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Potentials in Electrochemistry

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Potentials in Electrochemistry Viewpoint http://pubs.acs.org/journal/aelccp Potentially Confusing: Potentials in Electrochemistry Cite This: ACS Energy Lett. 2021, 6, 261−266 Read Online ACCESS Metrics & More Article Recommendations potential quantifies the capacity of a system to do causes transport. The flux (J) of species j (usually in mol· − − work. A simple example is from mechanics: by lifting cm 2·s 1) is given by: a weight, its potential energy increases. When the A CD weight is dropped, that potential energy is converted into jj J =− ∇μ kinetic energy. Applying the concept of potential to j j̅ − RT (2) electrochemical systems can be surprisingly confusing.1 4 “ ” Table 1 shows some potentials used in electrochemistry and The termsi C andy D are the concentration and diffusion 5 j j z j − their different units. coefficientsj forz the species j (e.g., in units of mol·cm 3 and 2· −1 k { ∇μ To start, let us consider a voltage measured with a cm s , respectively), and ̅j is the spatial gradient in the voltmeter for a given system. Analog voltmeters operate by electrochemical potentialthe underlying driving force for passing a small current through a calibrated resistor and wire transport. R is the gas constant, and T is temperature. coil, generating a small magnetic field, and thus deflecting a Chemical reactions can occur throughout the system and needle attached to a fixed magnet. The current passed progress in their thermodynamically favorable direction to μ through the resistor, which causes needle deflection, is ∂ j̅ minimize free energy. When ∇μ̅= 0 and = 0 for all proportional to the voltage. This voltage, however, is not the j ∂t electric potential difference of the system. Electric potential ϕ species j and everywhere in a system, the system is at is the line integral of the electric field E⃗along a path from a electrochemical equilibrium (i.e., the system cannot lower its reference point (often at infinite distance from the system) to total free energy via the net movement of any species a given position: electrons, ions, or molecules to another part of the system or via a chemical reaction). Equation 2 governs transport by drift/migration (movement of charged particles in the ϕ =−∫ E⃗·dS fi ff path (1) presence of an electric eld), di usion (movement due to a concentration gradient), and less-common processes (for ffi Electric fields are generated by (uncompensated) electric example, due to spatially dependent activity coe cients). “ ff ” charge. Thus, q·ϕ is a measure only of the electric Equation 2 also yields the common drift-di usion equation . Downloaded via UNIV OF OREGON on February 2, 2021 at 19:06:16 (UTC). The electrochemical potential for species j can be component of the work needed to move a test charge q 7 from a reference position to the position of interest in the conceptually decomposed: system. If the charge moves through different phases, i.e., μ αα=+μϕzF α See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. across interfaces of different materials, the electric work does jj̅ j (3) not fully account for the total work. μα Consider two metals with different work functions (i.e., the The term j is the chemical potential of j, relative to a ϕα energy required to remove an electron from the metal to reference state, and zjF is the electrostatic energy per mole α vacuum), e.g., Au and Ti. If Ti and Au are put in contact, of j in phase , relative to a reference state. The term zj is the signed charge number of j (e.g., +1, −1, +2, −2), and F is the initially electrons transfer from Ti to Au, generating an − fi Faraday constant (96 485 C·mol 1). The chemical-potential- interfacial electric eld and thus an electric potential μα ff term j is the partial molar Gibbs free energy, ignoring di erence across the interface. Yet if you connect a voltmeter fi with one lead to Ti and the other to Au, you measure 0 V. A electrostatic contributions. It is de ned as the derivative (at constant temperature, T, and pressure, P, and concentration voltmeter does not only measure the electric potential difference between the two points in the system. A voltmeter measures the difference in the electrochemical Received: November 23, 2020 μ ff Accepted: December 10, 2020 potential of electrons ( ̅e), because it is this di erence that drives the current through the voltmeter needed to make the Published: December 24, 2020 measurement.6 The electrochemical potential for electrons is also the Fermi level. In general, it is the gradient (i.e., derivative with respect to position, usually per cm) in μ̅that © 2020 American Chemical Society https://dx.doi.org/10.1021/acsenergylett.0c02443 261 ACS Energy Lett. 2021, 6, 261−266 ACS Energy Letters http://pubs.acs.org/journal/aelccp Viewpoint − of all other species, ni≠j) of