THE EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES AND ELECTRODE PROCESSES By S. BARNARTT (CHEMICAL DEPARTMENT WESTINGHOUSE RESEARCH LABORATORIES EAST PITTSBURGH PENNSYLVANIA U.S.A.) WHEN acoustic waves are propagated through a medium the particles of the medium are subjected to periodic accelerations and compressions. The pressure changes take place under practically adiabatic conditions even in the range of ultrasonic (inaudible) frequencies vix. above about 20 kilo- cycles/sec. Hence temperature fluctuations also occur. It is the changes in velocity pressure and temperature which cause the effects of acoustic waves on the properties of the medium and on reactions taking place therein. In this Review the medium is restricted to simple ionic solutions. Acoustic effects in colloidal solutions which have been reviewed by Sollner,l are largely omitted.Experimental procedures are not discussed since these have been covered in recent monographs.2 The subject of sound absorp- tion is specifically excluded. It will be clear from what follows that ultrasonic waves produce many interesting effects on electrolytes and electrode reactions. Although some of these have been known for over 15 years t'here is a striking paucity of data on them. (1) Compressibility (1.1) Compressibility from Acoustic Velocity.-The velocity of sound u in a fluid is related to its adiabatic compressibility ps = - (aV/aP),/V by t,he equation where d is the density of the fluid. If the specific heat at constant pressure C p is known then the isothermal compressibility p = - (aV/dP)T/V can he calculated from the thermodynamic formula where k = Cp/Cv is the ratio of the specific heats and a = (aV/aT)p/V is the coefficient of (cubic) thermal expansion.Conversely where iso- thermal conipressibility data are available sound velocities yield specific heats. U' = l/pad . * (1) p = kpa = pa + a2T/Cpd . * (2) 1 Sollner Chem. Reviews 1944 34 371 ; see also Alexander " Colloid Chemist>ry Theoretical and Applied " Vol. 5 p. 337 R,einhold Publishing Corp. New York 1944. 2 Bergmann " Der Ultraschall und Seine Anwendung in Wissenschaft und Tech- nik " 6th edn. S. Hirzel Verlag Zurich 1949 ; Carlin " Ultrasonics " McGraw- . Kill Book Co. Inc. N.Y. 1949 ; Richardson " Ultrasonic Physics " Elsevier Press Inc. Houston 1952 ; Vigoureux " Ultrasonics " Chapman and Hall Ltd. London 1950. 3 Markham Beyer and Lindsay Rev.Mod. Physics 1951 23 353. 84 BARNARTT EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES 85 The determination of ultrasonic velocity is the most accurate method of obtaining compressibilities of dilute solutions a t atmospheric pressure. Velocity measurements are greatly simplified at high frequencies since small samples of electrolytes are sufficient and reflections from the walls of the container can be made negligible. A resonance method is generally used wherein standing waves are produced in a column of the solution and the wave-length evaluated. Precise velocity measurements may be made with the acoustic interferometer developed by Pierce for gases and by Hubbard and Loomis for liquids. With this device a'bsolute velocities accurate to 0.06y0 are claimed.6 by an optical method originated by Debye and Sears and independently by Lucas and B i q ~ a r d .~ The optical method depends upon t,he fact that the passage of ultrasonic waves through a liquid sets up periodic density variations. The latter act as an optical grating which can be used to diffract a light beam or can be made directly visible. (1.2) Comparison of the Ultrasonic and Piezometric Methods.-Com- pressibility data from ultrasonic measurements on aqueous solutions have been shown to be in good agreement with direct piezometric determinations. Although the latter are high pressure measurements accurate compressi- bilities a t atmospheric pressure may be computed from them by invoking the concept of " effective pressure " introduced by Gibson.lo This concept follows from Tammann's hypothesis,ll that a t constant temperature the water in a given solution behaves as does the same weight of pure water under a constant effective pressure P, in addition to the external pressure.The pressure-volume relationship of pure water and of many other pure substances is given by Tait's equation where B and C are positive constants and v, is the specific volume of the substance. With Tammann's hypothesis the Tait equation applied to the water within a solution which is under a total pressure P +- P takes the form where v1 is the specific volume of the water in the solution and the constants C and B have the same values as in equation (3) for pure water. The specific Greater relative precision is obtainable - azJ,/aP = 0 . 4 3 4 3 ~ / ( ~ + P ) . ' (3) - a271/a~ = O.XMC'~(B + P 3- Y) .' (4) volume of the solution is given by v = x1v1 $- xzv2 - Proc. Amer. Acad. Arts Sci. 1925 60 271. ATature 1927 120 189 ; Phil. Mag. 1928 5 ti Freyer J . -4mer. Chem. Xoc. 1931 53 1313. 17 295. * ( 5 ) 1177 ; J . Opt Soc. Amer. 1926 i Bachem Z . Physik 1936 101 541 ; Falkenhagen and Bachem Z. Eklctrochem. 8 Debye ibid. 1932 33 849 ; Debye and Sears Proc. Nat. Acad. Sci. 2932 18 1935 41 570; Szalay Physiknl. Z. 1934 35 639. 409. Compt. rend. 1932 194 2132; 195 121; J . Phys. Radium 1932 3 464. lo J . Amer. Chem. Soc. 1934 56 4 865. l1 Z . physikal. Chern. 1893 11 676. 86 QUARTERLY REVIEWS Concn. % where x denotes the weight fraction and v2 the partial specific volume of the dissolved salt. Substitution for v1 in equation (4) leads to the Tait- Gibson equation lo6/? (bar-') NaCl KC1 1 KBr KI or in integrated form j (i) (ii) (i) (ii) (0 (ii) .40.4 40.6 41.7 41.8 43.5 43.2 . . . . 37.5 37.6 39.4 39.5 41.9 41.7 . . . . 33.4 33.2 36.2 36.3 . . . . 31-0 30.7 34.2 34.3 38.4 38.1 . . . 28.8 28.4 32.4 32.4 . . 34.8 34.6 . . . . 31.4 31.1 . . . .