ARTICLE pubs.acs.org/Langmuir
Liquid-Crystalline Polymer Composites with CdS Nanorods: Structure and Optical Properties Alexander A. Ezhov,†,‡ Georgii A. Shandryuk,† Galina N. Bondarenko,† Alexey S. Merekalov,† Sergey S. Abramchuk,‡ Alina M. Shatalova,† Pramit Manna,§ Eugene R. Zubarev,*,§ and Raisa V. Talroze*,† †
A.V. Topchiev Institute of Petrochemical Synthesis, RAS, Moscow 119991, Russia Department of Physics, M. V. Lomonosov Moscow State University, Moscow 119992, Russia § Department of Chemistry, Rice University, Houston, Texas 77005, United States ‡
bS Supporting Information ABSTRACT: We report on the structure, uniaxial orientation, and photoluminescent properties of CdS nanorods that form stable nanocomposites with smectic C hydrogen-bonded polymers from the family of poly(4-(nacryloyloxyalkoxy)benzoic acids. TEM analysis of microtomed films of nanocomposites reveals that CdS nanorods form small domains that are homogeneously distributed in the LC polymer matrix. They undergo long-range orientation with the formation of one-dimensional aggregates of rods when the composite films are uniaxially deformed. The Stokes photoluminescence was observed from CdS NRs/LC polymer composites with emission peak located almost at the same wavelength as that of NRs solution in heptane. An anti-Stokes photoluminescence (ASPL) in polymer nanocomposites was found under the excitation below the nanoparticles ground state. The mechanism of ASPL was interpreted in terms of thermally populated states that are involved in the excitation process. These nanocomposites represent an unusual material in which the optical properties of anisotropic semiconductor nanostructures can be controlled by mechanical deformation of liquid-crystalline matrix.
’ INTRODUCTION The ability to combine inorganic nanoparticles (NPs) and organic macromolecules into homogeneous composite materials is an important goal, which is often difficult to achieve due to a strong tendency of such systems to undergo a macrophase separation.13 The incorporation of small spherical NPs into polymer matrixes has been demonstrated via direct blending,4,5 in situ synthesis of NPs within polymer media,6,7 surface modification of NPs with monomers followed by polymerization from NP surface, and grafting of preformed functionalized polymers to NPs.818 However, not only in-matrix dispersion, but also organization and packing of NPs are very desirable for the fundamental studies of optoelectronic properties of such materials and their use in novel photovoltaic devices. One of the approaches currently developed is based on liquid crystals as tunable matrixes providing the alignment of NPs into larger organized structures in multiple dimensions.1923 LC polymers, which combine basic properties of conventional polymers and liquid crystals, also provide a way to control the arrangement of anisotropic nanostructures within the matrix. These include oriented single wall carbon nanotubes in a nematic LC polymer24 and gold nanorods in lyotropic LCs. We have previously used hydrogen-bonded LC polyacrylates as matrixes that govern the localization of CdSe quantum dots (QDs) due to the breaking of H-bonded dimers and the interaction of the polymer carboxylic groups with the QDs.25,26 It resulted in the formation of two-dimensional QD nanolayers embedded into LC r 2011 American Chemical Society
polymer matrix. Unlike spherical (QDs) nanostructures, anisometric nanorods (NRs) are expected to be aligned by the LC polymer matrix and control their orientation in a complex composite material. The primary goal of this Article is to introduce a nanocomposite system, in which a LC polymer serves as a matrix for CdS nanorods, and to describe their morphology, structure, and optical properties. Side-chain LC polymers, poly[4-(n-acryloyloxyalkoxy)]benzoic acids (BA-nPA) with a varying length of alkyl spacer, were used in this systematic study. These polymers are organized in smectic C phase amenable to macroscopic alignment when mechanical field is applied. For this study, CdS NRs with a diameter comparable to the thickness of the smectic layers were chosen to preserve the mesophase structure. As a control system, we have also used an amorphous copolymer of norbornene and methylmethacrylate.
