Quantum-Confined and Enhanced Optical Absorption of Colloidal PbS

This assumption permits to describe PbS QD light absorption by using bulk optical constants and to determine QD concentration in colloidal solutions f...
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Quantum-Confined and Enhanced Optical Absorption of Colloidal PbS Quantum Dots at Wavelengths with Expected Bulk Behavior Doriana Debellis,† Giuseppe Gigli,†,‡ Stephanie ten Brinck,§ Ivan Infante,§ and Carlo Giansante*,†,‡ †

Dipartimento di Matematica e Fisica ‘E. De Giorgi’, Università del Salento, via per Arnesano, 73100 Lecce, Italy NANOTEC−CNR Istituto di Nanotecnologia, via per Arnesano, 73100 Lecce, Italy § Department of Theoretical Chemistry, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV, Amsterdam, The Netherlands ‡

S Supporting Information *

ABSTRACT: Nowadays it is well-accepted to attribute bulk-like optical absorption properties to colloidal PbS quantum dots (QDs) at wavelengths above 400 nm. This assumption permits to describe PbS QD light absorption by using bulk optical constants and to determine QD concentration in colloidal solutions from simple spectrophotometric measurements. Here we demonstrate that PbS QDs experience the quantum confinement regime across the entire near UV−vis−NIR spectral range, therefore also between 350 and 400 nm already proposed to be sufficiently far above the band gap to suppress quantum confinement. This effect is particularly relevant for small PbS QDs (with diameter of ≤4 nm) leading to absorption coefficients that largely differ from bulk values (up to ∼40% less). As a result of the broadband quantum confinement and of the high surface-to-volume ratio peculiar of nanocrystals, suitable surface chemical modification of PbS QDs is exploited to achieve a marked, size-dependent enhancement of the absorption coefficients compared to bulk values (up to ∼250%). We provide empirical relations to determine the absorption coefficients at 400 nm of as-synthesized and ligand-exchanged PbS QDs, accounting for the broadband quantum confinement and suggesting a heuristic approach to qualitatively predict the ligand effects on the optical absorption properties of PbS QDs. Our findings go beyond formalisms derived from Maxwell Garnett effective medium theory to describe QD optical properties and permit to spectrophotometrically calculate the concentration of PbS QD solutions avoiding underestimation due to deviations from the bulk. In perspective, we envisage the use of extended π-conjugated ligands bearing electronically active substituents to enhance light-harvesting in QD solids and suggest the inadequacy of the representation of ligands at the QD surface as mere electric dipoles. KEYWORDS: Colloidal quantum dots, absorption coefficients, broadband quantum confinement, optical absorption enhancement, surface chemistry, conjugated ligands

T

implying that the density of states approaches continuum and the absence of strong resonances. These assumptions allow the description of the linear optical absorption properties of nanocrystal dispersions at energies far from the band gap by deriving effective optical constants from bulk values.13−15 Here we argue the validity of these assumptions for archetypal PbS quantum dots (QDs), which represent a benchmark system for materials in the strong quantum confinement regime due to the large length scale of electron−hole pair in bulk PbS (∼20 nm).16,17 We demonstrate that, at the energies proposed to be far above the band gap (i.e., >3.1 eV; experimentally measured between 350−400 nm), PbS QDs still present features of quantum confinement effects. Indeed, the absorption coefficients of colloidal PbS QDs measured at 400 nm differ from

he reduction of inorganic semiconductor material size below the electron−hole pair length scale in the corresponding bulk solid induces marked alterations in the electronic structure of nanoscopic crystals.1−4 Spatially confined charge carriers coupled to the nanocrystal lattice acquire excess (kinetic) energy that widens the band gap and experience reduced motion (quantized k-space) that induces discretization on the density of states compared to bulk analogues; the spatial confinement also results in larger overlap of electron and hole wave functions that increases the absorption coefficients of optical transitions near the band edges. Above the band gap these quantum confinement effects diminish, until vanishing at energies sufficiently far from the band gap. At such energies, which have been suggested to correspond to the near UV-blue spectral region (i.e., 350−450 nm) for a plethora of inorganic materials including III−V,5,6 II−VI,7−10 and IV−VI11,12 semiconductors, the absorption coefficients of (colloidal) nanocrystals are expected to match the values of corresponding bulk materials, consequently © 2017 American Chemical Society

