dependence of electrical conductivity of ethylene

Rev. Roum. Sci. Techn.– Électrotechn. et Énerg. Vol. 63, 3, pp. 243–248, Bucarest, 2018

Électrotechnique et électroénergétique

“Politehnica” University of Bucharest, MMAE Dept., Romania. E-mail: [email protected]

DEPENDENCE OF ELECTRICAL CONDUCTIVITY OF ETHYLENE-PROPYLENE RUBBER ON ELECTRIC FIELD AND TEMPERATURE

LUCIAN VIOREL TARANU, PETRU NOTINGHER, CRISTINA STANCU

Key words: Ethylene-propylene rubber (EPR), Space charge, Electric field, Temperature, Electrical conductivity, Experimental values, Empirical equation.

This paper presents the results of a study concerning the dependence of ethylene-propylene rubber's (EPR) conductivity on temperature and electric field. At first, the values of the electrical conductivity are determined experimentally on flat samples of EPR at temperatures of 30, 50 and 70 oC and for dc electrical fields of 5, 10, 15 and 20 kV/mm. Next, the electrical conductivity values are calculated with different empirical equations proposed in the literature, and the obtained results are compared with the experimental ones. It has been found that the difference between the experimental and calculated values is relatively high. As a result, in this paper, a new empirical equation is proposed for calculating the electrical conductivity as a function of temperature and electric field. Finally, it is shown that the differences between the experimental and calculated values for the conductivity using the new equation are much smaller.

1. INTRODUCTION Since 1960, ethylene-propylene rubber (EPR) has begun

to be used as insulation for power cables with rated voltages up to 69 kV (both in North and in South America and Europe), with much better flexibility than cross-linked polyethylene (XLPE), a high resistance to partial discharges and operating and emergency temperature limits identical to those of XLPE [1] EPR is a synthesized elastomer of ethylene and propylene (1:1 ratio), with an average molecular weight of 150000 ... 250000. For cable insulation, EPR vulcanized with peroxides is used (dicumyl and ditertiarybutyl peroxides), with a filling content that can exceed 50 %, a volume resistivity of ρv = 1013 – 1015 Ωm, dielectric strength Ebr = 36 MV/m, relative permittivity εr = 3.17 – 3.34, loss factor tg δ = (6.6–7.9)10–3 and continuous high-temperature limit T = 150 – 175 oC [1].

The existence of intense electric fields in the EPR insulations of power cables [2] causes the occurrence and/or the intensification of some associated phenomena, namely partial discharges, accumulation of space charge [3] and, especially, electrical and electrochemical treeing (specifically, water treeing) [4, 5], phenomena leading to the ageing and the degradation (breakdown) of the insulations [6, 7]. In the case of cable joints, especially of those in dc, at the interfaces between two insulating layers 1 and 2 subjected to a potential difference U, at the moment t after the voltage application a space charge of superficial density ρs(t) is separated [3]:

121221

1221

τexp1

σσσεσε

ρ tUgg

ts

, (1)

where g1 and g2 represent the thicknesses, σ1 and σ2 – the dc conductivities and ε1 = ε0.εr1 and ε2 = ε0.εr2 – the permittivities of the layers 1 and 2, ε0 = 8.85.10-12 F/m – vacuum permittivity and τ12 – the charge relaxation time:

1221

122112 σσ

εετgggg

. (2)

This additional charge determines a local increase of the

electric field, respectively of the degradations caused by the partial discharges and electrical trees, leading to the premature apparition of joints insulations breakdown. As shown in (1), the values of ρs(t) depend on the values of conductivities and permittivities of layers 1 and 2, whose magnitudes are influenced by the temperature and electric field values. On the other hand, increasing the electrical conductivity during the operation of the cables and joints causes an increase in the active component of the current in their insulations. As a result, the Joule losses in the insulations increase, which leads to increased insulation temperatures and hence to the intensification of ageing processes and to the reducing of their lifetime [6–8]. Therefore, for the realization of the insulation, it is necessary to have polymeric materials whose conductivity has values as low as possible, and which vary very little with temperature and electric field.

The electrical conductivity of polymers σ characterizes electrons, holes, ions and polarons displacement under an electric field, and has the expression:

n

1iiii

qn μ σ , (3)

where ni represents the concentration, qi – the charge, μi – the mobility of charge carriers of i species, and n – the number of species of charge carriers.

