he study of electrochemistry is the study of sys- theoretical through to the more practical. The sequence is tems. Whether the system is divided into the as follows: double layer studies, electron transfer theory, T three domains of mass transport, electron trans- molecular dynamics modeling, spectroscopic investiga- fer, and homogeneous kinetics or visualized as a thermo- tions, electroanalysis, and modified electrodes. These top- dynamic expectation restricted by kinetics and dynamics, ics and the content of the following reviews are by no the conceptualization remains that of a physical electro- means an exhaustive representation of the diverse com- chemist. The domain of physical electrochemistry ponents and research activities that constitute physical extends from the traditional elegance of thermodynamics electrochemistry. Nonetheless, they do highlight the through new materials, and efficient power sources, to critical coupling between theory and experiment that sophisticated modeling and experimental protocols. In is the hallmark of sophisticated research in physical what follows, several areas of physical electrochemistry electrochemistry. ■ are highlighted, and are ordered from the substantially

Recent Developments in Double Layer Studies by W. Ronald Fawcett

avid Grahame established double troscopy and scanning tunneling techniques such as flame annealing, and D layer studies in the United States. At microscopy for atomic and molecular by the experimental perturbations of the time of his famous review1 in 1947, level investigations, and major theoreti- adsorption and change in electrode experimental work was limited to ther- cal advances. Reviews of some of these potential. These problems are overcome modynamic studies at liquid mercury. In topics are found in Ref. 3. when electrodes are carefully prepared in 1997, Grahame’s pioneering work was Single crystals are needed to study the the working solution, and thermody- honored by a symposium of The double layer at solid electrodes. From the namic data are collected chronoampero- Electrochemical Society2, where three pioneering work of Frumkin, both the metrically.4 Questions about the inter- distinct advances over the last 50 years work function and the point of zero pretation of thermodynamic data at solid became apparent. First, experimental charge of a single crystal metal depend electrodes raised at the Montréal sympo- techniques for studying double layer on the crystallographic orientation sium2 are now resolved.5 phenomena at well-characterized solid exposed to solution. Hamelin and High quality data are important in metal electrodes are well established. Clavilier carried out pioneering work in the interpretation of double layer Second, a battery of spectroscopic tech- this area and on the preparation of single effects in electrode kinetics.6 Double niques allows characterization of the crystal metal surfaces. Lipkowski4 later layer data should be obtained by the metal/solution interface at a molecular obtained reproducible thermodynamic same technique used to obtain the level. Third— and perhaps the one most data for adsorption at single crystal gold kinetic data.7 Potential sweep voltam- easily overlooked advance—is the avail- surfaces. metry for the reduction of 3+ ability of high speed, powerful comput- Double layer studies at solid metal [Co(NH3)6] at various gold single ers. Grahame’s only tool for analyzing electrodes are plagued by the frequency crystal (Au(111), Au(110), and his capacity data was an adding dispersion of interfacial capacity because Au(210)) electrodes leads to the con- machine, 1940 version. single crystal surfaces are not atomically clusion that the species transported Here, some of the major advances in smooth, but have microscopic imperfec- through the diffuse double layer is an this field are outlined: thermodynamic tions such as steps. Surface reconstruc- ion pair with a net charge of +2. These aspects of double layer studies, spec- tion is induced by surface preparation experiments confirm ideas traceable to

22 The Electrochemical Society Interface • Winter 2000 Frumkin that outer sphere electron ence frequency generation, and second Carlo (MC) and molecular dynamics transfer kinetics at electrodes depend harmonic generation.3 (MD) calculations. In early work, MC on the point of zero charge of the Scanning tunneling microscopy simulations of the diffuse layer were metal electrode. (STM) is an invaluable tool for surface carried out at the primitive level, where A variety of spectroscopic techniques analysis.10 A related technique used in ion distribution functions were deter- is now available to study the structure of interfacial electrochemistry is scanning mined assuming a dielectric continuum the electrical double layer.3 A particular- electrochemical microscopy (SECM).11 for the solvent. These calculations ly powerful technique is subtractively Kolb studied reconstruction of gold elec- showed that classical Gouy-Chapman normalized interfacial FTIR spectroscopy trodes using STM3 to map the spatial (GC) theory overestimates the potential (SNIFTIRS). Faguy and Marinkovic18 arrangement of adsorbed atoms. The drop across the diffuse layer for 1-1, 2- described a hemispherical window for work function depends strongly on the 1, and 2-2 electrolytes.17 greatly enhanced sensitivity. To study atomic structure of the surface. This, in Recently, in non-primitive level MD the adsorption of organic molecules on turn, affects the point of zero charge and simulations for aqueous 1-1 elec- single crystal gold electrodes, Lipkowski, therefore double layer composition. trolytes,13,14 solvent molecules are et al.8 used SNIFTIRS with polarized Significant advances have been made included as discrete components; water infrared radiation to track the orienta- recently in double layer theory. molecules are described using the rigid tion of pyridine at the electrode/solution Schmickler12 emphasized the role of the SPC/E model with partial charges on interface. SNIFTIRS also tracked the metal in improving the model of the each atom; and ions are charged reorientation of solvent molecules at the double layer. Introduction of pseudopo- Lennard-Jones spheres. The electrode is interface as the sign of the electrode tentials into the simple jellium model modeled as a conducting wall with no potential was reversed.9 Other impor- accounts for effects of surface crystallini- specific chemical interactions with tant spectroscopic techniques include X- ty on derived double layer properties. either ions or water molecules, but ray scattering experiments, sum-differ- Another area of research involves Monte image interactions important in deter- mining the electrostatic energy of indi- vidual ions are considered. Results were obtained for concentrated solutions of NaCl and CsF, where specific adsorption is absent for the smaller cation Na+ but is present for Cs+ at negative charge densities. Correspondingly for anions, Cl– is specifically adsorbed at positive charge densities but the smaller, more strongly hydrated F– anion is not (Fig. 1). MD calculations yield valuable infor- mation about double layer structure. However, the model must be improved by incorporation of specific chemical interactions between the metal elec- trode and solution components. In spite of the impressive advances made in double layer simulation, there is still a critical need for an analytical model of the diffuse layer. All analyses –2 FIG. 1. Snapshot of the simulation of 2.2 M NaCl at a surface charge density of 9.9 µC cm . The small of experimental data rely on the GC spheres are Na+ ions and the larger ones, Cl– ions. The electrode is on the left. Reprinted from J. Electroanal. Chem., 450, 327 (1998) with permission from Elsevier Science. model in spite of its well-known imper- fections. In the early 1980s, attempts were made to develop an improved dif- fuse layer model based on the integral equation approach.15 However, the equations could not be solved analyti- cally and reasonable results over a wide range of electrode charge densities are only available using the hypernetted chain approximation (HNC). Important double layer parameters such as the potential drop across the diffuse layer φd are only obtained after lengthy iterative computer calculations. More recently, Fawcett and Henderson16 used a generalized mean spherical approximation (GMSA). With the HNC equations as a guide, an ana- lytical expression for the potential drop φd was derived. For 1-1 electrolytes, φd ο φd FIG 2. Plot of f estimated at 1 M by the GMSA ( ) against the GC estimate f GC where f = F/RT. The l exact agreement with the earlier MC MC results are shown ( ). The upper solid line gives the GC results. Data from J. Phys. Chem., 104, 17 6837 (2000). Reproduced by permission of the American Chemical Society. results of Torrie and Valleau is found

The Electrochemical Society Interface • Winter 2000 23 (Fig. 2). Further advances of the GMSA References 10. S. N. Magonov and M.-H. Whangbo, model will include detailed examination in Surface Analysis with STM and of the effects of ionic size, derivation of 1. D. C. Grahame, Chem. Rev., 41, 441 AFM, VCH Publishers, Weinheim ion-electrode correlation functions with- (1947). (1996). in the diffuse layer, and extension to 2. C. Korzeniewski and B. E. Conway, 11. A. J. Bard, F.-R. F. Fan and M. V. in The Electrochemical Double more complex electrolytes including 2-1, Mirkin, Electroanal. Chem., 18, 244 Layer, C. Korzeniewski and B. E. 2-2, and 3-1 systems. Improved estimates (1994). Conway, Editors, PV 97-17, The φd of will enhance the interpretation of Electrochemical Society Proceedings 12. W. Schmickler, Chem. Rev., 96, 3177 double layer effects in electrode kinetics. Series, Pennington, NJ (1997). (1996). The above is a brief introduction to 3. A. Wieckowski, Interfacial 13. E. Spohr, J. Electroanal. Chem., 450, some new, exciting developments in Electrochemistry, Theory, Experiment 327 (1998). double layer research, but it is by no and Applications, Marcel Dekker, New 14. E. Spohr, Electrochim. Acta, 44, 1697 means exhaustive. For example, consid- York (1999). (1999). erable effort has been expended to 4. J. Lipkowski and L. Stolberg, in 15. W. Schmickler and D. J. Henderson, understand the properties of polarizable Adsorption of Molecules at Metal Prog. Sur. Sci., 22, 323 (1986). interfaces modified by self-assembled Electrodes, J. Lipkowski and P. N. 16. W. R. Fawcett and D. J. Henderson, J. monolayers (SAMS).19 Finally, it has Ross, Editors, Chap. 4, VCH, Phys. Chem. B, 104, 6837 (2000). been my experience that quite a few elec- Weinheim (1992). 17. G. M. Torrie and J. P. Valleau, J. 5. J. Lipkowski, W. Schmickler, D. M. trochemists find the double layer a Chem. Phys., 73, 5807 (1980). Kolb, and R. Parsons, J. Electroanal. source of frustration that they wish 18. P. W. Faguy and N. S. Marinkovic, Chem., 452, 193 (1998). would disappear. Unfortunately, double 6. W. R. Fawcett in Electrocatalysis, J. Anal. Chem., 67, 2791 (1995). layers are present at all boundaries Lipkowski and P. N. Ross, Editors, 19. H. O. Finklea, Electroanal. Chem., 19, between phases that contain free charges Wiley-VCH, New York (1998). 109 (1996). such as ions. Thus, the ultimate irony is 7. M. Hromadova and W. R. Fawcett, J. that brain activity, whether it involves Phys. Chem. A, 104, 4356 (2000). About the Author love or contempt for the double layer, is 8. M. Hoon-Khosla, W. R. Fawcett, a manifestation of double layer phenom- A. Chen, J. Lipkowski, and B. Ronald Fawcett is with the ena. Hopefully, the work being carried Pettinger, Electrochim. Acta, 45, department of chemistry at the out at the metal/solution interface will 611 (1999). University of California at Davis. also find application in biological 9. N. S. Marinkovic, M. Hecht, He can be reached via E-mail at: systems. ■ R. Andreu, and W. R. Fawcett, [email protected]. J. Phys. Chem., 99, 6760 (1995).

