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Characterizing the electrostatic charging of polymer particles by impact charging experiments
Characterizingthe electrostaticcharging of polymer particles by impact charging experiments andHIDEO YAMAMOTO TATSUSHI MATSUYAMA Soka 1-236 Faculty University, Tangi-cho, Hachioji-shi, Department of Bioengineering, of Engineering, 192, Tokyo Japan received 9February 1995 inJPTJ Vol. 31No. version forAPT Published 3 (1994); English were conducted four kinds forimpactusing of polymers Abstract-Impact charging experiments systematically inalloftheir combinations. The metal with different work functions and three equilibrium particles targets ing foreach were ofthework function ofthemetal and were almost constant polymer. target charges independent inthe that the relaxation Discussion of the results of this experiment suggested charge particles separating process One isgenerated under conditions. determines theimpact ifthis atmospheric important impact charging charge istounderstand the mechanism. reason forstudying this relaxation Furthermore, particle charging charge process thecharacteristic which decides theamount ofcharge results that these discussions and experimental suggested ofthe material in in the is the dielectric constant etc., polymer dry powder processes generation, charge generation ofwhich theparticle consists. NOMENCLATURE radius ofparticle a [m] condenser c /M2, ] [F/m2] perunitareaofmodel capacitance contact d gap[m] electric e [eVN] elementary charge field E electric [V/m] strength minimum field[V/m] ES s spark form k conversion constant Q;toVi[V/C] proportional p pressure [Pa] ofa particle [C] Q charge AQ impact charge [C] e [C] Qe equilibrium charge initial [C] Q;i charge aparticle anda metal S contact areabetween ] target [M2] [m2] At contact time[s] contact difference between andmetal V [V] potential polymer induced via potential byinitial charge [V] induced atQ;= 6e[V] vi1: potential minimum v spark voltage [V] function of metal Wm work [eV] effective work function [eV] of particle Wp c relative dielectric constant [-] of polymer dielectric constant offreespace Eo [F/m] ofcontact relative dielectric constant ed gap[-] Q charge density [C/m2] condenser T timeconstant ofmodel [s] correction factor d) image [-]
212 1.INTRODUCTION ofinsulating Todiscuss theelectrification inthedry-handling itmust generated powder, tostudy thecharging behavior ofasingle beregarded asoneofthemost important points asacomponent From thisstand westudied theimpact of 'powder'. point, charging particle inwhich ofa single of particle through impact charging experiments polymer particles around 3mmindiameter wereusedandimpact collision charges generated bysingle thepolymer andmetal were measured onebyone[1-3]. Inthis between particle target weconducted thisimpact fourkinds ofpolymers for study, charging experiment using withdifferent andthreemetal workfunction forallthese impacting particles targets combinations inorder tocharacterize theelectrostatic ofpolymer systematically charging discussion ontheeffect ofthework function ofthetarget ontheimpact particles through ofpolymer charging particles. 2.OUTLINE OFTHE IMPACT CHARGING EXPERIMENT Because thedetail oftheimpact isdescribed inprevious work charging experiment [2], ofit willbedescribed here.Figure 1shows a schematic viewofthe onlyanoutline fortheimpact Theair-gun-launched apparatus charging experiment. spherical polymer a Faraday onthemetal Thecharge particle passes through cagebefore impact target. carried before the'initial is measured bytheparticle impact (called charge') bythis Thetarget metal isconnected totheelectrometer andthe Faraday cage. plate directly leftonthetarget ismeasured asthecomplement ontheparticle charge charge generated byimpact (called 'impact charge'). Inthisstudy, thisimpact wasconducted fourkinds of charging experiment byusing andthreemetal forallthesecombinations polymers Teflon, targets systematically. anddelrine of3.2mmdiameter were used nylon66, polystyrene particles (Moritex Corp.) forpolymer andformetal were Ti,CrandNiwith particles; targets, (>99.99%) high purity used. each metal wasbuffing-finished alumina. were Here, plate by0.3 ,um Experiments
1.Schematic view oftheexperimental Figure apparatus.
