Amin Benyoucef
email: benyoucef@laplace.univ-tlse.fr

Laurent Berquez
email: berquez@laplace.univ-tlse.fr

Gilbert Teyssedre
email: gilbert.teyssedre@laplace.univ-tlse.fr

Eddy Aubert
email: eddy.aubert@irt-saintexupery.com

Addressing space charge issues in aeronautical DC cables

The aircraft of the future will be more electrical and all electrical. Technological evolutions foresee an increase of the DC voltage up to 3 kV or 6 kV with keeping the thickness of insulations to the minimum. This results in a strong increase of the electric field in the insulations and space charge can become an issue for the reliability of the systems. Indeed, space charge accumulation is at the origin of a residual field that modifies the electric field and may lead to a premature aging of the dielectric. Besides, the field distribution in complex structures like multilayers cannot be anticipated under DC as easily as under AC because conductivity is trickier to estimate and varies much more than permittivity. To measure these effects, we propose to develop a test bench adapted to aeronautical cables based on the PEA (Pulsed Electro Acoustic) method. The final aim is to assess the capabilities of current cables to be used for DC voltages in future aircrafts.

Introduction

The increase in the power of the electrical systems of future aircraft goes with an increase of the AC and DC voltages of power networks. For DC systems, the phenomenon of partial discharges, well-known in case of AC voltage, is actively studied [1] with consequences much less as under AC as the frequency of occurrence is strongly reduced. However, other effects, such as space charge accumulation, are to be considered. For the insulation of terrestrial or submarine HVDC energy cable systems, with voltages of several hundreds of kV, the problem of space charge is known and deeply investigated for long. Even if the voltage levels in aeronautics are much lower, an increase of the DC buses beyond 3 kV or 6 kV is foreseen while the insulation thickness is minimized to optimize the mass of the aeronautical network. This means that a significant increase in the electric field in the insulations could occur, possibly to levels where space charges could be accumulated and the field threshold for non-linear conduction be reached. Therefore, space charge effects must be investigated, mastered and taken into account in future technologies. To meet these challenges, our objective is to develop a test bench to measure space charge distributions on aeronautical cables and to estimate the evolution of the electric field distribution in the samples and in particular in multilayer arrangements and to identify the stress regimes where these phenomena occur.

Effect of space charge on the electric field

Electrical insulators never have an ideal behavior. Through different mechanisms of generation and transport, space charge build up can be observed. The space charge is the set of positive or negative charges in the dielectric. In addition, it is possible to distinguish so-called intrinsic charges which are charges present initially within the dielectric itself or created by electro-dissociation of neutral species and the so-called extrinsic charges which are charges injected from electrodes to the insulator, such as electrons or holes [2].

We first provide some typical examples of the effects of space charges in energy transmission cables. Figure 1 shows the electric field distribution in a crosslinked polyethylene (XLPE) insulated model cable, with 5 mm inner radius and 9.5 mm outside radius for the insulation, measured along the insulation radius. The cable was subjected to -40 kV and -80 kV voltages at ambient temperature and different polarization times. The profile obtained short after the polarization at -40 kV/mm is very close to the geometric field distribution. For the other curves, as a function of time and bias voltage, the charge distribution modifies the distribution of the electric field. While the capacitive field should be greater on the core of the cable, under the effect of charge build-up the electric field is maximum on the outside of cable. One of the reasons can be the radius dependence of the conductivity due for example to a thermal gradient. The field distribution induced by such process is of the form:

E(r) = E c r c .σ c r.σ(r) (1)
where Ec and σc are the electric field and conductivity at reference radius rc.

The association of dielectrics is another example where charge build-up is at play. Figure 2 shows a space charge mapping for different applied voltages to a XLPE/EPDM (ethylene propylene diene monomer) bilayer material at room temperature. On ordinate axis on the left, the position in µm is represented (with total thickness 600 µm), on the right is represented the charge density in C/m 3 and on the abscissa the polarization time. The area defined by dotted lines represents the XLPE/EPDM interface. It can be seen that at the interface the charges are positive for average fields less than 15 kV/mm. For an average field between 15 kV/mm and 20 kV/mm, the positive charge density begins to decrease and become negative for fields greater than 20 kV/mm [START_REF] Vu | Correlating conductivity and space charge measurements in multi-dielectrics under various electrical and thermal stresses[END_REF]. The observed phenomenon is interface charge between the two materials, so called Maxwell-Wagner effect. This interface charge depends on the relative values of conductivity and permittivity of the two materials:

Σ s =  1 .σ 2 - 2 .σ 1 σ 2 .d 1 +σ 1 .d 2 (2)
where ε and d are the permittivity and thickness of materials 1 and 2.

Moreover in the present case, the conductivity and permittivity depend on the temperature and the electric field, which explains the change of sign of the interface charges depending on electro-thermal conditions [START_REF] Vu | Correlating conductivity and space charge measurements in multi-dielectrics under various electrical and thermal stresses[END_REF]. Accordingly, the field is maximum in one layer or the other, and by measuring the charge density distribution, the field distribution can be estimated as well. We discuss below about the occurrence of such process in aeronautic cables.

Different methods of measuring space charge

Above results were obtained using the pulsed electroacoustic technique. To measure the space charge density profiles, different principles have been developed over the years. Two categories can be distinguished [START_REF] Mizutani | Space charge measurement techniques and space charge in Polyethylene[END_REF].

Thermal methods consist in creating a thermal perturbation within the sample. The absorbed thermal energy diffuses and generates local deformations and local modifications of the permittivity. These changes move the charges relative to the electrodes creating a current in the outside circuit [START_REF] Holé | Non-destructive Methods for Space Charge Distribution Measurements: What are the Differences?[END_REF][START_REF] Toureille | Les charges d'espace : définition, historique, mesure[END_REF]. The transient current contains information on the quantity and the position of the space charge. A mathematical treatment is necessary to recover the space charge distribution.

Acoustic methods use an acoustic wave to disturb or carry information to quantify the charge amount and position in the material. One main advantage of acoustic methods is the speed of measurement, because it is related to the speed of sound for propagating waves in the material. One of the disadvantages of these methods is the sensitivity to noise [START_REF] Holé | Non-destructive Methods for Space Charge Distribution Measurements: What are the Differences?[END_REF].

The method chosen to measure the space charge in aeronautic cables is the PEA method (Pulsed Electro Acoustic).

PEA method on cable

For the first time in the 90's, a PEA system was introduced for the measurement of the space charge on cable for High Voltage transmission [START_REF] Yasuda | Measurement of charge distributions in coaxial cable using the pulsed electroacoustic method[END_REF][START_REF] Hozumi | Space charge distribution measurement in a long size XLPE cable using the pulsed electroacoustic method[END_REF]. The method consists in applying a voltage pulse to the sample, producing oscillation of the charges around their equilibrium positions, thus generating acoustic waves. The acoustic waves are then converted into an electrical signal through a piezoelectric sensor and this signal is amplified and digitally processed by a deconvolution algorithm (Fig. 3). in a dielectric material is [START_REF] Bodega | Space charge measurements on multi-delectrictrics by means of the Pulsed Electro Acoustic method[END_REF]:

𝑓 = 𝜌. 𝐸 - 1 2 . 𝐸 2 . 𝛻𝜀 𝑟 - 1 2 𝛻(𝐸 2 .

𝛾)

(3) where ρ is the space charge distribution, E the electric field generated by the static field 𝐸 𝐷𝐶 and the pulse field 𝐸 𝑝 , ε0 the vacuum permittivity, εr the relative permittivity of the dielectric and γ the electrostriction coefficient.

The different contributions are as follows:

-The first term represents the Coulomb force acting on the space charges present in the dielectric. -

The second term represents the force due to the permittivity gradient existing at the interface between two different dielectrics. -

The third term represents the effect of electrostriction.

For a coaxial cable where insulators are considered homogeneous, the second term may be neglected. But the third term cannot be neglected because in coaxial geometry the Laplacien field is divergent.