Hopping Across Interfaces: Heterogeneous Electron Transfer Dynamics by Robert J. Forster

rom molecular electronic devices to new insights with importance far outside by controlling the experimental F catalysis and corrosion, the dynamics the realm of electrochemistry. The future timescale, using stirred and flowing solu- of heterogeneous electron transfer will see increasingly detailed studies and tions, rotating the electrode or, more underpin key scientific and technologi- implementations in diverse areas includ- conveniently, using microelectrodes, i.e., cal advances. Microelectrodes and high ing biochemistry, sensors, molecular electrodes with critical dimension Շ 10 performance instrumentation enable the electronics, and advanced materials. µm. study of heterogeneous electron transfer Thermal Activation—In solution, the reactions under unusual conditions and The Elementary Steps energy of the donor Highest Occupied at short timescales. Localized, even Molecular Orbital (HOMO) or acceptor Figure 1 illustrates the elementary atomically resolved, measurements of Lowest Unoccupied Molecular Orbital steps in the overall electron transfer electron transfer dynamics allow con- (LUMO) vary continuously. Random process for a solution phase reactant: struction of precise maps of surface reac- thermal fluctuations and the ingress and transport, nuclear activation, electronic tivity. Adsorbed monolayers continue to egress of solvent dipoles from the solva- coupling of the redox center with the elec- tion shell cause donor and acceptor lev- revolutionize our understanding of the trode, and the instantaneous elementary effects of distance, molecular structure, els to fluctuate about some mean value, electron transfer event. In this ideal case, which may facilitate or hinder electroly- solvent reorganization, and microenvi- specific surface interactions between the ronment on electron transfer dynamics. sis at any particular instant. Electron redox centers and the electrode surface are transfer only occurs when the energy of Sophisticated theoretical models allow not considered. general conclusions to be drawn from electrode and molecular states are identi- Transport—Transient electrochemical cal, that is, resonance is achieved. specific chemical systems. The advan- measurements with a solution phase tages of electrochemistry over spec- Typically, only an extremely small frac- redox probe establish a competition tion of species adjacent to the electrode troscopy are increasingly recognized, between electron transfer at the surface to have sufficient energy to allow elec- particularly for providing direct informa- 1 and diffusion to and from the electrode. tron transfer to resonance because the tion and probing interactions with For successful measurement of electron free energy required to create these acti- tremendous sensitivity. Investigations transfer rates, the mass transport rate vated states is typically many times high- into heterogeneous electron transfer must exceed the electron transfer rate. er than the average thermal energy. have come of age, providing powerful Mass transport limitations are eliminated

24 The Electrochemical Society Interface • Winter 2000 Electronic Coupling—Once resonance constants will increase exponentially molecule. The free energies of both is achieved, donor and acceptor orbitals with electrical driving force agrees with outer sphere solvent reorganization, ∆ must couple electronically. The extent experiment only over a limited range of Gos, and inner-sphere vibrations, ∆ of electronic coupling between the overpotentials. Microelectrodes allow Gis, contribute to the total free energy ∆ redox centers and electrode typically the rate constant (k) to be measured over of activation, GTotal. The inner sphere increases exponentially with decreasing very wide ranges of η, where k initially free energy of activation represents the separation. depends exponentially on η but minimum energy required to change What about the timescale for elemen- becomes independent of η for more the internal structure of the redox cen- tary electron transfer? Because of the extreme values. Second, the Butler- ter to its nuclear transition state con- huge difference in the mass of electrons Volmer formulation fails to account for figuration. The outer sphere, or sol- and nuclei, electron transfer occurs the known distance dependence of het- vent, component arises because the instantaneously relative to nuclear erogeneous electron transfer rates. Third, redox center charge typically changes motion (i.e., the Franck-Condon princi- it cannot predict how changes in either significantly during electron transfer. ∆ ε ple applies). At the instant of electron redox center structure or solvent will Gos is dependent on the static ( s) and ε transfer, the redox center switches from affect k°. Marcus theory addresses these optical ( op) dielectric constants of the the oxidized to reduced form while issues directly and is widely accepted as solvent. Unlike the empirical Butler- maintaining its internal structure and the most powerful and complete descrip- Volmer model, the Marcus formulation solvation shell. Given instantaneous tion of electron transfer reactions. yields a heterogeneous electron trans- electron transfer, energy is not Marcus Theory—We concentrate first fer rate constant sensitive to both the exchanged with the surrounding medi- on the standard heterogenous electron structure of the redox center and the um. Therefore, as discussed above, the transfer rate constant, k°, when the elec- solvent. internal energy of the reactants and trochemical driving force is zero. The frequency factor, υ, describes products must be identical. Transition state theory focuses on the the success rate of transition state Butler-Volmer Model—The Butler- intersection of the free energy surfaces. crossings. Thus, υ is the product of the Volmer formulation is the oldest and The reaction rate depends on the prod- rate of motion along the reaction coor- υ least complicated model for heteroge- uct of the number of molecules with suf- dinate, n, and the probability of cross- neous electron transfer kinetics, but, as a ficient energy to reach the transition ing over from the reactant to product macroscopic model, it does not explicit- state at a particular instant in time and hypersurfaces once the transition state κ ly consider the individual steps the probability that they cross over the has been reached, el. described above. However, this empirical transition state. The number of mole- If electron transfer significantly dis- formulation does provide an experimen- cules at the transition state depends on torts the bond lengths and angles of ∆ ∆ ∆ υ tally accessible description of electrode the free energy of activation, G°. the molecule, i.e., Gis >> Gos, is kinetics. From a semi-log plot of the Marcus assumes that the dependence typically 1013 to 1014 s-1. If the molec- overpotential (η) versus current density, of ∆G° on the reaction coordinate is ular structure is largely unperturbed by α υ the symmetry factor ( ) and the stan- described as a simple parabola. That is, redox switching, then n is dictated by dard heterogeneous rate constant (k°) are each vibration involved in redox center the dynamics of solvent reorganization obtained. However, the Butler-Volmer activation behaves as a harmonic oscilla- and for typical electrochemical sol- formulation is deficient in a number of tor and the solvent energy depends qua- vents is 1011 to 1012 s-1. κ respects. First, the prediction that rate dratically on the charge density of the The magnitude of el varies from zero to unity, dependent on whether the electronic coupling is weak or strong. For strong electronic (adiabatic) coupling, there is significant flattening of the reaction hypersurface close to the transition state. The rate of crossing the barrier region is reduced but the probability of electron transfer actually occurring once the transition state has been achieved is close to unity. Adiabatic reaction rates are sensitive to the dynamics of solvent relaxation. Heterogeneous electron transfers are often assumed to be adiabatic because it simplifies the kinetic analysis, but this assumption is often not justified. In contrast, non-adiabatic reactions involve weak coupling and the transi- tion state appears as a sharp cusp. Potential Dependence of the Rate Constant—The sensitivity of heteroge- neous electron transfer rates to overpo- FIG. 1. Simplified elementary steps tential depends on the extent of elec- involved in heterogeneous electron transfer, diffusional charge trans- tronic coupling between the reactant 2 port, thermal activation, and elec- and the electrode. For strongly coup- tron tunneling between electrode led reactants, electron transfer occurs and the redox center. G and ● predominantly through states near the denote reduced and oxidized Fermi level of the electrode and the forms, respectively. adiabatic potential dependent rate con-

The Electrochemical Society Interface • Winter 2000 25 stant is given by the product of the fre- diverse range of species have been inves- current at short times ultimately limits υ 4 4 quency factor, n, and the density of tigated (anthracene , anthraquinone , the maximum rate constant that can be acceptor states in the molecule, Dox. benzoquinone5, ferrocene6, ferrcyanide7, measured. For diffusive species, the thick- 8 2+ 6 δ For non-adiabatic systems, electrons 9-fluorenone , and [Ru(bpy)3] ). The ness of the diffusion layer, , is defined as with energies below the Fermi level can magnitude of k° varies significantly. δ = (πDt)1/2, where t is polarization time be transferred and it is necessary to sum Large poly-aromatic hydrocarbons that and D is the diffusion coefficient. For D = over all electron energies, not just at the can be reduced with very little change in 1x10-5 cm2 s-1 and t = 10 ns, the diffusion Ε Fermi level, f. The effects of electronic bond lengths or angles exhibit very large layer thickness is Ӎ50 Å. For a 1 mM bulk coupling on k(Ε) only become apparent standard rate constants, e.g., k° for concentration of the electroactive at high driving forces. Perhaps the most anthracene9 is 3.5 cm s-1. Where molec- species, only 10,000 molecules would be significant consequence of the Marcus ular structure is significantly distorted by electrolyzed at a 1 µm radius microdisk. formalism is that, unlike Butler-Volmer the redox reaction, or where the reaction This yields an average current of 170 nA, theory, it predicts a curvature in plots of involves multiple steps, k°’s as small as which is too small to be detected with ln k vs. η in both the adiabatic and non- 10-9 cm s-1 are observed. That is, k° spans nanosecond time resolution. adiabatic cases. For extremely large ten orders of magnitude! Monolayers, self-assembled or driving forces, k no longer depends on To extend the upper limit of measur- spontaneously adsorbed on an electrode η and reaches a maximum when η Ӎ λ. able electron transfer rate constants, eliminate diffusion limitations and pre- This is the famous Marcus inverted measurements can be made at lower concentrate the redox probe. Under the region. temperatures, because even for diffusive conditions above, there are Electron Transfer Dynamics of Solution heterogeneous electron transfers with ≈1.7x10-20 mol of electroactive material Phase Reactants—Heterogeneous elec- negligible inner sphere reorganization within the diffusion layer; for a 1 µm tron transfer rate constants are conven- energies, activation barriers of 20-25 kJ disc this is an equivalent surface cover- iently measured using transient electro- mol-1 are expected. Considerably slower age of ≈5.4x10-13 mol cm-2. In contrast, chemical techniques with microelec- rates are observed by decreasing the tem- the surface coverage, Γ, observed for trodes being used in the majority of perature by a few tens of degrees. dense monolayers is typically > 100-fold studies. At short times, the diffusion Microelectrodes facilitate these measure- larger with coverages of the order of layer thickness is much smaller than the ments because solvents, such as alcohols 10-10 mol cm-2. This gives rise to much microelectrode radius and planar diffu- and nitriles, that remain liquid over a larger currents, easily detected at short sion dominates. Under these condi- wide temperature range, can be used timescales. tions, classical theories, e.g., that of without catastrophic ohmic effects. As exemplified by the work of Nicholson and Shain,3 can be used to Weaver and co-workers10 investigated Chidsey,11 Abrûna,12 and Finklea,13 elec- extract kinetic parameters from the scan ferrocene, ο-nitrotoluene and nitrometi- troactive adsorbed monolayers have rate (v) dependence of the separation sylene systems in acetonitrile, propioni- been developed that exhibit close to ideal between the anodic and cathodic peak trile, and butyronitrile at gold microdiscs reversible electrochemical behavior ∆Ε 4 -1 potentials ( p). Two complexities must using scan rates up to 10 V s between under widely varying experimental con- be considered. First, Faradaic and charg- 200 and 300 K. Experimental voltammo- ditions of timescale, temperature, sol- ing currents must be separated. In cyclic grams were simulated, taking activation vent, and electrolyte. These studies eluci- voltammetry, the charging current enthalpy, temperature-dependent diffu- dated the effects of electron transfer dis- increases proportionally to v, whereas sion coefficients, and double layer capac- tance, tunneling medium, molecular the Faradaic current for a diffusive itance into account. For ferrocene, k° structure, electric fields, and ion pairing species is proportional v1/2. Therefore, ranged from 0.083 cm s-1 at 198 K to on heterogeneous electron transfer the ratio of Faradaic to charging current ~5.5 cm s-1 at 298 K, and yields an acti- dynamics. Moreover, they have provided decreases with increasing scan rate. One vation enthalpy of 20 kJ mol-1. the detailed experimental data necessary strategy is to measure the charging cur- Adsorbed Monolayers—For solution to test contemporary models such as the rent in blank electrolyte and to subtract phase reactants, the diffusion controlled Marcus theory. First, as shown in Fig. 2, a it from the current observed in the pres- ence of the analyte. Second, ohmic drop can distort the wave shape when Table I. Rate Constants for Heterogeneous Electron Transfer heterogeneous electron transfer rates are Determined by Transient Methods. determined from the scan rate depen- ∆Ε dence of P. Ohmic effects not only ∆Ε -1 contribute significantly to P indepen- Analyte ...... Electrode ...... k° / cm s dent of heterogeneous electron transfer, but also vary with scan rate. Several Anthracene ...... Au, 6.5 µm ...... 3.46±0.55 strategies are used to decrease ohmic Anthraquinone ...... Pt cylinder, r = 25.4 µm, ....1.78±0.35 effects. Faradaic information can be l < 0.25 cm extracted either by means of convolu- tion of the voltammograms with the Benzoquinone ...... Au, 6.5 µm ...... 0.39±0.1 diffusion operator (πt)-1/2, or by simula- Ferrocene ...... Au, 5 µm...... 3.1±1.1 tion of the experimental voltammo- Ferrocyanide ...... C cylinder, r = 15 µm, ...... 0.0114±0.0022 gram using a model that incorporates l = 500 µm ohmic and capacitive factors. Ohmic 9-Fluorenone ...... Pt, 6 µm ...... 3 drops can be largely compensated using 2+ positive feedback circuitry during mea- [Ru(bpy)3] ...... Au, 5 µm...... 2.5 surements. As shown in Table I, the heterogen- * Dimension given is the radius of a microdisc electrode unless otherwise stated. eous electron transfer dynamics of a

