Physica E 116 (2020) 113724
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The size dependent thermal diffusivity of water soluble CdTe quantum dots using dual beam thermal lens spectroscopy T.K. Nideep *, M. Ramya, V.P.N. Nampoori, M. Kailasnath International School of Photonics, Cochin University of Science and Technology, Kochi, India
A R T I C L E I N F O
A B S T R A C T
Keywords: CdTe quantum dots Thermal diffusivity Thermal lensing Thermo-optic property
Size dependent thermal diffusivity of CdTe colloidal quantum dots samples has been studied using dual beam thermal lens spectroscopy. The thermal diffusivity values of the colloidal solution of CdTe quantum dots syn thesized in water were found to be less than that of pure water (1.4 � 10 7 m2/s) varying from 0.63 � 10 7 m2/s to 0.15 � 10 7 m2/s. The samples with this kind of very low value of thermal diffusivity can be good thermal insulators. To the best of our knowledge there are no reports on the study of thermal diffusivity of water soluble CdTe quantum dots. The non-radiative relaxation mechanism due to defect states, Brownian motion, capping agent etc. play major roles in controlling the thermal diffusivity of the nano-colloidal sample. The thermal diffusivity is found to be in inverse correlation with the emission intensity.
1. Introduction Quantum dots are basically semiconductor nanocrystals with zero dimensional structures which consists of few numbers of atoms [1,2]. In a quantum dot, the electrons are three dimensionally confined and hence they exhibit highly discrete energy levels [3,4]. The breaking of the continuous electronic band structure below the exciton bohr radius results in the discreteness in the absorption and emission properties [5]. The low cost synthesis method and unique optical properties make the semiconductor quantum dots more attractive than other conventional optical materials. With decrease in size of the quantum dots, the dif ference in energy between conduction and valence band increases leading to an increase in the band gap of the material. Therefore more energy is required for the excitation smaller quantum dots. As a conse quence more energy will be released during the de excitation of these nanostructures [6]. The colloidal synthesis is important as it leads to quantum dots with desired size more easily and quickly [7,8]. The size controlled thermal diffusivity behaviour of materials has special importance in the nano regime. In order to use the material for thermo-optic applications, such as coolant or thermal insulator, we should know about the thermal conductivity of the material. In case of colloidal nanoparticles, it is more easy to measure thermal diffusivity rather than thermal conductivity, which are closely related by the equation, D ¼ k=ρc, where D is the thermal diffusivity, k is the thermal conductivity, ρ is the density of the fluid and c is the specific heat
capacity of the fluid [9,10]. Several techniques are employed to determine the thermal diffu sivity of the nano-fluids, of them, photoacoustic technique and thermal lens technique are the most widely used due to the high sensitivity [11]. The basic principle behind thermal lens technique is self modified refractive index of a liquid due to the propagation of a laser beam through that liquid. Thermal lens technique is a direct measure of the non-radiative decay from the excited particles or molecules. This phe nomenon was first experimentally observed and theoretically explained by Gordon et al. using He-Ne laser at 6328 Å in liquid cells [12]. The thermal interaction between lattice and medium is more important, when considering the interaction between high power lasers and nanoparticles. Because the interaction between lasers and colloidal nanoparticle can even cause the structural modification of the nano particles [13,14]. Nanoparticles usually possess two important proper ties such as large surface area and surface defects comparing with the bulk materials. On excitation with intense radiation, the defect states trap the excited electric charges. The continuous absorption of photons by these trap states can cause the thermally induced change in refractive index of the material itself, which results in thermal lensing effect [15]. There are various factors affecting the thermo-optic properties of nanomaterials. The thermal conductivity of nanomaterials is usually higher due to the increase in heat transfer between nanoparticles and the base solvent. This is due to the convection current set up by the Brow nian motion of the nanoparticles [16]. However Brownian motion itself
* Corresponding author. International School of Photonics, Cochin University of Science and Technology, Kerala, India. E-mail address:
[email protected] (T.K. Nideep). https://doi.org/10.1016/j.physe.2019.113724 Received 17 March 2019; Received in revised form 25 August 2019; Accepted 13 September 2019 Available online 14 September 2019 1386-9477/© 2019 Elsevier B.V. All rights reserved.
