Cu composites with high thermal conductivity and yet low electrical conductivity

Journal Pre-proof Epsilon-negative BaTiO3/Cu composites with high thermal conductivity and yet low electrical conductivity Zhongyang Wang, Kai Sun, Peitao Xie, Yao Liu, Qilin Gu, Runhua Fan, John Wang PII:

S2352-8478(19)30254-0

DOI:

https://doi.org/10.1016/j.jmat.2020.01.007

Reference:

JMAT 268

To appear in:

Journal of Materiomics

Received Date: 25 November 2019 Revised Date:

25 December 2019

Accepted Date: 12 January 2020

Please cite this article as: Wang Z, Sun K, Xie P, Liu Y, Gu Q, Fan R, Wang J, Epsilon-negative BaTiO3/ Cu composites with high thermal conductivity and yet low electrical conductivity, Journal of Materiomics (2020), doi: https://doi.org/10.1016/j.jmat.2020.01.007. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 The Chinese Ceramic Society. Production and hosting by Elsevier B.V. All rights reserved.

Epsilon-negative BaTiO3/Cu composites with high thermal conductivity and yet low electrical conductivity Zhongyang Wang a,b,c, Kai Sun a,*, Peitao Xie d, Yao Liu b, Qilin Gu c,*, Runhua Fan a,

*, John Wang c,*

a

College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai

201306, China. b

Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials

(Ministry of Education), Shandong University, Jinan 250061, China. c

Department of Materials Science and Engineering, National University of Singapore,

117574, Singapore. d

State Key Laboratory of Bio-fibers and Eco-textiles, Institute of Biochemical

Engineering, College of Materials Science and Engineering, Qingdao University, Qingdao 266071, China *Corresponding author: [email protected] (Kai Sun), [email protected] (Qilin Gu), [email protected] (Runhua Fan), [email protected] (John Wang).

Abstracts: Epsilon-negative materials with high thermal conductivity and low electrical conductivity are of great importance for high power microwave devices. In this work, BaTiO3/Cu composites, as a class of epsilon-negative materials, are rationally designed to achieve a high thermal conductivity yet maintaining the electrical insulative character. Negative permittivity behavior induced by dielectric resonance and plasma oscillation is observed in these BaTiO3/Cu composites, which 1

can be explained by the Lorentz and Drude model respectively. An outstanding absorption ability is achieved near the zero-cross point of the permittivity. Benefiting from the positive temperature coefficient of resistance and the weak temperature dependence of thermal conductivity in BaTiO3/Cu composites, sample containing 22.3 vol% of Cu content exhibits a thermal conductivity of up to 17.7 W/(m·k) and an electrical conductivity down to 0.0022 (Ω·cm)-1 at 150 oC. Therefore, BaTiO3/Cu composite is a promising candidate for applications in electromagnetic attenuation and thermal management. Keywords: BaTiO3/Cu composite; Negative permittivity; Percolation; Thermal conductivity; Electrical conductivity.

1. Introduction Epsilon-negative (ε'<0) materials are inevitably required for new microwave equipment and high power electronic devices, such as microwave absorption, electromagnetic attenuation and novel capacitors [1-5]. Specifically, when the permittivity is near zero, there would be a near-perfect absorption of electromagnetic waves [6,7]. However, the large loss of epsilon-negative materials would convert the absorbed energy into heat, which deteriorates the lifetime and reliability of device. Thus, for practical applications, epsilon-negative materials also need to meet other strict performance requirements, especially a high enough thermal conductivity. For example, a high power travelling-wave tube is regarded as the core of defense electronic equipment and in order to dissipate the heat generated from high-loss as 2