213 Table 1. their and metal and relative dielectric List ofsample targets polymers constants and work functions
conducted under a normal airatmosphere withtemperature andhumidity mainpressure at24± 5°Cand25± 5%,respectively. tained andmetal and Sample polymers targets theirrelative dielectric constants andwork functions arelisted inTable 1. 3.RESULTS 3.1.Experimental results Asanexample theresults oftypical oftheimpact results, Fig.2shows charging experiment 2 compares tworesults ofdifferent using teflon(particle)/Cr(target). Figure impact 5 and10 m/s withimpact 60°.Thehorizontal axisrepresents theinitial velocity, angle oftheparticles, while thevertical axisrepresents theimpact Theimpact charge charge. decreases withincrease oftheinitial wecallthislinethe charge proportionally charge: line'ofitsimpact condition. There isa particular theintercept onthe 'charging point, horizontal axisofthecharging nonetcharge transfer occurs attheimpactline,atwhich contact duetoinitial thatspecial initial iscalled the'equilibrium points charge; charge charge' . 2indicates thatthisequilibrium isindependent oftheimpact conditions Figure charge andangle), while thecharging linedepends onthese. These (impact velocity experimental results werealready inourprevious works reported [1,2];ingeneral, impact charging a setofthecombination ofparticle andmetal withdifferent experiments, using target, conditions lines onthehorizontal axis. impact givedifferent charging crossing
Initial charg(. (pC) 2.Typical results oftheimpact Crtarget at60°, 5and Figure charging experiments. (Teflon partices impact 10mls).
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3.Schematic illustration ofthemodel condenser. Figure 3.2.Condenser model Theelectrification ofaparticle duetoimpact/contact withametal iscaused plate bythe transfer between theparticle andmetal thecontacting surfaces. charge Here, plate through thecharge double between thecontacting surfaces canberegarded asa layer generated therefore thischarge transfer duetocontacting ofparticle andmetal can condenser; plate beexpressed model. Theschematic illustration ofthismodel isshown bythecondenser inFig.3.Here, inthecase of where theparticle carries theinitial thischarge exists charge, notonlyontheelectrode ofthecondenser constructed atthecontacting butalsoon area, thewhole surface oftheparticle; therefore theeffect oftheparticle's initial cannot charge betreated asaninitial ofthemodel condenser. Thisproblem canbetreated charge by theeffect oftheinitial tothetermoftheelectromotive force connected reducing charge tothemodel thecharge transfer ontotheimpacted is condenser; here, process particle model as expressed bythiscondenser where theamount ofcharging, andc,S,AtandTrepresent AQrepresents capacitance per unitareaofthemodel electrode contact timeandtimeconstant, condenser, area, respecThese terms areregarded asfactors themagnitude ofcharge transfer and tively. deciding arecalled thegeometrical factor ofcontact. These factors totheimpact change according conditions such asimpact andvelocity; therefore itisessential todiscuss theimpact angle duetoa single Thisdiscussion wasshown inourprevious work charge impact. [3].The second termof (1) isa factor thedriving force ofthecharge deciding transfer;and v V contact difference andinduced between the represent, respectively, potential potential contact surfaces duetotheinitial oftheparticle. Theeffect oftheinitial is charge charge reduced inthetermofthecharge force asmentioned above. driving tothismodel, theimpact termof (1), According charge AQisdecided bythesecond i.e.thetermofthedriving under thesame conditions ofthegeometrical factors of force, such astheimpact andangle. thelinear oftheimpact Here, impact, velocity dependence ontheinitial is explained charge charge bythefactthattheinduced Vis potential totheinitial isindependent proportional charge Qi.Thefactthattheequilibrium charge of the condition isalsoexplained asfollows; thecharge force impact bythismodel driving amounts tozero when thecontact iscancelled potential V, bytheinduced Yedue potential toamounting oftheinitial totheequilibrium charge charge Qe. 3.3.Relation between theequilibrium andwork charge function ofthemetal plate Itwillbeshown laterindetail howVisdecided herewesuppose that1;is by Q;; simply = kQ;. toQ;as Y thatthesecond term tozero due Now, proportional suppose of (1) equals
