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630 I E E E nansactions on Dielectrics and Electrical Insulation Vol. 1 No. 4, August 1994

Basic Electrical Processes in

Dielectric Liquids

T. J. Lewis

School of Electronic Engineering andComputer Systems, University of Wales, Bangor,

United Kingdom.

ABSTRACT

The basic processes of electrical conduction in dielectric liquids

are reviewed, attention being drawn to the similarities between

conductive electrolytes and insulating liquids. The concepts of

the electronic amorphous solid state are employed to provide

a framework for the review. The conditions at met al elec-trodes can be incorporated naturally into the scheme, and it

is known that the space charge layers occurring on them can

control conduction. Although electrical breakdown itself is not

considered, the underlying electronic processes which will de-

velop when breakdown electrical fields exist in th e liquid are

considered.

1. INTRODUCTIONHERE is a very considerable and diverse literature

T oncerning the electrical conductivity and breakdownof insulating dielectric liquids. The liquids that have

been investigated range from simple atomic rare gas liq-uids through a wide variety of nonpolar organic liquids ofvarious molecular forms to polar liquids, including water,

which can be insuhting under appropriate conditions.The models necessary to describe the conduction pro-cesses in these liquids are more complex than those todescribe conduction in aqueous electrolytes where dis-

sociative reactions in the bulk and redox processes at

the electrodes are well understood. They also appear to

be more complex than those required to describe electri-

cal conduction in gases or in the solid state. Insulatingliquids generally exhibit low, fluctuating conductivities

which are sensitive to electrode conditions and impuri-

ties in unspecific ways. Under high electrical stress t heconduction current often becomes highly localized as a

prelude t o breakdown.

In spite of these complexities and the wide range of liq-

uids with different molecular or atomic properties, it is

possible to establish a number of fundamental processes

which form the elements of any model to describe their

overall electrica l behavior. It is the purpose of this paper

to review these but it should be noted that a number of

useful reviews presented from rather different viewpointsalready exist [l-71. The appended li st of references is

intended to be only representative of the li terature avail-able. Much use has been made of papers presented at the1993 IEEE 1 t h International Conference on Conductionand Breakdown in Dielectric Liquids.

The fundamental processes may be divided into two

categories, those associated with the bulk liquid and those,

occurring at the electrodes. Each will be discussed sepa-

rately an d th en the way in which they might act in com-bination will be considered. It will be found that, whilethe liquid processes a re analogous to those occurring inelectrolytes, descriptions in terms of energy stat es com-monly employed for explaining electronic processes in th eamorphous solid st ate, are part icularly valuable.

1070-9878/94/ $3.00 @ 1994 IEEE

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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1 No. , August 1994 631

2. BULK PROCESSES

Charge will arise in the bulk of an insulating liquid bythe dissocia.tive ionization of liquid molecules accordingto a general scheme

M - C ’ A - - C + + A - (1)

where C + A - is an associated ion pair complex and C+,

A - are separated cation and anion species. The molecule

M may separate into submolecular ionized parts in sever-

al ways especially if it is an organic molecule. If only an

electron is split off then this will seek to form an anion A -

with another molecule of th e liquid. The degree to whichthe equilibrium of the reaction shifts to t he right will de-pend on the strength of both short-range and long-range

(Coulombic) binding forces. In th e case of the electronicanion A - formed on another molecule, there also will bea stability requirement, which will be discussed below,

that the electronic energy of the state of C+ should lie

above A - . Dissociation will occur readily in polar liquids

because the high permittivity will weaken the Coulomb

attract ion between C+ and A-. In most pure insulatingliquids, where the Coulomb force will be strong, disso-

ciation will be wea.k and the equilibrium point of the

reaction will be to the left.

Dissocia.tion will not generate net charge in a liquid,

bu t charge ca.n a.rise by inject ion at an electrode. Because

only electrons ca.n transfer across a metal electrode-liquidboundary there will be an excess or deficiency of electrons

in the liquid as a result. Consideration of the propertiesof these electrons in the liquid and their transfer proper-ties at metal electrodes requires a single description for

the corresponding electronic energy states in the liquid

and metal.

-

I & IA1

I TpFigure 1.

Electronic energy states for positive and negativemolecular ions in gaseous and liquid phases.

The liquid electronic states arise from those of the in-

dividual molecules (or atoms in an atomic liquid). A

Figure 2.

The localized E - ( o o ) ( A 1 ) , E + ( o o ) ( Z l ) and de-

localized E - ( O ) , E+(m) nergy states of ionsin a liquid. - - - redox energy of the ion =

; [ E ( O ) + E(”.

molecule in a gaseous phase has two characteristic: sin-

gle charge states, a positive ion of energy I, in which

the molecule has lost an electron, and a negative ion of

energy A, in which an electron is attached to the mole-cule (Figure 1). In a liquid phase the energies of theseionized stat es a re modified by th e collective polarizationresponses of the molecules surrounding the ions. The

local reorganization of the liquid which occurs and the

associated solvation energy P has two parts, an ‘innersphere’ component in which changes in the force con-

stants, bond lengths and angles of the ion and neighbor

molecules occur and an ‘outer sphere’ component con-

sisting of the collective dielectric response of the moreremote molecules. Th e former depends on the specif-

ic molecular orbitals and their polarizabilities [8] and isdifficult to estimate, but the latter energy is frequently

represented by the Born approximation [9 ]

e’

87re,a-- (1 € ; I )

where a is the effective inner sphere radius and E, is the

local permitt ivity. For nonpolar liquids E, - 2 and the

energy is - 1.5 eV. Reorganization causes the positiveand negative ion energies (11 nd A I ) n the liquid to

become I, - P an d A, + P respectively (Figure 1). Forsimplicity P is assumed to be the same in both cases. To

stabilize a positive and negative ion pair (C++ A-) ina liquid it is necessary to have (I, - P) > (A , + P), a

situation encouraged in highly polar liquids where P --3 eV. If (I, - P) 6 (A , + P),dissociation will be weak

and temperature?? dependent.

When an ion state changes by gain or loss of an elec-

tron, the electronic component P,, ssociated with E~ ,

the pe rmittivity a t optical frequencies, will grow on atime scale comparable with t hat needed t o relocate the

electron but the remainder, A , involving atomic changes

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632 Lewis: Basic Electrical Processes in Dielectric Liquids

W( k I

E(-)--~Ej )

___--_

(b)

Figure 3

(a) Energy levels broadened into Gaussian dis-tributions W ( E )by thermal agitation of P . (b)Electronic energy bands in a liquid. States in thebands above E-(0) and below E+ (O) are quasi-free electron and hole states.

(which, according to the Franck-Condon principle, arefrozen during the initial stage) will take a longer time todevelop. The outer sphere component of X will be

( 3 )

corresponding to long-range dipole alignment about the

ion. T he inner sphere component involves stru ctur al re-

organization and local polarization to accommodate the

ion. For polar liquids X is 2 eV (1.7 eV for water [SI)

but even for nonpolar liquids it can approach this valuebecause the polarizability of individual molecular bonds

can be large, as in hydrocarbons for example, even when

the net dipole moment is small.