At the IRT Saint Exupery and in collaboration with the LAPLACE laboratory, we are developing a PEA bench for space charge measurement for aeronautical cables. For this we use: -A HVDC generator HCP350-35000 with a voltage range of -35 kV to 35 kV and a maximum current of 10 mA applied the DC Voltage to the cable conductor -A pulse generator FPG 2-10NM6 of 1600 V maximum amplitude , 6ns width and 10kHz of repetition rate to 10 kHz -A of 9 µm thick piezoelectric sensor (PVDF) to convert the acoustic waves into an electrical signal

Figure 4 shows the PEA cell that will be used to perform PEA measurements on aeronautical cables.

-.

Fig. 4: PEA cell for space charge measurement for aeronautical DC cables.

The specificity of aeronautic cables

Figure 5 shows a typical example of aircraft cable cross-section in which the insulation is wrapped over the multi-stands conductor designed for avoiding skin effect in the conductor. A Polyimide layer is generally wrapped directly on the conductor and is used because of its high mechanical strength, dielectric and thermal insulation properties. The outer tape of the cable is a fluorinated polymer set for limiting fire issues and arc tracking.

The PEA method has been successfully applied to measurements in cable geometry, and the typical thickness of insulations used in aeronautic cables, from some hundreds of µm to a few mm is of no problem for the technique. However several issues have to be solved to realize a PEA bench for aeronautical cables. The first is the lack of semiconductive sheath in aeronautical cable. The outer semiconducting sheath is usually used to decouple the polarization source and the pulse generator by using the internal capacitance of the measurement cable. So a replacing layer has to be installed, with acoustic impedance compatible with that of the tested insulation in order to avoid reflection effects. The second issue relates to the signal processing. A new approach has to be developed in order to take into account the cylindrical geometry of the cable and the presence of layers of different materials in the cable. Indeed, typically aeronautic cables are made of taped polyimide films and fluorinated polymers. So the set-up must combine the two features illustrated in Figures 1 and2, namely multilayer in cylindrical geometry. The set-up being currently developed does cover such features. It targets typically 10kV DC stress, and 20 nm resolution in space charge measurements. Along with hardware implementation for the test bench, dedicated deconvolution software is being developed, resolving attenuation ad dispersion of acoustic waves along with stacked dielectrics in a cylindrical geometry.

Giving the geometry shown in Fig. 9 the reasons for investigating space charges in such structure is twofold. First, as the insulating layer is directly wrapped on the conductor, and because of the geometry of the conductor strands, field strengthening happens at the interface with the insulation, favoring charge injection. So, charges can be potentially generated. Second, because of the multilayer nature of the dielectric, the field distribution in the different layers of the cable depends on conductivity of the different layers and on their field and temperature dependence, which can vary greatly. A direct measurement of the field distribution can be achieved to control model outputs.

Preliminary study

PEA measurements have been made on the dielectric materials of the aeronautical cables. A PEA measurement was carried out on PTFE (polytetrafluorethylene) 100 µm thick (FIG. 6) as well as on PI/PTFE (polyimide/polytetrafluorethylene) bilayer with PI thickness of 60 µm and a total thickness of 133 µm (FIG. 7). The objective of his measurements is to have a preliminary idea of the behavior of the dielectric materials that the aeronautical cables compose. Fig. 6: PEA calibration signal for a PTFE sample 100 µm thick Figure 6 shows a PEA calibration signal for a flat virgin PTFE sample 100 µm thick. For a calibration signal a 300V DC voltage and a 500V pulsed voltage with a repetition rate of 5 kHz are applied to the sample. We can observe 2 responses (around 175ns and 320ns) related to the capacitive charges at the sample surfaces. We also note that the second peak is attenuated and dispersed than the first peak. Indeed, this phenomenon due to the attenuation and the dispersion of the acoustic waves will have to be taken into account during the deconvolution to recover the space charge profile [START_REF] Ditchi | Broadband determination of ultrasonic attenuation and phase velocity in insulating materials[END_REF]. Fig. 7: PEA calibration signal for PI/PTFE bilayer sample with a total thickness of 130 µm.

Figure 7 shows a PEA signal for a PTFE/PI bilayer sample with a total thickness of 130 µm unload. For this measurement we apply to the sample a 1700V DC voltage and a 500V pulse voltage with a repetition rate of 5 kHz. Three peaks are observed in the PEA signal. Two peaks (175ns, 275ns) are related to the capacitive charges at the sample surfaces. The third peak located around 215ns is related to charges at the interface between the two layers. The charges at the interface can be due to the Maxwell-Wagner effect described above but the duration of polarization voltage application is too short to create these charges. We consider that these charges are present at the surface of one of the two layers and are trapped when the bilayer sample is realized. As a result, the interface charges change the distribution of the electric field in both layers.

Conclusions

In this paper, the rationale for developing space charge measurements on aeronautic cable has been highlighted. The accumulation of space charge results in the appearance of a residual electric field thus modifying the electrical stress on the insulator. Also the need for measuring directly electric field profiles in complex structures becomes evident when switching to dc networks. To evaluate the impact of this phenomenon, several space charge measurement methods have been developed over the last 40 years. They are distinguished mainly in two categories, thermal methods and acoustic methods. The selected method for space charge measurement on aeronautic cables is the pulsed electro-acoustic method. Advances with the development of the test bench will be presented at the conference.

Fig. 1 :

 1 Fig. 1: Electric field distribution in model cable stressed under -40 kV and -80 kV at room temperature and different times [3].

Fig. 2 :

 2 Fig. 2: Space charge mapping in XLPE/EPDM bilayer materials at room temperature for average fields given on the top scheme. Measurements at 20°C. EPDM to the top; XLPE to the bottom. Color bar provides charge density scale in C/m³ [4].

Fig. 3 :

 3 Fig. 3: Schematic diagram PEA witch an example of load profile. The general expression of electrostatic force density

Fig. 5 :

 5 Fig. 5: Section of aircraft cable with copper alloy with focus on insulator layers (picture on the right)

References 1 B

 1 . Cella, T. Lebey, C. Abadie «Partial discharges measurements at the constituent's level of aerospace power electronics converters», Proc. IEEE Electrical Insulation Conference (EIC), 2015, pp. 274-277. 2 C. Laurent, «Diélectriques solides et charge d'espace», Techniques de l'Ingénieur, 1999.


Leila Reddy

Matthew W Self

Benedikt Zoefel

Marlène Poncet

Jessy K Possel

Judith C Peters

Johannes C Baayen

Sander Idema

Rufin Vanrullen

Pieter R Roelfsema

Theta-phase dependent neuronal coding during sequence learning in human single neurons

The ability to maintain a sequence of items in short-term memory (STM) is a fundamental cognitive function. In the rodent hippocampus, the representation of sequentially organized spatial locations is reflected by the phase of action potentials relative to the theta oscillation (phase precession). We investigated whether the timing of neuronal activity relative to the theta brain oscillation also reflects sequence order in the medial temporal lobe of humans. We used a task in which human subjects learned sequences of pictures and recorded single neuron and local field potential activity with implanted electrodes. We report that spikes for three consecutive items in the sequence (the preferred stimulus for each cell, as well as the stimuli immediately preceding and following it) were phase-locked at distinct phases of the theta oscillation. Consistent with phase precession, spikes were fired at progressively earlier phases as the sequence advanced. These findings generalize previous findings in the rodent hippocampus to the human temporal lobe and suggest that encoding stimulus information at distinct oscillatory phases may play a role in maintaining their sequential order in STM.

