Further Study of High Field Dielectric Effects in HzO, D 2 0 and Ionic Solutions

BY ANN E. DAVIES, MARIJKE J. VAN DER SLUIJS

School of Physical and Molecular Sciences, University College of North Wales, Bangor, Gwynedd

AND

GWILYM PARRY JONES* Department of Physics,

University of Petroleum and Minerals, Dharan, Saudi Arabia

MANSEL DAVIES AND

Edward Davies Chemical Laboratories, University College of Wales, Aberystwyth, Dyfed

Received 22nd July, 1977

High field dielectric measurements of the Piekara factor Ac/E2 have been carried out for HzO and D20 at 293 K and as a function of temperature, and also in the case of HzO in the presence of small amounts of added electrolyte (KCI). The value of ( -A&/E2) at 293 K for both HzO and DzO was found to be (0.8k0.12) x m2 V-2. ( -Ac/E2) for both HzO and DzO was found to follow a 1 IT3 temperature dependence. Both sets of data indicate agreement between the measured values and the predicted values on the basis of the classical orientational dipolar non-linear effect. The data for the ionic solutions were found to be as expected for low conductivities, but for conductivities above about 5 x S m-I the occurrence of significant heat losses during the pulse and/or electrode polarisation effects is indicated.

Measurements of the non-linear dielectric effect (NDE), i.e., the Piekara factor ( - A&/E2), for water at room temperature were reported by Kolodziej, Parry Jones and Davies.l Measurements of the NDE in water as a function of temperature, isotope and solute were reported by Bradley, Parry Jones, Kolodziej and Davies2 Subsequent detailed measurements of H 2 0 and D20 have been carried out as a function of temperature, revealing some systematic errors in the previous measure- ments. In addition, measurements of A&/E2 for water have been carried out as a function of conductivity by the addition of small amounts of electrolyte (KCl).

EXPERIMENTAL

The equipment used for the original work by Kolodziej et al.' and Bradley et aL2 has been described by Bradley and Parry Jones.3 Details of modifications and improvements to the equipment and procedure have recently been described by Davies, van der Sluijs and Parry Jones.4

The main improvement to the equipment has involved moving the calibration capacitor from a position across the whole tuned circuit to being directly across the dielectric cell. The new arrangement is as close to a direct substitution as can be achieved. Lead effects,

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572 HIGH FIELD DIELECTRIC EFFECTS

however, still need to be borne in mind, but the use of very short connecting leads between the sample cell and the calibration capacitor makes the problem negligible below 20 M H z . ~

Another problem arises from the so-called fringe effect at the edges of the electrodes in the dielectric cell. This problem becomes apparent for the more highly conducting solutions when the diameter-to-gap ratio for the cell becomes small. The system may, however, be calibrated by means of measurements at various electrode gaps. Finally, the effect of resistive changes in the cell in the presence of high fields must be borne in mind,4 but are not serious for conductivities 0 5

The measurements were carried out at frequencies of - 10 MHz using electric field pulses in the range 5 to 40 ps. The sample temperature was controlled to + O . l K. It was found to be important to keep the stainless steel electrode surfaces highly polished to prevent spurious results. With more highly conducting solutions (involving ionic solutes) sonication of the solution prior to use was also found to be advantageous.

S m-'. The DzO (B.D.H.) had a quoted minimum isotopic purity of 99.7%. The D2O had a conductivity of - 5 x S m-l. The KCI used for the ionic measurements was of Reagent grade from BDH. As in previous work the experimental error is estimated to be - 15%.

S m-l.

The H 2 0 used was doubly distilled and deionized, having a conductivity of <

RESULTS

( -A&/E2) FOR H 2 0 AND D20 AT 293 K As explained in the experimental section various corrections have to be applied

in order to calculate the value of (- Ac/E2). Fig. 1 shows a plot of (-A€) against E2 for H 2 0 and D20 at 293 K where the conductivity was 5 x S m-l. These particular results were obtained for an electrode gap of d = 210 pm. The NDE has a good square-law dependence and the values for H20 and D 2 0 agree within the experimental error. The correction for the fringe effect is shown in fig. 2 where ( -Ac/E2) for water at 293 K is plotted as a function of electrode gap d/pm. The zero gap value corresponding to disappearance of the fringe effect is seen to be 0.8 x m2 V-2 . As a result, the value of (-A&/E2) for water at 293 K is (0.80+0.12) x m2 V-2 compared with the previously quoted value of (1.00$.0.15) x lo-'' m2 V-2.1 Measurements on D 2 0 of conductivity 5 x s m-1 gave an identical result.

