Article pubs.acs.org/JPCC
Size-Specific ZnO Quantum Dots as Onsager Cavity in Ooshika−Mataga−Lippert Equation Sudip Kumar Pal, Aradhana Devi, and Sujit Kumar Ghosh* Department of Chemistry, Assam University, Silchar-788011, India ABSTRACT: The influence of the surrounding solvent medium to a solute molecule in solution can be treated within the framework of Onsager reaction field model which is based on the assumption that the solute is reduced to a point dipole at the center of a spherical cavity inside the solvent that can be described as the homogeneous, polarizable medium of specific dielectric constant. When the solute molecules are excited in solution of the polar solvent, the changes in the photophysical properties of the solute are manifested through shifts in the maxima of absorption and fluorescence spectra and the observation can be interpreted in terms of the Ooshika−Mataga−Lippert equation. Over several decades, a wide variety of organic molecules as fluoroprobes have been explored to reveal the polarity of their immediate solvent environment. However, while these molecular probes, with diameters less than 10 Å, have been employed so far in the literature as Onsager cavities, the limiting value of their radii has not been restricted within the reaction field model. On the basis of these perspectives, we have investigated the validity of linear response approximation, predicted by Onsager model, for finite size-specific zinc oxide particles, with dimensions 1 order of magnitude higher (10−100 Å), and its consequences on the Ooshika−Mataga−Lippert equation.
1. INTRODUCTION The interaction between the solute and surrounding solvent medium in solution can be described using the Onsager reaction field model.1 This model is based on the assumption that the solute molecule is reduced to a point dipole placed at the center of a spherical cavity immersed in a homogeneous and polarizable solvent dielectric, which acts as the effective electric field on the solute molecule. The effective electric field has been coined as the reaction field as it arises from the inductive and orientation polarizations of the surrounding solvent molecules induced by the solute dipole. The field describes the interaction of solute−solvent system as a function of dipole moment and polarizability of the solute molecule and dielectric constant and refractive index of the solvent. The Onsager model with a clear and transparent physical basis of the cavity field and reaction field has, successfully, been adapted to explain the interactions in the solute−solvent system.2 When a molecule is dissolved in a solvent medium, it undergoes several intermolecular interactions, such as, dispersion and dipole−dipole interactions with the solvent. Before light irradiation, the solutes remain surrounded by the solvent molecules so as to attain the most stable configuration between solvents and the ground state of the solute molecules. Since, electrons move with much higher velocity than nuclei (Born−Oppenheimer approximation), absorption spectra can be considered due to an electronic transition from the ground equilibrium state to the Franck− Condon excited state.3 According to the classical concept, the phenomenon of light absorption creates enforced vibration of oscillators and consequently, the transition dipole induced in the molecules become stabilized by the reaction field of solvents surrounding the solute molecules responsible for light absorption.4 © XXXX American Chemical Society
As a consequence of this dispersion effect of solvent molecules, the absorption spectrum exhibit a red shift; this wavenumber shift of the absorption maximum of dyes was calculated by Ooshika5 and others6,7 using the second order perturbation theory. In order to accommodate the change in the electronic charge distribution of a solute, the solvent molecules, then, relax to a configuration of lower energy, which is in equilibrium with the electronically excited solute.8 Under such condition, if the excited state lifetime of the solute is greater than the reorientation time of the solvent dipoles, the maximum of the fluorescence spectrum appears at lower energy than that of the absorption spectrum.8 It is, therefore, evident that the interactions between the solvent and solute affect the energy difference between the ground and excited states and as a consequence, the spectral shift of fluorescence due to the solvent effect may differ, in general, from that of absorption.9 Thus, absorption and fluorescence spectral measurements on polar solutes which undergo a change in dipole moment upon electronic excitation provide important information on the solvation process and therefore, the excited state electronic structure. After Ooshika’s equation of the solvent effect on the absorption spectra had been presented, the somewhat simplified expression, was first derived independently by Lippert10 and Mataga et al.11,12 by applying Ooshika theory to the difference of solvent effect on fluorescence and absorption spectra and therefore, the effects of solvent polarity on the Stokes’ shift have, often, been interpreted in terms of the Ooshika−Mataga−Lippert equation. Received: December 8, 2016 Revised: February 10, 2017
A
DOI: 10.1021/acs.jpcc.6b12359 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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to study the effect of solvation employing finite-sized solid particles as the Onsager cavity in the Ooshika−Mataga−Lippert equation. In this article, we have explored the applicability of size-specific zinc oxide (ZnO) quantum dots (QDs) in lieu of molecular probes as Onsager cavity in Ooshika−Mataga−Lippert equation. Stabilizer-free ZnO QDs have been synthesized by refluxing zinc acetate dihydrate in methanol under alkaline condition and size of the particles has been tuned by variation of the concentration of alkali in the reaction medium. The ultrasmall particles so obtained have been characterized by absorption and fluorescence spectroscopy, transmission electron microscopy (TEM), high resolution transmission electron microscopy (HRTEM), selected area electron diffraction pattern (SAED) and energy dispersive X-ray (EDX) analysis. Now, we have measured the solvent shifts of the electronic spectra of size-specific ZnO QDs and analyzed the observations in the light of Lippert equation. Finally, the effect of particle size on the reaction field, dipolar solvation energy and the change in dipole moment between their ground and excited states have been elucidated.
