A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 93
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Another arrangement involves placement of the uitramicroelectrode in a flow channel with the solution flowparallel to the electrode surface (36). An example is a microband electrode 12 fim thickand 0.2 cm long positioned across a channel 116 /лт high and 0.2 cm wide (36). In thisconfiguration, an effective mass-transfer coefficient of 0.5 cm/s can be attained with volume flow velocities near 3.7 cm3/s. Flow cells of this type are useful as detectors, for example, in liquid chromatography (see Section 11.6.4). They have found less use inelectrochemical studies, probably because of the technical problems involved in settingup systems with solution flow.9.8 ELECTROHYDRODYNAMICSAND RELATED PHENOMENAThere are many phenomena involving convection in electrochemical systems (6).
Whileit is beyond the scope of this monograph to treat these in any depth, we will give a briefoverview as an introduction to more detailed treatments. In general, electrohydrodynamics deals with fluid motion induced by electric fields. Electro osmosis is one importantexample.Our previous examples of convective flow dealt with fluid flow induced by a pressuregradient (Section 9.2.2). At steady state, in the absence of gravitational effects (naturalconvection), the fluid velocity, v, could be obtained from the equationTJSV2V - VP(9.8.1)Similarly, the force generated by the interaction of an electric field on excess charge density in a fluid can induce fluid flow, that is,*?sV2v = -РЕЪ(9.8.2)where % is the electric field (V/cm) and PE is the charge per unit volume.9.8.1 Electroosmotic FlowLet us consider the application of an electric field along a glass capillary tube filled withan electrolyte solution, as shown schematically in Figure 9.8.1.
The walls of the capillarytube will be charged at most pH values, because of protonation/deprotonation equilibriainvolving surface Si-OH groups. At a pH above about 3, the surface charge will be negative. This charge causes the formation of a diffuse layer of counter (positive) charge in solution, just as at a charged electrode surface (Chapter 13). When an electric field isapplied along the capillary axis, this excess charge (in the form of electrolyte cations) willmove toward the cathode and the net viscous drag on the solvent will induce convectionof the solution. In most cases, the radius of the tube will be large compared to the thickness of the diffuse layer, so that curvature can be neglected, and the flow considered astaking place in a planar channel.
Then, (9.8.2) can be written (6) in terms of the field, %x,along the axis of the capillary,4ST|=-PE«X = «O7T«Xдуду(9-8-3)9.8 Electrohydrodynamics and Related Phenomena363Fixed charges on glass wallе- ©Anode©©©—©©Fluid velocityprofile©©Cathode0Figure 9.8.1Representation ofelectroosmotic flow ofa fluid (e.g., water) in aglass capillary.
Only ionsnear the glass walls areshown. Note that thevelocity profile here isflatter (so-called "plugflow") than the parabolicprofile seen with anexternal pressuredrop along a tube.where the charge density has been obtained from the Poisson equation, (13.3.5),д2фA single integration of (9.8.3), with dv/ду = 0 and дф/ду = 0 far from the walls (yyields=еео{дф1ду)%х(9.8.4)> oo),(9.8.5)A second integration from a position near the wall, where v = 0 and ф = g, to the middleof the channel, where v = U and ф = 0, gives the Helmholtz-Smoluchowski equation:U = -(9.8.6)The parameter £ is called the zeta potential, which is the potential in a not-very-well-defined position in the diffuse layer called the shear plane (37), and U is the electroosmoticsolution velocity past a plane charged surface.
For £ = 0.1 V and %x = 100 V/cm in anaqueous solution, C/ — 0.1 cm/s.Electroosmosis is one of several electrokinetic effects that deal with phenomena associated with the relative motion of a charged solid and a solution. A related effect is thestreaming potential that arises between two electrodes placed as in Figure 9.8.1 when asolution streams down the tube (essentially the inverse of the electroosmotic effect). Another is electrophoresis, where charged particles in a solution move in an electric field.These effects have been studied for a long time (37, 38).
