Transient Conduction of Weakly Dissociating

Vol. 126, No. 6

NICKEL OXIDE FILMS

19. G. C. Wood, W. H. Sutton, J. A. Richardson, T. N. K. Riley, a n d A. G. Malherbe, "Proc. of U. R. Evans Inter. Conf. on Localized Corrosion, 1971," p. 526, NACE, Houston (1974). 20. G. Bianchi, A. Cerquetti, F. Mazza, a n d S. Torchio, ibid., p. 399. 21. J. Z a h a n i a n d M. Metzger, ibid., p. 547. 22. G. Bianchi, A. Cerquetti, F. Mazza, and S. Torchio, "Proc. of F o u r t h Inter. Congr. on Met. Corr., Amsterdam~ 1969," p. 614, NACE, Houston (1972). 23. J. A. Richardson a n d G. C. Wood, Corros. Sci., 10, 313 (1970). 24. J. Kruger, This Journal, llO, 654 (1963). 25. T. P. Hoar, Trans. Faraday Soc., 45, 683 (1949). 26. J. C. Scully, "The T h e o r y of Stress Corrosion C r a c k i n g in Alloys," p. 1, NATO Science C o m m i t tee, Brussels (1971). 27. J. C. Scully, Corros..Sci., 8, 513 (1968). 28. R. W. Staehle, "The T h e o r y of Stress Corrosion C r a c k i n g in Alloys," J. C. Scully, Editor, pp. 252, 273, N A T O Science Committee, Brussels (1971). 29. B. Kabanov, R. Burstein, and A. F r u m k i n , Disc. Faraday Soc., 1, 259 (1947). 30. D. M. Kolb, M. Przasnyski, and H. Gerischer, Elektrokhimiya, 13, 700 (1977). 31. G. Horanyi, J. Salt, and F. Nagy, J, Electroanal.

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Chem. Interracial Electrochem., 31, 87 (1971); 31, 95 (1971). 32. H. H. S t r e h b l o w a n d B. Titze, Corros. Sci., I7, 461 (1977). 33. N. D. G r e e n e and M. G. Fontana, Corrosion (Houston), 15, 25t (1959); 15, 32t (1959). 34. J. M a n k o w s k i and Z. S z k l a r s k a - S m i a l o w s k a , Corros. Sci., 15, 493 (1975); 17, 725 (1977). 35. G. R. W a l l w o r k a n d B. Harris, "Proc. of U. R. Evans Inter. Conf. on Localized Corrosion, 1971," p. 292, NACE Houston (1974). 36. J. R. Galvele, This Journal, 123, 464 (1976). 37. H. S. Issacs, "Proc. of U. R. Evans Inter. Conf. on Localized Corrosion, 1971," p. 158, NACE, H o u s ton (1974). 38. I. L. Rosenfeld and I. S. Danilov, Corros. Sci., 7, 129 (1967). 39. T. P. Hoar, Disc. Faraday Soc., 1, 299 (1947). 40. T. P. H o a r and W. R. Jacobs, Nature (London), 216, 1299 (1967). 41. M. P o u r b a i x et al., Corros. Sci., 3, 239 (1963). 42. B. E. Wilde, "Proc. of U. R. Evans Inter. Conf. on Localized Corrosion, 1971," p. 342, NACE, H o u s ton (1974). 43. S. S m i a l o w s k a and M. Czachar, ibid., p. 353. 44. B. MacDougall and M. Cohen, This Journal, 123, 1783 (1976).