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Physica E: Low-dimensional Systems and Nanostructures 116 (2020) 113724
depends upon the size of the nanoparticles. The capping of the nano particles also plays an important role in controlling the thermal diffu sivity of colloidal nanoparticles. Here the cooling of nanoparticles due to the phonon-phonon interaction could be limited by the capping mate rials, which results in the long decay time [13]. So in the case of colloidal nanoparticles, the prediction of thermal diffusivity is very difficult. Hence the thermos-optic study of colloidal nanoparticles needs more attention. CdTe quantum dot is one of the widely used II-VI group semi conductor material with a bulk band gap of 1.5eV. In the quantum dot form, its absorption and emission can be tuned by changing the size. The synthesis, linear and nonlinear optical properties of CdTe quantum dots with varying sizes have already been reported from our previous ex periments. In the synthesis process we have used thiomalic acid as the capping agent for limiting the growth of the nanoparticle [17]. In the present work, we have studied the size dependent thermal nonlinearity of the same samples using dual beam thermal lens spectroscopy.
3
2 6 6 IðtÞ ¼ Ið0Þ61 4
θ 1 þ 2ðttc t0 Þ
θ2
1
7 7 �2 7 5
þ � 2 1 þ ðt tct0 Þ
where θ is the probe beam shift induced by thermal lens effect, tc is the time response of thermal lens. Here, � �� dn θ ¼ Pth λk dt where Pth is the power radiated as heat. dn =dt is the rate of change of refractive index with respect to temperature. λ is the wavelength of the laser and k is the thermal conductivity. The thermal diffusivity is given by the following relation � D ¼ ω2 4tc
2. Theory
where ω is the beam radius at the focal point of the lens. To eliminate the error factor in determining the beam radius, the thermal diffusivity of an unknown sample is calculated using water as the reference. Then the diffusivity of the unknown sample is obtained by the following relation,
The thermal lens technique can be used to measure very small changes in the refractive index of a material of the order of 10 8, which results from the variation in a temperature of ~10 5� C in liquids. A laser can very well be used to make such a very small change in refractive index [18,19]. A focused laser beam propagating through a liquid results in a thermal blooming due to the refractive index variation in liquid [20]. The focused laser beam creates another beam waist at the focus which depends upon the following factors such as the focal length of the convex lens used, wavelength of the laser and the diameter of the beam entering the lens [18,21]. When laser light passes through a material, some part of the light get absorbed. This absorbed light will be emitted from the material through two processes. One of them is radiative decay, in which light of higher wavelength emitted than the absorbed light. Second one is the non-radiative decay, in which the remaining part of energy absorbed is radiated as heat. This is called non radiative relax ation. This results in the heating of the material in which the light passes through. This non-radiative decay plays a major role in the thermos-optic properties of nanomaterials. The non-radiative relaxation includes vibrational relaxation, inter system crossing, external conver sion etc. [22–25]. Negative lensing results in the probe beam to expand. The heat generated inside the sample due to thermal lens effect depends upon absorbance of the sample, the power with which it is excited, and the fluorescence of the sample. Increase in fluorescence decreases the thermal lens effect [9]. The path of the laser beam inside the sample gets heated due to the induced absorption which depends upon the tem perature at different points of the beam. In the case of Gaussian beam, the maximum heating occurs though the axis of the beam. This results in the refractive index variation and a refractive index gradient will be produced normal to the beam axis depending upon the temperature gradient, dn =dt. Since most of the liquids expand on heating, the refractive index gradient will be negative with respect to change in temperature, which results in the formation of negative lens (diverging lens) [26]. In a thermal lens measurement, the intensity variation in the pump beam generates the lensing effect, which will be analyzed using a probe beam propagating collinear to the pump beam through the sample. The probe beam generates a spot at the far field which will increase in size called thermal blooming. We can calculate the refractive index gradient and various other photo thermal parameters of the sample using this thermal blooming. But the measurement of time dependent laser in tensity during the blooming is more convenient than measuring the beam spot dimensions [9,11]. The change in probe beam intensity with respect to time is given by
DSample ¼ DWater
tcWater tcSample
3. Experimentation A schematic diagram of the experimental set up for the thermal lens measurement is shown in Fig. 1. A Diode Pumped Solid State (DPSS) laser (VORTRAN Standus TM 405) having continuous wavelength of 403 nm with a maximum power of 100 mW was used as the excitation source. A 4 mW continuous wave He-Ne laser (JDS Uniphase) emitting 632.8 nm wavelength was used as the probe beam. The pump and probe beams are arranged in such a way that both the beams are passing through the same path using a beam splitter. In order to get a mode matched thermal lens configuration, two beams are focused using a convex lens into the sample cell such that the areas of the two beams are same. A 1 cm cuvette is used as sample cell. A mechanical chopper with frequency 3 Hz was used to make variation in the intensity of the pump beam. The thermal lens produced by the pump beam was analyzed using the probe beam. The output signal was collected using an optical fiber connected to a photoanode. In between the optical fiber and the sample cell, a filter was placed in order to filter the pump which allows only the probe beam to enter the detector. The detector is then connected to a digital storage oscilloscope (DSO; Tektronix-TDS 2024C).