215 totheequilibrium thentherelation toamounting oftheinitial ofthese charge charge, canbewritten as parameters herethattheeffective work function ofthepolymer weassume Furthermore, [6],WP, surface andmetal workfunction, areavailable; thecontact difference is Wm, potential written as From isyielded as (2)and(3),theequilibrium charge This formula alinear relation between themetal work function andequilibrium predicts onekind ofpolymer and charge given byasetofimpact charge experiments using particle some kinds ofmetal different work function values. targets having 4shows therelation between theequilibrium andthework function of the Figure charge metal asaresult oftheimpact conducted hereforcombinatarget charging experiments tionsofallarranged andmetal Thisresult iscontrary tothe polymer particles targets. theequilibrium areindependent ofthemetal work mentioned above; prediction charges foreach Wewilldiscuss these function; rather, theyareconstant polymer particle. experimental inthenextsection. results 4.DISCUSSION 4.1.Image correction Firstofall,asa preparation fordiscussion inthissection, wediscuss herehowwecan decide thepotential surfaces of difference, Y,induced bytheinitial charge, Qi,between theimpacting andmetal particle plate. nowthattheelectrostatic fieldisuniform nearthecontacting Suppose pointofthe andmetal Thepotential difference between thecontacting surfaces isgiven particle plate. as where thefieldstrength infreespace, contact E, dandCdrepresent gapandrelative dielectric constant ofthecontact inthecaseofasolitary here, gap,respectively; particle infreespace, thefield is E,nearitssurface charged uniformly strength,
Work function ofmetal (eV) target work 4.Relation between and function ofmetal Figure equilibrium charge target.
216
where theinitial andradius oftheparticle, Qianda represent charge respectively. Ontheother themirror effect must beestimated inthecase thattheparticle hand, image exists neartheconducting suchasthecasediscussed here.Inmany the plane, cases, electrostatic fieldaround thisparticle is approximated oftwofields bytheaddition located atthecenter oftheparticle and(ii)itsimage. This generated by(i)apoint charge could beregarded asthe0-thorder because ofneglecting thehigher-order approximation Inthestrictsense, theeffect ofthehigher order should be polarization. polarization such asthattheimage induces thepolarization ontheparticle andthe considered, charge field induces thehigher ontheparticle. image generated bythispolarization polarization Theelectrostatic field around thisparticle andtheconducting isgiven astheaddition plane ofallfields andtheir thisproblem was generated bythese polarizations images. Recently, solved thiswasshown inourprevious work anexample ofthis successfully; [7]andonly result willbeshown here. letusdefine theimage correction factor oftheelectrical field onthe Here, bytheratio located near themetal tothefield ofthesolitary topoftheparticle plate particle given by asfollows, (6);thisiscorrected
5shows thisimage correction relative dielectric conFigure factor,(e,d),forsome stants oftheparticle asfunctions ofcontact a.The radius, gap,d,normalized byparticle affects from thecontact theparticle andthiseffect saturates at image gapreaching radius, thecontact 10 of theparticle radius. gapreaching 4.2.Adifficulty model ofthecondenser Ithasbeen out that the condenser model hasadifficulty willbediscussed pointed [8]which inthissection. tothecondenser thecharge onthecontact areaisgiven Now, model, according density as,
5.Image correction factors of contact Figure (asfunctions gap).