Transient Conduction of Weakly Dissociating Species in Dielectric Fluids V. Novotnyand M. A. Hopper* Xerox Research Centre of Canada, Mississauga, Ontario LSL 1J9 Canada ABSTRACT The s t e a d y - s t a t e and t r a n s i e n t conductivities of solutions of an ionic s u r factant in a dielectric fluid w e r e i n v e s t i g a t e d e x p e r i m e n t a l l y o v e r a w i d e r a n g e of a p p l i e d voltages for various cell thicknesses. The o b s e r v e d n o n l i n e a r d e p e n d e n c e of s t e a d y - s t a t e c u r r e n t d e n s i t y on a p p l i e d field suggests t h e i m p o r t a n c e of d i s s o c i a t i o n - r e c o m b i n a t i o n processes in the bulk. The t r a n s i e n t c u r r e n t response was found to d e p e n d m a r k e d l y on t h e a p p l i e d voltage conditions. On the first a p p l i c a t i o n of a field a s t e a d i l y decreasing c u r r e n t was o b served; r e v e r s i n g the p o l a r i t y of the a p p l i e d field p r o d u c e d a w e l l - d e f i n e d c u r r e n t peak. The p e a k times a r e not d i r e c t l y p r o p o r t i o n a l to cell thickness or to the i n v e r s e of t h e a p p l i e d field. T r a n s i e n t c u r r e n t b e h a v i o r indicates a complex t r a n s p o r t process i n v o l v i n g b i p o l a r ionic conduction in the bulk. I n addition, conditions w h e r e space charge and e l e c t r o h y d r o d y n a m i c effects influence the transients a r e identified. The o b s e r v e d b e h a v i o r is characteristic of m a n y systems of w e a k l y dissociating species in dielectric fluid. S u r f a c t a n t s a r e w i d e l y used in p r e p a r i n g s u s p e n sions of particles in dielectric fluids. I n some cases the s u r f a c t a n t can act in a d u a l c a p a c i t y being both a suspension s t a b i l i z e r and controlling the charge of the particles. Studies of the electrical characteristics of these suspensions showed t h a t the conductivity of the s y s t e m can be d o m i n a t e d b y t h e c o n t r i b u t i o n from s u r f a c t a n t r e m a i n i n g in solution. Thus s t u d y of the electrical b e h a v i o r of surfactants in solution r e p r e sents a first logical step t o w a r d electrical c h a r a c t e r i z a tion of charged particles in suspension. M a n y e x p e r i m e n t a l techniques have b e e n e m p l o y e d to investigate charge t r a n s p o r t t h r o u g h dielectric fluids i n c l u d i n g p h o t o i n j e c t i o n of electrons f r o m a cathode (1), electron injection f r o m semiconducting diodes (2), ionization of liquid b y fast electrons (3), and i n j e c t i o n f r o m a photoconductor (4). I n all these t e c h niques, u n i p o l a r i n j e c t i o n and single c a r r i e r t r a n s p o r t is studied and the t r a n s i t times for the c h a r g e d species a r e u s u a l l y r e p o r t e d to be p r o p o r t i o n a l to the cell 9 Electrochemical Society Active Member. Key words: conductivity, surfactants, dissociation, transients, dielectric fluids.

thickness a n d i n v e r s e l y p r o p o r t i o n a l to t h e a p p l i e d electric field. The situation for two or m o r e carriers is m o r e complicated, as interactions b e t w e e n positive and negative ions m a y occur. Previous investigations (5-7) of conduction in d i electric liquids h a v e been confined to s t e a d y - s t a t e studies of " p u r e " fluids w h e r e the q u a n t i t y and n a t u r e of the ionic i m p u r i t i e s was not known. These c u r r e n t s show nonohmic b e h a v i o r and s a t u r a t e at high fields. To our k n o w l e d g e no d e t a i l e d s t u d y of both the s t e a d y state and t r a n s i e n t c o n d u c t i v i t y of a controlled solution of a w e a k l y ionizable species in a dielectric fluid has been documented. In this p a p e r results o b t a i n e d in an investigation of the t r a n s i e n t and s t e a d y - s t a t e electrical conductivity of solutions of ionic surfactants in dielectric liquids a r e reported. One system, Aerosol OT (AOT) in xylene, was studied in detail. The m e a s u r e m e n t s w e r e m a d e for a wide r a n g e of field strengths both as a function of AOT concentration and m e a s u r i n g cell thickness. Some e x p e r i m e n t s w e r e m a d e w i t h A O T in o t h e r d i electric fluids and, in addition, one o t h e r s u r f a c t a n t