Taking account of the relative slowness of the molecu-lar reorganization according to the F’ranck-Condon prin-

ciple it is possible to define two electronic energy states

for each ion (see Figure 2 ) . In the case of the negativeion state the energy is E - ( O ) at the moment an electron

is localized at a molecular site and E- (CO) when the elec-

tron is in a fully polarized state after reorganization hasoccurred. Likewise, for a positive ion (hole) state , E+(O)is the energy of the hole or positive ion a t th e moment anelectron leaves a neutral molecular site while E+(co) s

the subsequent energy of the fully polarized positive ionsta te. When the necessary energy associated with the

str uctu ral reorganization is taken into account, it may beshown that E ( 0 ) - E (m )x 2X for both negative and pos-

itive ion sites [9]. The mid-point energy $ [ E ( O ) - E(M) ]

is known as the characteristic redox energy for the ion

and is usually determined for the ion in water. In addi-

tion to the energy st ates E(0)and E(m) for electrons orholes there is also a band of states in between correspond-

ing to the gradual rel axational change of the polarization

component from zero to its full value A.Ther mal agit atio n will continually upset the molecular

arrangement about any ion site in the liquid and conse-

quently change P and the associated electronic energy

level from their mean values. Silinsh [lo] has discussedthis situation thoroughly for organic molecular crystalsand has concluded t ha t each level is replaced by a Gauss-ian dist ribut ion of levels centered on it. Similar conclu-

sions may be reached for liquids. The case of therm alfluctuations in the X component of P has been summa-

rized by Morrison [9] who shows that, for a Boltzmann

distribution in thermal energy fluctuations, the probabil-ity W ( E ) hat an energy state Ei fluctuates t o an energyE is given by

( E ; - E ) ’

[- 47rXkT ] ( 4 )( E )= (4~1cT)-~”xp

If X - 1 eV and the thermal fluctuation is - IcT, thenJE i- El - 0.3 eV. Figure 3(a) illustrates the situation.

The states E(0) an d E (m ) and the band of states inbetween corresponding to various degrees of localization

become broadened into bands of Gaussian shape for both

types of ion. For clarity only the bands based on E ( 0 )

an d E (M) are shown.

We should note that there is a range of possible statesabove E-(O) for electrons and below E + ( O ) for holes

which correspond to tr ansient occupancy by the charges.

For example it is possible for an energetic electron, pro-duced perhaps by high fields or by photoexcitation, to

move through a sequence of states above E - ( O ) in en-ergy without staying long enough on any one to induce

the full electronic polarization. The electron is then in a

quasi-free mobile st ate in a conduction band defined by a

band edge E - ( O ) (Figure 3(b)). Thus E - ( 0 ) is importantin marking th e dist inction between quasi-free a nd local-ized electron stat es even though the distinction is blurred

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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1 No. 4, August 1994 633

by thermal disturbance of the levels as discussed above.

It is usually assigned t he symbol VO l l] nd can be com-pared directly with the conduction band edge of a solid

sta te semiconductor. VOis the negative of the electron

affinity. In a similar way there is a band of quasi-freepositive hole states below E+ 0 ) which corresponds to

the valence band of the solid sta te. Th e band-gap en-

ergy [ E - ( O )- E+(O)J,etween the two sets of states is

the necessary energy to create a quasi-free electron-hole

pair, but is ill-defined because of thermal blurring of theedges. Values of E - ( O ) - E + ( O ) have been tabulated by

Schmidt [6] for a variety of liquids. They range from 4to 12 eV. The localized negative and positive ion states

E- ( m) an d E+ (m)will lie in the band g ap (Fig ure 3(b))and correspond to trap states in amorphous insulating

solids. In a liquid however such states are mobile ionsand can translocate.

Values of Vo have been determined for a number of di-electric liquids [5,6,12]. For organic liquids they rangefrom - 0 . 7 eV for tetramethyl tin to +0.5 eV for cyclohex-

ane. Helium has a value of $1.05 eV while the o ther rare

gas liquids Ar, Kr an d Xe have values between -0.2 an d-0.67 eV. Liquid nitrogen has a value of $0.35 eV. Theorganic liquids with more symmetrical molecules tend to

have lower values of VO consistent with the expectationthat the degree packing and orientation, and hence local

polarization would be greater in such cases.

Impurities in liquids can, by dissociation, be a directsource of ions but they can also influence the electron and

hole sta tes of the liquid itself. If the impurity is polar thisinfluence can be considerable and out of proportion to its

concentration. Th e reason is tha t t he nonuniform and es-

sentially radial field in the neighborhood of an ion will

produce dielectrophoretic forces causing the polar impu-

rity t o cluster round the ion. For example, water mole-

cules could be swept up to form solvation shells aroundelectrons [13]. The time scale for such a process is likely

to be relatively long so it will be most effective with 10-

calized states E-(m) an d E+(m).The shell is of higher

polarizability than the bulk liquid displaced, A is largerand the ion state becomes more localized in the bandgap. The additional energy can be estimated, using theBorn approximation again, to be

where is the effective perm itt ivi ty of the shell whoseouter ra.dius is T . If for example a = 0.15 nm, r = 0.25 nm

an d ,> E , then AA = 0 . 7 eV, a substantial change inthe solvation energy of an ion and in its electronic state .

Th e Born approximat ion is crude and takes no account ofchanges in the contribution from electronic polarization

but the detailed treatment by Kebarle et al. [14] confirms

how important the effect might be even when the impu-

rity concentration is extremely low. Cluster formation

involving water in tetram ethyls ilane has been studied re-

cently by Balakin et al. [15].

3. CHARGE TRANSPO RTElectrons and holes which have become fully localized

in dielectric liquids drift as ions with their accompany-ing polarization shells (polarons) in weak applied fields

with mobilities in the range IO-' to l o -* m2 V-'s-'

values corresponding to those of ions in electrolytes. If

sufficient energy can be gained by thermal fluctuations,

incident radiation or application of a high electric field,it will be possible for the electron or hole to be released

from the X polarization shell and to become quasi free,

either in the conduction or valence band with a muchhigher mobility. For localized electrons (negative ions)

it has been demonstrated [8] that electronic absorption

spect ra can be obtained with a limit corresponding to t he

band edge E-(0 ) . The likelihood of a freed electron or

hole becoming localized (trapped) again will depend on

several factors: energy-exchanging collisions with liquidmolecules as will be discussed below, thermal fluctua-

tions in the energies of the bands and localized states

and the kinetic energy imparted by drift motion in anapplied field.

In the quasi-free sta te t he mobility pf of electrons islikely to be determined by scattering collisions in which

the momentum and energy gained from an applied field

is lost in the stimu lation of vibrationa l modes of the liq-

uid molecules which are related to the electronic compo-nent of the polarization. In the case of organic liquids,the hydrocarbons for example, these modes could be as-

sociated with the CH, CH2 and CH3 groups having vi-

brational energy quanta in the infrared between 0.1 and

0.4 eV [16,17]. In more complex molecules similar vi-

brational modes are expected to be excited. In rare gasliquids however such modes will be absent but scatter-ing by deformation potentials created by fluctuations in

liquid density is likely. It is possible [6] to t ake account

of scatte ring collisions by writing p~ = e.r/m* where m*

is an effective electron mass and T = l / v t h where 1 is a

mean free path between scattering collisions and vth isthe therma l velocity of the electron.

