Teaching the Double Layer J. O'M. Bockris Texas A&M University, College Station, TX 77843 The Assumption Made in Writing this Article
faces." It has 36 lectures; seven are on the double layer. The General Attitude to be Induced in the Students
Teaching the double layer involves the same demand as other subjects. The point is to induce a sense of wonder and relevance. Most students regard electrochemistry as being about p H and acidity-perhaps conductance. I t is something which was probably done in their grandparent's youth. The first thine to brine" home. therefore. is that studies of the douhle layer are new and not part of old traditional electrochemistrv. Interest in double lavers increased in the 1950's. As far as metals other than mercury are concerned, the research began in the 1980's. Most of the things we shall talk about are around 10-15 years old. There is much advantage to be gained in injecting more marvel and wonder into all of this by referring to the breadth of the influence which the double layer has in real life. It is the stage upon which life takes place, for few real reactions take place in the pas phase: they mostly occur in the interphase. The third-and most important part of the wonder-generating opening session consists of proving the generality of very high electric field strengths in the interphase we treat. The high fields have to be emphasized. The way to do this is to make a thought experiment about the electronic equilibrium within a metal. One pictures all the electrons moving around. with ereat sneed. whereuoon. one interunts the course of the
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set up a new equilibrium in which they spill out of the metal into the gas phase, so the metal becomes positively charged. This is the first time one should play upon the word double layer and try to make it meaningful to the student. Here, in diagrams, one should show that the essence of a double layer has been produced by the metal-cutting example, i.e., there are the electrons outside the phase and there are the positive charges near the surface in it. One may dwell somewhat on all this, mentioning numbers. One may then deduce the strength of the electric field. The width of the double layer must he a few Angstroms and as for the magnitude of the potentials, they may be in volts. The field. then. must be about lo8 V cm-'. One can make comparisons from other machines which produce high voltages and indicate that the electrochemical field is some ten to the four times higher than those which can otherwise be obtained. It seems important to come in here with the widest series of examples one can find. One should disabuse the student's mind immediately with the idea that one is dealing with the mercury-solution interphase-and not the iron-solution interphase either. One is dealing with, e.g., the wood-solution interphase, and above all with the interphase between hiological materials and the surrounding solutions. The electronic conductivity of polymers and then of proteins may also be mentioned. Electrochemical transfer has much to do with living processes. The obiect of all this introduction, therefore, is to raise consciousness. And having done so, one then feels a little more justified in presenting the student with the problems.
The Problems
The first orohlem to strike the student with is the fact that. having said all this so blithely and confidently, one cannot measure the potential one has heen talking about. Of course, one should be cautious to note that there is no doubt about the ranse of volts. There is no suestion that it could be 5 V or, usu&y, less than 0.5 V, but i t can be somewhere in this range. I t is about one volt; that is certain. To prevent the student going into research from trying to measure the absolute potential difference (p.d.) a t the interphase, this task should be declared "Totally Impossible," with two or three examples of attempts people have made in the past (another unknown p.d. always turns up, of course). It should be stated that rough calculations are not impossible even now, however, and that more accurate calculations (e.g., to 1mV) could be possible in the not-so-far-off future. Measuring a Change in the P.D. at the Interphase and with What Accuracy
Before one can explain that it is possible to measure a change in p.d, even though the absolute value cannot be ohtained, one has to go through the idea of a polarizable and non-polarizable interphase because such words are at first meaningless to the student. He should be told that there are leaky bickets and non-leaky buckets, leaky capacitors and non-leaky capacitors, leaky electrodes and non-leaky electrodes, and the latter are called polarizable and the former, non-polarizable. A few examples should be given and some volts and amps put into place. Then, i t is explained that the non-polarizable ones are those which have high rates of electron crossine to and fro across the intemhase when the latter ones are those where is at e q u i l i h r k , and that the or so in both directions. Here, one the amps have sunk to should get over for the first time the idea that a microamp per cm2 on an electrode scale is a low current; however, electrochemists go to micro-microamps or even lower. The Conventional Scale
I teach the conventional scale of electrode potentials in a low-key way. I take a deprecating attitude that it is better that we use this scale rather than no scale. I emphasize that the conventional scales are rather complex. students should understand that each electrode potential on the scale has at least 3 or 4 component potentials and is given relative to a reference electrode (e.g., normal hydrogen reference). I poke gentle fun at physicists who (e.g., in photoelectrochemical kinetics) equate standard electrode potentials on the hydrogen scale with interphase differences in potential. Analyzing the Absolute P.D.