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J u n e 19 79

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926

solution was examined. All the observed electrical transients showed the same general behavior which is possibly characteristic of m a n y ionic surfactants or other w e a k l y dissociating molecules i n a wide r a n g e of dielectric fluids. I n the following section the e x p e r i m e n t a l procedure is described a n d some details of the e x p e r i m e n t a l apparatus are given. The Results section documents the e x p e r i m e n t a l results for the steady s t a t e - c o n d u c t i v ity, t u r n - o n , a n d field reversal transients. In the Discussion section these results are discussed in terms of the processes possible i n this type of system. Finally, the i m p o r t a n t results a n d some general conclusions are summarized. Experimental I n electrical t r a n s i e n t m e a s u r e m e n t s a voltage w a v e form is applied to a capacitor-like cell containing the sample, and the c u r r e n t response is monitored. The basic m e a s u r e m e n t technique is illustrated in Fig. i. The power supply charged the capacitor, C, to 99% of the final voltage w i t h i n 1 ~sec. The c u r r e n t passing through C and the series resistor, R, produced a voltage drop across R which was amplified and digitized. The response time of the amplifier was less t h a n 2 ~sec and the time resolution of the analog-digital converter extended from 10 #sec. At lower applied voltages, noise comparable to the signal was observed and appropriate signal averaging, using a Tracor N o r t h e r n m u l t i c h a n n e i analyzer (Model 510 or 1500), was e m ployed. The signal averager was connected to the l a b o r a t o r y computer which was used to fit a n d plot the t r a n s i e n t data. S t e a d y - s t a t e m e a s u r e m e n t s were made with a n electrometer (Keithley Model 616), readings being t a k e n typically 100 sec after the application of the electric field. The samples were studied in a cell h a v i n g the form of a plane capacitor with a Teflon spacer. Two glass plates with semiconducting (doped t i n oxide or i n d i u m oxide) or metallic (gold) coatings were used as electrodes. The system was clamped mechanically, creating a l e a k - p r o o f seal b e t w e e n the Teflon spacer and the electrodes. The area of the cell electrodes was 10 cm 2, the cell thickness used ranged from 60 to 1600 ~m, and the applied voltages ranged from 1 to 1500V. The liquids used in this study were of spectral grade and included p - x y l e n e , dodecane, n - h e x a n e , and a fluorocarbon. These fluids were dried over molecular sieves before use, as p r e l i m i n a r y experiments had i n dicated that steady-state and t r a n s i e n t currents were v e r y sensitive to the presence of water. The electrical resistivity of these fluids before the addition of s u r factants was of the order of 1 • 10z4 ~2cm. Highly concentrated solutions of the surfactants i n the dielectric fluids were prepared, dried, and t h e n diluted to the 10-~-10-3M range with dry fluid. The w a t e r content of the dried solutions was u n d e t e c t a b l e by K a r l Fischer titration, i.e., less t h a n 5 # g / m l of fluid. Most of our studies were carried out with Aerosol OT (sodium d i - 2 - e t h y l hexyl-sulfosuccinate) b u t sodium l a u r y l sulfate was also used. The p r e p a r a t i o n of samples and the m e a s u r e m e n t s were performed in a d r y box to r e duce the possibility of water contamination.

CELL

POWER SUPPLY

~ R

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Results

Steady-state conduction.--The steady-state c u r r e n t voltage behavior of solutions of AOT i n xylene is shown in Fig. 2. The c u r r e n t was m e a s u r e d 100 sec after application of the electric field. It drops very slowly and after 20 m i n had only decreased a few percent from the value at 100 sec. This allows us to assume that our c u r r e n t reading is a close approximation to the "true" steady-state current. Ohmic behavior was found only at very low applied fields (~0.005 V / # m ) . As the voltage applied to the cell increased, the c u r r e n t saturated. The steady-state c u r r e n t - v o l t a g e characteristics shown in Fig. 2 are r e m a r k a b l y like those reported for "pure" dielectric fluids (5,6). T h e c u r r e n t - v o l t a g e characteristics show no indication of a n y field-induced dissociation effects (7) even at the highest field e m ployed, viz. 5 V/#m. Transient conduction.JThe t r a n s i e n t electrical behavior of a solution of AOT i n xylene depended m a r k edly on the m a n n e r in which the voltage was applied to the conductance cell. The e x p e r i m e n t a l voltage w a v e f o r m (shown i n F~g. 3, curve a), a n d variations of this basic waveform, were employed in the t r a n s i e n t experiments. To illustrate the contrast b e t w e e n the observed t r a n sient currents a n d those expected from the simplest picture of conduction in this type of system, the c u r r e n t response to the w a v e f o r m of Fig. 3, curve a, is