Received: December 7, 2016 Revised: January 2, 2017 Published: January 5, 2017 1248

DOI: 10.1021/acs.nanolett.6b05087 Nano Lett. 2017, 17, 1248−1254

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Figure 1. Experimentally determined molar (a) and intrinsic (b) absorption coefficients at 400 nm, ε400QD and μ400QD, respectively, as a function of as-synthesized PbS QD size, dQD; open symbols represent mean values, vertical error bars account for two standard deviations of uncertainty on QD concentration as determined by elemental analysis via ICP-AES, and horizontal error bars account for one standard deviation of uncertainty on QD size as determined by TEM image analysis. Dashed lines show size-independent molar (a) and intrinsic (b) absorption coefficients at 400 nm, ε400bulk and μ400bulk, respectively, as a function of QD size. Solid lines represent fitted molar (a) and intrinsic (b) absorption coefficients at 400 nm as a function of QD size according the empirical eqs 1 and 2, respectively. Plot of ε400QD vs dQD in linear scale is shown in Supporting Figure S3.

the total mass concentration of Pb, and S, atoms in the aliquots and therefore, the QD concentration of the batch solutions (see Supporting Information for further details). Upon measuring the optical absorption spectra of QD solutions and by applying the Lambert−Beer law, it is possible to determine molar (per QD concentration) absorption coefficients at 400 nm, ε400QD, as a function of PbS QD diameter, dQD (Figure 1a). The intrinsic (per material unit) absorption coefficients at 400 nm, 2 ln(10) μ400QD, are derived as μ400QD = ε400QD, where a 3 N

bulk values, with larger divergences the smaller the QD size (up to 40% less than bulk). As a result of the broadband quantum confinement and of the high surface-to-volume ratio peculiar of QDs, we could attain a large, size-dependent enhancement of PbS QD absorption coefficients (up to 250% compared to bulk values) by suitable surface chemical modification, i.e., by exchanging pristine oleyl-based ligands for conjugated species. These experimental evidence demonstrate that the ligands at the QD surface cannot be conceived as mere dielectric shell and that the optical properties cannot be described within the framework of the Maxwell Garnett effective medium theory.15,18,19 We provide a simple empirical equation that relates PbS QD diameter and absorption coefficient at 400 nm, accounting for the broadband quantum confinement; we also suggest a heuristic approach to qualitatively predict the optical absorption properties of ligand-exchanged PbS QDs that includes the replacing ligand contribution to the density of states of the entire (ligand-)nanocrystal system. The possibility of enhancing QD optical absorption beyond bulk values across the entire near UV−vis−NIR spectral range may represent a reliable strategy toward the design of QD-based systems in which effective light-harvesting initiates charge carrier separation, such as for photovoltaic and photodetection applications, or redox processes for photochemical and photocatalytic reactions. Determination of As-Synthesized PbS QD Absorption Coefficients. According to the most employed procedure that uses Pb-oleate precursor(s),20 we synthesized PbS QDs with sizes ranging between about 2 and 7 nm (as determined by electron microscopy image analysis; see Supporting Information). We carefully determined QD chemical composition via a combination of elemental and thermogravimetric analyses and spectroscopic characterization.21 This analytical work enabled us to infer a chemical structure for the as-synthesized QDs, which is compatible with a fully Pb-terminated Archimedean truncated octahedron irrespective of QD size.21 This faceted, nonstoichiometric QD model is used to determine QD concentration in solution-phase by elemental analysis on known aliquots of QD solutions: elemental analysis provides

