Electrochemistry - Second Edition

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The objective of this second edition remains the discussion of the many diverse roles of electrochemical technology in industry. Those familiar with the first edition will note a significant increase in the number of pages. The most obvious addition is the separate chapter on electrochemical sensors but, in fact, all chapters have been reviewed thoroughly and many have been altered substantially. These changes to the book partly reflect the different view of a second author as well as comments from students and friends. In the preface to the first edition it was stated:.

Many a technologist will be led to the direct solution of a problem, or provided with inspiration for some lateral thinking. The authors are to be congratulated for bringing out such an enlightening book on industrial electrochemistry - Bulletin of Electrochemistry; The authors Their style of writing is also very good, making the book eminently readable whether you just want to dip into a specific topic or perhaps pursue a much larger section.

The practical aspects are well covered The authors are to be congratulated for bringing out such an enlightening book on industrial electrochemistry. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Chemistry Physical Chemistry. Free Preview. Buy eBook. Buy Softcover. FAQ Policy. About this book The objective of this second edition remains the discussion of the many diverse roles of electrochemical technology in industry.

Show all. Table of contents 12 chapters Table of contents 12 chapters Fundamental concepts Pages Pletcher, Derek et al. The words "small" and "appreciable" are ambiguous; the meaning depends upon the context of the experiment. In very high resistance circuits, leakage of current by a voltmeter with a low input resistance.

There are a number of between the meter terminals becomes critically important. Dust, oily causes of irreversible behavior in electrochemical cells which are films, or even a fingerprint on an insulator can provide a current path discussed in more detail in Chapter 5. Irreversible behavior usually having a resistance of - O.

This resistance in parallel with the results from an electrode process having slow reaction kinetics, in the meter as shown in Figure 1. Strictly speaking, in any reasonable model the resistance resistance and even comparable with the cell internal resistance.

We The problem of leakage resistance is generally encountered for any! In particular the glass electrode commonly used for pH Consider an electrochemical cell with an internal resistance Rlnt measurements has a very high resistance and is prone to just such connected to a voltage-measuring device having an input resistance leakage problems. Careful experimental technique with attention to Rmeter as shown in Figure 1. If we could draw zero current, the clean leads and contacts is essential to accuracy.

A potentiometer, shown in Figure 1. The potential drop between A and the slidewire tap is then equal to E s and, if the slidewire is linear in If the measured voltage is to be a good approximation to the cell resistance. Our perception of the can be determined. The switch is then thrown to the unknown cell, Ex, reversibility of a cell thus depends on the measuring instrument. The unknown potential can then be read from the slidewire calibration.

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Since the output impedance is low ca. JB meters typically are limited to an accuracy on the order of 0. Ex Figure 1. Reversible cell potentials measured with a potentiometer are usually accurate to 0. The apparatus is relatively inexpensive, but the method is slow, cumbersome, and 1.

Furthermore, although in principle the! I potential is read under zero current conditions, some current must be drawn in order to find the zero. The current is small, typically on the The standard half-cell potentials of all aqueous redox couples are order of A with a sensitive galvanometer, but may be large enough to given with respect to the hydrogen electrode, the primary reference cause serious errors for a cell with high internal resistance.

Unfortunately, however. For these reasons, other electrodes amplifiers with very high input impedances became available. Such are more commonly used as secondary references F1. Reference Electrodes A number of different designs have been used for electrometer circuits, but one which is particularly common in electrochemical A practical reference electrode should be easily and reproducibly instrumentation is the so-called voltage follower shown in Figure 1.

Two electrodes-the calomel triangle in the figure. The output voltage of an operational amplifier is and silver-silver chloride electrodes-are particularly common, meeting proportional to the difference between the two input voltages with very these requirements quite well. In a voltage follower, the output is connected to the The calomel! Suppose that the output voltage is slightly shorthand notation as follows: greater than that at the positive input. The difference between the inputs will be amplified, driving the output voltage down. The output is stable, of course, when the output and input are exactly equal.

Since the input impedance 1 Calomel is an archaic name for mercurous chloride, Hg2C This matter is discussed further in Sect. The latter designation implies that this electrode responds to indicates some iber junction fiber junction specific electrode half-reaction. At this point, it is appropriate to ask what determines the potential of an electrode. Consider a solution Figure 1. If Silver-silver chloride electrode. In practice it is often convenient to use saturated What then is the actual potential of the iron wire electrode?

We first note KCl solution as the electrolyte with a few crystals of solid KCl present in that in order to have a finite reversible potential at an electrode, all the the electrode to maintain saturation. In this way the chloride ion participating species must be present in finite concentration so that concentration is held constant from day to day and it is not necessary to appreciable current can be drawn in either direction.

Thus, as we have prepare a solution of exactly known concentration. The potential of the defined the system with no sulfur dioxide or gaseous hydrogen present, saturated calomel electrode abbreviated s. This is the right temperature dependent, there is a significant variation in potential with answer but for the wrong reason. Suppose that we bubbled some temperature, When this is a problem. There is another way to look at this system: , I 0. Just as these homogeneous reactions are very slow, the electrochemical reduction of S04 2. L 2F aFe2 the activities of the survivors, but the other couple remains at equilibrium and the concentration of the minor component can be or, at 25C, calculated.

