signal in ferrofluid based thermocells M. Vasilakaki 1 , J. Chikina 2 - - PowerPoint PPT Presentation

Enhancement of the thermopower signal in ferrofluid based thermocells

"DEMOKRITOS"

NATIONAL CENTER FOR SCIENTIFIC RESEARCH

• M. Vasilakaki1, J. Chikina2, V. Shikin3, A. Varlamov4 , K. N. Trohidou1

1 Institute of Nanoscience and Nanotechnology, NCSR “Demokritos,”Greece 2 IRAMIS, LIONS, UMR NIMBE 3299 CEA-CNRS, CEA-Saclay 3 Institute of Solid State Physics, Chernogolovka 142432, Russia 4CNR-SPIN Rome Italy. 1

• Currently, the liquid thermo-electrochemical cells receive increasing

attention as an inexpensive alternative to conventional solid-state thermo- electrics for application in low-grade, waste heat harvesting.

• Enhanced Seebeck effect has been reported * by using ionically stabilized

magnetic nanoparticles dispersed in electrolytes, opening in this way new perspectives to the design of a liquid-based thermoelectric device with relatively high efficiency and cost effectiveness.

*B.T. Huang, M. Roger, M. Bonetti, T.J. Salez, C. Wiertel-Gasquet, E. Dubois, R. Cabreira Gomes, G. Demouchy, G. Mériguet, V. Peyre, M. Kouyaté, C.L. Filomeno, J. Depeyrot, F.A. Tourinho, R. Perzynski, S. Nakamae, Thermoelectricity and thermodiffusion in charged colloids, J. Chem. Phys. 143 (2015). T.J. Salez, B.T. Huang, M. Rietjens, M. Bonetti, C. Wiertel-Gasquet, M. Roger, C.L. Filomeno, E. Dubois, R. Perzynski, S. Nakamae, Can charged colloidal particles increase the thermoelectric energy conversion efficiency?, Phys. Chem. Chem.

• Phys. 19 (2017) 9409–9416.
• T. Salez, S. Nakamae, R. Perzynski, G. Mériguet, A. Cebers, M. Roger, Thermoelectricity and Thermodiffusion in Magnetic

Nanofluids: Entropic Analysis, Entropy. 20 (2018) 405.

Introduction

2

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• Under a temperature gradient the charged species (ions/particles)

migrate acting as charge carriers, analogous to electrons in solids.

• An internal electric field is induced proportional to the temperature

gradient , known as Seebeck effect

• The resulting thermoelectric effect is a contribution from both

electrolytes and charged colloidal particles

Seebeck effect

 

tot

E S T

 

hot cold

| E | | | 



ICTP, Trieste, 11-15 March 2019

What about magnetic particle Seebeck coefficient? Aim of our work

• Total Seebeck coefficient of the complex fluid with nanoparticles consists of

the liquid background and interacting nanoparticle system's contributions

charged environment What about the magnetic particle contribution?

tot np background np np

( , ) ( ) ( , )   S T N S T S T N

Study the role of the magnetic nanoparticles characteristics, the inter-particle interactions, applied magnetic field and particle charge in the formation of the enhanced thermoelectric signal based on the thermodynamic approach and Kelvin formula.

4

Outline of the talk

 Theoretical calculation of the Magnetic Particle Seebeck coefficient  Modelling and Monte Carlo simulations  Effect of the magnetic particle anisotropy  Effect of the applied magnetic field  Comparison with the experimental data  Perspectives

ICTP, Trieste, 11-15 March 2019 5

Calculation of the Magnetic Particle Seebeck coefficient

Total Seebeck coefficient of the system that consists of all the subsystems of the carriers (electrolytes, interacting magnetic nanoparticles, electrodes ) is thermoelectric coefficient and the conductivity



tot tot tot

S /  

ηℓ, mobility, Qℓ the charge and the Nℓ number of particles of the ℓth subsystem

tot

    

 

Q

tot

   