’ EXPERIMENTAL SECTION Synthesis of CdS NRs. In a 100 mL three-necked round-bottom flask was mixed 7 g of trioctylphosphine oxide (TOPO) with 830 mg of tetradecylphosphonic acid (TDPA) and 230 mg of CdO. The mixture Received: August 20, 2011 Revised: September 11, 2011 Published: September 13, 2011 13353
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Figure 1. TEM images of CdS NRs at low (A) and high magnification (B). Inset shows the diffraction pattern collected from the central area in panel A. was heated under argon atmosphere to 80 C for 1 h. During this heating process, the mixture melted and turned into a dark red liquid. The liquid was rapidly heated to 320 C and was kept at that temperature for 30 min. This process allowed CdO to form a complex with TDPA rendering the mixture clear and colorless. The temperature was then decreased to 300 C, and 6 mL of 0.281 M sulfur solution in trioctylphosphine (S-TOP) was injected rapidly upon vigorous stirring. The reaction mixture was kept at 300 C with continuous stirring for another 1.5 h. After that, 14 mL of S-TOP solution was introduced into the reaction mixture in a dropwise fashion at a rate of ca. 0.2 mL/min. When the addition was complete, the heating was stopped and the reaction mixture was allowed to cool. When the temperature reached 80 C, the reaction mixture was transferred into several glass vials (30 mL), and 10-fold excess of acetone/methanol mixture (50% vol) was added. The vials were centrifuged at 3000 rpm for 5 min to obtain a yellow precipitate. The precipitate was dissolved in chloroform. NRs were then precipitated by adding excess acetone, followed by centrifugation at 8000 rpm for 4 min and subsequent removal of the supernatant. Polymer Synthesis. Monomeric 4-(n-acryloyloxyalkoxy)benzoic acids (BA-nA) were synthesized as described previously27 and polymerized in benzene at 63 C for 75 h to form the polymer, BA-nPA. 2,20 Azoisobutyronitrile (0.1% of the total weight of the monomer) was used as an initiator. Polymers were precipitated from the benzene solution at room temperature, then separated, dissolved in tetrahydrofuran (THF), reprecipitated with benzene, and dried overnight under vacuum. The isolated yield of resulting polymers was 8090%. Preparation of LC PolymerCdS NRs Composite Films. LC polymer was dissolved in 2 mL of THF at a concentration of 0.10.5 wt %, and the solution was stirred at room temperature for 2 h. CdS NRs solution in THF (2 mL of 0.10.2 wt %) was added dropwise to a polymer solution under vigorous stirring at room temperature. After 20 min of stirring, the composite product was precipitated from the solution by adding a 5-fold excess of hexane. The precipitate was separated, filtered, and washed 23 times with hexane and then dried under vacuum. To prepare film-like samples, the resulting composite powder was heated between two polyimide films at 200 C and pressed down to a designated thickness controlled by a metal foil spacer (0.050.2 mm) under a constant load (23 kg). Characterization of Composites. DSC curves were obtained on a differential scanning calorimeter DSC823e (Mettler Toledo) at a heating rate of 10 K/min under argon atmosphere. IR spectra were recorded with IFS 66 v/s (Bruker) (50 scans). Samples were prepared as tablets from the powder pressed together with KBr. High temperature
FTIR measurements were carried out with in situ temperature cell (Bruker). TEM images and small area electron diffraction (SAED) patterns were obtained on transmission electron microscope LEO912 AB OMEGA (Carl Zeiss) operating at 100 kV voltage. Samples were placed on copper grids coated by Formvar film. Filmed samples (75 nm thick) were sliced by ultramicrotome Ultracut (Reichert-Jung) equipped with an ultra diamond knife (DiATOME). SAED patterns were obtained at accelerated voltage 100 kV and drawtube length 290 mm. To establish the crystal structure of CdS NRs, the SAED patterns of NRs were analyzed in terms of the equation R = λL/dhkl that describes the relationship between the radius R of the peak in SAED pattern and dhkl spacing (L is the hardware constant, and λ is the wavelength of the electrons). The determination of the constant L in the equation was performed with the help of the SAED pattern of the well-known Au foil. These d-spacings were 0.23553 nm (111), 0.20396 nm (200), 0.14422 nm (220), 0.12299 nm (311), and 0.11776 nm (222). After the constant L determination, the dhkl spacings for CdS were