Size and phase dependent thermal conductivity of TiO2-water nanofluid with theoretical insight

Journal Pre-proof Size and phase dependent thermal conductivity of TiO2-water nanofluid with theoretical insight

Dipanwita Mitra, Promita Howli, Bikram Kumar Das, Nirmalya Sankar Das, Paramita Chattopadhyay, Kalyan Kumar Chattopadhyay PII:

S0167-7322(19)35134-7

DOI:

https://doi.org/10.1016/j.molliq.2020.112499

Reference:

MOLLIQ 112499

To appear in:

Journal of Molecular Liquids

Received date:

12 September 2019

Revised date:

1 January 2020

Accepted date:

12 January 2020

Please cite this article as: D. Mitra, P. Howli, B.K. Das, et al., Size and phase dependent thermal conductivity of TiO2-water nanofluid with theoretical insight, Journal of Molecular Liquids(2020), https://doi.org/10.1016/j.molliq.2020.112499

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© 2020 Published by Elsevier.

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Size and phase dependent thermal conductivity of TiO2-water nanofluid with theoretical insight Dipanwita Mitraa, Promita Howlib,1, Bikram Kumar Dasb, Nirmalya Sankar Dasc,2, Paramita Chattopadhyaya and Kalyan Kumar Chattopadhyayb, c* a) b)

Department of Electrical Engineering, IIEST Shibpur, Howrah-711103, India

Thin film and Nano science Laboratory, Department of Physics, Jadavpur University,

c)

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Kolkata -700032, India School of Material Science and Nanotechnology, Jadavpur University,

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Kolkata-700032, India *

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Corresponding author’s email: [email protected]; [email protected]

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Tel: 033 2414 6666

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Present address: Department of Physics, Prabhu Jagatbandhu College, Jhorhat, Andul,

Howrah 711302 2

Present address: Department of Basic Science and Humanities, Techno India, Batanagar

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Abstract Nanomaterial based heat transfer fluid has become one of the optimistic technologies that ushered a new horizon in the heat transfer process. In this work, TiO2 powder (Degussa P25) was subjected to mechanical milling for 0-16 h and the average particle size was varied from 21.8- 13.3 nm. A size induced phase transition of the TiO2 nanoparticles from anatase to rutile was observed and confirmed from both the XRD and RAMAN analysis. It was found that the

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rutile content increased gradually compared to anatase phase with decreasing particle size.

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Aqueous TiO2 based nanofluid systems of different milled samples were prepared and heat

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transfer properties were investigated experimentally. Particle size and phase of the TiO2 nanoparticles both affected the observed thermal conductivity. From the density functional

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theory based ab initio calculations it was found that the variation in lattice thermal conductivity

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became negligible when the dimension of the sample is greater than ~23 Å and ~26 Å for rutile and anatase TiO2 respectively, suggesting the phase to be the dominant factor for the observed

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variation above that size. The DFT study supports our experimental observation indicating that

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the thermal conductivity of rutile phase is less than that of anatase phase. This work presents for the very first time, a new investigation about the dependency of thermal conductivity on the phase content of TiO2 nanoparticles which may help in explaining various conflicting results in the literature about the thermal conductivity variation of TiO2 based nanofluids.

Keywords: Anatase; Rutile; Strain; Phase-transition; Vienna ab-initio Simulation Package; Thermal conductivity; Phonon

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1. Introduction The new class of engineered fluid that has potential applications in fields like energy harvesting, thermal management of high power electrical equipment is termed as ‘Nanofluid’ by Choi in the year 1995 at Argonne National Laboratory [1]. Nano sized particles having one of their principal dimension smaller than 100 nm are suspended in a base fluid to form a diluted suspension called ‘Nanofluid’ [2]. Thermal conductivity of heat transfer fluids is

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crucial in order to develop energy-efficient heat transfer equipment but poor thermal

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conductivity of traditional heat transfer fluids like water, oil, ethylene glycol mixture is a

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problem. Recent researches have shown that nanofluid can be considered as a next generation heat transfer fluid due to its enhanced heat transfer performance compared to base fluid due to

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exciting features of nanofluid based system. High surface to volume ratio of nanoparticles

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compared to those of conventional particles is one of the reasons for its enhanced heat transfer capability. Particles having size less than 20 nm can carry 20% of their atoms on surface thus

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allowing instantaneous thermal interaction and tiny-sized particles within base fluid induce