Freeman [18] and Schmidt [19] have tab ulat ed electron

mobilities for a range of liquids covering some seven or-

ders of magnitude from 2x10-1 for liquid Xe to 3 ~ 1 0 - ~m2V- ls- for the polar liquid ethanol . The mobility in

water is 2~10-' m2V-'s- l . The lower end of the rangecorresponds to typical ion mobilities in electrolytes. Elec-

tron mobilities in paraffinic hydrocarbon liquids rangefrom 0.1 to 1 ~ 1 0 - ~-lV-'s- I , the mobility decreas-

ing with increasing chain length. In tetramethylsilane,

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a liquid with a. large but spherical molecule, it is lo-’mzV- ls- ‘. The presence of double an d triple bonds en-

courages scattering loss and a lower mobility. When theliquid molecules are not spherical, the interaction with

electrons involves greater anisotropy of polarization a nd

more hindered rotation so that when a polarization shell

develops about an ion it will be more stable and longer

lasting.

In transit through a. liquid, electrons (or holes) can

exist in both the quasi-free and localized (tr apped) stat esand it is useful to define an effective mobility pe for thetran spor t. This may be done in two ways. If, in a swarmof drifting electrons, a fraction x is in a free state and

the rest trapped at a given time, then

Pe = X P ~ (1- X)Pt (6)

where pt is the mobility of the trapped state. It would

be possible for pe to be time?? dependent if x (changedas the swa.rm moved through the liquid. Alterna tively if

an electron spends an average time t f in the free state

between two traps and a time t t in a trap then

(7)

Depending on conditions pe may have any value be-tween pf and p t . When tr apping is weak so that t f >> t t ,

pe p j and when trapping dominates, t f << tt an d

The time in a trap t t is terminated by thermal activa-tion into a. free state in the conduction band and can be

expressed as t t = t o exp(Et/ kT) where Et is an activationenergy corresponding approximately t o E- 0) - E- (00)

(Figure 3(b)), and t o is the reciprocal of an attempt-to-

escape frequency. Thus pc can be an exponential func-tion of temperature. Fueki et al. [20] have suggested th atEt for hydrocarbons is - 0.24 eV.

The effect of scatter ing and t rapp ing is well illustrated

by the beha.vior of nitrogen admixtures with liquid argon.

When 15%Nz is added to LAr, the electron mobility is

reduced from 50 to 2 ~1 0- ~m ’/ Vs ecause of increased

scattering [21]. When the electron becomes trapped themobility falls to 10-7m2/Vs practically the same value

as for pure liquid Nz. Similarly addition of - 10% Xe

to LAr lowers the mobility to 25~10-~m~/Vs22]. Itis suggested that Nz and Xe cause disorder and localdensity increases in liquid Ar which enhances electronscattering and lowers the mobility.

In some rare gas liquids an d in molecular liquids suchas hydrogen, ethane and n-hexane there is evidence for

a state of low mobility in which an electron becomes

trapped in a low-density bubble within the liquid. In

these instances a stable state of lower energy ensues whenliquid is excluded from the immediate environment of the

electron, a situation likely to be related to the fact that

a positive Vo implies a negative electron affinity.

x 2X

I I 9

1 2

Figure 4.

Transfer of positive hole at energy E in the bandof E + ( O )states by electron tunneling from an oc-

cupied state at molecule 1 t o an unoccupied oneat molecule 2 through potential barrier V ( z ) ver

a distance N ( Z Z - 1).

There are relatively few reported values for positive

hole mobility in liquids. It may be expected however th athole transport will be more facile than that of the local-

ized positive ion since it requires, in effect, counter trans-

port of electrons through the valence band. The condi-

tions for this to occur are more stringent than those for

quasifree electron transfer t hrough t he extended states ofthe conduction band an d th e mobility will be lower. In

fact hole transpo rt will require quantum-mechanical res-

onance tunneling of an electron from an occupied energysta te in the valence band of E+(O)states to an equivalent

empty one (hole) on an adjacent molecule. If tunnelingoccurs at an energy E in the band of states through an

inter-molecular potential barrier V( a) , assumed for sim-plicity t o be one-dimensional (Figure 4) , then the prob-

ability of a transition depends on a factor

r 1

where 21 , a2 are t he spatial limits of a where V(a) = E(231. The rate of transfer depends strongly on V(z) andon the closeness of approach of the two molecules. It also

requires tha t, a t the moment of tunneling, the two states,one empty and the other occupied by an electron, have

a common energy E. The probability of this will depend

on the product of two Gaussian distributions similar tothose discussed above. If such a transfer becomes diffi-

cult and the hole remains for any length of time and X

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IEEE Transactions on Dielectrics and Electrical Insulation Vol.1 No. 4, August 1994 635

polarization sets in, it may become localized in an energy

state between E + ( O ) and E+(m).

The reported hole mobility for heptane is 2x10-6m2/Vs

[24]. Warman et al. [25] give a value of 9.5x10-'m2/Vsfor cyclohexane and 9 ~ 1 0 - ~ m ~ / V sor trans-decalin. Thecorresponding ion mobilities ar e 4x10-' and 2.6x10-'m2/

Vs, one order of magnitude less. The re are reported mo-bilities for liquified gases, such as 4He, 5.3~10-~;2, 0.8

t o 4 . 5 ~ 1 0 - ~ ;2 , 8 ~ 1 0 - ~ ;2 , 2 to lOxlO-' and methane,2 ~ 1 0 - ~ m ~ / V sut whether these are true hole, rather

than positive ion, mobilities is not certain [6].

Tra.p configurations, delocalization kinetics, scatteringprocesses and thus the ratio t f / t t are all likely to be af-

fected by the presence of high fields so that studies ofcharge ca.rrier mobilities under such conditions are valu-

able. The high field drift velocities of excess electrons

in a range of hydrocarbon liquids and a number of rare

gas liquids have been summarized by Schmidt [6]. Onthis subject there has been recent work by Faidas et al.

[26] on the so-called fast tetr amethyl liquids which have

spherica l molecules. In all cases the drift velocities overa range of fields up to l o 7 Vm-I are found to vary non-linearly with the field. In some cases the variation issublinear and the drift velocities show saturation at the

highest fields (methane, tetramethyl compounds, Xe, Kr,

Ar) while in others (ethane, He, H2, Ne) the variation is

superlinear, especially at th e highest fields. In the firstcategory the mobility decreases and in the second it in-creases with increasing field.