The commonly known Lippert equation describes the Stokes’ shifts, defined as the difference between absorption and emission maxima (expressed in cm−1 units), and in consequence, describes the energy change that arises due to solvation of the fluoroprobe. The formulation of the Lippert equation provides a useful framework for consideration of general solvent effect and ignores the specific solvent−fluoroprobe interactions, such as, hydrogen bonding, the formation of a charge-transfer state, etc.13 The Lippert equation, thus, only represents the effect of orientation polarization, and under realistic conditions, enables us to estimate the dipole moment of the excited molecule.14 The Lippert equation that describes the steady state Stokes’ shift of a polar fluoroprobe in a polar solvent has been generalized to treat the time-dependent Stokes’ shift by Mazurenko and Bakshiev,15 Bagchi, Oxtoby and Fleming,16 and van der Zwan and Hynes17 based on a generalized Onsager cavity model, in which the dielectric continuum has been described by a frequency-dependent dielectric function. Therefore, both steady-state and time-resolved spectroscopy have been employed to investigate the photophysical aspects of molecular probes exhibiting visible fluorescence that is sensitive to the solvent environment. Over several decades, a wide variety of organic fluorescent probes, like, coumarins, purines, pyrene derivatives, exalite dyes, curcuminoid dyes, hemicyanine dyes, hydroxycoumarin dyes, acridinedione dyes, fluorescein, flavones, 6-propionyl-2-(dimethylamino)naphthalene (PRODAN), 6-bromoacetyl-2-dimethylaminonaphthalene (BADAN), (6-acryloyl-2-dimethylaminonaphthalene) (ACRYLODAN), boron dipyrrolomethenes (BODIPYs), quinazolines, acridines, phenazines, substituted anthraquinones, and some laser dyes have been explored to reveal the polarity of their immediate environment.13,18 However, while these fluorescent molecular probes, with diameters less than 10 Å, have been employed as Onsager cavity, the limitation of the radii of the cavity is not restricted within the reaction field model. Therefore, it is quite reasonable to validate the hypotheses of Onsager model with fluoroprobes having the dimension with higher order of magnitude (10−100 Å) and materials, at the nanoscale dimension, with well-defined absorption and emission spectral features can, judiciously, be employed for this purpose. It is known that zinc oxide (ZnO) is a n-type semiconductor with a wide and direct band gap (3.37 eV) and large exciton binding energy (60 meV) at room temperature.19 Moreover, the ease of synthesis into variety of architectures, excellent interaction with the electromagnetic wave, and tunable electronic properties make them excellent candidates for numerous applications in the field of materials research.20 Since the high chemical and photochemical stability of the ZnO QDs deserves the possibility of using the semiconductor particles as efficient fluorescent labels,21 the characteristic fluorescence spectrum of the particles could serve as elegant probe to measure the interaction with the solvent molecules of the dispersion media. There are several advantages of using ultrasmall particles, at the nanoscale dimension, as fluoroprobes in comparison with the molecular probes: (i) due to advances in the characterization techniques, the dimension of the particles can be well-characterized and the volume of the particles can be assumed as the volume of the spherical cavity; (ii) the volume of the cavity could be manipulated by variation of the particle size miniaturizing the synthetic conditions of the reaction medium; and (iii) the surface of the particles can be naked, thereby reducing the possibility of short-range intermolecular/interparticle interactions.22 On the basis of these perspectives, it is quite reasonable
2. EXPERIMENTAL SECTION Reagents and Instruments. All the reagents used were of analytical reagent grade. Zinc acetate dihydrate (Zn(OOCCH3)2.2H2O) (Sigma-Aldrich) and potassium hydroxide (KOH) (S. D. Fine Chemicals, India) were used as received. Spectroscopic grade solvents, viz., methanol, ethanol, dioxane, dichloromethane, tetrahydrofuran (THF), dimethyl sulfoxide (DMSO), dimethylformamide (DMF), n-propanol, 2-propanol, acetone, and acetonitrile were obtained from Qualigens’ Fine Chemicals, India and were used for the spectroscopic measurements after purification. Solvents were dried according to published methods and freshly distilled before use except methanol, dichloromethane, acetonitrile and DMF which were dried using a Puresolv solvent purification system.23 Double distilled water was used throughout the course of the investigation. The temperature was 298 ± 1 K for all experiments. Absorption spectra were recorded in a PerkinElmer Lambda 750 UV−vis−NIR digital spectrophotometer taking the sample in 1 cm well-stoppered quartz cuvette. Fluorescence spectra were recorded with a PerkinElmer LS-45 spectrofluorimeter equipped with a pulsed xenon lamp and a photomultiplier tube with R-928 spectral response. The spectrofluorimeter was linked to a personal computer and utilized the FL WinLab software package for data collection and processing. Transmission electron microscopy was carried out on a JEOL JEM 2100 microscope with a magnification of 200 kV. Samples were prepared by placing a drop of solution on carbon-coated copper grids and dried overnight under vacuum. High resolution transmission electron micrograph and selected area electron diffraction pattern were obtained using the same instrument. Energy dispersive X-ray analysis was performed on a LEO 1530 field emission scanning electron microscope using X-ray detector. Synthesis of Size-Specific ZnO QDs. Stabilizer-free ZnO QDs have been synthesized by the precipitation of Zn2+ with −OH in an alcoholic solution by following the procedure of Weller group.24 In a typical synthesis (set A), an amount of 0.055 g zinc acetate dihydrate [Zn(ac)2·2H2O] was dissolved in 25 mL of methanol in a double-necked round-bottom flask by refluxing the mixture on a water bath at 45 °C for 45 min and subsequently, the temperature of the reaction mixture was increased to 60 °C. After 15 min, 13.5 mL KOH solution (0.3 M) was added to the mixture instantaneously and curdy B