Although it is difficult to predict the rates of electrode processes 1. First, electrode processes which involve gases are usually very slow unless a surface is present which catalyzes the reaction. We could easily set up Second, as a general rule, simple electron transfers which do not involve an electrochemical cell to take advantage of this property. Suppose that chemical bond breaking, e. The cell can be represented What then should we expect if the components of two reversible schematically by couples are present in the cell?

LL In D'11 so that the overall cell reaction is F aFe3 Cl' aq. L potential. Frequently this means that one of the components of the mixture is consumed reduced to a very low concentration. It is then It would be nice to have an indicator electrode which would respond most convenient to compute the potential of the indicator electrode from to only one specific ion. A membrane with perfect b selectivity is yet to be found, but there are quite a number of devices lead wire which come close.!

There are several approaches to membrane design, and we will not discuss them all. The oldests membrane electrode is the glass electrode, which has been used to measure pH since 4 but intemal solution properly understood only relatively recently. The electrode, shown in Figure 1. The glass electrode is insulation ca. The glass used in the membrane is a mixture of sodium and Ag wire coated. The glass is also quite hygroscopic and takes up a significant amount of water in a Figure l. Ui a pH-sensitive glass electrode; b schematic view of the glass surface layer perhaps as much as 0.

In the hydrated layers membrane. Hydrogen ions on the other side the pH range Above pH 11, response to alkali ions becomes of the glass penetrate a little deeper into the glass to replace the Na" ions important with some glasses and such electrodes become unusable that have migrated. This combination of ion migrations gives sufficient above pH The selectivity coefficient example, the Na- concentration in the hydrated layer of the glass may be depends on the equilibrium constant for the reaction of eq 1. These properties depend on the composition and structure of the glass and can be controlled to some extent.

Thus some glass electrodes now 1 See books by Koryta All , Vesely, Weiss, and Stulik D'l I , and by Koryta and available make use of glasses where lithium and barium replace Stulik for further details. A nerve cell wall can be activated to pass Na" ions to sodium ions, allowing measurements up to pH Corrections for and so develop a membrane potential which triggers a response in an adjacent cell. Chemists were slower in appreciating the potential of such a device, but we are catching up fast.

The glass surface is dehydrated on prolonged obtained. Thus a membrane potential ionic strength. Nonetheless, glass electrodes can be used e. Thus a Na20 - Al20a By surrounding the glass membrane of an ordinary glass electrode Si02 glass can be fabricated which is selective for sodium ions e. This technique, where an ion-selective solutions over the pNa range Electrodes are commercially available for dissolved NHa and N02, as well as for C Rapid progress has been made in recent years in the design of ion By incorporating an enzyme in a membrane, this approach can be selective electrodes which employ an insoluble inorganic salt as a extended to the detection of many other species.

For example, a urea membrane. For example, a lanthanum fluoride crystal, doped with a sensitive electrode can be constructed by immobilizing the enzyme little EUF2 to provide vacancies at anionic sites, behaves like a urease in a thin layer of polyacrylamide on a cation-sensing glass membrane permeable to F- ions. The only significant interference is electrode. F- and OH- are almost exactly the same size, but other catalysed hydrolysis of urea. Similarly, by coating a glass electrode with anions are too large to fit into the F- sites in the crystal.

The LaFa immobilized L-amino acid oxidase, an electrode is obtained which crystal, together with a solution of K. Clearly, the field of ion-selective gives a fluoride ion-selective electrode usable in the pF range I There Other solid membrane electrodes make use of pressed pellets of are literally thousands of potential applications in chemistry, insoluble salts such as Ag2S. Both types have some important advantages which will become apparent as we By replacing the glass or inorganic crystal with a thin layer of a discuss them.

For example, by using the calcium salt of an organophosphoric acid in an organic solvent as the liquid ion I For a good review, see Murray 5. The field is reviewed every two years in exchanger and contacting the ion-exchange solution with the aqueous Analytical Chemistry, e. Direct Method. The concentrations of other species, such. The measurement of pH using a glass electrode is by far the most 2 Standard addition method.

By first measuring the potential common of all electroanalytical techniques 9,D7,D10 and is also of an unknown solution and then adding a known amount of the characteristic of direct determinations using cell potentials. A typical.

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The half-cell reactions, errors. On the other hand, if the calibration curve was not linear, the knOwn addition method would introduce a large uncorrectable error. If only a few analyses are to be performed, the known addition method is usually faster. In either case, themethod lead to no net change so that the overall cell reaction is the nominal should have been carefully investigated to ferret out systematic errors. The cell potential was mV at 25C. After addition of 10 mL of 2.

M F- standard solution, the potential was m V. What 1 was the original concentration of fluoride? Thus the cell potential is directly proportional to the pH of the test In practice, this may not be exactly true because of a liquid junction potential at the salt bridge linking the reference electrode to the Thus Subtracting, we get! Two general procedures are used commonly. Assuming that we can replace the activities by molar 1 Calibration curve. The potential of a given cell can be concentrations, we have measured with standard solutions and a potential vs.