AOT in xylene d=lOO~m 9 10-3M 9 10-4M

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Vol. 126, No. 6

WEAKLY DISSOCIATING SPECIES

s h o w n i n Fig. 3, curves b and c. The idealized c u r r e n t response, shown i n Fig. 3, curve b, was obtained b y considering the c o n t r i b u t i o n of a single ionic species to the c u r r e n t and neglecting space charge effects. I n i tially the charge carriers are u n i f o r m l y distributed t h r o u g h o u t the cell and the first application of a voltage sweeps the ions to the oppositely charged electrode. A s s u m i n g ion n e u t r a l i z a t i o n occurs at the electrode, the idealized t u r n - o n c u r r e n t should decrease l i n e a r l y to zero at a time w h e n the last species reach the electrode. To produce a n y c u r r e n t on reversing the field, n e u t r a l molecules at the electrode must accept some injected charge. If these ions are released i n s t a n t a n e o u s l y to drift t h r o u g h the fluid as a sheet of charge of constant velocity the c u r r e n t will be constant u n t i l the charges reach the opposite electrode; it would t h e n drop to zero as shown in Fig. 3, curve b. Typical e x p e r i m e n t a l t u r n - o n and field reversal t r a n sients are s h o w n schematically i n Fig. 3, curve c. This portion of the figure also shows the e x p e r i m e n t a l q u a n tities referred to in the text below. The decay time, td, was obtained b y extrapolation of the initial slope of the t u r n - o n t r a n s i e n t c u r r e n t density. The time at which the c u r r e n t reached its m a x i m u m after reversal is tp. The c u r r e n t density at 10tp was designated as Is a n d the initial t u r n - o n c u r r e n t density in excess of Is is Io. The c u r r e n t density at tp i n excess of Is is the peak c u r r e n t density, Ip. The time integral of the c u r r e n t density i n excess of Is is the excess charge density Q. E x p e r i m e n t a l l y the t u r n - o n t r a n s i e n t is a "one-shot" technique and consequently a u n i p o l a r pulsed voltage t r a i n was used to simulate the t u r n - o n t r a n s i e n t conditions and thus allow signal averaging. At v e r y low pulse rates the t r a n s i e n t was identical to the first t u r n - o n transient. At increased pulse rates the m a g n i tude of the t r a n s i e n t c u r r e n t depended on the time the cell was m a i n t a i n e d u n d e r short circuit conditions before application of the s u b s e q u e n t m e a s u r i n g pulse. The c u r r e n t - t i m e behavior of a 100V pulse, 1 sec in duration, found using a 10-SM AOT in x y l e n e with a 500 ~m cell is shown in Fig. 4. The four curves shown correspond to the pulse being reapplied after 20, 1, 0.1, and 0.05 sec (curves 1-4, respectively) at short circuit. The data given i n Fig. 4 shows that as the frequency of the pulses increased Io decreased. This suggests that insufficient time elapsed b e t w e e n pulses to allow the system to r e t u r n to its initial e q u i l i b r i u m situation. For t h e case shown i n Fig. 4 the initial state was reestablished after a critical period of 20 sec at short circuit. Io + Is is a m e a s u r e of the total n u m b e r of ions i n the system at t -- 0. The field reversal t r a n s i e n t is best simulated using a bipolar square wave d r i v i n g voltage. U n d e r these conditions, a c u r r e n t peak was always observed (as