DOI: 10.1021/acs.jpcc.6b12359 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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function of wavelength illustrates that there occurs a sudden change in the real part of refractive index for ZnO from 400 to 300 nm range which accounts for the change in scattering efficiency at lower wavelength regime27 and therefore, two maxima appear in the absorption band of these ultrasmall particles.28 Moreover, it is seen that the maximum of the excitonic band is blue-shifted with increase in particle size; for instance, the lower wavelength absorption maxima are seen at 277 (4.48 eV), 275 (4.51 eV), 272 (4.56 eV), 270 (4.59 eV), and 266 nm (4.66 eV) for particles of sets A, B, C, D, and E, respectively. For semiconductor nanoparticles, the Fermi energy level lies in-between the valence and conduction bands, which comprise of discrete energy states due to strong electron confinement.29 The distance of the intervening gaps depends on the size of the particles as to the basis of the interaction with the confined electrons among the lattice points.28 The optical band edge bears the characteristic electronic transition energy taken place to promote the electrons to the energy states in the conduction band from the valence band, including, excitonic effects.28 As a result, a gradual blue shift of the absorption maximum is seen with increase in particle size of the ultrasmall particles.30 The steady state normalized fluorescence emission, excited at their corresponding higher intensity maximum, of colloidal dispersion of five different sizes of ZnO QDs exhibit two kinds of emissions: one is at narrow near band-edge ultraviolet emission with maximum near 390 nm (3.17 eV) and the other a weak broad green band with maximum at approximately 560 nm (2.21 eV). The mechanism of ultraviolet emission could be ascribed to the transition from conduction band edge to valence band (excitonic emission); whereas, the broad green visible emission band, is believed to stem from an electronic transition from deep donor level close to the conduction band edge to a defect related trapped state due to zinc interstitials, oxygen vacancies, as well as donor−acceptor pairs arising from n-type semiconducting properties of ZnO species.29,31 Moreover, it is noted that with increase in particle size, the maximum of UV emission is shifted to the red and the maxima of the excitonic emission arise at 384 (3.23 eV), 386 (3.21 eV), 390 (3.18 eV), 393 (3.15 eV), and 396 nm (3.13 eV) for particles of sets A, B, C, D, and E, respectively. This excitonic emission is directly linked to the confinement effects and consequently, depends on the size of the particles; as a result, with increase in particle size, a gradual red shift in the fluorescence emission is observed.28 The morphology, composition and crystallinity of the ZnO QDs have been described in Figure 2. Representative
white coloration was seen indicating the formation of ZnO particles. The refluxing was continued for another 1 h and the color of the dispersion became white indicating the completion of the reaction. Then, the water bath was removed and stirring was continued for 12 h at room temperature. The dispersion so obtained was washed for 3−4 times with methanol and separated by centrifugation at 5585g force for 10 min. The particles obtained by this method were redispersed in methanol and were found to be stable for a couple of months without any sign of agglomeration or precipitation of the particles. In this method, it is possible to control the particle size by varying [Zn(II)]:[−OH], and thus, five particle sizes have been obtained as has been summarized in Table 1. Table 1. Synthetic Conditions for the Preparation of Five Different Sizes of ZnO Quantum Dotsa set
[Zn(ac)2·2H2O] (mM)
[KOH] (M)
[Zn(II)]:[−OH]
A B C D E
10 10 10 10 10
0.30 0.45 0.60 0.75 0.90
1:30 1:45 1:60 1:75 1:90
particle sizeb (nm) 2.2 3.1 5.9 7.8 9.6
± ± ± ± ±
0.1 0.2 0.4 0.6 0.8
a
Total volume of the solution was maintained to 38.5 mL for all sets of particles. bThe particle size is represented as the mean diameter ± the standard deviation of the particle size distribution.
3. RESULTS AND DISCUSSION In this experiment, stabilizer-free ZnO QDs have been synthesized by alkaline hydrolysis of zinc acetate dihydrate in an alcoholic solution. Because of the adsorption of negatively charged acetate counterions on the particle surface, ZnO QDs are negatively charged.25 The high chemical and photochemical stability of the ZnO QDs render the investigation of their physicochemical properties by both absorption and fluorescence spectroscopy. Figure 1 shows the normalized absorption and fluorescence spectra of the methanolic dispersion of five different sizes of ZnO QDs. The absorption spectra (left panel) of the as-prepared QDs show two maxima, one near 270 nm (4.88 eV) and the other in the region of 330 nm (4.22 eV) that arise due to the excitonic transitions between the trapped energy states situated within the confinement region.26 The dispersion relation obtained by fitting to the first order Sellmeier equation showing the plot of refractive index as a
Figure 1. Normalized (left) absorption and (right) fluorescence spectra of colloidal dispersion of five different sizes of ZnO QDs in methanol. The colloidal dispersions of the particles have been excited at their corresponding high intensity absorption maxima to measure the fluorescence spectra. C
DOI: 10.1021/acs.jpcc.6b12359 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 2. (a−e) Transmission electron micrographs of ZnO QDs of sets A, B, C, D and E, respectively, (f) high resolution transmission electron micrograph of the ZnO QDs (set C), (g) selected area electron diffraction pattern of the ZnO QDs (set C), and (h) energy dispersive X-ray pattern of the ZnO QDs (set C). Insets in panels a−e show the corresponding diameter histogram of the ZnO QDs. The dotted yellow circles in panel f indicate the nearly spherical morphology of the ultrasmall particles.