Even though there is no experimental method of measuring value for absolute . n.d... there is no need for us to stop thinkineabout it, analyzing it, and having a good idea about what's happening at it. I go, therefore, into the question of psi, phi, and chi, namely, the outer potential, the inner potential, and the surface potential (see Fig. 1). I find this rather difficult to lecture on because the definitions are not only abstract, but also subtle. Of course, the psi involves bringing up, in the thought process, a plus one charge which does not interact other than electrically with the phase. One then has to stop Volume 60
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Jusi outsrde
reach o f
m o w forces
from rolution
Surfoce excess, Pi = L! Concentrollon of specier.i
wth charge.
forces
Adsorbed materid
Unll p o i l i v e tert c h a r g e
Distonce fram interface Figure 1. The outer, or $,. potential of the solution is the work done to bring a unit of positive charge fram infinity to a poimP just outside the reach of the image forces from the solution.
just outside the range of the image forces. In the inner potential, the definition is that the charge goes further than in the outer potential, and finally ends up in the phase of the electrode, having started in a vacuum. The surface potential is comparatively easy to explain, hut is more difficult to explain than the Galvani potential difference and the Volta potential difference, respectively, because one has to explain the interphase hetween a phase in a vacuum, and how it is then changed in the presence of the other phase, etc. This all gets into graduate level work, so I give it to undergraduates in a rather throw-away manner: "No big deal." You can look at this if you want to, hut don't try too hard on this one. Two Forgotten P.D.'s: The Metal-Metal P.D. and the Electron Overlap P.D. I do explain how the cells contain not onlv the n.d.'s of the interphases, hut also the contact p.d. hetween the'two metals in the wires outside the cells. I list the contact potentials and show that, approximately, they follow the p.d.'s in the cells themselves so that the content will take up more than half of the whole cell p.d. I tell them that there used to he a group of physicists who thought that the p'd' was the p.d. Lastly, I deal, in a hrief treatment, with the electron overlap p.d. Electrons do not realize where they are going and stumble over the cliff, so that one always has electrons just outside the surface. Consequently, the interphase is charged even in a vacuum. Thus, an interphase would have a double layer on it even in an extremely "pure" case of a metal in a high vacuum.
K
e
r
p
h
a
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e region
Figure 2. Thedistinction betweenthe amount of adsorbed material in the interphase region and the surface excess.
way of getting around the conceptual difficulties of the ahstractions. My first attention is to the electrochemical uotential. I don't
I then ask whether the chemical and electrical work can he determined separately, stating that this is so withpradients. hut not with-the quantities themselves: separation i n t i chemical and electrical terms is entirely conceptual. However, there is the criteria of equilibrium hetween the two phases and the quantity of electrochemical potential which defines it. After this comes a discussion of the thermodvnamics of the ~-~~ non-polarizahle interphase in equilibrium. At this point I am ready to launch into the rather unnleasant business of getting the fundamental equation. o n e gets the sum of all the work terms: PV, surface, electrical, and gravitational. ~
~
~
~
d V = TdS - P d V - ydA - M'AS ddg - zw,dn,
What I find difficult, though, is pointing out that each term represents the product of an intensive and extensive factor, and explaining how one can keep intensive factors like and p, constant while the extensive factors can he increased from the differential value to the ahsolute ones. The fact that one can differentiate this all again, hut not get back to the original equation from which one started, always seems to me to he expecting a little much in credulity from the students, If one can get this part across convincingly, then the rest is just pure algebra. One has to bring in the Gihhsian surface excess, and knowing Nernst, one can finally get to what I call the electrocapillary equation which is