dQD

A

1

truncated octahedral model with volume VQD = 2 dQD3 is assumed for the inorganic cores and NA is the Avogadro number (Figure 1b).15 As already mentioned, PbS QD absorption coefficients at (and above) 400 nm are commonly considered as size independent,12 with the molar absorption coefficient scaling linearly with QD volume (ε400bulk, dashed line in Figure 1a) and the intrinsic absorption coefficient invariant with QD size (μ400bulk, dashed line in Figure 1b). Our measurements (symbols in Figure 1) clearly show that PbS QD optical absorption coefficients at 400 nm are not size independent, with relevant deviation from bulk values the smaller the nanocrystals (up to 40% for QDs with 1.9 nm diameter). Such a deviation was not observed in previous studies,12 probably because data related to QDs with diameter ≤3.5 nm were not reported. The measurement of optical absorption at 400 nm under the assumption of size-independence represents a facile method to determine PbS QD concentration in solution regardless of nanocrystal size dispersion;12 however, such an assumption does not hold for small QDs, as shown in Figure 1. Sizeindependent optical absorption should take place at higher energies where, however, mere ligands and even solvents may contribute to the measured absorbance values. Nevertheless and albeit the steep QD absorption profile at energies far from the band gap, the estimation of QD concentration in solution by absorbance measurements at 400 nm is still convenient and more precise than at the first excitonic peak, as the larger density of states reduces the errors intrinsic to QD size polydispersion. We therefore applied an empirical correction to 1249

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Figure 2. (Top) Relaxed structures for nonstoichiometric PbS nanocrystals of different sizes computed at the DFT/PBE level of theory. (Bottom) Corresponding molecular orbitals (MOs) computed at the same level of theory. For each MO, the length of the different line sections represents the fractional contribution of Pb atoms (orange), sulfur atoms (yellow), and formate ligands (black). Formates are included to preserve charge neutrality and to emulate the effect of the anchoring carboxylate groups of the oleate ligands coming from the synthetic procedure.

and formate ligands preserving charge neutrality (rather than oleate ligands, which does not alter significantly the calculated density of states); nanocrystal size varies between 1.2 and 3.6 nm, which yield QD models in the strong quantum confinement regime that clearly show discrete density of states at energies of ±1 eV from the band edges (Figure 2). As expected, the energy level discretization is more evident the smaller the QD model and tends to reach continuum for larger nanocrystals. The assumption of size-independent absorption coefficient at 400 nm leads to underestimate the concentration of colloidal dispersions of PbS QDs with diameter of about 3 nm, which are those most suitable for photovoltaic applications due to their band gap values (1.3−1.4 eV) maximizing incident light absorption, thermalization losses, and radiative recombination.22 We thus provide a corrected equation that permits to spectrophotometrically calculate the concentration of PbS QD solutions by using the Lambert−Beer law and eq 1:

bulk absorption coefficients accounting for the experimentally observed deviations (Figure 1). The molar absorption coefficient, ε400bulk, as a function of PbS QD diameter, dQD, can be fitted with the following equation (solid line in Figure 1a): ε400

QD

=

dQD3 2

NA μ bulk (1 − e−PcoredQD/ a) ln(10) 400

(1)

−1

where μ400 = 1.71 × 10 cm is the bulk PbS intrinsic absorption coefficient at 400 nm as predicted by the Maxwell Garnett effective medium theory in the local field approximation,12,15 a = 0.5936 nm is the PbS lattice constant preserving dimensional homogeneity of the equation, and Pcore is a positive a-dimensional parameter accounting for the deviation from the bulk for the specific nanomaterial under investigation; fitting experimental data for PbS QDs in Figure 1a yields Pcore = 0.26. This empirical equation may be eventually applied to other nanomaterials with large exciton Bohr radii, such as indium pnictides, whereas deviation from bulk values for cadmium chalcogenide QDs may be difficult to be experimentally observed. Analogously, the empirical relation between PbS QD diameter, dQD, and intrinsic absorption coefficients, μ400QD, can be consequently obtained as (solid line in Figure 1b): bulk

5

μ400QD = μ400 bulk (1 − e−PcoredQD/ a)