Introduction:

Learning to memorize and maintain a sequence of items in short-term memory (STM) is fundamental for successful behavior. At the cellular level, this process is linked to sustained firing activity of individual neurons during the delay period between two stimuli [START_REF] Fuster | Neuron activity related to short-term memory[END_REF][START_REF] Kornblith | Persistent Single-Neuron Activity during Working Memory in the Human Medial Temporal Lobe[END_REF][START_REF] Konecky | Monkey prefrontal neurons during Sternberg task performance: full contents of working memory or most recent item[END_REF] , as well as by anticipatory activity before the onset of an expected stimulus [START_REF] Reddy | Learning of anticipatory responses in single neurons of the human medial temporal lobe[END_REF] . Short-term memory processes are also linked to various brain rhythms 5,6 , and there is converging evidence that neuronal firing activity during short-term memory can be timed (or phase-locked) to theta oscillations. In humans, the strength of theta phase locking is predictive of human memory strength [START_REF] Rutishauser | Human memory strength is predicted by theta-frequency phase-locking of single neurons[END_REF] and navigational goals [START_REF] Watrous | Phase-tuned neuronal firing encodes human contextual representations for navigational goals[END_REF] . In rodents, spiking activity of place cells [START_REF] O'keefe | The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat[END_REF] is locked to specific phases of the theta rhythm during spatial navigation. As a rat runs through a sequence of spatial positions, place cells that represent each of these locations fire at distinct phases of the underlying theta rhythm, and their spikes occur at increasingly early phases as the rat approaches the place fields. This process has been called phase-precession and has been proposed to play an important role in the learning of a sequence of spatial positions in the rodent brain [START_REF] Buzsaki | Space and Time: The Hippocampus as a Sequence Generator[END_REF] and it may, by extension, also play a role in the encoding and maintenance of any ordered list in STM [START_REF] Lisman | The theta-gamma neural code[END_REF] .

Here we asked whether a theta phase-dependent coding scheme is also observed in the human brain during sequence learning. Because humans are more visual creatures than rodents, we assumed that learning a sequence of visual objects could be analogous to learning a sequence of spatial positions in rodents. We hypothesized that theta phase could play an important role in stimulus encoding, and that the phase at which a given cell fires would vary with stimulus identity and order. In other words, while subjects are involved in learning a stimulus sequence, each item in the sequence might be represented by neuronal activity that is locked to a different theta phase. Will medial temporal lobe (MTL) neurons in human subjects that navigate a "conceptual" space, defined by a sequence learning task, exhibit the same form of phase precession that has been observed in rodents during spatial navigation? Do MTL neurons also fire at increasingly early phases when the subject approaches the concept that best activates the cells?

Results

To create an analogy with the navigation of spatial positions in rodents, we designed a conceptual space that consisted of a sequence of images. We defined a conceptual space in which images were displayed on the rim of a rotating "wheel" that moved in the clockwise direction. The wheel moved forward smoothly during the inter-stimulus interval (ISI; 0.5 seconds), during which period, a gray placeholder covered all the images. At the end of the ISI period, the wheel stopped for 1.5 seconds, and the placeholder at the topmost position of the wheel was replaced by the next image in the sequence (Figure 1A). We incentivized the subjects to learn the sequences by including probe trials (20% of trials). On probe trials we did not present the next stimulus, but showed two choice stimuli instead, and the observers had to indicate which stimulus was the next in the sequence. In our previous work with the same paradigm [START_REF] Reddy | Learning of anticipatory responses in single neurons of the human medial temporal lobe[END_REF] , we showed that human MTL neurons that initially responded to a particular ("preferred") image on the wheel started firing in anticipation of this preferred image as a result of sequence learning, during the immediately preceding stimulus and the intervening ISI. This finding is reminiscent of rodent place cells that show anticipatory activity in sequentially ordered spatial environments [START_REF] Mehta | Experience-dependent, asymmetric expansion of hippocampal place fields[END_REF] . In the current study, we ask whether theta-phase coding mechanisms observed in rodent place cells also occur while humans navigate this conceptual space. In other words, are different stimuli in the sequence assigned a particular theta phase for firing, and is the order of theta phases similar to that observed in rodent phase precession? C) For each neuron that we recorded from (N = 619) we determined the image that elicited the most spikes. This image was designated as the preferred image for that neuron. The images before and after the preferred image in the sequence were designated as the preceding and following images, respectively. The preferred image had the highest firing rate, which was significantly different from the neuronal response to the preceding and following images (p<0.00001, paired t-test performed on cross-validated data; see main text); the responses to the preceding and following images were not significantly different from each other (p=0.96 paired t-test). Error bars correspond to the standard error of the mean (SEM) across cells.

Nine human subjects learned the order of a fixed number of stimuli presented in a pre-defined sequence, while we recorded spiking and LFP activity from 619 neurons in the hippocampus, parahippocampal gyrus, and temporal cortex. Subjects rapidly learned the sequence order (>90% performance on test trials within 6 sequence presentations 4 ), and consequently all trials except the probe trials were included in the analyses. For each neuron we identified the stimulus that elicited the largest number of spikes (i.e., the "hot spot" in the sequence) and designated this stimulus as the preferred stimulus. The stimuli before and after the preferred stimulus were labeled as the preceding and following stimuli, respectively (Figure 1B, C; see below for results based on a cross-validated analysis). Here, we compared the thetaphase of firing for the preceding, preferred and following stimuli, and determined whether neuronal responses elicited by these stimuli are encoded at distinct theta phases, reflecting the order in which the sequence unfolds.

In accordance with previous studies [START_REF] Rutishauser | Human memory strength is predicted by theta-frequency phase-locking of single neurons[END_REF][START_REF] Watrous | Phase-tuned neuronal firing encodes human contextual representations for navigational goals[END_REF][START_REF] Kraskov | Local field potentials and spikes in the human medial temporal lobe are selective to image category[END_REF][START_REF] Bohbot | Low-frequency theta oscillations in the human hippocampus during real-world and virtual navigation[END_REF] , we observed prominent oscillatory activity in the LFP power and the spike-triggered power (STP) across all recording electrodes in the theta (4-8Hz) and beta (10-18Hz) bands (Figure 2 A,B). Neuronal spiking activity was significantly phase-locked (Raleigh test, p<0.00005) in both frequency bands (Figure 2C), with a preferred firing phase around the trough of the oscillation (pi radians).

Figure 2: LFP power and theta and beta phase-locking of neurons. A) LFP power (expressed in decibel units relative to a 1/f fit, see Methods) reveals prominent activity in the theta (4-8Hz) and low-beta (10-18Hz) bands. B) Theta and beta oscillations in the power spectra of the spike triggered power (STP) during the sequence learning sessions (relative to a 1/f fit). Again, peaks are observed in the theta and beta bands. In A) and B), the solid line and shaded area correspond to the mean and SEM across all recording channels, respectively. C) Distribution of preferred firing phases across cells in the sequence learning sessions with respect to the theta and beta oscillations. The colored dotted and angular solid lines respectively correspond to the mean and standard deviation of the preferred firing phase across cells. The p-values are from a Rayleigh test. .

To determine whether the neurons encoded the preceding, preferred, and following stimuli at different phases of the theta and beta cycle during sequence learning, we next compared the phase of firing for these stimulus types. The neurons fired at distinct phases for these stimuli in the theta band (Figure 3A,B). Phase coding did not occur in the beta band (Figure 3C, D) despite a strong beta band oscillatory component (Figure 2C). To determine significance, we applied a cross-validation procedure in which we based the neuron's preferred stimulus on all trials except one and analyzed phase-coding in the left-out trial (see Methods and Figure S1). The pair-wise difference in phase preferences for the different stimulus types was significant across cells (F(1,1241) = 24.0; p<0.0001 for preferred vs. preceding; F(1,1241) = 29.4; p<0.0001 for preferred vs. following; and F(1,1241) = 105.18; p<0.0001 for preceding vs. following; Watson-William test Bonferroni-corrected for multiple comparisons).

Importantly, similar to the phenomenon of phase precession in the rodent hippocampus, phases advanced to earlier values as the sequence progressed (mean angle ± standard deviation = 234°±23° (preceding), 178°±18° (preferred), and 118°±14° (following). The difference of ~58° between successive stimuli corresponds to a time difference of ~28ms with respect to a 6 Hz oscillation. Phase precession implies that the cycle of action potentials is slightly shorter than the theta band cycle in the LFP. It predicts a slightly higher frequency in spiking compared to the LFP theta oscillation [START_REF] O'keefe | Phase relationship between hippocampal place units and the EEG theta rhythm[END_REF] and this is indeed what we observed (Figure S2). To examine how the preferred phase evolved at a finer time scale as the sequence progressed from one stimulus to the next, we plotted the mean phase across cells as a function of time (Figure 4). We observed distinct phase-of-firing during the time periods in which the stimuli were presented, and a phase transition in between stimuli. A linear fit across cells through the phase values during stimulus presentation revealed a negative slope in the theta band (linear regression slope = -22.9 deg/s, r 2 = 0.92, p <0.0005), but not in the beta band (slope = 1.2 °/s, r 2 = 0.02, p = 0.4). The result was confirmed when we examined the phase slopes of individual cells, which were significantly negative in the theta band (t(613)=-4.8, p<0.00005), but not in the beta-band (t(613)=-0.2, p>0.5). The neurons showed significant phase locking only for the preferred and following stimuli (p<0.05, Raleigh test). In contrast to the theta band, the cells did not fire at distinct phases for the different stimuli. The format of these panels is similar to panels A and B.