ICTP, Trieste, 11-15 March 2019 6

Calculation of the Magnetic Particle Seebeck coefficient

In the case of a broken external circuit (no current, the voltmeter of infinite resistance) the Stot is related to the temperature derivative of the chemical potential by the Kelvin relation 4 for constant particle number Nℓ and charge Qℓ of each ℓth subsystem as :

Varlamov, A. A., Kavokin, A. V., Prediction of thermomagnetic and thermoelectric properties for novel materials and systems. EPL 103, 47005 (2013) Peterson, M. R. & Shastry, B. S. Kelvin formula for thermopower. Phys. Rev. B 82, 195105(5) (2010)

1        

 

tot N

d S S Q dT 

ICTP, Trieste, 11-15 March 2019 7

Calculation of the Magnetic Particle Seebeck coefficient

Thus, combining previous equations, the thermoelectric conductivity reads: Thus we can rewrite eq. for the total Seebeck coefficient as:

         

 

tot N

d S N dT    

         

 

N tot tot tot

d N dT S N Q     

ICTP, Trieste, 11-15 March 2019 8

Calculation of the Magnetic Particle Seebeck coefficient

Focus on the new term included in Stot namely the contribution to Seebeck coefficient Snp coming from the subsystem of interacting magnetic nanoparticles (ℓ=np) added to the ionic liquid. This term for a given total conductivity and number of magnetic nanoparticles Nnp is determined by the expression

np np np np

N np tot

np

d N dT N Q

S

                

Temperature derivative of chemical potential

ICTP, Trieste, 11-15 March 2019 9

Statistical average of the energy per particle over the temperature is calculated by means of the Monte Carlo simulation technique with the implementation of Metropolis algorithm Chemical potential is defined as the energy which is in average necessary to pay to add one particle to the system, thus for given nnp Nnp and σtot

np i

E   

i

Ep E exp( ) p T p Ep ex p( ) T p E    

 

np i

d d S ~ np dT dT E    

10

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NATIONAL CENTER FOR SCIENTIFIC RESEARCH

Calculation of the Magnetic Particle Seebeck coefficient

ICTP, Trieste, 11-15 March 2019

Outline of the talk

 Theoretical calculation of the Magnetic Particle Seebeck coefficient  Modelling and Monte Carlo simulations  Effect of the magnetic particle anisotropy  Effect of the applied magnetic field  Comparison with the experimental data  Perspectives

ICTP, Trieste, 11-15 March 2019 11

Model of Coherent Rotation Stoner-Wohlfarth

• Surf. Sci. Rep. 56 (2005) 189
• Phys. Rev. B 58 (1998) 12169

Atomic Scale Modelling Mesoscopic Scale Modelling

Mesoscopic Scale Modelling

• f random assemblies of Nanoparticles

12

• Dipolar strength gnp=μ0(MsV) 2/4πd3
• Effective Anisotropy constant Knp =KeffV

Keff: effective anisotropy constant including the surface,magneto-crystalline,shape anisotropy Uniaxial anisotropy for nanoparticles

Gazeau et al., JMMM 186 (1998) 175

Moumen et al.,J.Phys.Chem. 100 (1996) 14410 13

Mesoscopic Scale Modelling

• f random assemblies of Nanoparticles

 2

3 1

ˆ ˆ ˆ ˆ ˆ ˆ ( ) 3( ) ( ) ˆ ˆ ˆ

 

       

 

np np

N N i j i ij j ij np np i i ij i j i

s s s r s r E g K s e r

14

Temperature dependent model parameters

• γ-Fe2O3 Nanoparticles (9 nm size)
• Saturation magnetization Ms(T)=Ms(5K) – b1*T2.3

b1 is such that MS(300K)/MS(5K)=85%

(modified Bloch law (Hendriksen et al. PRB 48 1993), Ms(T)experimental results Safronov et al, 2013* γ-Fe2O3 nanofluid with electrostatic stabilizer)