~ where Pat. is atmospheric pressure. At moderate concentrations and pressures the terms containing v2 are negligible. (i) (ii) 44.3 44.3 41.7 41.7 38.0 37.8 33.7 33.4 Isothermal compressibilities at 25" and 1 bar computed by two independent methods (i) ultrasonic (ii) piexometric 6 10 16 20 24 30 40 45 ~ Using equation ( 7 ) Gibson l2 determined P for various alkali halide solutions from a single compression of each solution to 1000 bars and then calculated His data are compared in the Table with those computed from Freyer's ultrasonic velocity measure- ments.6 The excellent agreement shown by these entirely independent sets of data contributes strong support for the Tait-Gibson equation and the concept of effective pressure.(1.3) Correlation with the Debye-Huckel Theory.-Acoustic velocity and compressibility data may also be correlated with the interionic attraction theory of electrolytes. For solutions of a single salt the Debye-Huckel limiting law l3 evaluates the partial molal free energy of the dissolved salt G2 = (W/an,) p at a very low but finite molarity c as a t 1 bar from equation (6). G2 - = vRT loge c - AD-IT-*(Z Yizt)ic* . * (8) where A = (n.r6N3/103k)t and Gi is a function of temperature and pressure only ; Y = C vi where vc is the number of ions of the ith species per mole- cule ; x i is the valency of the ion D the dielectric constant E the electronic cha,rge N Avogadro's number and k Boltzmann's constant.From this 12 J . Anw. Chein. ~ o c . 1933 57 284. l 3 Physikal. Z . 1023 24 185. BARNARTT EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES 87 equation the partial molal volume of the dissolved salt 7 = (aCr,/i3P)~ becomes l4 v2 - v; =avc* . (9) where The partial molal compressibility of the dissolved salt K = - aV,/aP is then evaluated l 5 to be where K - K = a & . - (10) For direct comparison with experimental determinations it is more con- The apparent venient to use the corresponding apparent molal quantities. molal volume of the dissolved salt +v is defined by where nI and n2 are the numbers of moles of solvent and solute respectively Y is the volume of the solution and 8 the molal volume of pure solvent.It follows from this definition that which may be applied to extremely dilute solutions as or in integrated form a(c+v)/ac = v2 * (13) +v=:rV2.dc 0 . Substitution for V z from equation (9) yields where Sv = $ov. where subscript zero denotes pure solvent obeys the equation where S = $aK. #lv-+;=&7c* . - (15) $K = - a+v/ap = CBV - n,BoVo>/n - (16) $ K - + ; = S X C f . * (17) d - do = ac - bc; . * (18) Similarly the apparent molal compressibility defined as Equation (15) may be rewritfen in terms of density whence l6 where a = of the solute. combining equations (15) and (17) 71ix.l' where f = 10-3(p0& - +g) and g = Chem. 1931 A 155 65. - do#$) and b = 10-3d0Xv ; M is the molecular weight A similar expression for compressibility is obtained upon #? - go = -fc + gci .' (19) - poSv). l4 See Redlich Naturwiss. 1931 19 251 ; Redlich and Rosenfeld 2. physikal. Gucker Chem. Reviews 1933 13 111. l6 Root J . Amer. Chem. SOC. 1933 55 850. 1' Gucker ibid. p. 2709. 88 QUARTERLY REVIEWS Since all these equations have been derived from the limiting Debye- For such solu- Huckel law they apply only to extremely dilute solutions. tions the relationship u2 = L/Pd may be utilised in the form (20) where Au = u - uo etc. Substitution for Ad and Ap from equations (18) and (19) gives the acoustic velocity as a function of concentration only l8 where u - u0 = hc -jG . ' (21) and For a given solvent at fixed temperature the limiting slopes SV and XK which characterise the linear relationships between the apparent molal quantities and the square root of the concentration are constants for all salts of the same valency type.Hence the limiting slopes of the plots Ad/c-c* AP/c-c* and Au/c-c* are also constants for all salts of a given valency type. Experimentally the determination of any one of the five functions c&., $= Ad/c Ap/c and Au/c a t high dilution with sufficient accuracy to test the theoretical limiting slope is difficult. Some success has been achieved with density measurements ; the results obtained for strong electrolytes tend to support the interionic attraction theory. l9 The measurement of ultrasonic velocity or compressibility in very dilute solutions with the pre- cision required t o test the limiting theory has not yet been accomplished.A striking result is obtained when the experimental values of any one of the above functions are plotted against the square root of the concentration. A linear relationship is observed in each case,2o extending over wide con- centration ranges and down to relatively low concentrations. The coefficients of these empirical relationships differ from the theoretical values given by equations (15) (17) (18) (19) and (21). Furthermore the slopes of the observed lines are not constants for salts of the same valency type. No adequate explanation of these facts has appeared. In the case of the apparent molal compressibility the empirical square- root relationship first observed by Gucker l5 17 a t high concentrations has been found to hold within experimental error down to 0.03 molar the lowest concentration studied.The same relationship has been observed for some l9 Harned and Owen " The Physical Chemistry of Electrolytic Solutions " "(1 2o Barnartt ref. (18) ; Gucker ref. (17) ; Masson Phil. Mag. 1929 8 218 ; Root Barnartt J . Ghem. Phys. 1952 80 278. edn. p. 264 Reinhold Publishing Corp. New York 1950. ref. (16). BARNARTT EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES 89 60 strong electrolytes. 21 * I n most instances the adiabatic compressibility data determined from ultrasonic velocities were used without conversion to isothermal compressibilities since neither the linearity nor the slopes of the square-root plots are appreciably affected by this substitution. 