All the quantities in (3) are dependent on the temperature, electric field and on the environmental characteristics (humidity, radiation etc). The concentration of the charge carriers is determined by the intrinsic properties of the polymer, respectively by the width of the forbidden band gap (Fig. 1 a) and on the nature and concentration of its defects (impurities, oxidation by-products, dangling bonds, amorphous/crystalline interfaces etc.). The latter generate new possible states in the forbidden band gap, located near defects and called, simply, traps.

Carriers may encounter traps at conformational defects (chain folds) or at polar groups (in polyethylene, carbonyl groups). Acceptors (electron traps) are located below the conduction band while donors (hole traps) are situated slightly above the valence band (Fig. 1 b) [9]. As the time that a carrier spends trapped in localized states depends on

Conductivity of ethylene-propylene rubber 2

244

the depth of the trap (the energy needed to remove the carrier), temperature, electric field, etc. it follows that the values of σ will also be influenced by the values of E and T.

In the case of the EPR used in power cable insulations, the charge carriers are, in general, free electrons and holes, with low concentrations and mobilities (the charge carriers remaining trapped for long periods of time), which results in low electrical conductivity values (under 10-15 S/m) [1]. The movement of the charge carriers takes place within the conduction (free electrons) and valence (holes) bands, the mechanisms leading to conduction and carrier transport being dependent on the electric field (among other factors). On the other hand, it is more probable that the conduction mechanism is dominated by hopping between traps and/or the extended states (or tunneling for higher fields).

For field up to 106 to 107 V/m (low fields) the conductivity varies linearly with the electric field and the behavior falls in the ohmic regime regardless of carrier type. When the applied field is increased (>107 V/m) the voltage vs. current characteristic becomes super-ohmic with the current increasing faster than the voltage; the mobility and the conductivity being field dependent [8].

This paper presents an experimental study on the variation of the electrical conductivity σ with the temperature T and the electric field E, for EPR samples. Using the experimental results, the material parameters from 4 empirical equations are determined, and a new equation is proposed. Finally, the values of the material parameters of the EPR samples, corresponding to each of the empirical equations, are determined and the conductivities calculated with these equations and those determined experimentally are compared.

2. EXPERIMENTS Experimental determination of the electrical conductivity

was performed on flat disc samples made from non-vulcanized EPR tapes (60 cm in length, 10 cm in width and 1 cm in thickness), rubber milled to a thickness of g = 1 mm. From these bands, discs were taken and placed in a 13.5 cm diameter mold. The mold was placed between two plates (stainless steel) and then between the platters of a laboratory press preheated at 190 oC. After pressing at 160 bar for 10 minutes, the platters are opened and the plate-mold-plate assembly is carefully removed from the press and is then allowed to cool naturally to room temperature.

After their complete cooling, the samples were thermally conditioned at 50 oC for 48 hours in an oven with forced air circulation. Then, their thickness was measured in 8 points and the mean thickness was determined (g = 0.484 mm).

Fig. 2 – Setup for measuring the absorption/resorption currents

. In order to obtain the dc conductivity, the absorption/resorption currents were measured with a Keithley electrometer connected to a setup existent in the Laboratory of Innovation Technology (LIT) of the University of Bologna (Fig. 2), which allows for measurements at variable temperatures and electric fields.

3. RESULTS Absorption (ia(t)) and resorption (ir(t)) currents [11] were

measured on groups of 3 samples, for one hour, at 3 temperatures (30, 50 and 70 oC) and 4 values of the electric field (5, 10, 15 and 20 kV/mm). The computation of the dc conductivity was performed using the equation:

Sg

Utiti

t ra .)()(

)(σ0

, (4)

where σ(t) represents the conductivity value at instant t after voltage application U0 (U0 = 2.5, 5, 7.5 and 10 kV) and S – the surface of the measuring electrode [12]. A part of the results are presented in Figs. 3–13.

Figures 3-5 show the variations in the electrical conductivity σ(t) with the application time of the voltage t (t = 0...3600 s), measured at 30 oC (Fig. 3), 50 oC (Fig. 4) and 70 oC (Fig. 5), for 4 values of the electric field, respectively at 5 (curves 1), 10 (curves 2), 15 (curves 3) and 20 kV/mm (curves 4).

It is found that, in general, the conductivity decreases in time: at the beginning very fast (for t < 10 s) and then slowly, stabilizing at t > 3600 s (Fig. 3).

a) b)

Fig. 1 – Schematic representation of energy levels in a polymer: a) ideal; b) real (with defects) [9].