• Dipolar strength gnp=μ0(MsV) 2/4πd3 ~ gnp (T)=gnp (5K) – b2*T2.3

(gnp(300K)/ gnp(5K)=85%)

• Effective Anisotropy constant Knp=μ0HaMs /2 ~ Knp(T)= Knp(5K) – b3*T2.3

(Knp(300K)/ Knp (5K)=85% )

*A.P. Safronov, I. V. Beketov, S. V. Komogortsev, G. V. Kurlyandskaya, A.I. Medvedev, D. V. Leiman, A. Larrañaga, S.M. Bhagat, Spherical magnetic nanoparticles fabricated by laser target evaporation, AIP Adv. 3 (2013).

15

Reduced Dimensionless parameters used in Monte Carlo simulations

• In our calculations the energy parameters are normalised to the thermal

energy 5kB so they are dimensionless. The reduced temperature is defined as t = T(K) / 5K, the reduced dipolar strength as g and the reduced magnetic anisotropy k

• Snp is divided with the factor σtot / ηnp kB so we calculate the reduced

Seebeck coefficient at average temperature t

ICTP, Trieste, 11-15 March 2019

Monte Carlo calculation of the Snp for γ-Fe2O3 NPs

• Ms=249 kA/m at 5K

 typical value for a range of sizes of these nanoparticles used in stable ionic ferrofluids C. Filomeno et al., J. Phys. Chem. C, 2017, Priyananda et al, Langmuir , 2018, Nourafkan et al.,

• J. Ind. Eng. Chem. 2017, D. Cao et al, Sc.Rep.,2016)
• Effective anisotropy values Keff > Kbulk eff
• Kbulk eff : bulk value of effective magnetocrystalline anisotropy γ-Fe2O3

(Kbulk eff = Kcub bulk/12)= 0.04 104J/m3

16

γ-Fe2O3 Ms(5K) kA/m Ms(300K) kA/m Keff (105J/m3) g(t)=gnp(t)/5kB k(t) = Keff V/ 5kB 1 249 215 0.06 17-0.00019t2.3 33.7-0.00038t2.3 2 0.12 17-0.00019t2.3 67.4-0.00076t2.3 3 0.3 17-0.00019t2.3 168.5-0.0019t2.3 4 1.2 17-0.00019t2.3 673.8-0.0076t2.3 Keff corresponds to 1. D = 7 nm dispersed in a polymer matrix (Figueroa et al., Physics Procedia, 75 (2015) 1050–7) 2. D =7 nm colloidal attributed to the surface effects (Gazeau et al., J.M.M.M.186 (1998) 175) 3. D= 9 nm attributed to surface effects (Fiorani et al., Physica B 320 (2002) 122) 4. D= 9 nm produced by laser target evaporation technique (Safronov et al., AIP Adv. 3 (2013) 052135)

17

Calculation of the Snp for NPs

• Monte Carlo calculations of <E> are performed for various frozen ferrofluids

configurations at different temperatures (e.g.T1,T2,T3…)

• Constant temperature step ΔT=10K that is commonly used in experiments for

measuring Seebeck coefficient.

• Calculation of the d<E>/dT ~ Snp at average temperature Ti ( Ti-1 < Ti < Ti+1 )

as the average of the slopes between the energy at Ti and at Ti-1, Ti+1 respectively

i i 1 i i i 1 i 1 i i i 1

d E(T ) E(T ) E(T ) E(T ) E(T ) 1 dT 2 T T T T

   

                       

ICTP, Trieste, 11-15 March 2019

Outline of the talk

 Theoretical calculation of the Magnetic Particle Seebeck coefficient  Modelling and Monte Carlo simulations  Effect of the magnetic particle anisotropy  Effect of the applied magnetic field  Comparison with the experimental data  Perspectives

ICTP, Trieste, 11-15 March 2019 18

19

Theoretical calculation of Snp for nanoparticles with k=0

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NATIONAL CENTER FOR SCIENTIFIC RESEARCH