The phase precession observed for the preceding, preferred and following stimuli was not observed for the remaining stimuli in the sequence, indicating that the phase selectivity did not extend to stimuli that far away from their preferred stimuli in the sequence. This decrease in phase locking is not unexpected if the preferred stimulus reappears every 5-7 stimuli, because items that follow the preferred stimulus will, at some point, be perceived to precede its next presentation, causing a breakdown of phase coding.

We carried out a number of control analyses to rule out (1) that the phase differences were caused by differences in firing rates or (2) differences in LFP power. First, we considered the possibility that a difference in the number of spikes fired for each stimulus was responsible for the phase differences (Figures S1 andS3). The largest spike-phase difference was observed between the preceding and following stimuli (p<0.0001), even though the firing rates were not significantly different from each other (Figure S1A; p=0.87). Furthermore, the preferred stimuli elicited a significantly higher firing rate than both preceding and following stimuli, yet their spike phase was intermediate. It is thus unlikely that a difference in firing rates could explain the phase precession effect. We also matched the spike count of individual trials between preceding and following stimuli, only including the subset of trials for the preceding and following stimuli in which the difference was <=1 spike (Figure S3) and observed that phase differences were maintained (F(1,1149) = 73.95; p<0.0001; Watson-William test, Bonferronicorrected for multiple comparisons). We can therefore be confident that the differences in phase are a robust finding that is not caused by differences in the firing rate elicited by successive stimuli. Second, phase precession was also not caused by differences in LFP power, because LFP power was similar across the stimuli (Figure S1). Finally, we considered the possibility of a phase reset evoked by stimulus onset that could differentially affect spike-phase locking for the different stimuli (Figure S4). The absence of an influence of phase-reset was confirmed with a control analysis in which we removed precisely stimulus-locked spikes around the time of maximum phase reset (see Figure S4 and Methods). Theta oscillatory activity in the primate 17 and human hippocampus 18,19 is often observed to be fragmented, with alternating periods of low and high theta power. We therefore asked whether the stimulus specific phase encoding reported above was influenced by variations in theta power. For instance, differences in oscillatory power have been suggested to modulate the "duty cycle" of phase coding 20 . To address this question, we determined the median theta power for each recording channel. Spikes for each cell were then assigned to periods of low or high theta on the basis of the instantaneous theta power at the moment of the spike (median split). Within each period we then recomputed the phase of firing for the stimuli in the sequence. During both periods of low and high theta we found the same pattern of results as before: the neurons responded to the different stimuli at distinct theta phases, and the phase values shifted forward during the sequence (Figure S5). Thus, spike-theta phase coding was observed during periods of both high and low theta oscillatory activity.

Discussion:

Influential models of the hippocampus posit that this brain area structures incoming information by generating sequentially organized cell assemblies, each for a different input or event. In this scheme, a sequence of spatial locations (during navigation), or a sequence of items that has been learned, relies on the theta rhythm, which organizes the cell assemblies into sequences via phase precession [START_REF] Buzsaki | Space and Time: The Hippocampus as a Sequence Generator[END_REF]21 . Our results provide important new insights into phase precession by showing (1) that phase precession occurs in the human MTL and (2) occurs outside navigation, in a task that required the learning of a sequence of visual objects. Neuronal firing in the human MTL elicited by different items in a sequence was phase-locked to the theta oscillation at distinct phases, and we observed a gradual phase precession that spanned three items in the sequence, with spikes fired at successively earlier phases as the sequence progressed. The phase coding was a robust phenomenon repeatedly observed in numerous control analyses: with a cross-validated selection of stimulus selectivity, when rejecting the spikes close (<0.6s) to stimulus onset, when equating the numbers of spikes between the preceding and following stimuli, and for both low and high theta power trials.

Recent studies in human and non-human primates have investigated how a series of items during memory tasks is encoded in different brain regions. At the level of single neurons, it appears that the last presented item is the most reliably encoded in firing activity [START_REF] Kornblith | Persistent Single-Neuron Activity during Working Memory in the Human Medial Temporal Lobe[END_REF][START_REF] Konecky | Monkey prefrontal neurons during Sternberg task performance: full contents of working memory or most recent item[END_REF] , but these studies did not report phase locking to ongoing oscillations. Other studies have reported spike-phase coding with respect to higher frequency (32Hz) oscillations 22 , or elevated theta-gamma phase-amplitude coupling 23,24 . An MEG study Heusser et al.,23 is perhaps most relevant to the current study. They asked subjects to learn and recall the order of a sequence of images and showed that, on successfully encoded trials, consecutive items in the sequence exhibited higher gamma power at distinct theta phases. Our results go beyond by demonstrating theta-phase-coding of action potentials. This is important because phase-precession in rodents and, by extension, models of STM [START_REF] Lisman | The theta-gamma neural code[END_REF] and hippocampal function [START_REF] Buzsaki | Space and Time: The Hippocampus as a Sequence Generator[END_REF] , posit a key role for neuronal spiking activity phase-locked to theta rhythms.

Theta oscillations and phase precession are prominent in the rodent hippocampus during spatial navigation [START_REF] O'keefe | The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat[END_REF] . Spatial navigation in virtual environments in humans has revealed that navigational goals are represented in the firing activity 25 . Theta oscillations have also been observed in humans, with frequencies ranging from 3-9 Hz [START_REF] Watrous | Phase-tuned neuronal firing encodes human contextual representations for navigational goals[END_REF][START_REF] Kraskov | Local field potentials and spikes in the human medial temporal lobe are selective to image category[END_REF][START_REF] Bohbot | Low-frequency theta oscillations in the human hippocampus during real-world and virtual navigation[END_REF][26][27][28] . Watrous et al., (2018) [START_REF] Watrous | Phase-tuned neuronal firing encodes human contextual representations for navigational goals[END_REF] recently reported phase locking of action potentials to lower theta frequencies (3Hz) during navigation in a virtual environment. However, unlike our study, that study did not report a consistent directionality of theta phase coding with respect to the navigational trajectory of the subject, a difference that might be due to the different theta frequency range, or the different task. Here, we created a "conceptual" space, which consisted of a set of images that were ordered in a sequence and observed a distinct spike-phase code for successive items in the sequence.

The rate of phase precession in rodent place cells is not fixed, but varies as a function of the spatial extent of the place field, and the speed at which the animal crosses it 29 . For example, when the same place field is crossed at slow or fast speeds (~12 cycles or ~5 cycles respectively), the phase shift from cycle to cycle slows down or speeds up accordingly. In our sequence, the number of stimuli that elicit elevated spiking is one to two stimuli [START_REF] Reddy | Learning of anticipatory responses in single neurons of the human medial temporal lobe[END_REF] . In other words, in our experiment, it takes ~24 cycles (2 seconds/stimulus for a 6Hz oscillation) to traverse the region in stimulus space associated with increased activity. This is a large number of cycles compared to the number that pass by when a rat traverses a hippocampal place field, and consequently the phase shift from cycle to cycle (or the phase slope reported in Figure 4) may be lower than that reported during spatial navigation in rodents. Future work could test how the rate of phase precession in a conceptual navigation space in humans varies as a function of the presentation speed of the sequence.

