Electron and proton conduction in ice

Journal of Electrostatics, 12 (1982) 115--122

115

Elsevier Scientific Publishing C o m p a n y , A m s t e r d a m - - P r i n t e d in The Netherlands

ELECTRON AND PROTON CONDUCTION

IN ICE

John M. Warman, Marinus Kunst and Mattbijs P. de Haas Interuniversity

Reactor Institute, Mekelweg

15, 2629 JB Delft, The Netherlands

Johan B. Verberne Biophysics

Department,

Free University,

Amsterdam,

The Netherlands

INTRODUCTION The conduction of ice on irradiation produced

H20

in the following

>H20

H2 O+ + H20

can be described with the charge carriers

initial processes:

+ e

(I)

> H3 O+ + OH

(2)

Both the electrons

formed in (1) and the protons formed rapidly by proton transfer

+

from H20

in (2) are capable of movement

electrons

can take place via a delocalised

considered to move via a Grotthuss

in an electric

type mechanism which involves

of a proton along a hydrogen bond to a neighbouring positive

charge transport

of

successive

H20 molecule.

Negative

jumps and

can therefore take place in the rigid lattice without

necessity of moving whole molecules of the charge carriers

field. Displacement

or conduction band state. Protons are

through the medium.

and their interactions

the

A summary of the properties

with the lattice is given.

EXPERIMENTAL For the DC conductivity coaxial electrode

experiments

ice was grown in a 5 cm long cell with

geometry by slow immersion into a bath at -12°C. The radii of

the inner and outer electrodes were r I = 0.085 cm and r 2 = 0.27 cm respectively. The cell was pulse irradiated with X-rays produced by irradiation with 3 MeV electrons

from a Van de Graaff accelerator.

0.5 ns long (beam charge

1 nC) and resulted in a total dose of approximately

This dose was low enough to exclude both the possibility effects and the occurrence measurements.

of a Pt target

The X-ray pulse used was

of homogeneous

recombination

Because of the coaxial cell geometry,

give respectively

convex and concave current-time

only to discharge

at the electrodes.

0304-3886/82/0000--0000/$02.75

of appreciable

8 mrad.

space charge

on the timescale of the

inward and outward moving ions

curves when loss of ions is due

In the present experiments

the polarity

© 1982 E~e~er Scientific Publishing Company

116 of the applied voltage on the outer electrode was changed while the inner electrode was connected to an amplifier. elsewhere

(refs.

The technique

and data evaluation

for the increase in the yield of separated

ions due to application

The low field linear form of the field strength treatment

are described

],2) and have only been changed in that a correction has been made

dependence

(ref. 3-5) has been assumed to be applicable.

found to be obeyed for low fields in non polar liquids zero field is small. The enhancement by Vd, the applied voltage

of the field.

derived from the Onsager

This dependence has been for which the yield at

of the yield by the field is characterized

for which the initial yield is twice the yield at

zero field. For coaxial cell geometry,

in the low field linear region V d is given

by r, r~In2~r2~ J z

e T2

\rl/

r

vd =

(3)

(r2-r l)

9.64

where g

is the effective r the temperature in °K.

relative permittivity

for the recombination

and T is

For the condition that one charge carrier has a mobility much larger than the other ionic species present,

the following equation

for the transient

currents

can be derived

2~LpeVN ° i(t) = (_])m

with,

ln(

In() - - - -

\r]/

for inward movement

V rn(r m - a) exp (- t)

+

(4)

V d a(r2-r I)

of the charge carrier

m = I, n = 2 and a = ~ r22 - 2pVt/in (r~l') and for outward movement m = 2, n = I and a = ~ r l 2 + 2~Vt/in

(r)

In (4) L is the length of the cell, p is the mobility the electronic

charge

V is the applied voltage, N

of the charge carrier,

e is

is the initial concentration O

of charge carriers in the absence of a field and T is the decay time due to disappearance processes dose of approximately

other than draw-out by the field

For the

8 mrad per pulse used, taking a yield at zero field of l

escaped ion per 100 eV (G value = I)

the concentration N '

For the microwave experiments band waveguide

(e.g. trapping).

would be 4 x 109 cm -3 O

ice was grown in a short-circuited

piece of X-

containing triply distilled water by slow immersion into a bath

at -12°C. The sample was pulse irradiated with 3 MeV electrons

from a Van de Graaff

117

accelerator

using pulse widths

from 0.5 to 50 ns (0.7 to 70 nC beam charge)

total doses from )0 to )000 rads. The change in conductivity the sample was monitored by measuring

and

on irradiation of

the change in the power level of microwaves

reflected by the sample. The technique and the method of evaluating the data obtained have been described elsewhere

(ref. 6).

RESULTS AND DISCUSSION Electron transport Fig.

(DC measurements)

| shows current transients

-65°C with applied voltages

resulting from pulse irradiation of ice at

of +2500 V and -2500 V on the outer electrode.