Analytical approach for an assembly of dipoles without anisotropy gives

np i,dip

d d E g g 2 ( ) ( ) dT dT T T      

np np

d g S ~ ~ ( ) dT T  

 Monotonic T dependence of the Seebeck coefficient for given g

i

Ep E exp( ) p T p Ep ex p( ) T p E    

 

i

np E   

g ( ) ~ x T  

20

Monte Carlo calculation of Snp for nanoparticles with k=0

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NATIONAL CENTER FOR SCIENTIFIC RESEARCH

 Monotonic T dependence of the Seebeck coefficient

10 20 30

• 4.0
• 3.5
• 3.0
• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0

c=0.5% c=1%

Temperature (t) Normilised Energy <Edip>(x10

2)

(a)

10 20 30

5 10 15 20

Temperature (t) Dipolar Strength (g)

10 20 30 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Reduced Snp (x102) Temperature (t) c = 0.5% (α=-1.25) c = 1% (α=-0.88)

(b)

21

Monte Carlo calculation of Snp for nanoparticles with k=0

 Monotonic t dependence of Snp  Power law coefficient α-1.25 for c=0.5% and t<20 and α-0.33 on average for all concentrations at t>20

20 40 60 80 100 120

• 4
• 3
• 2
• 1

Temperature (t) Normilised Energy <Edip>(x10

3)

(a)

Increase of concentration

20 40 60 80 100 120

5 10 15 20

Temperature (t)

Dipolar Strength (g)

10 20 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Reduced Seebeck coefficient (x102) Temperature (t)

c = 0.5% Fit y=37.44 t -0.75 c = 1% Fit y=80.96 t

• 1.12

c = 1.5% Fit y=93.49-3.30 t+0.043 t2-0.0002 t3 c = 2% Fit y=140.69-4.44 t+0.05 t2-0.0002 t3 c = 3% Fit y=238.94-6.11 t+0.06 t2-0.0002 t3 c = 4.7% Fit y=369.67-6.30 t+0.02 t2+0.00005 t3

(b)

20 40 60 80 100 120 10 20 30 40

Reduced Seebeck coefficient Temperature (t)

c = 0.5% Fit y=87 t -1.69 c = 1% Fit y=364 t -1.69 c = 1.5% Fit y=720 t -1.68 c = 2% Fit y=1313 t -1.68 c = 3% Fit y=2776 t -1.66 c = 4.7% Fit y=5781 t -1.65

(c)

22

Monte Carlo calculation of Snp for nanoparticles with k=0

 Linear dependence of the Seebeck coeffficient on the nanoparticle concentration exists only at very low temperatures (t<4), for higher temperatures, this dependence follows a power law

1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Reduced Seebeck coefficient (x10

2)

Concentration of nanoparticles (c%)

t = 1 Fit y= -37+78 c t = 4 Fit y= 25 c1.55 t = 8 Fit y= 10 c1.75 t = 12 Fit y= 6 c1.80 t = 16 Fit y= 4 c1.82 t = 20 Fit y= 3 c1.82

• Snp(t) curve departs from the monotonic t dependence of the k=0 case
• Effect of the additional anisotropy energy barrier on the calculated Seebeck coefficient

versus temperature

23

Monte Carlo calculation of the Snp for γ-Fe2O3 NPs

20 40 60 80 100 120 0.0 0.5 1.0

Reduced Seebeck coefficient (x10

2)

Temperature (t)

k=0 k=33.7

20 40 60 80 100 120 10 20 30 40

effective anisotropy k dipolar strength g

Simulations parameters Temperature (t)

20 40 60 80 100 120

• 25
• 20
• 15
• 10
• 5

Ek Edip Etot Temperature (t) Normilised Energy <E>(x10

2)

c=1%

• Effect of the Interplay

between interparticle interactions and effective magnetic anisotropy on the calculated Seebeck coefficient versus temperature