calculated from the SAED pattern. The measured and calculated dhkl spacings were compared to dhkl spacings of Greenockite and Hawleyite (cadmium minerals that consist of CdS in hexagonal and cubic forms, respectively). The spacings of Greenockite were directly received from the published XRD data available from the PRUFF Project Database, whereas dhkl spacings of Hawleyite were calculated with the use of Bragg equation from simulated XRD powder pattern created with the aid of free software Mercury 2.4 (Build RC5) from the Cambridge Crystallographic Data Centre (CCDC) and data file obtained from Crystallography Open Database (COD) CIF collection. Additionally, the location of the peaks in SAED patterns was compared to those in simulated XRD powder patterns for Greenockite and Hawleyite, which were calculated as described previously. X-ray diffraction measurements were performed using monochromatic Cu Kα radiation with a wavelength λ = 0.15148 nm generated by a microfocus X-ray source (Rigaku Micromax M002+) and a 3-pinhole collimator (JJ-X-ray). The beam diameter was 0.2 mm. The scattered intensity was detected by a two-dimensional gas detector (1024 1024 pixels, Bruker HISTAR). As a calibration standard, silver behenate was used with d001 = 5.838 nm. All measurements were performed with the incident beam normal to the film surface and in the center of the sample. Simultaneous measurements of the wide-angle and small-angle reflections were done at a sample-to-detector distance of 232 mm. For a precise determination of the smectic layer spacing, additional measurements were performed in a SAXS setup with a sample-to-detector distance of 1759 mm. 13354
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Figure 2. Comparison of FTIR spectra. (A) CdS NRs capped with TOPO (1), TOPO in the crystalline (2) and molten states (3), BA-7PA polymer (4), and its composite with 33 vol % CdS NRs (5). (B) BA-7PA polymer (1) and its composite containing 17 vol % CdS NRs (2). UVvis absorption spectra of CdS NRs were measured in hexane and heptane solutions by double-beam spectrophotometers Specord UVvis, equipped with ADC for registration, and Specord M 82 (Carl Zeiss Jena). Blank hexane or heptane was used as a reference. The optical path was 1 cm. The photoluminescence (PL) steady-state emission spectra of CdS NRs in solutions were collected on LS-55 (PerkinElmer) luminescence spectrometer and Hitachi F-4010 fluorescence spectrophotometer. Local laser beam PL spectra from hexane solution of CdS NRs, dried CdS NRs, and NRs composite films were obtained on a LabRAM HR Raman microscope (HORIBA Jobin Yvon). The argon ion laser operating at 488.0 nm was used as a light source. The density of the laser power on a sample surface was varied from 0.5 to 50 W cm2. PL spectra of solutions were measured in a quartz cell, and quartz cover slides were used for dried CdS NRs and NRs composite films. All LabRAM HR Raman microscope measurements were carried out in the epi-illumination mode.
’ RESULTS AND DISCUSSION Structure of LC PolymerCdS NRs Composites. TEM examination shows that freshly prepared CdS nanostructures (Figure 1) have a rod-like shape (NRs) with an average diameter ca. 5 nm and the length ranging from 30 to 100 nm. TEM image of a high concentration sample (Figure 1A) clearly demonstrates that rod-like morphology is predominant under these synthetic conditions. However, the imaging at higher magnification and lower concentration (Figure 1B) also reveals the presence of branched structures and small fraction of tetrapods. The crystal structure of CdS nanorods was analyzed on the basis of the small area electron diffraction (SAED) pattern (Figure 1, inset), which was collected from the central area shown in Figure 1A. The comparison of dhkl spacings from SAED patterns (see Supporting Information Figure S1 and Table S1) with XRD data of Greenockite CdS (wurtzite hexagonal phase) and Hawleyite CdS (zinc blende cubic phase) obtained with simulated XRD data shows that CdS NRs have a wurtzite crystal structure, which is consistent with the literature reports. The FTIR spectrum of isolated CdS NRs indicates the presence of TOPO ligands on their surface, which generate signals similar to those observed in pure TOPO (Figure 2A,
Figure 3. SAXS curves of BA-10PA polymer (top) and its composite containing 6.5 vol % of CdS NRs (A). X-ray patterns of uniaxially oriented films of the pure polymer (B) and its composite with CdS NRs (C).
