The surface potential of perforated dielectric layers

The Surface Potential of Perforated Dielectric LayersRyszard KacprzykInstitute of Fundamentals of Electrical Enginering (I-7),Wrocław University of TechnologyWybrzeże Wyspiańskiego 27, 50-370 Wrocław, Polandand Włodzimierz MiśtaInstitute of Low Temperature and Structural Research,Polish Academy of Sciencesul. Okolna 2, 50-950 Wrocław, PolandABSTRACTThe maximum value of the surface potential or of the related equivalent voltage ofperforated dielectric sheets may be of special interest in application of materials suchas electrostatic–polymeric electret filters, fabrics, non-wovens and others.Experimental investigations carried out on polymeric fabrics with application of thecorona triode have shown that the surface potential is limited mainly by the backionization (back corona) phenomenon. It was also shown that the corona triode maybe a very useful tool for characterisation processes which occur in such materials.Particularly a simple correlation was found between the maximum value of thesurface potential and the threshold voltage (i.e. the voltage of the discharge currentincrease of the sample polarised in the corona triode system).Index Terms - Surface potential, dielectric breakdown, back corona.1 INTRODUCTIONGROWING application of non-uniform dielectric structures frequently requires determination of the maximum value of the surface potential, which can appear on them. The maximum value of the surface potential may allow to estimate or be a measure of technological achievements (e.g. in manufacturing of electret filters) or can be a significant factor allowing determination or estimation of electrostatic hazards or nuisances, which can occur in electronic, chemical and other industries. One of the most typical examples is the gluing phenomenon commonly occurring in the textile industry, especially in case of synthetic fiber technology.One of the mechanisms, which influence and limit the maximum value of the surface potential may be the back corona or back ionization phenomenon [1]. Electrical discharges associated with this phenomenon may spread along the surface of the perforated dielectric layer as well as in the gas–air channels across the layer [2]. In the last case it was found that electrical discharges may occur under the condition j·ρv≥ Εc - where j is the density of the corona current, ρv is the volume resistivity of the dielectric layer and Εc is the critical value of the electric field for the gas in the channel (i.e. the electrical strength of the gas layer). It was also stated [3] that for the usually observed current densities in case of corona discharges, the back corona was not seen in dielectric layers with volume resistivity ρV < 5x108 Ωm.A possibility of the back corona phenomenon, occurring on metal electrodes covered by glass fabric, was experimentally confirmed [4] and applied in the construction of the cold plasma reactor [5, 6]. However some questions associated with the unequivocal association of the back corona with the maximum attainable value of the surface potential still exist. Additional questions are associated with applicability of the Paschen’s law for the simple determination of the critical field intensity for the gas channels existing in dielectric layer and, finally, for estimation of the maximum value of the surface potential [10]. Parallel measurements of equivalent voltage on perforated dielectric layers as well as current – voltage characteristics of the air-triode with application of the same dielectric layer were proposed to solve these problems. High resistivity polymeric fabrics (containing regularly distributed gas channels) were used as perforated dielectric layers.2 EXPERIMENTALElectrical charge was deposited on the surface of the investigated samples by application of the corona method. A well-known air-triode circuitry was applied to control theManuscript received on 20 March 2006 in final form 5 July 2006.1070-9878/06/$20.00 © 2006 IEEEsurface potential of the charged samples [7]. A schematic picture of the applied circuit is shown in Figure 1. In the forming circuitry the grid–corona electrode and the grid–sample distances were kept constant and were equal to 50 and 10 mm respectively. Three Ni-Cu strings in a star-shaped configuration were applied as the corona electrode. The diameter of the strings was 30 μm. The corona electrode was polarised with the dc voltage U u =(+)8 kV and the grid voltage U s was regulated in the range of 0 to 3 kV. The total surface of the sample subjected to the corona charging was 8.0×10-3 m 2. The ammeter A was used for measurement of the total discharge current I u and the detection of the back corona (i.e. detection of a sudden increase in the current I u value). The equivalent voltage U z was measured after 15 s following completion of the sample charging process. The equivalent voltage U z was determined based on measurements of the electric field intensity in the air