The

initially more rapid decay of the current with the positive voltage on the outer electrode

is a clear indication

ice is negatively

that the major charge carrier in pulse irradiated

charged and hence a conduction electron.

"G c-

t..

O o

v

>

tO L~

0

i

a

!

0

a

|

I

!

i

i

I00

200

Time (ns) Fig. I. The change in conductivity observed on irradiation of ice with a 500 ps pulse (8 mrad) as a function of time at -65°C. The points marked + refer to an applied voltage of +2500 V and the points marked 0 to an applied voltage of -2500 V. The curves have been calculated using equation (4) with, for both polarities, T = 50 ns and V. = 2500 V corresponding to gr = 3.2. The three lower curves for the positive polarity were calculated using mobility values in cm2V-ls -| of 10, .... ; 25, ; and 40, ..... . The upper two curves were calculated using mobility values of |0, ---; and 40, ..... . As can be seen in fig. curves)

|, the current transient due to outward movement

is expected to be much more sensitive to the absolute magnitude

(lower

of the

118

mobility.

It is apparent

that a value of lO cm2V-Is -I results in a decay which is

much slower than observed and that for 40 cm2V-Is -l a somewhat too rapid decay is calculated. 25

± In

It may be concluded that the electron mobility

10 c m 2 v - l s fig.

-1

2 are

voltages.

at

lies in the range

-65°C.

shown

conductivity

transients

obtained

for

different

The effect of field on the initial yield of electrons

the increase of end-of-pulse

conductivity

appiied

is apparent as

per applied voltage with increasing

applied voltage.

t x

"'~ x

1

',X

~

".X ...'XX

I

%x

+

0.~'--.

+~

0c

;->..x

- +21~..¥.

-o2~co_

~

-~-v::-O~O=O="O= O ~ ,

i

i

0

i

i

i

,

,

i

I00

200 Time

(ns)

Fig. 2. The change in conductivity observed on irradiation of ice with a 500 ps pulse (8 mrad) as a function of time at -65°C. The applied voltage on the outer electrode is -500 V, O, -2000 V, +, -3000 V, x. The full and dashed curves have been calculated for V d = 1500 and 2500 Volts respectively, with T = 50 ns and = 25

cm2V-ls -1 .

By slightly varying zero field, reasonable which corresponds

(by approximately

to g

infrared frequencies

= 2, the value of the relative permittivity of ice at r or V d = 2500 V which corresponds to gr = 3.2, the value of

the relative permittivity

Electron transport

30%) the value of the initial yield at

fits to the data can be obtained using either V d = 1500 V,

of ice at microwave

frequencies.

(Microwave measurements)

Fig. 3 shows the transient

conductivity

induced by 500 ps pulses

(10 rad) for

119 temperatures

from -60 to -20°C. These results can be explained by formation of the

highly mobile conduction electrons and afterwards

localisation at pre-existing

trapping sites in the lattice.

e

-

kTNT >

+ T

eT

-

(5)

The trapping reaction is seen to be strongly thermally activated. At lower temperatures

(< -60°C) recombination with products

formed concurrently in the

pulse, presumably mainly the proton, becomes the predominant pathway for disappearance of electrons for the radiation intensities used. -

e

+

+ H30

(6)

I% products

I

=7

=0o=

4

I

"

I

I

-60°C

E

.-_c~ .->~1"

"°i f,

o

0

5

I0

15 Time (ns)

Fig. 3. The change in conductivity per nanocoulomb observed on irradiation of ice with a 500 ps pulse (I0 rad) as a function of time at the temperature (°C) shown. The lines were calculated with a simple trapping model (eqs. (I) and (5)). The initial after-pulse

conductivity gives, after correction for decay during

the pulse, the parameter G(e-)~(--), where G(e-) is the yield of electrons per I00 eV absorbed and ~(e-) is the mobility of the electron.

The value found is

5 cm2V-Is -I (I00 eV) -I at -50°C with indications of a small increase with decreasing temperature.

As it is known that G decreases with decreasing tempera-

120 ture this points to a negative It has been argued

activation energy for the free electron mobility.

(ref. 7) that the most probable

in ice is a vacancy possibly

trapping site for electrons

combined with a Bjerrum orientational

D-defect.

activation energy of the trapping rate kTN T is about 0.55 eV and is thought result to a large extent from the activation the defect responsible

for localisation.

The to

energy required for the formation of

From optical measurements

(ref. 8) the

mean time for the ingrowth of the absorption due to the solvated electron has been determined

to be about 400 ps at -5°C. The difference between this time and the

localisation

time of about 80 ps at the same temperature

if it is assumed that the solvation of electrons

e

kTNT)

+ T

Combined evaluation of localised

ks%

eT -

electrons

(ref. 7) can be explained

occurs in two steps as follows:

esol

(7)

of optical and microwave

data indicates

that also reemission

into the conduction band should most probably be taken

into consideration

k_ T >

eT

e

(8)

+ T

The solvation rate kso 1 h a s

an activation

energy

of

about

0.3

eV a n d

is

2 x 10 9 s - l

at -5°C.