spectra 1 and 2, respectively). Strong spectral bands in 700900 cm1 (PC bonds) and 10001200 cm1 (PdO bonds) regions are observed for a crystalline TOPO, which become much broader and slightly shifted in its molten state (Figure 2A, spectrum 3). The spectrum of CdS NRs (Figure 2A, spectrum 1) is consistent with the spectrum of molten TOPO, and one specific band appears at the same position in both spectra (νPdO at 1170 cm1). Similarly, a characteristic sharp signal is present at 1490 cm1 in these two spectra. In contrast, there is an intense band at 1102 cm1 in the CdS NRs (not present in pure TOPO), which may be assigned to the PdO bond strongly coordinated to CdS. This shift in CdS/TOPO spectrum indicates that the PdO π-bond is strongly delocalized due to its interaction with the CdS surface. On the other hand, spectral bands related to PC bond (700900 cm1 range) are similar in both systems (CdS NRs and pure TOPO). These results prove that CdS nanostructures are coated with TOPO 13355
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molecules, which strongly interact with the inorganic surface, but are not organized into a crystalline state. Figure 2A (spectra 4 and 5) and B shows the spectra of CdS/TOPO composite with BA7PA in comparison with the spectrum of the pure polymer. There Table 1. Thermal Characteristics of PB-nPA and Their Composites with CdS NRs polymer/CdS content, vol %
Tg, C
Tis, C
BA-7PA
95
181
6.5
97
174
9 17
97 97
178 178
33
96
176
38
97
181
BA-10PA
77
180
6.5
78
175
9
80
180
12
78
179
17 38
81 76
179 179
is no significant difference between the spectra of the polymer and its composite with CdS NRs. Moreover, there are no any spectral signs for the presence of TOPO in the composite. There may be two reasons for the absence of TOPO related spectral bands. The first reason could be related to the low content of CdS/TOPO within the composite (33%). The second reason could be the partial substitution of TOPO by a polymer on the NRs surface followed by washing of free TOPO molecules from the composite in the process of its preparation. It is conceivable that some TOPO ligands still remain on the surface of nanorods, but the sensitivity of FTIR is not sufficiently high to confirm it. Nevertheless, the absence of strong characteristic TOPO bands in the spectrum of nanocomposite suggests that the majority of these ligands has been replaced by the polymer. We do not have any specific spectral signature of the bonding between the matrix and CdS except for the change in the relative intensity of the spectral bands at 2552 and 2670 cm1, which are slightly decreased in the spectrum of CdS/BA-7PA (Figure 2B). These bands correspond to the vibration of OH bond in the cyclic dimers of carboxylic groups. The identical change in the spectra of a similar polymer BA-6PA was observed upon increasing the temperature and was attributed to the decrease in the number of
Figure 4. TEM images of BA-7PA composite containing 6.5 vol % of CdS NRs before (A,B) and after the uniaxial deformation (C). Double arrow indicates the direction of film stretching, and the insets show the respective ED patterns. 13356
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Langmuir hydrogen-bonded dimers.28,29 We also can envision that the above spectral changes in our system result from the conformational changes in the side groups of LC polymers, when they are brought into immediate vicinity with the surface of CdS nanorods. The presence of CdS NRs in the composites was confirmed by X-ray scattering data. As an example, the XRD patterns of BA10PA and its composite are given in Figure 3. The tilted SmC structure of the BA-nPA family of polymers30,31 is characterized by an amorphous halo in the angular region 2θ = 1330 (Figure 3A, black curve) related to the distance between the side chains of the macromolecules and two small angle peaks (2θ ≈ 2.6 and 5.2) corresponding to the first- and second-order reflections of the smectic H-bonded layers. Incorporation of CdS NRs into the polymer matrix leads to a slight shift (2θ ≈ 2.9 and 5.8) in the small angle maxima (Figure 3A, red curve), which indicates a 0.5 nm increase in the average value of the interlayer spacing. Most importantly, a well-defined maximum at 2θ = 27 (d = 0.325 nm) appears in the form of a spike on the amorphous halo, which is related to the crystal structure of CdS NRs. Comparison of the dhkl spacings calculated from XRD pattern of pure CdS NRs (see Supporting Information, Table S1) with that of CdS NRs embedded into LC matrix (Figure 3B) allows us to assign this peak at 2θ = 27 to the d002 spacing of the wurtzite phase (0.3315 nm). To assess the interactions between the continuous LC matrix and the dispersed phase of CdS NRs, we investigated the phase behavior of various nanocomposites by differential scanning calorimetry (DSC). Table 1 summarizes the glass transition temperatures (Tg) and LCisotropic phase transitions of composite samples. One can