continuum having the macroscopic dielectric constant, ϵ. The local field, F inside the cavity is, conveniently, written as the sum of a cavity field, G due to charge distribution at the center and a reaction field, R due to outside polarization, so that F = G + R. While the cavity field can exert a torque on the dipole and cause it to align in the applied field, the reaction field can polarize the dipole and cannot cause it to reorient because the dipole moment and reaction field are always in the same direction. The dielectric surrounding the dipole has two effects: it changes the effective dipole moment as observed from outside the cavity and it results in a reaction field, due to collective effects from the surrounding solvent molecules, which changes the dipole moment even in the absence of applied electric field. The dipole moment of the solute inside the cavity is called the “effective internal dipole moment” (μs).22 Therefore, in the absence of any applied field, the polarizable dipole is enhanced by its reaction field, so that the total moment can be expressed as the sum of spontaneous and induced contributions as gμ μs = μ + αR = μ + α s (1) V
transmission electron micrographs (panels a−e) of the five size-specific ZnO QDs shows that the particles are spherical or nearly spherical with average diameter (represented as mean diameter ± the standard deviation of the particle size distribution) in the range of 2.2 ± 0.1, 3.1 ± 0.2, 5.9 ± 0.4, 7.8 ± 0.6, and 9.6 ± 0.8 nm, respectively. Insets show the diameter histograms of the corresponding sets of ZnO QDs as determined from electron microscopic measurements. Typical high resolution transmission electron micrograph (panel f) of ZnO QDs (set C) shows the distance between two adjacent planes as 0.26 nm, corresponding to (002) planes in wurtzite ZnO.32 The dotted yellow circles in the HRTEM image indicate the nearly spherical morphology of the ultrasmall ZnO particles. Selected area electron diffraction pattern (panel g) of the ZnO QDs (set C) is consistent with reflections (100), (002), (101), (102), and (110), corresponding to the hexagonal wurtzite phase of ZnO particles.33 The energy dispersive X-ray spectrum (panel h) of the ZnO QDs (set C) indicates the presence of Zn elements in the particles. The signals of C, O and Si elements appear from the as-synthesized ZnO, acetate counterions adsorbed onto the particle surface and the silicon wafer used for the measurement. Now, let us concise a critical condensation of the theoretical perspectives to account for solvent dependence of the Stokes’ shift of the inorganic fluoroprobes at the nanoscale dimension. The solvent sensitivity of the Stokes shift is commonly explained by the Lippert equation which is based on Onsager’s reaction field theory. The foundation of the Onsager model of solvation of a dipolar solute in a polar solvent relies on the solution of the Poisson equation of a point dipole in a spherical cavity, separated by a boundary, from a continuum dielectric medium.1 The Onsager model consists of a polarizable point dipole having a permanent moment, μ and an isotropic electronic polarizability, α located at the center of an empty spherical cavity of volume, V. The cavity is surrounded by a
gμ
4π 2(ε − 1) . 2ε + 1
where, R = V s and g = 3 and simplifying, we get μ μs = ⎡1 − 2(ε − 1) α ⎤ ⎣ 2ε + 1 a 3 ⎦
Putting the value of g in eq 1
(2)
This leads to the situation the reaction field causes only some increase in the dipole moment through induction. The Onsager model assumes linear solvent response which implies that dielectric reaction field of the solvent (R) is a linear function of the dipole moment of the solute inside the cavity as given by34 R= D
1 2(ϵ − 1) μs 4π ϵ0 2ϵ + 1 a3
(3) DOI: 10.1021/acs.jpcc.6b12359 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C where ε is the dielectric constant of the solvent, μ the dipole moment of the solute, and a is the radius of the spherical cavity separated from the dielectric when a spherical solute is 1 2(ϵ − 1) 1 immersed in a solvent. In this expression, f = 4πϵ 2ϵ + 1 3 and 0
between these two effects implies that the index of refraction affects both the excitation and emission properties, while the solvent dielectric constant affects only the state responsible for emission.39 The orientation polarizability of the solvent, Δf, as defined by Lippert and Mataga, can be calculated as
a
is defined as the reaction field factor; however, if the shape of the cavity is deviated from sphericity, this factor must be replaced by a reaction field tensor.35 Thus, the reaction field generated in this manner is directly proportional to the dipole moment of the solute under the influence of solvation shell and inversely proportional to the third power of the cavity radius of the solute.35 The potential energy (Edipole) of a dipole in an electric field36 can be presented as
Δf (ε , n) =
1 2(ϵ − 1) μs 4π ϵ0 2ϵ + 1 a3
νa̅ − νf̅ =
(8)
Thus, the solvent induced spectral shifts can be interpreted in terms of the Lippert equation, which describes the change in the dipole moment (μ) (expressed in debye units) upon excitation and Onsager cavity radius (a) of the fluoroprobe and the dependence of the energy of the dipole on the dielectric constant (ε) and refractive index (n) of the solvent. The dielectric constant and refractive index data of the pure solvents can be taken from the literature. The linear relationship between the Stokes’ shift (measured in fluorescence and absorption experiments) and the solvent polarity function produces information about the ground and excited state dipole moments of the fluoroprobes. The ground state dipole moments of ZnO QDs can be calculated using the model proposed by Nann and Schneider,40 which is based on the small crystallographic deviation from ideal wurtzite structure that usually occurs in IIB−VI wurtzite lattices, for instance, ZnO, CdSe, and CdS. The deviation from ideal wurtzite structure is manifested by bond angle bending and bond length stretching as is evident on the basis of elementary point charge model, which results in huge permanent electric dipole moments and spontaneous electric polarization in ZnO QDs.41 According to this model, the total ground state electric dipole moment (μ) of a nanocrystal scales with its volume (V) as