Proton transport From the above it can be concluded solvated

in less than a nanosecond.

low level conductivity

that electrons

Despite

that this is due to proton conduction

conductivity,

slowly decaying, It is suggested

(ref. 9). This signal is found to decay

initial signal) which further decreases From the after-pulse

this a relatively

transient remains after a 50 ns pulse.

over a period of a few hundred nanoseconds

to a much lower level (10-20% of the

over microseconds.

after correction +

pulse,

in ice above -30°C are

(See insert fig. 4.)

for decay during the

+

one can derive the parameter G(H )M(H ), where G(H +) is the yield in ions

per 100 eV absorbed this parameter

and M(H +) is the mobility of the "bare" proton.

The value of

is 6.4 x 10 -3 cm2V-Is -I (100 eV) -l at -5°C and shows a slight in-

crease of about

10% between -5°C and -30°C. Taking the yield of protons to be -I equal to the yield of solvated electrons of ca l (100 eV) found in optical pulse radiolysis measurements

(ref.

10) results

in a mobility

of about 6 x 10-3 cm2V-Is -I

at -5°C. Since the yield of solvated electrons a pronounced negative

decreases

increase in M(H +) with decreasing

considerably

temperature,

from -5 to -30°C

corresponding

activation energy of at least 0.15 eV, is indicated.

to a

This can be best

121

io.6

H 0 %~.''2"

•

~

•

~

_............

~, ~1

E o

3

0 0 0

-~, o ~

,,\l\

10.7

r-

\

0

C

(A)

~

Z,',4 ~

mo Time(n$)

o',o

.--~--a ~ a ~

200

1 \_

ooc -

~T E ._> T

3 cO (.~

10-8 0

I00

200 Time (ns)

Fig. 4. Logarithmic plot irradiation with a 50 ns after subtraction of the per nanocoulomb observed

of the change in conductivity per nanocoulomb after pulse (1 krad) at -4.5°C, @; -]8°C, O; and -30°C, l, equilibrium level. Insert: The change in conductivity after irradiation with a 50 ns pulse (1 krad) at -4.5°C.

explained by small polaron band transport, i.e., concerted movement of charge and lattice deformations as discussed previously (ref. 9). The initial decay is independent of the charge in the pulse and can be attributed to a pseudo unimolecular reaction of "bare" protons with preexisting trapping sites. The most likely candidates are Bjerrum orientational L-defects which carry a partial negative charge + H30

+ L

kLNL . ~

+ H30 L.

(9)

The equilibrium level attained after a few hundred nanoseconds can be ascribed to the reverse reaction. Fig. 4 shows the first order decay of the proton conduction after subtraction of this level. The activation energy of the trapping

122

rate kLN L is found to be 0.3 eV. If polarization effects can be neglected, then the complexing of bare protons + with L-defects will result in a net drift mobility ~(H ,~), given by

+

[H30+]

~(H ,~) = M(H +)

= M(H +)

1

(10)

kLN L 1+-k_ L

[H 0 +] + [H30+L] 3

Since kLNL/k_L is found to be 7 at -5°C, this yields a value of 8 x 10-4 cm2V-ls -I for ~(H+, ~) at this temperature. The eventual slow decay of protons occurs on the same timescale as observed for the decay of the solvated electron absorption (ref. I0) and is therefore at least partially ascribed to the recombination reaction: + H30

+ eso I

> products.

(II)

REFERENCES 1

A.O. Allen, M.P. de Haas and A. Hun~nel, J. Chem. Phys., 64 (1976) 2587, where a printing error in formula 16b should be corrected and the right formula is as follows: Iri

= (2~) -1 I n /rl

2 3 4 5

+ t ~d

1 -

. rl

//

M.P. de H a a s , T h e s i s , L e i d e n , 1977 L. O n s a g e r , P h y s . R e v . , 54 (1938) 554 G.R. F r e e m a n , J . Chem. P h y s . , 39 (1963) 1580 A. Hur~nel, i n M. B u r t o n and J . L . Magee ( E d s . ) , A d v a n c e s i n R a d i a t i o n C h e m i s t r y , V o l . 4, W i l e y - I n t e r s c i e n c e , New Y o r k , ] 9 7 4 , pp 1-102 6 P.P. Infelta, M.P. de Haas and J.M. Warman, R a d i a t . P h y s . C h e m . , 10 (1977) 353 7 J.M. Warman, M.P. de Haas and J . B . V e r b e r n e , J . P h y s . C h e m . , 84 (1980) ]240 8 J.M. Warman and C.D. J o n a h , Chem. P h y s . L e t t e r s , 79 (1981) 43 9 M. K u n s t and J.M. Warman, N a t u r e , 288 ( t 9 8 0 ) 465 l0 G. N i l s s o n , H. C h r i s t e n s e n , P. P a g s b e r g and S.O. N i e l s e n , J . P h y s . C h e m . , 76 (1972) I000