Electrophoresis is widely usedfor separations of proteins and DNA (gel electrophoresis) and many other substances(capillary electrophoresis).9.8.2 Other Electrohydrodynamic PhenomenaElectrokinetic effects are not usually of importance in the type of electrochemical experiments considered in this monograph, because the electric fields at the walls of the glasscells are small and significant convection is not induced. Although electrohydrodynamicflow can be induced by the interaction of an electric field with the diffuse layer near anelectrode surface, the fields in the diffuse layer near the electrode surface are not sufficiently large in most electrochemical experiments to produce measurable fluid flow. However experiments in which very large fields are intentionally applied can produce364Chapter 9.
Methods Involving Forced Convection—Hydrodynamic Methodsconvection (39, 40). Related experiments involve the effects of applied magnetic fields onelectrochemical processes (39, 41). Hydrodynamic instabilities can produce convectivepatterns in thin-layer cells with resistive solutions. For example, a form of convection inthin-layer cells (sometimes called the Felici instability) can produce hexagonal patternsduring ECL experiments (Section 18.1) in organic solvents with very low concentrationsof supporting electrolyte (42, 43).9.9 REFERENCES1. V. G. Levich, "Physicochemical Hydrodynamics," Prentice-Hall, Englewood Cliffs, NJ, 1962.22. К. В. Prater and A.
J. Bard, /. Electrochem.Soc, 117, 207 (1970).2. R. B. Bird, W. E. Stewart, and E. N. Lightfoot,"Transport Phenomena," Wiley, New York, 1960.23. W. J. Albery and M. Hitchman, op. cit., Chap.10.24. S. Bruckenstein and G. A. Feldman, /. Electroanal. Chem., 9, 395 (1965).25. S.
Bruckenstein and D. T. Napp, /. Am. Chem.Soc, 90, 6303 (1968).3. J. N. Agar, Disc. Faraday Soc, 1, 26 (1947).4. J. Newman, Electroanal. Chem., 6, 187 (1973).5. J. S. Newman, "Electrochemical Systems," 2nded., Prentice-Hall, Englewood Cliffs, NJ, 1991.6. R. F. Probstein, "Physicochemical Hydrodynamics—An Introduction," 2nd ed., Wiley, NewYork, 1994.7. A. C. Riddiford, Adv.
Electrochem.trochem. Engr., 4, 47 (1966).Elec-8. R. N. Adams, "Electrochemistry at Solid Electrodes," Marcel Dekker, New York, 1969, pp.67-114.26. S. Bruckenstein and B. Miller, Accts. Chem.Res., 10, 54 (1977).27. С A. Salzer, С M. Elliott, and S. M. Hendrickson, Anal. Chem., 71, 3677 (1999).28. S. Bruckenstein and B. Miller, /. Electrochem.Soc, 117, 1032 (1970).29. B. Miller and S. Bruckenstein, Anal.
Chem., 46,2026 (1974).9. С Deslouis and B. Tribollet, Adv. Electrochem.Sci. Engr.,2, 205 (1992).30. K. Tokuda, S. Bruckenstein, and B. Miller, /.Electrochem. Soc, 122, 1316 (1975).10. W. J. Albery, С. С. Jones, and A. R. Mount,Compr. Chem. Kinet., 29, 129 (1989).31. J. L. Valdes and B. Miller, /. Phys. Chem., 92,525 (1988).32. J. L. Valdes and B. Miller, /. Phys. Chem., 93,7275 (1989).33. T. E. Mallouk, V. Cammarata, J. A. Crayston,and M. S. Wrighton, /. Phys. Chem., 90, 2150(1986).11. V. Yu. Filinovskii and Yu. V. Pleskov, Compr.Treatise Electrochem., 9, 293 (1984).12. J.
S. Newman, /. Phys. Chem., 70, 1327 (1966).13. V. Yu. Filinovskii and Yu. V. Pleskov, Prog, inSurf. Membrane Sci., 10, 27 (1976).14. J. Newman, /. Electrochem. Soc, 113, 501,1235 (1966).15. W. J. Albery and M. L. Hitchman, "Ring-DiscElectrodes," Clarendon, Oxford, 1971, Chap. 4.16. С. М. Mohr and J. Newman, /. Electrochem.Soc, 122, 928 (1975).17. V. G. Levich, op. cit., p.