217 let difference hasnoinitial when thecontact is Vandtheparticle here, charge; potential asfollows. 0.1 andEd -1,the ustryanorder estimation V, d= 10 A Suppose= Vc becomes J = 10 3 C/m2; thetotalcharge ofa particle, of the charge density magnitude with thischarge with1.5mminitsradius charged uniformly density becomes 105 ==pC. is greater thanthevalue ofequilibrium Thisorder ofmagnitude Qe -103 pC charge intheimpact Lowell's forexample, this measured charging experiments. group, pointed tothis, the realcontact tobeaproblem depth; according gapbecomes of charge penetration asusual, andtheyarestudying thisproblem from these view thanthatconsidered bigger itmust beregarded asveryimportant topoint outthattheir Ontheother hand, points. were conducted inhigh vacuum while ourimpact contact charging charging experiments inopenairunder normal andpressure. Inthe were conducted temperature experiments ofthecharge relaxation viagaseous willbe a possibility section, following discharge discussed. 4.3.Discharge relaxation process surfaces increases withanincrease of the Thepotential difference between thecontact ofcharged surfaces forexample, contact [see(8)].Here, process gapintheseparating difference tothecontact difference within tunnel relaxation thispotential potential keeps therange of the contact thetunnel current affects. Because thetunnel current gapwhere affects difference increases atthelarger contact A,thepotential upto = 10 rapidly gap. wecanunderstand thatthepotential difference reaches over thegaseous breakdown Here, limit atthecharge estimated above. density oftheparticle 6 shows a schematic illustration oftheseparating and Figure process metal Thecharge transferred between thesurfaces atcontact forms thedouble plate. charge between thecontact isfixed surfaces layer 6a),theelectrostatic byseparating (Fig. charge these surfaces thischarge attheseparating viasome (Fig.6b);here, mayrelax process routes duetogaseous weassume here) (mainly discharge, (Fig.6c)andtheremaining isobserved ormeasured asaresult of these 6d).Toestimate charge finally processes (Fig. theimpact itisrequired tostudy when andhowthecharges relax. therefore, charge, Thetheory inthecase ofa short distance between thedischarging of gaseous discharge, wasestablished andtheoretical electrodes, byTownsend's studyand experimental Pachen's lawinwhich thebreakdown isexpressed the potential byproduct,ofpd dischargtothislaw,thebreakdown inggap,d,andthegaseous pressure, p,atthisgap.According as Y,isgiven potential,
6.Schematic illustration ofthecharge relaxation with process particle leaving. Figure
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7.Minimum field ofair. Figure spark
forthedischarging aredetermined touse Here, whereand V,(pd).i. experimentally gases. inthediscussion thistobreakdown electrostatic field and below, Yes, strength, byreducing realvalues fornormal air,thisyields bysubstituting required pressure Thisspark field asa function ofdischarging inFig.7. computed gap,d,isindicated inaprocess After thebeginning of the relaxation ofseparation between the discharge andtarget, theparticle loses itscharge onthecurve of the field impacting particle spark duetothedischarge because thisspark field with decreases increase of the relaxation, gap. itisrequired todiscuss theterminal ofthedischarge because thespark field Here, point inFig.7. curve hasnominimum asshown point, 4.4Relation between andrelative dielectric constant equilibrium charge of the polymer Asmentioned inSection correction factor isafunction of the contact 4.1,theimage gap anditseffect islostfrom acertain aseparating therefore, in relaxation gaprapidly; process, aparticle itscharge, onthespark field curve with increase of the contact losing gap,leaves thiscurve from below acertain of the field of the contact gapduetoadecrease strength oflosing theeffect of the wetrytoestimate theequilibrium Here, gapbecause image. under tosimplify thefield thisproblem as:onthispoint where charge rough assumptions of the leaves thespark field curve mentioned can above, (i)thecharge topof the particle beregarded asuniform and(ii)thecharge of this timecanberegarded astheequilibrium charge. Thepoint where thefield leaves thespark curve below duetothedecrease of strength thecorrection factor of mirror isgiven asthepoint where therateof the image image lessthan therelative rateof the correction factor asafunction of the contact gapbecomes field curve herethese ratesarenegative because funcspark (notice theyaredecreasing isgiven to(7),thecharge field Yes tions). Qatthispoint bythespark strength According andimage correction tothecontact factor(e,d)corresponding as; gap atthis d point
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8.Relation between and relative dielectric constants ofpolymers. Figure equilibrium charges From thisprocedure, theequilibrium asa function oftherelative Qeisgiven charge thesample dielectric constants ofthepolymer 8shows absolute making particles. Figure asexperimental values ofequilibrium ofthepolymer results and charge particles given estimated foreachdielectric constant of bythisprocedure bya 0.5stepfortherange 1.5
220 andMrTakashi ofSoka fortheir technical intheexperiments Moriya University support andtheoretical calculations. REFERENCES 1.H.Yamamoto and B.Scarlett, Part. Charact. 3,117, 1986. 2.T.Matsuyama and H.Yamamoto, J Soc. Powder 1987. Technol., 24,765, Japan 3.T.Matsuyama and H.Yamamoto, In:Conf Rec. 1992 IEEE Ind. Soc. Annual Appl. Houston, 1992, Meeting. p. 1446. 4.Seidennki Handbook. 1981. 1. Ohmusha, Tokyo: 5.Kagakubinran-Kisohen. Maruzen 1984, Tokyo: p.II-493. 6.D.K.Davies, J.Phys. D.2,1553, 1969. 7.T.Matsuyama, etal.In:Proc. 1993 Ann. Inst. Electros. 1993. Chino, Meeting 8.W.J.Brennan, etal.,J.Phys. 1992. D,Appl. Phys. 25,1513, 9.J.G.Simmons, J.Appl. 1963. 34,1793, Phys.