It is of interest to consider the response of multiple neurons (with distinct stimulus selectivities) within a single theta cycle. The finding that it is possible to track the phase advance of one neuron across theta cycles implies that a sequence of items is represented by a set of neurons tuned to different pictures within every theta cycle, firing at specific phases (Figure 5). During the cycle, neurons whose preferred stimulus is the previous item fire at the earliest phase and are followed by neurons coding for the current and following stimulus, analogously to the behavior of place cells. ). A neuron whose preferred stimulus is S2 fires at the trough of the oscillation during the presentation of S2 (~180°; see Figure 3B). S1 and S3 are the preceding and following stimuli for this neuron and it fires at phases ~230° and ~120° when S1 and S3 are presented, respectively (Figure 3B). The thickness of the bars represents the firing rate. The stippled lines for the theta rhythm indicate that the theta cycles are not necessarily consecutive. B) While stimulus S2 is the preferred stimulus for one neuron, it is also the following stimulus for the neuron selective to S1, and the preceding stimulus for the neuron selective to S3. When S2 is presented on the screen, the neuron whose preferred stimulus is S2 fires around the trough of the oscillation. The neuron whose preferred stimulus is S1 (in blue) will fire at ~120° (S2 is the following stimulus for this neuron). Finally, the neuron whose preferred stimulus is S3 (in yellow) will fire at ~230° (S2 is the preceding stimulus for this neuron). Thus, in a given theta cycle, successive items are represented in the same order as the temporal order of the sequence.

In summary, learning and maintaining the order of a series of stimuli or events is crucial in many tasks. An accurate encoding of a sequence of ordered stimuli enables an organism to predict the future based on regularities learned in the past. Some authors have argued that the role of the hippocampus is to encode events that occur in a temporally organized sequence 30,31 , by generating sequentially organized cell assemblies [START_REF] Buzsaki | Space and Time: The Hippocampus as a Sequence Generator[END_REF]21 . Our results are broadly consistent with these hypotheses in that we observe distinct theta phase firing for successive items in a sequence, that reflects the sequence order. Nevertheless, the importance of phase coding is still under dispute, given that some species, such as bats, have excellent navigational capabilities and similar neuronal place coding strategies, which do not depend on the theta rhythm [32][33][34] . The precise role of theta-phase precession therefore remains to be determined. It is encouraging that it is now possible to systematically study theta phase-coding in the human brain so that future studies can also use this approach to test the generality of theta-phase shifts during sequence coding, navigation in real and conceptual spaces, STM, and other cognitive functions.

Methods

Participants were nine patients (four females, age range 18-36 years) with pharmacologically intractable epilepsy undergoing epileptological evaluation at the Amsterdam University Medical Center, location VUmc, The Netherlands. Patients were implanted with chronic depth electrodes for 7-10 days in order to localize the seizure focus for possible surgical resection 35,36 . All surgeries were performed by J.C.B and S.I. The Medical Ethics Committee at the VU Medical Center approved the studies. The electrode locations were based entirely on clinical criteria and were evaluated based on the pre-surgical planned trajectories on the basis of structural MRI scans. The accuracy of the implantation was always checked using a CT scan co-registered to the MRI. We only included electrodes that were within a 3mm deviation from the target (based on visual confirmation). Each electrode contained eight microwires (Behnke-Fried electrodes, Ad-Tech Medical) from which we recorded single/multi-unit activity and local field potentials, and a ninth microwire that served as a local reference. The signal from the microwires was recorded using a 64-channel Neuralynx system, filtered between 1 and 9000 Hz, sampled at 32KHz. On average, each patient was implanted with 34 ± 11.8 microwires. Participants sat in their hospital room at the Epilepsy Monitoring Unit, and performed the experimental sessions on a laptop computer. All patients participated in the two types of experimental sessions described below.

Sequence Learning (SL) Sessions:

The patients performed a total of 27 sequence learning (SL) sessions. In each SL session, subjects were presented with a sequence of 5-7 images (image number determined as a function of the difficulty level and the availability of the patient). The images were always in a pre-determined order such that a given image, A, predicted the identity of the next image, B, and so on. Subjects were asked to remember the order of the stimuli in the sequence. Each stimulus was presented for 1.5s with an inter-stimulus interval (ISI) of 500ms, resulting in individual trials of 2000ms (Figure 1). The sequence was repeated continuously 60 times resulting in experimental sessions of ~10-14 minutes, not including time spent by the subject to respond on probe trials. 20% of trials were "probe" trials in which, instead of being presented with the next image of the sequence, subjects were shown two images side by side and asked to decide (by pressing one of two keys on the keyboard) which of the two was the next image in the sequence.

To further the impression of a sequence of images we used the following display arrangement (Figure 1): Each image was presented at the center of the screen while placeholders (empty gray squares) were presented to the left and right of the central image. At the end of the 1500ms presentation period, the central image was replaced by a gray placeholder and all the gray squares moved one "step" forward in a clockwise direction for the duration of the ISI, such that each placeholder eventually occupied the next placeholder position. At the end of the ISI, the placeholder that now occupied the central position was replaced by the next image in the sequence. The viewer's subjective impression at the end of the ISI interval was that the central image had been hidden, and then moved clockwise, while the central position was replaced by the next image in the sequence.

Spike Detection and Sorting: Spike detection and sorting were performed with wave_clus 37 . Briefly, the data were band pass filtered between 300-3000Hz and spikes were detected with an automatic amplitude threshold (Figure S6). Spike sorting was performed with a wavelet transform that extracted the relevant features of the spike waveform. Clustering was performed using a super-paramagnetic clustering algorithm. Clusters were visually reviewed by the first-author for 1) the mean spike shape and its variance; 2) the ratio between the spike peak value and the noise level; 3) the inter spike interval distribution of each cluster; 4) the presence of a refractory period for the single-units; i.e. fewer than 1% of spikes in a 3ms or smaller inter-spike interval; 5) the similarity of each cluster to other clusters from the same microwire. Based on manual inspection of these criteria, clusters were retained, merged or discarded. Unit quality metrics are shown in Figure S7.

Number of neurons and their locations:

Over the nine patients we recorded from 619 neurons (single and multi-unit) in the left and right hippocampi (N=491), temporal cortices (N=110), and parahippocampal cortices (N=18) in the sequence learning sessions. In the main analyses, all cells were pooled together. We did not notice differences in theta power between the hippocampal and parahippocampal/temporal electrodes (two-sample t-test, p = 0.56; mean ± SEM = 21 ± 1 vs. 22 ± 1 uV), or in the strength of phase locking as measured by the kappa concentration parameter 38 (F =1.0, p=0.98). Additionally, when the main analyses were performed on only hippocampal cells, the same pattern of stimulus specific phase-locking was observed as in the main analysis (all p-values < 0.0001; Watson-William test for equal means, Bonferroni-corrected for multiple comparisons).

Data Analysis: All analyses were performed with the FieldTrip toolbox 39 and custom Matlab code.

Estimation of theta-band oscillatory activity

All LFP analyses were performed with the FieldTrip toolbox in Matlab 39 . The LFP was recorded from the same microwires as the spiking activity. It was downsampled to a 1,000-Hz sampling rate and notch filtered (between 45-55Hz and 98-102Hz) using a second order Butterworth filter. For each channel, we computed the time-frequency decomposition for 28 different frequencies: f = 2 x with x ∈ {6/8, 8/8, 10/8,…60/8} 7 . The time frequency decomposition was performed with the multitaper method over a 3 second epoch encompassing the preceding and preferred stimuli of the raw LFP trace, using two cycles per time-window at each frequency. We estimated whether significant theta activity was present in the LFP by fitting a 1/f function to the power spectrum and taking the ratio (in units of decibels) between the actual power spectrum and the 1/f fit (Figure 2A). Significance was estimated with a t-test, Bonferroni corrected for multiple comparisons (28 frequencies). In addition to estimating theta power with the raw traces, we also measured the power spectrum of the oscillations around the time of each spike (spike triggered power; Figure 2B). We extracted a 1s LFP segment centered on each spike and extracted the frequency spectrum of each segment. The average power spectrum of these LFP traces was estimated by taking the average of the absolute values (the power) of the spectra of all LFP segments 40 . The resultant power spectrum was fitted to a 1/f function, and the ratio (in decibel units) computed.