• Snp(t) curve shows a

maximum for both concentrations c=1% and 4.7% at t=6

• Snp(t) increase with the

increase of the particle concentration

24

Monte Carlo calculation of the Snp for γ-Fe2O3 NPs

ICTP, Trieste, 11-15 March 2019

20 40 60 80 100 120 1 2 3 4 5

Reduced Seebeck coefficient (x10

2)

Temperature (t)

1% (k=0) 1% (k(t=1) =33.7) 4.7% (k=0) 4.7% (k(t=1) =33.7)

20 40 60 80 100 120 10 20 30 40

effective anisotropy k dipolar strength g

Simulations parameters Temperature (t)

25

Monte Carlo calculation of the Snp for γ-Fe2O3 NPs

• Strong particle magnetic anisotropy enhances Seebeck coefficient
• Shifting of the maximum Snp towards higher temperatures as the magnetic anisotropy

increases

ICTP, Trieste, 11-15 March 2019

20 40 60 80 100 120 0.0 0.2 0.4 0.6 0.8 1.0

Reduced Seebeck coefficient (x103) Temperature (t)

c=1% k(t=1) = 67.4 k(t=1) = 168.5 k(t=1) = 673.8

t’

20 40 60 80 100 120

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.0

Reduced Energy (x105) Temperature (t)

20 40 60 80 100 120 100 200 300 400 500 600 700 k(t=1)=67.4 k(t=1)=168.5 k(t=1)=673.8 g(t=1)=17

Simulations parameters Temperature (t)

Monte Carlo calculation of the Snp for CoFe2O4 NPs

Temperature dependent Model Parameters

26

CoFerrite Ms(5K) kA/m Ms(300K) kA/m Keff (105J/m3) g(t) k(t) OA 432 333 7.4 9.3-0.00017t2.3 700-0.01300t2.3 DEG 624 572 4.8 19.4-0.00012t2.3 455-0.00300t2.3 Uncoated 381 305 8.8 7.2-0.00012t2.3 832-0.00130t2.3

• Calculations were made for D = 5 nm taking into account Ms and Keff values reported in

Vasilakaki, M. et al. Nanoscale 10, 21244–21253 (2018) Ntallis, N., Vasilakaki, M., Peddis, D. & Trohidou, K. N.(submitted) Torres, T. E. et al. J. Phys. Conf. Ser. 200, 72101 (2010)

• Assume the same power low T dependence but different ratios MS,g,k
• OA MS(300K)/MS(5K)=77%
• DEG MS(300K)/MS(5K)=92%
• Uncoated MS(300K)/MS(5K)=80%

• Similar behaviour of Snp(T)

27

Monte Carlo calculation of the Snp for CoFe2O4 NPs

1 2 3

c=1% c=4.7%

Reduced Snp (x10

3)

Reduced Snp (x10

3)

uncoated Oleic Acid

20 40 60 80 100 120

• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0

Norm Energy (x10

t

20 40 60 80 100 120

1 2 3 4 200 400 600 800

Simulated parameters

k g

Simulated parameters 20 40 60 80 100 120

200 400 600 800

k g

Temperature (t) Temperature (t)

20 40 60 80 100 120

• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0

Norm Energy (x10

t

• Broader maximum of the Snp(t) curve in the case of diethylene glycol coating

comparing to the other cases

28

Monte Carlo calculation of the Snp for CoFe2O4 NPs

20 40 60 80 100 120

0.0 0.5 1.0 1.5 2.0

DEG

c=1% c=4.7%

Resuced Snp (x103)

Temperature (t)

20 40 60 80 100 120

100 200 300 400 500 600 700 800 Simulation parameters k g

Temperature (t)

20 40 60 80 100 120

• 1.4
• 1.2
• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.0

Norm Energy (x105) t

• it is advantageous for

thermoelectric applications to have MNPs with high magnetic anisotropy with weak temperature dependence

• f their anisotropy, in order to
• btain maximum values of

Seebeck coefficient for a broad temperature range, especially at temperatures above 300K.