gap between the sample placed on a grounded metal sheet and a sensitive aperture of the field-meter (field-mill FM981-METRA). If the field meter body is on the ground potential, the U z voltage may be determined from the relation:⎟⎠⎞⎜⎝⎛+=εt l E U z (1)where E - electric field intensity in the air gap l between the sample and the sensitive aperture of the field-meter, t – sample thickness, ε - electrical permittivity of the sample material. In the experimental setup the air gap thickness lFigure 1.The air triode circuit for charging of fabric layer and measurementsof back corona current. fulfilled relation l >>t and was kept constant and equal to 10 mm. This allowed for application of a simplified relation: El U z ≅ (2) The measurements of the total discharge current I u in the air triode system and the equivalent voltage U z were carried out in a circuit with a metal electrode, which was covered with fabric samples. The samples of fabrics Nos. 1 to 3 were woven from yarns made of polypropylene (PP) fibre. The samples Nos. 4 and 5 warp and weft yarns, were made of polyamide (PA) and polyethylenterephtalate (PET) fibres respectively. The yarns were free from any dyes or other additives, which should potentially permit to obtain high volume resistivity and charge storage time of the fabrics utilized. The characteristic data of the investigated fabrics were collected in Table 1.Table 1. The properties of the investigated fabrics *Fabricthickness t Warp width Weft width Channel width (1)Channel width (2)SampleNo[μm] [μm] [μm] [μm] [μm]1 600 1350-PP 1350-PP 45 902 600 1800-PP 1800-PP 150 4003 500 1050-PP 825-PP 45 2004 600 975-PA 600-PET 30 605 600 975-PA 600-PET 30 200 *Average values of 20 measurement results obtained with an optical microscope. The fibre material given in warp and weft columns.The air channels in the fabric had a rectangular cross-section area, with dimensions of width (1) × width (2) (see Tab.1). The values of the half-decay time, measured on fabric samples in the state “as produced”, were in the range of 4 -10 s. This is why, prior to the measurements of the electrical properties, all of the samples were submitted to a washing process. The process consisted of basic washing in water containing surfactant, rinsing in water and finally rinsing in distilled water. The applied washing facilitated removal of the textile finish. This was confirmed by measurements of charge decay characteristics and volume resistivity. The appropriate investigations have shown that the charge decay was lower than 10% after 1000 s long discharge time, and the resistivities of samples Nos. 1 through 5 have reached the level of ρV =2.4x1014 − 1.7x1015 Ωm.3 RESULTS AND DISCUSSIONThe examples of the triode current I u (U s ) dependencies for the fabric No. 1 are shown in the Figure 2. In case of the applied charging circuit and polarization conditions the transient time of the charging current I u was of the order of a few seconds. The values of the current shown in the Figure 2were measured in a steady state. An example of the equivalent voltage Uz (U s ) dependency for the same fabric is shown in the Figure 3. Similar dependencies were observed for all of theinvestigated samples. Some regularities were found to exist between the aforementioned dependencies obtained for all of the samples. In order to compare I u (U s ) and U z (U s ) curves, some specific points were chosen on them. These were: - U sin – the grid voltage value for which a sudden increase in the air triode current I u was observed on I u (U s ) characteristics;- U ss – the grid voltage value for which a “knee” was observed on U z (U s ) relationship, resulting from saturation of the equivalent voltage U z to the saturation value U zmax . All of the mentioned characteristic voltage values are shown on Figures 2 and 3 and collected in Table 2.Figure 2. The dependence of the air triode current I u on the grid voltage U s forflat electrode of the triode covered with PP fabric – sample No 1. Measurements in the following air conditions: temperature T = 22 o C, relative humidity h=40%.Figure 3. The dependence of the equivalent voltage U z on the grid voltage U s for the fabric sample No. 1 charged in the air triode. Measurements in the following air conditions: temperature T = 22 o C, relative humidity h=40%.Table 2. Characteristic voltages for triode current I u and equivalent voltage U zdependencies on grid voltage.U sin U ss U zmax U zp εySample No V V V V - 1 1300 1300 1100 2020 1.08 2 700 700 550 2020 1.11 3 700 700 600 1720 1.244 500 450 420 2020 1.635 300 300 360 2020 1.42In a circuit with an air triode in the range of low voltages, the equivalent voltage U z depends linearly on the grid voltage U s [6] and the differences between the U z and U s values are usually in the range of 100 – 200 V. Similar linear relationship between U z and U s voltages was observed on U z (U s ) curves obtained for all of the investigated samples (Nos. 1 to 3) and for grid