(5)
where, m(μ, μ′) is a function describing the change in dipole moment of the solute upon relative transition between the ground and excited state, f(ε, n) a solvent polarity function which involves both the dielectric permittivity, ε and refractive index, n of the solvent medium and g(a) a geometrical function describing the shape of the cavity containing the fluoroprobe, respectively. The “constant” term reflects the Stokes shift that results from the vibrational relaxation and internal conversion effects, i.e., it describes the unperturbed Stokes shift between absorption and emission bands in vacuum and therefore, is independent of the solvent medium. The difference, the Stokes’ shift (ν̅a − νf̅ ), where, νa̅ and νf̅ are the frequencies of absorption and emission in wavenumbers (cm−1), is dependent on some factors that are intrinsic to the fluoroprobes, and some are due to interaction of the fluoroprobes with the environment. Assuming the same excited state to be involved in both absorption and emission, i.e., ignoring the influence of geometric relaxation in the excited state, the Lippert−Mataga expression for the Stokes’ shift can be expressed as νa̅ − νf̅ =
2(μ′ − μ)2 Δf (ε , n) + constant 4πε0hca3
2(μ′ − μ)2 ⎡ ε − 1 n2 − 1 ⎤ − 2 ⎥ + constant 3 ⎢ 4πε0hca ⎣ 2ε + 1 2n + 1 ⎦
(4)
Therefore, the Onsager approach relies on two parameter model and does not provide any restriction either on the radius of the cavity or the dielectric constant of the solvent.37 The Onsager reaction field model for dipole solvation has, conveniently, been employed in dipole spectroscopy in order to correlate the solvent-induced spectral shifts with solvent dielectric properties.10−12 The derivation of Lippert equation is based on the assumptions of a spherical core, the dipole vectors for the ground and excited states are similar which is obvious for the most fluoroprobes and the specific solvent interactions that can stabilize the excited state could be ignored. The most reliable linear correlation between the wavenumber of absorption and fluorescence maxima, ν̅ (a, f) and a solvent polarity function to account for the solvatochromic change can be expressed in the following generalized form ν ̅ (a , f ) = m(μ , μ′)f (ε , n)g (a) + constant
(7)
The solvatochromic shift showing the relationship of the absorption/emission spectra and the orientation polarizability of the solvent can be expressed as,
2
Edipole = −μs R = −
ε−1 n2 − 1 − 2 2ε + 1 2n + 1
μ=
⎛V ⎞ ⎜ ⎟μ ⎝v⎠ 0
(9)
where μ0 is the permanent electric dipole moment obtained by bond vector addition and volume of hexagonal unit cell of each dipole. For ZnO, the polarization, P =
( μv ) = 0.048 C m 0
−2
and the eqn. 7 can be simplified to μ (C m) = 0.048 (C m−2) × V (m 3)
(10)
Onsager assumed the cavity volume to be the same as the average volume occupied by the solute dipoles. However, according to Gibbs−Wulff theorem, the thermodynamic equilibrium shape of an anisotropic material is a polyhedron in which center of each facet is connected by a central point by a vector whose length is proportional to the surface energy of the facet.42 Under ambient and near-ambient conditions, ZnO forms with a wurtzite crystal structure with three primary cleavage planes, the {101̅0}, {112̅0}, and {0001}. Using density functional theory calculations, the surface and edge energies for surfaces of zinc oxide nanoparticles and their intersections have been computed by several groups to predict the thermodynamically optimal shape of zinc oxide nanoparticles as a function of
(6)
where h is Planck’s constant, c the velocity of light in vacuum, and ε0 the permittivity of the free space. It is known that the refractive index is a property arising due to the electrons of the solvent molecules, while the dielectric effects are originated from both electronic and molecular orientation effects and therefore, the effects of the index of refraction are different from those arising due to the dielectric effects.38 The difference E
DOI: 10.1021/acs.jpcc.6b12359 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 3. Absorption spectra of ZnO QDs of set B in different solvents.
Figure 4. Fluorescence spectra of ZnO QDs of set B in different solvents. The colloidal dispersions of the particles have been excited at their corresponding high intensity absorption maxima to measure the fluorescence spectra.
Table 2. Account of “Effective Internal Dipole Moment” (μs) for Size-Specific ZnO QDs in Different Solventsa effective internal dipole moment (μs in C m) solvents
dielectric constant (ε)
refractive index (n)
2(ε − 1)/2ε + 1
dioxane dichloromethane THF DMSO DMF n-propanol 2-propanol acetone ethanol acetonitrile
2.25 8.93 7.58 46.7 36.7 20.1 20.8 20.7 24.5 37.5
1.4224 1.4241 1.4072 1.4793 1.4305 1.3829 1.3770 1.3580 1.360 1.3441
0.4545 0.8409 0.8143 0.9682 0.9596 0.9271 0.9295 0.9292 0.9400 0.9605
set A 2.73 2.74 2.74 2.74 2.74 2.74 2.74 2.74 2.74 2.74
× × × × × × × × × ×
10−28 10−28 10−28 10−28 10−28 10−28 10−28 10−28 10−28 10−28
set B 7.58 7.58 7.58 7.58 7.58 7.58 7.58 7.58 7.58 7.58
× × × × × × × × × ×
10−28 10−28 10−28 10−28 10−28 10−28 10−28 10−28 10−28 10−28
set C 5.11 5.11 5.11 5.11 5.11 5.11 5.11 5.11 5.11 5.11
× × × × × × × × × ×
10−27 10−27 10−27 10−27 10−27 10−27 10−27 10−27 10−27 10−27
set D 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09
× × × × × × × × × ×
10−26 10−26 10−26 10−26 10−26 10−26 10−26 10−26 10−26 10−26
set E 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26
× × × × × × × × × ×
10−26 10−26 10−26 10−26 10−26 10−26 10−26 10−26 10−26 10−26
Here, sets A, B, C, D and E correspond to ZnO QDs with average diameters 2.2 ± 0.1, 3.1 ± 0.2, 5.9 ± 0.4, 7.8 ± 0.6, and 9.6 ± 0.8 nm, respectively.
