FILM FORMATIGN mononkmsncs or THE SILVER HALlDES‘ - ' ,, Thesis for the Degree cf PM, ' ' MlCHlGAN STATE UNIVERSITY 8GB DUANE BLEASDELL 1971' * L g, L I B RA R Y . Michigan State - University This is to certify that the thesis entitled Film Formation Reaction Kinetics of the Silver Halides presented by Bob D. Bleasdell has been accepted towards fulfillment of the requirements for Ph.D. Chemistry degree in , x A4, Up Major professor Date July 13, 1971 0-7639 ABSTRACT FILM FORMATION REACTION KINETICS OF THE SILVER HALIDES BY Bob Duane Bleasdell The double layer capacitance and exchange current are two kinetic parameters that are determined from each pulse in the current impulse technique. By observing variations in these two quantities as a function of experimental vari- ables such as anion, concentration and applied charge, the silver halide film growth process is examined. The double layer capacitance is found to be independent of the specific anion present and also of the concentration of anion. A plot of capacitance or exchange current g§_charge applied to the electrode shows an initial flat portion where there is no change in capacitance followed by a region where the capacitance decreases rapidly. From microscope pictures and anodic chronopotentiograms the decrease in capacitance is felt to be due to a decrease in the uncovered area of the electrode. The flat portion at the beginning is believed to be due to an initial increase in height of the deposit al- ready present on the surface. As the halide in solution is changed there is a dramatic change in the quantity of charge Bob Duane Bleasdell that must be applied to cover the surface. Since there is 100% current efficiency in applying the film, the difference in total charge means a difference in height of the three deposits. The exchange current is dependent upon the anion present in solution. It is also dependent upon surface coVerage which means the observed exchange rate is occurring on the uncovered surface area. A reaction order plot shows there is no concentration dependence of the exchange current. This implies a constant concentration of silver ion at the electrode surface. This equivalent concentration :hs cal- culated by comparing the exchange current with the halide present and the reaction order plot for the silver-silver(I) system. Kinetic parameters of the silver-silver(I) system are also measured and compared to the literature values. FIIM FORMATION REACTION KINETICS OF THE SILVER HALIDES BY Bob Duane Bleasdell A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1971 C ‘7/ 7.9 3 ACKNOWLEDGMENTS The author would like to express his appreciation to Professor C. G. Enke for his help and encouragement through- out this study. He would also like to express appreciation to his wife, Linda, for her encouragement and understanding. He also gratefully acknowledges a NDEA Fellowship which supported him during his tenure at Michigan State University. ii I. II- III. IV. TABLE OF CONTENTS INTRODUCTION AND HISTORICAL . . . . . . . . . . A. B. C. D. E. IntrOduCtion O I O O C O O O O O O O O O O O A Brief Outline of Electrode Kinetics and the Electrical Double Layer . . . . . . . . . . Description of the Current Impulse Technique Measurements of Film Formation Reactions . . Studies on Silver Halide Formation . . . . . EXPERIMENTAL . . . . . . . . . . . . . . . . . A. B. C. Solutions . . . . . . . . . . . . . . . . . Cells and Electrodes . . . . . . . . . . . . Instrumentation . . . . . . . . . . . . . . EXPERIMENTAL RESULTS . . . . . . . . . . . . . A. B. Silver-Silver(1) System . . . . . . . . . . 1. Capacitance . . . . . . . . . . . . . . 2. Apparent Exchange Current . . . . . . . Silver-Silver Halides . . . . . . . . . . . Double Layer Capacitance Measurements . Capacitance—Charge Relationship . . . . Microscope Pictures . . . . . . . . . . Other Halides . . . . . . . . . . . . . Apparent Exchange Current . . . . . . . Concentration Dependence of the Apparent Exchange Current in Halide Solutions . Anodization Current . . . . . . . . . . Anodic Chronopotentiometry . . . . . . Cyclic Coulometry . . . . . . . . . . . Relaxation Curves . . . . . . . . . . . I-l ocoooq mmthb-I C CONC LUS I ON 0 O O O O C O O O O O O O O O Q 0 O A. B. Model . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . REFEHNCE S O O C O . O O O O C O O O O . O O . iii 2 6 10 13 16 16 16 18 22 23 23 26 33 34 41 45 45 54 6O 67 68 71 79 83 83 84 86 Table 1. LIST OF TABLES Page Apparent exchange current density for 3.0 x 10-2 to 7.5 x 10"5 M AgClO4 in 1.0 g HC104 o o o o o o o o o o o o o o o o o o o o o 28 Comparison of kinetic parameters for the Silver-Silver(1) SYStem o o o o o o o o o o o o 32 Equivalent silver ion surface concentration in halide solutions obtained by exchange current measurements (Figure 15) . . . . . . . . . . . 66 iv Figure Page 1. Electrical analog for a current impulse experiment . . . . . . . . . . . . . . . . . 7 2. Block diagram of experimental system . . . . 21 3. Differential capacitance from charging and discharge curves for silver as a function of silver ion concentration in 1 M_HC104 . . . . 25 4. Reaction order plot for the silver-silver(1) SYStem in 1 _M- HC104 o o o o o o O o o o o o o 31 5. Differential discharge capacitance of silver as a function of halide ion concentration in 1 M; KNOS o o o o o o o o o o o o o o o o o o o o 37 6. Anodic and cathodic capacitance as a function of pulse current density in 1 M KBr and 1 M.KN03. Pulse width held constant at 1_ x 10' 7 sec. . 40 7. Capacitance in 1 M KBr as a function of applied charge density . . . . . . . . . . . 43 8. Microscope pictures . . . . . . . . . . . . . 47 9. Capacitance in 1 M HCl as a function of applied charge density . . . . . . . . . . . . . . . 49 10. Capacitance in 1 M_KI as a function of applied charge density . . . . . . . . . . . . . . . 51 11. Capacitance as a function of applied charge density in 1 M halide solutions . . . . . . . 53 12. Anodic and cathodic values of the apparent ex— LIS T OF FIGURES change current as a function of pulse current density in 1 M KBr. Pulse width held constant at 1 x 10'7 sec . . . . . . . . . . . . . . . 56 LIST OF FIGURES (Cont.) Figure 13. 14. 15. 16. 17. 18. 19. 20. Double layer capacitance and apparent exchange current as a function of applied charge density in 1 M_KBr . . . . . . . . . . . . . Apparent exchange current density as a function of bromide ion concentration . . . . . . . . Reaction order plot for the silver-silver(I system with no halide present (open circles the horizontal lines are obtained when the halide ion indicated is present . . . . . . . Anodic chronopotentiogram in 1. 0 M KBr with a current density of 1 mA/cm2 . . . . . . . . . Anodic chronopotentiogram in 0.1 M KBr with a current density of 1 mA/cm2 . . . . . . . . . Capacitance as a function of applied charge in 1 .0 fl KBr O O O O O O O O O O O O I O O O Capacitance as a function of applied charge in 1 .0 ! KBr O O O O O O O C O C I I O O O O O C Current impulse relaxation curves in 1.0 M_KBr vi Page 58 63 65 7O 73 76 78 81 I. INTRODUCTION AND HISTORICAL A. lntroduction The formation or precipitation of films at electro- chemical interfaces occurs in many systems. Common examples include the silver halides on silver, calomel on mercury, lead sulfate on lead and many oxides on their respective metals. Film formation reactions are inherently different from other types of electrochemical processes in that the ap- plication of a steady-state polarization does not produce a steady-state electrode surface condition. Each increment of charge contributes to the film growth thereby altering the state of the system. Traditionally, electrolytic film formation reactions have been studied by constant current or constant overpotential techniques in order that one vari- able might be well defined. At the same time, conventional techniques yield only a single parameter (current or over- potential) to correlate with film growth. Because the cur- rent impulse technique yields two kinetic parameters (double layer capacitance and exchange current) to correlate with film growth, this study of film formation reactions was undertaken with the hope that some additional insight into the film growth mechanism might be attained. 