[QD] =

(3)

where A400 is the measured absorbance at 400 nm, b is the optical path length in cm, constant values are obtained by fitting experimental data with eq 1, dQD values are in nm, and [QD] has the dimensions of mol/L. Note that the first term applies for size-independent absorption coefficient values, and the second term is our empirical correction accounting for sizedependence; such a correction becomes relevant at dQD < 10 nm (as shown in Figure 1). Inter-QD interactions leading to excitonic and/or electronic coupling may alter the QD absorption profile thus preventing the use of this relation in dense-packed QD solids. Broadband Optical Absorption Enhancement of PbS QDs above the Bulk. The broadband quantum confinement of as-synthesized PbS QDs might leave much room for increasing the density of optically active states. Indeed, we have previously demonstrated that conjugated ligands coordinating the PbS (and CdS) QD surface via the thiolate anchoring group, upon quantitatively displacing pristine oleyl-based ligands, yield ligand/core adducts with increased density of occupied states.23 The inherent electronic coupling between

(2)

We note that the empirical ε400 (μ400 ) values tend to approach ε400bulk (μ400bulk) at QD diameters of ∼10 nm and tend to zero for negligible QD sizes; the convergence to bulk values is reached at QD sizes well below the electron−hole pair natural length scale of bulk PbS (∼20 nm), as we are monitoring a spectral region far above the optical band gap. We can relate the empirical correction to absorption coefficients in eqs 1 and 2 to the density of states of PbS QDs contributing to the optical absorption at 400 nm. Such correction suggests that the density of states at energies around 3.1 eV tends to reach continuum for QDs with diameters larger than ∼10 nm; therefore, QDs of smaller sizes are still in the quantum confinement regime up to the near UV−vis spectral region. In order to further substantiate this statement, we performed density functional theory (DFT) calculations on PbS truncated octahedral nanocrystals with excess Pb atoms QD

A400 1 A400 1 = b ε400QD b·22400·dQD3 1 − e−0.443dQD

QD

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Figure 3. Spectrally resolved enhancement of PbS QD optical absorption induced by thiol(ate)-terminated ligands. Ratiometric spectra were obtained upon dividing the spectrum acquired when extra replacing ligand addition does not induce further spectral changes by the spectrum of assynthesized QDs; related as-recorded spectra are shown in the Supporting Information. (a) Absorption increase upon addition of pmethylbenzenethiolate ligands as a function of as-synthesized QD size, dQD; color legend appears on the right side of the panel. (b) Absorption increase upon addition of p-methylbenzenethiolate (solid line), p-aminobenzenethiolate (dashed line), and 1-butanethiol (dotted line) ligands to PbS QDs with excitonic diameter of about 2.9 nm; replacing ligands appear on the right side of the panel.

Figure 4. Experimentally determined (symbols) and calculated (according to the empirical eq 4; lines) intrinsic absorption coefficients of ligandexchanged PbS QDs at 400 nm, μ400LE−QD, as a function of as-synthesized PbS QD size, dQD; the chemical structures of the corresponding ligands appear on the right side of the figure. Symbols represent mean values; errors deriving from the uncertainty on QD concentration and size are omitted for clarity and are shown in Supporting Figure S11.

size dependence (Figure 3a): the smaller the nanocrystal the larger the optical absorption increase, up to more than 200% for PbS QDs with diameter of about 1.9 nm (whereas such an increase is limited to about 20% for QDs with diameters larger than 6 nm). The spectrally resolved optical absorption enhancement shows also a marked replacing ligand dependence (Figure 3b): in the case of PbS QDs with diameter of about 2.9 nm, the presence of an electron-donating group in para position of the benzene ring, as for the p-aminobenzenethiolate ligand, further enhances the optical absorption above 250% in the entire visible spectral region (and beyond 300% at 400 nm, dashed line in Figure 3b), whereas saturated analogues, such as 1-butanethiol, show only a slight absorption enhancement of about 20% (dotted line in Figure 3b).