FIG. E2/1014 V2 m-2

at 293 K. 1 .-Plot of -A& against E2/V2 m-2 at an electrode gap of 210 p m for H 2 0 (0) and DzO (0)

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A. E. DAVIES, M. J. V A N DER SLUIJS, G. P A R R Y JONES A N D M. D A V I E S 573

I I I I I 1 1 1 0 100 200 300 400

dlPm FIG. 2.-Plot of -(Aa/E2)/1015 m2 V2 against electrode gap d/pm for water at 293 K.

V A R I A B L E TEMPERATURE MEASUREMENTS ON H20 AND D20 The value of A&/E2 was measured as a function of temperature in the range 273

to 333 K for both H20 and D20. The variation of ( -A&/E2) with gap must also be taken into account and fig. 3 shows ( -A&/E2) against T-3/K-3 for water, for two experimental electrode gaps and also the corresponding zero gap plot. Extrapolation to infinite temperature is seen to give a value of zero for (- A&/E2) in all cases.

T3/108 K-3 FIG. 3.-Plots of -(A&/E2)/1015 m2 V2 against T3/108 K-3 for electrode gaps of 320 pm (e),

210 pm (0) and the theoretical plot for 0 pm (A). All the data are for HzO.

Fig. 4 shows a plot of ( - A & / E 2 ) for H,O and D20 against T-3,’K-3. Both samples were of conductivity 5 x S m-1 and the gaps were identical. It is seen that the data for both H20 and D20 are in close agreement (well within experimental errors) and that adherence to a P 3 dependence is good. These data are to be compared with a variable temperature plot,2 which showed a minimum in A&/E2 for H 2 0 at about 277K. Numerous measurements which form the basis of the present plot (fig. 4), however, have failed to show the existence of anything other than a good P3 dependence both for H 2 0 and D20.

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574 HIGH FIELD DIELECTRIC EFFECTS

P3/108 K-3

data are for an electrode gap of 210 pm and the line is a least squares fit (for both liquids).

The cause of the minimum at 277 K in the previous measurements is not known. The procedure outlined above which has been followed in the present set of measure- ments undoubtedly has produced more accurate values of A&/E2, but will not account for the previous apparent temperature behaviour. It is thought that the most likely reason for the 277 K minimum may have been due to insufficient time being allowed for equilibration between readings : as a result, the measurements would be affected by oscillator frequency drifts. A combination of cooling and heating runs could then account for the earlier data reported. In the present measurements, great care was taken to ensure temperature and frequency stabilization before readings com- menced.

FIG, I.-Plots of -(Aa/E’)/lO’’ m2 V-’ against P3/108 K-3 for H 2 0 (0) and DzO (0). The

MEASUREMENTS OF DILUTE SOLUTIONS O F KCl I N H20 (- A&/E2) has been measured for water to which small quantities of KCl had been

added. The molar concentrations of KC1 used ranged from 1 x to 2 x

I 1 1 I I 0 0.5 1.0 15 2.0

a/103 S m-l FIG. 5.--PIot of -(A&/E’)/10i5 m2 V-2 against conductivity u/103 S m-1 for H 2 0 containing small

amounts of KCl at 293 K.

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A E. DAVIES, M. J. V A N D E R SLUIJS , G. P A R R Y JONES A N D M. D A V I E S 575

The data are shown in fig. 5 as a plot of (- A&/E2) against conductivity in S m-l. All these data correspond to d = 0 and were taken at 293 K.

Inspection of the plot shows (- A&/E2) to be virtually constant up to a o-value of - 5 x Bearing in mind the experimental uncertainty of rt 15 %, the data are found to be reasonably constant to o = S m-l, but tending to increase for larger 0.

DISCUSSION

The new value of ( - A & / E 2 ) at 293 K for H20 and D20 of 0.8 x 10-15 m2 V-' compares with the previous value of 1.0 x 10-15 m2 V-2 . The Piekara factor for the classical NDE can be calculated from the equation