1 2 The silver halides were chosen for this study because of the relative simplicity of the systems involved. Silver can be obtained in a very high purity, halide solutions are generally quite stable and easy to prepare, and the charge transfer reaction involves only a single electron. B. A Brief Outline of Electrode Kinetics and the Electrical Double Layer The silver halide film formation reactions were studied by the measurement of two electrochemical quantities, the double layer capacitance and the exchange current. Detailed discussions of double layer theoryl“4 and electrode kinetics3'4 are readily available so all that will be given here is a very brief introduction to these two topics. When a metal is placed in solution there is almost always a difference in potential between the two. This dif- ference in potential causes ions of one sign to gather at the metal side of the interface and ions of opposite charge to gather at the solution side. This spatial separation of charge at the interface of two dissimilar, conducting phases is referred to as the electrical double layer. The original concept of the double layer is credited to Helmholtz, who pictured the double layer as approximating a capacitor with parallel plates. As the potential difference between the electrode and solution is increased, the charge at the interface is also increased. However, unlike an electrical capacitor the potential difference across the double layer 3 is usually not directly proportional to the charge at the interface. The capacitance of the electrical double layer is a fundamental property of the electrode-solution inter- face and its study has been a primary method in gaining in— formation about that interface. Two types of capacitance are usually distinguished when discussing the double layer. The integral double layer capacitance is defined as: C1 = (Qa'Q1)/(Ez‘E1)A where q1 and qz are the charge at E1 and En respec- tively and A is the area of the test electrode. The differential double layer capacitance is defined as: cd = (dq/dE) (l/A). In any later discussions, the term double layer capacitance will refer to the differential double layer capacitance per unit area unless otherwise noted. The overall reaction occurring at an electrode is5:°: k 0 + ne- 2—2—9 R (1-1) k a where O and R are the oxidized and reduced species and kc and ka are the cathodic and anodic rate constants. The oxidized and reduced species may be in solution or they may be in separate phases, such as when the reduced species is a metal. 4 Considering the general case of the reactants both being in solution, their concentrations will be C3 (moles cm_3) and C; at the electrode surface. The rate of the forward reaction (cathodic) will be proportional to C0, the proportionality constant being kc (cm sec-1). Since the reaction is occurring at the electrode surface, the rate will also be proportional to the electrode surface area, A (cmz). If the rate is expressed in mole-cm-z-sec-l, it can be equated to iC/nFA, where ic(amps) is the cathodic current and nF is the number of coulombs per mole of re- actant. The overall current is equal to the cathodic current minus the anodic current ._._-= 0- o _ 1 — 1c 1a nFA(chO kacR) . (1 2) The rate constants can be represented by7: k. = k0 exp [-anF/RT1 <1-3) ka k° exp [(1 - a) nF(E-E°)/RT] (1-4) where E0 is the standard electrode potential (0 and R at unit activity), a is the transfer coefficient, k0 (cm/sec) is the value of the rate constant for E = E0, R is the gas constant and T is the absolute temperature. The transfer coefficient, a. is the fraction of the change in electrode potential that goes to increase the rate of the cathodic reaction. From Equations (1-2), (1-3), and (1—4) it follows that i - nFAk°{cgexp[-anF(E-E°)/RT]-cgexp[a-a)nF(E-E°)/RT]} (1-5) 5 At the equilibrium potential, E = Eeq' the overall faradaic current is equal to zero, and the surface concentrations C8 and CR are equal to the bulk concentrations CO and CR. Under these conditions Equation (1-5) yields Eeq = E0 + (RT/nF)ln(CO/CR) (1-6) Defining the overpotential, n as: q E - Eeq (1-7) 3 ll ._ 0- E E (RT/nF)ln(CO/CR) Equation (1-5) can be rewritten as: i = nFAk° {c3 exp[-anF(”+(RT/nF)ln(CO/CR))/RT]} (1-8) - {cg exp[(1-a)nF(n+(RT/nF)ln(CO/CR))/RT]} which after simplification becomes: <1-a> - _ o 1 — nFAk C0 Céa){(cg/Co)exp[-annF/RT] -(c§/CR)exp[(1-a)nnF/RT]} (1-9) 1°{(cg/co)exP[-aan/RT]-(c§/CR)exp[(1-a)nnF/RT]1 where 1° 2 nFAk° cél"a)céa) (1-10) and i° (amperes) is defined as the exchange current of the system, 1:2, the current flowing at equilibrium. From Equation (1-10) a plot of log 1° y§_log CR (a re- action order plot) should yield a straight line with a slope of a. Knowing a and i° for known CO and CR’ 6 Equation (1-10) can be used to calculate a value for the standard rate constant, k°. For very small values of n in Equation (1-9), the overpotential is proportional to the current, which is the so-called linearized i-n relationship: 1 = i°(nF/RT) n . (1-11) The reciprocal of the slope of the current—overpotential curve at zero current (the equilibrium potential) is called the polarization resistance. It is the effective resistance imposed at the electrode surface by the finite rate of the electron transfer process: Rf = (dq/di)E = RT/nFi° . (1-12) eq This brief treatment of electrode kinetics has neglected any double layer effects so that the kinetic parameters should be called the apparent rate constant, the apparent transfer coefficient and the apparent exchange current. Unless otherwise noted all kinetic parameters will be the apparent values. C. Description of the Current Impulse Technique In the current impulse techniques, the electrode poten- tial is observed as a function of time when a constant cur- rent pulse of limited duration is applied as shown in Figure 1. This technique is a refinement of the coulostatic method Current Pulse applied to C3 d L l l * 'Zm(t )"'" as —-—1 km— Rf Double layer capacitance 0 Do I Faradaic resistance Solution resistance :11 I Mass transport impedance N B d I Observed Response /(d17/dt) -- it/Cd 1; = n‘aoexM-t/Rf Cd) Figure 1 Electrical analog for a current impulse experiment 8 preposed by Delahay9I1° and Reinmuthlltlz, both of whom give priority to Barker13. Initially the electrode is at equilibrium. A constant current pulse of brief duration is applied to the electrode in such a way that the cell is essentially at open circuit once charging is complete. The potential departs from the equilibrium value because of the change in charge density. The potential drifts back to its equilibrium value as the excess charge in the double layer is consumed by the faradaic process. The relaxation of the overpotential from the ini- tial value determined by the impulse is directly related to the kinetics of the reaction through which the relaxation occurs. The increment of charge is q = qm - qi (1-13) where qi is the charge density at the equilibrium potential for the electrode reaction 0 + ne -—9 R and qm is the charge density immediately after charging. The duration of the pulse must be short enough so no faradaic reaction occurs during charging. The overpotential (n ' E - Eeq) at time t after charging is T] = (q ' qi)/Cd (1‘14) where q is the charge density at time t and Cd is the differential double layer capacitance of the electrode. If variations in n are kept below 5 mV, Cd is assumed to be constant. The charge density q is 9 ft ' dt 1 15) 2 + l _ q qm o ( where the integral is equal to the number of coulombs con- sumed by the electrode process at time t. From Equations (1-13), (1-14), and (1-15) it follows that — t u n - [(q - q1)/Ca] + (1/cd) f0 1 dt (1-16) - 1 t s - nt-o + ( /cd) f0 1 dt where nt=o = Aq/cd (1-17> is the overvoltage after charging at t - 0. In order to solve Equation (1-16) 1 must be known as a function of n. Using the linearized i-n relationship in the absence of mass transfer [Equation (1-11)] 1 = 1; (nF/RT)n (1-18) where 13 is the apparent exchange current and other terms have their usual significance. Combining (1-16) and (1-18) ”/nt-o = exp [-(ig/cd)(nF/Rr)t] (1-19) which is identical to the relationship for the voltage-time variation for discharge of a capacitor across a constant resistance. The apparent exchange current of the reaction can be calculated from the slope of the 1n n y§_ t curve by the relationship 1o 1; = (slope)(Cd)(RT/nF) (1-20) if the capacitance is known. There are two methods of obtaining the double layer capacitance from a current impulse experiment. Extrapo- lating the log n.!