The concentration of an unknown may then be read from the calibration curve given the potential of the unknown. When The difference, [F-J - [F-Jo, corresponds to the number of moles this method is used, it is important that the unknown solution have the of'F: added. Such accuracy is We first compute the equilibrium constant for the reaction. For concentrations of chemical species Consider the hypothetical cell not the one being measured in. Thus we have l! The reaction will go to completion if the available. Other ion-selective electrodes can be used to determine titration Consider the situation when 10 mL of titrant has been added.

For example, organic thiols may be determined by titration with Since we have added 0. The titration reaction is must remain. The cell potential is given by Example 1. EIV Interest in electrochemical cells as power sources has revived recently 10,11 as society has become more concerned for the 1. Electric-powered automobiles offer the hope of substantially reduced environmental pollution and direct conversion of fossil fuel 0. In this section, we will review briefly the operation of 80me electrochemical cells which convert chemical energy into 0.

A flashlight I: cell is used until all the chemical energy has been converted to electricity and is then discarded. A fuel cell in a spacecraft converts hydrogen and [Ce3t] Oxygen to water, extracting the energy as electricity. A storage battery, on When 30 mL of titrant has been added, there will be 0.

The ratio is 2. Carrying out several such calculations, we can sketch the We first consider three common primary cells which have a family titration curve shown in Figure 1. The ''Dry Cell". The so-called "dry cell" used to power flashlights is descended from 1. The carbon rod cathode is surrounded by a effort was devoted to the development of inexpensive, efficient power cells thick layer of Mn02 mixed with a little graphite to improve the and storage batteries.

A paper barrier separates the Mn02 from the aqueous into use in the 's and electrical power began to be widely distributed, electrolyte which is gelled with starch or agar so that the cell is "dry" electrochemical power cells started into a long decline. In the recent and the zinc anode which forms the cell container. A newly prepared past, galvanic cells have been used mostly as small portable power cell has an open circuit potential of about 1. Accordingly, mercury cells have often been used to provide a voltage reference in electronic instrumentation. Upon discharge, this layer becomes largely ZnIMn02 dry cell.

The alkaline electrolyte is contained in a layer of adsorbent material and the zinc amalgam anode is pressed into the cell top. In addition to the relatively constant potential, mercury cells have a leads to an increase in pH which is buffered by the NH4Cl. The cell long shelf life and a high energy-to-volume ratio. The major reaction is only partially reversible, so that dry cells are not readily disadvantages are that power output drops precipitously at recharged.

It may be precipitated as a hydroxide or oxychloride or environmental problems. On diffusion into the Mn02 phase, however, precipitation as ZnO-Mn20a occurs. There is some The Silver Cell evidence that formation of this phase is responsible for the irreversibility of the cell.

ZnlMn02 dry cells have a relatively short shelflife because of A close relative of the mercury cell is the ZnJAg cell: diffusion processes which amount to an internal short circuit. When potential is less constant during discharge. The silver cell has a higher 'iii voltage than the mercury cell, about 1. It also operates successfully at , significantly lower temperatures. However, the shelf life of an alkaline cell is much longer than that of the Leclanche cell, and the alkaline ZnlMn02 cell turns out Fuel Cells to be well adapted to applications where a steady low-level drain of power is required, a situation where polarization of the traditional dry cell When hydrogen or a hydrocarbon fuel is burned in a heat engine, would lead to degradation of performance.

For an for the U. Army during World War II. Using the or. The HV02 system was efficiency decreases with increasing temperature but is usually much studied very early in the history of electrochemistry see Section 1. This is hardly a new idea. Ostwald the hydrogen-oxygen fuel cell was first described by Grove in The major heat engines.

The reduction of oxygen is an even more serious and K, and b in an electrochemical cell operating under problem, as this rate is quite slow even on precious metal electrodes. The H fuel cell remained a gleam in the eye of electrochemists and an occasional laboratory curiosity until the U. With a need defined and a the maximum useful work, assuming that Mf is temperature customer willing to pay development costs, several companies began independent, is kJ mol-I.

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The standard free energy of formation of H20 g is kJ The operation of a H fuel cell is limited by the slow rate of the mol-J, and all this energy is theoretically convertible to electrode reactions and by ohmic heating of the electrolyte solution. The electrical work. While the reactions do go faster at higher temperatures, eq 1.

Together with Arrhenius and so that a compromise is involved. Increasing the surface area is an van't Hoff, Ostwald is regarded as one of the founders of physical effective strategy provided that the increased surface can be contacted by chemistry. His laboratory at Leipzig spawned a generation of physical both the gas phase and the electrolyte solution. Sir William R. Grove was a barrister by The solution to the problem of the H fuel cell in general has profession, but he maintained an active scientific career on the side. He is remembered for his work on galvanic cells and as a founder of The involved the use of electrode materials such as porous graphite with a Chemical Society of London.