effectively as possible, the attenuating element in it requires a high thermal conductivity [8,9]. Meanwhile, the low electrical conductivity of the attenuating element is also of much concern for preventing electromagnetic interference [10]. Thus, an ideal epsilon-negative material for signal attenuating accessories should possess a high thermal conductivity and at the same time a low electrical conductivity. However, paradoxically most of the materials with high thermal conductivity generally possess high electrical conductivity [11,12]. Some exceptions include diamond, BeO, AlN, BN and SiC, which are thermally conductive and electrically insulating [13]. While diamond is too expensive and BeO is toxic, AlN, BN and SiC require a rather complex preparation process and exhibit poor attenuating performance. Therefore, they are all not very suitable for attenuator applications. Recent advances in negative permittivity have been demonstrated in both artificial metamaterials [14,15] and natural materials [16-18]. For artificial metamaterials, negative permittivity is induced by the resonance of periodic metallic units [19]. As it is well known, thermal conductivity of most metals is directly proportional to their electrical conductivities, following the Wiedemann-Franz Law [20]. Therefore, it is difficult to simultaneously achieve high thermal conductivity and low electrical conductivity in artificial metamaterials. Alternatively, it is understood that certain natural materials exhibit negative permittivity. The negative permittivity can be realized by the plasma-like oscillations in insulator-conductor percolating composites [21,22] and dielectric resonance in ferroelectrics [23,24]. For insulator-conductor percolating composites, despite some polymer-matrix percolating 3

composites show negative permittivity and remarkable high loss, it is difficult to process them into desirable attenuators, because of their low thermal conductivities (less than 3 W/(m·k)) [25,26]. Ceramic-based percolating composites are feasible for achieving high thermal conductivity by employing intrinsically thermal conductive fillers, such as metallic particles [27], graphite platelets [28] and carbon nanotubes [29]. However, in pursuit of epsilon-negative behaviors in ceramic-based percolating composites, electrically conductive pathways already exist [27,28]. In this regard, ferroelectric materials can be used to achieve negative permittivity and maintain a low electrical conductivity at the same time. When metal fillers are incorporated into the ferroelectric matrix at a content below the critical concentration, where the conductive pathways are formed, the thermal conductivity can be improved without dramatically deteriorating

the

electrical

insulation.

Therefore,

a

properly

designed

ferroelectric-metal system can provide a potential avenue to realize the negative permittivity with high thermal conductivity and yet a low electrical conductivity. It is worth noting that both the electrical conductivity and thermal conductivity in insulator-conductor composites should obey the percolation behavior [27,28]. Thus, the optimal thermally-conductive and electrically-insulating properties can be achieved when the percolation threshold of thermal conductivity is lower than that of the electrical conductivity. In this work, metallic Cu fillers are incorporated into the ferroelectric BaTiO3 matrix to achieve the epsilon-negative behavior. Thermal and electrical percolation behaviors of the composites are then systematically investigated. Interestingly, the composites possess an almost perfect absorption along with the 4

improved thermal conductivity and yet relatively low electrical conductivity, when the negative permittivity is near zero. Benefiting from the positive temperature coefficient of resistance (PTCR) and the weak temperature dependence of the thermal conductivity of BaTiO3/Cu composites, the thermal percolation threshold is less than the electrical percolation threshold at 150 oC.

2. Experimental procedure 2.1. Fabrication of BaTiO3/Cu composites BaTiO3 (~99.5%) and CuO (~99.5%) powders were purchased from Aladdin Chemistry Co. Ltd (China). BaTiO3 and CuO powders were mixed together homogeneously at different volume fractions, by ball milling for 10 h. Each of the slurries was dried and compacted at 30 MPa to form cylindrical green bodies, 15 mm in diameter and about 2 mm in thickness. Afterwards, the green bodies were transferred to a tubular resistance furnace and first calcined at 600 oC for 2 h in a hydrogen atmosphere, to reduce copper oxide particles into copper. The temperature was then increased to 1200 oC at a ramping rate of 5 oC/min and held for 2 h. Finally, BaTiO3/Cu composites were obtained by the aforementioned two-step sintered process, with different volume fractions of copper from 6.9% to 26.5%, which were denoted as BT-6.9% Cu, BT-26.5% Cu and so on. 2.2. Characterization and measurements Phase composition and crystalline structure of the samples were analyzed by X-ray diffraction (XRD, D/Max2550VB+/PC, Japan). The morphology was observed by 5

using field emission scanning electron microscopy (FESEM, SU-70, Japan). The permittivity of BaTiO3/Cu composites was measured by using an impedance analyzer (Agilent E4991A RF Impedance, USA) equipped with 16453A dielectric test fixture in the frequency range from 10 MHz to 1 GHz. The dependence of dc electrical conductivity on temperature was measured using a high resistance meter (TH2864, China) from room temperature to 200 oC. Thermal conductivity was measured by using a laser flash technique (LFA427, Nanoflash, Netzsch, Germany) equipped with a temperature controller in an inert atmosphere.