voltages U s <U ss – see Figure 3. Local partial discharges will occur if the field intensity in the air channels, which exist in the structure of the fabric, is higher than their electrical strength E c . Such discharges, appearing in channels and sometimes spreading over the adjacent area [2] on the surface of the dielectric layer are known as the back corona. The aforementioned discharges, occurring for voltage U s > U ss , lead to a saturation effect observed on U z (U s ) dependencies. The discharges also lead, in case of all of the investigated samples, to a sudden increase in the discharge current I u , visible on I u (U s ) dependencies – seeFigure 2.The saturation effect, appearing on U z (U s ) dependencies (e.g. Figure 3), is responsible for the limitation of the surfacepotential of the sample placed on a metal electrode to amaximum value U zmax . An increase in the current density in the circuitry as in theFigure 1, excluding the grid, allows to observe back coronaphenomenon in a dark environment. Photographs of the backcorona on a PP fabric (sample No 3) obtained for negative andpositive polarization are shown in the Figures 4 and 5. It isevident that the back discharges occurred for both polarities in the channels regions and with surface regularity determined by their density. The results obtained for all of the samples indicate that thegrid voltage U sin , for which a sudden increase in the dischargecurrent is observed, is practically equal to the “knee” voltageU ss . The equality of the mentioned voltage values suggests that the basic mechanism limiting the maximum value of the equivalent voltage U zmax is the back corona. The finite width of the “knee region” results from statistical distribution of thedimensions of the air channels in the fabric structure.A possibility of a discharge in a gas void is determined bythe critical field intensity E c . The field intensity E c may be determined on the basis of a Paschen’s law. Assuming uniform field in the air gap (i.e. no space charge) at the temperature 20 °C and a range of the product pd from 10-2 to5×102 (bar cm), the Paschen’s law [8] may be written as:p d p E c 4,2472,6+= (3)where E c [kV/cm] is the critical field intensity, p [hPa] – the gas pressure in the gap, d [m] – the thickness of the air (gas) gap between the electrodes. In the first approximation, the values of the breakdown voltage of the air channel (existing in the fabric) could be determined from the relation: U zp = E c t (4) U zp values, calculated on the basis of E c value determined from relation (3) for d =t , were collected in Table 2. In all of the cases U zp values significantly surpassed the measured values of the voltage U zmax . The consideration of the space distribution of yarn in the fabric (i.e. waving of the warp and weft yarns), leads to the conclusion, that the effective air channel length d in the fabric structure should be lower than the fabric thickness t . Such conclusion could be fully justified particularly in a situation when one of the “electrodes” was created by ionized gas (i.e. the gas penetrating the fabric structure). The assumption, in the first approximation, d =t /2 leads to U zp voltage value of 1120 V for samples Nos. 1, 2, 4, 5 and of 960 V for sample No 3.Figure 4. Back corona on a PP fabric (sample No 3) in a point-to-plane system, with a negative point, for average current density of 5.7 A/cm 2. Picture observed in the air in normal conditions (pressure and temperature). The lighting point above the fabric surface represents the corona discharges near the point electrode.Figure 5. Back corona on a PP fabric (sample No 3) in a point-to-plane system, with a positive point, for average current density of 8.4 A/cm 2. Picture observed in the air in normal conditions (pressure and temperature). Lighting point above the fabric surface represents the corona discharges near the point electrode.The relative electrical permittivity ε y of the yarn “material” was estimated for the investigation of its effect on the voltage U zmax . The estimation thereof was carried out on the basis of Wiener’s border relations [11]:yya a mεθεθε+=1(5a)y y a a m εθεθε+= (5b)1=+y a θθ (5c)where εm , εa , εy are the relative electrical permittivities of the fabric (measured), air and the yarn respectively. The volume contents of the air θa and yarn θy , in the total volume of the fabric was estimated on the basis of observation and measurements of the fabric cross-sections under an optical microscope. The electrical permittivity εm , for the fabric samples, was determined from their capacitance as measured in a tree-electrode system on the frequency of 1 kHz. The electrical permittivity εy of the yarn was calculated as the average value obtained from the serial and parallel Wiener border relations (5a) and (5b), respectively. It should be emphasized that the yarn is made of an isotropic “composite material” consisting of regularly twisted polymer (PP, PA or PET) fibers with