Fig. 1. Schematic diagram of dual beam thermal lens setup. C-Chopper, BSBeam Splitter, L-Convex lens, S-Sample, F-Filter, OF-Optical Fiber, DSODigital Storage Oscilloscope. 2
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Physica E: Low-dimensional Systems and Nanostructures 116 (2020) 113724
CdTe quantum dot samples were synthesized using a previously adopted method with water as the solvent [17]. The same samples were employed in this experiment. A detailed synthesis procedure is described as follows. Aqueous solution of CdCl2 (1 mM), thiomalic acid (4 mM), Na2TeO3 (1.5 mM) prepared separately and sonicated for 10 min each. These solutions were then mixed together followed by vigorous stirring for 5 min at room temperature. To this 0.25 mg of NaBH4 was added. Stirring was continued for the next 10 min and the pH was adjusted to 8 by adding appropriate amount of NaOH (1 M) solution dropwise. The prepared sample is then subjected to heat at 80 � C in a closed vessel. The samples were taken out at an interval of 30 min. The initial non heated sample was named as C0. The other samples with heated at different time intervals such as 30min, 60min, 90min, 120min are named as C30, C60, C90, C120 respectively. The prepared samples were found to exhibit size dependent absorption and emission with respect to the re action time. The size dependent thermal lens measurement of the CdTe quantum dot sample was done at a concentration of 0.05 mg/mL. For the opti mization of the concentration, we mainly focused on the sample with lowest thermal diffusivity for the purpose of application in thermal in sulators. The selectivity of the concentration was done by using the following procedure. Initially, the size dependent thermal diffusivities of the CdTe quantum dot samples were done at a particular concentration of 0.01 mg/mL. The thermal diffusivity was found to be varying with size of the quantum dots and there was an optimum size (2.55 nm), at which the thermal diffusivity was minimum for sample C60. The size dependent thermal diffusivity of CdTe quantum dots at a concentration of 0.01 mg/mL was given in Fig. 2(a). The optimization of concentration was done by measuring the thermal diffusivities of the C60 sample at different concentrations such as 0.01 mg/mL to 0.07 mg/mL. This experiment revealed that for the C60 sample at a concentration of 0.05 mg/mL was having the lowest thermal diffusivity. This concen tration was selected as the optimum concentration for the measurement of the thermal diffusivity of the entire quantum dot sample with respect to size. Fig. 2(b) shows the concentration dependent thermal diffusivity of sample C0. Further measurements are carried out at 0.05 mg/mL concentration. The absorption spectra of the quantum dot samples were recorded using UV–visible absorption spectrophotometer (Jasco V-570) and the fluorescence emission spectra were taken using Cary Eclipse Fluores cence Spectrophotometer (VARIAN).
Fig. 3. TEM image of the CdTe quantum dot sample C30.
in shape. As shown in Fig. 4 the absorption spectra show a red shift with in crease in the time of synthesis of the samples. The samples C0 and C60 show excitonic absorption peak at 487 nm and 530 nm respectively. The red shift in the absorption spectra is attributed to the quantum confinement effect and it is an indication of the increase in size of the nanoparticle. In semiconductor quantum dots, the size of the particle is directly related to the excitonic absorption peak. The sizes of the quantum dots can be calculated using the model proposed by peng and coworkers [7,27,28]. The diameter of the quantum dots can be found out by the following relation, � � D ¼ 9:8127*10 7 λ3 1:7147*10 3 λ2 þ 1:0064*λ 194:84 where D is the diameter of the quantum dots and λ is the wavelength of the first excitonic absorption peak. The diameters of the quantum dots calculated using the above equation were found to be ranging from 1.94 nm to 2.98 nm. It was observed that the Photoluminescence (PL) spectra of the CdTe quantum dots samples also show a red shift. This is yet another
4. Results and discussion The morphology of the synthesized samples was analyzed using TEM image which is shown in Fig. 3. The particles were found to be spherical
Fig. 2. (a) Size dependent variation of thermal diffusivity of CdTe quantum dots at a concentration of 0.01 mg/mL, (b) Concentration dependent variation of thermal diffusivities of sample C60. 3
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Physica E: Low-dimensional Systems and Nanostructures 116 (2020) 113724
Fig. 5. Relative intensities of fluorescence peak of the CdTe quantum dots.