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micro-convection thus increases heat transfer [3]. The works of Eastman and others indicate that there is a large enhancement in effective thermal conductivity of traditional heat transfer fluids upon the addition of small amount of nanoparticles [4, 5]. Various factors like large surface area, Brownian motion of particles, ordering of liquid molecules near the surface of particles and interfacial resistance at fluid-particle interface are reported to be the reasons for the enhancement in effective thermal conductivity. Parameters like material type, particle concentration, size, shape, viscosity, Brownian motion, acidity, particle agglomeration, clustering effect, surface modification and interfacial layer thickness, type of base fluid and temperature show significant influence on the heat transfer enhancement of nanofluid [6-12]. Wang et al. reported 40% enhancement in thermal conductivity of 8%(volume fraction) alumina-water nanofluid system and observed a linear relationship between volume fraction 3

Journal Pre-proof and thermal conductivity [5] but Murshed et al. and Choi et al. found a non-linear relation between thermal conductivity and particle volume fraction and explained the trend as a result of interactions amongst nanoparticles [13, 14]. From the observations of Kim et al., Beck et al., Williams et al., Das et al., Chon et al., it is confirmed that the nanofluid have enhanced thermal conductivity which enhances with concentration and temperature [15-19]. However, there are many contradictory reports regarding the trend of variation of heat transfer with particle concentration indicating the need of further research in this field [16, 20-22]. Several

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experiments have already been conducted to know the effect of particle size on thermal

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conductivity. Kim et al., Li and Peterson showed positive trends in effective thermal

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conductivity enhancement of nanofluid with particle size [15, 20], whereas Yu et al. showed a

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negative trend [21]. Xie et al. have studied nanofluid system containing five different sizes of alumina nanoparticle and reported an increase followed by a decrease in the thermal

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conductivity with particle size both in ethylene glycol and pump oil as base fluid [22]. Beck et

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al. measured the thermal conductivity of nanofluid containing seven sizes of alumina nanoparticles ranging from 8 to 282 nm in diameter and reported that thermal conductivity

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decreases with particle size below 50 nm due to enhanced phonon scattering phenomenon [16]. These opposite trends are explained in two different aspects. Firstly, smaller nanoparticles may undergo “mixing effect”, resulted due to the event of pushing and pulling of the base fluid molecules by the dispersed nanoparticles. This phenomenon causes the effective mixing of base fluid molecules at high temperature zone with that of low temperature zone causing a higher thermal conductivity. Secondly, on the other hand, if the dimension of the dispersed nanoparticle becomes close or smaller than the phonon mean free path then the thermal conductivity reduces due to increased random phonon scattering at the particle boundary. Shima et al. observed an increase in thermal conductivity with particle sizes in range of 2.8-9.5 nm for Fe3O4 nanoparticle based nanofluid and attributed the enhancement to agglomeration of

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Journal Pre-proof nanoparticles [23]. Hamid et al. showed that heat transfer performances of TiO2 nanofluid in water-EG based mixture are significantly influenced by concentration, temperature and Reynolds numbers [24]. Khedkar et al. showed that addition of nanoparticles to base fluid increases thermal conductivity as compared to viscosity at higher volume fraction from his study on TiO2-EG based nanofluid [25]. For the prediction of thermal conductivity of nanofluid based on rheology Chen et al. proposed a method and Sen et al. reported their observations on the electrochemical activity of TiO2 nanofluid by the approach of surface

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modification [26, 27]. Recently, Maheshwary et al. have shown the effect of concentration,

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particle size and shape on thermal conductivity of TiO2-water based nanofluid prepared by

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probe sonication method [28]. They have shown that thermal conductivity rises with increasing

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concentration of nanoparticles in base fluid and also reported the enhancement of thermal conductivity with decreasing particle size. The phase dependence on heat transferring

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capability of nanofluid is not clear till now and only a very few reports are there to enlighten

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the scientific fact behind it. Owing to enhanced heat transferring capability compared to commonly known heat transfer fluids, TiO2 based nanofluid seems to be very promising in

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solar power plants now-a-days and has been studied widely in the literature [29]. Cabaleiro et al. have studied thermal conductivity for dry anatase powder and mixture of anatase and rutile powder separately [30]. They have reported that anatase-TiO2 based nanofluid presents superior thermal conductivity than (anatase + rutile) based nanofluid. However, the controlled studies on the impact of phase transition of TiO2 based nanofluid on its heat transfer property is absent in the literature. Recently, various surface modifications of the milled/grinded nanoparticles have been reported for materials other than TiO2 to prepare nanofluids for different applications [31-33].