24 (1.4) Solvation from Compressibility Data,-Compressibility data may be correlated with the degree of solvation of dissolved salts.The correlation is based on the assumption that the water molecules in the immediate vicinity of an ion have modified physical properties similar to those of pure water under high pressure. An ion may be considered to be surrounded by one or two (or possibly several) shells of bound water molecules which are under such high pressure as to be virtually incompressible. As a first approximation the water of hydration about one ion is conceived as a sphere a t the boundary of which the compressibility falls abruptly from that of pure water down to zero. It follows then if ni is the number of moles of incompressible solvent in the solution that l a - B O V O v aP v * @ = - -{Vo(nl - ni)> = (nl - ni)- and therefore where s is the solvation expressed in moles of solvent per mole of solute.The study of solvation in this manner originated with Pa~synski,~5 who used the following modification of equation (23) Solvation numbers calculated from equation (24) decrease slowly with increasing concentration 25 25a and are qualitatively in harmony with Bernal and Fowler's theory of ionic hydration. 26 (1.5) Solutions of More than One Salt.-Measurements of ultrasonic velocity in solutions containing more than one salt have been confined to sea water. These measurements are important for oceanic depth studies and for sonar ranging. In an investigation of a synthetic sea water con- taining 7 salts Weissler and Del Grosso 23 found that t,he contributions of = (n1b2N - B / P o ) * * (24) 21 Bachem ; Falkenhagen and Bachem ref. ( 7 ) ; Giacomini and Pesce Ric.Sci. 1940 11 605 ; Gucker refs. (15) (17) ; Lunden Svensk Chem. Tidskr. 1941 53 86 ; 2. physikal. Chem. 1943 192 345 ; Prozorov J. Phys. Chem. U.S.S.R. 1940 14 383 391. 22 Krishnamurty Current Sci. I n d i a 1950 19 87 ; J . Sci. Iizd. Res. India 1950 9 B 215; Prakash Saxena and Srivastava h'ature 1951 168 532. 2 3 Weissler and Del Grosso J . Acoust. Soc. Amer. 1951 23 219; Lunden ref. 21. 2 4 Bachem ref. (7). 25 Acta Physicochim. U.R.S.S. 1938 8 385. 25Q Giacomini and Pesce ref. 21. 26 J. Chern. Phys. 1933 1 515. * Recent reports from India 2 2 present data on alkali halide solutions which do not obey this relationship. The ultrasonic velocity measurements however exhibit concentration dependence quite. different from that shown by the more accurate measurements of other authors,7~ 2 1 7 2 3 and must be tentat'ively considered as unreliable.90 QUARTERLY REVIEWS each salt to the sound velocity and compressibility of the solution were additive. Thus from the data on simple solutions of each of the seven salts the increments (u - uo) and (/? - Do) were obtained a t the same concentration as that at which the individual salt is present in sea water. Then the velocity and compressibility for the sea water were calculated by summing up the increments and combining the sums with the corresponding value for distilled water. The calculated values agreed with the measured values within experimental error (0.1 %). (2) Conductivity Since the conductivity of an electrolyte varies with temperature and pressure the passage of ultrasonic waves is accompanied by periodic con- ductance changes.The change in conductivity of an electrolyte dK brought about by a small adiabatic compression may be written where y = ( l / ~ ) ( a ~ / a P ) is the pressure coefficient and 6 = ( l / ~ ) ( a ~ / a T > the temperature coefficient of conductivity. Substitution for dT from the general thermodynamic relationship leads to the equation If the amplitude of the conductance change produced by an acoustic wave be measured in an electrolyte whose coefficients y and 6 are known from static measurements the pressure amplitude of the wave may be computed by means of equation (27). From the pressure amplitude p the sound intensity I is computed from where I is the average energy flow per sq. em. per second. Thus the measurement of the conductance changes in an electrolyte may be used to determine acoustic intensity.Conversely if the intensity is also evaluated experimentally then the pressure coefficient of conductivity may be calcu- lated for electrolytes whose temperature coefficients are known. In their method a filament of constant alternating current of frequency fl is passed between the ends of two fine wire electrodes brought close together. The current filament is arranged perpendicular to the direction of a travelling ultrasonic wave and may be made essentially small in comparison with the wave-length if the acoustic frequency f o is not too high. Under these conditions two side bands of frequency (fo + f l ) and (fo - fi) are produced with a voltage that depends upon the conductance changes. Measurements of the side-band voltages for sodium chloride and copper sulphate solutions showed satisfactory agreement with the voltages calculated from the known conductivity coefficients.A method of measuring the conductivity effect employing stationary dK/K = y d P + 6 dT . . (25) (aT/aP)s = aT/Cpd . * (26) dK/K = ( y -/- &T/Cpd)dP . * (27) I =p2/2ud . * (28) The conductance effect was first studied by Fox Herzfeld and 27 Phys. Review 1946 70 329. BARNARTT EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES 91 acoustic waves has been described by Lichter and Khaikin.28 A constant alternating current having the same frequency as the sound wave is applied to fine wire electrodes situated in a pressure antinode of the standing wave. Location of the electrodes in a velocity node eliminates possible complications from velocity variations.A phase difference is maintained between the applied voltage and the sound wave. The phase displacement produces a rectified voltage which is a measure of the conductivity