3 Lucian Viorel Taranu, Petru Notingher, Cristina Stancu

245

Fig. 3 – Variation of electrical conductivity (σ) with voltage application time (t) for T = 30 °C and E = 5 kV/mm (1),

10 kV/mm (2), 15 kV/mm (3) and 20 kV/mm (4).

Fig. 4 –Variation of electrical conductivity (σ) with voltage application time (t) for T = 50 °C and E = 5 kV/mm (1),


Fig. 5 – Variation of electrical conductivity (σ) with voltage application time (t) for T = 70 °C and E = 5 kV/mm (1),


This type of variation of the conductivity can be explained by the variations in the concentration and mobility of the charge carriers [13]. Thus, after approx. 1 ns from the application of voltage, the capacitor having the measuring electrode and the high voltage electrode as the metallic plates and the sample as the dielectric (Fig. 2) is fully charged. At the conduction process participate the bonded charge carriers (generating the polarization components ip(t) of the absorption/resorption currents), carriers corresponding to the space charge components iss(t) of the absorption/resorption currents and the carriers emitted from the electrodes (generating the conduction components ic(t) of the absorption/resorption currents) [14].

The bonded charges (associated with the electrical dipoles), although in high concentration, make very small movements that take short times. As a result, their contribution to the conduction is quickly cancelled over time. The space charge carriers (generated by the fracturing of molecules or by injection from the electrodes) are fixed on traps of different depths (corresponding to molecular chain ends, lattice defects etc.) (Fig. 1), and, in time, under the action of the electric field, move on shorter or longer distances, until they fall in another trap or are captured by the electrodes.

As a result, their concentration and therefore, their contribution to the conduction process, decreases in time (but slower than in the case of bonded charges). Only a part of the carriers emitted by the electrodes or generated by ionizing collisions of the molecules of material pass the entire thickness of the sample, generating the conduction current ic (considered constant and characterizing the intrinsic conductivity of the material). In our experiments it was considered that, after 3600 s, as in the case of cross-linked polyethylene [14], the contribution of the space charges is negligible in relation to the contribution of the carriers corresponding to the conduction current and, as such, can be considered that, after 3600 s, the conductivity remains constant.

Variations in EPR’s measured conductivity with the application time for measurements performed at 70 °C (Fig. 5) differ slightly from the other cases. Thus, the values of σ are larger by about one order of magnitude than those obtained at 50 °C, and the variation in time of σ is similar to those of Figs. 3 and 4 only for E = 5 kV/mm (curve 1). For E > 5 kV/mm, it is found that, immediately after applying the voltage, the conductivity decreases sharply, and then increases slightly in the next tens of seconds and remains almost constant until the end of the measurement. This may be due to the increase in both the charge injection from the electrodes (due to the growth of E and T) and the mobility of the charge carriers (with the growth of T), which facilitates the movement of the charge carriers in the samples and, therefore, increases the conductivity.

Increasing the electric field (from 5 to 20 kV/mm) leads to an increase in the electrical conductivity values, about 1.5 – 2 times at temperatures below 50 °C (Fig. 6, curves 1 and 2) and more (about 3.5 times) for temperatures higher than 70 °C (Fig. 6, curve 3 and Table 1). Increasing the temperature also leads to significant increases in electrical conductivity (Fig. 7). For example, at E = 20 kV/mm, the increase in temperature from 50 to 70 °C determined an increase in the σ values about 35 times (Table 1). The increases are due, on one hand, to the increase of the charge concentration and, on the other hand, to the increase of their mobility. The increase in concentration is mainly due to the increase in the probability of detrapping of the charge carriers due to the reduction of the potential trap heights in which they are trapped by increasing the electric field and the temperature, whereas the increase in the mobility is mainly related to the increase of the diffusion coefficient of the ionic carriers with the rise in temperature. It should also be noted that the more significant increases of the conductivity with E are obtained at higher temperatures (70 °C) (Figs. 6 and 7).

Fig. 6 – Variation of electrical conductivity (σ) with electric field (E), for T = 30 °C (1), 50 °C (2) and 70 °C (3), t = 3600 s.


246

Fig. 7 – Variation of electrical conductivity (σ) with temperature (T), for E = 5 kV/mm (1), 10 kV/mm (2), 15 kV/mm (3) and 20 kV/mm

(t = 3600 s).