3. Results and discussion XRD patterns of the sintered samples are shown in Fig. 1a, which show the main diffraction peaks of tetragonal BaTiO3 and Cu, and no impurity is observed. The morphologies of the BaTiO3/Cu composites with different volume fractions of Cu are shown in Fig. 1b-1d. The melting point of Cu is 1083 oC, which is lower than the sintering temperature (1200 oC). Thus, during sintering process, Cu particles are converted into liquid state, which is helpful in densifying the composites. As shown in Fig. 1b, when the volume fraction of Cu is 6.9%, Cu particles are mainly aggregated at the grain boundaries (inset in Fig. 1b). As Cu content further increases to 14.4 vol%, some of Cu particles are coated on the surface of BaTiO3 grains, and most of the cavities are filled with Cu (Fig. 1c). Further increasing the Cu content to 26.5 vol% causes more Cu particles to cover the grains of BaTiO3, demonstrating that conductive pathways should have been entirely formed (Fig. 1d). The corresponding energy dispersive spectrometry (EDS) show the signals of Ba, Ti, O and Cu elements, which 6

further confirms that the components are consisted of BaTiO3 and Cu (Fig. 1e). According to the above structural characterization results, we can conclude that the BaTiO3/Cu composites have been successfully prepared.

Fig. 1. (a) XRD patterns of BaTiO3/Cu composites. (b)-(e) SEM images of BaTiO3/Cu composites with different volume fractions of Cu content: (b) 6.9 vol%, (c) 14.4 vol%, (d) 26.5 vol%. (e) The energy dispersive spectrometry graph of (d).

Dielectric properties and absorption spectra of BaTiO3/Cu composites are shown in Fig. 2. The permittivity spectra of BaTiO3/Cu composites with various Cu content from 10 MHz to 1 GHz are shown in Fig. 2a and Fig. 2c. Two types of epsilon-negative behaviors are observed. When Cu content is low, the negative 7

permittivity of composites is induced by dielectric resonance of BaTiO3 (Fig. 2a), which is explained by a collective resonance of Ti4+ in Ti-O octahedral sites under an external alternating electric field [23]. Such a resonance of permittivity can be described by the Lorentz model, presented as following equation [23], ε r′ = 1 +

ω 02 − ω 2 Nq 2 meff ε 0 (ω 02 − ω 2 ) 2 + ω 2ω τ2

(1),

where ω is the angular frequency, ωτ is the collision frequency containing the damping effect, ω0=2πf0 is the characteristic frequency, q is the charge of an oscillator, meff is the effective mass of the oscillator, and N is the numbers of the oscillator per unit volume. There is a good agreement between the fitted Lorentz model and experimental data (red solid lines in Fig. 2a). With the increase in Cu content, damping effect of dielectric resonance gets enhanced, and the value of negative permittivity is weakened. The loss tangent shows a loss peak corresponding to the zero-cross point of permittivity, which indicates a high absorption of electromagnetic waves (Fig. 2b). In addition, when Cu content is further increased to 22.3 vol%, the other type of negative permittivity induced by plasma oscillation of free electrons is observed (Fig. 2c) [30]. As the effective concentration of free electrons in BaTiO3/Cu composites is diluted compared with that of pure Cu, a low-frequency plasma is obtained. Plasma-like negative permittivity can be well described by the Drude model [31,32], and the expressions are shown as follows:

ωp2 ε r′(ω) = 1 − 2 ω + ωτ2 8

(2),

neff e 2

ω p = 2π f p =

meff ε 0

(3),

where ωp is the plasma frequency, neff is the effective concentration of free electrons and meff is the effective mass of the free electrons. Drude model can effectively fit the experimental data (red lines in Fig. 2c). Increasing Cu content can obviously result in a higher ωp, thus the composite with 26.5 vol% Cu content exhibits a negative permittivity in a wider frequency range. The corresponding loss tangent in Fig. 2d is larger than 1, which would be beneficial for the attenuation of electromagnetic waves (Fig. 2d). Similarly, loss tangent of composite with 22.3 vol% of Cu content shows a loss peak near zero cross-point of permittivity (inset in Fig. 2c). A desirable attenuating material should absorb rather than reflect electromagnetic waves [33]. In recent years, it has been demonstrated that a near-perfect absorption of electromagnetic waves can be achieved, based on the attenuated total reflection (ATR) configuration, when the permittivity is near zero [7,34]. Since both BaTiO3 and Cu are non-magnetic materials, the magnetic permeability of the composites can be approximatively regarded as 1. In this case, taking one-resonance and one-port system into consideration, the absorption can be given by the following Equation [7], Absorption =

4TT i r 2 (ω − ωPA ) + (Ti + Tr ) 2

(4),

where ωPA is the perfect absorption frequency, Ti is the intrinsic damping constant of the system, Tr is the radiative damping constant, Ti and Tr are given by 1 Ti = ωPAε r′′(ω ) (where ε r′ ( ω ) → 0 ) 2 πd ωPA n03 sin θ tan θ Tr =

λ

9

(5), (6),

where εr" is the imaginary part of permittivity, d is the thickness of attenuator, λ is the wavelength of electromagnetic waves, n0 is the refractive index of the incidence medium (here consider it is air, n0=1), and θ is the incident angle of electromagnetic waves. Permittivity-near-zero behaviors are observed in most samples. Without loss of generality, herein BaTiO3/Cu composite with 10.6 vol% of Cu content is selected to calculate the absorption performance. Thickness d here is assumed to be the sample’s thickness (2 mm). Absorption as a function of incident angles and frequency is retrieved in Fig. 2e. At incident angle of 60o, BaTiO3/Cu composite with 10.6 vol% of Cu content shows nearly 100% absorption at 44.9 MHz, where permittivity is slightly smaller than zero, rather than being exactly zero. Once known that the maximum absorption is at incident angle of 60o, absorption spectra as a function of thickness and frequency are studied in Fig. 2f. The red region (0 dB) corresponds to 100% absorption of electromagnetic waves. It can be seen that with the increase in thickness, the frequency band of the perfect absorption becomes wider. In conclusion, BaTiO3/Cu composites with slightly negative permittivity show good attenuation performance, and the perfect absorption properties are dependent on the zero-cross points of permittivity, incident angle and thickness.

10

Fig. 2. Dielectric properties and absorption spectra of BaTiO3/Cu composites. (a, c) The permittivity spectra of resultant composites, where the red solid lines in (a) and (c) are fitted by the Lorentz model and Drude model, respectively. The insets in (a) and (c) show the details of negative permittivity near the zero-cross points. (b, d) The loss tangent of the corresponding composites. (e) The absorption spectra of the composite with 10.9 vol% of Cu content as a function of the incident angles and frequency (f). Absorption spectra of the composite with 10.9 vol% of Cu content at various thickness and frequency (incident angle=60o).

11

Frequency-dependent reactance (Z") of BaTiO3/Cu composites is shown in Fig. 3a and Fig. 3b. When Cu content is low, the permittivity changes from positive to negative corresponding to the changes in reactance from negative to positive (Fig. 3a). While, when the Cu content reaches above 22.3 vol%, the Drude-type negative permittivity still corresponds to the positive reactance (Fig. 3b). As the reactance consists of capacitive reactance (ZC=-1/ωC, C is the capacitance) and inductive reactance (ZL=ωL, L is the inductance), obviously, the positive Z" means that the inductive reactance dominates in the total reactance [35]. This demonstrates that Lorentz-type as well as Drude-type negative permittivity can both be attributed to the inductive character of composites [36].