26 The Electrochemical Society Interface • Winter 2000 plot of ln k° vs. the number of repeating states.14 Studies on metal centered oxi- adsorbed and Langmuir monolayers, units in the bridging ligand (typically the dation and ligand based reduction respectively. Given that the reorganiza- number of methylene units in an alkane processes reveal that matching the ener- tion energies are indistinguishable for chain) is linear. This result indicates that gy of states within the redox center and the two systems, this result suggests tunneling rates decay exponentially with the bridge can significantly increase that molecular orientation can signifi- distance. The slope of this plot yields the k°.15 Few systems allow orientational cantly affect k. tunneling parameter, β, which for alkane- effects on heterogeneous electron trans- thiol systems is 1.0-1.1 Å-1. Second, as fer to be probed, but we compared the Conclusions and Future Directions illustrated in Fig. 3, ln k vs. η is not linear heterogeneous electron transfer rates for for all driving forces. Unlike the predic- spontaneously adsorbed and Langmuir Novel Experimental Approaches— tions of the Butler-Volmer model when monolayers of [Os(dpp)2 Qbpy](ClO4)2 Models that describe heterogeneous η ≈ λ, curvature is observed and k eventu- where dpp is 4,7-diphenyl-1,10-phenan- electron transfer across the ally becomes independent of the driving throline and Qbpy is 2,2’:4’,4”:4”4”- electrode/solution and electrode/film force. This behavior is consistant with that quarterpyridyl.16 In spontaneously interfaces are now well developed and predicted by the Marcus theory. Third, by adsorbed monolayers, Qbpy acts as a cast in forms that are amenable to using temperature dependent measure- bridge between the redox center and experimental investigation. The most ments of k and Ε°′, the activation microelectrode surface. In horizontal promising results are expected from enthalpy and reaction entropy are touch experiments on Langmuir films, applying experimental innovations, obtained. These values are used to calcu- Qbpy was in the aqueous sub-phase and e.g., nanometer dimensioned electrodes late the free energy of activation and, pro- electrical contact occurred through the for ultrafast measurements and scan- vided k° is known, the pre-exponential diphenyl-phenanthroline ligands. ning probe microscopies for monitor- factor can be determined. Heterogeneous electron transfer rate ing localized, even single electron Our group has assembled similar constants measured at an overpotential events. The twin strengths of powerful monolayers and probed the dynamics of of 50 mV were 1.2±0.3x106 and new experimental approaches and both ground and electronically excited 1.7±0.2x105 s-1 for the spontaneously accessible theory enable complex reac- tions to be meaningfully probed. Despite the success of the Marcus and related theories, ambiguities remain in determining some parameters even for FIG. 2. Semi-log plots of the standard heterogeneous mechanistically simple reactions. For electron transfer rate con- example, the adiabaticity of the elec- stant, k°, versus the number tron transfer primarily affects the pre- of methylene units in the exponential term in the rate expres- alkane-thiol bridge. The sion. To determine the pre-exponential symbols ●, ▲, ❑, and ✧ term, the exponentially dependent free denote HS(CH2)n 2+ energy of activation must be accurately CONHCH2py-Ru(NH3)5 , HS(CH2)nNHCO-Ferrocene, known. Moreover, the pre-exponential κ υ HS(CH2)nOOC-Ferrocene factor includes both el and n, which and Cytochrome C electrosta- are often difficult to deconvolve. tically adsorbed on However, electrochemists are becoming HS(CH2)nCOOH. (Reprinted, (abstracted/excerpted) with increasingly aware that voltammetric permission of Science, 251, experiments alone cannot provide 919 (1991). American accurate measurements of all the para- Association for the meters necessary for a complete theo- Advancement of Science). retical description. Quantum Chemical Models—The next decade will see a shift away from phe- nomenological models toward micro- scopic (atomic level) descriptions of electrode kinetics. Novel approaches will benefit from interplay between quantum chemistry and modern theor- ies of charge transfer. It is now almost 25 years since the cluster model of the FIG. 3. Tafel plots of ln(k) vs. metal surface was first used to describe overpotential for a mixed self- the structure and composition of the assembled monolayer contain- electrical double layer. Now quantum ing HS(CH2)16OOC-Ferrocene chemical calculations of model super- and HS(CH2)15CH3 in 1.0 M molecules such as metal cluster plus HClO4 at three temperatures. The symbols, ▼, ❍, and ❑ reactants promise to provide truly ele- denote data obtained at 1, 25 mentary insights into heterogeneous and 47°C. The solid lines are electron transfer. In particular, ab-initio the predictions of the Marcus calculations, using the computationally theory for a standard heteroge- less demanding density functional the- neous electron transfer rate ory coupled with the Kohn-Stam for- -1 constant of 1.25 s at 25°C malism, would appear to be an espe- and a reorganization energy of 0.85 eV (54.8 kJ mol-1). cially attractive approach.

The Electrochemical Society Interface • Winter 2000 27 Analytical Applications—When of k on distance and molecular structure 8. D. O. Wipf and M. R. Wightman, attempting to determine the concentra- allows monolayers with excellent block- Anal. Chem., 60, 2460 (1988). tion of a particular redox active species ing properties to be developed. 9. C. P. Andrieux, D. Garreau, P. in a complex mixture, typically the Understanding electrostatically driven Hapiot, J. Pinson, and J. M. Savéant, response of the target analyte is separat- interfacial binding will lead to advanced J. Electroanal. Chem., 243, 321 ed from redox active interferences on chemical sensors tailored for interfacial (1988). the basis of different formal potentials. reactivity and especially heterogeneous 10. L. K. Safford and M. J. Weaver, J. There have been relatively few reports electron transfer. ■ Electroanal. Chem., 331, 857 (1992). on using electrochemical reactivity, i.e., 11. C. E. D. Chidsey, Science, 251, 919 electrode kinetics, to differentiate the References (1991). concentration of a target analyte based 1. M. I. Montenegro, Applications of 12. D. Acevedo and H. D. Abruña, J. on the difference between its time con- Microelectrodes in Kinetics, Research Phys. Chem., 95, 9590 (1991). stants and those of the interferents. in Chemical Kinetics, Vol. 2, R. G. 13. H. O. Finklea and D. D. Hanshew, J. Because the width of the electrochemi- Compton and G. Hancock, Editors, Am. Chem. Soc., 114, 3173 (1992). cal response for any species is a sizeable p. 1 (1994). 14. R. J. Forster, and T. E. Keyes, J. Phys. fraction of the potential window, the 2. C. J. Miller, Physical Electrochemistry: Chem. B, 102, 10004 (1998). potential axis alone provides very limit- Principles, Methods, and Applications, 15. R. J. Forster, Inorg. Chem., 35, 3394 ed resolution. Coupling of the time and I. Rubinstein, Editor, Dekker, New (1996). potential axes makes discrimination of York (1995). 16. R. J. Forster, T. E. Keyes, and M. the analyte considerably more likely. 3. R. S. Nicholson and I. Shain, Anal. Majda, J. Phys. Chem. B, 104, 4425 The time-resolved approach will benefit Chem., 36, 706 (1964). (2000). significantly from the dramatic expan- 4. J. O. Howell and R. M. Wightman, sion in time window provided by high Anal. Chem., 56, 524 (1984). speed instrumentation and microelec- 5. M. I. Montenegro and D. Pletcher, J. About the Author trodes. Electroanal. Chem., 200, 371 (1986). Robert Forster is at the National A very positive outcome from the 6. D. O. Wipf, E. W. Kristensen, M. R. Centre for Sensor Research at the more widespread understanding of the Deakin, and R. M. Wightman, Anal. Dublin City University in Ireland. factors that influence heterogeneous Chem., 60, 306 (1988). He can be reached at: robert.forster electron transfer is the rational design 7. A. Neudeck and J. Dittrich, J. @dcu.ie. of modified surfaces for analytical appli- Electroanal. Chem., 313, 37 (1991). cations. Understanding the dependence