Significance was estimated with a t-test, Bonferroni corrected for multiple comparisons over 28 frequencies. Both measures of quantifying oscillatory power revealed prominent theta activity in the 4-8Hz range and beta activity in the 10-18Hz range.

Estimation of spike-LFP phase-locking

The LFP phase was estimated using a Hanning taper over the entire duration of the session (i.e., without epoching), using five cycles per time-window at each frequency. A phase of zero corresponds to the peak of the LFP oscillation, and a phase of ± 180 corresponds to the spike being at the trough of the oscillation. Phase-locking was evaluated by comparing the distribution of phase angles against the uniform distribution using the Rayleigh test. We observed significant phase locking in the 4-8 Hz (theta range) and 10-18 Hz (beta range). For subsequent analyses, the LFPs were therefore band-pass filtered with a second order Butterworth filter in these frequency ranges. A phase value for each spike in each frequency range was extracted using the Hilbert transform on the band-passed signal.

Stimulus specific spike-phase-locking

To determine whether the spikes for the different stimuli occurred at different phases, we assigned phase values to each stimulus depending on the time at which the spikes were fired. Phase values were binned into 15 bins. For visualization purposes only, a smoothing of two bins in both directions was applied. To compare the phase distributions between stimuli the Williams-Watson test from the Circular Toolbox for Matlab 38 was applied to the unsmoothed data.

The preferred image of a neuron was the stimulus that elicited the most spikes. The images before and after the preferred image in the sequence were designated as the preceding and following images, respectively. The phase analysis was also performed using k-fold cross-validation. For each neuron, we determined the preferred, preceding, and following stimuli on all trials except one. The phase values for these stimuli were then extracted on the left-out trial and all the analyses were performed on the data of the left-out trial.

To control for the effect of spike number on phase between the following and preceding stimuli (Figure S3), we equalized the number of spikes for each neuron by only including the subset of trials in which the difference on each trial between the two stimuli was <=1 spike. We re-computed the preferred phases for the preceding and following stimuli, while only considering the reduced number of trials.

Phase-Reset and Inter-trial Coherence (ITC)

We controlled for the possible influence of phase-reset of the theta oscillation caused by stimulus onset on measures of phase precession (Figure S4). We computed the inter-trial coherence at each time and frequency point. On each trial of the following, preferred and preceding stimuli we extracted an LFP segment in the time window of [-0.5 1.5] sec (time 0 corresponds to stimulus onset). The phase and power at each time and frequency point was extracted from a time frequency transform of the signal.

The parameters for the time-frequency transform are the same as described above: namely, the multitaper method with 2 cycles per frequency on the notch-filtered and down sampled signal, at 28 frequencies, and in a time interval of -0.5s to 1.5s in steps of 50ms. The inter-trial coherence is the absolute value of the average spectrum normalized by its amplitude 41 , and varies between zero (no phase-locking) and one (perfect phase-locking). Equal numbers of trials were used for the different stimuli.

Statistical Testing:

We used two-tailed tests unless otherwise specificed. All statistical tests performed on circular data were performed with the Circular Toolbox for Matlab 38 , applied to the unsmoothed data. Quiroga, R. Q., Reddy, L., Kreiman, G., Koch, C. & Fried, I. Invariant visual doi:10.1016/j.cub.2017.10.062 (2017). Jensen, O., Bonnefond, M. & VanRullen, R. An oscillatory mechanism for prioritizing salient unattended stimuli. Trends in cognitive sciences 16, 200-206, doi:10.1016/j.tics.2012.03.002

Figure 1 :

 1 Figure 1: Experimental Design. A) In the sequence learning experiment, a sequence of 5-7 images was presented to the subjects in a fixed order. Each image was presented for 1.5s followed by an ISI of 0.5s. During the image presentation period (1.5s), an image was presented at the center of the screen, flanked by gray placeholders. During the ISI period, a placeholder replaced the central image, and all the placeholders moved in the clockwise direction. At the end of the ISI period, the central placeholder was replaced by the next image in the sequence. B) An example of a 5-image sequence. The sequence was repeated 60 times in each experimental session.

Figure 3 :

 3 Figure 3: Phase encoding of successive stimuli. A, Distribution of spike phases relative to the theta band LFP for the preceding (blue), preferred (red) and following (yellow) stimuli across cells (N = 619). The dashed colored lines indicate the mean phase, the shaded areas correspond to the SEM across cells. The spike distributions have been smoothed for display purposes, but the mean phase (dashed lines) is calculated on unsmoothed data. B, Circular histogram of the firing phase across all cells (N=619), with colors as in panel (A). The dashed colored lines indicate the mean phase, and the colored angular lines correspond to the standard deviation across cells. The phase distributions were significantly different from the uniform distribution, indicating phase locking (p <0.05 for all stimulus types, Rayleigh test). The pvalues above the rose plots are the results of a multi-sample Watson-William test for equal means, Bonferroni-corrected for multiple comparisons. C, D, Spike phase distribution and preferred phase histograms relative to the beta band oscillation for the three stimulus types. The neurons showed significant phase locking only for the preferred and following stimuli (p<0.05, Raleigh test). In contrast to the

Figure 4 :

 4 Figure 4: Phase transition over time in the theta (left) and beta (right) bands.The blue, pink and yellow shaded areas correspond to the stimulus periods of the preceding, preferred and following stimuli. The white regions between stimuli are inter-stimulus intervals, when the display rotates. The black dots and lines respectively correspond to the mean and standard deviation across cells. A negative phase slope was observed in the theta band (slope = -22.9 °/s, r 2 = 0.92, p <0.00001), but not in the beta band (slope = 1.2 °/s, r 2 = 0.02, p = 0.4).

Figure 5 :

 5 Figure5: A subject views a sequence of three images (S1 to S3). A neuron whose preferred stimulus is S2 fires at the trough of the oscillation during the presentation of S2 (~180°; see Figure3B). S1 and S3 are the preceding and following stimuli for this neuron and it fires at phases ~230° and ~120° when S1 and S3 are presented, respectively (Figure3B). The thickness of the bars represents the firing rate. The stippled lines for the theta rhythm indicate that the theta cycles are not necessarily consecutive.

  representation by single neurons in the human brain. Nature 435, 1102-1107 (2005). 495 Jutras, M. J., Fries, P. & Buffalo, E. A. Oscillatory activity in the monkey hippocampus during visual exploration and memory formation. Proceedings of the National Academy of Sciences of the United States of America 110, 13144-13149, doi:10.1073/pnas.1302351110 (2013). Ekstrom, A. D. et al. Human hippocampal theta activity during virtual navigation. Hippocampus 15, 881-889, doi:10.1002/hipo.20109 (2005). 500 Z, M. A. et al. Theta Oscillations in the Human Medial Temporal Lobe during Real-World

	Ambulatory	Movement.	Current	biology	:	CB	27,	3743-3751	e3743,

Acknowledgments:

We are grateful to to C.J. Stam, E. van Dellen, L. Douw, P. Ris, S. Claus, D. Velis, and R. Joosten for help with obtaining ethics approval and for technical help with the patients and recordings. This work was supported by grants from the French Agence Nationale de la Recherche (ANR-12-JSH2-0004-01), the Fyssen foundation, and the Université Paul Sabatier, Toulouse, France (BQR, 2009 and Appel à Projets de Recherche Labellisés, 2013), to L.R., the European Research Council (ERC Consolidator Grant P-Cycles number 614244) and an ANITI (Artificial and Natural Intelligence Toulouse Institute) Research Chair (ANR-19-PI3A-0004) to R.V., the Studienstiftung des Deutschen Volkes (German Academic Scholarship Foundation) to B.Z., the European Union (ERC Grant Agreement n. 339490 ''Cortic_al_gorithms'' and grant agreements 720270 and 785907 ''Human Brain Project SGA1 and SGA2') and the Friends Foundation of the Netherlands Institute for Neuroscience to P.R.R.

Data Availability:

The data supporting the findings of this study are available from the corresponding author upon reasonable request.

Code Availability:

The code supporting the findings of this study are available from the corresponding author upon reasonable request.