29

Monte Carlo calculation of the Snp for CoFe2O4 NPs

20 40 60 80 100 120

0.0 0.2 0.4 0.6 0.8

Reduced Snp (x10

3)

c=1% bare c=1% OA c=1% DEG

Temperature (t)

20 40 60 80 100 120

• 0.6
• 0.4
• 0.2

0.0

Norm Energy (x10

5)

t

Outline of the talk

 Theoretical calculation of the Magnetic Particle Seebeck coefficient  Modelling and Monte Carlo simulations  Effect of the magnetic particle anisotropy  Effect of the applied magnetic field  Comparison with the experimental data  Perspectives

ICTP, Trieste, 11-15 March 2019 30

• Applied magnetic field shifts the maximum Seebeck coefficient towards higher T

31

Field effect on the Snp for γ-Fe2O3 NPs (c=1%)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Reduced Snp (x10

2)

h=0 h=5 h=50 h=100 h=500

k g

Temperature

k=33.7 (t=1)

0.2 0.4 0.6 0.8 1.0 1.2 1.4

k=67.4 (t=1)

k g

Temperature

20 40 60 80 100 120 0.6 0.8 1.0 1.2 1.4 1.6

Reduced Snp (x10

2)

Temperature (t)

k=168.5 (t=1)

k g

Temperature

20 40 60 80 100 120 2 4 6

Temperature (t)

k=673.5 (t=1)

k g

Temperature

• Field effect depends on temperature and magnetic particle anisotropy

32

Field effect on the Snp for γ-Fe2O3 NPs (c=1%)

0.0 0.2 0.4 0.6 0.8

t=20 t=40 t=60

Reduced Snp (x10

2)

k(t=1)=33.7

0.2 0.4 0.6 0.8 1.0

t=20 t=40 t=60

k=67.4 (t=1)

100 200 300 400 500 0.8 1.0 1.2 1.4

t=20 t=40 t=60

Reduced Snp (x10

2)

h

k=168.5 (t=1)

100 200 300 400 500 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

t=20 t=40 t=60

h

k=673.8 (t=1)

0.0 0.2 0.4 0.6 0.8

OA

h=0 h=100 h=500 h=1000

(c) (b)

Redueced Snp (x10

3)

(a)

uncoated

20 40 60 80 100 120

0.0 0.2 0.4 0.6 0.8

20 40 60 80 100 120

0.05 0.10 0.15 0.20 0.25

Tempereature (t)

DEG

Reduced Snp (x10

3)

Tempereature (t)

• Applied magnetic field lowers the

maximum Seebeck coefficient

33

Field effect on the Snp for CoFe2O4 NPs (c=1%)

Outline of the talk

 Theoretical calculation of the Magnetic Particle Seebeck coefficient  Modelling and Monte Carlo simulations  Effect of the magnetic particle anisotropy  Effect of the applied magnetic field  Comparison with the experimental data  Perspectives

ICTP, Trieste, 11-15 March 2019 34

35

Experimental from CEA-CNRS

• EAN-FF(1%) :

maghemite MNP d~9.3nm

• Na counterions + free citrate ions)
• I2/LiI redox couples @ 10mM.

ΔSe ~Snp for  = 0-0.8%,DT=10K

Monte Carlo (k(t=1)=67.4, g(t=1)=17)

20 40 60 80 100 120

10 20 30 40 50 60 70 80 90 100 110 120

Reduced Snp c=0.1% c=0.2% c=0.4% c=0.6% c=0.8% Temperature (t)

0.0 0.2 0.4 0.6 0.8

5 10 15 20

Reduced Snp

t=60 t=62 t=64

Concentration (%)

• There are differences between experiment and simulations results attributed to the

additional charge effect of the MNPs

Snp versus particle concentration

36

Experimental from CEA-CNRS

• FF(0.05%) : maghemite MNP d~9.3nm
• SMIM counterions
• CoII/III(ppy)TFSI and ColII/III(ppy)TFSI @ 5mM.