212 1.INTRODUCTION ofinsulating Todiscuss theelectrification inthedry-handling itmust generated powder, tostudy thecharging behavior ofasingle beregarded asoneofthemost important points asacomponent From thisstand westudied theimpact of 'powder'. point, charging particle inwhich ofa single of particle through impact charging experiments polymer particles around 3mmindiameter wereusedandimpact collision charges generated bysingle thepolymer andmetal were measured onebyone[1-3]. Inthis between particle target weconducted thisimpact fourkinds ofpolymers for study, charging experiment using withdifferent andthreemetal workfunction forallthese impacting particles targets combinations inorder tocharacterize theelectrostatic ofpolymer systematically charging discussion ontheeffect ofthework function ofthetarget ontheimpact particles through ofpolymer charging particles. 2.OUTLINE OFTHE IMPACT CHARGING EXPERIMENT Because thedetail oftheimpact isdescribed inprevious work charging experiment [2], ofit willbedescribed here.Figure 1shows a schematic viewofthe onlyanoutline fortheimpact Theair-gun-launched apparatus charging experiment. spherical polymer a Faraday onthemetal Thecharge particle passes through cagebefore impact target. carried before the'initial is measured bytheparticle impact (called charge') bythis Thetarget metal isconnected totheelectrometer andthe Faraday cage. plate directly leftonthetarget ismeasured asthecomplement ontheparticle charge charge generated byimpact (called 'impact charge'). Inthisstudy, thisimpact wasconducted fourkinds of charging experiment byusing andthreemetal forallthesecombinations polymers Teflon, targets systematically. anddelrine of3.2mmdiameter were used nylon66, polystyrene particles (Moritex Corp.) forpolymer andformetal were Ti,CrandNiwith particles; targets, (>99.99%) high purity used. each metal wasbuffing-finished alumina. were Here, plate by0.3 ,um Experiments
1.Schematic view oftheexperimental Figure apparatus.
213 Table 1. their and metal and relative dielectric List ofsample targets polymers constants and work functions
conducted under a normal airatmosphere withtemperature andhumidity mainpressure at24± 5°Cand25± 5%,respectively. tained andmetal and Sample polymers targets theirrelative dielectric constants andwork functions arelisted inTable 1. 3.RESULTS 3.1.Experimental results Asanexample theresults oftypical oftheimpact results, Fig.2shows charging experiment 2 compares tworesults ofdifferent using teflon(particle)/Cr(target). Figure impact 5 and10 m/s withimpact 60°.Thehorizontal axisrepresents theinitial velocity, angle oftheparticles, while thevertical axisrepresents theimpact Theimpact charge charge. decreases withincrease oftheinitial wecallthislinethe charge proportionally charge: line'ofitsimpact condition. There isa particular theintercept onthe 'charging point, horizontal axisofthecharging nonetcharge transfer occurs attheimpactline,atwhich contact duetoinitial thatspecial initial iscalled the'equilibrium points charge; charge charge' . 2indicates thatthisequilibrium isindependent oftheimpact conditions Figure charge andangle), while thecharging linedepends onthese. These (impact velocity experimental results werealready inourprevious works reported [1,2];ingeneral, impact charging a setofthecombination ofparticle andmetal withdifferent experiments, using target, conditions lines onthehorizontal axis. impact givedifferent charging crossing
Initial charg(. (pC) 2.Typical results oftheimpact Crtarget at60°, 5and Figure charging experiments. (Teflon partices impact 10mls).