fluctuations. Elec- trode polarisation is minimised by changing the sign of the rectified voltage periodically. This is accomplished by changing the phase of the applied voltage to the opposite phase f' times per second where f' <fo. With this method the pressure coefficient y was determined a t 20" for 0.005~- silver nitrate solution for which the temperature coefficient 6 was known. Then y being assumed to be independent of temperature 6 was determined ultrasonically over the temperature range 5-60'. These values of 6 agreed with those from static measurements within experimental error.Recently Krishnamurty 28a announced that the conductivities of nitrate solutions as measured by the usual Kohlrausch method decrease when the solution is subjected to ultrasonic vibrations. Conductance changes as high as 20% were reported for an ultrasonic frequency of 2-51 megacycles/sec. at an unspecified intensity. In addition the passage of current through each solution was accompanied by an increase in the velocity of ultrasonic waves in it and consequently by a decrease in its compressibility. These effects merit confirmatmion. (3) Space Charge (the Debye Effect) In 1933 Debye L9 predicted that ultrasonic waves create space charge in electrolytic solutions. The space charge arises because the ions owing to their inertia lag behind the solvent in the sound field.Since the positive and negative ions will usually move with different velocities the electrical potential at a given point in the irradiated solution will acquire an alternating component having the same frequency as the acoustic wave. Debye derived the magnitude of the effect to a first approximation specifically omitting diffusion and interionic attraction as being second- order considerations. The force on an ion in a plane ultrasonic wave was considered to comprise an electrical force resulting from the space charge and a frictional force resulting from the difference in velocity of the ion and the surrounding liquid. where ei pi c2 and mi are respectively the charge friction constant velocity and mass of the ion ; vo is the velocity of the solvent ; and X is the electric field int,ensity .Combination of this equation with the equation of continuity and Poisson's equation leads to the following general solution 29 The equation of motion is then eiX - p i ( ~ * i - v0) = midvi/dt . . (as) 28 J. Exp. Theor. Phys. U.S.S.R. 1948 18 661. 2aa J . Sci. I d . Res. Indin 1051 10 By 149. 29 J . C'henz. Phys. 1033 1 13. 92 QUARTERLY REVIEWS Here E is the amplitude of the potential oscillations mH the mass of the hydrogen atom a. the velocity amplitude of the solvent K the conductivity of the solution in electrostatic units D the dielectric constant of the solvent Mi the effective gram-ionic weight of the ion and m/2n the frequency. If the frequency is not too high the expression on the extreme right can be made equal to unity. Under these conditions equation (30) applied to an aqueous solution of a uni-univalent salt reduces to Thus the Debye effect provides a measure of the relative masses of ions and hence their degree of solvation.With a solution of known ionic masses the effect may be used to determine a, from which the acoustic intensity may be calculated by the equation I=+uda,2 . * (32) The order of magnitude of E may be revealed by putting p+ = p- and M - M- = 15 whence E becomes volt per unit velocity amplitude. Oka 30 extended the derivation to include interionic attraction by adding terms to equation (29) for the electrophoretic force and the force of relaxation. The added forces however applied only to dilute solutions and represented small corrections. Hermans 31 pointed out that equation (29) fails to show that the space charge must disappear when the densities of the ions and solvent are equal.He remedied this by taking into consideration the force on the ion resulting from the pressure gradient in the acoustic wave. The equation of motion then becomes eiX - pi(^< - u0) = midvi/dt - Vidoduo/dt . * (33) where Vg is the volume of the ion and do the density of the solvent. Bugosh Yeager and Hovorka 32 extended the calculations to include not only this pressure-gradient term but also the forces resulting from diffusion and interionic attraction. The extended solution has only theoretical interest at the present time however since experimental evi- dence for the Debye effect is as yet qualitative. Yeager Bugosh Hovorka and McCarthy 33 first demonstrated the existence of the effect in simple electrolytes utilising a stationary ultrasonic field.The apparatus used did not permit determination of the velocity amplitude within the test solution hence comparison of the data with the predictions of equation (31) was not possible. In agreement with theory however the measured alternating potentials were found to be roughly independent of concentration for dilute uni-univalent electrolytes and to vary with the electrolyte used. With the standing-wave technique elaborate screening precautions are necessary to prevent electromagnetic coupling between the high-frequency source and the detecting cell. This complication can be minimised by the 30 Proc. Phys. Math. SOC. Japan 1933 15 413. 31 Phil. Mag. 1938 25 426. 3 3 I b i d . 1049 17 411. 32 J . Ghem. Phys. 1947 15 592. BARNARTT EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES 93 use of pulse-modulated ultrasonic whereby the acoustical effects are separated in time from electromagnetic coupling and are measured under essentially free-field conditions.A potential amplitude of 5 microvolts per unit velocity amplitude has been obtained recently by the pulse method in 0~005~-potassium chloride solution. 