28 The Electrochemical Society Interface • Winter 2000 Atomistic Modeling and Simulation by Michael R. Philpott

ersonal computers (PCs) are cheap, subject to the boundary conditions on been developed. In these potentials, the P and Moore’s law increases are still the entire system. Information about stretching of covalently bonded atomic available in CPU speed (currently 1.3 the trajectories is stored. The interaction pairs is described by a pair of exponen- GHz) and information storage density potentials of the atoms must be known tials as in the Morse potential for (about 40 Gb in-2). In short, the com- (usually an analytical formula) and a diatomic molecules. In the limit of large bination of price, hardware advance, thermostat must be specified. For sys- bond extensions, the potential describes and user-friendly software has put tems in equilibrium, the MC method is homolytic bond fission. By these means advanced modeling capabilities firmly useful because only the potential energy some of the key aspects of chemical in the office and laboratory. Figure 1 function of the system is used to calcu- bond breaking and formation are depicts the main regimes of modeling. late time independent properties like included. Each provides an important level of molecular distribution functions. In Car-Parrinello MD—In condensed insight and ideas for new experiments. practice, MC is often combined with phases, forces are intrinsically many The atomic scale is concerned with MD in a hybrid scheme to improve the bodied because they are dependent on electronic structure and atomic efficiency of the random moves of the the local environment around the motion. In continuum modeling, the MC part. Simulations of electrochemical atoms. The use of empirical potentials is atomic details are averaged to simpler phenomena have greatly increased our avoided in this important molecular quantities at length and times scales appreciation for how solvent and ions dynamics method that combines densi- that are larger than those of molecules. are distributed and how their motion is ty functional theory (DFT) with MD.4 The third regime uses kinetics to follow correlated near flat electrodes. The main The effective potentials determining the changes in composition due to reac- drawbacks are the short simulation forces acting on individual atomic tions, temperature, and pressure. Here, times and the low quality of the inter- nuclei are found simultaneously using the main interest is on atomic scale atomic potentials. For water, there are DFT for the electron density and classi- modeling with a focus on molecular about a dozen empirical models for sim- cal mechanics for the atomic nuclei. dynamics (MD). ulating the properties of the bulk liquid Applications to all types of materials at room temperature and pressure. and their combinations have been Atomic Scale Modeling These models are used in studies that reported. In electrochemistry, these range from clathrates to electric double include bulk water, ionic solutions, The main tools for atomic scale layers. Attempts to improve on empiri- water on oxide surfaces, and water modeling are electronic structure and cal potentials by fitting to the results of between metal electrodes. Because the MD codes. An impressive array of soft- electric fields obtained from ab initio electronic part of the simulation is very ware for doing quantum electronic quantum chemistry calculations have computationally intensive, the calcula- structure and geometry optimizations not so far resulted in any superior mod- tions have been performed on systems is available with friendly graphic user els for condensed matter properties. of small size and for short times. interfaces. You do not have to know MD with Bond Order Potentials—Bond Another strategy is to extend the any Fortran, C++, or even own a slide order potentials were introduced to time scale by placing some constraints rule. A good account of MD and Monte describe solids like silicon, germanium, on the nuclear or electronic motion to Carlo (MC) methods in chemical mod- and diamond, which have directed reduce the computational burden. eling and simulation can be found in a covalent bonds.2 Potentials specialized Recently, our group in Singapore devel- recent book.1 A lot of research is devot- to hydrocarbon materials including oped the notion of “chemistry in a box ed to increasing system size (using par- two, three, and four atom terms3 have MD,” a modification of the Car- allel computers) and to increasing the simulation time scale. Voter at Los Alamos National Laboratory has described several schemes that give Three Modeling Regimes orders of magnitude increase in time span. In electrochemistry, the most important interactions are sums of Atomic scale modeling electrostatic interactions. In three Electrons, atoms, molecules, ions & polymers: dimensions, these sums over q1q2/r12 metals, surface & interfaces, liquids, self & are shape dependent. The best meth- supra-molecular assemblies, soft matter, crack ods to compute these sums are the propagation, grain boundaries reaction field, Ewald method, plane- wise slab summation, fast multipole c c FIG. 1. Atomic scale, method, and the particle mesh continuum scale, and Continuum modeling Mechanical properties, Kinetics modeling method. The last two provide the kinetic modeling—the Diffusion, migration, reaction field and current fastest algorithms. three regimes of mod- rates & yields, concentration distribution, stream lines, Newtonian MD and MC—In a MD eling used in electro- gradients

concentration profiles, c simulation, Newton’s equations of chemical materials science systems. micro-electronics & motion for the degrees of freedom of packaging, composites the atoms (or molecules) are solved

30 The Electrochemical Society Interface • Winter 2000 Parrinello MD scheme useful when all uncharged. Figure 2 also shows, on the charged cations and details of water the electrons involved in the chemistry left side graph, a plot of the radial distri- geometric distortions examined. are localized, and when all the mole- bution function g(r) of water around the Exchange of molecules in solvation cules of the surroundings not involved ion and the solvation number n(r) with shells is experimentally measurable in the chemistry can be treated by clas- a plateau at n = 4. using NMR. The coupling of the hydra- sical MD using empirical potentials.5 tion shell to the local solvent H bond Though this is a departure from the spir- Some Fundamental network, and then to long-range corre- it of the Car-Parrinello MD, it has a Electrochemical Mechanisms lations that determine the dielectric pragmatic twist in that simulation times constant, is not understood. The ana- of tens of picoseconds are accessible on Fundamental mechanisms are those lytical work of Henderson and cowork- a single processor workstation. Figure 2 with a large conceptual impact. A prior- ers on solutions using the Ornstein- shows a metal cluster immersed in con- itized list for electrochemistry could be Zernike equation has been of impor- centrated approximately 2M salt solu- the following: water > water and ions > tance in establishing a platform of tion. The snapshot of cluster and mole- electrons > protons > ions at interfaces understanding. cules illustrates two features of the >… . In water and its solutions, the Theory of Electric Double Layers and method—a small box frame around the hydrogen bond is poorly understood, Structure of the Inner Layer—The Gouy- cluster connected with the electronic because few experiments are able to Chapman continuum theory of electric calculation and the larger box frame for probe the electron distribution.6 double layer screening of charged elec- the MD calculation. The Car-Parrinello Electron transfer processes pervade trodes has been the basis for interpret- method is applied to the metal cluster much of electrochemistry and the ing many of the seminal experimental 7 only and the species in solution are description by Marcus theory is very findings in this field. Extensions to treated by classical mechanics with ana- widely applied in interpreting experi- include the molecular structure of the 8 lytical potentials. Interactions between ments. In MD simulations, Heinzinger inner layer have provided a compre- the cluster and solution species are pro- and coworkers have performed pioneer- hensive working model of the solution portional to cluster electron density as a ing work on numerous aspects of elec- side. The complex problem of integrat- factor in the otherwise analytical poten- trolyte solutions. ing into one theory the metal elec- tial. The middle part of Fig. 2 shows an Debye-Hückel Theory of Ion Solvation trons, adsorbed ions, and water adatom slightly displaced from the clus- and Electric Charge Screening—Theory remains a very difficult task. There ter along with all water molecules in its and computer simulation reveal details have been very beautiful experimental first solvation shell. All other solution of the inner structure of the first solva- studies of adsorption of ions and neu- species are omitted for visual clarity. The tion shell. For example, the distortion of trals on metal and semiconductor elec- key physics is the stabilization of the the solvent geometry and electronic trode surfaces. In situ STM and AFM metal adatom as a monovalent cation polarization of highly charged ions like have revolutionized the experimental by the presence of the polar solvent. If Al3+ ions. The Car-Parrinello MD field. There has been some progress the atom were to be removed from the method has been applied to several using classical MD to study the transi- cluster in vacuum it would be tion from bulk to inner Helmholtz layer. An intact double layer compris- ing Stern layer and outer layer has been simulated in a system large enough Dissolution of Metal in Aqueous Electrolyte that the bulk electrolyte region was clearly identifiable.9 More calculations are needed to study the expansion of the double layer at lower salt levels. Noble Metal Deposition and Dissolution—The continuing work of 10 d = 4.0 a.u. Kolb on metal underpotential deposi- tion and deposition from probes exem- plifies some of the fine experimental n(r) work in progress. A recent book sum- marizes the traditional viewpoint quite 5 well.10 Movement of adions from kink sites onto terraces and then into solu- g(r) tion is a computational grand chal- lenge by almost any measure. The sol- 0 vent stabilizes the cation. However, the composition of the supporting elec- 0 5 10 15 trolyte influences the reaction path as r, a.u. shown in the STM experiments of cop- per metal dissolution in halide and sul- phate media.11 These represent big FIG. 2. Chemistry in a box molecular dynamics simulation. Electrochemical example showing some aspects of challenges for theory and computer a small metal cluster surrounded by aqueous electrolyte. (The figures are described moving clockwise from the simulation. right hand side.) First is a snapshot of an entire system consisting of the electronic box containing a 35 atom metal cluster and the molecular dynamics box containing aqueous electrolyte surrounding the cluster in the Electron and Proton Transfer—Due to electronic box. Second is a graphic of a larger 91-atom cluster with an adion surrounded by four stabilizing the exquisite control that experimen- water molecules belonging to the first hydration shell. All other water molecules and ions are omitted for clar- talists have over selective electron ity. Third is a plot of the radial distribution function g(r) for water around the adion depicted in second (mid- transfer, these reactions have been dle) picture along with the water occupation number n(r) as a function of distance from the adion. extensively studied. Marcus theory pro-

