesis and characterization of surface-modified colloidal CdTe quantum dots
,”
J. Phys. Chem.
97
,
11999
12003
(
1993
).
25.
C. A.
Leatherdale
,
W.-K.
Woo
,
F. V.
Mikulec
, and
M. G.
Bawendi
, “
On the absorption cross section of CdSe nanocrystal quantum dots
,”
J. Phys. Chem. B
106
,
7619
7622
(
2002
).
26.
C.
de Mello Donegá
and
R.
Koole
, “
Size dependence of the spontaneous emission rate and absorption cross section of CdSe and CdTe quantum dots
,”
J. Phys. Chem. C
113
,
6511
6520
(
2009
).
27.
Z.
Hens
and
I.
Moreels
, “
Light absorption by colloidal semiconductor quantum dots
,”
J. Mater. Chem.
22
,
10406
10415
(
2012
).
28.
P.
Yu
,
M. C.
Beard
,
R. J.
Ellingson
,
S.
Ferrere
,
C.
Curtis
,
J.
Drexler
,
F.
Luiszer
, and
A. J.
Nozik
, “
Absorption cross-section and related optical properties of colloidal InAs quantum dots
,”
J. Phys. Chem. B
109
,
7084
7087
(
2005
).
29.
C.
Xia
,
W.
Wu
,
T.
Yu
,
X.
Xie
,
C.
van Oversteeg
,
H. C.
Gerritsen
, and
C.
de Mello Donega
, “
Size-dependent band-gap and molar absorption coefficients of colloidal CuInS2 quantum dots
,”
ACS Nano
12
,
8350
8361
(
2018
).
30.
W. W.
Yu
and
X.
Peng
, “
Formation of high-quality CdS and other II–VI semiconductor nanocrystals in noncoordinating solvents: Tunable reactivity of monomers
,”
Angew. Chem., Int. Ed.
41
,
2368
2371
(
2002
).
31.
D. V.
Talapin
,
A. L.
Rogach
,
A.
Kornowski
,
M.
Haase
, and
H.
Weller
, “
Highly luminescent monodisperse CdSe and CdSe/ZnS nanocrystals synthesized in a hexadecylamine–trioctylphosphine oxide–trioctylphospine mixture
,”
Nano Lett.
1
,
207
211
(
2001
).
32.
W. W.
Yu
,
Y. A.
Wang
, and
X.
Peng
, “
Formation and stability of size-, shape-, and structure-controlled CdTe nanocrystals: Ligand effects on monomers and nanocrystals
,”
Chem. Mater.
15
,
4300
4308
(
2003
).
33.
S. A.
Tovstun
and
V. F.
Razumov
, “
Theory of size-selective precipitation
,”
J. Nanopart. Res.
19
,
8
(
2017
).
34.
A.
Narayanaswamy
,
L. F.
Feiner
, and
P. J.
van der Zaag
, “
Temperature dependence of the photoluminescence of InP/ZnS quantum dots
,”
J. Phys. Chem. C
112
,
6775
6780
(
2008
).
35.
O. I.
Mićić
,
S. P.
Ahrenkiel
, and
A. J.
Nozik
, “
Synthesis of extremely small InP quantum dots and electronic coupling in their disordered solid films
,”
Appl. Phys. Lett.
78
,
4022
4024
(
2001
).
36.
S. A.
Tovstun
,
S. B.
Brichkin
,
M. G.
Spirin
,
V. Y.
Gak
, and
V. F.
Razumov
, “
Specifics of luminescence of nanoclusters consisting of InP@ZnS colloidal quantum dots stabilized by oleylamine
,”
High Energy Chem.
51
,
449
454
(
2017
).
37.
J. R.
Lakowicz
,
Principles of Fluorescence Spectroscopy
, 3rd ed. (
Springer
,
New York
,
2006
), p.
54
, Eq. (2.4).
38.
S. A.
Tovstun
,
E. G.
Martyanova
,
S. B.
Brichkin
,
M. G.
Spirin
,
V. Y.
Gak
,
A. V.
Kozlov
, and
V. F.
Razumov
, “
Förster electronic excitation energy transfer upon adsorption of meso-tetra(3-pyridyl)porphyrin on InP@ZnS colloidal quantum dots
,”
J. Lumin.
200
,
151
157
(
2018
).
39.
Y.
Wang
,
A.
Suna
,
J.
McHugh
,
E. F.
Hilinski
,
P. A.
Lucas
, and
R. D.
Johnson
, “
Optical transient bleaching of quantum-confined CdS clusters: The effects of surface-trapped electron-hole pairs
,”
J. Chem. Phys.
92
,
6927
6939
(
1990
).
40.
M.
Abdellah
,
K. J.
Karki
,
N.
Lenngren
,
K.
Zheng
,
T.
Pascher
,
A.
Yartsev
, and
T.
Pullerits
, “
Ultra long-lived radiative trap states in CdSe quantum dots
,”
J. Phys. Chem. C
118
,
21682
21686
(
2014
).
41.
O. I.
Mićić
,
J.
Sprague
,
Z.
Lu
, and
A. J.
Nozik
, “
Highly efficient band-edge emission from InP quantum dots
,”
Appl. Phys. Lett.
68
,
3150
3152
(
1996
).
42.
H.
Ruf
, “
Data accuracy and resolution in particle sizing by dynamic light scattering
,”
Adv. Colloid Interface Sci.
46
,
333
342
(
1993
).
43.
W.
Tscharnuter
, “
Photon correlation spectroscopy in particle sizing
,” in,
Encyclopedia of Analytical Chemistry: Applications, Theory and Instrumentation
, edited by
R. A.
Meyers
(
John Wiley & Sons, Ltd
,
2006
).
44.
Z.
Kojro
, “
Influence of statistical errors on size distributions obtained from dynamic light scattering data. Experimental limitations in size distribution determination
,”
J. Phys. A: Math. Gen.
23
,
1363
1383
(
1990
).
45.
R.
Finsy
,
N.
De Jaeger
,
R.
Sneyers
, and
E.
Geladé
, “
Particle sizing by photon correlation spectroscopy. Part III: Mono and bimodal distributions and data analysis
,”
Part. Part. Syst. Charact.
9
,
125
137
(
1992
).
You do not currently have access to this content.