35 From equation (31) this corres-a ponds to a mass difference between the potassium and chloride ions of 70 or approximately 4H20 per mole of potassium ion on the basis of Bernal and Fowler's conclusion 26 that the chloride ion is not hydrated. This result may be compared with the values 6-7H20 from compressibility data 25 and 2H,O from ionic-activity data.36 Hermans 31 and independently Rutgers 37 pointed out that the Debye effect should be much larger in colloidal solutions where the positive and negative ions exhibit greater differences in mass.Approximate theoretical treatments for this case have been presented by Hermans 313 38 and by Enderby. 39 Both theories assume that the vibration potentials in colloidal solutions arise primarily from periodic distortion of the double layer around each colloidal particle and that the relative motions of small positive and negative ions contribute very little. The distortion occurs because the heavy colloidal particle moves more slowly than the ionic charges outside it. The result,ing asymmetric charge distribution is equivalent to a dipole situated at the centre of the particle. The potential differences developed by the acoustic wave may be computed by summing up the dipole moments of all the particles.Hermans's derivation predicts that potential ampli- tudes of the order of a volt should be attainable.38 Much smaller potentials are indicated by Enderby's theory. The following simple formula for estimating the potential amplitude in colloidal solutions has been given by Vidts 4O where is the electrokinetic potential of the colloidal particles m their mass per c.c. and The first measurements reported for a silver iodide s0l,4O9 41 indicated potential amplitudes two orders of magni- tude smaller than those predicted by equation (34). More recent measure- ments in a colloidal arsenic trisulphide solution,42 however gave an amplitude of 1.5 mv as compared with 7 mv calculated from the formula. the viscosity. (4) Effects on Electrode Potentials (4.1) Unpolarised Electrodes.-When an unpolarised electrode is mb- jected to acoustic vibrations the electrode potential should acquire an 3 4 Hunter Proc.Phys. SOC. 1050 B 63 58 ; Yeager Bugosh and Hovorka ibid. 35 Yeager Dietrick Bugosh and Hovorka J. Acoust. SOC. Amer. 1951 23 627. 36 Stokes and Robinson J. Anzer. C'hem. SOC. 1948 70 1870. 37 Physica 1938 5 46. 39 Proc. Roy. Soc. 1951 A 207 329. 4* Bull Acad. roy. Belg. Classse mi. 1945 No. 3 p. 5. *l Rutgers Nature 1946 157 74. 4 2 Rutgers and Vidts {bid. 1960 165 108. 1951 By 64 83. 38 Phil. Mag. 1938 26 674. 94 QUARTERLY REVIEWS alternating component resulting from the periodic compressions. Where the electrode is composed of condensed phases only the alternating com- ponent should be very small.Moriguchi 43 observed no change in the potential of copper electrodes in dilute copper sulphate solution upon irradiation with ultrasonics. Schmid and Ehret 44 confirmed this observa- tion and also noted no change of potential for nickel electrodes in nickel chloride solution. These workers however did not attempt to reveal small alternating components. The potential of a gas electrode is much more sensitive to compression and in this case an appreciable temperature variation will occur in the gas phase if the compression is adiabatic. Schmid and Ehret 44 reported that the potential of a hydrogen electrode in dilute sulphuric acid became indefinite to & 5 mv in the presence of ultrasonics. Again no attempt was made to reveal an alternating component. A t,heoretical derivation of the alternating component has been given recently by Yeager and Hovorka 4 5 9 46 for the hydrogen electrode.If it is assumed that the irradiated electrode is reversible the change in electrode potential may be evaluated by thermodynamics. The added acoustical pressure in the gas phase Pa produces a change in potential given by the general equation where P is the time average of the gas pressure and F the Faraday of elec- tricity. With the restriction of low acoustic intensity so that Pa is a small fraction of P, the approximation log (1 + Pa/Pg) = Y,/Pg may be applied t o equation (35) to give AE = RTPa/'zFPg . (36) or E = RTp/xFP . . (37) where E is the potential amplitude and p the pressure amplitude. At low audio-frequencies where the thickness of the gas film is small compared with the wave-length the acoustic compressions in the gas phase may be almost isothermal in which case the potential amplitude would approach the value given by equation (37).At higher frequencies the compressions would be practically adiabatic and providing the electrode behaves reversibly the potential amplitude is readily shown 4 5 to be approximately where S is the molar entropy of the gas and CP its molar heat capacity a t constant pressure. Yeager and Hovorka 46 have expressed doubt whether gas electrodes can remain reversible a t ultrasonic or even a t the upper audio-frequencies. They proposed a kinetic treatment and developed a 4 3 J . Chem. SOC. Japan 1934 55 749. 4 p 2. Elektrochem. 1937 43 697. 4 6 J . Chem. Phys. 1949 17 416. 48 J . Electrochem. SOC. 1961 98 14.BARNARTT EFFECTS OF TJLTRASONIC WAVES ON ELECTROLYTES 95 general equation for the hydrogen electrode which is applicable to both unpolarised and polarised electrodes and which reduces to equation (37) at low frequencies. This electrode effect like the conductivity and Debye effects may prove useful for the absolute measurement of acoustic intensity in liquids and consequently for exploring complex ultrasonic fields. All three effects do not have a characteristic frequency as the usual crystal gauges do. They have the further advantage that the electrolyte surrounding the electrodes may be selected so that its characteristic acoustic impedance (ud) is nearly equal to that of the irradiated liquid. Since the electrodes may be made small in comparison with the wave-length reflection of the wave a t the measuring instrument can be avoided.(4.2) Polarised Electrodes.