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Journal Pre-proof In brief, regarding the thermal conductivity analysis of nanofluid, reports published so far mention the effect of NP dimension, concentration of the dispersed phase etc. separately. However, complex effect contributed by three or more parameters together is rarely explained. Herein we report the impact of strain induced phase transition of the dispersed phase on the thermal property of aqueous TiO2 based nanofluid system with adequate support from theoretical analysis. Possible explanations of the observed variation of thermal behaviour of the nanofluid with phase transition as a major factor has been discussed in-depth by theoretical

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analysis.

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2. Experimental methods

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2.1. Materials

Commercially available Degussa P25 Titanium dioxide, Evonik (anatase: rutile = 80: 20) and

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purity = 99.9% was purchased and used in the experiment. De-ionized water having resistivity

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18.2 MΩ cm at 250C obtained from a Millipore water purification plant and was used throughout this experiment.

2.2 Pre-treatment of TiO2 nanopowder Commercially available TiO2 sample (TP) was subjected to Planetary Micro-Mill, PULVERISETTE-7 Premium line of FRITSCH. Initially, 5 gm of commercial TiO2 sample was taken in each of the grinding bowl made of hard metal tungsten carbide with steel casing and 20 number of grinding balls made of Tungsten carbide were kept in each of the bowl to grind the sample. The ball to powder ratio was kept fixed at 10:1 in each of the grinding bowl. The weight of the sample and grinding balls in two bowls was kept same so that proper balance is achieved for smooth rotation. The bowls were rotated with a speed of 300 rpm with a pause 6

Journal Pre-proof of 5 minutes after each cycle of 30 minutes to avoid the unwanted heat generated due to grinding. For fine grinding, more number of small sized balls of 10 mm diameter was used compared to balls having diameter of 20 mm in both of the containers. After 4 hours of milling, sample (T4) was collected in 15 mL culture tube. Following this procedure, after 8 hours, 12 hours and finally after 16 hours, samples named respectively T8, T12 and T16 were collected. Fig.1(c) shows the digital images of the samples - A (TP), B (T4), C (T8), D (T12) and E (T16).

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A considerable variation of the colours of the samples can be observed. The possible reason

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behind this phenomenon may be attributed due to the change of band gap and also changes of

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scattering due to change of particle size

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2.3. Characterization

The composition, phases and crystallinity of milled samples were characterized by Bruker D8

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Advance X-ray diffractometry using Cu-Kradiation (λ = 1.5406 Å) operating at 40 kV and

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40 mA in a 2θ range of 20-90°. The morphologies of different TiO2 samples were investigated by Field Emission Scanning Electron Microscope (FESEM, Hitachi S-4800) operating at 5 kV.

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High Resolution Transmission Electron Microscope (HRTEM, JEM 2100; JEOL, Ltd.) was operating at 200 kV, used to further investigate particle size variations of the as-obtained samples. A confocal Raman Spectrometer (alpha 300, Witec, Germany) having laser source of  =532 nm was used to record Raman spectra of the samples at room temperature. 2.4. Preparation of Nanofluid solutions For each of the samples (TP, T4, T8, T12 and T16) different 100 mL nanofluid solutions were prepared by dispersing nanoparticles having different concentrations ranging from 0 to 0.1 wt. % within the de-ionized medium followed by one hour of ultra-sonication for proper dispersion of nanoparticles within the base medium. No surfactant was used to achieve stability

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Journal Pre-proof throughout the experiment. Each solution was kept undisturbed throughout the measurement. After the preparation of different nanofluidic systems on day-1, the complete set of nanofluid was kept undisturbed to observe the stability of the dispersed phase. Fig. 1(a) shows different nanofluid systems of TP, T4, T8, T12, T16 samples at particle concentration of 0.1 wt. % as

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prepared on day-1 and Fig. 1(b) shows the same after 100 days.

Figure 1. (a, b, c) Digital photograph of dispersed solution of different samples of different particle size at day1, day-90 and at day 100. (d) Colour variation due to mechanical milling of Titania powder: A: TP, B: T4, C: T8, D: T12, E: T16. 2.5. Thermal conductivity measurements To study the heat transfer capability of nanofluid systems containing different milled samples KD2 Pro Thermal Properties Analyser of Decagon Devices, USA was used. Amongst different sensor kits available in the package, KS-1 single needle sensor having measurement range of thermal conductivity within 0.02 to 2.00 W/(m-K) with accuracy range ± 5% from 0.2 to 2 W/

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Journal Pre-proof (m-K) ± 0.01 W/ (m-K) from 0.02 to 0.2 W/(m-K) was used to measure the thermal conductivity of nanofluid solutions. We chose KS-1 sensor as it applies a small amount of heat to the needle preventing free convection in liquid sample. Attaching KS-1 sensor to KD2-Pro controller and immersing 1.5 cm length of the sensor needle vertically at the centre of the nanofluid; the thermal conductivity was measured thrice with an interval of 15 minutes between each of the measurements for a single nanofluid sample, thus thermal conductivity of nanofluid for different concentrations were recorded. Readings were taken at room temperature

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(300 K) with precautions against free convection within liquid.