Fig. 4. Redshift in the absorption spectra of the CdTe quantum dot samples.
confirmation of the quantum confinement effect [29]. In the PL spec trum shown in Fig. 5, there is a variation in the highest PL peak intensity for each of the sample. Initially, the normalized relative intensity in creases from sample C0 to C60 and then it decreases. This can be explained on the basis of Ostwald ripening mechanism and dynamic growth process [30,31]. Initially the synthesized nanoparticles are having several defects. But as the reaction progress, the number of de fects decreases and reaches a balanced state, where the growth and dissolution are in equilibrium. In this state, the nanocrystals show higher photoluminescence efficiencies and stability. Under conditions far away from this equilibrium, the surface of nanoparticles become more rough with defects and there is an increase in the probability of non-radiative recombination. These defects are assumed to be having the main contribution in the thermos-optic properties of the sample. A typical pump beam intensity modulation obtained from the digital oscilloscope output of a thermal lens measurement is shown in Fig. 6. The thermal diffusivity can be estimated using the equation tc ¼ ω2 = 4D where ω ¼ 120.9 μm measured at the sample position. The theoretical fitting towards the experimental curve on the ther mal lens decay of sample C0 and C60 are given in Fig. 7. The calculated values of thermal diffusivity for all the quantum dot samples corre sponding to each of the tc are tabulated in Table 1. The variation of the thermal diffusivity and PL peak intensities for different particle sizes were plotted in Fig. 8. It is clear that the sample C60 having the highest PL peak intensity have the lowest diffusion compared to the other samples. The sample with the lowest PL peak intensity is having the highest diffusion of 0.63 � 10 7 m2/s. This value is found to be very close to but less than the diffusivity of water (1.43 � 10 7 m2/s) [32]. It is a general condition that the thermal diffusivity decreases with increase in PL emission intensity due to the reduction in non-radiative recombination and the release of most part of the absorbed energy in the form of radiative energy. This is the reason for getting lowest ther mal diffusivity for the sample C60. But in the case of other samples, the defect state will be higher which will lead to increase in non-radiative decay and production of more heat. This results in a decrease in the dissolution of thermal energy which in turn reduces the thermal diffu sivity of the sample. Size, shape, capping, Brownian motion, etc. of nanoparticles are the other major factors affecting the thermal diffusivity. Brownian velocity ffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffi. of the nanoparticles is given by v ¼ 18kb T πρd3 , where kb T is the
Fig. 6. Typical thermal lens output signal.
considerable Brownian motion, leading to the easy thermal diffusion. But as the size increases, the Brownian motion decreases and there will be reduced interaction between the particles and the fluid medium resulting in lower values of the thermal diffusivity. Moreover, as the size of the particle increases, the overall surface area reduces and the number of trap states due to the defect states comes down, which in turn reduce the non-radiative recombination and thermal diffusivity. The capping agent also has a role in reducing the thermal diffusivity. Due to the covering of the capping agent on the surface of the quantum dots, the cooling of the nanoparticles become slower due to decrease in time rate of heat transfer to the surrounding solvent. The slight increase of ther mal diffusivity for the samples C90 and C120 is due to the increase in number of defects, which enhances the non-radiative decay, that dom inates all other factors decreasing the thermal diffusivity of the sample. 5. Conclusion Dual beam thermal lens technique has been used to measure the thermal diffusivity of CdTe colloidal quantum dots prepared in water. The thermal diffusivity is found to be decreasing with increase in par ticle size up to an optimum value. The correlation between emission and
thermal energy, d is the diameter of the particle and ρ is the density of the medium [16,33,34]. So with increase in the particle size, the velocity of the nanoparticles decrease. For smaller particles, there will be 4
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Physica E: Low-dimensional Systems and Nanostructures 116 (2020) 113724
Fig. 7. Experimental and theoretical curve of thermal lens output signal of sample (a) C0 and (b) C60.
Acknowledgement
Table 1 The size dependent variation in values of probe beam shift (θ), thermal response time (tc ) and thermal diffusivity (D) of the CdTe quantum dot samples. Sample
Size (nm)
C0 C30 C60 C90 C120
1.94 2.25 2.55 2.79 2.98
θ 1.60 2.86 4.07 4.06 3.60
tc (sec)
D(�10
0.05 0.11 0.24 0.22 0.20
0.63 0.32 0.15 0.16 0.17
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The author Nideep T K acknowledges E-Grantz Kerala Govt., India and DST-SERB grant number EEQ/2008/000468 for the financial support.
m2/s)
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