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depicted in Fig. 3, curve c). At higher fields, peaks were observed for the fluid without added surfactant; i n these cases the peak currents are m u c h smaller t h a n those observed for the lowest surfactant concentrations (1 • 10-SM) used in this study. A typical c u r r e n t - t i m e dependence found i n these experiments is shown i n Fig. 5. It should be pointed out that the c u r r e n t Peak occurs after each reversal of the applied voltage. Typical c u r r e n t density vs. time traces r e corded using applied voltages of 10, 25, a n d 100V with a 500 #m cell are presented i n Fig. 6. For a n y constant field a n d cell spacing, tp did not v a r y with AOT concentration. C u r r e n t transients were d e t e r m i n e d for cell thicknesses r a n g i n g from 60 to 1600 ~m for fields e x t e n d i n g from 0.01 to 4 V/#m. The m e a s u r e d dependence of tp on applied field, E, at various cell spacings is shown in Fig. 7. It should be noted that this field dependence m a y be approximated b y a n expression of the form tp ,~ E -n, over a significant range of electric fields. However, the exponent, n, depends on cell thickness. The tp vs. E plot shows that n decreases from a value of 1.35 at cell spacing o f 1600 ~m, to about 1.1 for a 60 ~m cell. W h e n this data is replotted as a function of cell thickness, with the applied field as a parameter, we find tp ~ dm. E x p e r i m e n t a l l y , m decreases with increasing electric field being 0.9 at 5 • 10 -3 V/~m a n d 0.3 at 2 V/~m. To d e t e r m i n e w h e t h e r the c u r r e n t peaks were related to the n a t u r e of the electrode material, similar e x p e r i ments were performed using sputtered gold as the electrical contact. The c u r r e n t - t i m e dependences determ i n e d i n this e x p e r i m e n t were not essentially different from those obtained with tin oxide electrodes. For the same applied field and cell spacing the c u r r e n t peaks occurred at the same time as the data plotted i n Fig. 7.

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J. EZectrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y

928 lOOO

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Space charge and electrohydrodynamic eJ~ects.-Two effects which m a y p l a y a significant role in the t r a n s i e n t c o n d u c t i v i t y of fluid systems deserve a t t e n tion. These a r e t h e influences of space charge fields a n d e l e c t r o h y d r o d y n a m i c processes. S e v e r a l o b s e r v a tions concerning t h e p e a k c u r r e n t density, fp, a n d the c h a r g e density, Q, can be made. The ratio of c u r r e n t densities Ip/Is was found to v a r y from 0.2 at v e r y low fields to 10 at v e r y high fields. T h e p e a k c u r r e n t d e n s i t y i n c r e a s e d l i n e a r l y w i t h t h e electric field and also i n creased w i t h increasing cell spacing at a given surfacrant concentration; this l a t t e r d e p e n d e n c e was, h o w ever, sublinear. The excess charge density, Q, a p p e a r s to be v e r y w e a k l y d e p e n d e n t on a p p l i e d voltage at fixed cell thickness and s u r f a c t a n t concentration. A t a n y given concentration Q was p r o p o r t i o n a l to the cell thickness. A t low voltages the c h a r g e t r a n s p o r t e d t h r o u g h the cell c o n s i d e r a b l y e x c e e d e d the C-V p r o d uct. Thus at h i g h solute concentration a n d for low fields the conduction was s p a c e - c h a r g e limited. A n o t h e r i m p o r t a n t aspect of the t r a n s i e n t c u r r e n t d a t a was t h a t the shape of the c u r r e n t r e v e r s a l t r a n sient differed n o t i c e a b l y w i t h the a p p l i e d field. A t low fields t h e c u r r e n t i n i t i a l l y rose a p p r o x i m a t e l y e x p o n e n t i a l l y w i t h convex c u r v a t u r e to the c u r r e n t p e a k and t h e n d e c a y e d r o u g h l y exponentially. A t high fields t h e rise a n d d e c a y h a d the same concave c u r v a t u r e a n d t h e c u r r e n t - t i m e c u r v e was cusplike ( c o m p a r e Fig. 6a and 6b w i t h 6c).