Faidas et al. [26] have suggested that the sublinear

behavior is due to electrons undergoing trapping and de-

trapping while in transit between the electrodes whichproduce a dispersion in the transit times. This situation

would arise if electrons were injected at a cathode into

localized states and subsequently, while drifting to theanode, were thermally excited into a delocalized state

which was sufficiently long lived for the electron to reach

the anode without being localized again. The electronwould move an average distance p t t tF in a low-mobility

localized state and d - ptt tF in a free state where F isthe applied field and d the electrode spacing. The overall

drift velocity would then be

which has a. sublinear F-dependent characteristic withd v / d F - p f at low fields and tending to a limit p : / p f

for F = d / ( p t t t ) at which point v / F = pt (Figure 5(a)).

On the other hand if electrons are initially injected intodelocalized states and subsequently become localized the

drift

V I

V

d/Clftf F

Figure 5.

Electron velocity vs. ield characteristics resulting

from (a) localized+

delocalized and (b) delo-calized -+ localized motion between cathode andanode.

velocity is then

pt d FU =

d - F t f P f - P t )

which has a superlinear characteristic (Figure 5(b)). At

low fields, pe - pt an d pe+ p f at high fields.

The measurement technique for these studies is to pho-toinject electrons a t the cathode. Injection into local-

ized, rather than delocalized, states might be expected

a t a cathode for liquids with positive VO nd into delo-calized states when Vo s negative. The two groups of

liquids cited above fall into these categories. Moreover,

those with sublinear characteristics have high low-fieldmobilities and those with superlinear characteristics have

low low-field mobilities in agreement with the argument

above.

At high fields the potential energy barrier localizing anelectron will be lowered on the anodic side (Figure 6) , and

this will reduce t t so that pe (Equation (7)) will increase,ultimately to the limit p f . The electron then effective-

ly remains delocaliaed in the conduction band where thevarious collision processes involving vibra tional modes of

th e liquid molecules and microscopic density fluctuations

will serve to limi t the electron energy. Normally the drift

velocity U would be much less than the thermal veloci-

ty v t h but at very high fields transfer of energy to the

liquid by collisions can become less efficient and 'v couldthen exceed 21th. Referring to the liquid hydrocarbons,on which a lot of work has been done at high fields, pf

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Figure 6

Potential energy barrier V( ), localizing an elec-tron, is reduced on anodic side by applied field.Activation energy becomes - Et - eEz ' ) and t t

is reduced.

is found to be - o - ' m2/Vs and in a breakdown fieldof lo s Vm-' the drift velocity would be 10' ms-'. Theelectron would then acquire energy from the field at the

rat e of 1014 eVs- l. Magee [27] has estima ted a mean

energy loss of 7 ~ 1 0 ' ~Vs-'. for electrons in hydrocar-

bon liquids with a mean kinetic energy of 6 eV. It has

been suggested above that in the case of hydrocarbon liq-uids an energy quantum to stimulate a vibrational modemight be as much as 0.4 eV [16]. To acquire this ener-gy in a field of 10' Vm-I a free path of - 4 x lo- ' m

would be required. Holroyd et al. [28] have suggested a

mean range of 4.2x10-' m between strong collisions in

n- hexane.

IK2 K

>

Figure 7.

Plot of hypothetical energy per unit path in thefield direction as a function of the kinetic energy

K of the electron.- oss to liquid, - - - - gainfrom field F. Conditions are stable at Fl andunstable at Fz. or K > KZ field Fa ) the elec-

tron can accelerate to energies of next collisionbarrier.

In the high-field prebreakdown phase in hydrocarbonliquids stimulation of the various vibra tional modes asso-

ciated with the molecular bonds appears to be the mostimpo rtan t energy-dissipating mechanism. The collision

cross section Q for the excitation of a particular vibra-tion of quantum energy hv will increase from zero when

the electron kinetic energy K corresponds to hu and will

reach a peak value at rather higher energy. Thereafter

for higher values of K a steady decrease in Q can be

expected. The mean free pat h for the collision is then

[NQ(K)]-' where N is the number density of the vi-

brational centers in the liquid. The energy loss per unitpath length will be N Q h u while the kinetic energy gain

K from the electric field, assuming that v >> v t h will be

eF. The situation will be stable and energy from thefield will be lost to collisions until a field is reached such

that e F > N Q h u (Figure 7) . For higher fields than this

and correspondingly higher values of K th e collision pro-cess is increasingly less efficient in removing energy and

the electron will be able to accelerate to the range of

energies corresponding to excitation of the next higher

vibra tiona l mode of the liquid molecules. After movingthrough the sequence of energies corresponding to these

modes, the next more energetic processes will be those ofmolecular dissociation and free radical pro duction, elec-

tronic excitation an d ionization. For hydrocarbon liquids

the associated energies are - , 6 an d 9 eV, respective-

ly. Collisions involving these processes would result in

considerable loss of forward electron momentum and en-ergy causing the electron to fall back to a low energy.

The cycle of electron acceleration through the various

collision barriers would then begin all over again. There

are important consequences of collisions in the high-field

high-energy regime. Molecular dissociat ion will lead to

degradation of the liquid and electronic excitation will

generate photons which will trans port energy to part s of

the liquid remote from the electron path and especially

to th e electrodes where further electrons could be inject-ed. Light emission has frequent ly been observed as a

precursor to electrical breakdown.

Finally the process of ionization is very important inthe context of electrical breakdown because it generatesa second electron and a positive hole or ion. A repeat-

ing cycle of electron acceleration to ionization energieswill then generate an avalanche or a-process, a cascade

of electrons and positive holes or ions increasing in con-centration with distance 2 , a t a rate proportional to

exp(a2). The a process, which is a common feature of

electrical breakdown in gases, has been difficult to ob-

serve in liquids although there is now growing evidence

for it when the electric field is exceptionally high.

Early work by Derenzo et al. [29] determined an a-

coefficient for liquid Xe in fields from 4x107 to 2x108Vm-l , the value being- x107 m-l at th e highest field,

while recent work by, among others, Gosse and cowork-

ers [30,31] has established the likely existence of electron

avalanches in cyclohexane, n-decane, toluene an d ben-

zyl toluene. The fields required are > lo 9 Vm-' andare attained in small volumes of the liquid adjacent to

tungsten point cathodes of radii < 0.5 pm. Bonifaci et

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IEEE nansrlctions on Dielectrics and Electrical Insulation Vol.1 No. , August 1994 63

al. [32], using the same technique, report similar effects

with tetramethyl silane, a. range of paraffin liquids, and

liquefied Ar, Kr and N z . The avalanches produce cur-

rent pulses and are accompanied by light emission indi-

caking excitation processes an d associated 'ho t' electronswhich in liquid Nz have energies > 10 eV. The analysis

by Atrazhev e t al. [33] of impa.ct ionization in atomic and

molecular liquids is relevant. They argue that in lique-fied Ar, Kr and Xe, where electrons have high mobilityand can be heated to as much as 8 or 9 eV by the field,the absence of energy loss by inelastic scattering leads

to low breakdown str ength whereas in molecular liquids,energy loss to vibrational modes is very significant and

leads to a higher electrical strength.