see that the observed transition temperatures do not change significantly with the insertion of as much as 38 vol % of CdS NRs. These data confirm that no appreciable distortion of the polymer matrix takes place and that the smectic mesogenic ordering is fully preserved. On the other hand, it also suggests a fairly weak interaction between the NRs and the polymer matrixes. This phase behavior is consistent with the X-ray data (Figure 3A) showing only a slight increase in the interlayer distance. The internal structure and morphology of the composites were analyzed by TEM imaging of microtomed films measuring ca. 75 nm in thickness (Figures 4). CdS NRs were found to form small domains (100200 nm) in the LC polymer matrix. Although the interaction between BA-nPA polymers and CdS NRs appears to be fairly weak, these domains are evenly distributed throughout the LC matrix, and the composites remain stable without a macroscopic phase separation (Figure 4A,B). However, the system is not entirely homogeneous, and some segregation of NRs takes place. The packing density of NRs inside the domains is relatively low and does not change appreciably in any LC polymer used in our studies. We also performed a control experiment by dispersing CdS NRs in an amorphous matrix of norbornenemethyl methacrylate copolymer. As shown in Figure S2, there is a significant phase segregation manifested by a much higher packing density of CdS NRs (see Supporting Information Figure S2). This comparative study supports the idea that the carboxylic acid groups of the substituted benzoic acids are capable of at least partial replacement of TOPO ligands and favorable interaction with the surface of CdS NRs. In contrast, when the polymer lacks functional groups (norbornene methyl methacrylate copolymer) that could strongly bind the surface of NRs, only a limited dispersion of nanorods can be achieved.
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Figure 5. UVvis absorption (1) and PL spectra (excitation wavelength 400 nm) of CdS NRs in heptane solution (2), in amorphous matrix (3), and in LC polymer (BA-10PA) matrix (4) at 2 wt % content.
The uniaxial deformation of the composite films above the glass transition temperature results in a partial coalescence of small domains and the formation of elongated wire-like structures (Figure 4C). A combination of TEM images and ED patterns clearly demonstrates that the CdS nanocrystals are mainly oriented along the stretching direction.32 The orientation of NRs proceeds together with the alignment of the polymer matrix as previously shown by the XRD pattern (Figure 3C). Four condensed wide angle maxima with an alternating azimuthal distribution indicate the smectic C tilt within the layers.30,31 The small angle maxima in XRD patterns of the composite system are localized at the equator (Figure 3C) and serve as a proof for the alignment of the smectic layers along the stretching axis.33 As for Æ002æ reflection of CdS NRs, it appears as two well-defined arcs at the meridian of the XRD pattern (Figure 3C). This meridian position proves that (002) planes of CdS NRs are oriented perpendicular to the stretching direction. Because [002] is known to be the growth direction of CdS NRs (perpendicular to their long axis), one can conclude that the nanorods are mainly aligned parallel to the direction of external mechanical field. This important information is not only inferred from the X-ray analysis, but is strongly corroborated by direct TEM visualization (Figure 4C). Optical Properties of Composites. Generally, the wavelength of the exciton absorption decreases with the particles size due to the quantum confinement of photogenerated electronhole pairs. Typical absorption and PL spectra of CdS NRs in hexane solution (Figure S2) exhibit a well-defined absorption peak at about 447 nm, which is considerably blue-shifted relative to the peak of bulk CdS, indicating the quantum confinement effect.10,11 If CdS NRs are excited at 380 nm, the emission peak appears at 466 nm, which implies that the Stokes shift is 19 nm (0.12 eV). This PL maximum is significantly blue-shifted from the macroscopic band gap of bulk CdS (500515 nm), which is consistent with the strong confinement model34 and the nanorods diameter of 5 nm.35,36 This well-defined maximum can be assigned to the optical transition of the first excitonic state. The influence of the polymer matrix on PL properties was studied with the 2 wt % CdS NRs composites with amorphous and LC polymers. Figure 5 shows the absorption and PL spectrum of CdS NRs in heptane solution (excitation at 400 nm) as well as PL spectra of NRs in amorphous and LC 13357
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Figure 6. PL spectrum of BA-7PA composite with 33 vol % of Cd S NRs (A). The part of the same spectrum presented on the energy scale (B) that shows the ASPL shift. Dotted lines indicate the wavelength and energy position of the exciting laser beam.