Other 1~uids and sur~actants.--Apart f r o m xylene, t r a n s i e n t c u r r e n t s for AOT w e r e i n v e s t i g a t e d in d o d e cane, n - h e x a n e , and a fluorocarbon. Q u a I i t a t i v e t y these results show the s a m e f e a t u r e s as those found w i t h the A O T / x y l e n e system. W i t h a square w a v e d r i v i n g v o l t a g e the p e a k times also e x h i b i t e d similar n o n linearities w i t h cell thickness and a p p l i e d electric field. The shapes of the c u r r e n t - t i m e transients w e r e s i m i l a r to those found w i t h A O T / x y l e n e . The p e a k times at a n y field did not scale e x a c t l y w i t h t h e inverse of fluid viscosity. Nevertheless, c o m p a r e d to the x y l e n e data, t h e p e a k times reflect the different fluid viscosities, b e ing longer in dodecane, s h o r t e r in n - h e x a n e , a n d almost the s a m e in the fluorocarbon. These results also i n d i c a t e d that the e x t e n t of dissociation of AOT in these liquids is of the same degree as it is in xylene. E x p e r i m e n t s w i t h sodium l a u r y l sulfate as a n a l t e r n a t i v e s u r f a c t a n t w e r e also performed. This m a t e r i a l was selected because a different organic m o i e t y only is involved. I n this case the o b s e r v e d p e a k times w e r e

June 1979

s u b s t a n t i a l l y s h o r t e r ( b y a factor of a p p r o x i m a t e l y t h r e e ) w h e n c o m p a r e d w i t h AOT u n d e r o t h e r w i s e identical conditions. A l l t h e q u a l i t a t i v e f e a t u r e s of t h e e x p e r i m e n t a l transients found w i t h A O T w e r e o b served. Discussion I n this s t u d y the w e a k l y dissociating species w e r e sodium salts of f a i r l y l a r g e organic acids. The estim a t e d degree of dissociation in o u r systems is 1 in l0 T. We expect these molecules to ionize, p r o d u c i n g two ions of opposite polarity, and in a fluid system both ions can be mobile. Combined w i t h the r e v e r s e process of ionic recombination, this b u l k dissociation of n e u t r a l s p r o v i d e s an e x p l a n a t i o n for most of the d a t a p r e sented above. The s t e a d y - s t a t e c u r r e n t - v o l t a g e characteristics a r e not u n u s u a l for systems i n v o l v i n g dielectric fluids (7). S i l v e r (8) m o d e l e d this t y p e of s t e a d y - s t a t e c u r r e n t voltage b e h a v i o r using a modification of t h e ideas discussed b y the Thomsons (9) for ionic conduction in gases. I n the Thomson m o d e l the r a t e of ionization of n e u t r a l molecules into ions is considered to l i m i t the process, b u t ionic r e c o m b i n a t i o n is accounted for. T h e a p p l i e d field acts to s e p a r a t e the ions leading to t h e d e v e l o p m e n t of regions w h e r e the influence of space charge effects on the local electric field m u s t be considered. G a s p a r d (10) has p o i n t e d out the i m p o r t a n c e of slow dissociation kinetics in dielectric fluids and has c o n t r a s t e d this characteristic w i t h the aqueous solution situation. R e c e n t l y Malecki and P i e r a n s k i (11) e x t e n d e d Silver's m o d e l a n d p r e d i c t e d t h e characteristic c u r r e n t - v o l t a g e d e p e n d e n c e of our e x p e r i m e n t a l data. The o b s e r v a t i o n of a p e r s i s t e n t s t e a d y - s t a t e c u r r e n t implies charge flow across both f l u i d / e l e c t r o d e i n t e r faces a n d an almost ohmic contact at these surfaces. This means t h a t ions have to be n e u t r a l i z e d and possib l y g e n e r a t e d e l e c t r o c h e m i c a l l y at these boundaries. Analysis of the t r a n s i e n t c u r r e n t b e h a v i o r is complex, as it is obvious t h a t simple models cannot describe the n u m e r o u s features of the p r e s e n t data. As outlined in the previous section, we find t h a t the total charge passing t h r o u g h the system can exceed the C-V p r o d uct at most a p p l i e d voltages. In a d d i t i o n to this o b s e r v a t i o n t h e r e a r e two results which s u p p l y definite evidence that m o r e t h a n a single m o b i l e c a r r i e r is i n volved in the conduction process. The o b s e r v e d d e p e n dence of the p e a k time on the a p p l i e d field and, in p a r ticular, its dependence on cell thickness (at constant a p p l i e d field) is inconsistent w i t h single ion t r a n s p o r t even considering the influence of space c h a r g e limited conditions. The second result is that n e i t h e r t h e s t e a d y - s t a t e nor the p e a k c u r r e n t densities increase as V2/d 'z, which is the r e s u l t p r e d i c t e d b y t r e a t m e n t s of single c a r r i e r space c h a r g e - l i m i t e d t r a n s p o r t (12-14). In our opinion a n y a d e q u a t e description of the t r a n sient c u r r e n t d a t a in these systems m u s t include dissociation of t h e n e u t r a l species, ionic recombination, and the motion of at least t w o ionic species. In addition, the effects of space charge have to be accounted for fully. This r e q u i r e s finding t h e t r a n s i e n t solutions of the Thomson model discussed above. Solutions of t h e linearized form of t h e s e e q u a t i o n s have been discussed b y M e a u d r e and M e s n a r d (15) and b y M a c d o n a l d (16), but t h e y a p p l y only at v e r y low voltages (V < kT/e), while our d a t a are all in the r e g i m e of V > > kT/e. C o m p u t e r solutions of the complete Thomson m o d e l will be p r e s e n t e d in a l a t e r p u b l i c a t i o n (17) and w e will outline only the q u a l i t a t i v e results here. I n the t u r n - o n e x p e r i m e n t , ions g e n e r a t e d b y slow dissociation of molecules in the b u l k a r e swept to the electrodes. The c u r r e n t - t i m e b e h a v i o r found is nonlinear, as space charge effects and the dissociationr e c o m b i n a t i o n process m o d i f y t h e i n t e r n a l fields. The o b s e r v a t i o n of a critical p u l s e r a t e for reestablishing initial e q u i l i b r i u m in t h e b u l k gives an indication of the dissociation rate. This r a t e can also be d e t e r m i n e d f r o m the s t e a d y - s t a t e c u r r e n t densities at high field.