(metal−)organic ligands and inorganic cores results in a broadband optical absorption enhancement (and at energies well below the HOMO−LUMO gap of the unbound ligands). The spectrally resolved optical absorption enhancement induced by thiol(ate)-terminated ligands at the PbS QD surface can be obtained upon dividing the spectrum of the ligand-exchanged QDs, acquired when extra replacing ligand addition does not induce further spectral changes, by the spectrum of the corresponding as-synthesized QDs,23−25 as shown in Figure 3. As-recorded absorption spectra of assynthesized and ligand-exchanged colloidal PbS QDs are shown in the Supporting Information. The spectrally resolved optical absorption enhancement induced by p-methylbenzenethiolate ligands shows a marked 1251

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On the Description of QD Optical Absorption. The experimentally observed PbS QD optical absorption enhancement induced by surface ligands highlights the limitations of formalisms mutuated from classic electromagnetism in describing the linear optical absorption of colloidal semiconductor nanocrystals. Indeed, the optical absorption of dilute dispersions of small colloidal crystals (where dilute stands for noninteracting particles, the volume fraction is much lower than one, and small indicates that the particles are much smaller than the wavelength of the incident light) surrounded by a dielectric medium (with much lower refractive index than the particle itself) is commonly described using formalisms derived from the Maxwell Garnett effective medium theory.12−15 In this framework, the nanocrystal intrinsic absorption coefficient at energies sufficiently far from the band gap (3.1 eV; i.e., 400 nm for PbS QDs), under the assumption of a continuum density of states and in absence of intense transitions, matches, up to a multiplicative constant, the bulk value rescaled for the dielectric confinement as19

The intrinsic absorption coefficients at 400 nm of ligandexchanged PbS QDs, μ400LE−QD, as a function of dQD are plotted in Figure 4. We applied a further empirical correction to bulk absorption coefficients in the attempt to account for the effect exerted by the replacing ligands. The μ400LE−QD values as a function of dQD can be fitted with the following equation (lines in Figure 4): μ400 LE − QD = μ400 bulk (1 − e−PcoredQD/ a)(Plig e−PcoredQD/ a + 1) (4)

where the constants μ400 and a (the bulk PbS intrinsic absorption coefficient and lattice parameter, respectively) were previously defined, Pcore = 0.26 being the same a-dimensional parameter determined by eqs 1 and 2 as we assume that the inorganic core is unaltered upon ligand exchange (as suggested by electron microsocopy image analysis shown in the Supporting Information), and Plig is an empirical a-dimensional parameter related to the contribution of the replacing ligands to the density of states: the aliphatic ligand, 1-butanethiol, slightly contributes to the density of occupied (valence) states via the 3p orbitals of the sulfur anchoring atom and Plig = 0.87; the conjugated ligand, p-methylbenzenethiolate, provides a relevant contribution to the density of states also via the π orbitals of the aromatic ring and Plig = 3.2; the presence of electronically active substituents on the conjugated ligand, as for p-aminobenzenethiolate, further enhances optical absorption (Plig = 7.8) likely due to the electron-donating effect of the amino group in para position of the benzene ring that contributes to the density of states;23 eq 2 implicitly assumes that the pristine oleate ligands negligibly contribute to the QD density of states and the Plig value is indeed negligible (Plig < 10−4). The corresponding molar absorption coefficients, ε400LE−QD, can be derived as bulk

ε400 LE − QD = ε400QD(Plige−PcoredQD/ a + 1)

μ400(LE−)QD ∝ α400 |fLF(LE−)QD |2

(6)

where α400 is the thickness-independent absorption coefficient of homogeneous, bulk PbS and f LF represents the Lorentz local field factor that relates the external, applied electric field and the electric field within the QD, which accounts for the dielectric effect of the surroundings (the ligand shell and the solvent) on as-synthesized PbS QDs, f LFQD, and on ligand-exchanged PbS QDs, f LFLE−QD.19 Such factor can be used to evaluate the intrinsic absorption coefficients at 400 nm with an expression derived for core/shell QDs,26 albeit the severe approximation of assuming a dielectric constant for a sort of organic ligand monolayer at the inorganic core surface: |fLF(LE−)QD |2