Fig. 3. The frequency-dependent reactance (Z") of BaTiO3/Cu metacomposites. The insets in (a) and (b) show the details of reactance switching. 12

Fig. 4 shows the temperature dependence of resistivity and thermal conductivity of BaTiO3/Cu composites with different Cu content. As shown in Fig. 4a, the resistivity of BaTiO3/Cu composite decreases from 36.9 Ω·cm to 0.6 Ω·cm when the volume fraction of Cu increases from 6.9 vol% to 26.5 vol%. BaTiO3 sintered in H2 atmosphere is an n-type semiconductor, which shows a PTCR behavior [37], thus the electrical resistivity of BaTiO3 increases by several orders of magnitude near Curie temperature (120 oC) [38,39]. In this work, resistivity of BaTiO3/Cu composite is increased sharply near the Curie temperature. PTCR jump is enhanced by two orders of magnitude, which is smaller than that of pure BaTiO3 [40], and the main reason is the aggregation of Cu particles at grain boundaries reducing its resistance. Fig. 4b shows the temperature dependence of thermal conductivity of BaTiO3/Cu composites. When Cu content reaches to 22.3 vol%, thermal conductivity is significantly enhanced due to the formation of heat flow paths. It can be observed that thermal conductivity shows good temperature stability, which is in sharp contrast to that of electrical conductivity, indicating that thermal and electrical transport mechanisms are disparate. Electrons are forced to pass only through molten copper pathways, whereas heat can conduct through both BaTiO3 and Cu phases. For most of ceramics, an increase in temperature would lead to an enhancement in phonon-phonon scattering, which causes a decrease in thermal conductivity [41]. While for BaTiO3, the temperature coefficient of thermal conductivity is slightly positive, which is related to the competition between two factors: on one hand, the increase in symmetry will improve the thermal conductivity, however, on the other hand, BaTiO3 with a

13

paraelectric phase can reduce thermal conductivity. Thus, the change in thermal conductivity is mitigated at the Curie temperature [42]. The weak temperature dependence of thermal conductivity in BaTiO3/Cu composites is attributed to the combined effects of phonons vibration, electrons transport and interfacial defects scattering [43,44], resembling thermal conductive behavior which is also observed in BaTiO3/Ag composites [45]. The different temperature dependences of thermal and electrical conductivity make it possible to achieve a heat conductor with a high electrical resistivity at certain temperatures.

Fig. 4. Temperature dependences of: (a) electrical resistivity, and (b) thermal conductivity in BaTiO3/Cu composites with various volume fractions of Cu.

14

Thermal conductivity and electrical conductivity of BaTiO3/Cu composites as a function of Cu content are studied at 30 oC and 150 oC, as shown in Fig. 5. Electrical and thermal conductivities of BaTiO3 are much lower than that of Cu, consequently, the addition of Cu fillers into the BaTiO3 matrix will eventually lead to a percolation behavior. Thermal conductivity (λ) and electrical conductivity (σ) follow power laws with the increasing Cu concentration, which is shown as follows [28],

λ ∝ (V T − V ) − q for V < VT

(7),

σ ∝ (VE − V ) − t for V < VE

(8),

where the VT and VE are the percolation threshold of thermal and electrical conductivity, respectively, V is the volume fraction of Cu, q and t are the critical exponents. When Cu content is low, the heat conduction is mainly dependent on the vibration of phonons, while the electrons in Cu play a minor role in the overall thermal conductivity. Phonon scattering effect makes it very difficult to improve thermal conductivity significantly. Thus, as shown in Fig. 5a, thermal conductivity demonstrates a mild increase with the increase in Cu content at the beginning. When Cu content is further increased to 22.3 vol%, it is sufficient to make Cu phase interconnected with each other, and electrons can move freely while carrying heat, thus a percolation behavior occurs. The experimental data are fitted well by Equation (7) (red dotted line in Fig. 5a), where the thermal percolation threshold VT is 23.7 vol%. While, for electrical conductivity of composites, σ rises sharply when Cu volume fraction increases from 22.3% to 26.5%. After fitting experimental data by Equation (8) (blue solid line in Fig. 5a), the electrical percolation threshold VE is