§.t plot to t = 0 as defined by termina- tion of the pulse, Equation (1-17) yields nt=o ' q/Cd = itT/Cd (1-21) where q is simply the pulse height it times the pulse duration T. The capacitance can also be calculated by measuring the slope of the overpotential-time curve while charging the double layer with a constant current from the relationship14 cd = it/(dn/dt) (1-22) These two values of capacitance are called the discharge and charge capacitance respectively. With the value of the exchange current (1-20) Equation (1-10) can be used to calculate a value of a from the slope of a log 10 y§_log CO or log CR plot. Knowing a, Equa- tion (1-10) then yields a value for k°. D. Measurements of Film Formation Reactions The growth of films on electrodes may occur in a variety of ways. However, two extreme types of behavior can be differentiated. Initial deposition may take place at 11 discrete sites. Continued growth at these sites then occurs with a definite geometry until the separate precipitates meet and the surface is covered. The other extreme is where deposition takes place uniformly on the surface forming a continuous film until the surface is covered with a mono- layer. Additional layers may be formed or not depending on the electrical conduction mechanism through the film. The formation of the silver halides is an example of the first type of behavior although in general the dividing line between these two extremes is not clear and some combination of the two usually exists. The growth of the film changes the surface and hopefully some measurable characteristic of that surface. These char- acteristics include electrochemically measurable quantities such as current, electrode potential, double layer capaci- tance, exchange current or resistance. Many of the common electrochemical relaxation techniques have been modified for studying the film growth process. There are several good reviews available of electrochemical relaxation methods as applied to normal electrode reactionsl5013. Some of the more common relaxation techniques include the current step meth- od17‘19, the potential step methodz‘“21 and the impedance method92'23. Another electrochemical technique which is frequently used to study film growth is chronopotentiometry34'25, A constant current is applied to the cell and the overpotential is recorded as a function of time. If both 0 and R are soluble, the electrode potential will be dependent upon the concentration of species at the electrode surface which 12 depends upon the rate of diffusion of reactant to and product from the surface. However, in the case of film formation, both species are insoluble under pr0per experimental condi- tions. The reduced species (Ago) is present at the surface as is the oxidized species (Agx) so no diffusional control of electrode potential would be expected. The potential of a clean electrode shifts to the film formation potential when the current is applied and remains at a nearly constant value until the surface is virtually covered and another process begins to occur. After the surface becomes covered, the electrode potential depends upon the charge transfer through the film. If the film conducts by an ionic mechanism, the silver ions formed at the metal surface travel to the. film surface where they react. In this way the film thick- ness increases as the quantity of electricity passed. The film's resistance to the conduction of the ions increases as the film grows in thickness and the electrode potential increases indefinitely due to an increase in the IR drop in the film. The total quantity of electricity needed to cover the surface can be calculated by noting the time the potential begins to rise rapidly and multiplying by the value of the applied current. Reversing the current will yield an equivalent quantity of charge required to remove the film if the process is 100% efficient. In addition to electrochemical relaxation techniques for the study of film formation, Optical techniques such as electron diffraction and electron microscopy have been 13 used37‘39. Since the effects of light and air on the de- posits are unknown, these techniques cannot be used without a degree of uncertainty. E. Studies on Silver Halide Formation Although work on anodic formation reactions have been carried out for well over a century, little interest was shown in the kinetics of formation and the properties of these electrolytically formed deposits until the 1950's. Since then a number of systems30’33 have been studied. The silver halides3"""3 are among those which have been studied extensively. In 193544, Kurtz studied the overpotential-time curves when a silver anode was anodized in chloride and bromide solutions by means of a constant current. He related the general shape of the overpotential-time curves to various stages of growth in the film. The four stages he observed are: (1) A supersaturated solution of silver and chloride ions must be present on the electrode surface. (2) A nucleation step in which initial formation of silver chloride takes place. (3) The silver chloride nuclei grow to cover the electrode. (4) Once the surface is covered there is a continued thickening of the deposit. Lal, Thirsk and lovynne-Jones‘fit46 observed overpotential- 14 time curves for silver anodes in chloride, bromide and iodide solutions for a range of current densities and anion concentration. From their observations they came to basi- cally the same conclusions as Kurtz concerning the various stages of growth. They examined the thickening of the film, calculated the specific conductivities of the deposited layers and listed the specific conductivities as a function of current density and anion concentration. Fleischmann, Thirsk and Sowerby4'7'49 examined the deposition of silver chloride on single crystals of silver by both constant current and constant overpotential tech- niques. They found that the kinetics of formation of silver chloride were strongly influenced by the cathodic pretreat- ment of the silver single crystal surfaces used as sub- strates. The factors causing this variation were investi— gated which gave evidence for the existence of surface smoothing under cathodic conditions. They suggested that silver chloride formation is con- trolled by two rate constants. The formation of nuclei is controlled by the rate of nucleation and the geometry of growth determines the rate of increase of surface area. They attempted to separate the rate constants by maintaining the overpotential for a short, determined time at a high overpotential so as to "preform" a large number of nuclei and then follow the growth of these nuclei at a second, lower overpotential. From these studies and the use of an electron microscope they concluded that nucleation is 15 confined to the initial stages of growth. They derived equations relating the growth geometry of the deposit to current-time variations if the electrode is held at a constant overpotential. From the current-time variations they stated that the growth of silver chloride nuclei is two-dimensional. The current impulse technique is potentially a more sensitive technique than the other electrochemical tech- niques which have previously been used to study film growth. Application of a constant current or constant overpotential and examination of the resulting overpotential-time or current-time curves requires that the reaction under study be continually driven while making the measurement. Only a single parameter (current or voltage) is measured and correlated with film growth. The advantage of the current impulse technique is that a very small quantity of elec- tricity is contained in a single pulse (enough charge to form 10-4 of a monolayer) so that it is possible to study the growth process by applying a series of pulses and noting variations in the kinetic parameters close to equilibrium as the film is formed. Also this technique allows simul- taneous direct measurement of two kinetic parameters (ex- change current and double layer capacitance) to correlate with film growth. II . EXPERIMENTAL A. Solutions Solutions were prepared directly by weight or volume from ACS reagent grade chemicals without further purifica- tion. They were saturated with the appropriate silver halide by prolonged standing in contact with the silver salt. Perchloric acid was G. F. Smith double-distilled lead free acid at 70% strength.