air filling the space between them . The estimated values of the electrical permittivity for the yarn “material” εy were collected in Table 2.The comparison of the results collected in Tables 1 and 2 indicated the following regularities: - the U zmax voltages for all of the investigated fabrics were generally lower in comparison to the values determined from Paschen’s equation;-an increase in the cross-section area of the air channels leads to a significant decrease of the U zmax voltage (see results obtained for samples of the same thickness, i.e. Nos. 1 and 2 or Nos. 4 and 5);-an increase in the electrical permittivity of the yarn material leads to a decrease of the U zmax voltage (see results obtained for samples with similar thickness and channel dimensions Nos. 1 and 4, respectively);The observed regularities and especially the much lower values of the surface potential (in comparison with those determined from the Paschen’s equation), may result from partial penetration of the air channels by the charge carriers in the space above the fabric surface. The ions appearing in the gas channels are submitted to electrical forces generated by the local electrical field. The intensity of the electrical field in the channel will be influenced by at least the following components: - the external, polarizing field;- the field generated by the charge deposited on the fabric surface (more precisely – on the yarn, around the channel);- the field from the space charge of the ions in the channel; -the field from the mirror effect.Thus the specific geometry of the channel (i.e. the shape of the cross-section area, widths, length) as well as the electrical permittivity of its neighborhood (yarn) will strongly affect the local value of the electrical field intensity and its critical value E c .One of the components of the aforementioned local field, which creates mainly a tangential component (to the surface of the electrode with the fabric placed on top of), is associated with the mirror charge effect [9]. This effect occurs when an electrical charge appears in the vicinity of an interface dividing regions with different electrical permittivities. If acharge is placed in a gas with permittivity εa and the neighboring yarn has permittivity εy >>εa , the mirror effect component E m of the local field may be estimated in the first approximation [9] from the relation:ya ya a m x q E εεεεπε+−=2 (6)Where: q – the electrical charge of the ion in the channel, x – the distance between the ion and the interface - yarn. The amount of the charges in the channel as well as the distance x are influenced and limited by the width of the gas channel. According to equation (6) the component E m should increase with an increase in the yarn permittivity εy . This dependence may explain the observed lowering of the U zmax voltage for fabrics made of high permittivity yarns (Nos. 4 and 5). The expression (6) also illustrates the influence of the channel width (which determines the distance x ) on the tangential component of the local field. The effect of the channel cross-section area on the tangential component of the local field should lead to changes in the trajectory of the ions in the channel. In case of broader air channels this should finally lead to a deeper penetration of the channel space by the ions and to a shortening of their insulating length. Consequently, the latter should be observed as a decrease of the channel breakdown voltage and the measured U zmax value. Considering the above hypothesis one could conclude that both the electrical breakdown voltage of the channel and finally the U zmax voltage should decrease with an increase in both: - the air channel width; - the electrical permittivity of the material surrounding the channel. The observed influence of the value of the yarn permittivity on the U zmax voltage may also be associated with the three dimensional structure of the fabric. Gas channels with much smaller cross-section areas are also present in the yarn structure. Partial discharges occurring in the yarn volume would create additional charge carriers supplying the gas channels in the fabric. The electrical field in the gas voids existing in yarn depends, among others, on the electrical permittivity of the fiber polymer. An increase in permittivity of the fiber material would lead to an increase in the electrical field in the yarn gas voids, an increase in the intensity of the partial discharges as well asto generation of a higher concentration of the chargecarriers for lower values of the U zmax voltage. All of the aforementioned hypotheses are under study. The values of the U zmax voltage obtained from direct measurements were lower in comparison to the estimatedvalues of U ss and U sin voltages. The measured difference appeared to be constant and was in the range of 150-200 V. The difference could have resulted from both the averaging properties of the field–meter (there was no chargedeposited on a finite area of the existing air channels) andthe potential difference necessary for the charge transfer in the grid - sample surface region of the air triode system. The results of modeling and of the appropriate calculations lead to the conclusion [1] that the ratio of both voltages, i.e. of the average value (measured by a field-meter) and the potential of the yarn, may be as high as 0.85. A similar relation between the voltages U zmax and U ss appeared in samples Nos. 1 and 3. The lower value of the voltage ratioin case of sample No. 3 (respectively 0.78) probably resulted from a relatively large cross-section area of the air channels existing in the fabric, which the sample was made of (see Table 1). 