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  8. The interface between the H2 and 02 gas phases and the aqueous electrolyte phase occurs within the body of the porous electrode. The lead-acid cell 17 , familiar because of its use in automobile. While there has been significant progress and pilot-plant. For more details on fuel cells, see Bockris and Srinivasan G1 , Pletcher G6 , or reviews by Eisenberg 15 When the acid concentration is greater than about 2 M, the formal cell or Cairns Both the lead sponge used as the anode material and the lead dioxide cathode Storage Batteries mixed with an "expander" such as BaSO, to increase the surface area are packed into lead grids which provide the electrical contacts.

    When Energy storage cells secondary cells have somewhat different the battery is discharged, nonconducting PbS04 is formed at both the requirements than primary energy conversion cells. A storage cell anode and cathode and the internal resistance of the cell increases. The rate of which convert components into unusable forms. Because storage cells recovery is thus tied to the diffusion rate and is much slower at low are mostly used in situations requiring a portable power source, the temperatures.

    Since the density of PbS04 is less than that of either lead energy available per unit weight should be as large as possible. A or Pb02, excessive discharge would rupture the lead grids. Since discharge of the By far the largest use of storage cells at present is in automobile cell reduces the concentration of sulfuric acid, the density of the H2 S04 batteries. Here the major requirement is that the battery be capable of electrolyte solution provides a convenient measure of the state of charge delivering high power for a relatively short time to start the engine.

    Storage cells are also used to power many small appliances. A Given the half-cell potentials, recharging a lead-acid battery should potentially important application of storage cells is in powering electric result in generation of H2 instead of reduction of PbS04 to Pb and 02 cars and trucks. Electrically powered vehicles were popular in the instead of oxidation of PbS04 to Pb Fortunately, these processes are period around World War I but did not successfully meet the competition very slow at lead electrodes and thus are operationally irreversible.

    With society's recently acquired However, when the battery is fully charged, H2 g and 02 g production awareness of the environmental damage of automobiles, there has been may occur if the charging potential is high enough. Since gas evolution a revival of interest in electric cars and in efficient light-weight batteries tends to dislodge PbS04 from the grids, this is undesirable and thus to run them.

    Another potentially important application of storage cells regulation of the voltage of a battery charger is required.. Lead-acid storage batteries have undergone many generations of engineering improvement and are now reasonably efficient and reliable. Because of the low internal resistance, the lead-acid cell is capable of impressive bursts of power up to about 10 kW for a few seconds , and can be charged and discharged for years.

    The principal disadvantage is weight. II devote a large fraction of their load-carrying capacity to batteries, a restriction which has severely limited development. Example 1. The theoretical maximum energy density is about J g-1 0. The Edison cell has several other advantages: the basic solution is less corrosive than the concentrated acid used in a lead battery; the electrode assemblies are more rugged and less susceptible to damage by complete discharge or overcharging. However, the smaller cell potential requires more cells per battery than a lead-acid cell and, because nickel is more I expensive than lead, the initial cost is greater.

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    On the other hand, an The electrical energy delivered at 2 V is Edison cell has a much longer service life than a lead-acid cell and so may be cheaper in the long run. If or 0. The Nickel-Cadmium Cell. The cell, which has a nominal. Ii' Gaston Plante was Professor of Physics in Paris; he is best known for his work on storage batteries. Thomas Alva Edison was a prolific inventor whose persistence made up for his lack of formal scientific training.

    Although Edison acknowledged a debt to Michael Faraday for his electrical and electrochemical inventions, his potential of 1. It is intrinsically more expensive and has a lower energy density, but it has found an important niche in small rechargeable batteries used in transistor radios, tape recorders, pocket calculators, etc. There have been many The alkaline iron-nickel cell can be represented as attempts to develop cells based on the much more exoergic reactions of the alkali metals.

    A successful cell based on the reaction of lithium or Fe s INi02 S ,Ni S IKOH aq IFe s IFe s sodium with fluorine or oxygen would combine high cell potential with The half-cell reactions light weight, but there are some obvious technical problems in building such a cell. Liquid This cell was perfected by Edison in as a power source for electric sulfur supports the ionization of Na An inert metal such as vehicles.

    The nominal cell potential is about 1. The cell voltage is about 2 V, depending on the state of charge, and the theoretical maximum energy density is about J g-1 1. Na atom diffusion into grain boundaries in the [3-alumina membrane causes short circuits and structural failure. The sodium-sulfur cell is probably not practical 1. One beaker problem , but as a power plant load-leveling device it has some promise. Reference numbers preceded by a letter, e. AI , refer to a book listed in e Compute the actual potential of the cell neglect activity the Bibliography.

    Frost, J. Ebsworth, Educ. Delahay, M. Pourbaix, and P. Haber and Z. Klemenciewicz, Z. Chem, , 67, Murray, Electroanalytical Chemistry , 13, Janata, Anal. Furman in Treatise on Analytical Chemistry, I. Kolthoff and P. Elving, eds, New York: Wiley, Part I, Vol. Weissberger and B. KCI 3. Rossiter, eds, New York: Wiley, , pI. Given that the Gregory, Modern Aspects ofElectrochemistry , 10, Dordesch, Modern Aspects of Electrochemistry , 10, McBreen and E.