(5)

where ε400 is calculated according to eq 1. The inclusion of the ε400LE−QD values in eq 3 permits to determine the concentration of PbS QDs in solution taking into account ligand contribution to optical absorption. Figure 4 shows that the calculated μ400LE−QD values tend to approach μ400QD (and μ400bulk, consequently) at QD diameters of about 10 nm and tend to zero for negligible QD sizes, whereas reach maximum values for dQD of about 2−3 nm (such maximum tends to diameters of 1.5 nm for Plig approaching very large, albeit physically unattainable, values). This size range thus represents the most advantageous compromise between the density of states of the PbS inorganic core and its surface-tovolume ratio dictating the extent of organic ligand contribution to the density of optically active states of the entire organic/ inorganic, ligand/core system (the colloidal QD itself). This finding can have relevant implications for photovoltaic applications: the enhancement by several times of the optical absorption of PbS QDs with diameter of about 3 nm can indeed contribute to the optimization of the photoactive QD layer thickness, which reflects the necessity to mediate effective absorption of the incident light and transport to (and extraction at) the electrodes of the photogenerated charge carriers, thus ultimately determining the external quantum efficiency of the devices. Exploitation of the ligand-induced optical absorption enhancement in QD solids for photovoltaic applications must, however, rely on ligands that also promote effective inter-QD charge transport. QD

2

9εlig εsolv

=

aεlig + 2bεsolv

(7)

with 3 ⎛ d − L lig + QD ⎜ 2 a = εcore⎜3 − 2 d ⎜⎜ L lig + QD 2 ⎝

dQD 3

(

dQD 3

lig

+ 2εlig

⎞

) ( ) ⎟⎟ ( ) ⎟⎟⎠ (L + ) − ( ) (L + ) 2

3

dQD 3

2

2

dQD 3

lig

2

(8)

and

b = εcore

(L

dQD 3

dQD 3

) −( ) (L + ) ⎛ ⎞ −( ) ⎟ L + ⎜ ( ) ⎜3 − ⎟ ⎜⎜ (L + ) ⎟⎟⎠ ⎝ lig

+

2

2

3

dQD

lig

2

dQD 3

lig

+ εlig

dQD 3

2

2

dQD

lig

2

3

(9)

where the high-frequency dielectric constant value is assumed as the dielectric constant for the PbS core, εcore;27 the square of oleic acid and p-methylbenzenethiol ligand refractive indexes and of tetrachloroethylene are assumed as the dielectric 1252

DOI: 10.1021/acs.nanolett.6b05087 Nano Lett. 2017, 17, 1248−1254

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Nano Letters constants for the ligand shell and the solvent, εlig and εsolv, respectively; 1.8 nm for oleate and 0.6 nm for pmethylbenzenethiolate are assumed as the ligand lengths, Llig. The optical absorption enhancement, μ400LE‑QD/μ400QD, ascribable to changes in the internal electric field expected upon exchanging oleate ligands for p-methylbenzenethiolate species is small, when calculated as the local field factor ratio for ligand-exchanged and as-synthesized PbS QDs, |f LFLE−QD|2/ |f LFQD|2 (dashed line in Figure 5). The ligand-induced enhancement of QD optical absorption experimentally observed upon exchanging oleates for p-methylbenzenethiolates is instead much larger than expected by mere dielectric confinement (symbols in Figure 5). The optical absorption enhancement, μ400LE‑QD/μ400QD, as a function of dQD can be appropriately calculated as the ratio of eqs 4 and 2, (Plig e−PcoredQD/a + 1) (solid line in Figure 5).