- The water used was pre- pared by redistillation of an alkaline permanganate solu- tion of laboratory distilled water. No variations in ex- perimental results were observed if laboratory distilled water without further purification was used. Nitrogen used to purge oxygen from the cell was Liquid Carbonic prepurified gas, dried over calcium chloride, passed through an oven containing copper turnings at 3500 to remove traces of oxygen, passed through traps containing activated char- coal at liquid nitrogen temperatures, presaturated in dis- tilled water, and fed to the cell yia_a glass and Teflon train. B. Cells and Electrodes Both two and three electrode systems were used. No appreciable difference in the noise level was observed 16 17 between the two configurations. The cell was Pyrex, cap— able of holding 25 ml of solution and fitted with a Teflon lid. The cell was constructed with a gas inlet and an auxiliary hole was drilled in the lid to allow deaeration of the solution. The cell was painted black to eliminate light. A silver-silver halide electrode was used as a ref- erence electrode in all of the halide studies and a silver electrode was used as a reference for the Ag-Ag(I) system. When a three-electrode system was used a large platinum wire gauze was used as a counter electrode. The gauze was placed concentrically about the test and reference elec- trodes. The reference electrode was made much larger than the test electrode to minimize polarization effects. The test electrode was a silver wire set in epoxy resin in a 1-1/2 inch length of three mm glass tubing. The epoxy was removed from the end of the wire, exposing the cross section to the solution. Originally there was some concern about the use of epoxy resin to seal the electrode. Several electrodes without epoxy were used with no change in results. The geometric area of the test electrode was determined to be 0.028 cm2 with no surface roughness effect taken into account. The area was measured with a Bausch and Lomb microscope fitted with a micrometer eyepiece, and a calibrated micrometer slide. Several methods of electrode pretreatment were tried with varying degrees of reproducibility. The best method 18 found was as follows: the electrode surface, ground flat with emery cloth, was polished with gold rouge on a Beckman velvet strip. The electrode was then washed with concen- trated nitric acid and distilled water. The electrode was left with some imperfections that were visible under the microscope. C. Instrumentation The cell was plugged through multipin connectors to a grounded copper circuit board. The board was connected directly to the output of the pulse generator by means of a BNC connector. A 10 ohm precision resistor in series with the cell was used to measure the magnitude of the current going into the cell. Potentials were measured with a Tektronix P 6046 differential amplifier which plugs into coaxial jacks mounted on the copper plate. The differ- ential probe used in connection with a Tektronix 1A5 ampli— fier and a Tektronix 556 oscilloscope has a maximum sensi- tivity of 1 mV/cmand a risetime of 9 nsec. The pulse generator used was an Intercontinental Instruments Model PG-33. It has a maximum current output of 200 mA in the current mode with risetimes of less than 7 nsec and durations as short as 30 nsec. The pulse gener- ator was triggered from the delayed-trigger output of the oscillosc0pe. All experimental dataimze recorded photographically using a Tektronix 350/0 35 mm camera and Kodak Tri—X film. 19 The constant current used to form or remove the film can be obtained from several sources. One of the easiest is to place the cell in the feedback loop of an operational amplifier. Since there is a definite resistance associated with the cell, it is advisable to have the cell in series with a much larger resistance (in this study 100 K) so even if the cell resistance changes, the change in total resistance will be negligible. A block diagram of the experimental system is shown in Figure 2. 20 .Emummm Hmucmeflummxm mo Enummao xoon .N musmflm 21 .N musmfim uncomjnzomo mom x_zom._.¥u._. -Iluullln till! In .1: In I... IIIIII II IIIIIJ _: ..................................... : . ._ n. __ _ __ _ u u _ _ o: 4 HI _ _. 2.: . ._ u. .L... m..- . 1H... r... .r IIWHHHH “Mel 512.53...» .9...» Jun ¢0b4¢uzuo manna mm on. ma>h mhzmzamhmz. n_<._.zwz:.zoomu._.z_ III. EXPERIMENTAL RESULTS This chapter describes all experiments performed and the results of those experiments. Explanations of observed phenomena will be given where appropriate. Part A is a study of the silver-silver(I) system. This system was studied to determine if the current impulse technique would yield results comparable to those of other investigators. Values of the capacitance and exchange current at a variety of concentrations of silver(I) were measured and from these a transfer coefficient and rate constant were calculated and compared to the literature values.. Part B is a description of the experiments used to determine how the halide films are formed on a silver sur- face. A 1.0 M KBr solution is used as an example. The changes in the capacitance and the exchange current show how the film grows. The capacitance was found to be inde— pendent of experimental measurement conditions such as which anion is present, concentration of anion or number of coulombs in the pulse. The exchange current was measured in several concentrations of the three halide solutions and found to be dependent upon which anion is present but not upon the concentration of that anion. When an anodizing 22 23 current is applied, the variations in capacitance and ex- change current are identical and it is postulated that this is due to a change in uncovered surface area. Further evi— dence of an area mechanism is given by microscope pictures and anodic Chronopotentiometry. Two other halides (Cl-, I-) were examined with similar results. A. Silver-Silver(I) System The kinetics of the silver-silver(1) system were measured at a total of six concentrations in 1 M_HClO4. The concentration range covered was 3.0 x 10-2 M to 7.5 x 10‘5 11 silver ion. 1) Capacitance The capacitance values as a function of the log of the concentration of Ag(I) are shown in Figure 3. Differ- ential double layer capacitance values were obtained by two separate techniques: first, by direct calculation from the initial slope of the charging curve which is known as the charge capacitance (Cd = it/(dn/dt)); and second, by extra- polation of the relaxation data on a log n Kg t (plot to t = 0 which is known as the discharge capacitance (Cd = itT/nt=o). Calculation of the charge capacitance assumes that the faradaic process has consumed none of the charge on the time scale of the measurement. Since the charging of the double layer is a linear process, any deviation from linearity will signify that some faradaic process is occurring. 24 .vOHUm.m a as coflumuucmocoo GOA HO>HHm mo cowuocsm m mm HO>HHm Mom mm>usu omnmzomflo ocm mafimnmso Eoum mocmuwummmo amaucmHmMMAQ .m ousmfim 25 0.... .m musmflm muh_4\mu402 .00. 90.. 9&1 06.. O.¢ .. 