The Electrochemical Society Interface • Winter 2000 31 vided a versatile theory at an early stage and out of the electrodes affects the that has guided generations of experi- kinetics and ability of the battery system mentalists. Modern theoretical work to deliver current. This is a fertile field involves exploring and expanding the for theorists willing to work with exper- early framework by explicitly including imental materials scientists. ■ effects and features previously inaccessi- ble without computers (metal band Summary structure, molecular electronic struc- ture). Next in importance is understand- Judicious use of simulation has pro- ing the transfer of protons in solution, vided important insight into numerous ice, and biomolecules. In water, the fundamentally important electrochemi- structure and dynamics of the hydrated cal mechanisms. However, it is always proton continue to be hotly debated. important to remember that the results + 2+ The structure of H3O and H5O has of all our simulations have to be more been studied by Car-Parrinello MD as than just pretty, expensive pictures. well as by purely quantum chemical What are needed are clever theories and cluster techniques. The reaction path models to guide the computer simula- and transition state for transfer is still tions. under discussion. STM and AFM Probes—Basic under- References standing of how STM works and how the images are interpreted quantitative- 1. D. Frenkel and B. Smit, in ly is a quantum scattering problem. The Understanding Molecular Simulation, sensing fields involve spatially delocal- From Algorithms to Applications, ized states with electric current entering Academic Press, San Diego (1996). or leaving a tip that ends in a small col- 2. J. Tersoff, Phys. Rev. B, 37, 6991 lection of atoms. However, because the (1988). experimentation is now so well 3. D. Brenner, Phys. Rev. B, 42, 9458 advanced, it would be unusual for theo- (1990). ry to overturn the way the instrument is 4. R. Car and M. Parrinello, Phys. Rev. used. Still the field is a long way from Lett., 55, 2471 (1985). enjoying the sort of design and develop- 5. S. V. Izvekov, M. R. Philpott, and R. ment that exists for TEM. AFM is con- I. Eglitis, J. Electrochemical Soc., ceptually simpler since the sensing 147, 2273 (2000). fields and interactions are short range. 6. E. D. Issacs et al., Phys. Rev. Lett., Here the obstacles are lack of accurate 82, 600 (1999). interatomic potentials. 7. D. C. Grahame, Chem. Rev., 41, Batteries—In the last few years, there 441 (1947). has been progress in the calculation of 8. J. O’M. Bockris, M. A. V. the electronic structure of Li ion battery Devanathan, and K. Müller, Proc. materials and related rocking chair sys- Roy. Soc. (Lon.), A274, 55 (1963). tems. Modern DFT codes that calculate 9. M. R. Philpott and J. N. Glosli, J. the metal band structure have been used Electrochem.Soc., 142, L25 (1995). to predict the battery voltage. It is possi- 10. E. Budevski, G. Staikov, and W. J. ble to make a survey of hypothetical Lorenz, in Electrochemical Phase new electrode materials without going Formation and Growth, VCH, in the laboratory. This may speed Publishers, New York (1996). research for better materials.12,13 There 11. O. M. Magnussen and R. J. Behm, has also been exploratory work on Mat. Res. Soc. Bulletin, July, p. 16 mechanisms of phase transitions as Li (1999). ions are depleted or stored. Newman 12. G. Ceder, Y-M. Chiang, D. R. (UCB) has described kinetic modeling of Sadoway, M. K. Aydinol, Y-I. Jang, the whole battery system. The intercala- and B. Huang, Nature, 392, 694 tion of metal and other species into (1998). graphite has been studied using quan- 13. C. Wolverton and A. Zunger, Phys. tum chemistry cluster models. Issues Rev. Lett., 81, 606 (1998). concerning the electronic structure and possible phase transitions in the cath- ode materials like LixCoO4 provide unprecedented insights and reinforce About the Author the conceptual foundation for materials Michael R. Philpott is head of development. Another area where theo- the department of materials science ry has provided a deep level of under- at the National University of standing is in the transport of Li ions Singapore. His e-mail address is: through liquid polymer electrolytes [email protected]. (MPI polymer). Finally, it is worth men- tioning that the motion of Li ions in

32 The Electrochemical Society Interface • Winter 2000 Electrochemical Surface Spectroscopy by Michael J. Weaver and Sally A. Wasileski

ne of the most notable broad-based mation for electrode-solution interfaces obtained for chemisorbate species in O developments in surface electro- in the absence of surface enhancement many cases. Such EC-IRAS measure- chemical research in recent years by using potential-modulation strate- ments have been used extensively to involves the capability of probing mol- gies, especially in conjunction with elec- examine reactive as well as stable elec- ecular-level properties of electrode-solu- trochemical thin-layer cells so to mini- trochemical systems. tion interfaces by means of spectro- mize the solution optical path length.4,5 Another seminal development scopic techniques. The original purview The interfacial portion of the optical encouraging the application of EC-IRAS of surface spectroscopy lay almost absorbance is sensitive to electrode and other in situ optical spectroscopies exclusively in ultrahigh vacuum potential via double-layer field and other involved the recognition by Clavilier (UHV)-based systems. This is due to the effects, such that it can often be extract- (1980) that ordered, monocrystalline lack of bulk-phase interferences, the ed from the dominant bulk-phase inter- metal electrodes could readily be pre- applicability of electron as well as pho- ferences by potential modulation with a pared by annealing in an oxy-gas flame. ton spectral probes, as well as the lock-in amplifier.4,5 While this strategy While originally controversial, this and unique degree of surface cleanliness, was initially applied to the UV/visible related tactics have become a standard compositional control, and structural spectral region,4 it was subsequently re- means of preparing Pt-group and order attainable in UHV environments. cognized that the infrared spectral coinage-metal surfaces for electrochemi- Triggered by the development of UHV region was also accessible, despite the cal use. Furthermore, the emergence of technology, the rapid advances made in strong light absorption by aqueous sol- in situ scanning tunneling microscopy surface science, starting 30 to 40 years vent.5 Measurements with a grating (STM) a decade later enabled the spatial ago, encouraged the spectroscopic spectrometer, dubbed “electrochemical- structure of such ordered electrodes to be examination of electrode interfaces by ly modulated infrared spectroscopy” scrutinized down to the atomic level. controlled surface transfer between (EMIRS), yielded the first vibrational Taken together, the applicability of electrochemical and UHV environ- spectra for chemisorbates at transition- microscopic-level techniques to ordered ments. Such ex situ characterization metal electrodes. The rapid commercial- monocrystalline metal electrodes has strategies provided much of the original ization of Fourier transform infrared established multifaceted links between spectroscopic insight into chemisorbate (FTIR) spectrometers in the early 1980s, related electrochemical and UHV-based structure at electrodes, using tech- together with their adoption for infrared interfaces, thereby rendering electro- niques such as X-ray photoelectron reflection-absorption spectroscopy chemical surface science as a coherent spectroscopy (XPS) and Auger electron (IRAS) at metal-UHV interfaces, led to (and sophisticated) research discipline. spectroscopy (AES) for atomic structure, the widespread use of FTIR at electro- Electrochemical interfaces have also and electron energy-loss spectroscopy chemical interfaces. While potential-dif- been investigated by other in situ spec- (EELS) for vibrational characterization.1 ference spectral strategies are required to troscopic methods in recent years. Non- Starting in the 1970s, several cou- eliminate bulk-phase solution interfer- linear spectroscopies, especially visible-IR pled developments facilitated a detailed ences, these are more flexible than the sum frequency generation (SFG) and sec- microscopic-level characterization of in modulation tactics required in EMIRS, ond-harmonic generation (SHG), in prin- situ electrochemical interfaces by enabling absolute infrared spectra to be ciple share the advantage of SERS of means of optical spectroscopy. The first strategy to exert a major impact was based on the discovery and realization of surface-enhanced Raman scattering (SERS) in the mid-1970s.2 While origi- nally limited to coinage-metal surfaces (largely silver electrodes), SERS provid- ed the first potential-dependent vibra- tional spectra for adsorbates at metal- solution interfaces. Although also requiring some degree of nanoscale sur- face roughness for the SERS effect, as outlined below, recent strategies expand the technique to encompass FIG. 1. Stretching other interfacial materials. These devel- frequencies for opments, together with the dramatical- saturated CO and NO adlayers ly improved sensitivity and flexibility on Pt-group low- of Raman instrumentation, now endow index surfaces in SERS with much promise for the vibra- aqueous electro- tional characterization of diverse inter- chemical compared faces.3 with UHV environ- Another important development ments at equivalent surface potentials. initiated during the 1970s was the Data are taken extraction of optical absorbance infor- from Ref. 10.

34 The Electrochemical Society Interface • Winter 2000 Ε being based on phenomena occurring chemisorbate properties of electrochem- by matching the (adjustable) m and Φ only at surfaces, therefore being intrinsi- ical and vacuum-based interfaces. m values by taking the absolute poten- cally surface-sensitive methods.6 The for- A basic property of chemisorbates in tial of the standard hydrogen electrode mer provides molecular vibrational infor- electrochemical systems is that their to be 4.8 (± 0.1) V, in harmony with mation, akin to IRAS and SERS. While vibrational frequencies depend on the independent estimates of this 10 Φ hampered by sensitivity and bandwidth applied electrode potential. This effect, quantity. Note that the m values constraints, even NMR is now providing commonly termed Stark tuning, arises vary by over 1 eV, and the Stark-tuning ν/ Ε intriguing information on the electronic both from chemical and electrostatic (d d m) slopes are sufficiently large properties of metal-solution interfaces.7 effects on the surface bonding. Shifts in (ca. 30-80 cm-1 V-1), so that this near- We now describe very briefly three exam- electrode potential can also alter the sur- uniform agreement is a clear indication ples of recent applications of vibrational face binding energetics, including the of the dominant effect of the average spectral methods (each culled preferred binding geometries. These fac- interfacial potential (and hence field) in unabashedly from results in our labora- tors are important, and have been par- determining the chemisorbate vibra- tory) to fundamental structure and bond- ticularly well studied for CO and NO. It tional properties. Consequently, the ing issues in surface electrochemistry. is of fundamental interest to compare electrostatic, rather than more specific The first concerns the archetypical potential-dependent C-O and N-O vibra- chemical (such as solvational), proper- ν ν case of carbon monoxide chemisorption tional frequencies, CO and NO, at ties of the double layer are dominant on Pt-group metals. This chemisorbate is monocrystalline electrodes with corre- here. Similar, although less quantita- of broad-based interest in both electro- sponding data obtained at clean metal- tive, results along these lines are chemistry and UHV-based surface sci- UHV interfaces to ascertain the influ- obtained for low chemisorbate cover- ence for several reasons, including its ence of double-layer solvation/charge ages, suggestive in some cases of a more common presence as a poison in electro- effects on the former.10 specific role of coadsorbed solvent catalytic oxidations, but (more positive- Figure 1 shows a global comparison under these conditions.11 ly) as a simple coordinating diatomic along these lines for saturated coverages The second brief illustration of the species with vibrational properties that of CO and NO on (111) and (100) sur- fundamental value of vibrational spec- are sensitive to the chemical and electro- faces of Pt, Rh, Ir, and Pd surfaces with troscopy to electrochemistry involves ν static environment. Partly for the latter the aqueous electrochemical and UHV- the metal-chemisorbate modes ( M-X) reasons, CO (along with the related based frequencies forming the x- and y- themselves. While these vibrations species NO) have been widely studied by axes, respectively. An essential point is occur at frequencies (≤ 600 cm-1), too vibrational spectroscopy, especially on that the former frequencies are all mea- low to be accessed in most cases by Ε oriented single-crystal electrodes by sured at electrode potentials, m, equiv- IRAS, they are readily observable with 8,9 Φ means of IRAS. Given that related alent to the observed work function, m, SERS. Although the SERS effect itself is IRAS measurements have been widely for the (solvent/charge-free) metal-UHV limited chiefly to Group IB metals, pursued in UHV, the spectra can also interfaces. The best concordance, shown coating such surfaces with ultrathin provide a unique means of linking the by the unit slope (x=y) line, was found (nanoscale) films imparts comparable enhancement also to the overlayer and adsorbates found thereon.3 In particu- lar, we have examined transition metal, oxide, and compound semiconductor surfaces by this overlayer SERS approach.3 Figure 2 shows the effect of altering the electrode on the surface-halogen force constants, fM-X, for chloride and bromide adlayers bound to Group VIII and IB substrate, extracted from SERS ν 12 M-X data. The fM-X values show a systematic correlation with the d-band occupancy; the stronger bonding (high- er fM-X values) seen with fewer d-elec- trons suggesting the increasing impor- tance of halide-metal electron dona- tion. Consistent trends are found for ν Ε the Stark-tuning (d M-X/d ) slopes, indicating that the sensitivity of the bond frequency to the electrostatic field diminishes as the halide-metal bonding becomes less ionic.12 The third brief example also con- cerns harnessing SERS for examining FIG. 2. Surface-adsorbate force chemisorption at Pt-group electrode- constants for halides solution interfaces, but now for poly- chemisorbed on Group VIII atomic adsorbates, specifically aromatic and IB metal electrodes in aqueous solution plotted versus species. Figure 3 contains a pair of SER d-electron occupancy. Data spectra obtained for benzonitrile extracted from SERS data in (C6H5CN) and toluene (C6H5CH3) on Ref. 12. palladium. Their molecular structure

