1044 Lecture #14 of 18

Transcription

1 Lecture #14 of

2 1045 Q: What s in this set of lectures? A: B&F Chapter 13 main concepts: Section 1.2.3: Diffuse double layer structure Sections 13.1 & 13.2: Gibbs adsorption isotherm; Electrocapillary / Surface excess / Lippmann s equation; Point of Zero Charge Section 13.3: Section 13.5: Models: Helmholtz, Gouy Chapman (Poisson Boltzmann), GC Stern Specific adsorption

3 data for NaF from B&F is qualitatively similar 1046 Flat? Eh. Why were both of these measured using fluoride salts? In order to minimize specific adsorption! Grahame, Chem. Rev., 1947, 41, 441

4 1047 For the purposes of this class, we want to understand the microscopic origin of the most prominent features of these C d versus potential data: a) A minimum in C d exists at the pzc. b) C d is quasiconstant at potentials well positive and well negative of the pzc. c) This quasiconstant C d is larger when E is (+) of pzc than when it is ( ) of pzc. d) C d increases with salt concentration at all potentials, and the dip disappears.

5 1048 Three traditional models for double layer structure: 1) Helmholtz 2) Gouy Chapman (GC) 3) Gouy Chapman Stern (GCS)

6 Models of Electrical Double Layer: ) The Helmholtz Model: this is the simplest possible model. It postulates that ions (anions and cations) occupy a plane a distance, d, from the electrode surface, and that the effective "dielectric constant" operating in the DL is potential independent: for a parallel plate capacitor, C is independent of E because the permittivity of the capacitor, εε 0, and its spacing, d, are both independent of applied potential d

7 so the Helmholtz model says: Hey, the electrical double layer acts like a parallel plate capacitor 1050 C d is therefore independent of E because the permittivity of the capacitor, εε 0, and its spacing, d, are both independent of applied potential Question: What C d do we calculate for this model, using the known "dielectric constant" (permittivity = IUPAC) of water?

8 recall, here s what the double layer really looks like 1051

9 and here s what the double layer looks like, in the Helmholtz approximation 1052

10 and here s what the double layer looks like, in the Helmholtz approximation 1053 now, what s ε r? 4Å = 0.4 x 10 9 m

11 first, what s ε r for water? Well, that depends can it rotate? 1054 for water at 20 o C

12 first, what s ε r for water? Well, that depends can it rotate? 1055 for water at 20 o C 78.4 Scenario is where electric field oscillates slow enough that molecules do reorient Scenario is where electric field oscillates too quickly for molecules to reorient 5.9

13 and here s what the double layer looks like, in the Helmholtz approximation 1056 Answer: ε r 78 (static relative permittivity) 4Å = 0.4 x 10 9 m

14 and here s what the double layer looks like, in the Helmholtz approximation 1057 Is this what is observed? OK, now what? 4Å = 0.4 x 10 9 m

15 now, what if the water dielectric is saturated, and thus fixed? so that water cannot rotate ε r Å = 0.4 x 10 9 m much more reasonable!

16 if the Helmholtz model is correct, we d get this exactly: 1059 σ M = dγ de μi

17 here are electrocapillary data for various electrolytes. Hey, you can already see that the Helmholtz Model fails mostly on the left 1060

18 1061 Notwithstanding, notice particularly the following: a) the γ vs. E parabola is independent of salt at potentials negative of the pzc b) but strongly dependent positive of pzc c) and pzc itself depends on the electrolyte we ll get to this later

19 if C is dependent on potential, then the γ vs. E parabola will be asymmetric 1062 for example

20 and a flat C d is in no way observed? We need something more sophisticated 1063 H.H. Girault, Analytical and Physical Electrochemistry, EPFL Press, 2004, Figure 5.13

21 and specifically one where the model of the double layer captures these elements? 1064 these Cd s are not constant and there is a minimum in the C d at the pzc H.H. Girault, Analytical and Physical Electrochemistry, EPFL Press, 2004, Figure 5.13

22 1065 Three traditional models for double layer structure: 1) Helmholtz 2) Gouy Chapman (GC) 3) Gouy Chapman Stern (GCS)

23 Models of Electrical Double Layer: ) The Gouy Chapman Model: this model adopts all the same assumptions as for Debye Hückel Theory, which are the following: a) ions are considered to be point charges; their polarizability is neglected b) interactions between ions, and between ions and the electrode are purely electrostatic (i.e., no specific (chemical) adsorption); thus, the IHP and OHP will not exist in this model since these explicitly require finite ion size = polarizability) c) the metal is considered a planar surface with a surface charge density, σ M d) ions are distributed according to Maxwell Boltzmann statistics