a
their size.43,44 It has been found that for cross-sectional area below 10 nm2, competition between avoidance of edges and minimization of surface area results in a hexagonal crosssection being the most stable, but for larger nanostructures dodecagonal cross-section is found to be optimal. However, these calculations are based on considering only naked ZnO surfaces; for solution based synthesis, the presence of surface capping layer may stabilize one facet over another and change
the Wulff optimal shape.43,44 In the present experiment, the adsorption of acetate counterions is expected to alter the theoretically predicted optimal shape of the ZnO QDs synthesized by wet chemical approach. However, under such circumstances, although the reaction field can be calculated assuming the dipole to be evenly distributed over the ellipsoids45,46 and since for the sphere, such a dipole gives the same reaction field as a point dipole at the center, Scholte F
DOI: 10.1021/acs.jpcc.6b12359 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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νf̅ (cm−1) 25000.00 23255.81 19841.26 20833.33 19920.31 25062.65 19047.61 19723.86 19531.25 20120.72 3310.83 4159.23 6263.72 7041.52 7378.83 7638.01 7579.77 7572.23 7954.97 8034.73 26809.65 25252.52 22471.91 22988.50 22471.91 22123.89 21321.96 21413.27 22075.05 20618.55 3541.79 4329.00 5705.28 6218.73 6494.46 6484.65 6423.25 6461.28 6828.17 6835.31 3458.85 3837.17 4867.95 5220.20 5240.37 6039.09 5312.85 4439.22 5487.80 5605.12 3308.93 3746.00 4324.70 4423.62 4506.64 4228.29 4596.08 4495.61 4570.45 4850.74 0.0198 0.0841 0.2096 0.2630 0.2743 0.2745 0.2768 0.2850 0.2895 0.3054 dioxane dichloromethane THF DMSO DMF n-propanol 2-propanol acetone ethanol acetonitrile
32894.73 29585.79 32573.28 31746.03 36764.70 29673.59 30303.03 28248.58 30211.48 29850.74
ν̅f (cm−1) 29585.79 25839.79 28248.58 27322.40 32258.06 25445.29 25706.94 23752.96 25641.02 25000.00
ν̅a − ν̅f (cm−1)
ν̅a (cm−1) 31948.88 30864.19 30120.48 29850.74 30303.03 31746.03 31152.64 29069.76 30487.80 26881.72
ν̅f (cm−1) 28490.02 27027.02 25252.52 24630.54 25062.65 25706.94 25839.79 24630.54 25000.00 21276.59
νa̅ − ν̅f (cm−1)
ν̅a (cm−1) 30864.19 30303.02 29069.76 29154.51 29325.51 30581.03 29411.76 31152.64 30030.03 28248.58
νf̅ (cm−1) 27322.40 25974.02 23364.48 22935.77 22831.05 24096.38 22988.50 24691.35 23201.85 21413.27
νa̅ − ν̅f (cm−1)
ν̅a (cm−1) 30120.48 29411.76 28735.63 30030.03 29850.74 29761.90 28901.73 28985.50 30030.03 28653.29 G
νa̅ (cm−1)
Thus, with the knowledge of the ground state dipole moment calculated using the Nann and Schneider model and determination of Δμ from the slope of the curve, the excited state dipole moment of the particles can be obtained. Now, in order to provide an experimental demonstration of the above theoretical perspectives, we have studied the steady state absorption and fluorescence emission properties of different sizes of ZnO QDs in a series of organic solvents of varying polarities. All the absorption and emission measurements have been repeated thrice and excellent reproducibility which indicates the intrinsic accuracy of the determination of solvatochromic shifts of the spectral profiles of the ZnO QDs. Figure 3 shows the representative normalized absorption spectra of ZnO QDs (0.5 mM) of set B in sequence of organic solvents. It is seen that ZnO QDs show an intense absorption band in the UV−vis region in all the solvents employed for the present experiment. Moreover, it is noted that the absorption spectra of ZnO QDs is highly sensitive to the polarity of the surrounding environment. On the basis of the solvent medium, the absorption maxima of ZnO QDs are found to be located in the different wavelength (nm) region: acetone (320, 334), acetonitrile (207, 372), dichloromethane (239, 286, 322), 1,4-dioxane (219, 322), dimethylfomamide (262, 328), dimethyl sulfoxide (276, 335), ethanol (219, 320), 2-propanol (210, 285), n-propanol (238, 265, 313), and tetrahydrofuran (230, 320). Thus, the appreciable change in the energy of transitions in different solvent medium suggests that solvent stabilization of the ground state of the ultrasmall particles is significant.49 The representative normalized fluorescence spectra of ZnO QDs, excited at their corresponding higher intensity maxima of set B in solvents with different polarity are presented in Figure 4.