0.0 .. o a 1 “02350533 wo¢> [1/nF(1/coD(1)/3)]2 . Delahay's criterion is satisfied by a factor of approxi- mately four at CAg+ = 10-3 M, The two sides of the in- equality are equal with a concentration of CAg+ = 3 x 10-4 M, This inequality is the condition for pure charge transfer control throughout the entire relaxation process. A recent study50 has shown that the validity of the simple charge transfer assumption is dependent on the ratio of charge transfer (Tc) and diffusional (rd) time constants for the relaxation (where To = RTCd/nFIo and Td = [RTCd/n3F3(1/CODé/S)3])as well as the time of measurement. A curve fitting routine"1 which takes into account both the charge transfer and mass transport characteristics and calculates values of the exchange current and double layer capacitance was used to fit the experimental curves. Table 1 compares the values of the exchange currents that were calculated using the simple charge transfer approximation for both the charge and discharge capacitance and the values obtained from the computer curve fitting routine. The ex- change currents from the curve fitting routine are somewhat higher than the average extrapolated values due to the fact that the reaction is partially mass transfer controlled even at the short measurement times used in this study. At concentrations below 10-3.M,the reaction becomes completely mass transport controlled (at the measurement times used) and the computer program used to fit the decay curve can no 28 Table 1. Apparent exchange current density for 3.0 x 10-2 o 7.5 x 10"5 £1. AgClO4 in 1.0 M H0104. c119cm 1° 1° Ioave 10 (T2123? (discharge) (charge) (amps/cm”) (corrected) 3.0 x 10‘2 0.96 0.99 0.98 0.97 1.0 x 10"2 0.67 0.88 0.78 0.76 1.5 x 10"3 0.45 0.45 0.45 0.54 1.0 x 10'3 0.34 0.45 0.40 0.51 3.0 x 10“ 0.27 0.28 0.28 --- 7.5 x 10" 0.17 0.19 0.18 --- 29 longer provide a fit by adjusting the charge transfer vari- ables. In each case below 10-3 Mgthe experimental decay curves decayed more rapidly than the simple charge transfer and diffusion model will allow. Capacitance values from the curve fit routine agreed with the experimental values within experimental error. A reaction order plot is shown in Figure 4. The open circles correspond to those values of the exchange current which were calculated assuming the relaxation curve fol- lowed the simple decay law in the absence of mass transfer. The squares correspond to those values of the exchange cur- rent which were obtained from the curve fitting routine. Using the corrected rate constant and transfer coefficient (from the corrected exchange currents), theoretical decay curves were generated by the computer. Exchange currents were measured from these theoretical decay curves by as- suming the simple exponential decay law was satisfactory and these are shown on the reaction order plot by the darkened circles. There is good agreement between the two extrapo- lated values down to concentrations of 10"3 M, At lower con- centrations the experimental exchange currents are much higher than the model predicts. The higher exchange currents suggests that the concentration of oxidized species [Ag(I)] is much higher than predicted. This could be accounted for by specific adsorption of silver ions. At concentrations of 10-3 Mgor above the amount of adsorbed silver ion is small compared to the bulk concentration of silver ion. At lower 30 .voHUm.m H CH Ecummm AHVH0>HHquo>Hfim opp How uoam Hmouo cofluummm .¢ madman 31 .0..- cottage: .60. so... 0.“- 0...”- of- 06. _ q _. .v canoe...“ . ... 0 ... ... I o.- .. ~ ~- Q. o .. I o.~ ~~ so see N. I N.N .. eso. .. o.~ a was... 2.82.8 I 0:0. .3 some...“ 3.22.2.5 c \\ 8 38230 D 9. 3 3.22.226 o zuczvmt¢r>901 32 bulk concentrations the adsorbed silver ion concentration is no longer negligible and in fact becomes the dominating concentration. From the corrected values of the exchange current and capacitance a transfer coefficient and rate constant were calculated and compared to the literature values. A wide range of values (a = 0.24-1.0) of the apparent transfer co- efficient were found in the literature52’55, however, no values were given for the apparent rate constant. Two authors listed enough data so ko could be calculated. Table 2 shows a comparison of the kinetic parameters for the silver-silver(I) system as obtained by three different techniques. The wide range of values for the kinetic para- meters is probably due to differences in preparation of the electrode surface. Table 2. Comparison of kinetic parameters for the silver- silver(I) system. Apparent Std. rate Investigators Technique Transfer Const. ’ Coeff. (cm sec-1) . -2 Ggfigzfigfiizand Potentiostatic 0.24 4.1 x 10 Mggékgggsa Galvanostatic 0.62 2.5 x 10-5 Bleasdell and Current Impulse 0.81 7.1 x 10-5 Enke 33 B. Silver-Silver Halides This study was undertaken to demonstrate the usefulness of the current impulse technique for the study of film forma- tion reactions on solid electrodes. A series of equally- spaced, constant current pulses of fixed pulse duration is equivalent to the application of a constant current with an added advantage. Each pulse constitutes a separate experi- ment that provides the film forming current and yields values of the double layer capacitance and the apparent ex- change current for the process by which the film is formed. Other studies in the literature have observed the presence of a nucleation step which occurs over a relatively short period of time after initial application of a constant cur— rent or overpotential4‘v49. Since the duration of the nucleation step appeared to be dependent upon the quantity of charge applied to the electrode, it was felt that the current impulse technique would be eSpecially valuable for this type of study as the quantity of film in a single pulse can be made extremely small. However, preliminary examina- tion showed the absence of a nucleation step for electrodes as prepared for this study. Using a series of pulses for the film formation current for post nucleation studies was found to be too slow. Therefore the anodization current was supplied by means of an external constant current source for the majority of the experiments. 34 Several of the previously mentioned studies have been concerned almost exclusively with the thickening of the film. This study was concerned with the formation kinetics from a "clean“ surface to that time when the surface is completely covered by the film. No attempt was made to study the thickening or continued growth of the film. It is seen that the kinetics are dependent upon the uncovered silver surface area and are independent of the halide ion concen- tration in the solution. 1) Double Layer Capacitance Measurements In order to obtain correlations between several experi- mental variables (time, concentration, anion, applied charge, etc.), it was necessary to use several electrodes, with the electrode sueface being renewed many times. Due to the pre- treatment decided upon, some variations were noted in the initial capacitance values. Charging and discharge values agreed quite well, but variations of up to 20% between suc- cessive surfaces were sometimes observed. This problem was minimized but could not be eliminated experimentally. Varia- tions of this order are not uncommon with the use of solid electrodes and are probably caused by the differences in surface area between different electrodes. Therefore it was found to be advantageous to normalize the initial capacitance. Normalizing the initial capacitance is simply adjusting the area between different surfaces to a common value of initial capacitance/cm“. All geometric areas used in this study 35 were the apparent areas, 1:33 the area measured under a microscope with no surface roughness factor taken into account. As the surface is changed by addition of the film, the dielectric of the capacitor changes and therefore the value of the capacitance changes. Since the change in capaci- tance is what is to be determined, it is necessary to know if there are any possible variations in the capacitance due simply to changes in eXperimental conditions that are not related to simultaneous changes in film growth. For example, no difference would be expected in charging and discharge capacitance values and no difference other than experimental error is found. Typical capacitance values of silver in 1.0 M;KBr with 1.0 M_KN03 as supporting electrolyte are fOund to be about 12 uF/cmz. No variations other than ex- perimental error are observed if the anion is changed to either chloride or iodide or the concentration is changed over several orders of magnitude as shown in Figure 5. These results are consistent with the results shown earlier for the silver-silver(I) system. It was necessary to use different current densities through the different series of measurements and it was important to know that the number of coulombs applied in a single pulse had no appreciable effect on the capacitance estimate. With the pulse width being kept constant at 0.1 usec, the current density was varied between 140 mA/cm2 and 500 mA/cma. The upper limit was determined by limiting the 36 .nozx.m a ca coaumnuccocoo GOH moflamz mo COADUCDM m mm Ho>HHm mo wocmuwommmo mmumzomfio Hmausmummmwn .m musmflm 37 .m musmflm mmtdwmnoz .xo. 8.. IO 0 awe/:1" 30NVlIOVdVO IO 0 N 0.0 o._ - on- on .. o... - a . . . a c 01 a a o m m ~98. 