ΔSe ~Snp for  = 0-0.8%,DT=10K

100 200 300 400 500 600 700 800 900 1000 1100

20 40 60 80

Reduced Snp

t=60 t=62 t=64

h

Monte Carlo simulations k(t=1)=67.4 g(t=1)=17 c=1%

• There is a qualitative agreement between experimental and MC results probably

because the Zeeman energy dominates over the other energies

Snp versus applied magnetic field

Outline of the talk

 Theoretical calculation of the Magnetic Particle Seebeck coefficient  Modelling and Monte Carlo simulations  Effect of the magnetic particle anisotropy  Effect of the applied magnetic field  Comparison with the experimental data  Perspectives

ICTP, Trieste, 11-15 March 2019 37

Jele: Electrostatic strength between two particles with effective charge Q=σΑ where σ=εοεrζ/λ :surf charge density and A: surface area ζ: zeta potential, λ:Debye length(~1/T), r: pair distance taken from MC particle configurations

r ele

2 2 A 1 J ~ 2 2 4 d k T B      

38

Effect of electrostatic energy term of charged γ-Fe2O3

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NATIONAL CENTER FOR SCIENTIFIC RESEARCH

Q Q Q Q 1 j i j i E J ele ele 2 4 d r r r 0 ij ij i 1 j 1,i j i,j 1,i j         

  

• Jele depends on charge value & temperature

  

tot dip k ele

E E E E

ICTP, Trieste, 11-15 March 2019

Experiments show that the nanoparticles possess the charge Q, which is due to the polaron effect of ions in the electrolyte.

 dE/dT depends

• n Jele that

depends on :  Charge value  Charge distribution  λ, ζ

ele

Q Q i j E J ele rij i,j 1,i j   



39

Effect of electrostatic energy term of charged γ-Fe2O3 for g=17 , k=168.5 (t=1) (c=1%)

20 40 60 80 100 120

• 1

1 2 3 4 5 6

Normilised E(x10

4)

Temperature (t)

Ek Edip Eele (Qi=1 Qj=1) Eele (Qi=1 Qj=-0.5) Eele (Qi=-0.5 Qj=1.0)

Jele=0.5/4πε0εrd=1500

20 40 60 80 100 120

• 50

50 100 150

λ=2.1 nm Huang et al., J. Chem. Phys. (2015) ζ=-35mV (standard value for stability) Reduced Seebeck coefficient Temperature(t) Qi=1 Qj=1 Qi=1 Qj=-0.5 Qi=-0.5 Qj=1.0 Qi=Qj=0

• 1

1 2 3 4 5 6

Normalised E(x10

4)

Ek Edip Eele (Qi=1 Qj=1) Eele (Qi=1 Qj=-0.5) Eele (Qi=-0.5 Qj=1.0)

Jele=0.5/4πε0εrd=5 Charge distribution 60% Qi , 40%Qj

• 100

100 200

Reduced Seebeck coefficient Qi=1 Qj=1 Qi=1 Qj=-0.5 Qi=-0.5 Qj=1.0 Qi=Qj=0

Concluding Remarks

• We study for the first time the role of the magnetic particle anisotropy in the

formation of the enhanced thermoelectric signal based on a thermodynamic approach and Kelvin formula and Monte Carlo simulations.

• Our results show that Seebeck coefficient (through dE/dT) is enhanced with the

increase in the magnetic particle anisotropy following a non-monotonic temperature dependence.

• Optimum values of Snp can be achieved with MNPs of high magnetic

anisotropy with weak temperature dependence of their anisotropy for a broad temperature range, especially at temperatures above 300K.

• Seebeck coefficient value increases with the particle concentration, the magnetic

applied field, the magnetic particle charge distribution

• Next steps : Introducing DFT charge parameters

Inclusion of Van der Waals interactions

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ACKNOWLEDGMENTS

• This work is supported by the European Union's Horizon 2020 Research and

Innovation Programme: under grant agreement No. 731976 www.magenta-h2020.eu

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