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2.6. Computational details

Vienna ab-initio Simulation Package (VASP) [34-36] interfaced with Phono3py [37] was used

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to calculate the thermal conductivities of rutile and anatase TiO2. The force constants were

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calculated using the supercell approach with finite atomic displacement of 0.03 Å. 2×2×2

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supercells of both the rutile and anatase TiO2 unit cell were employed to determine the force constants. Running many super-cell first principles calculations to determine the third-order

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force constant require massive computational time. To reduce the computational cost, we implemented the real space cut-off pair distance as a constraint to lessen the number of supercells with displacements. All the first principles calculations were carried out by VASP with the projector-augmented-wave (PAW) [38, 39] methods. The Perdew–Burke–Ernzerhof (PBE) [40] functional within the generalized gradient approximation (GGA) was deployed to deal with the exchange-correlation terms. A plane wave energy cut-off of value 500 eV was used during force calculation of all the supercells. The resulting forces were converged with accuracy better than 10-8 eV/Å. Monkhorst-Pack k-points meshes of 3×3×1 and 2×2×4, centred at gamma point, were applied during the force constant calculation of anatase and rutile TiO 2 supercells. Finally, to compute the thermal conductivities of both anatase and rutile TiO2 a finer k-point mesh of 17×17×17 was used for reciprocal space sampling. The tetrahedron 9

Journal Pre-proof method was implemented to integrate within the Brillouin-zone and calculate the imaginary part of the self-energies. Using Phono3py we calculated the thermal conductivities of both the TiO2 system within the temperature range of 100 K- 900 K. Also, Phono3py was used to determine the dependency of thermal conductivities on phonon frequency and mean free path. 2.7. Stability analysis techniques The stability of nanofluid was analysed with dynamic light scattering analyser (Zetasizer,

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Nano-series) at room temperature for different samples for a concentration of 0.01 wt. %.

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Tyndall effect of the colloidal solution containing the nanopowder having smallest particle size

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compared to other samples was observed with the red-laser beam to analyse the stability of the

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system.

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3. Results and discussion

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3.1. Crystallite size and structural analysis

We at first, wanted to investigate the consequences of size reduction on thermal conductivity of

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nanofluid but eventually, it was found that with the increase of grinding time, the phase of TiO2 changed significantly along with the reduction in crystallite size. Crystallinity and phase purity of the samples (TP, T4, T8, T12 and T16 ) were analysed by using X-Ray powder diffraction and the XRD plot is shown in Fig.2(a). For the sample TP, strong diffraction peaks at 2θ values of 25.3, 37.8, 48.07, 55.1, 70.3, 75.1 and 82.7 degrees can be ascribed due to the lattice planes of (101), (004), (200), (211), (220), (215) and (224) respectively which are wellmatched with JCPDS card no: 84-1286 indicating the presence of anatase phase within the sample. Apart from the intense peaks of anatase phase, some additional small peaks also be observed from the diffraction pattern of TP. At 2θ of 27.4, 54.3, 62.7 and 69.0 degrees the corresponding lattice planes are (110), (211), (002) and (301) respectively which are for the

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Journal Pre-proof rutile phase (JCPDS card no: 78-2485). Thus it is confirmed from the diffraction pattern of XRD that there exist two different phases of TiO2. Now when the particle size is reduced step by step with the rise of milling time, gradually the peaks of rutile phase are observed to be more prominent compared to the anatase phase as observed from the XRD pattern of fig. 2(a). From the XRD patterns of the various TiO2 samples, the percentages of individual phase content (anatase and rutile) in each of the samples were calculated [41] and are depicted in the

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fig. 2(b).