107.18. W. J. Albery and M. Hitchman, op. cit., Chap. 3.19. W. J. Albery and S. Bruckenstein, Trans. Faraday Soc, 62, 1920(1966).20. Yu. G. Siver, Russ. J. Phys. Chem., 33, 533(1959).21. S. Bruckenstein and S. Prager, Anal. Chem., 39,1161(1967).34. X. Gao and H. S. White, Anal. Chem., 67, 4057(1995).35. J. V. Macpherson, S. Marcar, and P. R. Unwin,Anal. Chem., 66, 2175 (1994).36. N. V.
Rees, R. A. W. Dryfe, J. A. Cooper, B. A.Coles, R. G. Compton, S. G. Davies, and T. D.McCarthy, /. Phys. Chem., 99, 7096 (1995).37. A. W. Adamson, "Physical Chemistry of Surfaces," Wiley-Interscience, New York, 1990, pp.213-226.38. D. A. Maclnnes, "The Principles of Electrochemistry," Dover, New York, 1961, Chap. 23.39. J.-P.
Chopart, A. Olivier, E. Merienne, J. Amblard, and O. Aaboubi, Electrochem. Solid StateLett., 1, 139 (1998).9.10 Problems36540. D. A. Saville, Annu. Rev. Fluid Mech., 29, 27(1997).42. H. Schaper and E. Schnedler, /. Phys. Chem.,86,4380(1982).41. J. Lee, S. R. Ragsdale, X. Gao, and H. S. White,/. Electroanal Chem., 422, 169 (1997).43. M.
Orlik, J. Rosenmund, K. Doblhofer, and G.Ertl, /. Phys. Chem., 102, 1397 (1998).9.10 PROBLEMS9.1 Consider an RDE with a disk radius, r\, of 0.20 cm, immersed in an aqueous solution of a substance262A (C* = 10~ M, DA = 5 X 10~ cm /s) and rotated at 100 rpm. A is reduced in a \e reaction, v «20.01 cm /s. Calculate: vr and vy at a distance 10~3 cm normal to the disk surface at the edge of thedisk; vr and vy at the electrode surface; f/0; // c ; mA; 8A; and the Levich constant.9.2 What dimensions (r 2 and r^) can a rotating ring electrode have to produce the same limiting currentas an RDE with r\ = 0.20 cm? (Note that many possible combinations of r 2 and r^ are suitable.)What is the area of the ring electrode?9.3 From the data in Figure 9.3.8, calculate the diffusion coefficient for O 2 in 0.1 M NaOH and kf forthe reduction of oxygen at 0.75 V.
Assume a totally irreversible initial electron transfer at the RDE.Take v = 0.01 cm2/s.9.4 Figure 9.10.1 contains current-potential curves at an RRDE for a solution of 5 mM CuCl2 in 0.5 MKC1 showing (1) /D vs. ED and (2) iR vs. ER. For the electrode used there, TV = 0.53.(a) Analyze these data to determine D, p, and any other possible information about the electrodereaction at the first reduction step [Cu(II) + e —» Cu(I)].2fo = 0)1000- 2000800-- 1600\600- 1200400-- 800200-- 400о^^У+0.2iii0-0.2-0.4EDorER(Vvs. Ag/AgCI)1-0.6Figure 9.10.1 Voltammograms at an RRDE.
Curve 1: /rj vs. E^ Curve 2: /R VS. ER (at/D = 0). Solution contained 5 mM CuCl 2 and 0.5 M KC1. ы = 201 s" 1 ; disk area = 0.0962 cm 2 ;v = 0.011 cm2/s.366Chapter 9. Methods Involving Forced Convection—Hydrodynamic Methods(b) If the ring voltammogram were obtained with ED = -0.10 V, what value of / R ? / c (at ER =-0.10 V) would be expected?(c) If ER is held at +0.4 V and ED = -0.10 V, what value of /R is expected?(d) What process occurs at the second wave? Account for this wave shape.(e) Assume the ring is held at +0.4 V. Sketch the expected plot of /R vs.
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