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V o i 126, No. 6

W E A K L Y D I S S O C I A T I N G SPECIES

The existence of current peaks on voltage reversal provides further evidence for bulk dissociation-recombination processes. Pieranski and Malecki (18) neglected space charge effects and solved the Thomson model for field reversal. Their solution predicted a current peak on voltage reversal. This peak arises from the readjustment of the spatial concentration of ions that follows a change in polarity of the applied field. We have considered recombination-dissociation and space charge effects (17) and can explain the electric field dependence of the peak times. We find that these peak times are related to the ionic transit time at high fields but reflect the relaxation time of the dissociation-recombination process at low fields. The Thomson model fails to predict the observed ratios of the peak to steady-state current drensities I?/Is. This is possibly associated with processes occurring at the electrode fluid interface with these systems. When ions are neutralized at the electrode, on voltage reversal there is then a possibility that these species can accept charges and act as a source of current. Inclusion of this possibility into the framework of the Thomson model leads to better agreement with the experimental results. At first glance the unusual dependence of the peak time on field and thickness appears similar to the results obtained for stochastic transport in amorphous solids (19). However, treatments of that process (20, 21) lead to transit times that should scale universally as (E/d) -P where 2 > p > 1, which we do not observe. One factor that should be borne in mind is that, in a solid, carriers are released from a localized trap, whereas, in a fluid, recombination and dissociation may occur at quite different spatial positions. One effect whch may modify the transient behavior of a fluid system is the occurrence of electrohydrodynamic motion. According to Atten (22), application of a voltage greater than a certain critical voltage leads to a cusplike current-time trace. Using his criteria, a theoretical estimate of the critical voltage is about 50V, while the experimental value is N100V. It should be noted that no noticeable discontinuity in the tp vs. E plots was found at this critical voltage.