Figure 2. (a) XRD patterns of Titania samples having different sizes. (b) Variation of percentage phase content of anatase and rutile as a function of milling hours. To analysis the particle size and strain Williamson-Hall (W-H) method [42] was followed here. This method is based on the fact that the size broadening (βd) and strain broadening (βe) vary differently with the Bragg angle (θ), followed as equation (1), 𝑘λ

𝛽𝑑 = 𝐷𝐶𝑜𝑠𝜃 ; 𝛽𝑒 = 𝐶𝜖 𝑡𝑎𝑛𝜃

(1)

When the above two contributions are to be considered then the expression is written as on basis of the combine effect, followed as equation (2),

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Journal Pre-proof 𝛽 Total = βd + βe =

𝑘λ 𝐷𝐶𝑜𝑠𝜃

+ 𝐶𝜖 𝑡𝑎𝑛𝜃

(2)

Now by plotting 𝛽 Total𝐶𝑜𝑠𝜃 versus 𝑆𝑖𝑛𝜃, the strain component can be found from 𝐶𝜖 and the size component from the intercept

𝑘λ 𝐷

. The results of average crystallite size and micro-strain

of different samples are furnished in Table-1(Fig S1. and Fig S2. represents the W-H plots of different samples in supporting information).

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Table-1: Average crystallite size and micro-strain analysis from W-H method Average crystallite size (nm)

Micro-strain (%)

TP

21.8±2.3

2.5

T4

18.2±2.4

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Name of the sample

16.0 ±2.2

T12

19.7

14.0±1.8

23.0

13.3± 1.9

24.5

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T16

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T8

The above analysis indicates a significant rise in micro-strain whereas the average crystallite size variation due to mechanical milling is negligibly small. Thus the enhanced effective tensile strain may be the reason of the significant phase transition from anatase to rutile [43]. This phase transformation from anatase to rutile was further confirmed by RAMAN spectroscopic analysis and the Fig. 3 shows the corresponding results. In fig. 3(a) the combined data for the samples Tp, T4, T8, T12, and T16 is depicted where the indication of phase transformation is clear with decreasing the particle size. Fig. 3(b-f) demonstrates the Raman spectra for Tp, T4, T8, T12, and T16 samples with the clearly marking of anatase and rutile peaks. The peaks around 144,197, 399, 519 and 639 cm-1 are attributed to the Raman- active modes of

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Journal Pre-proof anatase phase with symmetries of Eg, Eg, B1g, B1g, Eg respectively whereas the peaks around 235, 447 and 612 cm-1 are attributed to two phonon scattering Eg, A1g modes of rutile phase of TiO2 [44]. Initially, in sample TP, it can be seen that the intensity of Raman peak related to rutile phase is very weak compared to anatase-phase, but in case of T16, peaks of rutile phase are more intense compared to that of anatase, indicating a prominent change in phase of the

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Figure 3. (a) Combined Raman spectra of Titania samples having different sizes indicating phase transition. (b-f) Individual magnified Raman spectra of different samples. Thus from XRD and as well as from RAMAN analysis it is cleared that although complete phase transformation did not occur but with increasing the milling time the anatase phase content decreased gradually and subsequently the rutile phase content increased. 3.2. Size and morphological analysis

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Journal Pre-proof Figure 4 shows the FESEM images indicating the morphology of the samples synthesized at different milling hours (T4, T8, T12, T16). The FESEM image of the commercial TiO2 sample (Degussa P25) is provided in the supporting information (shown at Fig S3.). From each of the FESEM images of the ball-milled TiO2 samples, agglomerated particles can be observed. As the particle size is reduced by the process of milling, surface to volume ratio of individual particle increases, as a result of that, surface energy of small individual particle is also enhanced. Owing to high surface energy, individual small particles tend to agglomerate and

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form a larger chunk to diminish the energy thus small particles are more prone to form

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agglomerated clusters. Due to agglomeration, it is difficult to measure the average particle size

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accurately of the individual samples.

Figure 4. FESEM images of (a) T4, (b) T8, (c) T12, (d) T16 samples. Magnified images are shown at the inset of individual FESEM images of different samples. Particle size reduction due to increase of grinding were studied through the high-resolution transmission electron microscopy (HRTEM) and is shown in Fig.5. Fig.5(a) and 5(c) indicates 14

Journal Pre-proof HR-TEM image of T4 and T16 samples respectively. The HR-TEM image of commercial TiO2 sample and corresponding histogram has been provided in supporting information (See Fig S4.). Comparing the two HR-TEM images, a decrement of particle size can be clearly observed. From histogram analysis, the calculated average particle size for T4 sample is found 30.3 nm whereas for T16 sample the value is 16.6 nm, thus the average particle size reduces significantly due to mechanical grinding as is shown in Fig.5(b) and 5(d). Fig.6 clearly demonstrate the presence of both anatase and rutile crystallites having d-spacing equal to 0.35

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nm and 0.248 nm respectively within the single particle of T16 sample. In addition to TEM studies, the variation of particle dimension after 16h milling was also

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studied from DLS analysis [Fig S8] and substantial decrement of particle dimension due to

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milling was confirmed from that.