    Cairns, Adu. Ostwald, Z. Grove, Phil. Eisenberg, Adu. Cairns, Adv. You Burbank, A. Simon, and E. Willihnganz, Adv. Milner and U. Thomas, Adv. What is the pH ofa saturated solution ofSb at K? I I Problems The potential is o. Calculate the cell potential when 1, 10, 30, 45, 50, 55, and 70 mL of the silver solution has been added.

    The solubility product constant of AgCI is 2. Neglect activity coefficients. Reprint in Figure 1. What was the concentration of mercuric ions in the ed with permission from R. Overman, Anal. Assuming that all the power is used for such pumps and 1. Na" out of the brain cells per second. Assuming that the brain has 10 8 cells and that each nerve impulse results in an uptake of has a potential of If the only significant reaction mole of Nat, estimate the firing rate of the brain cells.

    The reduction of the conversion of malic acid to oxaloacetic acid, From the data given in quinone is reversible on platinum: Table A. Go for the oxidation of Be- by HzOz. Go for the oxidation of HzOz by Brz. Most of peroxide solution. We relied on thermodynamics and a Calculate the pH of the unknown solution. We shall now look more b If a possible junction potential introduces an uncertainty of closely at the interface between an electrode and an electrolyte solution. There are four ways in which a surface may acquire a charge: 1.

    Surface charge effects are particularly b If the uncertainty in the potential measurements was 0. The surface-to-volume ratio of a V, what was the uncertainty in the sodium concentration of the biological cell is large and most biochemical reactions occur at or near unknown? We begin in 2. We digress slightly in 2. Returning to electrodes in 2. The ideas b At what solution pH would the apparent pH computed developed in our discussion of charged surfaces can be extended to the assuming pH linear in potential without correction be too low by interaction of small ions in solution, and we conclude this chapter with 0.

    A charged surface in contact with an electrolyte solution is expected b If the cell potential is 1. Two parallel layers of charge are formed-the charge on the surface itself and the layer of oppositely charged ions near the surface. Helmholtz Gouy Stem model model model. His contribution to the theory of the electric double layer was an extension of his interest in Brownian motion.

    David L. Chapman was a Fellow of Jesus College, Oxford. Most of his scientific work was on gas-phase reaction kinetics. Figure 2. Gouy-Chapman Theory structure is called the electric double layer. For reviews of double layer The immediate goal of a theoretical description of the electrified theory, see Grahame 1 , Parsons 2 , Mohilner 3 , or Reeves 4. He assumed that a layer of The electric potential at any point in the solution is related to the net counter ions would be immobilized on the surface by electrostatic charge density at that point by a fundamental relationship derived from attraction such that the surface charge is exactly neutralized.

    The surface. They suggested that the ions which neutralize the surface operator '11 2 is, in Cartesian coordinates, charge are spread out into solution, forming what is called a diffuse double layer. According to the Gouy-Chapman model, the potential falls 2 i i fJ2 more slowly to the bulk solution value, as shown in Figure 2. Gouy-Chapman model adequately accounts for the properties of the and in spherical polar coordinates, double layer and suggested that the truth lies in a combination of the two models. This model is also pictured The space charge density p is related to the concentrations and charges schematically in Figure 2.

    However, since and finally, substitution of eq 2. No kT The solution to this differential equation is the potential as a which gives the equilibrium ratio of the number Nl of particles having function of the position in the solution. In order to proceed further, we must specify the geometry of the problem and decide upon the method of energy E 1 to the number No with energy Eo.

    In the equation, k is Boltzmann's constant the gas constant divided by Avogadro's number, k solution. Integration of eq 2. The Boltzmann equation is methods which may be used in dealing with the summation: 1 a applied here to calculate the relative concentrations of ions at positions general, but approximate, solution obtained by expanding the of different electrostatic potential energy. Cio L 2.

    Combining eqs 2. Notice that this result differs from eq 2. Cl or MgS04, eq 2. First, we look at the shape of the solutions represented by eq 2. In Figure 2. Indeed, boundary conditions. However, the distance of closest approach to the surface must be at least as large as the ionic radius. If there are ions at this closest approach distance, then their 1.

    If this first layer of ions is essentially an immobilized Helmholtz layer, then we expect that the 0. We assume 2 then that eq 2. Values of XA are given in Table 2. Judging from the plots of Figures 2. I As we see in Table 2. If the system as a whole is electrically Consider the case of aIM NaCI solution in contact with a surface with neutral, then the net surface charge ti. According to eq 2. This space charge in the Gouy layer. If o is the net surface charge density in corresponds to approximately 30 chloride ions per cubic nanometer C m- 2 , then, for a planar surface, very nearly a closest packed layer of chloride ions.

    This absurdity points up the major weakness in the theory: we take account of electrostatic interaction between ions in solution and the charged surface, but neglect interactions between ions. This is a reasonable 1 In the context of Debye-Huckel theory Section 2. There are several less serious problems. We have tacitly assumed We first ask why large particles such as proteins should be stable in that the' charge density p is a smoothly varying continuous function of soluti'on. Atoms or small molecules are subject to so-called London the distance from the surface.

