CHEM465/865, 2006-3, Lecture 6, 18 th Sep., 2006
Electrochemical Thermodynamics
– Interfaces and Energy Conversion
ϕϕϕ Where does the energy contribution F∑∑∑ zi d N i come from? i First law of thermodynamics (conservation of energy): ∆U = TS ∆ +∆ W
Move small amount of charge ( ∆∆∆Q ) of species i through electrical potential difference ϕϕϕ .
ϕϕϕ ≠≠≠ 0 ϕϕϕ === ∆ =∆=ϕ ϕ ∆ 0 Wel QzFi N i
∆Q = zF ∆ N i i i Work on charge against inner potential difference. Corresponding differential of the internal energy: ɶ =−+µ + ϕ dddUTSpV∑ii d NFz ∑ i d N i i i Corresponding differential change of Gibbs free energy ɶ =− + +µ + ϕ dG STVp d d∑ii d NFz ∑ i d N i i i Important observation: Only differences µµβα−=−+ µµ βα ϕϕ βα − ɶii ɶ ((( ii))) z i F ((( ))) between phases ααα and β are experimentally available.
Gibbs, conclusion of fundamental importance: Electrical potential drop can be measured only between points which find themselves in the phases of one and the same µα=== µ β chemical composition, i.e. i i , and thus, µɶβ−−− µ ɶ α ∆βϕ = ϕ β − ϕ α = i i Galvani potential ααα zi F Otherwise, when the points belong to two different phases , µα≠≠≠ µ β ∆∆∆ βββϕϕϕ i i , experimental determination of ααα is impossible ! Recall: • general situation considered in electrochemistry: phases in contact
ααα βββ V σσσ V
∆ βββϕ • potential differences ∆∆ααα ϕϕ control equilibrium between phases and rates of reaction at interface ∆ βββϕ The problem is: ∆∆ααα ϕϕ is not measurable! What is the electrostatic potential of a phase? Related to work needed for bringing test charge into the phase. α α α ϕ= ψ + χ
Vααα
ϕϕϕααα ψψψααα
10 -5 – 10 -3 cm
ααα ϕϕϕ : inner or Galvani potential ; work required to bring a unit point charge from ∞ to a point inside the phase ααα; electrostatic potential that is actually experienced by a charged particle in that phase.
ααα Unfortunately: ϕϕϕ cannot be measured! Why not????? § Involves transfer across interface with its inhomogeneous charge distribution § Real charged particles interact with other particles in that phase, e.g.: bring an electron into metal
⇒⇒⇒ not only electrostatic work (potential of other charges),
but: work against exchange and correlation energies (Pauli exclusion principle).
ααα ψψψ : outer or Volta potential ; work required to bring a unit point charge from ∞ to a point just outside the surface of phase ααα; “just outside”: very close to surface, but far enough to avoid image interactions (induction effects in metal), 10-5 – 10 -3 cm from surface. ααα ψψψ can be measured! Why can this be measured????
ψ ααα = e.g.: no free charges, metal, uncharged ⇒⇒⇒ ψψ == 0
ααα Why is a metal uncharged? Why is ψψψ === 0 ?
Inner and outer potentials differ by surface potential : α α α χ= ϕ − ψ
α α Uncharged phase (metal): χ=== ϕ
ααα χχχ ≠≠≠ 0 due to inhomogeneous charge distribution at surface
α α Metal: χ=== ϕ , electroneutrality inside of metal positive charge resides on metal ions, fixed at lattice sites, electronic density decays over ~ 1 from bulk value to 0
ionic excess charge density
electronic excess charge metal density
surface dipole
⇒⇒⇒ resulting surface dipole potential: ~ a few Volts
(smaller surface potentials at surfaces of polar liquids)
ααα Different surface planes of metal single crystal: different χχχ Bring charged particles (species i) into uncharged phase ααα: Electrochemical potential: µµαα= + χψ αα = ɶi izF i , 0 µM= µ M − χ M =− metal: ɶe eF, z e 1 Electrons in metal:
Highest occupied energy level is the Fermi level EF , === µµµ M At T = 0: EF ɶe
2 1 πππ k T µµµ M = − B Finite T: ɶe EF 1 3 2 E F Correction ~0.01% at room T negligible in most cases!
Work function , ΦΦΦ M : minimum work required to take an electron from inside the metal to a place just outside
⇒⇒⇒ extract an electron from Fermi-level