High Field Dielectric Measurements in Water

BY H. A. KOkODZIEJt AND G. PARRY JONES* School of Physical and MoIecular Sciences,

University College of North Wales, Bangor, Gwynedd

MANSEL DAVIES Edward Davies Chemical Laboratory, University College of Wales,

Aberystwyth, Dyfed

AND

Received 6th June, I974

High field dielectric measurements of the " Piekara factor " have been carried out for pure water at 293 K. The measurements have been made possible by the development of a new technique capable of measuring permittivity changes AE/E as low as loe5 in samples with conductivities as high as C2-1 m-' gave Ac/E2 = - (1 .OO k 0.15) x m2 V-'. The results are interpreted in terms of the low field dipole polarization factor R, and the non-linear field effect correlation factor Rs. The behaviour is that of the " classical " non-linear effect of a negative A& due to permanent dipoles.

C2-l m-I. Reproducible results with water having conductivities in the range 1 to 4 x

Non-linear effects are seen as small changes in the relative electric permittivity (A&) at high electric fields. The first recorded measurements of non-linear dielectric effects are due to Herweg in 1920. Herweg measured A& in diethyl ether, finding it to be negative and quadratically dependent on field. The development of the subject since the initial work has been due almost exclusively to Piekara and his ~ ~ l l a b o r a t o r ~ . ~ ~ ~ The non-linear effects have attracted increasing attention as a means of investigating both inter and intra molecular effects, especially in polar liquids. Non-linear effects are often termed dielectric saturation, but this nomenclature is not really suitable since only in exceptional cases for macromolecules is true saturation observed, The vast majority of media give only the first order departure from linearity, A& being quadratically dependent on field.

In the normal " classical " effect, A& is negative, being due to alignment of the dipoles along the field. A similar competition between the field and thermal forces for a non-polar but anisotropic molecule will give rise to a positive A&. Another class of phenomena is due to the change in the dipole moment of the molecule itself, giving rise to a change of permittivity which is positive, i.e. a decrease in the interaction energy ( - p E ) or a stabilization of the system. This change in dipole moment has been attributed to conformational changes,6 ionization of hydrogen bonds, formation of molecular assemblies, e.g., dimers, micelles,' etc.

All measurements prior to 1962 involved the use of steady (d.c.) electric fields, the work being confined to liquids with conductivities ;5 lo-'' C2-I m-l. introduced a pulse method at this time which enabled conductivities up to C2-I

m-l to be tolerated. This system used ms pulse fields, thus reducing the heating effect. As a result, studies of the lower alcohols down to butanol became possible.

Recause of its general importance and in the context of biological systems it is

Malecki

t present address : Institute of Chemistry, University of Wroclaw, Poland.

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270 HIGH F I E L D DIELECTRIC MEASUREMENTS

desirable to be able to study water and aqueous solutions. The conductivity of de- ionized water normally available from an ion exchange resin deionizer in the labora- tory is about 112-l m-l and hence is three orders of magnitude outside the limits of the Malecki system. A recently developed short pulse system enables measure- ments to be carried out on liquids with conductivity as high as S2-I m-l , h ence allowing the study of pure water and aqueous solutions of many biological molecules.

In previous methods 9 9 lo the heating effect due to conductivity and the resulting decrease in permittivity were kept within experimental error by choosing liquids with sufficiently low conductivity, specific heat, pulse width, etc. In the present method, the heating effect is minimized by using short pulses but is also corrected for in the calculation of the result. Another effect which must be borne in mind is the electrode polarization which is again minimized in this case.

EXPERIMENTAL The apparatus used in this work is described elsewhere.ll The dielectric cell is part of

the talk circuit of an oscillator. During the high field pulse the frequency (v) of the oscillator is measured on a computing counter ; this frequency is compared with that before the pulse, the quantity Av/v being displayed on the counter. The heating effect due to the conductivity gives rise to a ramp in the response as shown in ref. (11) and (12). In the case of the measure- ments reported here, 6 p s field pulses were used, the frequency of approximately 10 MHz being sampled over 1 ps intervals. The heating effect for water was of the order of 25 % of the total response.

Due to the high conductivity of the water it was not possible to use the transistor oscil- lator l 1 but rather the valve oscillator l1 with substantial feedback. The radiofrequency voltage applied to the cell was about 1.5 V peak to peak. Assuming a conductivity of lo-" R-I m-l results in a cell resistance of 30 k!2 and an input power of about 8 x W. This will result in an initial increase of temperature at the rate of about lo-' K s-I, gradually approaching thermal equilibrium. The corresponding change in A& is about lo-* s-l. Since the counter measured the oscillator frequency deviation over an interval of a few ms then the maximum possible change due to oscillator heating is seen to be completely negli- gible compared with the non-linear effect,

ox:iLlat

FIG. 1.-Diagram of the tank circuit of the measuring oscillator. The liquid of permittivity E gives a total cell capacitance KO, CB is the bypass capacitor, Cc the calibration capacitor and CS the stray

capacitance.