-In the case of electrodes polarised by current flow pronounced depolarising effects can be produced by the application of ultrasonic waves. Acoustic agitation is particularly violent at a liquid- solid interfa~e.~' At the electrode surface therefore the concentration changes in the diffusion layer are reduced and the products of electrolysis largely removed. From a study of the electrolysis of copper sulphate solution with copper electrodes Moriguchi 43 concluded that the diffusion layer at each electrode was eliminated by irradiation with ultrasonics. With ordinary stirring the plot of current through the cell against applied voltage deviated considerably from linearity (Ohm's law).When ultrasonic waves were substituted for the stirring however a linear plot was obtained indicating that polarisation was eliminated a t both a,node and cathode. It is possible however that appreciable polarisation remained if it were approximately proportional to the current density. Where one of the products of electrolysis is a coating over the surface of the electrode ultrasonics may give rise to considerable depolarisation by removing the coating. The surface layer tends to be disrupted and dis- persed colloidally in the liquid especially when it is brittle or does not adhere tenaciously to the substrate.4s The mechanism whereby the coating is torn off probably involves cavitation the periodic formation and collapse of cavities which occurs most readily a t interfa~eS.~8 49 Depolarisation by removal of a coating from the electrode surface was first demonstrated by Moriguchi using smooth platinum electrodes for the electrolysis of aqueous solutions.Ordinarily the liberation of hydrogen and oxygen at smooth platinum electrodes requires approximately 1.7 volts. When the anode was irradiated with ultrasonics the voltage required a t moderate current densities was reduced to about 1.2 which is close to the equilibrium value for the oxygen and hydrogen electrodes. Most of this depolarisation resulted from the removal of an anodic coating (presumably 47 Richards J . Amer. Chem. SOC. 1929 51 1724 ; Richards and Loomis ibid. 4 8 Sollner Trans. Paraday SOC. 1938 34 1170. 49 Bondy and Sollner ibid. 1935 31 835. 1927 49 3086. J . Chem. SOC. Japan 1934 55 761. 96 QUARTERLY REVIEWS platinum oxide) which was found to be dispersed in the electrolyte.At relatively high current densities the anodic film was not all removed and the marked depolarisation no longer occurred. Several other examples of ultrasonic action on electrode coatings have been described by Schmid and Ehret 50a The formation of an anodic coating on lead in sodium carbonate solution is retarded. On aluminum anodes in sodium sulphate solution on the other hand the anodic film forms more rapidly in the presence of ultrasonics ; however a thinner film and decreased polarisation are obtained. The grey layer that passivates iron in concen- trated sulphuric acid is removed and the iron continues to dissolve as long as the ultrasonic waves are applied. The reactivation of passive chromium in concentrated hydrochloric acid occurs much more rapidly.In concen- trated nitric acid the passivity of chromium is not affected by ultrasonics but that of iron is quickly destroyed. Roll 5 l has shown that the passivating film which causes pronounced polarisation of silver anodes in cyanide plating solutions at relatively low current densities does not form in an ultrasonic field until much higher current densities are applied. In intense ultrasonic fields marked depolarisation occurs at gas elec- trodes even in the absence of surface coatings on the electrodes. At constant current density there exists generally an intensity above which depolarisation suddenly increases. Similarly a t constant intensity there exists a current density above which the depolarising action rapidly dimin- ishes.Figs. 1 and 2 taken from Schmid a,nd Ehret’s data 44 show typical curves obtained for hydrogen evolution at nickel cathodes in 0*2~-sodium sulphate solution (pH 4.2) with an acoustic frequency of 284 kilocycles/sec. Curves similar to that of Fig. 1 were obtained for hydrogen deposition from sodium sulphate solution on eight other metal electrodes. Anodic deposition of chlorine on platinum from hydrochloric acid solution also gave the same type of curve. In all cases a hissing noise characteristic of cavitation began a t the intensity at which the potential jumped. That the jump in potential is produced by the cavitation was later confirmed by Polotskii and F i l i p ~ o v ~ ~ who reproduced the potential jump for both hydrogen and chlorine liberation when cavitation was brought about by superheated steam.Fig. 2 shows that the pronounced depolarisation disappears a t relatively high current densities. This behaviour was also observed by Piontelli 53 for hydrogen deposition from several other electrolytes. According to Schmid and Ehret,44 the depolarisation mechanism is a mechanical one. When cavitation occurs the gas being deposited a t the electrode is drawn into the cavities and the gas pressure at the electrode decreases. At low current densities where the gas is liberated very slowly the gas pressure a t the electrode may be reduced considerably below atmospheric pressure and the electrode polarisation may become negative when based upon the equilibrium potential for one atmosphere pressure (see Fig. 2). At high current densities only part of the liberated gas is removed by cavitation.I O U 2. Elektrochern. 1937 43 408. 5 1 2. Metallk. 1950 41 413. 62 J . Uen. Chem. U.X.S.R. 1947 17 193. b 3 Piontelli Atti Accad. Lincei Classe sci. fis. mat,. nat. 1938 27 367 681. BARNARTT EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES 97 4 6 8 I0 ( CURRENT IN OSCILLATOR CIRCUIT amp.) RE L AT1 V E I NTE N SI TY FIQ. 1 Effect of ultrasonic intensity on hydrogen deposition potential at 2.5 milliamp./crn.