Table 1 Values of the electrical conductivity with electric field and temperature

T (oC)

E (kV/mm) 5 10 15 20

30 1.07∙10-14 1.31∙10-14 1.65∙10-14 1.71∙10-14 50 6.06∙10-14 9.37∙10-14 12.31∙10-14 14.01∙10-14

70 142.17∙10-14 231.95∙10-14 352.81∙10-14 497.19∙10-14

4. COMPUTATION OF THE ELECTRICAL CONDUCTIVITY

Based on the experiments performed, in Figs. 6 and 7 the variation curves of the conductivity with the temperature and electric field using a relatively reduced number of points are presented. For the computation of the electric field and space charge values, both in medium and/or high voltage EPR insulation cables and bi-layer insulation of joints (when the conductivity values in each point of the computation domain and for each temperature must be known) the analytical expressions of dependency between conductivity and E and T (respectively σ(T,E)) are very useful. For that, a number of empirical equations are proposed, where σ = f(T) [2], σ = f(E) [15] or σ = f(T,E) [16–23] are considered, the most known being (5) [16–19], (6), (7) [20–21], (8) [22–23] and (9) [14]:

E

EbaTkTEATE a

sinhexp),(σ (5)

E

EbaTkTEATE a

2sinhexp),(σ

(6)

E

EbaTkTEATE a

3sinhexp),(σ

(7)

EbaT

kTEATE a sinhexp),(σ (8)

E

EbaTkTEATE a lnsinhexp),(σ

, (9)

where Ea is the activation energy, A, a, b and α – material constants, k – Boltzmann constant and E – the applied electric field (reported, dimensionless).

Equations (5)…(8) were previously used, especially on low and high density polyethylene, and (9) – for cross-

linked polyethylene [14]. In the following section, the correctness of using these equations for ethylene-propylene rubber is verified.

Using the experimental values of the conductivity presented in Table 2 in equations (5)-(9), 4 (for equations (5)…(7) and (9)), respectively 5 equations systems (for (8)) were obtained. The unknown quantities were A, Ea, a, b and α and the equations were solved with the Matlab software, using the fsolve function from the Optimization Toolbox package. For the equations (6) – (8), values 1–4 (Table 2) of the conductivity were used – for T < 50 oC and 3-6 (Table 2) – for T > 50 oC. In the case of equation (9) the values 1–5 of conductivity were used (Table 2) – for T < 50 oC and 4–8 (Table 2) – for T > 50 oC.

Numerical values obtained for A, Ea, a, b and α that corresponds to (6)–(9) are presented in Table 3. On their basis the variation curves of the conductivity σ = f(T,E) were drawn, for fields between 1 and 40 kV/mm and temperatures between 30 and 70 oC (Figs. 8–10).

Analyzing the results presented in Figs. 8–10 it may be seen that the conductivity values computed with equations (5)–(9) are more or less different from those experimentally determined, depending on the equation used and on the temperature and electric field values.

Table 2 Values of the electrical conductivity for different values of temperature (T)

and electric field (E) No. T (oC) E (kV/mm) σ (fS/m) 1 30 5 10.7 2 30 20 17.15 3 50 5 60.65 4 50 20 140.15 5 50 10 93.75 6 70 5 1421.70 7 70 20 4971.90 8 70 10 2319.55

Table 3 Values of A, Ea, a, b and α that corresponds to (5) – (10)

Eq. T (°C) A (S/m) Ea (eV) a (1/K) b (-) α (-)

(5)

≤ 50 103 0.6

2.1194 ∙10-9

–5.4786 ∙10-6

- ≥ 50 7.4065

∙103 3.9184 ∙10-9

–1.216 ∙10-6

(6)

≤ 50 3.7222 ∙106

0.8616

6.4955 ∙10-7

6.2283 ∙10-4

- ≥ 50 4.6451

∙106 1.9718 ∙10-5

–5.586 ∙10-3

(7)

≤ 50 2.2236 ∙104

0.7631

5.3697 ∙10-5

2.211 ∙10-3

- ≥ 50 2.037

∙104 3.7914 ∙10-4

–10.2906∙10-2

(8)

≤ 50 180 0.73

1.2239 ∙10-13

–3.0763 ∙10-11 0.0138

≥ 50 2.2322 ∙10-12

–7.1407 ∙10-10 0.0202

(9)

≤ 50 4.4046 ∙10-9 0.5571

2.163 ∙10-3 0.9205

- ≥ 50 2.5388

∙10-9 7∙10-3 –0.61

(10) ≤ 50 2.3903

∙10-7 0.6 0.0016 0.16 0.21

≥ 50 5.47015∙10-9 0.0065 –1.17 0.23

5 Lucian Viorel Taranu, Petru Notingher, Cristina Stancu

247

Fig. 8 – Variation of the electrical conductivity (σ) with electric field (E), experimentally determined (curve 1) and computed with equations (5) – curve 2, (6) – curve 3, (7) – curve 4, (8) – curve 5, (9) – curve 6

and (10) – curve 7, for (T = 30 °C).


and (10) – curve 7, for T = 50 °C.


and (10) – curve 7, for T = 70 °C.