Figure 5. (a, c) Higher magnification TEM images of T4 and T16 samples. (b, d) corresponding histogram plots showing particle size distribution.

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Figure 6. HR-TEM image indicating d spacing of phases present within a single particle of T 16

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3.3. Thermal conductivity studies

Figure 7. (a) Experimental plot of thermal conductivity (W/m-K) of Nanofluid Vs. weight percentage (%) of different samples as obtained at 300 K.

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conductivity with different nano-filler concentration depicted in Fig.7(a) can be divided into

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three regions: (i) 1st part of the plot reveals the increasing nature of thermal conductivity with

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nano-filler concentrations; (ii) 2nd part indicates an almost saturation region over a certain

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range of additive concentrations. Thermal conductivity does not change significantly due to the change of weight percentage (%) of the particles in this region; (iii) 3rd part shows a rapid fall

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of thermal conductivity due to further increase of particle concentration. The thermal

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conductivity of nanofluid is also seen to decrease significantly with the rise of milling time from 0-16 hours.

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In the 1st region of the experimental plot, it is observed that thermal conductivity rises with particle concentration up to a certain limit of weight percentage, which is related to the various previous reports indicating the enhancement of thermal conductivity of nanofluid with particle concentration [19-23]. In our experiment, beyond certain limiting weight percentage, the saturation of thermal conductivity was observed and then with further increase of concentration, decreasing trend of thermal conductivity was notified. This saturating and decreasing portion of the curve cannot be explained by any well-known established model. The dramatic change in thermal conductivity may be influenced by a number of parameters. As the range of variation in crystallite size of the samples is considerably small in this study, there may be two major 17

Journal Pre-proof parameters that are playing important role in determining the thermal conductivity of nanofluid and the factors are: concentration of dispersed particles and phase composition of the nanomaterial. The combined effect of these parameters are to be analysed to find out the reason of such trend in thermal conductivity. At low weight percentage of nanoparticle, the heat conduction is mainly attributed by Brownian motion of the particles and thermal conductivity uplifts with some extent of concentrations. At higher concentration due to high mass loading aggregated nanoparticles start settling down and thermal conductivity of the system degrades.

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thermal conductivity of the system degrades.

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Table-2 represents the experimental results of thermal conductivity as a function of rutile

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content (%) in different samples.

Thermal conductivity (W/m-K) 0.67

Rutile content (%) 15.2

0.66

53.2

0.65

84.0

T12

0.639

84.7

T16

0.626

85.0

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Table-2: Variation in thermal conductivity value with rutile content (%) in different milled samples

T4 T8

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TP

Although the individual impact of phase change and particle size on thermal conductivity of nanofluid cannot be ascertained separately from the experimental observations, hence theoretical insights were further employed to explain the variation of thermal conductivity as described in the next section (section 3.3).

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Journal Pre-proof The effect of phase-content of dispersed nanomaterial in thermal conductivity was also analysed experimentally. For this, pure anatase powder (Avra Synthesis Ltd., India) having average particle size around ~ 26 ± 3 nm and a mixed phase TiO2 powder of Degussa P25 having average particle diameter around 25 nm with anatase and rutile in ratio of 80:20 were used. The thermal conductivity test of two kinds of nanofluid systems made out of these two samples were carried out at a same concentration (0.05 Wt%) in order to perceive the impact of

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phase.

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The outcome [depicted in fig. ES7] showed that, pure anatase phase resulted in higher thermal conductivity. i.e., presence of other (rutile) phase in pure anatase phase of identical dimension

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observed due to the presence of rutile (20%).

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in turn causes lower thermal conductivity. Almost 19% reduction in thermal conductivity is

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As an attempt to understand the effect of particle dimension (milling time) on the thermal

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conductivity, a fixed concentration (0.05 Wt %) was considered and the thermal conductivity was found to decrease with decreasing dimension of the NPs (figure ES9). Considering the

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theoretical and experimental outcome, the significant impact of phase content on thermal conductivity can be stated.

