Double layer theories Grahame

Largely through the painstaking work of Grahame in the 1940s, electrocapillarity effectively established the first experimental basis for the now accepted double layer theory. The basic picture of the electrode/electrolyte interface was thus in place. 

D.C. Grahame, Diffuse double layer theory for electrolytes of unsymmetrical valence types, J. Chem. Phys. 21 (1953) 1054-1060. 

Refs. [i] Grahame DC (1947) Chem Rev 41 441 [ii] Delahay P (1965) Double layer and electrode kinetics. Wiley, New York [Hi] MohilnerDM (1966) The electrical double layer Part I. Elements of double-layer theory. In Bard AJ (ed) Electro analytical chemistry, vol. 1. Marcel Dekker, New York... 

It is evident now why the Helmholtz and Gouy-Chapman models were retained. While each alone fails completely when compared with experiment, a simple combination of the two yields good agreement. There is room for improvement and refinement of the theory, but we shall not deal with that here. The model of Stem brings theory and experiment close enough for us to believe that it does describe the real situation at the interface. Moreover, the work of Grahame shows that the diffuse-double-layer theory, used in the proper context (i.e., assuming that the two capacitors are effectively connected in series), yields consistent results and can be considered to be correct, within the limits of the approximations used to derive it. 

Fig. 5G Experimental test of the diffuse-double-layer theory. Concentration of NaF (a) O.OIM (b) O.IOM. Solid lines experimental values of C. Dashed lines C calculated from Eq. 19G. Reprinted with permission from Grahame, J. Am. Chem Soc. 76, 4819. Copyright 1954, the American Chemical Society.

See, e.g., D. C. Grahame, The electrical double layer and the theory of electrocapillarity, Chem. Rev. 41 441 (1947) C. W. Outhwaite, Modihed Poisson-Boltzmann equatioh in electric double layer theory based on the Bogoliubov-Born-Green-Yvon integral equations, J.C.S. Faraday 7/74 1214 (1978) and the references cited therein. 

R. O. James and G. A. Parks, Characterization of aqueous colloids by their electrical double-layer and intrinsic surface chemical properties. Surface and Colloid Science 12 119 (1982). Perhaps the most complete review of the triple layer model from the perspective of Gouy-Chapman-Stem-Graham e double layer theory. 

The early concept of an electrochemical supercapacitor (ES) was based on the electric double-layer existing at the interface between a conductor and its contacting electrolyte solution. The electric double-layer theory was first proposed by Hermann von Helmholtz and further developed by Gouy, Chapman, Grahame, and Stem. The electric double-layer theory is the foundation of electrochemistry from which fhe electrochemical processes occurring at an electrostatic interface... 

D. C. Grahame, /. Chem. Phys., 21, 1054 (1953). Diffuse Double Layer Theory for... 

The more detailed analysis by Grahame distinguishes two kinds of molecular condenser (see 4d, p. 134). The distance of closest approach of the cations to the interface is called by Grahame the outer Helmholtz plane We wish to introduce the name limiting Gouy plane thereby expressing the fact that up to this plane the double layer may be treated completely according to the diffuse double layer theory. 

Grahame therefore suggests that a test of double layer theories should in the first place be directed to a case, where specific anion-adsorption may be expected to be absent, that is practically to the case of fluorides. Owing to the strong electronegativity of the F ion this ion will not be dehydrated and thus not enter into the Stern plane . 

Grahame DC (1947) The electrical double layer and the theory of electro capillarity. Chem Rev 41 441-449... 

Undoubtedly, the mercury/aqueous solution interface, was in the past, the most intensively studied interface, which was reflected in a large number of original and review papers devoted to its description, for example. Ref. 1, and in the more recent work by Trasatti and Lust [2] on the potentials of zero charge. It is noteworthy that in view of numerous measurements of the double-layer capacitance at mercury brought in contact with NaF and Na2S04 solutions, the classical theory of Grahame [3] stiU holds [2]. According to Trasatti [4], the most reliable PZC value for Hg/H20 interface in the absence of specific adsorption equals to —0.433 0.001 V versus saturated calomel electrode, (SCE) residual uncertainty arises mainly from the unknown liquid junction potential at the electrolyte solution/SCE reference electrode boundary. 

D. C. Grahame, The Electrical Double Layer and the Theory of Electrocapillary, Chem. Revs. 41 441 (1947 . 

Grahame derived an equation between a and based on the Gouy-Chapman theory. We can deduce the equation easily from the so-called electroneutrality condition. This condition demands that the total charge, i.e. the surface charge plus the charge of the ions in the whole double layer, must be zero. The total charge in the double layer is /0°° pe dx and we get [59]... 

A convenient point of departure is to recall what Grahame [213] stated in his 1947 review of the electrical double layer and the theory of electrocapillarity ... 

Modem theory describing the structure of the EDL was developed by G. Gouy, D. Chapman. O. Stem, A. Frumkin, D. Graham and others, and is based on the analysis of the electrostatic interactions between ions in the double layer and comparison of these interactions with the intermolecular interactions and thermal motion of ions [11,17]. 

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