Therefore, for values between 5 and 20 kV/mm, these differences may exceed 90 % – for equation (5), 50 % – for equation (6), 26 % – for equation (7) and 35 % – for equation (8). For E < 5 kV/mm these differences may take values even to 500 % (for equations (5) – (8)) and for E > 20 kV/mm – 100–300 % (equations (5) – (8)). This may be due to the errors given by the prolongation of experimentally curves for values of the electric field outside of the measurement range (5–20 kV/mm). The smaller differences are for equation (9), respectively below 20 % – for 5 < E < 20 kV/mm, 70 % – for E < 5 kV/mm and below 20 % – for E > 20 kV/mm (Figs. 8–10, curves 6).

In order to reduce the differences between the computed and measured values of the EPR conductivity, a new empirical equation for conductivity calculation σ(E,T) was proposed in this paper, respectively:

E

EbaTkTEATE a lnsinhexp),(σ . (10)

The newer values of parameters A, Ea, a,b and α are presented in Table 3 (Eq. (10)), and the variation curves with E and T of the conductivity – in Figures 8–10 (curves 7). It may be seen that the conductivity values computed with (10) are very close to those experimentally determined (curves 1, Figs. 11–13). The differences between the computed σc(E,T) and experimental values σm(E,T) of the conductivity, reported to the measured ones, εr(E,T):

),(/σ)),(σ),((σ),(ε TETETETE mmcr (11)

being, as average value, below 10 % for each value of the temperature and electric field higher than 5 kV/mm (Table 4).

It is found that for values below 5 kV/mm (especially for 1 kV/mm) and temperatures higher than 50 oC, the computed values using equation (10) are further from those experimentally determined by as much as 45 %. Consequently, for a more accurate determination of the parameters A, Ea, a, b and α, measurements in fields lower than 5 kV/mm should also be performed.

Fig. 11 – Variation of the electrical conductivity (σ) with electric field (E), experimentally determined (curve 1) and computed with equations

(9) – curve 2 and (10) – curve 3, for T = 30 oC.






248

5. CONCLUSIONS Experiments performed on ethylene-propylene rubber

samples show an important influence of the electric field and temperature on the electrical conductivity values σ (their values being about 2 times higher at 30 oC and 4 times at 70 oC as the field increases from 5 to 20 kV/mm and about 10 to 30 times higher when the temperature increases from 30 to 70 oC).

Differences between the experimental values and those obtained using known empirical equations can be higher than 60 % for fields between 5 and 20 kV/mm and even 500 % for values lower than 5 kV/mm.

The empirical equation (10) proposed in this paper for computation of the electrical conductivity of ethylene-propylene rubber allows the calculation with a higher accuracy and on larger intervals of E of the electrical conductivity values. Also, this equation may be used for electric conductivity calculation of other polymers (polyethylene, polypropylene etc.)

ACKNOWLEDGEMENTS The authors express their acknowledgement to ICME

ECAB Bucharest and to the Laboratory of Innovation Technology (LIT) of the University of Bologna for technical support regarding the samples manufacturing and conductivity measurements.

The work has been funded by the Sectoral Operational Programme Human Resources Development 2007-2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/132395.

Received on May 31, 2018

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Table 4 Values of the differences between the computed and measured conductivities εr(E,T) (%)

Eq. T (oC) E (kV/mm) 1 2 3 4 5 10 15 20 25 30 35 40

(9) 30 43.25 27.87 19.91 15.04 17.82 0.30 0.06 13.97 13.56 17.38 19.97 21.66 50 25.59 16.73 10.12 5.85 3.22 3.73 2.18 7.80 12.06 13.80 16.59 17.52 70 70.04 50.00 39.66 33.08 19.46 26.78 14.92 2.42 4.80 3.25 1.68 0.16

(10) 30 15.19 2.25 2.49 4.42 2.14 7.66 2.04 9.60 7.75 8.55 8.55 8.03 50 37.18 29.57 18.75 11.98 7.66 3.98 0.38 4.53 7.64 8.54 9.56 10.02 70 45.08 32.34 25.16 20.58 9.18 9.00 9.55 1.28 1.89 1.09 0.14 0.85

dependence of electrical conductivity of ethylene

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