The Electrochemical Society Interface • Winter 2000 35 (and thereby the bulk-phase Raman application of electrochemical spectro- 8. C. Korzeniewski and M. W. Severson, spectra) are similar, but the correspond- scopic methods to problems critical to Spectrochim. Acta., A51, 499 (1995). ing SER spectra are markedly different. emerging technologies as well as to fun- 9. M. J. Weaver and S. Zou, in Advances There are numerous aromatic ring damental science. ■ in Spectroscopy, Vol. 26, R. J. H. Clark modes observable in the frequency and R. E. Hester, Editors, Chap. 5, region shown, reflecting the excellent References Wiley, Chichester, UK (1998). 10. M. J. Weaver, S. Zou, and C. Tang, J. sensitivity as well as liberal surface selec- 1. A. T. Hubbard, Chem. Rev., 88, 633 Chem. Phys., 111, 368 (1999). tion rules offered by SERS. (Very few of (1988). 11. M. J. Weaver, Surf. Sci., 437, 215 these modes appear, and only weakly, in 2. (a) M. Fleischmann and P. J. (1999). corresponding IRAS data.) Note, howev- Hendra, Chem. Phys. Lett., 26, 163 ν 12. M. F. Mrozek and M. J. Weaver, J. er, that several ring modes (e.g., the 12 (1974); (b) D. L. Jeanmaire and R. P. mode at ca. 1000 cm-1) are much broad- Am. Chem. Soc., 122, 150 (2000). van Duyne, J. Electroanal. Chem., 13. S. Zou, C.T. Williams, E. K-Y. Chen, er in the toluene than the benzonitrile 84, 1 (1977). spectra, and are shifted significantly (in and M. J. Weaver, J. Phys. Chem. B, 3. M. J. Weaver, S. Zou, and H. Y. H. some cases up to 50-100 cm-1) from 102, 9039, 9743 (1998). Chan, Anal. Chem., 72, 38A (2000). their uncoordinated values. These and 14. F. Illas, F. Mele, D. Curulla, A. Clotet, 4. See papers in Symp. Faraday Soc., other spectral dissimilarities reflect dif- and J. Ricart, Electrochim. Acta, 44, Vol. 4 (1970). ferences in the chemisorbate coordina- 1213 (1998). 5. A. Bewick and S. Pons, in Advances 15. M. T. M. Koper, R. A. van Santen, S. tion (and orientation) geometries of in Infrared and Raman Spectroscopy, A. Wasileski, and M. J. Weaver, J. benzonitrile and toluene, being tethered Vol. 12, R. J. H. Clarke and R. E. Chem. Phys., 113, 4392 (2000). to palladium via the nitrile and benzene Hester, Editors, Chap. 1, Wiley, moieties, respectively.13 Similarly to the Chichester, UK (1985). simple halogen cases mentioned above, 6. A. Tadjeddine and A. Peremans, in About the Authors a number of the intramolecular (as well Advances in Spectroscopy, Vol. 26, R. Mike Weaver and Sally as the metal-adsorbate) modes are J. H. Clark and R. E. Hester, Editors, Wasileski are with the department dependent on the metal; altering the Chap. 4, Wiley, Chichester, UK of chemistry at Purdue University. electrode material can therefore yield (1998). Mike can be reached at: mweaver@ rich insight into the chemical nature of 7. Y. Y. Tong, E. Oldfield, and A. purdue.edu. Sally can be reached at: the surface bonding. Wieckowski, Anal. Chem., 70, 518A [email protected]. Overall then, our broad-based under- (1998). standing of electrode-chemisorbate sur- face bonding can now be advanced sub- stantially by the judicious use of in situ vibrational spectroscopy. Also worth mentioning in this context is the cur- rent emergence of Density Functional Theory (DFT) as a practical means of analyzing as well as predicting surface vibrational properties in terms of ab ini- tio quantum chemistry. Although appli- cations of DFT to electrochemical sys- tems are still in their infancy,14,15 it is clear that such approaches have much to offer in enhancing our understand- ing of surface vibrational spectroscopy in particular, as well as advancing great- ly our quantum-chemical appreciation of electrochemical surface bonding on a broad front. Finally, it should be emphasized that this brief summary is grossly incom- plete, as well as strongly biased. Besides merely acknowledging the importance of spectroscopies beyond vibrational methods, we have scarcely mentioned the growing emphasis on utilizing such strategies to examine reactive as well as stable electrochemical systems. Indeed, the application of time-resolved spectral tactics (especially in conjunction with transient electrochemical information), to elucidate catalytic reaction pathways FIG. 3. SER spectra for and other dynamical phenomena, clear- benzonitrile (upper) compared with toluene ly constitutes a crucial (and largely (lower) on palladium in unsurmounted) challenge in electro- aqueous solution. chemical surface science. Overall, the Data adapted from future holds much for the expanding Ref. 13.

36 The Electrochemical Society Interface • Winter 2000 Electrochemistry as an Analytical Technique by Lou Coury

ttempting to define the boundaries guished from one another, which may quently measured using electrochem- A of electroanalytical chemistry would not be the case if an atomic spectro- istry is concentration (or more precisely, be a difficult exercise, and any result metric approach is used. as noted above, activity). Measurement would be subject to constant revision Third, electrochemical methods of solution pH, ion activities using an anyway. For the purposes of this brief yield an electrical signal directly; no ISE, solution conductance by laboratory overview, electroanalysis will be charac- primary signal transduction step is nec- water purifiers, water content of organ- terized as involving the application of essary (e.g., photomultiplier tube or ion ic solvents by Karl Fischer titration, glu- one or more electrochemical techniques collector). This situation has several cose in whole blood with hand-held for measuring some quantity of interest. benefits including straightforward gen- meters, oxygen in blood by clinical This quantity of interest is as likely to be eration of real-time signals, useful for blood gas analyzers, and oxygen in a rate constant as a concentration, for sensors and flow stream monitoring. automotive exhaust gases with solid example. Also, the lack of this transduction stage electrolyte-based sensors are all eco- Textbooks credit Michael Faraday as results in ease of miniaturization. nomically important examples of elec- being the father of electroanalytical Micro-electrodes are used in neuro- troanalytical measurements falling into chemistry through the formulation of science for this reason, in addition to this category. his laws of electrolysis. Although the the fact that their small size results in An example from the research realm experimental techniques he used were in high spatial resolution. of how sophisticated this class of mea- large part developed by his mentor Fourth, electrochemical detectors are surements has become is shown by Humphry Davy during his discovery of selective, not universal. Some analytes work by Wightman and colleagues.1 In many of the alkali and alkaline earth do not undergo redox reactions at an their work, release of the neurotrans- metals, it was Faraday who related a mea- appreciable rate within commonly mitter dopamine from intracellular vesi- surable parameter (weight of a plated accessible solvent windows. Thus, in cles in single neurons isolated from metal) to other numerical quantities some cases, electrochemical sensors and mouse retinas was described. Their (charge passed through a solution and detectors are used without a prior sepa- experimental protocol involved a com- elemental equivalent weight). Hence, ration step. To illustrate this point, if all bination of optimized electronics and Faraday rather than Davy is credited with the species present in human blood data acquisition, high-precision posi- realizing that electrochemical methods gave a signal at the potential used for tioning of carbon fiber microelectrodes, may be used for analytical purposes. This enzymatic glucose detection, the and the ability to evoke dopamine article will consider a few representative prospects for making direct determina- release through delivery of specific examples of things that can be measured tion of glucose in a drop of whole blood reagents via a pressure ejection using electrochemistry. would be (at best) remote. micropipet. In this way, they were able Fifth, electrochemical signals result to show that individual secretion events Why Electrochemistry? from processes occurring at a surface. result in the release of between 8 and Whereas there are some clear drawbacks 170 zeptomoles of dopamine, with an The use of electrochemistry in the to this, there are also advantages. average value of 52 zmol or about service of measurement science is likely Because surfaces may naturally (or can 32,000 dopamine molecules. to be taken for granted by members of be made to) accumulate ions and mole- Measurement of Kinetic Rate Constants ECS, given our backgrounds and biases. cules from solution (e.g., adsorption, ion to Elucidate Charge Transport in DNA However, it is appropriate to list the exchange, electrodeposition), precon- Strands—Kinetic measurements are fre- characteristics that make electrochem- centration strategies are often coupled quently performed using electrochemi- istry especially useful to analytical with electrochemical detection steps. cal methods. Because current is a deriv- chemists. First, techniques such as Anodic and cathodic stripping voltam- ative signal, it is inherently indicative of coulometry and electrogravimetry are, metry are common examples. Such rate. Using various electroanalytical at least in theory, absolute methods. techniques are capable of giving very techniques and measurement time They may therefore be used in certain low limits of detection (sub-nanoMolar, scales, heterogeneous electron transfer, situations where a suitable standard is in some cases). solution electron transfer or solution unobtainable. This is in contrast to cali- atom (group) transfer rates may be bration-based analyses that require the What Can Be Measured? probed. Classic papers in this area were generation of standard curves using a published by Nicholson and Shain,2,3 reference standard. The remainder of this report and Savéant.4 More recently, the devel- Second, electrochemical methods summarizes a few examples of unusual opment of efficient computational algo- give signals that vary with the activities parameters and phenomena measured rithms and the rise of powerful yet inex- of analyte species rather than their con- using electrochemical techniques. No pensive personal computers have result- centrations. For solution phase reac- attempt is made to provide a compre- ed in the widespread use of digital sim- tions, the former are relevant for under- hensive list. Rather, the focus is on a rel- ulation techniques for the extraction of standing, e.g., thermodynamic behav- atively small number of studies that kinetic parameters from voltammetric ior. Similarly, electrochemical methods illustrate the diversity of electroanalyti- data.5 are useful for speciation studies. cal measurements. An interesting example of electro- Elements present as ions having differ- Concentration Measurements at the chemical rate measurements used to ent oxidation states may be distin- Cellular Level—The quantity most fre- probe an issue of fundamental import-