3.3. Theoretical insight from DFT analysis To have a deeper insight about the heat transfer capability of rutile and anatase phases, a detailed theoretical analysis was done. From the theoretical analysis about the heat transfer capability of rutile and anatase phases following results were obtained: thermal conductivities of both the anatase and rutile TiO2 system decrease continuously with the increase in temperature. Thermal conductivity becomes less dependent on the temperature as the temperature increases because of the increase in anharmonicity. Fig.8(b) shows the plot of thermal conductivities (along a/ b lattice vector of the unit cell) as a function of temperature 19

Journal Pre-proof between 250 K and 400 K. The plots clearly show that the thermal conductivity of the anatase phase of TiO2 is greater than that of rutile at a specific temperature. The values of thermal conductivities of rutile and anatase TiO2 at 300 K were calculated to be 4.059 W/m-K and

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5.818 W/m-K respectively.

Figure 8. DFT analysis of anatase and rutile phase of TiO2: (a) Unit cell structures of anatase and rutile TiO2. (b) Variation of Thermal conductivity (W/m-K) with temperature for individual anatase and rutile phases. Variation of cumulative lattice thermal conductivity (W/m-K) with frequency (THz) for (c, d) anatase and (e, f) rutile phase. We further carried out detailed theoretical calculation based on Density Functional Theory (DFT) on the thermal transport properties of the rutile and anatase TiO2 in order to acquire

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Journal Pre-proof clear interpretation. The optimized lattice parameters and space group of each unit cell is presented in Table 3. Table 3: Optimized lattice parameters and space group of each unit cell System

Space group

Lattice parameters a (Å)

b (Å)

c (Å)

P42/mnm

4.592

4.592

2.957

Anatase TiO2

I41/amd

3.784

3.784

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Rutile TiO2

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We calculated the lattice thermal conductivity (kL) by solving the linearized Boltzmann

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transport equation, computed with single mode RTA method. The arrangement of the atoms in

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the unit cell is anisotropic for both rutile and anatase TiO2 which results in anisotropic thermal conductivity values along the lattice vectors for both of them. For rutile TiO2, the kL values at

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room temperature (300 K) were calculated to be 4.059 W/m-K (along a and b lattice vectors) and 4.538 W/m-K (along the c lattice vector) whereas the same for anatase TiO2 were

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calculated to be 5.818 W/m-K (along a and b lattice vectors) and 1.657 W/m-K (along the c lattice vector). We further calculated the contribution in the thermal conductivity from phonon modes of different frequency ranges as shown in the plot of cumulative kL vs frequency plots Fig.8(c-f). These plots clearly denote that phonon modes up to frequency 10 THz which is contributed mostly by the three acoustic phonon modes contribute mostly to the lattice thermal conductivity. The contribution from the low frequency acoustic modes are greater for kL along the a and b lattice vectors (~88% for both rutile and anatase TiO2) than kL along c lattice vector (~79% and ~84% for rutile and anatase respectively). To analyse the anisotropic k L and contribution of phonon modes in the kL, we plotted the lifetime of each frequency mode with their frequencies at 300 K Fig.9(a, b). It can be clearly observed from the plots that the low

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Journal Pre-proof frequency acoustic modes (<10 THz) overall have greater lifetime for anatase than rutile TiO 2 which corresponds to the larger kL value for anatase TiO2 along a and b lattice vectors than rutile. But the high frequency phonon modes that contribute by a significant amount for kL along c lattice vector have greater lifetime for rutile than anatase TiO2 which explains why the value of kL along c lattice vector is greater for rutile than anatase TiO2. From these observations we conclude that the lattice thermal conductivity of anatase TiO2 is mostly contributed by the low frequency acoustics modes resulting in its greater kL value whereas

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there is a significant contribution in the lattice thermal conductivity from the high frequency

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optical modes for rutile TiO2 resulting in its overall low lattice thermal conductivity. Size

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effect on thermal conductivity for each system was also investigated. The plot of cumulative

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thermal conductivities with phonon mean free path is shown in Fig.9(c, d). For rutile TiO2, the MFPs corresponding to 50% accumulation conductivity at 300 K were calculated to be about

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19.3 Å (along a or b lattice vector) and 23.1 Å (along c lattice vector) whereas the same for

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anatase were calculated to be 25.8 Å (along a or b lattice vector) and 18.1 Å (along c lattice vector). It can be inferred from these observations that the variation in lattice thermal

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conductivity will be much less when the dimension of the sample is greater than ~23 Å and ~26 Å for rutile and anatase TiO2 respectively.

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Figure 9. Variation of lifetime (Ps) with phonon frequency (THz) for (a) anatase and (b) rutile

rutile.