24 RECALL: Debye Hückel equation log γ x = 0.51z x 2 I (in water at 25 C) α x I 1067 α = effective diameter of hydrated ion (nm) derivation is long and the main idea is that you balance thermal motion (Boltzmann) with electrostatics (Poisson/Gauss) Physicist & PChemist Physicist & PChemist Peter Joseph William Debye ( ) from Wiki Erich Armand Arthur Joseph Hückel ( )

25 d) ions are distributed according to Maxwell Boltzmann statistics 1068 where e is the elementary charge, and ϕ is the potential relative to the bulk solution ni 0 ni

26 the charge density, i.e. charge per unit volume, ρ(x), is defined as: 1069 so substituting from the last slide and now the Poisson Equation gives us another expression for ρ(x): substituting, we get the Poisson Boltzmann Equation (no Maxwell)

27 if we apply the PB eq to a 1:1 electrolyte, we obtain the following (see B&F, pp ): 1070 and if we further assume that ϕ 0 is small: φ = φ 0 exp κx where here, κ has units of 1/distance. We commonly refer to κ 1 as λ D, the Debye (screening) length characterizing the solution.

28 Does a more sophisticated model of the double layer capture these elements? 1071 how the Gouy Chapman Model views the potential variation near the electrode (compare to Helmholtz ) φ = φ 0 exp κx Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

29 how does the Gouy Chapman Model do in terms of predicting the right C d? 1072 Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

30 About GC Theory we can say the following: a) it predicts a dip in C d, that becomes more capacitive with increased ionic strength = Good! b) but it predicts a Cd that is WAY too high as the potential becomes far from the pzc = Bad!... c) and the C d is symmetrical about the pzc (why?); this is not what is observed experimentally 1073

31 Getting close? 1074 Notably, near the pzc?

32 example. How big is the diffuse layer near our electrode in, say, aqueous 0.1 M NaClO 4 solution? Answer: The diffuse layer thickness is approximated by λ D. Let s calculate it. 1075

33 example. How big is the diffuse layer near our electrode in, say, aqueous 0.1 M NaClO 4 solution? Answer: The diffuse layer thickness is approximated by λ D. Let s calculate it. 1076

34 example. How big is the diffuse layer near our electrode in, say, aqueous 0.1 M NaClO 4 solution? Answer: The diffuse layer thickness is approximated by λ D. Let s calculate it. 1077

35 example. How big is the diffuse layer near our electrode in, say, aqueous 0.1 M NaClO 4 solution? Answer: The diffuse layer thickness is approximated by λ D. Let s calculate it ions ions / m 3

36 example. How big is the diffuse layer near our electrode in, say, aqueous 0.1 M NaClO 4 solution? Answer: The diffuse layer thickness is approximated by λ D. Let s calculate it nm about the same thickness as the compact layer Wow!

37 example. How big is the diffuse layer near our electrode in, say, aqueous 0.1 M NaClO 4 solution? 1080

38 this means that the electrostatic repulsion between charged colloid particles, for example, is very short range at high electrolyte concentrations Suspensions of these particles frequently precipitate Paul Hiemenz, Raj Rajagopalan. Principles of Colloid and Surface Chemistry, Third Edition. Dekker, New York: 1997, p. 514

39 1082 Three traditional models for double layer structure: 1) Helmholtz 2) Gouy Chapman (GC) 3) Gouy Chapman Stern (GCS)

40 Models of Electrical Double Layer: ) The Gouy Chapman Stern Model: basically, the idea is to use both the Helmholtz Model and the Gouy Chapman Model in series: (E) (E)

41 Models of Electrical Double Layer: ) The Gouy Chapman Stern Model: basically, the idea is to use both the Helmholtz Model and the Gouy Chapman Model in series: Parallel plate capacitance of compact layer from (H)elmholtz model (E) NonPP capacitance of (D)iffuse layer from GC model (E) NonPP capacitance of (d)ouble layer from GCS model

42 Models of Electrical Double Layer: ) The Gouy Chapman Stern Model: basically, the idea is to use both the Helmholtz Model and the Gouy Chapman Model in series: Parallel plate capacitance of compact layer from (H)elmholtz model (E) NonPP capacitance of (D)iffuse layer from GC model (E) Wait a minute! This is just one interface with two sides, but there are two capacitors (and thus in total there should be four sides) what gives?

43 Models of Electrical Double Layer: ) The Gouy Chapman Stern Model: basically, the idea is to use both the Helmholtz Model and the Gouy Chapman Model in series: Parallel plate capacitance of compact layer from (H)elmholtz model (E) NonPP capacitance of (D)iffuse layer from GC model (E) Wait a minute! This is just one interface with two sides, but there are two capacitors (and thus in total there should be four sides) what gives? If it barks like a dog, and smells like a dog, then What are the units?