38 The Electrochemical Society Interface • Winter 2000 ance, viz., the charge transport charac- ing peak separations in cyclic voltam- different redox activities are shown for teristics of double-stranded (ds) DNA, is mograms3 (along with the other mea- the three different types of breast cells. provided in recent work by Heller, et al.6 surements used by these authors) pro- Because SECM generates a map of trans- By comparing current densities for the vides an interesting example of the membrane charge transfer rates, the electroreduction of H2O2 at soybean power of electroanalytical measurement authors point out the possibility of peroxidase-modified electrodes electri- techniques. using the technique to detect aberrant cally wired with either ds-DNA or a Spatially-Resolved Kinetic Measurements responses in large arrays of cells and hydrophilic Os redox polymer, they for Probing Differences Between Cancerous tumor specimens. were able to determine that the diffusiv- and Normal Biological Cells—The tech- Measurement of Mass Transport- ity of electrons in unaligned and nique known as scanning electrochemi- Limited Currents to Understand unstretched calf thymus DNA is less cal microscopy (SECM) allows many Transdermal Transport—The administra- than 10-11 cm2 s-1. This result led the types of electrochemical measurements tion of some pharmaceutical com- authors to conclude that, in the absence to be made as a precise function of posi- pounds poses a challenge either because of chain alignment, ds-DNA is not an tion.7 In one implementation of this the drugs may be metabolized in the electrical conductor. experiment, an ultramicroelectrode is gastrointestinal tract before they can be Heller et al., conclude that ds-DNA scanned with respect to position over a absorbed, or because the compounds may undergo an insulator-to-semicon- surface, and amperometric or voltam- are simply poorly absorbed into the ductor transition upon parallel align- metric data may be obtained as a func- bloodstream. One alternative strategy ment. The organization of ds-DNA into tion of x, y, and z-coordinates. that is receiving increasing attention is aligned arrays is further discussed in the In an upcoming paper, Mirkin and called iontophoretic transdermal drug context of an evolutionary strategy for colleagues demonstrate the use of SECM delivery. This technique uses an applied preserving genetic information. Because to distinguish differences between non- current on the order of a few hundred addition of a hole or electron to the motile, non-transformed human breast microamps per square cm to force mol- semiconducting form of DNA has the epithelial cells; breast cells with a high ecules across layers of skin. Both effect of dispersing the charge over a level of motility; and highly metastatic charged species (ions) as well as neutral large number of atoms, this situation breast cancer cells.8 In their work, they compounds may be delivered in this prevents any particular atom in the demonstrate that effective rate con- way. assembly from being particularly reac- stants can be measured for bimolecular White and collaborators at the tive, which could result in genetic dam- reactions between small diffusing mole- University of Utah and ALZA age. The fact that such an important cules (i.e., redox mediators) and intra- Corporation have recently investigated concept could be developed by examin- cellular redox moieties. Significantly, the mechanism of transport of neutral

The Electrochemical Society Interface • Winter 2000 39 molecules using SECM.9 In their exper- Sun and Crooks10 of a Coulter counter controlled by thiolate self-assembly iments, the flux of hydroquinone for nanometer-sized particles. Coulter chemistry. More recently, the same across samples of skin taken from hair- counters are commercially-available researchers are focusing on the use of less mice was monitored as a function instruments used to determine the vol- single carbon nanotubes to form the of the applied transdermal current. ume of particles suspended in a con- pores in their Coulter counters. Thus, Both voltammograms and amperomet- ductive liquid. The electrical quantity it is conceivable that this work may ric data were collected with an SECM, that is actually measured is the change soon lead to the ability to count indi- and the signal recorded was due to the in resistance (e.g., change in current at vidual (macro-) molecules as they pass oxidation of hydroquinone that tra- constant potential, or vice versa) across through such well-defined orifices. ■ versed the mouse skin sample at various a small aperture as particles pass sites. By altering the polarity of the cur- through the opening. The change in Acknowledgments rent, its magnitude and the pH of the resistance recorded is related to the vol- bathing solution, the authors were able ume of liquid displaced by the particles. Lou Coury wishes to thank Michael to show that neutral molecules are car- Also, the number of particles in a Mirkin for an advance copy of ried through hair follicles in the skin defined volume can be counted. In Reference 8, and Johna Leddy for via electro-osmotic flow. Furthermore, addition to particle analytes, measure- advice and assistance during manu- they were able to determine that the ments on cell suspensions are common- script preparation. isoelectric point of the follicles occurs ly performed. at pH 3.5. Hence, the authors could Commercial implementations of References change the direction of transdermal this technology are usually restricted to fluid flow by changing the solution pH examination of particles with mean 1. S. E. Hochstetler, M. Puopolo, S. from below to above pH 3.5. The latter diameters in the micrometer range. Sun Gustincich, E. Raviola, and R. M. observation is important in applica- and Crooks have recently extended the Wightman, Anal. Chem., 72, 489 tions such as non-invasive glucose range of such measurements to (2000). monitoring, where movement of ana- nanometer-size polystyrene particles 2. R. S. Nicholson and I. Shain, Anal. lyte from below the surface of the skin through construction of a single pore in Chem., 36, 706 (1964). to an external sensor is required. a gold membrane.10 One advantage to 3. R. S. Nicholson, Anal. Chem., 37, A Nanoscopic Coulter Counter—The the use of gold as the membrane in 1351 (1965). final example highlighted in this brief their device is that the surface chem- 4. See for example: C. P. Andrieux report concerns the construction by istry of the interior of the pore can be and J.-M. Savéant, in Molecular Design of Electrode Surfaces: Techniques of Chemistry, Vol. XXII, Chap. 5, R. W. Murray, Editor, John Wiley & Sons, New York (1992). 5. M. Rudolph, D. P. Reddy, and S. W. Feldberg, Anal. Chem., 66, 589A (1994). 6. G. Hartwich, D. J. Caruana, T. de Lumley-Woodyear, Y. Wu, C. N. Campbell, and A. Heller, J. Am. Chem. Soc., 121, 10803 (1999). 7. A. J. Bard, F.-R. Fan, and M. V. Mirkin, in Scanning Electrochemical Microscopy, in Electroanalytical Chemistry, Vol. 18, A. J. Bard, Editor, p. 243, Marcel Dekker, New York (1994). 8. B. Liu, S. A. Rotenberg, and M. V. Mirkin, in “Scanning Electrochemical Microscopy of Living Cells: Different Redox Reactivities of Human Breast Cells and Metastatic Breast Cancer Cells,” Proc. Nat. Acad. Sci., in press. 9. B. D. Bath, H. S. White, and E. R. Scott, Pharm. Res., 17, 471 (2000). 10. L. Sun and R. M. Crooks, Langmuir, 15, 738 (1999).

About the Author Lou Coury is with Bioanalytical Systems, Inc. in Lafayette, Indiana. He can be reached at: coury@ bioanalytical.com.

40 The Electrochemical Society Interface • Winter 2000 Architecture on Electrodes — Modeling Meets Materials by Johna Leddy

odified electrodes developed as a nat- polyvinyl ferrocene and polymers of Monolayer modified electrodes were M ural consequence of paradigm bipyridyl transition metal complexes formed as Langmuir Blodgette films, self changes for physical electrochemical were among the first evaluated. Ion assembled monolayers (SAMs), and cova- measurements. In the first half of the exchange matrices such as Nafion provid- lently attached layers such as alkanethiols twentieth century, measurements were ed the flexibility of easily coating an elec- on gold. Monolayers on electrodes made at mercury electrodes in aqueous trode and intercalating a redox species. allowed detailed investigation of electron electrolytes; pristine electrode surfaces Polyaniline, polythiophene, and polypyr- transfer effects. Because the redox probes were the rigor of the day. Solid electrodes role were among the electron conducting are held immediately at the electrode sur- came into use in the 1950s. This in turn polymers investigated next. Inorganic face, measurements are not complicated led to the use of nonaqueous solvents. polymer-like materials such as clays, zeo- by mass transport. The properties of The emphasis in electrochemical mea- lites, and sol gels were also studied. monolayers are described not in terms of surements shifted from the thermody- Polymer films were largely viewed as a bulk and macroscopic extent, but rather namic to the dynamic. The expectation bulk, homogeneous matrix, and their in terms of molecular and nanoscopic of rigorously clean surfaces diminished, properties were discussed in terms of either length scales. Monolayers provide for ver- and evolved into an interest in intention- macroscopic or molecular length scales. satile surface modification and excellent ally modified electrode surfaces. Merz Experimental studies focused on mass control of structure across a two-dimen- and Bard1 reported the first polymer transport effects and the design of matrices sional surface, but introduce little elec- modified electrode in 1978. for optimized cross exchange and mediat- troactive material. ed reactions. Polymers provide a versatile Composites are multi-component, Evolution of Modified Electrodes method for surface modification and high heterogeneous matrices usually formed material loading of electroactive moieties. either by self-assembly or layering of Polymers were the first materials used However, polymer structures tend to form components. Detailed architectures are to build matrices on electrode surfaces. randomly, and true architectures are diffi- achievable in three dimensions. Electroactive or redox polymers such as cult to orchestrate. Composites can provide greater architec-