0 .. “9.8% o mo_m0.=..0 O . 38 total overpotential to a maximum of 5 mV. The lower limit was determined by how accurately the overpotential could be read when the total overpotential was only of the order of 1 mV with a line width of 0.2 mV and a rapid decay to less than 1 mv. No attempt was made to go to lower current densities as the signal/noise ratio continues to become more unfavorable and a total overpotential of less than 1 mV cor- responds to an unreal situation experimentally. The total variation in capacitance is not affected bv the current used which will be shown to be very important later on. Although this study was conceived to study the film formation reaction, at various points data were taken to observe the film removal reaction to compare the kinetics of the cathodic process to those of the anodic process. With only small potential excursions from equilibrium (5 mV), anodic and cathodic processes would be expected to yield similar results. This is because we are working so close to equilibrium that the reaction should be, and is, com- pletely reversible. Typical of this result is Figure 6 where both anodic and cathodic capacitance values are shown as a function of applied current density. One final point about capacitance measurements in general: the capacitance values obtained in this study are somewhat lower than the typical value of 20 uF/cm2 used by other authors for ”clean" metal surfaces. No attempt will 39 I. lwomm h.IOH x H um ucmumcoo onn nuoHB omHsm .nozx 2 H can me 2 H :H muHmsoo ucmuuso mmHsm mo :oHuocsm m mm mocmuHommmo 0Hoonumo was UHoOG< .m musmHm 40 .m musmflm «EO\._..mzma Plum-3:0 ou_4mm¢ 0.00:...(0 0.002< 000 00¢ 00» 00a 00. 0 00. 00m 00m 00¢ 00.» _ — H _ H H H H _ _ _ 000000 000000 I O O N 0 to zwoufi acuulovavo 41 be made to compare the surface used for these studies to those used in other studies other than to say that more elaborate preparations leave the electrode surface in a state which is difficult to reproduce and impossible to maintain for extended lengths of time. 2) Capacitance-Charge Relationship When a constant current is applied to the electrode, all of the coulombs must go toward formation of silver ions, which in turn, will form a known quantity of the appropriate silver halide which can be calculated from Faraday's Law. In terms of the formation reaction the most convenient variable is charge, although time could be used if the anodization current was kept constant. As the anodization current is applied the film will grow (possibly in more than one direction) until the elec- trode surface is completely covered. At various stages of growth, relaxation curves and charging curves for both anodic and cathodic pulses were recorded. Figure 7 shows a typical capacitance-charge curve for 1.0 M_KBr. For this plot and for most of the work that was subsequently done, the discharge capacitance is the one that is reported since no discrepancies appeared between the two capacitance values. The plot has a flat portion at the beginning and extending to about 175 mCoul/cma. At this point there is a rapid de- crease in capacitance until about 400 mCoul/cm’. This behavior must be due to a change in area, dielectric constant, 42 .>UHm:mo tomato ooHHmmm mo COHDUGSM m mm Hm&.m H CH mocmuHommmo .h musmHh 43 .b musmHm «£02.30... >....mzua u0¢<10 cuss—.2 00¢ 00m 00m 00. _ I0 _ a . _ 0.. annals" aouulowvo 44 and/or dielectric thickness° If the capacitance was much larger on the uncovered surface than on the covered surface, the total capacitance would be dependent upon the uncovered surface area. When a silver electrode (as prepared for this study) is placed in a bromide solution it assumes the potential of a silver bromide electrode. For this to occur there must be enough solid silver bromide crystals of unit activ- ity on the surface to yield this potential. If these crystals grew in height upon application of constant cur- rent, there would be no effective change in the uncovered silver surface area and therefore the capacitance-charge curve would be level at the beginning. Associated with this growth in height there would be expected to be some outward growth of each crystal, but the effect of this area change could be minimal. Once the upward growth into the solution was completed for the original crystals on the surface, there would be a growth around each crystal and upward, and this would cause a measurable change in area. Thus the capacitance would start to decrease as a function of the uncovered area. When the applied charge reaches the vicinity of 400 mCoul/cmz, the capacitance is extremely small, and the absolute magnitude of the capacitance is not very accurate. This is because the coulombic content of the pulse is very small and the overpotential becomes very large. This only affects the calculation of capacitances below 1 uF/cmz. 45 No attempt was made to study the effect of additional coulombs once the surface appeared to be completely covered. 3) Microscppe Pictures To determine if the shape of the capacitance-charge plot reflects the surface coverage by the silver bromide some pictures of the electrode surface were taken through the microscope. Figure 8 shows a series of pictures cor- responding to known quantities of charge applied. The pictures show there is a definite decrease in uncovered area corresponding to the decrease in capacitance and an increase in the total quantity of charge applied. 4) Other Halides To determine if the previous conclusions were applicable to more than one system, two additional halides were ex- amined (chloride and iodide). In Figures 9 and 10 are shown the capacitance-charge curves for these two anions. Similar curve shapes are exhibited for each of the anions, however, the quantity of charge is quite different. In Figure 11 the capacitance-charge curves for all three anions are shown to compare the quantity of charge involved. Further evidence was obtained from microscope pictures to confirm that the sharp decrease in capacitance was due to surface coverage. From the difference in total charge that is required to obtain complete coverage, it can be seen that about twice 46 Figure 8. Microscope pictures (Magnification 30X) 0 mCoul/cm2 50 mCoul/cm2 150 mCoul/cm2 275 mCoul/cm2 ) ) ) ) 225 mCoul/cmz ) ) 325 mCoul/cmz ) 375 mCoul/cm2 47 Figure 8. 48 .muflmcoo mmumno owHHmmm mo COHDOCSN m mm Hom.m H CH mocmuHommmo .a musmHm 49 .2338... Cazmo moquo 8.3114 00. . Om .0 whoon 00 0e 0N _ O — H d awn/.4" sowvuovavo 50 .muHmcmo mmumno ooHHmmm mo coHuchm m mm H&.m H CH mocmuHommmo .6. 6.56.. 51 .oH musmHm «50:300.: >....mzwo m0mh.mzuo M0833 ou...¢m¢ GOO 000 005 000 00¢ 00¢ 00” 00“ OO- . _ H . . a 4 _ . O O _ I. 4 O I 4 O I Q o I 4 D 4 o I 3.3. 4 d a 3.223 D D 4 D 01 mo.¢0.