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3.Schematic illustration ofthemodel condenser. Figure 3.2.Condenser model Theelectrification ofaparticle duetoimpact/contact withametal iscaused plate bythe transfer between theparticle andmetal thecontacting surfaces. charge Here, plate through thecharge double between thecontacting surfaces canberegarded asa layer generated therefore thischarge transfer duetocontacting ofparticle andmetal can condenser; plate beexpressed model. Theschematic illustration ofthismodel isshown bythecondenser inFig.3.Here, inthecase of where theparticle carries theinitial thischarge exists charge, notonlyontheelectrode ofthecondenser constructed atthecontacting butalsoon area, thewhole surface oftheparticle; therefore theeffect oftheparticle's initial cannot charge betreated asaninitial ofthemodel condenser. Thisproblem canbetreated charge by theeffect oftheinitial tothetermoftheelectromotive force connected reducing charge tothemodel thecharge transfer ontotheimpacted is condenser; here, process particle model as expressed bythiscondenser where theamount ofcharging, andc,S,AtandTrepresent AQrepresents capacitance per unitareaofthemodel electrode contact timeandtimeconstant, condenser, area, respecThese terms areregarded asfactors themagnitude ofcharge transfer and tively. deciding arecalled thegeometrical factor ofcontact. These factors totheimpact change according conditions such asimpact andvelocity; therefore itisessential todiscuss theimpact angle duetoa single Thisdiscussion wasshown inourprevious work charge impact. [3].The second termof (1) isa factor thedriving force ofthecharge deciding transfer;and v V contact difference andinduced between the represent, respectively, potential potential contact surfaces duetotheinitial oftheparticle. Theeffect oftheinitial is charge charge reduced inthetermofthecharge force asmentioned above. driving tothismodel, theimpact termof (1), According charge AQisdecided bythesecond i.e.thetermofthedriving under thesame conditions ofthegeometrical factors of force, such astheimpact andangle. thelinear oftheimpact Here, impact, velocity dependence ontheinitial is explained charge charge bythefactthattheinduced Vis potential totheinitial isindependent proportional charge Qi.Thefactthattheequilibrium charge of the condition isalsoexplained asfollows; thecharge force impact bythismodel driving amounts tozero when thecontact iscancelled potential V, bytheinduced Yedue potential toamounting oftheinitial totheequilibrium charge charge Qe. 3.3.Relation between theequilibrium andwork charge function ofthemetal plate Itwillbeshown laterindetail howVisdecided herewesuppose that1;is by Q;; simply = kQ;. toQ;as Y thatthesecond term tozero due Now, proportional suppose of (1) equals
215 totheequilibrium thentherelation toamounting oftheinitial ofthese charge charge, canbewritten as parameters herethattheeffective work function ofthepolymer weassume Furthermore, [6],WP, surface andmetal workfunction, areavailable; thecontact difference is Wm, potential written as From isyielded as (2)and(3),theequilibrium charge This formula alinear relation between themetal work function andequilibrium predicts onekind ofpolymer and charge given byasetofimpact charge experiments using particle some kinds ofmetal different work function values. targets having 4shows therelation between theequilibrium andthework function of the Figure charge metal asaresult oftheimpact conducted hereforcombinatarget charging experiments tionsofallarranged andmetal Thisresult iscontrary tothe polymer particles targets. theequilibrium areindependent ofthemetal work mentioned above; prediction charges foreach Wewilldiscuss these function; rather, theyareconstant polymer particle. experimental inthenextsection. results 4.DISCUSSION 4.1.Image correction Firstofall,asa preparation fordiscussion inthissection, wediscuss herehowwecan decide thepotential surfaces of difference, Y,induced bytheinitial charge, Qi,between theimpacting andmetal particle plate. nowthattheelectrostatic fieldisuniform nearthecontacting Suppose pointofthe andmetal Thepotential difference between thecontacting surfaces isgiven particle plate. as where thefieldstrength infreespace, contact E, dandCdrepresent gapandrelative dielectric constant ofthecontact inthecaseofasolitary here, gap,respectively; particle infreespace, thefield is E,nearitssurface charged uniformly strength,
Work function ofmetal (eV) target work 4.Relation between and function ofmetal Figure equilibrium charge target.