Author Contribution: L.R and P.R.R designed the study. J.C.B and S.I performed the surgeries. M.S, B.Z, M.P, J.K.P, J.C.P and L.R. collected data. L.R analyzed the data with input from R.V. L.R. wrote the first version of the manuscript. L.R and P.R.R finalized the manuscript. All authors commented on the finalized version of the manuscript.


Y Kemari

A Mekhaldi

M Teguar

G Teyssedre

AC Conductivity Analysis and Chemical Changes of Thermally Aged PVC/B Insulation for Medium Voltage Cables

Keywords: ; polyvinyl chloride, dielectric, thermal aging, FTIR, conductivity

This work aims to study the correlation between the chemical changes and the variation of the electrical conductivity of thermally aged Polyvinyl chloride class B (PVC/B) material intended for medium voltage cables. For this purpose, thermal aging experiments were carried out on PVC/B samples at 80, 100 and 120 °C for a maximum total duration of 5040 hours (210 days). Chemical changes were assessed by Fourier Transform Infrared Spectrum (FTIR). Besides, Frequency domain dielectric spectroscopy was used to analyze the electrical conductivity of PVC/B samples before and after aging. The results have shown that aging has a significant influence only at 100 and 120 °C. It has been found that the main chemical aging mechanism of PVC/B is dehydrochlorination which leads to a noticeable change in the color of the material. Additionally, more polar molecules are being released which enhance the electrical conductivity mainly at low frequencies.

n AC A DC ω σ ω ε ωε ω σ + = = ) ( " ) (

Introduction

With the advent of synthetic insulation materials in the middle of the 20 th century, polymers continue to be extensively used in cable manufacturing [START_REF] Metwally | The Evolution of Medium Voltage Power Cables[END_REF]. In Algeria, Polyvinyl chloride (PVC) is widely used as an insulation in medium voltage cables. In practice, PVC presents a dielectric constant of about 5 to 9, and a dissipation factor of 4 to 12 % at 20 °C and a maximum operating temperature of 70 °C [START_REF] Metwally | The Evolution of Medium Voltage Power Cables[END_REF].

Furthermore, power cables are exposed to thermal stresses during their operating conditions in which the insulation may suffer degradation and structural changes. In extreme cases, failure may occur, which could result in not only the deterioration of to the power cable, but also environmental and financial damages [START_REF] Wald | Evolution of Medium Voltage Cable Technology in Europe[END_REF]. The chemical and physical changes during aging may affect the dielectric properties of the insulation and lead to increase the electrical conductivity [START_REF] Nedjar | Influence of thermal aging on the electrical properties of poly (vinyl chloride)[END_REF][START_REF] Marzinotto | Investigation on thermal endurance of PVC compounds for low-voltage cable insulation[END_REF].

In reality, the AC conductivity (σ'AC) may include dipole orientation as well as charge carrier migrations (by space charge polarization). According to the theory of dielectric physics, a typical dielectric response implies that, at low frequencies, σ'AC is independent of frequency. However, at higher frequencies, conductivity increases with an empirical power law as expressed in Equation (1) [START_REF] Diaham | Étude du Comportement sous haute température de Matériaux Polyimides en vue de la Passivation de Composants de Puissance à Semi-Conducteur Grand Gap[END_REF]: [START_REF] Metwally | The Evolution of Medium Voltage Power Cables[END_REF] where ω is the angular frequency, ε0 is the vacuum permittivity, ε" is the imaginary part of the complex dielectric permittivity, A is a temperature-dependent parameter and n is the exponent of the universal powerlaw.

On the other hand, since thermal degradation is due to the acceleration of chemical reactions, it is very important to assess the evolution of the main chemical groups in the material. For this, Fourier Transform Infrared Spectroscopy (FTIR) is commonly used in order to determine the chemical composition of a material [START_REF] Diaham | Étude du Comportement sous haute température de Matériaux Polyimides en vue de la Passivation de Composants de Puissance à Semi-Conducteur Grand Gap[END_REF].

The work presented here aims to study the effect of thermal aging on the chemical and dielectric behavior of PVC/B samples. These samples were subjected to artificial thermal aging for 5040 hours at 80 and 100 °C and for 1008 hours at 120 °C. After that, FTIR characterization is used to study the chemical structure changes of samples. Additionally, the evolution of the AC conductivity with aging is proposed as a diagnostic parameter to reflect the degradation level of the insulation. Therefore, frequency domain dielectric spectroscopy has been performed. Moreover, comparing the properties of virgin and aged PVC/B samples allows the effect of thermal aging to be assessed. Besides, we aim to study the correlation between the chemical processes and electric conductivity, which leads to a better understanding of aging and degradation mechanisms.

Experimental

Material and thermal aging experiments: According to IEC 60502-2 standard [START_REF]Power cables with extruded insulation and their accessories for rated voltages from 1 kV up to 30 kV[END_REF], PVC class B compound (or PVC/B) is intended for cables with rated voltages U0/U = 3.6/6 kV. In fact, PVC/B is used as electrical insulation in medium voltage cables manufactured by CABEL factory located in Algiers, Algeria.

Polyvinyl chloride resins (SE-1200) manufactured by the company SHINTECH (USA) were blended with di-isodecyl phthalate (DIDP) plasticizer and calciumzinc Stabilizer (Ca-Zn). Additionally, aluminosilicate anhydrous (Whitetex N°2) were used as fillers to obtain calendaring and extrusion that perfectly lined. PVC resins and additives were mixed at 140 °C for 20 min and melt compressed at 170 °C for 5 min under a pressure of 300 MPa in order to obtain square plates of about 25 cm x 25 cm and thickness of (2 ± 0.3) mm. In order to perform electrical and chemical analysis, PVC/B plates were cut into circular shaped samples with a thickness of (2 ± 0.3) mm and a diameter of (46 ± 0.2) mm. Accelerated thermal aging was performed according to the IEC 60216 standard [START_REF]Guide for the Determination of Thermal Endurance Properties of Electrical Insulating Materials[END_REF]. The circular samples were vertically arranged inside air-circulating ovens for a total duration of 5040 hours (210 days) at 80 and 100 °C. Moreover, since the degradation process of PVC/B is very fast at 120 °C, samples have been aged for a maximum duration of 1008 hours (42 days). Note that the samples that were aged for longer periods at 120 °C can be easily broken.

Fourier Transform Infrared Spectroscopy (FTIR):

FTIR characterizations were carried out in Attenuated Total Reflection (ATR) mode since our samples present relatively high thickness of about 2 mm. Samples were analyzed and starting with a background spectrum acquisition without the sample. Then, 24 scans were recorded in the wavenumber range of 430 -5000 cm -1 with a resolution of 2 cm -1 for each sample. The obtained ATR-FTIR spectrum present the average of three spectra recorded from three different samples that have been aged in the same conditions (temperature and time).

Frequency Domain Dielectric Spectroscopy: AC conductivity σ'AC measurements were performed using Novocontrol Alfa-A High Performance Analyzer dielectric spectrometer with a ZGS active sample cell. The system can control the temperature under N2 atmosphere by a Quatro cryosystem within ± 0.1 °C. Prior to the dielectric measurements, gold electrodes were deposited onto both surfaces of the PVC/B circular samples by sputtering. The diameter and the thickness of the sputtered electrodes are respectively 35 mm and 30 nm. The AC conductivity was measured in the frequency range 10 -2 to 10 5 Hz at 20 and 70 °C.

Results and Discussions

Color Changes: Figure 1 shows the change in color of PVC/B. It has been clearly observed that the color changes significantly for aging temperatures of 100 and 120 °C and the color has become very dark brown. This change is attributed to the dehydrochlorination mechanism and the formation of the C=C bond, as will be discussed latterly. Also, we notice that aging at 120 °C engenders shrinking of the samples (Figure 1d ande).