Δf
(12)
solvents
4πε0hca3 (slope) 2
Table 3. Calculation of Stokes’ Shift of Size-Specific ZnO QDs in Different Solvents
Δμ = (μ′ − μ) =
νf̅ (cm−1)
ν̅a − ν̅f (cm−1)
ν̅a (cm−1) 28571.42 28653.29 28409.09 29498.52 29239.76 34129.69 28328.61 28818.44 28985.50 29761.90
9.6 ± 0.8 7.8 ± 0.6
and, in consequence, the difference between dipole moments in the excited and ground states, Δμ can be represented as,
5.9 ± 0.4
particle diameter of ZnO (nm)
(11)
3.1 ± 0.2
2(μ′ − μ)2 4πε0hca3
2.2 ± 0.1
slope =
νa̅ − ν̅f (cm−1)
assumed that this would be nearly true for ellipsoids of small eccentricity.47 Assuming the particles to be spherical and in view of relatively large distribution of the particles, the average 4 particle volume, V = 3 π ⟨a3⟩, where, ⟨a3⟩ has been obtained from the Gaussian fit of the corresponding histogram of the size distribution using ImageJ software and calculated as 5.65 × 10−27, 15.67 × 10−27, 105.75 × 10−27, 224.70 × 10−27, and 467.60 × 10−27 m3 for ZnO QDs of sets A, B, C, D, and E, respectively. Then, using eq 10, the ground state dipole moment (μ) of ZnO QDs has been estimated as 273.32 × 10−30, 757.94 × 10−30, 5115.22 × 10−30, 10869.29 × 10−30 and 22618.88 × 10−30 C m, respectively, consistent with the earlier results48 calculated using this model. However, in the present experiment, we can assume that adsorption of acetate ions would not alter the dipole moment of ZnO QDs significantly as has been exemplified from the dielectric dispersion studies by Shim and Guyot-Sionnest for dodecanethiol- and trioctylphosphine- (TOPO-) capped CdSe nanocrystals.41 According to eq 8, a plot of Stokes’ shift (νa̅ − νf̅ ) as a function of orientation polarizability of the solvent, Δf(ε, n) is expected to show linear relationship with the slope of the curve as,
3571.42 5397.48 8567.82 8665.19 9319.44 9067.03 9280.99 9094.57 9454.25 9641.18
The Journal of Physical Chemistry C
DOI: 10.1021/acs.jpcc.6b12359 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
H
10−17 10−17 10−17 10−17 10−17 10−17 10−17 10−17 10−17 10−17 × × × × × × × × × ×
Edipole (J)
−1.89 −3.50 −3.38 −4.02 −3.99 −3.85 −3.86 −3.86 −3.91 −3.99 1008 1009 1009 1009 1009 1009 1009 1009 1009 1009 × × × × × × × × × × 8.35 1.55 1.5 1.78 1.76 1.7 1.71 1.71 1.73 1.77 10 10−17 10−17 10−17 10−17 10−17 10−17 10−17 10−17 10−17
× × × × × × × × × × −8.13 −1.50 −1.46 −1.73 −1.72 −1.66 −1.66 −1.66 −1.68 −1.72 10 1009 1009 1009 1009 1009 1009 1009 1009 1009 8.14 1.51 1.46 1.73 1.72 1.66 1.66 1.66 1.68 1.72
× × × × × × × × × ×
10 1009 1009 1009 1009 1009 1009 1009 1009 1009
−4.16 −7.70 −7.46 −8.87 −8.79 −8.49 −8.51 −8.51 −8.61 −8.80
× × × × × × × × × ×
10 10−18 10−18 10−18 10−18 10−18 10−18 10−18 10−18 10−18
7.48 1.38 1.34 1.59 1.58 1.53 1.53 1.53 1.55 1.58
× × × × × × × × × ×
08
0.4545 0.8409 0.8143 0.9682 0.9596 0.9271 0.9295 0.9292 0.9400 0.9605 dioxane dichloromethane THF DMSO DMF n-propanol 2-propanol acetone ethanol acetonitrile
8.39 1.55 1.5 1.79 1.77 1.71 1.72 1.72 1.74 1.77
× × × × × × × × × ×
10 1009 1009 1009 1009 1009 1009 1009 1009 1009
−2.29 −4.25 −4.12 −4.90 −4.85 −4.69 −4.70 −4.70 −4.75 −4.86
× × × × × × × × × ×
10 10−19 10−19 10−19 10−19 10−19 10−19 10−19 10−19 10−19
8.31 1.54 1.49 1.77 1.76 1.7 1.7 1.7 1.72 1.76
× × × × × × × × × ×
10 1009 1009 1009 1009 1009 1009 1009 1009 1009
−6.30 −1.17 −1.13 −1.34 −1.33 −1.29 −1.29 −1.29 −1.30 −1.33
× × × × × × × × × ×
10 10−18 10−18 10−18 10−18 10−18 10−18 10−18 10−18 10−18
Edipole (J)
−18 08 08 08
2(ε − 1) 2ε + 1
solvents
R (V m‑1)
Edipole (J)
−19
R (V m‑1)
Edipole (J)
−19
R (V m‑1)
5.9 ± 0.4 3.1 ± 0.2 2.2 ± 0.1
Table 4. Account of Reaction Field and Dipolar Potential Energy of Size-Specific ZnO QDs in Different Solvents
In these experiments, quite dilute dispersion of the ZnO colloids (0.5 mM) have been used so as to minimize the effects of excitation attenuation and dispersion self-absorption (so-called “trivial effects”). On the basis of the solvent medium, the fluorescence maxima of ZnO QDs are located in the wavelength (nm) region: acetone (407), acetonitrile (470), dichloromethane (400), 1,4-dioxane (352), dimethylfomamide (399), dimethyl sulfoxide (406), ethanol (401, 488), 2-propanol (387), n-propanol (388), and tetrahydrofuran (396). It is, therefore, evident that fluorescence emission of the ZnO colloids is strongly sensitive to the polarity of the solvent environment, which indicates a change in the charge density distribution in the excited state compared to the ground state of the ultrasmall particles.49 A comparative study of the absorption and emission spectral profiles shows that fluorescence band maxima are largely redshifted with increase in solvent polarity, compared to absorption band under similar experimental conditions. This can be explained by considering the rearrangement of the solvent molecules in the ground and excited