    While this is not true on an forces, which give rise to a van der Waals potential energy of interaction. One must over the solution. A more serious defect results from the use of the bulk consider the van der Waals attraction of each atom in one molecule for dielectric constant of the solvent in calculating electrical forces over every atom in the other molecule. Some complicated integrals arise and short distances; since the water dipoles are oriented around ions or at we shall not go into the details of the calculation. The theory is very useful, where R is the distance between the particle surfaces.

    The parameter A however, as a means of gaining a qualitative understanding of is essentially empirical and usually is on the order of to J. The phenomena which are affected by the electrified interface. While the multiple attraction of the many atoms in a macromolecule results in the Gouy-Chapman approach continues to be used as a starting point for van der Waals energy falling off with distance much more slowly than theoretical treatments of charged surfaces, some theorists have turned might have been expected. With relatively long-range attractive forces, to molecular dynamics calculations where the motion of ions near a uncharged particles are expected to associate and eventually precipitate charged surface is followed in a computer simulation; potential and from solution.

    As So what keeps them apart? The free energy change, tJ. S, it turns out, the qualitative results of the computer modeling studies are governs the equilibrium behavior. We would expect that tJ. S for in good agreement with the insights obtained from Gouy-Chapman coagulation would be negative, but for a relatively small number oflarge theory. Short-range repulsion sets in when applications of the ideas obtained from Gouy-Chapman theory.

    In light the electron clouds overlap, but by the time this interaction is important, of the weaknesses just discussed, we should not hope for high accuracy, van der Waals attraction has already coagulated the particles. Notice, however, that according to eq 2. If XA is very small, the diffuse layer is very compact and the particle's charge is shielded up to very short distances. Particles in colloidal suspensions te.

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    In general, therefore, colloidal particles have ion atmospheres. In this section we shaIl We expect therefore that when the ionic strength is increased, the examine some of the characteristics of such particles which may be double-layer thickness will decrease and the coIloid will precipitate. I See Shaw 9 for further discussion of this problem. The calculation of the electrostatic repulsion between two particles, Iii iii' , I. All the difficulties attending Gouy-Chapman theory remain, of course, and the question of what happens when the two ion atmospheres begin to "".

    If it is hi", m " 0. When the less, the effect is largely independent of the nature of the electrolyte and thickness is 10 nm, there is a small barrier to coagulation about 3. Many proteins remain in and coagulation would be expected to occur fairly rapidly e- 3. When high concentrations of atmosphere is 20 nm thick, the barrier is even greater. Protein and polymer chemists depends on the temperature and the dielectric constant of the medium sometimes refer to the lyotropic series of cations and anions, which show as well as the size of the particle.

    Since Salts with low solubility such as CaS04 are of little use in salting-out, of protein solubilities are such intricate functions of ionic strength, COurse; the most commonly used precipitants are very soluble salts with temperature, dielectric constant, and pH, it is not surprising that protein a component high on the lyotropic series, such as ammonium sulfate or magnesi um chloride. Ignoring this problem, eq 2. When lauric acid is added to a solution of should be higher than that of the bulk solution; above the isoelectric pH, dodecylsulfate micelles, the long-chain carboxylic acid the surface is negatively charged because of -C02" groups , and the molecules are included in the micelles.

    A pH titration of the surface pH should be less than the bulk pH. Thus, to a degree, the carboxylic acid yields an apparent pKa the pH of the half surface pH on a protein tends to be self-buffered toward the isoelectric neutralization point of about 7 under these conditions. Since pH. Thus eq 2. Although we must be cautious about quantitative predictions from Gouy Chapman theory, the qualitative effect is real and has important 2. Four rather peculiar effects, known as the electrokinetic Example 2. Compute theory of the diffuse double layer l2,B8. Assume an ionic strength of mM.

    The Phenomena. The surface charge density is Consider an electrolyte solution flowing through a capillary as 19 shown in Figure 2. As the solution flows through the capillary, some of the space charge is swept along with it and, if The surface potential derived using the linearized Poisson electrodes are provided at either end of the capillary, a current, called Boltzmann equation see Problems is the streaming current, can be measured between them.

    The Electrified Interface 2. The effect of liquid flow under the action of an electric potential difference is called electroosmosis. The relation of this steady-state head phenomenon, called the electroosmotic pressure, to electroosmosis is J analogous to the relation of streaming potential to streaming current. When the flux goes to zero, the pressure Figure 2. The Zeta Potential Electrokinetic effects arise because of motion of the diffuse layer of If, on the other hand, we replace the ammeter with a voltmeter, ions in solution relative to the solid surface.

    We might guess that the essentially no current flows and ions swept through the capillary Helmholtz layer is stationary and that the Gouy layer moves with the accumulate at one end, producing an electric potential difference across bulk solution, but this is an oversimplification. The behavior is as if the capillary, called the streaming potential.

    If the experiment starts there were a slipping surface located in the diffuse part of the ion with a homogeneous solution, the streaming potential grows with time atmosphere. The potential at the slipping surface is given the symbol C until it is big enough that electric migration of ions upstream exactly zeta and is called the electrokinetic potential or simply the zeta cancels the flow of ions downstream. The two effects, streaming current and streaming potential, may be In a quantitative treatment of the electrokinetic effects, the jointly expressed by one phenomenological equation: appropriate form of the V2 operator in the Poisson equation depends on the geometry of the problem.