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phase. Cumulative lattice thermal conductivity Vs. mean free path (Å) for (c) anatase and (d)

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The above theoretical analysis provides a substantial insight about the heat transferring properties of different phases of TiO2 material. Thus the experimental plots of thermal conductivity (fig.7(a)) showing decreasing trend with rise of milling time can be wellexplained with theoretical validation. The inferior heat transfer property of rutile phase is the dominating factor in determining the thermal conductivity of nanofluid system as the rutile content (%) raises considerably as milling time increases from 0-16 hours. 3.4. Stability analysis from Zeta potential distribution curves A particle surrounded by liquid layer contains inner stern layer and outer diffuse region. Zeta potential is the potential at the boundary inside the outer layer where the ions and particles are in stabilized condition. If the absolute value of zeta is high, the repulsive force between the

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Journal Pre-proof nanoparticles dominates over attracting van der Waal force thus the nanofluid is in a stable state. For a low value of zeta, the attractive force dominates over the repulsive force and particles tend to aggregate slowly. The zeta values and zeta potential distribution curves for samples T4, T8, T12 and T16 are provided in supporting information (shown at Fig S5.). The results indicate that mechanical grinding affects the stability of the nanofluid significantly. Phase transition plays an important role in determining the stability of the system as the impact of size variation is minimal in our case. For T16 sample, we obtain a zeta potential value around

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- 34.5 mV which indicates moderate to good stability. But, in case of TP sample the value is

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only -14.2 mV. The variation of zeta potential values with phase content of rutile (%)

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demonstrates improvement in zeta-values with the rise of rutile phase content (%) in sample

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(See supporting information Fig S5.). The phenomenon of scattering of light by colloidal particles is known as Tyndall effect. True solution can never show Tyndall phenomenon as the

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size of molecules is too small to scatter the light. From the Zeta-analysis, it was found that the

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T16 colloidal sample shows the best zeta potential value (-34.5 mV). Zeta value-stability relationship table is shown in supporting information (See Table-II). Using red-laser torch we

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observed the Tyndall effect of the T16 solution (see Fig S6. of supporting information). From the date of solution preparation, the nanofluid sample was kept undisturbed to observe the stability of the solution.

4. Conclusions Now-a-days, the heat transfer mechanism of different nanomaterial based nanofluid systems are investigated widely and tried to improvise their performance. In this work five different TiO2 samples were produced by following the mechanical grinding of the commercial TiO2 powder. With the increasing grinding time the obtained products gradually changed their phase content. With decreasing particle size of TiO2, the enrichment of rutile phase was observed; 85.0 % rutile phase content in final smallest sample was observed whereas initially it was only 24

Journal Pre-proof 12.5 % in commercial TiO2 sample. Experimentally it was observed that the heat transfer property diminishes with decreasing particle size and that was influenced by the crystalline phase content in TiO2 sample of different particle sizes. The DFT calculated results showed superior thermal conductivity of anatase phase compared to rutile phase of TiO 2 and the values are 5.818 W/m-K and 4.059 W/m-K respectively at 300 K. Again theoretically, it was found that the variation of lattice thermal conductivity would be negligible when the dimension of the

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sample is greater than ~23 Å and ~26 Å for rutile and anatase TiO2 respectively.

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Acknowledgements

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D Mitra would like to acknowledge the financial assistance received from MHRD, Govt. of

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India towards her Doctoral fellowship. The authors would like to thank the University Grants Commission, the Government of India for the University with potential for excellence scheme

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(UPEII). Authors would also like to acknowledge the Central Power Research Institute (CPRI,

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Bengaluru) for providing instrument facility (KD2-pro analyser). One of the authors Bikram Kumar Das would like to acknowledge the financial support by DST INSPIRE FELLOWSHIP

References

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for continuing his research.

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Conflict of interest statement:

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The authors declare that there is no conflict of interest.

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Authors’ statement:

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The authors declare that the work is original and is not sent elsewhere for publication. We also declare that the work is sent to Journal of Molecular Liquid with full consent of all the co-authors.

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Journal Pre-proof Graphical abstract

Highlights

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Different size variation of TiO2 nanoparticles are prepared by subjecting mechanical grinding of commercial TiO2 nanoparticles. Anatase to Rutile phase transition of TiO2 occurs due to the strain induced size reduction. Experimentally rutile TiO2 shows inferior heat transfer property as compared to anatase TiO2. DFT analysis describes the behaviour of lattice thermal conductivity of rutile and anatase TiO2. Variation in lattice thermal conductivity is negligible for dimension greater than ~23 Å and ~26 Å for rutile and anatase respectively.

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

31