=..0 O O 339/3“ SONVLIOVdVO 54 as many coulombs are needed when the anion is iodide than when the anion is bromide. Likewise, five times as many coulombs are needed for complete coverage when the anion is bromide than when the anion is chloride. Chronopoten- tiometry was used to verify 100% current efficiency in ap- plication of the three deposits. It must be concluded, therefore, that the extra charge goes into formation of the appropriate silver halide, and consequently the three films grow to different heights. Silver iodide films grow to twice the height of silver bromide films and silver iodide films are nearly ten times as high as silver chloride. 5) Apparent Exchange Current The apparent exchange current is the other quantity which is available at each point the capacitance measurement is made. Like the capacitance, the exchange current was found to be the same within experimental error for both anodic and cathodic pulses and for varying applied current densities. This is shown in Figure 12. Figure 13 is a plot of exchange current y§_charge superimposed on the capacitance-charge curve for 1.0 M KBr. The same curve shape is observed in both cases. If the capacitance change is related to an area change, then the exchange current must also be a function of the uncovered electrode surface. This implies that the uncovered area is where the charge transfer reaction takes place at the measured rate. This is not to say that the exchange cannot 55 I. .omm ~.IoH x H as ucmumcoo och suoHB mmHsm .me 2 H cH muHmcmo ucmuuso mmHsm mo coHuocsm m mm accuuso mmcmnoxm ucmummmm exp mo mmsHm> UHoogumo ocm UHUOGm .NH musmHm 56 .NH musmflm N.55.... >232. ...zuccao 33...... 0.003530 0.00,: 00h 00¢ 00m 00m 00. 0 00. 00m 00m 00¢ 00v. . _ a . . _ . a H . . o o o o o o o o o o c o 00» 00¢ 00» 000 ' ZWOIVW 1.138800 SONVHOXB 57 .um&.m H cH muamcmo woamno ocH w mm ucmuusu omcmsoxm ucwummmm ocm mocmuHom ... mmm mo coHuocsm mu HmmmH cHnsoa .mH musmHm 58 would aouvuovavo o 0. .MH mnsmHm «52.58... ......mzuo 35:8 33...... 00¢ 00» com 00. H. H - _ _ .. c o c .. c .. o o c o c .. c c c o I O O O 00.00 .3. ca... 00» 00¢ 00» tug/V“ LNSUW’IO 39NVHOX3 0 59 occur on the covered surface, only that it must proceed much slower than on the uncovered area or have much less charge associated with it. The exchange currents for a variety of concentrations of the different halides were measured on silver electrodes with surfaces in the region where Cd and I0 are inde- pendent of charge. Surprisingly, no concentration dependence of the exchange current was observed for any of the three anions over three orders of magnitude; though the value of the exchange current measured depended upon the anion species present. The two possible charge-transfer reactions which give rise to the equilibrium exchange current are AgX + e- > Ag + x- (I) and Ag+ + e > Ag . (II) Reaction (II) is one step of a two-step mechanism in which the other step is the equilibrium between Ag+, X-, and AgX. If reaction (I) were the charge-transfer step, one would expect to see the exchange current increase as the AgX/Ag boundary increases. Instead, 1° decreases steadily as the AgX covered area increases showing that the reaction rate depends on the Ag area alone. Also one would expect the x' concentration to directly affect the exchange cur— rent in the case of reaction I. This leads to a considera— tion of reaction (II). The dependence of 1° on the Ag area is correct. To explain the independence of I0 on X 60 concentration, it is necessary to postulate a constant surface concentration of Ag+ over the range of anion con- centrations measured with a different Ag+ surface concen- tration for each halide species present (or silver halide formed). 6) Concentration Dependence of the Apparent Exchange Current in Halide Solutions It has been postulated that the first step in the silver halide film formation is Ag —_-: Ag+ + e- < The exchange current for the formation of the silver halides therefore would be expected to be dependent upon the concen- tration of silver ion in the solution which in turn would be dependent upon the equilibrium constant of the solid silver bromide and the bulk anion concentration. With rela- tively high concentrations of bromide ion (1 M_to 10-3 a) and given that the equilibrium constant for silver bromide is 2110-13, it can be seen that the bulk silver ion concen- tration is extremely small (< 10-10 M). In the discussion of the silver-silver(I) system it was shown that the values of the exchange current that were obtained for concentrations of bulk silver ion below 10-3 M were inaccurate and could not be corrected by taking into account the mass transfer characteristics. This would seem to rule out the possibility of obtaining meaningful exchange rates for the silver halide formation. 61 When a series of exchange currents were measured at a variety of bromide concentrations the reaction order plot shown in Figure 14 was obtained. The exchange current measurements were made on the flat region at the beginning of the exchange current-charge plot. There are two important features of this plot. First, there is obviously no concen- tration dependence of the measured exchange rate. The con- centration range is listed to 10'.10 M_KBr which corresponds to infinite dilution. When current impulse experiments were run on solutions of supporting electrolyte with no bromide ion present the decay rate was too slow to obtain an exchange rate. Thus, small amounts of bromide ion and/or silver bromide must be necessary to stabilize a constant silver ion concentration and therefore the exchange rate. The second fact available from the reaction order plot is that the measured exchange rate must correspond to a definite concen- tration of silver ion. Additional concentration studies were run for chloride and iodide ions and the three reac- tion order plots were superimposed on the corrected silver- silver(I) reaction order plot. This is shown in Figure 15. The exchange currents for the bromide and chloride correspond to a region of silver ion concentration where the exchange rates are valid and correctable. The iodide exchange rate does not correspond to a known concentration of silver ion and is beyond the correctable range. Values of the silver ion concentration corresponding to these values of the ex- change currents are shown in Table 3. 62 .coHumuucmucoo coH moHEOHQ mo coHuocsm m mm muHmcmo ucmuuso mmcmnoxm ucmummmd .oH musmHm 63 .VH musmHm cutameHOI HLoo. 00.. 0..- 0.N- 06- 0.¢- 06- 0.0- 0N- 0.0- 0.0- 0.0.- H H ml 1 H H H H H H ¢.N 0.N 0.» zWOIVW (on 901 64 .ucmmwum mH ooumoHocH coH moHHmn on» c033 omchqu mum mmcHH HmDCONHHos on» .AmmHoHHo cwmov ucmmwum moHHms 0c LDHB Emumhm AHvuo>HHmIHo>HHm mnu How uon “mono coHuommm .mH oHsmHm 65 .mH cusmHm mm....-.\mw...02 H00. 00... 9&- 0.»- 0.¢ - 0.0 - 1 4f? I' I” I “i N l (D 00 + I 0.5. <1c3tnr- IO‘GIDIO 21110] VII] (01) 901 66 Table 3. Equivalent silver ion surface concentration in halide solutions obtained by exchange current measurements (Figure 15). Anion I(measured; I(corrected) CAg+ (amps cm"2 (amps cm‘z) (moles/liter) c1’ 0.480 0.590 2.1 x 10‘3 Br" 0.430 0.530 1.4 x 10"3 1‘ 0.320 --- < 10’3 The absolute value of the exchange current for iodide is in doubt but the effect of halide ion on the exchange rate is clear. There is a definite difference in the ex- change rate caused by a difference in effective silver ion surface concentration. The quantity of silver ion corresponding to the measured exchange rates is much larger than expected. As in the case of the silver—silver(I) system the existence of an unusually large silver ion concentration is probably due to specific adsorption. With the equilibria involved there is no way such a large concentration of silver ion in the bulk of the solution could be obtained. Somehow the halide ion, even in the vicinity of infinite dilution, or a small quantity of silver bromide is able to stabilize a relatively large silver ion concentration at the electrode surface. All three anions yield an apparent transfer coefficient (a) of 1.0. Although relatively uncommon, there have been 67 several other systems reported in the literature with similarly high transfer coefficients56. Often these sys- tems have involved a halide ion. Originally it was suggested that this might be due to the presence of complex ions in the solution57. After further work on such systems, Barker13 concluded that the real cause of the large values of a was the specific adsorption of metal ion553I59. So it has been shown that a change in anion not only affects the total quantity of charge necessary to obtain complete coverage of the electrode surface but also it af- fects the rate of the reaction. 