The usual quantity measured in the experiment Avlv, i.e., the fractional change in fre- quency due to the electric field must be related to the change in permittivity of the water. This can be done in two ways : (a) theoretically from a knowledge of the capacities of related parts of the circuitry and (b) via a calibration capacitor. The theoretical calculation may be explained by reference to fig. 1 , which shows the tank circuit of the oscillator with related capacitors. CB is the blocking or bypass capacitor and is normally a few nF ; C, is the wire and cell stray capacitance normally a few 10 pF ; the capacitance of the empty cell is C, (full KO). In addition to the cell the blocking capacitor is also subjected to the high field

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H . A . K O L O D Z I E J , G . P . JONES A N D M. D A V I E S 27 1

pulse and is liable to distort, producing a change ACB. The change in CB was found to vary dramatically from one capacitor to another, being both positive and negative for different types of capacilor. ACB was found to be very small for good quality coaxial cables and CB was eventually made up using a length of UR 43 cable. The relationship between A& and Av/v can be shown to be

It will be noticed that the ACB effect depends quadratically on E and hence is relatively serious for water. In principle, this problem can be removed by making CB very large; this, however, cannot be done in practice due to the resulting long rise and decay times of the pulse. Using a CB of % 3 nF made up from UR 43 cable, the effect was found to be negligible for water. Co was normally z 1 pF. Taking the case of a very large blocking capacitor, the equation reduces to

which is the equation quoted previously.", l2 In the case (b), (i.e., the calibration capacitor method) the capacitor CC is in parallel with C,. The capacitor is previously calibrated on a high quality bridge (Wayne Kerr B331) and is adjustable to 10-16F. The procedure adopted was to adjust the capacitor (by a known amount) to give the same Av/v as the non-linear effect. Since the cell is in series with CB a small correction has to be applied.

The heating effect in water was corrected for by measuring the response towards the end of, and immediately after, the pulse. The difference between these two readings corrected for heating during the decay of the pulse gives the non-linear effect. A large positive effect following the pulse was found initially ; this effect has been found to be unique to water. It was eventually removed by using highly polished stainless steel electrodes and is thought to have been caused by microbubble formation due to degassing of the water. Degassing of the water under a partial vacuum was also found to alleviate the problem.

RESULTS The validity of the results for water is a first concern since this is the medium of

highest conductivity measured with the system. The results of Malsch l3 which have long been quoted show a negative effect amounting to A& = -8 x at E = lo7 V m-l; despite the great uncertainty in his procedure this result agrees well with ours. The system used here has been assessed in a number of ways : (a) comparison of short pulse A&/E2 values for liquids such as diethyl ether and hexanol, the agreement with other workers 14-16 being excellent ; (b) checking the heating effect as measured against the theoretical value involving specific heat, interelectrode volume, &/aT etc.12 ; (c) deliberately increasing the conductivity of the medium by adding traces of ionic conducting impurities and checking the theoretical and measured heating effects ; (d) some of the specimens were measured in the same cell in separate systems (FM system, etc.).

The data for water at 293 K have been repeatedly checked with various samples (0 = 1 to 4 x The reproducible results always showed A& = - 10.6 x Fig. 3 shows a plot of A& against E2, the quadratic dependence being very good. This plot gives the best value of A&/E2 for water at 293 K to be ( lO.O+ 1.5) x m2 V-2. With the measuring frequency of the order of 10 MHz there was no observable element of dispersion in the water behaviour. The critical frequency for dispersion at the temperature of the experiment is near 3 x 10-l' Hz so that essentially static factors are being observed.

Such checks confirmed the validity of the data reported here.

s1-l m-l) at various dates. at E = lo7 V m-l as shown in fig. 2.

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272 HIGH FIELD DIELECTRIC MEASUREMENTS

Qualitatively, the result shows that water is behaving as a normal rigid polar molecular system up to lo7 V m-l. Specifically there is no field effect on the polarity of the H bonding system (as in the alcohols ') as this would necessarily give rise to a positive change in A&.

X

4 I

0 20 LQ 60 80 too 120

E/105 V m-l FIG. 2.-Plot of ALE against E/1O6 V rn-l for pure water (a~3!1O-~ SZ-' m-' ) at 293 K.

2 4 6 8 10

E2/1013 V2 m-2 FIG. 3.-Plot of AE against E2/1013 V2 m-2 for pure water ( a ~ 5 l O - ~ IR-' rn-l ) at 293 K.