The Accumulation of Material at the lnterphase To discuss the accumulation of material at the intemhase. tungsten, hut also there is an option for a more complex kind where "one knows the shore is approaching," and that one can see the concentration in the solution chaneine u " as the surface is approached. Finallv, I eet to the definition of the Gihhs surface excess (see ~ig.-2).lexplain that it really is adsorption, hut not the kind of adsorption one is used to thinking of in the gas phase. Eventually, I produce the definition for the surface excess. I talk about it in terms of the concentration near the interphase minus the hulk concentration showing a diagram where the difference is plotted against distance. Surface excess is the integral of the difference in concentration from zero at the electrode to infinity in the hulk. The Thermodynamics of Electrified Interphases I find thermodynamics of electrified interphases difficult to teach. The fact that I teach it to undergraduates at the junior or senior level does not mean that I have found some magic 266
Journal of Chemical Education
worry about the specificity of the reference electrodes to be used. I am at pains to stress that all the esoteric potentials were really mere auxiliary variables, and one is left firmly holding the electrometer readings. Before I summarize the electrocapillary thermodynamics I try to point out what it would all mean in practice. Here, I still retreat to mercury for good examples hecause there is much more of it. I draw graphs, such as in Figure 3, and point out to them the reasonableness of all one has found, e.g., when the potential is more negative, the positive charges will tend to increase, hut the negative charges will now remain constant and slightly negative because of repulsion in the diffuse layer. Finally, I summarize with a list of equations. But before I let it go I inject another dose of wonder. I don't let them leave the suhject of the thermodynamic reasoning in electrocapillary
(a)
Double layer
Tr~plelayer
Potential difference ( V in volts vs calomel electrode I potential.
~i~~~~ 3. Components of charge density as a functionof the applied V, in a 1 N NaCl solution.
Figure 4. [a) An electrical double layer and (b) an electrical triple layer. Compensating charges in the diffuselayer are not shown.
thermodvnamics without nointine out what a nowerful thine it is. ~ltl&ughGibbs invented a rather murkiversion in the 19th century, it was only in the 1950's that Parsons and Devanathan turned i t into something real and believable. It is remarkable that measurements of the surface tension a t a mercury drop give not only the excess of electric charge on the drop, but also the electric capacity of the angstromthick region. This allows one to find out the number of particles and distinguish between the various types. Is there anything more remarkable about this than getting the identity of materials in stars by looking a t photographs of the spectroanalysis of the light?
I do not find that the mathematical development of the simple Gouy model of the double laser causes any difficulty a t all and soon we reach the equation
The Structure of the Interphase There should be a preliminary to the topic of structure of the interphase. The easiest way to do this is to suggest that the students ask themselves what would happen if one had a simple picture with a Helmholtz layer (see Fig. 4). It is obvious from the figure that the p.d. will just be 4 4 6
This gives us a functional relationship between charge and potential in the Lippmann equation, and it becomes repeatedly obvious that one could eliminate charge from this and obtain the equation
This is the point a t which one can start bringing in the electrocanillarv . . curve. It is easv to show that the canillarv . . curve is not parabolic, nor is it symmetrical. Therefore, there must be somethine wronz with the simwle analvsis eiven, and it is then easy to ask what kind of other analyses one could give.
But it is easy to expand this equation and give rise to the simple approximation
and thereby see an exponential decay with potential, differing, of course, from the real situation, hut making sense. With the Stern model of the double layer, one sticks the diffuse and the compact layer together. I tend to go through this quickly, as it is something quite obvious and easy to understand. Next,'I begin to acquaint my students with facts about the two different kinds of adsorntion: one simnlv electrostatic, but the other rather sticky with chemical meaning and irreeularitv. For nerhaws half a lecture or so, we are con- ~ . t m ~ , dx tl s c ~ r p ~ i mand " w r m d nit11 ~nonm e tilink: ,>IJ.,UI 111 t l l e d c ~ r r r n ~ . i.,I . n~~h~~~- ~a d w r ~ ~ l i . , n ,~h