Hole propagation is also expected to be easier a t highfields since the potential barrier for resonance electron

tunneling will be reduced (the transition probability is

an exponential function involving the barrier height andwidth). If the mean intermolecular tunneling distance

were 5x10-" m, then each resonance transfer in a fieldof l o 8 Vm-' would result in 50 meV of energy being

available for conversion via molecular vibrat ion modesto thermal energy. Since only - 10 0 meV per molecule

might be needed to raise the temperature of a typical hy-

drocarbon liquid from normal tempe rature t o its boilingpoint, this energy source, derived from interaction withthe electric field, is not insignificant.

Th e electric field interacting with charges also gener-

ates momentum which, via the various elastic collision

processes, will induce bulk liquid motion. In the pres-

ence of charges of both sign, counterflows and turbulencemight be expected but where net space charge exists it

is likely to i mpar t a directed motion to the liquid. These

electro-hydrodynamic effects can be complex and havebeen reviewed in detail by Atten [34].

4. ELECTRODE PROCESSESBeca.use current continuity will require electron trans-

fer across the metal electrode/liquid interfaces at cathode

and anode, electrode conditions will always have a ma-

jor role in influencing electronic processes in dielectricliquids.

In equilibrium (zero applied voltage) charge layers will

be established at the electrode/liquid interfaces to en-sure tha t t he net electric current is zero. Typically these

layers have several components (F igure 8). First an elec-

tron cloud will exist in the metal surface, extending out

beyond the positive metal cores and a monolayer of ionsand molecules from the liquid will adsorb chemically and

physically to this, to form the socalled inner Helmholtzlayer (IHL). If the molecules are polar this layer can

be highly struc tured with properties qu ite different from

I l l I Ia b c d e

Figure 8.

The metal electrode liquid dielectric interface.(a) positive metal cores; (b) outer electron cloud;(c) inner Helmholtz monolayer of ions and mole-cules (IHL); (d ) outer Helmholtz layer; ( e ) Gouy-Chapman diffuse space-charge layer.

those of the bulk liquid. Beyond this, in the outer Helm-holtz layer (OHL ) , ions will begin to acquire the polar-

ization sheath which they would have in equilibrium inth e bulk liquid. Because the ions will have a very dif-ferent environment in the IHL and OHL from that in

the bulk, the corresponding electronic energy states will

be different. Beyond the OHL is a diffuse region, theGouy-Chapman space-charge layer, the extent of which

depends on the net charge concentration. For electrolytesthe extent might be only - o-' m bu t for insulating di-

electric liquids it could be as much as m.

1-etal liquid I

(9) (b)

Figure 9.

Conditions at a metal electrode. Liquid contact

assuming metal Fermi level El < $(E+(O)E-(0)) . (a) before and (b) after contact whenan equilibrium double layer ( - q , q ) has been es-

tablished. q is negative in the present example.

These spontaneously arising layers involve a combina-

tion of processes: ion separation from the bulk liquid,ordering of polar or polarizable liquid molecules on themetal surface, and transfer of electrons to or from th e liq-

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uid through the interface. Together with counter ‘image’

charges in the metal, an overall double layer is estab-

lished at the interface in which the electric field couldbe as much as l o 9 Vm -l . The energy level scheme de-veloped above for the electronic states in the liquid canbe used together with the familiar energy level scheme

for a metal to obtain the equilibrium electronic condi-

tions for the interface as in Figure 9. For the metal, theimportant energy states will be the occupied and emptyones in the neighborhood of the Fermi energy E f ,and for

the liquid the band of delocalized and localized negative

states, E-(O) and E-(oo) at the band edge Vo , and the

similar band of positive states E+ (O) an d E+(oo)withenergies 4 o 12 eV below. Equilibrium will require tha t

the Fermi level for the bulk liquid states (- i E + ( O ) ora pure liquid) equates to E f . For this to happen, aninterface double-layer potential difference, as described

above, will have to come into existence. For the energy

levels illustrated in Figure 9 it is necessary for there to

be a net negative charge on the liquid side of the inter-face and if negative ions were not available in the liquidthen it would be achieved by electron transfer from the

metal to the liquid. The work functions of most metals

l E f l are between 4 an d 5 eV and since IE+(O)l is like-

ly to be larger than this for the liquids of interest, thesituation shown in Figure 9 with negative charge on theliquid side of the interface is most likely. However therewill be situations where equilibrium will require positivecharge on the liquid side and the double-layer sign would

be reversed.

Conditions will change when a potential difference is

applied between t he electrodes in the liquid. At th e cath-ode negative ions and electrons in the liquid interface

will be repelled and positive ions and holes will be drawn

in from the bulk liquid. At th e same time electron in-jection into the liquid will be encouraged and will tend

to neutralize any incoming positive charge. In a similarway negative ions and electrons will be drawn to the an-ode where positive hole production will be encouraged byelectron ejection from the liquid to the electrode, tend-ing to neutralize the negative charge. The liquid is likely

to become more conductive as a result of these processes

but the converse may sometimes happen where impu-

rity ions in the liquid are swept to the electrodes and

neutralized without further action [35]. These various‘redox’ actions on the liquid molecules require electron

transfer across the potential barriers at the electrodes. If

the transfer is difficult at either electrode, the interface

becomes excessively polarized and the effective resistance

of the overall system becomes large, whatever the condi-tions in the liquid.

The accumulation of charges in the Helmholtz and

Gouy-Chapman layers a nd th e orientation of any dipolar

Figure 10.

Potential energy barrier V ( z )at a metal liquidinterface. - - - image law; . double-layer po-

tential energy for negative charge in liquid.

molecules present at the interface together with image

charges in the metal electrode will result in a net inter-facial charge q per unit area in the liquid and a countercharge -4 on the metal. The associated potential energydifference 4 across the interface will then modify, perhapssignificantly, the classical image law representation of thepotential energy barrier at a metal surface. The overallpotential energy barrier V ( z ) (represented for simplici-

ty as a function only of the distance z from the metalsurface) will be as shown in Figure 10. It should be not-ed that the image law fails within 0.1 nm or so of the

surface.

Figure 11

Potential energy barrier V ( z ) Fz at a cathodein an applied field F. Situation (a) at moderatefields and (b ) at fields > l o 8 Vm-’.

An applied potential difference between electrodes inthe liquid will modify V ( z ) t each electrode. Th e situa-

tion at the cathode is shown in Figure 11. There is now a

maximum in V( z ) which moves in towards th e metal as

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IEEE Transactions on Dielectr ics an d Electr ical Insulation Vol. 1 No. 4, Au g u s t 1994 639

the applied potential difference increases. At the high-

est fields (> lo 9 Vm-’) the maximum can be expected

to move in to within atomic distances of the metal sur-face, thereby removing the effects of the double layer andexposing the metal.

below the Fermi energy Ef with a distribution N ( E )

(Figure 1 2(a) ) while t he possible E- and E+ states liein bands given by Gaussian distributions L ( E )describedearlier. Not only must the energies of the two states beequal but their spatial separation and the magnitude of

the potential energy barrier between them is important.