Figure 7. PL spectra of BA-7PA composite with 33 vol % CdS NRs recorded at different power density of the excitation light (A) at 488.5 nm and the intensity of the exciton (480481 nm) and trap (676677 nm) PL peaks as a function of the power density (B).
polymer films. One can see that the emission peak of NRs does not significantly change when their dispersion in LC matrix (467 nm) is compared to a homogeneous heptane solution (468 nm). In contrast, the peak maximum moves up by 7 nm if the amorphous polymer matrix is used. The intensity of the second broad PL peak in 570700 nm range is negligibly small in the spectrum of CdS NRs in solution, but it strongly increases if NRs are dispersed in polymer matrixes. This peak may be interpreted as a PL of the defects (traps) usually localized at the nanoparticles surface. The intensity ratio between the exiton and trap peaks becomes much lower in the amorphous matrix in comparison with the LC polymer. This fact together with the 7 nm red shift of the exciton peak in the amorphous matrix may be explained by much greater phase segregation of CdS NRs (Figure S3) followed by reabsorption of the high energy component of the exciton spectrum.
When the photoluminescence of CdS NRs in LC polymer matrix was induced at a wavelength longer than the PL emission peak, we observed an anti-Stokes photoluminescence (ASPL). As an example, the PL spectrum of BA-7PA composite containing 33 wt % of CdS NRs obtained under the excitation with the Ar+-laser (488 nm) is given in Figure 6. The intensity of the antiStokes part of the spectrum is comparable to Stokes luminescence, whereas the PL maximum is located below the wavelength of the excitation source. This phenomenon was previously observed in various systems, which include bulk semiconductors, epitaxial heterostructures, and self-assembled quantum dot layers.3743 However, there are no reports to date on the observation of ASPL in CdS nanorods. There are three mechanisms that may explain ASPL, a twophoton absorption recombination,4446 Auger effect,47 and surface state processes.40 Whereas the first two mechanisms are 13358
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Langmuir nonlinear and require the initial photon to populate an intermediate state, the ASPL via surface state processes involves thermally populated midgap states, which absorb a single photon leading to higher energy luminescence. In addition, surface state processes show single photon power dependences.43 The corresponding ASPL spectra (A) and the intensity of ASPL peak (B) are shown in Figure 7 at different power density. One can see that the intensity of ASPL depends linearly on the power density of the exciting radiation. The same linear curve corresponds to the dependence of PL intensity of surface traps on the power density. This linear relationship offers definitive proof that the ASPL of CdS NRs is governed by the surface state processes. In summary, we described the first example of CdS NRs composites in LC polymers. The distribution of the small domains of NRs in the LC matrix is much more homogeneous than in amorphous matrix, as confirmed by TEM analysis of microtomed composite films. Importantly, the combination of X-ray and TEM data unambiguously proves that nanorods undergo long-range orientation when the composite films are uniaxially deformed. In addition, an interesting formation of one-dimensional aggregates of rods is observed within the LC polymer matrix. We also demonstrated that the extent of CdS NRs microphase separation strongly influences their optical properties. These include the changes in the intensity, width, and position of the Stokes exiton emission peak as well as the ratio of intensities of the Stokes emission over trap emission peaks. The position of the CdS NRs emission peak in an LC matrix is nearly the same as it is in a homogeneous solution, whereas it is red-shifted in the amorphous matrix. The number of defects is much higher in the amorphous phase, and the trap emission prevails over the exciton emission. An anti-Stokes photoluminescence (ASPL) in polymer nanocomposites is found under the excitation below the nanoparticles ground state. Experimental evidence indicates that thermally populated states are involved in the ASPL process.
’ ASSOCIATED CONTENT
bS
Supporting Information. Experimental details describing the XRD data and TEM images of nanocomposites, and UVvis spectra of CdS NRs. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (E.R.Z.);
[email protected] (R.V.T.).
’ ACKNOWLEDGMENT TEM and SAED measurements were performed in the Research Center “Transmission Electron Microscopy”, and UVvis absorption and PL measurements were performed in part in the Research Center “Technology of the production and complex investigation of new nanostructured materials” of M. V. Lomonosov MSU. We are thankful to Prof. V. Yu. Timoshenko for helpful discussions. This work was supported by the Ministry of Education and Science of the Russian Federation (902.740.11.516, P914, P918) and the Presidium of the Russian Academy of Sciences (no. 21). E.R.Z. acknowledges financial support provided by NSF (DMR-0547399, DMR-1105878).
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