The Electrochemical Society Interface • Winter 2000 41 tural flexibility than monolayers and the ual components of the photosynthetic holes in the film, the homogeneous high material loading of polymer films. reaction center of bacteriochlorophyll model is applicable. Amatore, Savéant, With composites, order is induced over into a phosphatidylcholine film, and and Tessier8 presented a model for cyclic several length scales, ranging from the demonstrated electroactivity. In another voltammetry that allowed assessment of molecular, through the nanoscopic, study, this group6 demonstrated electro- pinhole dimensions based on the peak microscopic, and macroscopic. chemical and electrocatalytic activity in a splitting. Andrieux and coworkers9 pre- Microscopic components can be used to layered structure of myoglobin and sented steady state models for homogen- create a nanoscopic interface that con- cytochrome P450cam. In these successful- eous films on electrodes wherein diffu- trols the characteristics of the system. For ly engineered systems, a balance of mass sion of substrates, exchange of electrons, example, self-assembly at the interface transport of substrates and counter ions and mediation reactions were considered. between a microscopic particle and ion as well as electron transfer and homoge- The commercial simulation program exchange polymer can create an ordered neous reaction kinetics must be achieved. DigiSim allows modeling of homoge- nanoscopic interface that facilitates flux neous thin layers where diffusion from of permeants through the composite sev- Evaluating Modified Electrodes solution is precluded. eral fold.2 Models for composites differ in that In the realm of physical electrochem- Composites provide a promising route they must allow for the heterogeneous istry, modified electrodes are evaluated to devices on electrodes, including structure. Heterogeneity introduces com- through a combination of experiments mechanical actuators and switches. plexities of mixed length scales, inter- and modeling. Experimental studies are Materials can be graded for enhanced faces, multi-dimensionality, and porosity. largely voltammetric with three main mass and electron transfer. Templates on Voltammetric studies of composites often classes of investigation: evaluation of a microscopic level can be used to form register effects over a range of length electron transfer across and through new composite materials. On a molecular scales such that the system response is monolayers; assessment of the electro- scale, Makote and Collinson3 templated governed by several parameters in addi- chemical properties of electroactive and dopamine in an inorganic-organic hybrid tion to the film thickness. To the extent electron conducting moieties in films; sol-gel matrix by co-casting dopamine in that effects depend on length scales and determination of the flux of perme- the sol-gel, and then extracting the microscopic and smaller, composites are ants from solution through the modify- dopamine from the dried film. The result- sometimes governed by rules different ing layer to the electrode surface. Imaging ing sol-gel modified electrode has from those for macroscopic materials. and spectroscopy often augment electro- enhanced affinity for dopamine as com- Composite properties are often dominat- chemical studies. pared with other structurally similar neu- ed by interfaces. By their microscopic and The experimental evaluation of poly- rotransmitters and compounds. nanoscopic nature, composites have a mers, monolayers, and composites follow very high ratio of internal surface area to very similar protocols. The assessment Fundamentals for All volume. From classical physical chem- bifurcates in the modeling of the physical istry, strong forces and gradients are often Modified Electrodes systems. Polymers and monolayers are established at interfaces, and such forces traditionally treated as homogeneous As in all electrochemical systems, can impact composite characteristics. matrices, whereas composites, by their three effects must be considered: mass The protocol to appreciate the role of very nature, are heterogeneous micro- transport, electron transfer, and structure in composite behavior is to eval- and nano-structures. homogeneous kinetics. These effects uate composites as a function of an Traditional models for polymers treat must be designed into the matrix of a suc- appropriate characteristic dimension. For the layer as a homogeneous matrix where cessfully modified electrode. Transport example, in composites formed of spher- only flux in the coordinate normal to the can be sustained through either elec- ical microparticles embedded in an ion electrode is considered. For electroactive trolyte filled porous structures or a vis- exchange polymer, vary microparticle films, systems are evaluated under one of cous but liquid-like modifying layer. radius at fixed particle volume fraction two limiting conditions. For diffusion Electron transfer must be charge compen- and measure flux of a redox probe length less than film thickness, voltam- sated by ion motion throughout the through the composites. Such characteri- metric results are analogous to those for films. Homogeneous kinetics are intro- zation of composites will usually demon- redox probes in solution, provided there duced when films contain mediators and strate a variation of properties with char- are no strong inter-moiety interactions in catalysts. Selectivity can be introduced by acteristic length. Often, the relationship the film. In the second limiting case, dif- structure-based restrictions on size, between properties and characteristic fusion length far exceeds film thickness, charge, and hydrophobicity. length is fractal. Fractal systems have and the response is evaluated under thin The correct balance between mass three characteristics. First, the images layer conditions. Models for permeation transport, electron transfer, and (e.g., SEM) often appear visually self-simi- of redox probes through electrochemical- homogeneous kinetics provides the basis lar over different length scales. Second, a ly inert layers were first presented by for building many elegant structures on noninteger power law characterizes the Gough and Leypold7 for steady state, electrodes. Among the most impressive mathematical relationship between the rotating disk voltammetry. For transient systems are those that wire biologically measured property and the characteristic methods, data are collected either at early significant molecules (e.g., proteins and dimension. enzymes) to the electrode such that there times when the diffusion length of the is direct electronic communication as permeant is less than the film thickness Property α [Characteristic Length]-µ well as electrocatalyzed consumption of or under conditions where the diffusion substrates. Armstrong and coworkers length far exceeds the film thickness. Third, for a system to be fractal, the power recently studied intramolecular electron Whether for steady state or transient law must apply over at least an order of transfer relays in an electroactive enzyme, models, the polymer is treated as a magnitude in characteristic length. It has fumarate reductase, and identified indi- homogeneous matrix. That is, if the dif- been shown that for microspheres embed- vidual electron transfer steps.4 Rusling fusion length is larger than either the ded in Nafion, the flux of redox probes and coworkers5 incorporated the individ- diameter of or the distance between pin- through the composite increases with

42 The Electrochemical Society Interface • Winter 2000 decreasing microsphere radius. A power because the trans configuration generates Dendrimer structures on electrodes pro- law characterizes the relationship a more porous film.11 Coating liquid vide the opportunity to design three- between flux and radius with an expo- crystals on the electrode forms an electro- dimensional matrices; spherical den- nent of 0.78.2 The same power law char- chemically activated switch, where the drimers form monolayers with higher acterizes the increase in ion exchange electronic conductivity changes by 105 dimensionality than the two dimension- capacity with decreasing particle radius.10 under electrochemical perturbations.12 al structures provided by alkane based self The exponent of 0.78 is consistent with An electrochemically actuated mechani- assembled monolayers.18 Here, on the transport along the two dimensional sur- cal system relies on the flux of lithium electrode normal, the length scale is high- face of the microspheres. While fractal ions in and out of a 3.5 cm long carbon er than molecular. Scaffolds of nanometer exponents are not intuitively transparent, nanotube to generate displacements of length scales are formed of nanometer they do provide information about what several centimeters.13 Size selectivity has sized gold nanoparticles linked with 19,20 is dominating system responses. been engineered into a film by exploiting organic binders. Microscopic scaf- Guidance in the form of a fractal relation- pores that occur naturally in the crystal folding is formed by microparticles ship enables tailoring and optimizing structure of a rhenium complex.14 The bound to an electrode by a matrix such as 2 composites for specific electrochemical orientation of peptide nanotubes perpen- an ion exchange polymer. activity. It should be noted that when dicular to the electrode surface provides Thus, new tools are evolving for the assessing the role of structure in compos- size selectivity for small redox probes.15 construction of true three-dimensional ites formed of permeable and non-perme- Such structures lead one to conjure architectures on electrode surfaces. These able material, it is necessary to normalize plumbing and electrical wiring of devices structures hold the promise of actuation measured parameters such as flux by the on electrodes. by external stimuli, as well as the design fraction of permeable material. Scaffolding has been built on scales of graded materials. Devices, reactors, from the molecular to the nanoscopic. transducers, and switches on a molecular Current Trends Savéant and coworkers build a highly to microscopic length scale are possible ordered, multilayer enzyme modified constructs on electrodes. Some recent trends point to the devel- electrode by exploiting antigen-antibody opment of device components and and avidin-biotin binding.16 Alternating Future Directions switches on electrodes. Electrodes modi- layers of polyoxometalates and cations We can expect a greater variety of fied with a monolayer containing cis- 17 have formed multilayer structures. nano- and microscopic structures on elec- azobenzene precludes direct electron Such structures have order on the molec- trodes, with design ideas drawn from the transfer to a redox species in solution, but ular to nanometer length scale normal to macroscopic world. Surprises will arise as upon photoconversion to trans-azoben- the electrode and longer length scales in behavior at submacroscopic length scales zene, direct electron transfer occurs the plane parallel to the electrode.

The Electrochemical Society Interface • Winter 2000 43 often differs from that at the macroscop- logical applications, more robust materi- 3. R. Makote and M. M. Collinson, ic. Successful developments will require als will be needed. Rapid response sen- Chem. Mater., 10, 2440 (1998). advances in modeling, experimentation, sors will depend on enhancing transport 4. H. A. Heering, J. H Weiner, and F. A. and design paradigms. through composites. Composite arrays Armstrong, J. Am. Chem. Soc., 119, The modeling of homogeneous films with addressable sites in three dimen- 11628 (1997). would be advanced by models for cyclic sions would have applications in sensors 5. J. Kong, Z. Lu, Y. M. Lvov, R. Z. B. voltammetry of permeants through inert and information storage; photoelectro- Desamero, H. A. Frank, and J. F. and ion exchanging films. Ion exchange chemical methods might be appropriate. Rusling, J. Am. Chem. Soc., 120, models have the added complexity of As submacroscopic systems often yield 7371 (1998). electroneutrality requirements. No fractal (i.e., nonlinear) responses, it is 6. Y. M. Lvov, Z. Lu, J. B. Schenkman, voltammetric models account for the conceivable that amplification schemes X. Zu, and J. F. Rusling, J. Am. Chem. changes that occur when ions of charge may be developed. In general, design par- Soc., 120, 4073 (1998). n+ initially loaded into an ion exchang- adigms will evolve that will allow com- 7. D. A. Gough and J. K. Leypoldt, ing film undergo electrolysis. More posites to be tailored for specific applica- Anal. Chem., 51, 439 (1979). sophisticated models will be developed tions. Such paradigms would find appli- 8. C. Amatore, J. M. Saveant, and D. as composite structures become more cation in the design of heterogeneous Tessier, J. Electroanal. Chem., 147, 39 complex. Experimentally, nondestructive structures such as fuel cell catalyst layers. (1983). imaging methods that view the interior Designing architectures on electrodes can 9. C. P. Andrieux, J. M. Dumas- of composites with molecular to micro- be viewed as plumbing, wiring, con- Bouchiat, and J. M. Saveant, J. scopic resolution would allow a better structing, engineering, modeling, or Electroanal. Chem., 131, 1 (1982). appreciation of the role of the interface. nonlinear optimization, but the rich 10. T.-Y. Chen and J. Leddy, Langmuir, A greater variety of design schemes complexity of the domain leaves the 16, 2866 (2000). will evolve including templates on all researcher with opportunities on many 11. D. G. Walter, D. J. Campbell, and C. length scales, lost wax processes for length scales and ample room to play. ■ A. Mirkin, J. Phys. Chem. B, 103, microscopic structures and intercalating 402 (1999). components into interfaces, and more References 12. B. A. Gregg and R. A. Cormier, J. robust as well as switchable scaffolding. Phys. Chem. B, 102, 9952 (1998). 1. A. Merz and A. J. Bard, J. Am. Chem. Formation has thus far relied on self 13. G. Che, S. A. Miller, E. R. Fisher, and Soc., 100, 3222 (1978). assembly to a large extent; more elabo- C. R. Martin, Anal. Chem., 71, 3187 2. L. A. Zook and J. Leddy, J. Phys. rate chemistries will evolve. Composites (1999). Chem. B, 102, 10013 (1998). will serve as microscopic transducers. If 14. S. Belanger, J. T. Hupp, C. L. Stern, composite matrices are to find techno- R. V. Slone, D. F. Watson, and T. G. Carrell, J. Am. Chem. Soc., 121, 557 (1999). 15. K. Motesharei and M. R. Ghadiri, J. Am. Chem. Soc., 119, 11306 (1997). 16. N. Anicet, C. Bourdillon, J. Moiroux, and J.-M. Savéant, J. Phys. Chem. B, 102, 9844 (1998). 17. A. Kuhn, N. Mano, and C. Vidal, J. Electroanal. Chem., 462, 187 (1999). 18. H. Tokuhisa, M. Zhao, L. A. Baker, V. T. Phan, D. L. Dermody, M. E. Garcia,R. F. Peez, R. M. Crooks, and T. M. Mayer, J. Am. Chem. Soc., 120, 4492 (1998). 19. M. Lahav, T. Gabriel, A. N. Shipway, and I. Willner, J. Am. Chem. Soc., 121, 258 (1999). 20. S. J. Green, J. J. Pietron, J. J. Stokes, M. J. Hostetler, H. Vu, W. P. Wuelfing, and R. W. Murray, Langmuir, 14, 5612 (1998).

About the Author Johna Leddy is with the department of chemistry at the University of Iowa, e-mail: [email protected].

44 The Electrochemical Society Interface • Winter 2000