44 Models of Electrical Double Layer: ) The Gouy Chapman Stern Model: basically, the idea is to use both the Helmholtz Model and the Gouy Chapman Model in series: Parallel plate capacitance of compact layer from (H)elmholtz model (E) NonPP capacitance of (D)iffuse layer from GC model (E) Wait a minute! This is just one interface with two sides, but there are two capacitors (and thus in total there should be four sides) what gives? If it barks like a dog, and smells like a dog, then What are the units? This means that the potential drop in the Helmholtz Layer (inside of the OHP) will be linear, and a quasiexponential potential drop will extend from this point and into the bulk solution

45 our three models for the potential distribution near a charged electrode immersed in an electrolyte solution 1088 Helmholtz (H) GouyChapman (GC) Gouy Chapman Stern (GCS)

46 History Physician & Physicist 1089 Physicist Hermann Ludwig Ferdinand von Helmholtz ( ) Physicist PChemist Otto Stern ( ) Nobel Prize (Physics, 1943) Louis Georges Gouy ( ) David Leonard Chapman ( ) from Wiki

47 1090 splice a Helmholtz capacitor to a GC capacitor, right here and then thank Stern! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure

48 the mathematical details are on B&F, pp , but qualitatively, what GCS does is it uses the smaller capacitance of either C H or C D(GC) 1091 C H << C D(GC) C d C H C D(GC) << C H C d C D(GC)

49 what effect does specific adsorption have on the pzc? The answer is hinted at in the data we looked at earlier 1092 Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

50 but to really reveal specific adsorption, one must look carefully at the concentration dependence of the pzc. If there IS one, then specific adsorption is occurring The sign of the shift in pzc is the sign of the ion that is adsorbing for this we define the constant EsinMarkov coefficient for a given σ M (= 0), as follows: pzc 1093 Bockris and Reddy, Plenum Press, 1973, Figure 7.57

51 why a negative shift with anion adsorption? ( ) here, I am indicating excess charges, not all charges E WE pzc (+) + +

52 why a negative shift with anion adsorption? ( ) here, I am indicating excess charges, not all charges 1095 pzc E WE (+) +

53 why a negative shift with anion adsorption? 1096 ( ) E WE pzc (+)

54 at the pzc, q M = 0 and there is no excess positive or negative charge in the solution. ( ) 1097 pzc (+)

55 now, an adsorbing anion is added and a fixed negative charge is added to the solution side of the interface. This new q S is matched by an equal q M on the electrode side. ( ) 1098 image charges + + old pzc (before + Result: We are no longer at the pzc at this potential adsorption) + + (+)

56 a new pzc exists at the potential required to neutralize this charge using charges on both sides of the interface ( ) new pzc old pzc (+)

57 but to really reveal specific adsorption, one must look carefully at the concentration dependence of the pzc. If there IS one, then specific adsorption is occurring pzc 1100 image charges The sign of the shift in pzc is the sign of the ion that is adsorbing for this we define the constant EsinMarkov coefficient for a given σ M (= 0), as follows: specific adsorption Bockris and Reddy, Plenum Press, 1973, Figure 7.57

58 a new pzc exists at the potential required to neutralize this charge using charges on both sides of the interface specific adsorption! 1101 Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

59 what about uncharged adsorbates, like organic molecules? 1102 Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

60 what about uncharged adsorbates, like organic molecules? 1103 Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

61 what about uncharged adsorbates, like organic molecules? 1104 ~25 µf ~5 µf, why Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

62 what about uncharged adsorbates, like organic molecules? 1105 what is the origin of these sharp C d transients? ~25 µf ~5 µf, why Gunk is blocking 80% of surface! Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

63 what about uncharged adsorbates, like organic molecules? 1106 what is the origin of these sharp C d transients? ~25 µf ~5 µf, why Gunk could be redoxactive and whose capacitance is called the chemical, or quantum, capacitance Gunk is blocking 80% of surface! Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure

64 In conclusion, with the GCS Model, we have a semiquantitative understanding of this interface with some predictive power 1107 OHP IHP

65 1108 Q: What was in this set of lectures? A: B&F Chapter 13 main concepts: Section 1.2.3: Diffuse double layer structure Sections 13.1 & 13.2: Gibbs adsorption isotherm; Electrocapillary / Surface excess / Lippmann s equation; Point of Zero Charge Section 13.3: Section 13.5: Models: Helmholtz, Gouy Chapman (Poisson Boltzmann), GC Stern Specific adsorption

66 In conclusion, with the GCS Model, we have a semiquantitative understanding of this interface with some predictive power Now what about this behavior 1109 plus Faradaic chargetransfer kinetics?!?!?! Oh yeah!!! Now we're talking! OHP IHP