which is quoted by Kolodziej et aZ.,' and T h i i b a ~ t . ~ E corresponds to relative permittivity and is taken as 80.1 ; n is the refractive index, which has initially been taken as &(= 1.77), the lowest possible value for E , ; ,uo is the effective molecular moment of water assumed to be 6.20 x C m (i.e., 1.85 D) ; k the Boltzmann constant ; T the absolute temperature is 293 K ; N is the number of dipoles per unit volume (m3)>; go the permittivity of free space, and Rs the non-linear field effect correlation factor defined by Piekara and Kielich.8 As pointed out in the previous paper Rs z R; where RP is the low field dipole correlation factor and is essentially equal to the Kirkwood g-factor, which, for the four-coordinated tetrahedral pattern of H,O molecules in water,9 can be taken as 2.68. Substituting the above values and Rs = R; = 19.3 into eqn (1) gives a ( - A & / E 2 ) value of 0.8 x 1O-l' m2 V-'. It is seen, therefore, that the new experimental value of A&/E2 is identical with the theoretically calculated value, although the agreement is fortuitous in view of the experimental uncertainty of 15 %. The data, therefore, are consistent with this theoretical representation.

In eqn (1) the factor in braces is the internal field expression relevant for the non- linear effect. In appropriate instances the measurement of the latter (NDE) can provide excellent discrimination between alternative theoretical expressions for the internal field factor.1° In the present case there are limitations to the discrimination possible if only because all that can be evaluated from the static measurement of &(water) is the factor RP . pg =g . ,u& The values used above are those usually accepted on the basis of the Onsager-Frohlich internal field and the g-value of Kirk- wood," the latter being evaluated on the assumption that ,uo(H20) is not significantly different for the molecules in the liquid from its value in the gaseous state. There are general grounds for accepting the essential correctness of this assumption.

However, another factor which comes into question is the value of n2, which should be that found in the infrared at the termination of the absorption arising from the angular reorientation of the H20 molecules. Owing to the extensive absorption due to the librational motion of the water molecules, it is now well understood that this n2 cannot be equated to for the Debye microwave dispersion (i.e., 4.65) l2 and n2 = 1.85 has been suggested,13 corresponding to the value for water near ij = 400 cm-'. A check on this is possible. If the value n2 = 2.0 is used in eqn (1) with the other factors unchanged, then (- A&/E2) increases by 26 per cent above its value for n2 = 1.77.

Many assumptions are involved in any current quantitative account of the dielectric properties of water. Very probably the most dubious in the present evalua-

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576 HIGH FIELD DIELECTRIC EFFECTS

tions are the acceptance of p0(H20) as the vapour value and the approximations involved in writing g = 2.68 : these become acceptable by keeping Occam’s razor in mind. On this basis, and within the +15 per cent significance of our data, two deductions are not inconsistent with the observations: (i) up to lo7 V m-1 water behaves as a polar medium with molecules of constant polarizabilities and dipole moments; (ii) the n2 value of the Onsager and other dielectric equations [e.g., our eqn (l)] is not the E , of the Debye dispersion process and is probably (because 26% > 15 %) below 2.0.

Conclusion (i) finds further support in the fact that the variable temperature data follow a 1/T3 dependence as shown in fig. 4. A least-squares-fit procedure on the data in fig. 4 gave identical slopes (to well within experimental error) and an intercept of zero at infinite temperature in both cases. As a result, the data are seen to be in agreement with the predictions from eqn (I), the model for which is seen to hold over the temperature range 273-335 K.

Coffey and Scaife l4 give an equation for the Piekara factor :

R1 and R2 are defined by Coffey and Scaife l4 and the other symbols have their previous meaning.

Using the previous value of ,u, etc., and the experimental value of (- A&/E2) of 0.8 x 10-15 m2 V-2 in eqn (2) gives what is effectively an R, of 24.3 compared with an R, = 19.3 (= It;) from eqn (1).

The relatively constant value of A&/E2 for very dilute KCI solutions up to a con- ductivity of - S m-1 is consistent with the very small concentration of Kf and C1- ions present. Even for the maximum concentration, the ratio of ions to water molecules is only a few parts per million. Assuming a hydration shell of 5 water molecules per ion l5 and a consequent loss of a contribution to A&/E2 from these molecules gives a decrease in the classical NDE of - 1 in lo5. From this simplistic point of view A&/E2 should remain virtually constant over the range of coiicentrations used. The tendency for (- A&/E2) to become numerically larger at conductivities above - S m-1 could be due to a number of causes. Wiih increasing con- ductivity the heat generated during the pulse will increase. Previously, it has been assumed that there is no significant heat loss during the pulse, i.e., that the total heat generated is siill present in the measured sample after the pulse. With higher con- ductivities any loss of heat during the pulse will become more significant and could partially explain the increase in (- A&/E2) as being due to an insufficient correction as calculated from the measured heat following the pulse. The heat loss would be due to diffusion into the water outside the electrode gap and also to transmission into the steel electrodes. Calculations for typical dimensions indicate the heat loss via the electrodes to be - 50% higher than via the water.