The transmission probability at an energy E can be ex-

pressed as

An ion approa.ching the interface from the liquid will

have to undergo complex interactions with the surfacedouble layer which will involve not only long-range elec-- -

l l

trical forces but a.lso short-range ones resulting from the = a

necessity for structural reorganizations of the polariza-

tion shell of the ion and the surface double layer. Trace

impurities, especially of a polar nature like water, would

have a profound effect on he organization of the interfaceand the nature of the potential barrier.

p ( E ) = exp [ ~![2m(v(z) - da: (12)

where s., z2 are the two spatial positions where V(z) =E and m is the effective electron mass.

E((]).

e

+U

--+e

I E

+eC

1 I

I j E ) N(E)Figure 12.

For most liquids E - ( O ) is in the range -0.5 to $0.5 eVand E j is typically -4.5 eV so that a large potential

difference has to be generated by the double layer andany applied voltage if the two bands of states located byE - ( O ) and Er are t o overlapso th at tunneling can occur.

On the other hand neutralization of positive holes and

ions should be facile since the band of these empty statesat E+(O) may be expected to be well below Er wherethere are occupied metal states. In practice however,

structural restrictions in the double layer might preventpositive ions from approaching close enough to the metal

for tunneling to occur. In t hat case the incoming ionswould remain to st rengthen t he double layer. It should be

noted that tunneling will be influenced by temperaturebecause the widths of the bands of states in the liquid

are dependent on the temperature-dependent Gaussianfunction.

At a n anode (Figure 12(b)) the situation is tha t ox-

idation of reduced negative ion states in the liquid E -whether in the conduction band or localized should oc-

cur easily since these s tates will be opposite empty st atesof the metal above Er. Generation of positive hole or

ion states however will require the band of E+ occupiedstates in the liquid to be raised in energy by the combi-

nation of double layer and applied potentials to that of

the unoccupied metal states above Ej.

The ra te of transfer of electrons of energy E from met-a1 to l iquid will depend on N ( E ) , he density of electron

states in the metal and on L ( E ) , he density of the appro-priate electronic states in the liquid. It will also depend

on the probability fm that the metal state is occupied,on (1 - l), the probability that the liquid state is emp-

ty, and on the tunneling probability p ( E ) , (Equation (2).

Transfer in the opposite direction will depend on fl and

(1 - m ) , the probabilities that the liquid state is oc-

cupied and the metal st at e empty. In equilibrium theserates will be equal but in an applied field there will be a

Electron transfer (a) at a cathode to electronstates E- (difficult),or positive ion or hole statesE+ (easy) and, (b ) at an anode from electron or

negative ion states E- (easy) or positive hole, E+states (difficult).

Electrons injected at a cathode will need to enter ei-ther electron or negative ion E - states or reduce incom-ing positive ion or hole states E+. For these processes tooccur electron tunneling must take place between states

of equal energy in the metal and liquid interface. Th epossible metal states are essentially those with energies

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net current

m

-- M

where F , = f m ( l - i ) , Fl = f i ( 1 - m ) , which involvesall the energy sta tes. The applied field will shift theGaussian distributions L ( E )down in energy relative toN ( E ) at a.cathode and up at an anode.

Equation (13) is too general for practical usefulnessand a simpler formula, common in electrochemistry, may

be used which recognizes the role of thermal energy (man-

ifest in th e Gaussian distributions) in bringing the energylevels into line for tunneling. Thus the current of elec-trons from a cathode to reducible (negative) state s in theliquid is given by [9 ]

Values of c turn out to be unrealistically large and Feli-

ci concludes that ion accumulation on the electrodes, as

discussed above, is responsible.

In moderate applied fields the ion-creating process could1occur on the metal side of the potential maximum, V,(Figure 11), n which case subsequent movement of the

ion away from the interface is likely to be governed byfield-assisted diffusion [38] which will lead to departuresfrom the Butler-Volmer law. If the cathode is made

strongly negative, electron transfer to the liquid domi-nates and

(17)a e A 4

J -+ JO exp-cT

the Tafel equation, which predicts a thermally activated,

field-dependent current. The expression for J resembles

the classical Schottky thermionic emission law which of-ten has . been employed to represent experimental d ata

but has often yielded unrealistic physical constants forthe interface. A similar law can be developed for posi-

where ko is a rate consta.nt an d N and LO are respectively tive generation at an anode.

the concentrations of electrons in the metal a nd reduciblestat es in the liquid. The reverse current of electrons from

reduced states L , in the liquid to unoccupied metal statesP in the cathode is

J z = k,PL,exp --[ $1WO, W, are the energies necessary to bring the meanelectronic energy levels of the liquid states to the Fer-

mi energy E f . In equilibrium J1 = Ja = .To, an ‘ex-change’ current. The double layer conditions adjust toachieve this condition by developing the appropriate po-tential difference q5 across the metal-liquid interface. Ap-plication of a voltage to increase say the electron current

from the cathode causes changes, A4 (an overpotential)

in q5 and in WO and W, which become WO- aeA$ andW, + (1 - a )e Ad , respectively. The current becomes

where Aq5 is the amount by which the mean energy bar-rier for electron transfer from metal to liquid is lowered.Equation ( 1 6 ) is the Butler-Volmer law [36].

The value of Ad, is difficult to determine for insulat-

ing liquids because, unlike conditions in an electrolyte, a

major pa rt of the applied voltage appears across the bulkliquid and relatively little across the electrode interfaces.Felici [37] has discussed using A4 = az F where z s the

distance of nearest approach of the liquid molecular st at e

to the metal, a (< 1 ) is the ra tio of permittivities of thefree liquid and interface regions and F is the applied field.

The laws above apply to homogeneous electrodes whichare not likely to be obtained in practice. For example, the

local work function IEf(f the electrode will depend onthe crystallographic orientation of th e face through whichelectrons are transferring and deviations by as much as1 eV from average values can occur [39]. Thus electrontransfer processes a t elect rodes could be highly localized,an important feature in influencing electrical breakdown.In practice most metal surfaces will also have insulatingoxide and other tarnish layers [4] which could have a pro-found effect on electron transfer. On first consideration,it might be concluded that such layers at a cathode forinstance, would inhibit electron transfer but in fact they

might enhance it if positive ions or holes which come tothe interface from the liquid are prevented from being

neutralized and instead increase the local double-layerstrength. Athwal and Latham [40] have proposed that

oxide micro-regions of - l o F s m radius and thicknessm with the characteristics of an amorphous solid-

state semiconductor having many charge-trapping cen-ters and a 2 to 3 eV band gap, form Schottky barriers to

the underlying metal. Details of the application of thismodel (a similar one has been proposed by Kao [41]) toliquids have been given by Lewis [4]. At a cathode it

is plausible for electron transfer across the barrier from

metal to oxide to be enhanced considerably by positive

holes transferring from the liquid through the valenceband of the oxide to the barrier. Electrons transferredto the oxide are accelerated by the field to become ‘hot’electrons on emission into the liquid. The Lath am mod-

el predicts Fowler-Nordheim current characteristics, al-though the parameters have very different meanings. It

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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1 No. 4, August 1994 641

can be shown [4 ] tha t similar oxide layers should enhance

hole injection into a liquid at an anode.