4 CONCLUSIONS The results of the measurements of the corona triode charging current and of the equivalent voltage, carried out on the fabrics made of polymeric yarn and characterized by high volume resistivity, proved that the back ionization (back corona) phenomenon is the basic mechanism responsible for the limitation of the maximum value of the equivalent voltage U zmax . It was found that the values of the U zmax voltage, determined by direct application of the Paschen’s law were much higher in comparison to those obtained experimentally. The observed incompatibility in the U zmax values can be explained by:- a significant influence of the charge deposited around the channel on the intensity of the local field inside it; - penetration of the channel depth by the charge carriers entering from the ionized space above the sample. The latter may be confirmed by significant influence of channel dimensions (widths) and electrical permittivity of the yarn on the measured U zmax values.ACKNOWLEDGMENTS This work was carried out in part as a statutory project, supported by the State Committee for Scientific Research (KBN). Additional financial support provided by the Ministry of Scientific Research and Information Technology, (Grant 3T09B 110 28 [2005-7]) is also gratefully acknowledged. REFERENCES[1] H.J. White, Industrial Electrostatic Precipitation , Addison-Wesley Publ. Co., Pergamon Press, Oxford, 1963.[2] S. Masuda and A. Mizuno, “Initiation condition and mode of backdischarge”, J. Electrostatics, Vol.4, pp.35-52, 1977/1978. [3] A. Mizuno, “Electrostatic Precipitation”, IEEE Trans. Dielectr. Electr.Insul ., Vol. 7, pp.615- 627, 2000.[4] R. Kacprzyk, B. Mazurek and J. Ziaja, “Discharges in the system with electrode covered by perforated dielectric layer”. (in Polish) PraceNaukowe Instytutu Podstaw Elektrotechniki i Elektrotechnologii Politechniki Wroclawskiej nr 38, Ser. Konf. No. 13, pp.147-150, 2003.[5] W. Mista, R. Kacprzyk and W. Witkowski, Decomposition of Benzeneby Using a Plasma Reactor with Back Corona. Polish J. Environmental Studies, Vol.14, Suppl. IV pp.215-218, 2005.[6] W. Mista, R. Kacprzyk, M. Bartkowiak, “Decomposition of TolueneUsing an Atmospheric Pressure Non-Thermal Plasma Reactor at Room Temperature”, Polish J. Environmental Studies, Vol.14, Suppl. IV pp.219-221, 2005.[7] J.A. Giacometti, G. F. Leal Fereira and B. Gross, A summary of coronacharging methods. IEEE 6th Int. Symp. Electrets (ISE6), Oxford, England, pp. 87-91, 1988,.[8] E. Kuffel, W. S. Zaengl and J. Kuffel, High Voltage Engineering,Elsevier, Amsterdam, 2005.[9] J. Cazaux, ”The Electric Image Effects at Dielectric Surfaces”, IEEETrans. Dielectr. Electr. Insul., Vol..3, pp.75-79, 1996.[10] M. N. Horenstein, “Surface Charging Limit for a Woven Fabric on aGround Plane”, J. Electrostatics, Vol. 35, pp.31-40, 1995.[11] S. P. Neelekanta, Handbook of Electromagnetic Materials, CRC Press,Boca Raton, New York, 1995.This paper is based on a presentation at the 12th IEEE International Symposium on Electrets (ISEI 12), Salvador, Bahia, Brazil, 11-14 September 2005.Ryszard Kacprzyk was born in Poland in 1948. Hereceived the M.Sc. degree in solid state technologyfrom the Faculty of Electronics of WarsawUniversity of Technology in 1973, the Ph.D. andD.Sc degrees in electrical engineering from theWroclaw University of Technology in 1979 and2005, respectively. He has been an AssociateProfessor at the same Institute since 1980. He is aspecialist in electrostatic metrology. He has alsobeen engaged in measuring systems and devices for dielectric materials investigations, in applied electrostatics, and generally in electromagnetic materials research. He is the author and a co-author of more than 80 published worksWlodzimierz Mista was born in Poland in 1956.He received the B.Sc. degree in chemistry from theUniversity of Wroclaw in 1980 and the Ph.D.degree in heterogeneous catalysis from the PolishAcademy of Sciences, Wroclaw in 1995. He iscurrently a Researcher with the Institute of LowTemperature and Structure Research PolishAcademy of Sciences in Wroclaw, Poland. Hisresearch interests include the application of discharge plasma process to environmental protection and characterisation of heterogeneous catalysts. He is the author of more than 40 published works.。