Another factor which assumes increasing importance with conductivity is the electrode polarization effect. Whenever the potential and charge distribution of an electrode are abruptly changed, corresponding changes occur in the composition and structure of the diffuse double layer at the electrode. Experiments with dilute electrolytes have revealed that the concentration and charge distribution are dis- turbed at distances far greater than the equilibrium thickness of the double 1ayer.l’ To achieve equilibrium, this over-extended layer must contract as neutral salt with a characteristic time z = L2/D, where L is the distance over which the disturbance extends and D the salt diffusion coefficient.18

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A. E. DAVIES, M. J. VAN DER SLUIJS, G. PARRY JONES AND M. DAVIES 577

When the electrodes are charged by a potential of 1 kV for lops, it is a good approximation to assume that the K+ and C1- ions move with equal velocities in opposite directions (since their mobilities are essentially equal - 7 x lo-* m2 s-l V-I). If the potential is applied across 250pm, then it follows that during the charging process virtually all of the C1- ions which were within 3 ,urn of the cathode surface have been driven away, and an equal number of K+ ions will have entered. Similarly, K+ ions will be driven from the anode to be replaced by C1- ions. The salt diffusion coefficient for KCl is - 2 x m2 s-l and hence the characteristic time for the attainment of electroneutrality is - 4.5 ms.

The observed increase in (-A&) at higher KCl concentrations is about 0.1 in a field of lo7 V m-l, which may be equated to a change in capacitance AC of - 0.1 pF. If this effect were due to electrode polarization it would involve removal of a few parts per million of the ions present in the electrode gap and hence would not affect the conductivity.

Note the behaviour of ( -A&/E2) (following the pulse) as a function of time. Fig. 6 shows the presence of two distinct time constants. The long time constant of 80 ms must correspond to temperature equilibration, while the initial decay with a time constant of N 5 ms would seem to be consistent with ionic migration effects discussed above.

1.0

N

0.5 “E

I

0.1 4 0 20 10 60 80

tlms FIG. 6.-Plot of Ac/E2 (following a 15 ps pulse)/l0l5 m2 against time. The sample was a

solution of KCI in water of conductivity 0.995 x S m-’ at temperature 293 K.

This work was supported by an S.R.C. grant. One of us (A. E. D.) wishes to express her gratitude to the S.R.C. for a research studentship held during the course of the work.

H. Kolodziej, G. Parry Jones and M. Davies, J.C.S. Faraday 11, 1975,71,269. P. Bradley, G. Parry Jones, H. Kolodziej and M. Davies, J.C.S. Faraday 11, 1975, 71, 1200. P. Bradley and G. Parry Jones, J. Phys. E., 1974, 7,449. A. E. Davies, M. J. van der Sluijs and G. Parry Jones, in press. ’ C. T. O’Konski and A. Edwards, Rev. Sci. Instr., 1968, 39, 1456. J. C. Lestrade, J. P. Badialli and H. Cachet, in Dielectric and Related Molecular Processes (Specialist Periodical Report, The Chemical Society, London, 1975), vol. 2. ’ J. M. Thikbaut, Thtse de 38me cycle (Nancy, 1968).

* A. Piekara and S. Kielich, J. Phys. Radiation, 1957, 18, 490. N. E. Hill, W. E. Vaughan, A. H. Price and M. Davies, in Dielectric Properties and Molecular Behaviour (Van Nostrand, London, 1969) chap. 1, p. 34.

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578 HIGH FIELD DIELECTRIC EFFECTS

lo ref. (9), pp. 18-34. l1 M. Davies, Electric and Optical Aspects of Molecular Behuviour (Pergamon Press, London, 1964). l2 M. Davies, Ann. Rep. Chem. Soc., A, 1972. l3 A. D. Buckingham, Disc. Furaduy Soc., 1967,43,208,238. l4 W . T. Coffey and B. K. P. Scaife, Proc. Roy. Irish Acud., 1976, 76, A195. l5 G. H. Haggis, J. B. Hasted and T. J. Buchanan, J. Chem. Phys., 1948,16,1. l6 G. Parry Jones and T. Krupkowski, J.C.S. Furaduy 11, 1974,70, 862. '' F. C. Anson, R. F. Martin and C. Yarnitzky, J. Phys. Chem., 1969, 73, 1835.

J. Newman, J. Phys. Chem., 1969, 73,1843.

(PAPER 7/1322)

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