    However, when the current is zero e. Ifwe assume that a, the radius of the capillary, is much larger than the A related effect may be observed if, instead of applying a pressure diffuse layer thickness XA, then we need not rederive an equation for the difference, we impose a potential difference between the two electrodes. There is little drag on the bulk solution, which has zero net charge. Near the surface, where the coordinate r is measured from the center of the capillary.

    If the cylindrical shell of solution near the of the capillary is nearly zero. The coefficients in eqs 2. The coefficient Cli is the current and per unit pressure difference when the potential difference is zero. P is the pressure difference over the length L of the tube. The streaming current is the electric current per unit flux Substituting eqs 2. For further discussion, see Bockris and Reddy B8. Notice that the streaming potential and electroosmotic flow are predicted to be completely independent of the dimensions of the capillary Zeta Potentials at Glass-Water Interfaces tube.

    Indeed, it can be shown that the results we have obtained for a cylindrical capillary are independent not only of the dimensions, but also Glass-water interfaces appear to acquire a double layer through of the shape of the holes through which the liquid flows, provided only selective adsorption, usually of OH- ions. The surface potential therefore that 1 the flow is laminar ii.

    The zeta potential is strongly dependent on the electrolyte than the thickness of the double layer. The electroosmotic pressure and the streaming current, on the other hand, depend on the radius of the capillary, and in general, on the average pore size when flow is through a porous plug or membrane. Example 2. K NO 3, and c HN03 deter.

    Substitution into eq 2. The lines. Thus equation. Reprinted with per. Rutgers and Faraday Soc. Equation 2. In addition, if Substitution into eq 2. If 1 is independent of electrolyte concentration, then S should be a monotonic decreasing function of C. The situation is somewhat more complicated if the surface charge 2. Indeed, there is a effects arising because of motion of the electrolyte solution past the minimum in the sus. Several related phenomena arise when the balance between 1 increasing with increasing concentration and XA interface is also free to move.

    This interpretation is supported by the behavior of HN03, for which the zeta potential falls more rapidly with increasing concentration, presumably because of surface charge neutralization. The origin of the behavior is shown in Figure 2. Reprinted with per-mission from H. For example, the relative viscosity of a solution Figure 2.

    The upper aqueous solution interface us. The lower curve determined by electroosmotic flow effective hydrodynamic size of the colloid and thus increases the viscous shows the behavior expected when through a glass capillary. Reprinted drag when the molecule moves in solution. Rutgers charged functional groups results in an extended conformation of the on the surface forming a "triple and M.

    Faraday starch molecule. When the ionic strength is higher, intergroup layer" and reversing the sign of the Soc. Royal Society of Chemistry. Again the effective hydrodynamic volume is reduced and the solution viscosity is lower. The first effect can be treated theoretically but it is usually considerably smaller than the second. Sedimentation Potential Q 41ta 2 a. JL a XA particles may leave some of their ion atmosphere behind, especially if the diffuse layer is very thick low ionic strength.

    Thus charge combining these expressions, we have the electrical force on the separation may accompany sedimentation, leading to the development of particle: an electric potential gradient along the length of the sedimentation tube. The phenomenon is thus analogous to the streaming potential discussed Fe.

    Micromachining Using Electrochemical Discharge Phenomenon

    A sedimentation potential is generally an unwanted complication When the particle reaches terminal velocity, the acceleration is zero, and in an ultracentrifugation experiment. To reduce the magnitude of the according to Newton's second law, the resultant of forces must be zero. The phenomenon of electrophoresis is characterized by the unity, the mobility should increase; however, the variation is more electrophoretic mobility, u, defined as the velocity per unit electric field complicated than we might expect from this approach.

    Suppose that the particle is very 2. We then regard the surface as approximately planar and consider the relative motion of the If v is expressed in m s-l and E is in Y rrr l, u apparently must have solution past the surface. The calculation, which is very similar to that units of m 2 y -1s Typical mobilities of ordinary small ions in aqueous for the electrokinetic coefficient 04, gives solution are on the order of 5 x m2V-1s- 1 ; proteins generally have mobilities in the range 0.

    Charged particles of intermediate size distort the electrical lines of Consider first the motion of a small spherical particle of radius a force and a more sophisticated approach is required. More exact through a medium of viscosity n. The mobility is, however, generally found to be proportional to the dielectric constant and to the zeta potential, and inversely where v is the velocity of the particle.

    On the other hand, the electrical proportional to the viscosity. This mobility is typical boundary between the colloid and for charged macromolecules see 3. Practical Electrophoresis boundary was observed by measurement of the refractive index. Fairly Although eq 2. Thus the electrophoretic mobility is expected to decrease with increasing ionic Arne W. Tiselius was a Professor at the University of strength of the electrolyte solution.

    The mobility is also proportional, of Uppsala with research interests in biophysical chemistry. He received the Nobel Prize in Chemistry in for his work on electrophoresis. Because of the dependence of the electrophoretic mobility on ionic marriage of electrophoretic migration with paper chromatography. By strength and pH, a mechanism for control of protein mobilities is using a solid support of filter paper, most of the problems associated available which is used in practical separation techniques.