7) Anodization Current It has been stated that the initial values of capaci- tance and apparent exchange current are independent of the bulk anion concentration. Also, it has been shown that the capacitance and exchange current are dependent upon the un- covered electrode surface area at a concentration of 1 M halide ion. Similar results are observed at 10-1 M_halide ion. At concentrations below 10—1 M the anodization current used to form the film must be reduced drastically to assure 100% efficiency. The anodization current was limited to 1 mA/cm2 for iodide and bromide and 0.1 mA/cm2 for chloride at the highest concentrations used. With these as the upper limits the current densities could be lowered at least an order of magnitude with no change in the overall capacitance (exchange current)—charge curve shape. Cathodic 68 Chronopotentiometry confirmed 100% current efficiency at all anodization current densities used. If the same current density is used at 10.2 M KBr as was used at 1 M_KBr, some of the silver ions diffuse into the solution and form AgBr as there are not enough anions at the surface to react with all of the silver ions formed. This means that a different capacitance-charge curve re- sults at lower concentrations (using the same current density) because of less than 100% current efficiency. Lower anodization currents were used to maintain low over- potentials and 100% current efficiencies at concentrations below 10‘1 M, The capacitance (exchange current)-charge curves are the same as those at higher concentrations and current densities. 8) Anodic Chronopotentiometry One other technique was used to determine the capaci— tance-charge curve relationship to coverage. As mentioned earlier, it is possible to use anodic Chronopotentiometry to study film growth. An anodic chronopotentiogram with 1 E. KBr was run using the same current density as in the original film formation. The chronOpotentiogram is shown in Figure 16. There is a well defined transition time at approximately the same number of coulombs (400 mCoul/cmz) that corresponded to complete coverage of the electrode surface on the capaci— tance-charge curve (Figure 7). It has been postulated that this transition occurs because the film on the electrode 69 .NEU\....mzwo m0¢....wzmo m0muso mmumnolmocmuaommmo man can maamoflnosumo Umoswmn Edam mnu .«EU\HDOUE cow 0» coaumnwoocm amauflCH cm Hmumm cmcflmuno uoam on» on @commmunou mmHoHHo ammo .mUMMHSm moouuomam omnmmmnm masmwum m mcfim: uoam m we mafia ofiaom .Hm&.m o.H CH mmnmno Umflammm m0 coauocsm m mm mocmuflommmo .mfi musmflm 78 .mn madman m2.32:5... {.823 3.2.8 can con Hum—Hun: oo. 7 1 VI- A. o a film/i" SONVLIOVJVO 79 sites grow together. However, preanodization to complete coverage is quite an extreme pretreatment process so other surface effects might be present. 10) Relaxation Curves A typical relaxation curve is shown in Figure 20a. There is an initial fast decay and then a long time decay. The kinetic parameters were taken from the short time (< 1 nsec) decay. The long time decay does not fit the simple diffusion model and is independent of concentration, anion, and experimental conditions. Only when the surface is completely covered is a more normal decay curve observed which looks like that shown in Figure 20b. No long time decay is observed and the initial decay is more rapid. This long time "hangup" on an uncovered surface must be associ- ated with the non-uniform silver ion concentration profile caused by the excess silver ion concentration near the electrode surface. The electrode surface and the electrical double layer can be thought of as a capacitor and the faradaic reaction as a resistor across this capacitor. The film acts as a dielectric and decreases the value of this capacitor. When less than complete coverage occurs the electrode interface can be thought of as many capacitors in parallel, the un- covered areas of the electrode having larger capacitance/cm2 and the covered areas having smaller capacitance values. Whenever the double layer is being charged, all of the 80 Figure 20. Current impulse relaxation curves in 1.0 g_KBr. (3) Less than complete coverage by film. (b) Surface completely covered by film. 81 (a) qu 0D *0! ‘5 (I l I 2 3 4 :5 H (b) ‘. - > .. E 3 GP 21.. |‘ _. l l 1‘*J-"ffl I 2 3 4 TIME pSEC Figure 20. 82 capacitors must charge and discharge so the reaction is occurring on both the covered and uncovered areas simul- taneously. Since the capacitance of the uncovered areas is of the order of 100 times larger than the capacitance of the covered areas, only the discharge of the larger capacitance through the reaction on the uncovered areas is observed. However, once the electrode is completely covered only the low capacitance surface remains, and the reaction taking place by discharge of the smaller capacitors is ob- served, i;g, the reaction occurring on the film surface. The two rates must necessarily approach each other as the surface becomes covered but the range over which this occurs would be very small. A study of such an effect together with a study of the decay rate on a covered surface might be a method of studying transfer through films. IV. CONCLUSION A. Model A simple model is suggested by this study. The first step is the charge transfer reaction: > Ag+ + e- <— A9 It has been shown that this reaction is occurring predomin- ately on the uncovered silver surface area, however, the growth of the silver halide film is occurring at discrete sites. This suggests that the silver ions formed by the electron exchange reaction react in either of two ways. The silver halide can form at the charge transfer site and diffuse to the growth site (Path 1) and/or the silver ions can diffuse to the growth sites where the silver halide is formed in the growth lattice (Path 2). The present method of study has no way of distinguishing between the two alter- natives. The overall process can be represented by : 83 84 + A9 2:: Ag (adions) + e + .— Ag (adions) + X <-——=- Agx (charge trans- r ----------------------------- , fer site) I Path 1 g I I diffusion : : diffusion : I J’ EHHEEEEHE HHHHHHHHHHHHHHHHHH —>L' + _ Ag (adions at + X < > AgX (growth site) growth site) B. Summary Silver halide film growth on silver anodes was studied using the current impulse technique. Variations in the capacitance and exchange current were examined as a func- tion of pulse measurement variables and the film growth conditions. When a halide anion is placed in solution, the silver ion concentration is stabilized at the electrode surface. The "concentration" of surface silver ion is de- pendent upon which halide is present but not upon the bulk concentration of halide. The present method of study gives no indication of why or how the silver ion concentration is stabilized at the electrode surface. Changes in measurement conditions such as the cou- lombic content of the pulse or the pulse direction have no effect on the kinetic parameters. As film growth occurs, the capacitance and exchange current are observed as a func- tion of applied charge. Changes in these two parameters are explained by a decrease in the uncovered silver surface 85 area. The nucleation process was not studied as it ap- pears to have occurred before the first anodic charge was applied. Upon application of a constant current the nuclei grow in height followed by an outward growth over the sur- face. This pattern of growth further clarifies step 3 of Kurtz‘f The three halide films grow similarly but to dif- ferent heights. Since the exchange current is dependent on the free silver surface area, the silver-silver ion exchange must be taking place there with the resulting Ag+ forming sil- ver halide either before or after it transfers to the growth site. 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