In spite of the conditions to be expected with practicalcathodes it is interesting t o note t hat electron field emis-

sion currents of the classical Fowler-Nordheim type have

in fact been reported on several occasions, notably for

pure cyclohexane using etched tungsten electrodes withtip radii < 0.5 pm [30]. It is then possible to obtainfields in excess of 2x10’ Vm-I in the immediate neighbor-

hood of the tips, a condition necessary to induce Fowler-

Nordheim emission. Wit h such fields the maxim um V

(Figure 11) is likely to have moved inside the IHL so that

the double layer on the electrode is no longer affectingelectron transfer. Assuming tha t only the classical im-age law remains, the V, would be < 5 x lo-‘’ m from

the metal surface and at an energy of - 2 .5 eV below

th e Vo zero field level. Since in the Fowler-Nordheim lawthe effective work function would be I E j J+ V , a correla-tion between V , and the onset voltage for field emission

would be expected, as indeed Bonifaci et al. 1321 have

demonstrated clearly.

The space-charge layer on an electrode is likely to be a

source of electrohydrodynamic forces. The sudden appli-

cation of a field will move at least par t of the homochargein this layer out into the liquid as well as possibly in-

jecting new charges. Both processes would imp art mo-

mentum t o the liquid an d generate electrohydrodynamicinstabilities. Jayaram and Cross [42] have presented ev-

idence to show tha t it is the charges pre-existing in theOHL and Gouy-Chapman layers which are responsiblefor the instability rather than charge injection from the

electrode. Th e injected momentum leads to transient en-hanced ion mobility and conductivity. The full review of

these electro-hydrodynamic effects by Atten [34] already

has been mentioned.

However, in considering the mechanical processes thatmight accompany electrical stresses in liquids, one inter-facial mechanism has not been considered hitherto. It isthe Lippmann electrocapillary effect in which a changeqAq5 in the energy associated with a n interface, as might

be caused by the application of a field, can be relateddirectly to an interfacial mechanical strain. Such effectshave been measured recently in a number of polar and

nonpolar liquids [ 4 3 , 4 4 ] . The strain would add to thedisturbance of the double layer and would be a source of

pressure waves in the liquid, which have often been ob-

served under high-field incipient breakdown conditions.

5. CONCLUSIONST has been demonstrated that a common elec tronic en-

I rgy state scheme, which will describe electron transfer

not only through a dielectric liquid but also through the

cathode and anode interfaces when the liquid is put under

electrical stress, can be employed. The concepts involved

are those of the electronic amorphous solid state and ofredox electrochemistry except th at the liquid, instead of

being a highly ionized electrolyte capable of supportingonly a weak electric field, is initially hardly ionized at all.Redox processes are induced only by resort to consider-

able overpotentials. The Gouy-Chapman diffuse layer,which, in an electrolyte, is confined to a region extend-

ing perhaps only lo-’ m from an electrode, is, in aninsulating liquid, much more extensive and a significant

electric field exists right through the liquid. Felici [37]

in particular has drawn at tent ion to t he usefulness of us-

ing electrochemical concepts in seeking to underst and thebehavior of insulating liquids under high electrical fields.

The combined electrochemical and amorphous solid-state

electronic models provide a firm basis for exploiting theelectrical properties of dielectric liquids in an intelligent

REFERENCES

N. J . Felici, “A Tentative Explanation of theVoltage-Current Characteristics of Dielectric Liq-

uids”, J. Electrostatics, Vol. 12 , pp. 165-172,

1982.

N. J. Felici, “High Field Conduction in DielectricLiquids Revisited”, IEEE Trans. Elec. Insul., Vol.

T. J. Lewis, “Electronic Processes in DielectricLiquids under Incipient Breakdown Stress” IEEETrans. Elec. Insul., Vol. 20, pp. 123-132, 1985.

T. J . Lewis, T he Liquid Stat e and it s Electrical

Properties, pp. 431-453, E. E. Kunhardt, L. G .

Chrisophorou and L. H. Luessen, eds. Plenum

Press, New York, 1987.

W. F. Schmidt, “Electrons in Non-polar DielectricLiquids”, IEEE Trans . Elec. Insul, Vol. 26, pp. 560-

567, 1991.

W. F. Schmidt, “Electronic Conduction Processes

in Dielectric Liquids” , IEEE Trans. Elec. Insul.,

E. 0 . Forster, “Progress in the Field of Electric

Properties of Dielectric Liquids” , IEEE Trans.

Elec. Insul., Vol. 25, pp. 45-53, 1990.

N. R. Kestner, The Liquid State and its Electri-

cal Properties, pp. 143-172. E. E. Kunhardt, L.G. Christophorou and L. H. Luessen, eds. Plenum


S. R. Morrison, Electrochemistry a t Semiconductorand Oxidised Metal Electrodes, chap. 1, Plenum


20, pp. 233-238, 1985.

Vol. 19 , pp. 389-418, 1984.

7/27/2019 00311706



[lo]E. A. ilinsh, Organic molecular crystals, Springer-Verlag, Berlin, 1980.

[ll] R.A. Holroyd, S. Ta,mes and A. Kennedy, “Effectof Temperature on Conduction Band Energies ofElectrons in Non-polar Liquids”, J. Phys. Chem.,

[12]R.A. Holroyd, The liquid State and its ElectricalProperties, pp. 221-233, E. E. Kunhardt, L. G .Christopherou and L. H. Luessen, Plenum Press,

New York, 1987.

[13] . Jortner and A . Gaathon, “Effects of Phase Den-

sity on Ionization Processes and Electron Localiza-tion in Fluids”, Can. J. Chem., Vol. 55,pp. 1801-

1819, 1977.

[14]P. Kebarle, W. R. Davidson, M. French, J . B. Cum-

ming and T. B. McMahon, “Solvation of Nega-tive Ions by Protic and Aprot ic Solvents: Infor-mation from Gas Phase Ion Equilibria Measure-

ments”, Fa.rad. Disc. Chem. Soc., Vol. 64, p. 220-

229, 1977.

1151 A. A. Bala.kin, B. J. Kunnasarov and B. S. Yakolev,“Formation of Cluster Ions 02-(HzO) and Con-(HzO) in Water Solutions in Non-polar Liquid”,Proc. IEEE 11th Int. Conf. on Conduction andBreakdown in Dielectric Liquids, pp. 81-85,BadenDattwil, Switzerland, July, 1993.

[16]T. J . Lewis, “Mechanism of Electrical Breakdown

in Saturated Hydrocarbon Liquids”, J . Appl.

[17]K. Hiraoka. and W . H. Hamill, “Characteristic En-

ergy Losses by Slow Electron Impact on Thin FilmAlkanes at 77” K”, J. Chem. Phys., Vol. 59,pp.

[18]G. R. Freeman, The liquid St ate and i ts Electrical

Properties, pp. 251-272, E. E. Kunhardt, L. G.Christophorou and L. H. Luessen, Plenum Press,

New York, 1987.

[19]W. F. Schmidt, “Eiectron Mobility in Non-polarLiquids: the Effect of Molecular Structure, Tem-

perature and Electric Field”, Can. J. Chem., Vol.