ATR-FTIR Spectroscopy Results:

We present in Figure 2 the FTIR spectra results of the virgin PVC/B sample and of those aged at 80 and 100 ° C for 5040 h and at 120 ° C for 1008 h. Also, the main characteristic peaks of pure PVC (without additives) are summarized in Table I. The degradation of PVC/B includes three main mechanisms: dehydrochlorination, oxidation and loss of plasticizer. From Figure 1b, a significant increase of the absorbance intensity from 1500 to 1680 cm -1 was found. This band is attributed to the -C=C-double bond of unsaturated groups vinylidene and trans-vinyl. In addition, a new band corresponding to vinyl groups appears after aging at 1624 cm -1 . These observed bands are due to the dehydrochlorination which also leads, under the effect of the high temperature, to the release of hydrochloric acid HCl [START_REF] Coltro | Performance evaluation of new plasticizers for stretch PVC films[END_REF][START_REF] Salivon | Vieillissement thermique d'isolants en PVC et PELX de câbles électriques en environnement automobile[END_REF]. Besides, after consumption of the stabilizer, the HCl molecules accumulate which results in a drastic increase of the dehydrochlorination rate with aging time [START_REF] Quennehen | Étude de la dégradation de la fonction isolation de câbles HT isolés au PVC[END_REF].

The second mechanism of chemical degradation is oxidation, which leads to the scission of macromolecular chains and to the formation of oxidation by-products [START_REF] Quennehen | Étude de la dégradation de la fonction isolation de câbles HT isolés au PVC[END_REF]. When the antioxidant is consumed, hydroperoxides (ROOH) will be formed which subsequently generate free radicals. As a result, we observe an absorption zone between 3000 and 3700 cm -1 relative to the -OH function of the hydroxyl groups (Figure 2a) [START_REF] Salivon | Vieillissement thermique d'isolants en PVC et PELX de câbles électriques en environnement automobile[END_REF]. In addition, the oxidation can be characterized by the peaks at 1464 and 1539 cm -1 which present respectively -C-O-C stretching and COOvibration. Moreover, the characteristic peaks of C-O function could be found at 1127 and 1288 cm -1 . Also, the carbonyl group C=O is related to the absorbances at 1624 and 1722 cm -1 [START_REF] Machado | Lipase degradation of plasticized polyvinyl chloride endotracheal tube surfaces to create nanoscale features[END_REF][START_REF] Wypych | PVC Degradation and Stabilization[END_REF].

The third degradation mechanism in PVC/B consists of the loss of plasticizer. In fact, the peaks at 1127, 1288 and 1722 cm -1 could also indicate the presence of phthalate plasticizers (DIDP). Therefore, it appears difficult to distinguish between the physical loss of the plasticizer and oxidation reactions by FTIR method. We can also assume that the decrease at 1127, 1288 and 1722 cm -1 (Figure 2b) is related to the diffusion of plasticizer molecules from the core of the material to the surface.

Therefore, it can be concluded from FTIR spectra that thermal aging at 80 °C has a weak effect on the chemical structure of PVC/B. In the contrast, at aging temperatures 100 and 120 °C, a significant increase of vinylidene and trans-vinyl groups has been observed which reflect the increase of hydrochloric acid in the material. Besides, hydroxyl groups are released rapidly. Also, 1008 hours of aging at 120 °C were enough to observe a significant chemical degradation against 5040 hours at 100 °C. Meaning that the higher the aging temperature is, the faster is the degradation process in the PVC/B material. 3 and4 show the variation of AC conductivity σ'AC at 20 and 70 °C respectively, for different PVC/B samples before and after thermal aging.

AC Conductivity Results: Figures

From the obtained results, and at aging temperature of 80 °C, the conductivity remains unchanged at 20 °C where a slight decrease observed at 70 °C for frequencies lower than about 1 Hz. This decrease is probably due to thermal agitation which disturbs the interfacial polarization and decreases the mobility of dipoles at the electrodes over macroscopic distances. Moreover, σ'AC changes linearly for frequencies higher than 0.1 Hz at 20 °C and 1 Hz at 70 °C, exhibiting a slope close to unity [START_REF] Diaham | Dielectric measurements in large frequency and temperature ranges of an aromatic polymer[END_REF].However, a noticeable deviation could be observed for samples aged at 100 and 120 °C, as illustrated in Figure 3 and4. In fact, σ'AC becomes progressively independent of the frequency and tends towards a higher constant value as the degradation of the material is more accentuated. This constant value presents the DC conductivity σDC of the material which is in agreement with Equation 1 [START_REF] Diaham | Étude du Comportement sous haute température de Matériaux Polyimides en vue de la Passivation de Composants de Puissance à Semi-Conducteur Grand Gap[END_REF]. Furthermore, the frequency range corresponding to the horizontal conduction plateau extends towards the high frequency when the temperature increases. Such a behavior demonstrates the thermally activated character of the DC bulk conductivity [START_REF] Diaham | Dielectric measurements in large frequency and temperature ranges of an aromatic polymer[END_REF].

In fact, the dehydrochlorination mechanism in PVC/B leads to the creation of conjugated double bonds. The electrons then become mobile over the length of these conjugations. Hence, the mobility of electrons participates in the overall conduction of the material [START_REF] Coltro | Performance evaluation of new plasticizers for stretch PVC films[END_REF]. On the other hand, at high temperatures, dehydrochlorination leads to the creation of ions and then the conductivity will depend strongly on the mobility of the ions and their concentration.

When the material temperature is low, the mobility of the ions is low and therefore the electronic conduction assumes the leading role. As the material temperature increases, the ions become more and more mobile and the ionic conduction may play the most important role in conduction [START_REF] Diaham | Étude du Comportement sous haute température de Matériaux Polyimides en vue de la Passivation de Composants de Puissance à Semi-Conducteur Grand Gap[END_REF][START_REF] Coltro | Performance evaluation of new plasticizers for stretch PVC films[END_REF].

Moreover, the interfacial polarization (Maxwell-Wagner-Sillars) is established after a relatively long time. Hence, the AC conductivity will show a significant change at very low frequencies due to interfacial polarization and to the accumulation of mobile charge carriers in the insulation bulk. After the stabilizer was consumed after aging at 100 and 120 °C, dehydrochlorination process will be accelerated and as a result, more ions (e.g. Cl -and H + ) will be released which drastically enhance the conductivity σDC.

Conclusion

This paper highlights the evolution of the AC conductivity in PVC/B samples with thermal aging. Also, the chemical structure of the material was investigated. The main conclusions of this study can be summarized as follows:

1) The color change of PVC/B to dark brown reflect the deterioration of the material. This change is attributed to the formation of vinylidene and vinyl groups.

2) The degradation of PVC/B is caused mainly by the dehydrochlorination mechanism which is accompanied with the accumulation of molecules of hydrochloric acid HCl.

3) During thermal aging, thermo-oxidative reactions and loss or migration of the plasticizer occur, leading to accelerate the decomposition of PVC/B and facilitate the release of more polar groups such as hydroxyl OH. 4) The formation of polar groups implies a significant increase in the AC conductivity. The origin of this latter in the virgin PVC/B sample is the interfacial polarization (Maxwell-Wagner-Sillars). 5) When the thermal stress is high (100 and 120 °C), the conductivity increases with aging mainly at low frequencies. Meaning that σDC conductivity is strongly correlated with the material degradation. 6) If the mobile charges are of ionic origin, the ionic conduction may play an important role in the conduction behavior of PVC/B.

Figure 1 :

 1 Figure 1: Color change of PVC/B samples: (a) before aging, (b) aged at 80°C for 5040 h, (c) aged at 100 °C for 5040 h, (d) aged at 120 °C for 1008 h, (d) aged at 12 0°C for 1512 h.

Figure 3 :

 3 Figure 3: Frequency dependence of the AC conductivity at 20 °C in PVC/B samples before and after aging.

Figure 4 :

 4 Figure 4: Frequency dependence of the AC conductivity at 70 °C in PVC/B samples before and after aging.

Table 1 :

 1 Characteristic peaks of pure PVC by FTIR.

	Wavenumber	Functional group and	Reference
	(cm -1 )	vibration
	600 -700	C-Cl Stretching	[8]
	1040, 1072 C-C Stretching	[9]
	1123	-CH Stretching	[8]
	1271	-CH angular deformation	[10]
	1425	Cl-CH2 angular deformation	[11]
	1464	-CH Scissoring	[12]
	2855, 2926 -CH2 Stretching	[12]
	2870, 2957 -CH Stretching	[12]