states.50 While the fluorescent moieties exhibit a higher dipole moment in the excited state, as typically happens in case of polar fluoroprobes, the solvent molecules rearrange themselves to stabilize the greater charge separation. Since the excited state lifetime of the ZnO QDs is large enough (usually in the range μs to ns),31,51,52 the solvent rearrangement can take place in the time scale of 10−11−10−10 s, to be adapted with the altered properties of the excited fluoroprobes. Since the solvent reorientation is too slow to occur during absorption processes, the absorption is much less sensitive compared with the solvent effects on fluorescence. As a consequence, the rearranged solvent molecules stabilize the excited state of the fluoroprobes, and therefore, lower the overall energy of the system.50 The dielectric permittivity (ε) and refractive index (n) of the pure solvents have been taken from the literature53 and according to eq 2, assuming the value of isotropic polarizability, α = 1.78 × 10−30 m3, the “effective internal dipole moment” (μs) for size-specific ZnO QDs in different solvents were calculated as have been summarized in Table 2. Now, from the solvent dependent measurements, we have calculated the wavenumber of maximum absorption (ν̅a) and fluorescence (νf̅ ) and Stokes’ shift (νa̅ − νf̅ ) from the corrected spectra in each solvent systems for five different particle sizes and knowing the values of dielectric permittivity (ε) and refractive index (n) of the pure solvents, the orientation polarizability of the solvents, Δf(ε, n) has been estimated according to eq 7 as has been enunciated in Table 3.
particle diameter of ZnO (nm)
R (V m‑1)
7.8 ± 0.6
Figure 5. Plot of Stokes’ shift (νa̅ − νf̅ ) as a function of solvent orientation polarizibility, Δf(ε, n) of five size-specific ZnO QDs.
Edipole (J)
−18
R (V m‑1)
9.6 ± 0.8
The Journal of Physical Chemistry C
DOI: 10.1021/acs.jpcc.6b12359 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
Figure 6. Plot of (A) reaction field (R) and (B) dipolar potential energy (Edipole) as a function of 2(ε − 1) in different solvents for five size-specific ZnO QDs. 2ε + 1
Table 5. Estimation of Excited State Dipole Moment (μ′) as a Function of Particle Size of ZnO QDsa particle size (nm)
slope (cm−1)
± ± ± ± ±
4465.34 7242.95 11408.27 16869.47 20638.58
2.2 3.1 5.9 7.8 9.6
0.1 0.2 0.4 0.6 0.8
Δμ = (μ′ − μ) (C m) 81.03 172.64 568.95 1051.74 1588.34
× × × × ×
10−30 10−30 10−30 10−30 10−30
μ (C m) 273.32 757.94 5115.22 10869.29 22618.88
× × × × ×
10−30 10−30 10−30 10−30 10−30
μ′ (C m) 354.35 930.58 5684.18 11920.96 24207.22
× × × × ×
10−30 10−30 10−30 10−30 10−30
The value of Δμ has been estimated from the slope of (ν̅a − ν̅f) vs orientation polarizability curve, and μ has been calculated by using the Nann and Schneider model.40
a
Profiles showing the plot of Stokes’ shift (νa̅ − νf̅ ) as a function of orientation polarizability of the solvents, Δf(ε, n) for five sizeselective ZnO QDs are depicted in Figure 5. It is observed that the Stokes’ shifts correlate linearly with the orientation polarizability of the solvents for all the five different sizes of the ZnO QDs. The increase of the Stokes’ shift as a function of orientation polarizability of the solvents indicates there is an increase in the dipole moment on excitation and in consequence, a higher solvation of the excited electronic state of the ZnO QDs. Moreover, it is noted that the slope of the curve indicates increased solvation of the excited state with increase in particle sizes. Again, with the knowledge of effective internal dipole moment (μs) of the particles under the influence of solvation shell, the reaction field (R) and dipolar potential energy (Edipole) have been calculated according to eqs 3 and 4, respectively for all the particle sizes in ten different solvents as summarized in Table 4. Profiles showing the linear variations of the reaction field and dipolar potential energy as a function of 2(ε − 1) , as presented in Figure 6, indicate the validity of the
Figure 7. Plot of the difference between excited and ground state dipole moments (Δμ) as a function of particle volume (V) for five size-specific ZnO QDs.
particles, the properties of the ZnO|solution interface (e.g., surface polarization and surface conductivity) must play a role, while for larger particles, the electric double layer and the asymmetric adsorption of acetate counterions can modify, significantly, the Onsager’s reaction field, in more polar solvents of better conductance which can explain the deviations from the linear dependence.56 It is, therefore, evident that smaller clusters of ZnO follow the ideal nature of Onsager cavity and substantially, deviates at larger particle sizes. Therefore, it could be concluded that, for fluoroprobes, a transition from subnanometer (