[20] K. Fueki, D-F. Feng an d L. Kevan, “A Seri-

empirical Estimate of the Scatte ring Cross-sectionand Mobility of Excess Electrons in Liquid Hydro-carbons”, Chem. Phys. Lett., Vol. 13,pp. 616-618,1972.

[21]T.Kimura, Y. akai, H. Tagashira and S. Naka-

mura, “Fast and Slow Electrons in Liquid Argonand Nitrogen Mixtures”, Proc. IEEE. 11th. Int.

Conf. on Conduction and Breakdown in Dielectric

Vol. 79, p. 2857-2861, 1975.

Phys., Vol. 27,pp. 645-650, 1956.

5749-5757, 1973.

55,pp. 2197-2210, 1977.

Liquids, pp. 116-120,Baden-Dattwil, Switzerland,July, 1993.

[22] A. F. Borghesani, S. Cerdonio, E. Conti, R.Onofrio, G. Bressi and G . Carugno, “ExcessElectron Molbility in Liquid Xe - Ar Mixtures”,Proc. IEEE. 11th. Int. Conf. on Conduction and

Breakdown in Dielectric Liquids, pp. 106-110,

Baden- Da wil, Swi tzerland, July, 19 93.

[23]L. I. Schiff, Quan tum Mechanics, 2nd. ed.,

McGraw-Hill, New York, 1995.

[24]R Mehnert, 0. rede, J. Bos and W. Naumann,“Transferof the Positive Charge in Non-polar Liq-uids Studied by Pulse Radiolysis”, J. Electrostat-ics, Vol. 12,pp. 107-114, 1982.

[25] . M. Warman, M. P. De Haas and A. Hummel,

“The Mobilities of Electrons, Holes and Molecu-lar Ions in Liquid Cyclohexane and Trans-Decalin” ,Conf. Record, 9th . Int. Conf. on Conduction and

Breakdown in Dielectric Liquids, pp. 44-49, Sal-

ford, U. K., July, 1987.

[26]H. Faidas, L. G. Christophorou and D. L. Mc-Corkle, “Electron Transport in Fast Dielectric Liq-uids at High Applied Electric Fields”, EEE Trans.Elec. Insul., Vol. 26,pp. 568-573, 1991.

[27] J . L. Magee, “Electron Energy Loss Processesat Subelectronic Excitation Energies in Liquids”,

Can. J. Chem., Vol. 55,pp. 1847-1859, 1977.

[28]R.A. Holroyd, B. K. Dietrich and H. A. Schwarz,“Ranges of Photoinjected Electrons in Dielectric

Liquids”, J. Phys. Chem., Vol. 76, pp. 3794-3800,

1972.

[29]S. E. Derenzo, T. S. Mast, H. Zaklad and R. A.Muller, “Electron Avalanche in Liquid Xenon”,

Phys. Rev., Vol. A 9,pp. 2528-2591, 1974.

[30]A. Denat, B. Gosse and J. P. Gosse, “ElectricalConduction of Purified Cyclohexane in a Divergent

Electric Field”, IEEE Trans. Elec. Insul., Vol. 23,

[31]M. Brouche, J P. Gosse and B. Gosse, “High Field

Conduction in Aromatic Hydrocarbons”, Proc.IEEE. 11th. Int. Conf. on Conduction and Break-

down in Dielectric Liquids, pp. 96-99, Baden-

DBttwil, Switzerland, Ju ly, 1993.

[32]N. Bonifaci, A. Denat and V. M. Atrazhev, “WorkFunctions for a HV Cathode in Non-polar Liq-

uids”, Proc. IEEE. 11th. Int. Conf. on Conductionand Breakdown in Dielectric Liquids, pp. 367-371,

Baden-Dattwil, Switzerland, July, 1993.

[33]V. M. Atraehev, E. G. Dmitriev and I. T. Iakubov,“The Impact Ionization and Electrical Breakdown

pp. 545-554, 1987.

7/27/2019 00311706


I E E E Transactions on Dielectrics and Electrical Insulation Vol. 1 No. 4, August IQQ4 643

Strength for Atomic and Molecular Liquids”,

IEEE. Tra.ns. Elec. Insul., Vol. 26, pp. 586-591,

1991

[34] P. Atten, “Electrohydrodynamic Instability and

Motion Induced by Injected Space Charge in In-sulating Liquids”, Proc. IEEE. 11th. Int. Conf. on

Conduction and Breakdown in Dielectric Liquids,

pp. 20-29, Ba.den-Dattwil, Switzerland, July, 1993.

[35] S. Barret, F. Gaspard and F. Mondon, “Monitor-ing of Injection Processes in Dielectric Liquids”, inConduction and Breakdown in Dielectric Liquids,

pp. 94-97, J. M. Goldschvartz, ed., Delft Universi-

ty Press, Delft, Netherlands, 1975.

[36] J. O’M. Bockris and A. K. N. Reddy, Modern

Chemistry, Vol. 2, chap. 8 , Plenum Press, NewYork, 1970.

[37] N. J. Felici, “High Voltage Conduction in Liquid

Dielectrics and Conditions at the Compact DoubleLa.yer”, Compt. Rend. Seances Acad. Sci. Paris,Ser. 2 , Vol. 296, pp. 523-528, 1983.

[38] K. P. Charle and F. Willig, “Generalised One-

dimensional 0nsa.ger Model for Charge Carrier In-jection into Insulators”, Chem. Phys. Lett., Vol.

[39] A. Hamelin, Modern Aspects of Electrochemistry,

chap. 1 , B. E. Conway, J. O’M. Bockris and R.White, eds., Plenum Press, 1986.

57, pp. 253-258, 1978.

[40] C. S. Athwal and R. V. Latham, “Switching andOther Non-linear Phenomena Associated with Pre-

breakdown Electron Emission Currents”, J. Phys.

[41] K. C. Kao, “New Theory of Electrical Dischargeand Breakdown in Low Mobility Condensed Insu-

lators”, J . Appl. Phys.. Vol. 5 5, pp. 752-755, 1984.

[42] S . Jayaram and J. D. Cross, “Influence of ElectrodeProcesses on Transient Conduction Phenomena inNon-polar Liquids” , J. Electrostatics, Vol. 29, pp.

[43] T. J. Lewis, J. P. Llewellyn and M. J. van der Slui-js, “Electrokinetic Properties of Metal-dielectric

Interfaces”, IEE Proc. A Vol. 140, pp. 385-392,

1993.

[44] T. J. Lewis, J. P. Llewellyn and M. J. van der Slui-

js, “Liquid Motion Induced by Electrocapillary Ac-tion a t Solid Metal-liquid Interfaces”, J. Coll. Inter.

Sci., Vol. 162, pp. 381-389, 1994.

D. Appl. Phys., Vol. 17, pp. 1029-1043, 1984.

55-72, 1992.

This paper is based on a presentation given at the 1Ith Internation-

al Conference on Conduction and Breakdown n Dielectr ic Liquids,Baden-Ddttwil, Switzerland, July 1993.

Manuscript waa received on 30 January 1994, in final form 13 May

1994.

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