heteroatoms, either as electron-donor substituents or as part of the conjugated system. Here we have shown that colloidal PbS quantum dots experience broadband quantum confinement regime and therefore also in the near UV−vis spectral region (between 350 and 400 nm) already proposed to be sufficiently far above the band gap to suppress quantum confinement. The quantum confinement is inherently size-dependent, thus particularly relevant for PbS QDs with diameter of ∼3 nm that are those most suited for photovoltaic applications. We provide an empirical relation to determine the molar and intrinsic absorption coefficients at 400 nm of PbS QDs, which can be used to calculate the concentration of PbS QD solutions avoiding underestimation due to deviations from bulk values. As a result of the broadband quantum confinement and of the high surface-to-volume ratio peculiar of small PbS QDs, we could attain a marked enhancement of the absorption coefficients (up to 250%) compared to bulk values by suitable surface chemical modification with conjugated thiolateterminated ligands, attributed to a large increase in the density of states of PbS QDs (although a concomitant increase of the oscillator strength of the relevant electronic transitions cannot be regarded as negligible). The possibility of reducing QD film thickness while preserving the same absorbance of incident photons may represent an undeniable advantage for photovoltaic and photodetection applications by reducing the path length to the electrodes for the photogenerated charge carriers; however, conjugated ligands responsible for the optical absorption enhancement should be designed to combine enhanced light-harvesting with effective inter-QD charge transport. Our findings could not be described and explained within the framework of the Maxwell Garnett effective medium theory, thus highlighting the limitations of formalisms mutuated from classical electromagnetism in describing the linear optical absorption of strongly quantum confined (ligand−)nanocrystal systems. We suggest a heuristic approach to qualitatively predict the optical absorption properties of colloidal QDs accounting for the ligand contribution to the overall density of states and foresee the use of larger (bidentate) π-conjugated systems bearing electron-donor substituents for further broadband enhancement of QD (solid) optical absorption. In addition, our findings cannot be interpreted by considering ligands at the QD surface as mere dipoles, which may affect the overall description of ligand/nanocrystal system properties, including relevant band energies.

Figure 5. Experimentally determined (symbols) and calculated (according to the empirical eqs 4 and 2; solid line) intrinsic absorption coefficient ratio at 400 nm of ligand-exchanged PbS QDs, μ400LE−QD, and as-synthesized QDs, μ400QD, as a function of QD size, dQD; dashed line represents the local field factor ratio between ligand-exchanged and as-synthesized PbS QDs as a function of dQD, according to eqs 6−9.

This experimental evidence cannot be therefore interpreted on the basis of the Maxwell Garnett effective medium theory,12,15 which does not properly describe the linear optical absorption properties of ligand-exchanged colloidal PbS QDs with dQD smaller than about 10 nm. Analogously, it appears unlikely that surface dipole effects can account for the experimentally observed ligand-induced QD optical absorption enhancement. As benzenethiol derivatives also induce PbS QD energy level shifting,28 we suggest that conceiving ligands at the QD surface as mere dipoles may be inadequate. More broadly, optoelectronic properties of colloidal QDs should not be described as the sum of ligand and core component features, which is particularly relevant in the strong quantum confinement regime.23,29 The inherent electronic coupling between (metal−)organic ligands and inorganic cores may increase the density of states, as for colloidal PbS QDs capped with conjugated ligands.23−25 Here we have empirically described such a ligand-induced increase of optically active states by the Plig parameter appearing in eqs 4 and 5, which could be heuristically (and roughly) estimated by the extent of π conjugation on the entire ligand and by the presence of

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b05087. Details on experimental and computational methods, transmission electron microscopy image analysis, and further spectrophotometric characterization of PbS QDs (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ivan Infante: 0000-0003-3467-9376 Carlo Giansante: 0000-0003-4558-5367 1253

DOI: 10.1021/acs.nanolett.6b05087 Nano Lett. 2017, 17, 1248−1254

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Nano Letters Notes

(28) Brown, P. R.; Kim, D.; Lunt, R. R.; Zhao, N.; Bawendi, M. G.; Grossman, J. C.; Bulović, V. ACS Nano 2014, 8, 5863−5872. (29) Soreni-Harari, M.; Yaacobi-Gross, N.; Steiner, D.; Aharoni, A.; Banin, U.; Millo, O.; Tessler, N. Nano Lett. 2008, 8, 678−684.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.G. thanks the “Future In Research” program by Regione Puglia (‘Sol-Urbis’, code: ZCZP7C3). I.I. would like to thank The Netherlands Organization of Scientific Research (NWO) for providing financial support within the Innovational Research Incentive (Vidi) Scheme (Grant No. 723.013.002). DFT calculations were carried out on the Dutch national einfrastructure with the support of SURF Cooperative.

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DOI: 10.1021/acs.nanolett.6b05087 Nano Lett. 2017, 17, 1248−1254