Summary The transient and steady-state currents observed with a controlled solution of surfactant in a dielectric fluid are due to migration of species of opposite polarity. The steady-state currents exhibit nonohmic behavior and saturate at higher fields. When the ionic species are swept out of a uniform equilibrium distribution, currents decaying nonlinearly with time are observed. On reversal of the applied field characteristic current peaks always appear. The current peak times increase sublinearly with cell thickness and superlinearly with the inverse of the applied field. These observations are not consistent with a simple model in which two oppositely charged species migrate through the liquid without interruption. The most important processes that have to be considered in describing conduction in this type of system are ionic dissociation and recombination. These effects can explain the steady-state current-voltage behavior and some aspects of both the turn-on and field reversal transients, including the appearance of the reversal current peak. Space charge has to be taken into account at low electric fields and/or high solute concentration.

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Finally, electrohydrodynamics can influence the ionic motion at high applied voltages. The unusual transient behavior was observed in several surfactant-dielectric liquid systems and appears characteristic of many solutions of weakly ionizable solutes in a dielectric medium. In a later paper a realistic model of ionic conduction in this type of system is developed.

Acknowledgments The authors would like to acknowledge discussions with Drs. J. H. Becker, G. C. Hartmann, C. C. Yang, and K. Watson on electrical transients, and to thank K. Gammie and T. Koch for their technical assistance. Manuscript submitted Aug. 30, 1978; revised manuscript received Dec. 12, 1978. Any discussion of this paper will appear in a Discussion Section to be published in the December 1979 JOURNAL. All discussions for the December 1979 Discussion Section should be submitted by Aug. 1, 1979.

Publication costs o] this article were assisted by Xerox Research Centre o] Canada Limited. REFERENCES 1. (a)bO.() H. LeBlanc, J. Chem. Phys., 30, 1443 (1959); J. E. Brignell and A. Buttle, J. Phys. (Appl. Phys.), D4, 1560 (1971). 2 M. Silver, D. G. Onn, and P. Smejtek, J. AppL Phys., 40, 2222 (1969). 3. P. K. Watson, J. M. Schneider, and H. R. Till, Phys. Fluids, 13, 1955 (1970). 4. (a) G. C. Hartmann and F. W. Schmidlin, J. Appl. Phys., 46, 266 (1975); (b) C. C. Yang and J. Noolandi, Can. J. Chem., 55, 2107 (1977). 5. I. Adamczewski, "Ionization, Conductivity and Breakdown in Dielectric Liquids," Taylor and Francis, London (1969). 6. E. O. Forster, J. Chem. Phys., 37, 1021 (1962). 7. T. J. Gallagher, "Simple Dielectric Liquids," p. 43, Clarendon Press, Oxford (1975). 8. M. Silver, J. Chem. Phys., 42, 1011 (1965). 9. J. J. Thomson and G . P . Thomson, "Conduction of Electricity Through Gases," Cambridge University Press, London (1928). 10. F. Gaspard, in "4th International Conference on Conduction and Breakdown in Dielectric Liquids," Typografia, p. 47, Hiberniae, Dublin (1972). 11. J. Malecki and P. Pieranski, Acta Phys. Pol. A, 50, 581 (1976). 12. M. A. Lampert and P. Mark, "Current Injection in Solids," Academic Press, New York (1970), and the references therein. 13. G. C. Hartmann and N. O. Lipari, J. Appl. Phys., 44, 1676 (1973). 14. M. Zahn, C. F. Tsang, and S. C. Pao, ibid., 45, 2432 (1974). 15. R. Meaudre and G. Mesnard, J. Phys. C, 7, 1271 (1974). 16. J. R. Macdonald, ibid., 7, L327 (1974) and 8, L63 (1975). 17. M. A. Hopper and V. Novotny, To be published in

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18. P. Pieranski and J. Malecki, Acta Phys. Pol. A, 59, 597 (1976). 19. G. Pfister and H. Scher, Phys. Rev. B, 15, 2062 (1977). 20. H. Scher and E. W. Montroll, ibid., 12, 2455 (1975). 21. (a) F. W. Schmidlin, ibid., 16, 2362 (1977); (b) J. Noolandi, ibid., 16, 4474 (1977). 22. (a) P. Atten, Phys. Fluids, 17, 1822 (1974); (b) P. Atten, in "Conduction and Breakdown in Dielectric Liquids," p. 119-122, Delft University Press, Delft (1975).

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