An accepted molecular interpretation of the dielectric behaviour of water is not unequivocally established ; much depends on the evaluation of the absorption/ dispersion between E, (Debye: at 10I1 Hz) and n&. Wishing to avoid such discussion, the present treatment will be restricted to a simple model of which the Kirkwood-Oster representation is typical. In this model the measurable mean effective square moment p p = gp 02 where g is the Kirkwood local dipole configuration factor and p o is the effective molecular moment ( 6 . 2 0 ~ C m). With these factors, the Kirkwood-Oster relation for water can be written to include the first non- linear term in the expansion of the Langevin function. The expression for E is

14N(n2 +2)'p1[ 96E2pt(n2 + 2 ) 2 ] 19Sk2T2

E = n 2 + 1- 27~okT (3)

where E~ is the permittivity of free space, N the number of dipoles per unit volume and n the refractive index at the termination of the dipole contribution to E .

The value of E is obviously very dependent on the refractive index ; at 293 K for n2 = 1.77 (= n i ) and E = 80 (experimental value 79), the Piekara factor becomes

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H . A . K O L O D Z I E J , G . P . JONES AND M. DAVIES 273 &/E2 = 12.0 x m2 V-2. The agreement with the measured value is as good as the evaluation could justify. This degree of concurrence is of major significance, as it shows that liquid water behaves in its high field effect in a fashion consistent with its low field polarization. The physical reason for this simplicity may well be due to the fact that the maximum applied field (10' V m-l) is still small compared with the interdipolar fields in the water itself. The indications are that any molecular model which satisfactorily explains E (low field) for water will, with the use of the Langevin function, also reproduce the observed A&/E2.

A formally inore complete representation of E and A E / E ~ is given by the Piekara- Kielich treatment of polar 1 iq~ ids . l~ The Langevin function applied to the case of a non-interacting dipole molecules gives :

p 2 E p;E3 3kT 45k T

{ p } =2-.--.--- 3 3+"" r E (4)

When there is interaction of the molecules the behaviour can be represented formally by

where ,u, = En2 + 2 / 3 ] p 0 and R, and Rs are correlation factors for the low field dipole polarization and for the non linear field effect respectively.

For the dipoles (1, . . . j , k . . . N ) within the Frolich sphere these factors are

R , =

Ks =

A&

N

(I - c cos O j k ) j = 1

/ N N N \

k = l Z=1 m = l

- - - [E(n2 +2)14 ,u; E2 ( 2 ~ ~ + n 4 ) ( 2 ~ + n2)2 45k3T3RS*

Using the 4-coordinated tetrahedral pattern of H 2 0 molecules in water,20 R,, which is essentially equal to the Kirkwood g-factor is 2.68. The Piekara-Kielich formulation gives Rs z Ri x 19.3. From eqn (8) and the experimental Ae/E2 the value of Rs is 24. This agreement again establishes that the behaviour of water is consistent with the first terms of the Langevin function.

This work was supported by a S.R.C. Grant. One of us (H. A. K.) expresses his gratitude to the S.R.C. for a Postdoctoral Research Fellowship held during the course of this work.

J. Herweg, 2. Phys., 1920, 3, 36. A. Piekara and B. Piekara, Compt. rend., 1936, 203, 852, 1058. A. Piekara, Proc. Roy. SOC. A, 1939, 172, 360. A. Piekara, S. Kielich and A. Chelkowski, Arch. Sci., 1959, 12, 59. G. Parry Jones, M. Gregson and M. Davies, Chem. Phys. Letters, 1969, 4, 3 3 . A. Piekara and A. Chelkowski, J. Chem. Phys., 1956, 25, 794. ' J. Malecki, J. Chern. Phys., 1965, 43, 1351.

G. Parry Jones, M. Gregson and T. Krupkowski, Chem. Phys. Letters, 1972, 13, 266. J. Malecki, Acta Pliys. Polon., 1962, 21, 13.

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274 HIGH F I E L D D I E L E C T R I C M E A S U R E M E N T S

lo A. Piekara, Acta Phys. Polon., 1959, 18, 361.

l2 G. Parry Jones and T. Krupkowski, J.C.S. Faraday 11, 1974, 70, 862. l3 J. Malsch, Phys. Z. , 1928, 29, 770; 1929,30, 837. l4 F. Kautzsch, Phys. Z., 1928, 29, 105.

l 6 J. Malecki and Z. Dopierala, Acta Phys. Polon., 1969, 36, 385.

P. A. Bradley and G. Parry Jones, J. Phys. E., 1974, 7,449.

A. Piekara, A. Chelkowski and S. Kielich, 2. phys. Chem., 1957, 206, 375.

J. B. Hasted, Dielectric and Related Molecular Processes, ed. Manse1 Davies (The Chemical Society, London, 1972), vol. 1, p. 121.

l 8 G. Oster and J. G. Kirkwood, J. Chem. Phys., 1943, 11, 175. l9 A. Piekara and S. Kielich, J. Phys. Rad., 1957, 18,490. 2o J. Morgan and B. E. Warren, J. Chem. Phys., 1938,6, 666.

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