216
where theinitial andradius oftheparticle, Qianda represent charge respectively. Ontheother themirror effect must beestimated inthecase thattheparticle hand, image exists neartheconducting suchasthecasediscussed here.Inmany the plane, cases, electrostatic fieldaround thisparticle is approximated oftwofields bytheaddition located atthecenter oftheparticle and(ii)itsimage. This generated by(i)apoint charge could beregarded asthe0-thorder because ofneglecting thehigher-order approximation Inthestrictsense, theeffect ofthehigher order should be polarization. polarization such asthattheimage induces thepolarization ontheparticle andthe considered, charge field induces thehigher ontheparticle. image generated bythispolarization polarization Theelectrostatic field around thisparticle andtheconducting isgiven astheaddition plane ofallfields andtheir thisproblem was generated bythese polarizations images. Recently, solved thiswasshown inourprevious work anexample ofthis successfully; [7]andonly result willbeshown here. letusdefine theimage correction factor oftheelectrical field onthe Here, bytheratio located near themetal tothefield ofthesolitary topoftheparticle plate particle given by asfollows, (6);thisiscorrected
5shows thisimage correction relative dielectric conFigure factor,(e,d),forsome stants oftheparticle asfunctions ofcontact a.The radius, gap,d,normalized byparticle affects from thecontact theparticle andthiseffect saturates at image gapreaching radius, thecontact 10 of theparticle radius. gapreaching 4.2.Adifficulty model ofthecondenser Ithasbeen out that the condenser model hasadifficulty willbediscussed pointed [8]which inthissection. tothecondenser thecharge onthecontact areaisgiven Now, model, according density as,
5.Image correction factors of contact Figure (asfunctions gap).
217 let difference hasnoinitial when thecontact is Vandtheparticle here, charge; potential asfollows. 0.1 andEd -1,the ustryanorder estimation V, d= 10 A Suppose= Vc becomes J = 10 3 C/m2; thetotalcharge ofa particle, of the charge density magnitude with thischarge with1.5mminitsradius charged uniformly density becomes 105 ==pC. is greater thanthevalue ofequilibrium Thisorder ofmagnitude Qe -103 pC charge intheimpact Lowell's forexample, this measured charging experiments. group, pointed tothis, the realcontact tobeaproblem depth; according gapbecomes of charge penetration asusual, andtheyarestudying thisproblem from these view thanthatconsidered bigger itmust beregarded asveryimportant topoint outthattheir Ontheother hand, points. were conducted inhigh vacuum while ourimpact contact charging charging experiments inopenairunder normal andpressure. Inthe were conducted temperature experiments ofthecharge relaxation viagaseous willbe a possibility section, following discharge discussed. 4.3.Discharge relaxation process surfaces increases withanincrease of the Thepotential difference between thecontact ofcharged surfaces forexample, contact [see(8)].Here, process gapintheseparating difference tothecontact difference within tunnel relaxation thispotential potential keeps therange of the contact thetunnel current affects. Because thetunnel current gapwhere affects difference increases atthelarger contact A,thepotential upto = 10 rapidly gap. wecanunderstand thatthepotential difference reaches over thegaseous breakdown Here, limit atthecharge estimated above. density oftheparticle 6 shows a schematic illustration oftheseparating and Figure process metal Thecharge transferred between thesurfaces atcontact forms thedouble plate. charge between thecontact isfixed surfaces layer 6a),theelectrostatic byseparating (Fig. charge these surfaces thischarge attheseparating viasome (Fig.6b);here, mayrelax process routes duetogaseous weassume here) (mainly discharge, (Fig.6c)andtheremaining isobserved ormeasured asaresult of these 6d).Toestimate charge finally processes (Fig. theimpact itisrequired tostudy when andhowthecharges relax. therefore, charge, Thetheory inthecase ofa short distance between thedischarging of gaseous discharge, wasestablished andtheoretical electrodes, byTownsend's studyand experimental Pachen's lawinwhich thebreakdown isexpressed the potential byproduct,ofpd dischargtothislaw,thebreakdown inggap,d,andthegaseous pressure, p,atthisgap.According as Y,isgiven potential,
