This work presents a study on the electrical and structural properties of composites based on graphite dispersed into a polyester matrix. Their structural characterization was performed using small-angle neutron

scattering (SANS), providing information about the dispersion of fillers within the matrix. Electrical measurement was carried out in the frequency range from 1 Hz to 10 MHz and temperature from 30 to 100 °C. It was

found that when the filler concentration is above the percolation threshold, the positive temperature coefficient in resistivity phenomena is identified. The mechanism responsible for this behavior was attributed to the

tunneling effect. The Nyquist representations of the complex impedance spectra were modeled using the Cole-Cole model. The obtained values of the α exponent that gauges the broadening of the loss spectrum are

near zero, suggesting a behavior close to a model of a single relaxation time. Furthermore, the relaxation time versus temperature follows an Arrhenius behavior.

R. Belhimria1, S. Boukheir1,2, Z. Samir1, A. Len3,4, M. El Hasnaoui1,*, M.E. Achour1, N. Éber5, L.C. Costa6, A. Oueriagli2 1LASTID Laboratory, Physics Department, Faculty of Sciences, Ibn-Tofail University, BP 133, 14000 Kenitra, Morocco.

2Laboratoire LN2E, Département de physique, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, 40000 Marrakech, Morocco 3 Nuclear Analysis and Neutron Spectroscopy Department, Centre for Energy Research, H-1525, Budapest, P.O.Box 49, Hungary

4Civil Engineering Department, Faculty of Engineering and Information Technology, University of Pécs, Boszorkány Str 2, 7624 Pécs, Hungary. 5Complex Fluids Department, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, H-1525, Budapest, P.O.Box 49, Hungary

6I3N and Physics Department, University of Aveiro, 3810-193 Aveiro, Portugal

*Corresponding author, Mohamed El Hasnaoui: med.elhasnaoui@uit.ac.ma

SANS characterization and impedance spectra analyses of polyester/graphite composite

Complex impedance analysis

Zs : Impedance at low frequency Z∞ : Impedance at low frequency α : Parameter between 0 and 1, represents

the deviation from Debye behavior. τ : Relaxation time

Composites preparations Experimental procedures

For electrical measurements, the samples were prepared as discs of thickness about 1 mm, with aluminium electrodes of 10 mm diameter on the opposite sites of the sample. The electrical contacts were formed by silver paint. The dielectric measurements were performed using and Agilent 4294A Impedance Analyzer in the frequency range from 100 Hz to 1 MHz and temperature range from 200 to 400 K.

Small-angle neutron scattering (SANS) analysis

Conclusion

Table 1: Power Law Exponents of the Samples Measured on Yellow Submarine SANS

Fig. 3: SANS scattering at small Q range

Fig. 1: Nyquist representation of the complex impedance of matrix (0 %), composites with 12 and 15 % of Gt (below the ɸc), and composite with 17 % of Gt (above the ɸc), at different temperatures

0 10 20 30

0

10

20

30

40

50

70°C

80°C

90°C

100°C

Z''(

G

)

Z'(G)

neat matrix

Temperature

0 5 10

0

5

10

15

20

25

50°C

60°C

70°C

80°C

90°C

100°C

Z''(

G

)

Z'(G)

12 % < c

Temperature

0 3 6

0

3

6

9

12

15

50°C

60°C

70°C

80°C

90°C

100°C

Z''(

G

)

Z'(G)

15%< c

Temperature

0,0 0,2 0,4 0,6

0,2

0,4

0,6

0,8

1,0

30°C

40°C

50°C

60°C

70°C

80°C

90°C

100°C

Z''(

G

)

Z'(G)

17% > c

Temperature

SANS method

Surface fractals : 3< α <4 Mass fractals : 2< α<3

SANS gives information about the nano-sized inhomogeneities , porosity , and their surface characteristics

Fractal dimension (Fd)

10-1

101

103

105

107

104

106

108

1010

100

102

104

106

0

30

60

90

(D

eg)

f(Hz)

0%12%15%

17%

F(Hz)

|Z

*|(

)

0%12%15%

17%

Regime IIRegime I

11Fd

n

ϕ (%) Fd (SANS) Fd (Impedance

Spectroscopy)

0 - 2.006

12 2.58 2.007

15 2.63 2.014

17 2.55 2.253

The relaxation process appeared in the impedance spectra

was interpreted using the Cole-Cole model. The relaxation

time and parameter α are calculated. The small values of α

ranging from 0.01 to 0.08 suggested a behavior close to the

state of a single relaxation time. The relaxation time is

temperature dependent which confirms the thermal activation

behavior.

Small angle neutron scattering proved to be an adequate

method that contributes to the characterization of the

composites, giving information about the whole volume of the

sample.

The fractal dimension of fracture surfaces or of the bulk

volume is linked to the strength and electrical conduction

properties of the composites.

Table 2: Values of the fractal dimensions (Fd) obtained respectively from the impedance spectroscopy and by the SANS measurements

Fig. 4: Frequency dependence of the magnitude and phase of the impedance of Graphite Gt/Poly composite for different concentrations

The Fifth International Symposium on Dielectric Materials and Applications

ISyDMA’5 : Virtual Conference 15-17 April 2020 Presented in

Nyquist representation of impedance spectra were analyzed using Cole-Cole model :

( ) pI Q AQ bg

2 2( ) ' ( ) '' ( )n

CFEZ Z ZA

A : capacitance parameter

n : parameter in the range [0,1]

The fractal dimension is:

The samples used in this investigation are composed of graphite (Gt) particles randomly dispersed in an insulating polymer matrix. - Matrix : unsaturated polyester resin 154TB, containing 31 wt% of styrene monomer and required 30 minutes for gelation at room temperature (Cray Valley/Total, USA). - The Gt particles (from Ceylon Graphite Corp NWNYF) have a diameter between 80 and 100𝜇𝑚, a density of 2.26 g/ cm3 and a direct current electrical conductivity of 1.25×105 to 2×105 Ω.m-1 at 20 °C. - The Gt/Polyester composites have been prepared by mixing in a beaker, 5.57 g of liquid polyester resin, and 0.2 wt% of cobalt octanone as a reaction activator. Then, we added the Gt particles in different concentrations, the percolation threshold is ϕc =16 %.

*

1( )

1 ( )

sZ ZZ Z

j

Concentrations (%)

Average diameter (nm)

Exponent (p)

0 - -

12 84.69 ± 0.03 3.42 ± 0.01

15 82.01 ± 0.05 3.37 ± 0.01

17 114.30 ± 0.03 3.45 ± 0.01

2

3

sin( ) cos( )( )

Qr Qr QrI Q B bg

Qr

Power law model:

Sphere model with Schultz-Zimm size distribution

p : power law exponent (fractal dimension: Fd=6-p) Q : scattering vector A, B : fitting parameters containing instrumental and sample macroscopical characteristics r : radius bg: incoherent background