15

calculated to be 23.6 vol%. Although VT is very close to VE, the BaTiO3/Cu composite with 22.3 vol% of Cu content shows a high thermal conductivity and relatively low electrical conductivity. As PTCR effect of BaTiO3 can vigorously reduce its electrical conductivity when temperature is above the Curie temperature (Fig. 4a), we have studied the dual percolation behavior at 150 oC, as shown in Fig. 5b. An increase in temperature does not make thermal conductivity change dramatically compared with that at 30 oC. However, electrical conductivity is decreased by two orders of magnitude. Therefore, the change in electrical conductivity with the increase in Cu content is no longer significant. The fitted values of VT and VE are 23.5 vol% and 30.3 vol% by using Equation (7) and (8), respectively. Obviously, VT is smaller than VE, so a high thermal conductivity simultaneously with electrical insulating properties can be obtained once the Cu content is lower than VT. Specifically, the BaTiO3/Cu composite with 22.3 vol% of Cu content exhibits a thermal conductivity of λ=17.7 W/(m·k) and an electrical conductivity of σ=0.0022 (Ω·cm)-1, which is not only very important for practical applications in high-power traveling-wave tubes, microwaves attenuation and shielding [46,47], but also significative in thermal management applications, such as insulation of motors, substrates for light-emitting diodes and solar cells [11,12].

16

Fig. 5. Thermal conductivity and electrical conductivity of BaTiO3/Cu composites as a function of Cu content at: (a) 30 oC, and (b) 150 oC, respectively. The red dotted line and blue solid line in (a) and (b) are fitted by the percolation power law.

4. Conclusions In summary, BaTiO3/Cu composites have been rationally constructed to achieve epsilon-negative behavior with high thermal conductivity and low electrical conductivity. Two types of negative permittivities are observed: (i) when Cu content is low, negative permittivity is induced by the dielectric resonance of BaTiO3, which can

17

be explained by the Lorentz model; (ii) while when Cu content is above the critical concentration, negative permittivity caused by the plasma oscillation of free electrons is observed, which is described by the Drude model. Perfect absorption of electromagnetic waves is obtained at the near zero-cross point of permittivity, especially when the negative permittivity is slightly smaller than zero. In addition, the temperature dependence of electrical resistivity for BaTiO3/Cu composites increases by two orders of magnitude near the Curie temperature. Thermal conductivity shows a weak temperature dependence. With the increase in Cu content, both the electrical conductivity and thermal conductivity of BaTiO3/Cu composites are enhanced, following the percolation behavior. Because of the PTCR effect in BaTiO3, thermal percolation threshold is lower than the electrical percolation threshold at 150 oC, which provides an effective opportunity to achieve a heat conductor with high electrical resistivity. In particular, BaTiO3/Cu composite with 22.3 vol% of Cu exhibits an epsilon-negative behavior simultaneously with thermally conductive and electrically insulating properties, showing great potential for application in high-power

microwave

devices,

electromagnetic

attenuation

and

thermal

management.

Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

18

Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51601105, No. 51803119, No. 51871146), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 2019-01-07-00-10-E00053) and Chenguang Program supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (Grant No. 18CG56). John Wang and Qilin Gu acknowledge the support of National Research Foundation Singapore (NRF-CRP17-2017-01), for research conducted at National University of Singapore. Zhongyang Wang acknowledges the support from the China Scholarship Council.

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Zhongyang Wang

Qilin Gu

Highlights Lorentz-type and Drude-type negative permittivities are observed in the BaTiO3/Cu composites. Detailed perfect absorption performance is investigated near the zero-cross point of the permittivity. An effective strategy is proposed to realize thermally-conductive and electrically-insulating epsilon-negative materials.

Zhongyang Wang currently works as a joint Ph.D. student at National University of Singapore. He obtained his B.S. degree in Material Science and Engineering from Northwestern Polytechnical University, Xi’an, China, in 2014. He is pursuing the Ph.D. degree in Material Science and Engineering at Shandong University, Jinan, China. His current research mainly focuses on the dielectric performance of ceramics, metamaterials and electronic devices.

Qilin Gu is Research Fellow at Department of Materials Science and Engineering, National University of Singapore. He obtained his Ph.D. degree from College of Materials Science, Nanjing University of Aeronautics and Astronautics, China in June 2017. His current research mainly focuses on electronic ceramics, and inorganic membranes for water sustainability.

Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.