6.Schematic illustration ofthecharge relaxation with process particle leaving. Figure
218
7.Minimum field ofair. Figure spark
forthedischarging aredetermined touse Here, whereand V,(pd).i. experimentally gases. inthediscussion thistobreakdown electrostatic field and below, Yes, strength, byreducing realvalues fornormal air,thisyields bysubstituting required pressure Thisspark field asa function ofdischarging inFig.7. computed gap,d,isindicated inaprocess After thebeginning of the relaxation ofseparation between the discharge andtarget, theparticle loses itscharge onthecurve of the field impacting particle spark duetothedischarge because thisspark field with decreases increase of the relaxation, gap. itisrequired todiscuss theterminal ofthedischarge because thespark field Here, point inFig.7. curve hasnominimum asshown point, 4.4Relation between andrelative dielectric constant equilibrium charge of the polymer Asmentioned inSection correction factor isafunction of the contact 4.1,theimage gap anditseffect islostfrom acertain aseparating therefore, in relaxation gaprapidly; process, aparticle itscharge, onthespark field curve with increase of the contact losing gap,leaves thiscurve from below acertain of the field of the contact gapduetoadecrease strength oflosing theeffect of the wetrytoestimate theequilibrium Here, gapbecause image. under tosimplify thefield thisproblem as:onthispoint where charge rough assumptions of the leaves thespark field curve mentioned can above, (i)thecharge topof the particle beregarded asuniform and(ii)thecharge of this timecanberegarded astheequilibrium charge. Thepoint where thefield leaves thespark curve below duetothedecrease of strength thecorrection factor of mirror isgiven asthepoint where therateof the image image lessthan therelative rateof the correction factor asafunction of the contact gapbecomes field curve herethese ratesarenegative because funcspark (notice theyaredecreasing isgiven to(7),thecharge field Yes tions). Qatthispoint bythespark strength According andimage correction tothecontact factor(e,d)corresponding as; gap atthis d point
219
8.Relation between and relative dielectric constants ofpolymers. Figure equilibrium charges From thisprocedure, theequilibrium asa function oftherelative Qeisgiven charge thesample dielectric constants ofthepolymer 8shows absolute making particles. Figure asexperimental values ofequilibrium ofthepolymer results and charge particles given estimated foreachdielectric constant of bythisprocedure bya 0.5stepfortherange 1.5
220 andMrTakashi ofSoka fortheir technical intheexperiments Moriya University support andtheoretical calculations. REFERENCES 1.H.Yamamoto and B.Scarlett, Part. Charact. 3,117, 1986. 2.T.Matsuyama and H.Yamamoto, J Soc. Powder 1987. Technol., 24,765, Japan 3.T.Matsuyama and H.Yamamoto, In:Conf Rec. 1992 IEEE Ind. Soc. Annual Appl. Houston, 1992, Meeting. p. 1446. 4.Seidennki Handbook. 1981. 1. Ohmusha, Tokyo: 5.Kagakubinran-Kisohen. Maruzen 1984, Tokyo: p.II-493. 6.D.K.Davies, J.Phys. D.2,1553, 1969. 7.T.Matsuyama, etal.In:Proc. 1993 Ann. Inst. Electros. 1993. Chino, Meeting 8.W.J.Brennan, etal.,J.Phys. 1992. D,Appl. Phys. 25,1513, 9.J.G.Simmons, J.Appl. 1963. 34,1793, Phys.