$ (from Schmid and Ehret Z. Elektrochem. 1937 43 597). z 2.5 5.0 7.5 10.0 CURRENT DENSITY milliump./cm2 FIG. 2 Variation of hydrogen deposition potential with current density A-in the presence of strong agitation ; B-in the presence of intense ultrasonics ; &equilibrium potential at hydrogen pressure of 1 atm. (from Sch,mid and Ehret.loc. cit.). This mechanism is in accord with the observations that the acoustic intensity required to produce the potential jump increases with current density and that the potential jump is practically independent of the nature of the cathode metal. Q 98 QUARTERLY REVIEWS Limited data on the anodic deposition of oxygen indicate somewhat different behaviour in an ultrasonic field. Schmid and Ehret,44 using a platinum anode in 0-2lur-sodium sulphate solution found no sudden potential jump rather a gradual depolarisation with increasing ultrasonic intensity. In this case the mechanism is complicated by oxidation of the platinum surface. Depolarisation a t relatively low acoustic intensities where cavitation is absent has been studied by R0ll.5~9 s4 During the simultaneous deposition of hydrogen with nickel with silver and with copper the depolarising action of ultrasonics was similar to that of strong agitation.This was true also for anodic dissolution of silver in the argentocyanide plating bath. For copper dissolution in the acid sulphate bath neither ultrasonics nor agitation produced any appreciable change in polarisation. The acoustic depolarisation is greatly dependent upon the frequency. At a given acoustic intensity level the cathodic depolarisation during nickel deposition was found to increase with decreasing frequency.55 The presence of an alternating component in the potential of a polarised gas electrode subjected to acoustic vibrations was demonstrated by Nikitin 56 a t audible frequencies and by Yeager Bugosh Hovorka and McCarthy 33 at ultrasonic frequencies.A theoretical treatment of this effect has been given for the hydrogen electrode by Yeager and H ~ v o r k a . ~ ~ Pulse techniques have been used recently to measure the alternating component for polarised hydrogen electrodes. 5' The following results were obtained.58 With platinised platinum in dilute hydrochloric acid or sodium sulphate solutions the potential amplitude increased linearly with the polarising current at low current densities but a t higher current densities the curves exhibited regions of almost constant amplitude. The amplitude was practically independent of the electrode metal although with platinised platinum the alternating component was steadiest with respect to rapid time fluctuations. At a given current density the amplitude was an increasing but not a linear function of ultrasonic intensity.Measurements in sodium sulphate solutions of different concentrations indicated that the amplitude is roughly inversely proportional to the conductivity of the solution. (5) Electrodeposition Since ultrasonic waves change the polarisation of electrodes a t which metals and hydrogen are liberated they can influence the current efficiency of metal deposition the grain growth of the depositing metal the composition of alloy deposits a,nd other important factors in electroplating. In addition the purity of the deposit can be increased. It was pointed out by K e l ~ e i i ~ ~ who first proposed the use of ultrasonics in electroplating that suspended 54 2. Metallk. 1950 41 339. b5 Roll and Schrag ibid. 1951 42 197.56 Compt. rend. Acad. Sci. U.R.S.S. 1934 4 309 ; 1936 [ Z ] 2 67 ; J . Gen. C?Lern. 57 Yeager Bugosh Dietrick and Hovorka J. Acoust. SOC. Amer. 1950 22 686. 58 Yeager Personal communication. Austrian Patent 121,986 (1931); Chem. A h . 1931 25 2926. U.S.S.R. 1936 6 1393 1401; 1940 10 97. BARNARTT EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES 99 impurities in the electrolyte would not adhere to the electrode since the relatively massive electrode will not follow the movements of $he particles. He stated also that the hydrogen content of the metal could be reduced in some cases by preventing the deposition of unstable metal-hydrogen alloys. A patent by Dutt 6* claimed that metals such as aluminum and mag- nesium may be electrodeposited from aqueous solutions in an ultrasonic field.However Schmid and Ehret 50cs did not succeed in depositing aluminum or magnesium by the method described in the patent and from the action of ultrasonics on the deposition potential of hydrogen at mag- nesium electrodes 44 they concluded that the electrodeposition of magnesium from aqueous solution appears unlikely. On the other hand these workers demonstrated that metal deposition can indeed be promoted by an intense ultrasonic field. Thus a uniform nickel deposit was obtained from a nickel sulphate solution under conditions that fail to yield nickel in the absence of ultrasonic^.^^ In the electrodeposition of metals at high current densities where hydrogen is co-deposited the agitating action of ultrasonic waves should increase the current efficiency of metal deposition just as ordinary stirring does.This effect has been demonstrated in the deposition of chromium from chromic acid solution,61 of nickel 5 4 9 5 5 and copper 51 from sulphate solution and of silver from cyanide s0lution.5~ The current efficiency increases continuously as the ultrasonic intensity is raised. 51j 54 According to Roll,54 the agitating action is unusually violent because the motion of the hydrogen bubbles a t the electrode surface is speeded up by the acoustic field. In support of this mechanism he found that air bubbles in aqueous glycerol rise more rapidly when irradiated with ultrasonics. 