the Gibbs free energy with eld; fi respect to the number of particles (in the phase in question): = 96485 α F μ =∂(/)Gn ∂ j intjTPn , , i≠j (4) The term Gint isthechemicalfreeenergyneglecting “ ” ff contributions from long-range electrostatic e ects, and nj is the number of moles of species j. In a mixture, the chemical potential is determined as a function of the activity, drive the transport, transfer, α α j ̅ μ aj , and referenced to the chemical potential at standard state, μo of the electrons in solution and tic terms that describe electron j . ” μα =+μo α jjRTln aj (5) erences in ff α γα α o,α γα ffi cance/example of use The term a = C /C , where is the activity coe cient, Fermi level j j j j j fi “ a factor that allows the use of ideal thermodynamic equations usive transport α o,α o,α ff with concentrations Cj and Cj as inputs. The term Cj is a reference concentration, usually taken to be 1 M for soluble μo describe driving force for reactions between uncharged species species. The term j is determined relative to a reference α j μo ° μ state (e.g., H+ 0at25 C in water). The activity term takes into account that the chemical potential increases with 1 − concentration. In physics, the electrochemical potential is mol fi nes direction of electron transport in metals; gradient gives electric nes criteria for equilibrium; di · erences in often not de ned explicitly, instead the electrostatic energy fi fi ff F gives the heat released, above that required by thermodynamics, per mole used to calculate electric potential energy and reactivity of both charged and uncharged species and the direction of di of electrons in electrode redox equilibria; related to equivalent to the solution reduction potential of electrons to drive an electrochemical process at a given rate; C α · ϕ “ ” de di indicates oxidizing or reducing power of an electrode; related to the Fermiindicates level oxidizing or reducing power of electrons involved in electrochemical de η zjF is included directly in the chemical potential , and an intrinsic or internal chemical potential without long-range a electrostatic effects is defined as a new quantity.7 The fact that gradients in electrochemical potential, not electric potential, drive charge flow explains why a voltmeter cannot measure the electric potential between two metals, i.e., μTi μAu ϕTi ≠ ϕAu Δϕ above ̅e = ̅e but . A voltmeter measures between two points in a system only if they have a common chemical potential. Consider a metal wire acting as a resistor. The concentration of electrons is large, ∼1022 cm−3, and the density of electronic states at the Fermi level is high. Thus, α even when current flows the chemical potential of electrons is dinger equation are included. ̈ ff neglecting electrostatic contributions invariant across the length of the wire. Thus, for two di erent c point in space from a reference point α α β fi locations and in the same metal in phase j nition signi αβα αβ β fi Δμμee̅ = ̅ − μ e̅ =− μ eFFF ϕ −+ μ e ϕ =−Δ ϕ in phase j (6) −Δμ A voltmeter thus measures e̅ =Δϕ between two points in F a common metallic phase. By definition, electrons flow to μ regions of more-negative ̅e (to lower their free energy), but to more-positive ϕ. Under this condition, eq 2 simplifies to a form of Ohm’s law. The foregoing discussion emphasizes that all measurements of potential are necessarily measurements of erence between the applied electrode potential and the electrode potential when ff electrochemical potential and any inferences about electric nite distance) divided by the value of the charge fi potential require one or more assumptions. Now let us consider the term electrode potential, Ewe,in the context of these other potentials (the “we” refers to the working electrode). The electrode potential, with units of V, (often at in associated ion/solvent movement/rearrangement)electrode) from to a the reference working state electrode (often aassociated reference ion/solvent movement/rearrangement)electrode) from into a the reference bulk state of (often a a solution reference via a redox reaction in equilibrium with the target electrochemical reaction ff μ is given by the di erence in ̅e, per charge, in the working μ electrode, relative to ̅e in a second electrode that is typically set via a reversible electrochemical half reaction (i.e.,a V electric work needed to move a test charge to a speci V generally, the di J/mol partial molar GibbsJ/mol free energy of partial a molar given free species energy of a given species V free-energyV change divided by the electron charge associated with free-energy moving change an divided electron by (and the any electron charge associated with moving an electron (and any reference electrode, indicated by "re"): electrostatic interactions due to uncompensated charge, as would be described by the Poisson equation in classical electrostatics.
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