    Even further electrophoresis experiments are done on a suspension of colloidal improvement can be obtained if a more homogeneous solid support such particles in liquid solution, and, indeed, the early experiments were. Thus, in classic experiments done in the 's, Tiselius found that The manifold of electrophoresis techniques now available, electrophoretic mobilities of protein molecules in solution could be including a host of procedures for detecting the protein molecules, goes measured by a moving boundary method Tiselius' apparatus was far beyond the space available here.

    Several rather long chapters would essentially a U-tube, shown in very simplified form in Figure 2. The be required to do the subject justice, and the reader is referred to a more U-tube was constructed so that the solution of the colloid could be placed specialized text for further details. Electrodes were then mounted in the two ends of the U-tube and a high voltage applied. When the protein molecules 2. To Unlike a protein molecule where the surface potential and the ion minimize convective mixing of the solutions and blurring of the atmosphere are a response to the solution pH and ionic strength, the boundary, it was necessary to very carefully thermostat the U-tube, and, potential of an electrode, and thus the nature of the double layer, can be since the rate of change of the density of water with temperature is controlled by external circuitry.

    This control permits quantitative smallest near the density maximum 4C , best results were obtained experimental studies of double-layer effects. In this section, we will when the system was thermostated at about C. In practice, the discuss two effects which have important consequences in electrochemical experiments to be described in subsequent chapters. When the electrode is a rigid solid, the effects of interfacial tension are difficult to discern, but when the electrode is nonrigid, a e e!

    A mercury drop forms at A plot of interfacial tension vs. The if the flow through the capillary is constant, in the lifetime of a mercury gravitational force weight , corrected for the buoyancy of the solution, is drop. If a second electrode is provided, where d and dHg are the densities of the solution and mercury, we can change the mercury-solution potential difference and thus respectively, and g is the gravitational acceleration. The surface tension induce a positive or negative charge on the mercury drop by passing a force holding the drop to the capillary is small current through the external circuit.

    Similarly, we can change the drop size by allowing mercury to flow through the capillary. However, the simple theory predicts identical curves for all and redifferentiated electrolytes of equal ionic strength. The curves of Figure 2. When the T,P potential is made sufficiently negative, anions are desorbed and all Substituting for J from eq 2. Grahame was Professor of Chemistry at Amherst College. He is remembered for his exceedingly careful and thorough studies of the electric double layer.

    The potential. KSCN facial tension, see 0. KI with permission from D. Grahame, Chern. EIV Figure 2. The potential scale is adjusted so that zero potential occurs at the electrocapillary maximum for a capillary-inactive differential capacitance electrolyte. Reprinted with permission from D. Consider first the is highly negatively charged. Differentiating eq 2.

    Minima are surface. Since adsorption is often potential dependent, very rapid observed experimentally and provide a way to determine the potential of changes in interfacial tension and thus drop time with potential are zero charge for an electrode The capacity vs.

    Double-Layer Capacitance Example 2. When the potential applied to an electrode immersed in an electrolyte solution is decreased from zero, the surface charge becomes The double-layer thicknesses for these concentrations are negative and the net space charge of the double layer must increase to Table 2. Assuming the dielectric maintain overall electrical neutrality. Capacitance is defined as the ratio of charge stored to vol tage for 0. Debye was one of the outstanding physical minimum of about 0. At one time or another, he held chairs at the computed in Example 2.

    His m- 2 and for 0. Erich Huckel was a student of Debye's; their collaboration continued and 0. The reason for these apparent in quantum chemistry. These also contribute to the capacity. From the point of Calculation ofan Ionic Activity Coefficient view of the external circuit, these two contributions-C H for the Helmholtz layer and Ca for the Gouy layer-behave like capacities in We begin by outlining the thermodynamic part of the argument. Thus the total observed capacity is given by The chemical potential of a species i is given by. If the standard state is an ideal 1 M solution.!

    Indeed, it is found that at zero If we now assume that the departure from ideality is due entirely to potential the double-layer capacity initially increases with concentration electrostatic interactions of the ion with its surroundings, then the and then levels off. By calculating the electrostatic free energy of interaction of an Thus if we can calculate the electrostatic contribution to the chemical ion with its atmosphere, an estimate of the activity coefficient can be potential of an ion, we will have the activity coefficient.

    We now Boltzmann equation. Since most practical work employs the molar concentration scale, we shall use the 1 M standard state here. The penalty for this choice is that most data tabulations must be converted to molar concentration units. The work done in this Finally, we substitute this expression into eq 2. In charging process is the change in the Gibbs free energy, which in this doing so, we also multiply by Avogadro's number! Mean Ionic Activity Coefficients Notice that this chemical potential has units of energy per ion; we will convert to a molar basis later.

    We define the mean chemical of the ion atmosphere called the Debye length in this context. Subtracting this from eq 2. For a Inserting the values of the constants and assuming a temperature of symmetrical electrolyte , , etc. Thus 25C and the dielectric constant of water