51 For metal deposition a t low current densities and relatively high current efficiencies the influence of ultrasonics on current efficiency cannot be explained by agitation. A reduction in current efficiency has been reported for zinc,G2 nickel,54 55 and copper 51 6 2 plating from sulphate solutions and for silver plating from nitrate solutions.63 The decrease in current efficiency may be only an apparent one however resulting from colloidal dispersion of part of the electrodeposited metal.Such dispersion is likely to occur if the deposit does not adhere strongly to the substrate 64 or if it consists of fine -grained aggregates having poor cohesion,63 particularly a t acoustic intensities above cavitation levels.65 Ultrasonic waves do not disperse solid substances of high cohesion such as glass and ductile metals 48 and large- grained ele~trodeposits.6~ The dispersion of cathodically deposited metal by ultrasonic irradiation during electrolysis is an effective method for the preparation of very finely 6 O F.P.749,007 (1933) ; Chem. Abs 1933 27 6657. 61 Miiller and Kuss Helv. Chim. Actn 1950 33 217. 6 2 Rummel and Schmitt, Korrosion u. Metullschutz 1042 19 101. 63 Levi Ric. Sci. 1949 19 887. 6 4 Clans 2. tech. Physik 1935 16 80. 6 5 Roll 8. Metallk. 1951 42 271. 100 QUARTERLY REVIEWS divided metal. The method originated with C l a ~ s ~ ~ ~ 66 who showed that the degree of dispersion obtained depends upon several factors. A smooth electrode surface low cathode current density high acoustic energy and high frequency all favour finer particle size. The most suitable cathode materials are those to which the depositing metal adheres poorly. Practi- cally all metals which separate out electrolytically can be dispersed.67 This method should find use in the preparation of metal powders sols catalysts etc.In the case of electrodeposits which are not dispersed the action of ultrasonics on grain growth is the resultant of two opposing tendencies. The violent agitation in the solution decreases the cathode polarisation and therefore promotes the growth of large grains. On the other hand the mechanical vibrations may induce prolific nucleation in the depositing metal as they do during the solidification of metallic melts.68 Rummel and Schmitt 62 noted an increase in the grain size of copper deposits from an acid sulphate bath exposed to ultrasonics. On the other hand Levi 63 found that silver crystals in deposits from irradiated silver nitrate solutions were invariably very fine. Greater hardness and tensile strength of electro- deposited copper and nickel 61 and increased hardness of chromium deposits 6 1 s 69 have been produced by ultrasonics.This is indirect evi- dence for refinement of grain size in these deposits since reduced grain size generally increases the hardness and tensile strength of electroplated metals.70 The influence of an acoustic field on grain growth should increase as the intensity of the field is increased. This has been demonstrated by Roll 71 with nickel plating. The current-density range for bright nickel plating from a sulphate solution was shifted to continuously increasing current densities as the intensity was raised. For example the maximum current density for bright deposits which was 3 milliamp./cm.2 in the unstirred solution and 9 milliamp./cm.2 with agitation was raised to 10 and 43 milliamp./cm.2 respectively with ultrasonic intensities of 0-02 and 0.3 watt/cm.2. Muller and Kuss 61 reported that the acoustic effects on copper nickel and chromium electro- deposits diminished with an increase in frequency from 16 to 320 ldo- cycles/sec. They also made the interesting observation that brass deposits had higher zinc content when plated in the presence of ultrasonics. In general the effects described above refer to electrodes situated per- pendicular to the direction of propagation of the sound. An interesting phenomenon was observed by Young and Kersten v 2 when electroplating Frequency is also an important factor. 6 6 2. tech. Physik 1935 16 202. 67 Claus and Schmidt Kolloid-Beih. 1936 45 41. 68 Schmid and Ehret 2. Elektrochem. 1937 43 869 ; Schmid and Roll ibid.1939 6@ Ishiguro and Haramai J. Centr. Aeronaut. Res. Inst. 1944 No. 3 201 ; Chm. 70 Blum and Kogaboom " Principles of Electroplating and Electroforming " 3rd 7 1 Z . ,Wetallk. 1951 42 238. 73 J . Chem. Phys. 1936 4 426. 45 769 ; Sokoloff Acta Physicochim. U.R.S.S. 1935 3 939. Ah. 1948 42 1515. edn. p. 66 McGraw-Hill Book Co. Inc. New York 1949. BARNARTT EFFECTS OF ULTRASONIC WAVES ON ELECTROLYTES 101 metals on a cathode whose surface was parallel to the acoustic beam. Rippled deposits were obtained from several plating baths. The distance between ripples was equal to half the ultrasonic wave-length. Other investigators have also observed this 6 2 Young and Kersten interpreted their results as indicating that stationary waves were set up and that the metal ions were relatively more concentrated in layers 0-5 wave- length apart.According t o the Debye effect the periodic changes in ion concentration and the potential differences arising therefrom would be minute-too small to cause gross ripples in the deposit. It is more probable that the ripples result from the depolarising action of the acoustic field which can vary considerably from the nodal positions to the antinodes. In the process of concentrating deuterium by preferential elect,rodeposi- tion of hydrogen it has been shown that ultrasonic vibrations increase the efficiency of ~eparation.'~ The explanation of this effect is based upon the assumption that some of the deuterium evolved at the cathode is not dis- charged directly but is liberated by reactions such as H + HDO + HD + H,O which are catalysed by the electrode surface. The longer the discharged hydrogen remains in contact with the cathode the greater the quantity of deuterium liberated. Ultrasonic agitation speedily removes the dis- charged hydrogen from the electrode surface and therefore diminishes deuterium evolution. 73 Mason Biddick and Boyd J. Chem. Phys. 1951 19 1551.