957 Lecture #13 of 18

Transcription

1 Lecture #13 of

2 958 Q: What was in this set of lectures? A: B&F Chapter 2 main concepts: Section 2.1 : Section 2.3: Salt; Activity; Underpotential deposition Transference numbers; Liquid junction potentials Sections 2.2 & 2.4: Donnan potential; Membrane potentials; ph meter; Ion-selective electrodes

3 the breakthrough discovery of Ernö Pretsch (ETH Zürich) orders of magnitude more?!?!?!?! It s real, general, and new, after 91 years! How did he do it? Sokalski,, Pretsch, J. Am. Chem. Soc., 1997, 119, 11347

4 What did Ernö Petsch do? a simple solution replace the inner filling solution of the ISE with a metal ion buffer! 960 Sokalski,, Pretsch, J. Am. Chem. Soc., 1997, 119, 11347

5 What s a metal ion buffer? Well, first of all, what s a ph buffer? 961 HA + H 2 O A + H 3 O + a weak acid a weak base K a = H 3O + H 3 O + HA A = K a HA A make these large lock in [H 3 O + ] at a small value ph = log H 3 O + = pk a + log A HA Henderson Hasselbalch equation

6 Case in point: Phosphate = three equilibria, three buffers 962

7 What s a metal ion buffer? Just like it sounds 963 Y 4 + M n+ [MY](n 4)+ EDTA EDTA metal chelate

8 What s a metal ion buffer? Just like it sounds 964 Y 4 + M n+ [MY](n 4)+ EDTA EDTA metal chelate K MY = MY n 4 + Y 4 M n+ make these large lock in [M n+ ] at a small value

9 What s a metal ion buffer? Just like it sounds 965 Y 4 + M n+ [MY](n 4)+ EDTA EDTA metal chelate K MY = M n+ = MY n 4 + Y 4 M n+ MY n 4 + Y 4 K MY make these large lock in [M n+ ] at a small value pm = log M n+ = pk MY + log Y 4 MY n 4 +

10 buffering occurs AFTER the equivalence point Why? 966 pm no buffering here (started with M n+ in solution) pm = log M n+ = pk MY + log Y 4 MY n 4 +

11 K MY is adjustable based on ph here is data for Ca

12 so, what does a metal ion buffer have to do with an ISE? 968 conventional ISE filling solution, [M n+ ] = 10-4 M leaked M n+, [M n+ ] 10-6 M so you can t detect anything lower than this!

13 so, what does a metal ion buffer have to do with an ISE? 969 conventional ISE with metal ion buffer filling solution, [M n+ ] free = M leaked M n+, [M n+ ] M and so ~10 12 M can be measured

14 the breakthrough discovery of Ernö Pretsch (ETH Zürich) 970 THANK YOU, Ernö! Sokalski,, Pretsch, J. Am. Chem. Soc., 1997, 119, 11347

15 971 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

16 the charge on an electrode, q M, is compensated by the accumulation of oppositely charged ions in solution: q M = q S we want to understand the details of how these metal solution interfaces are structured 972 the bulk solution region is called the quasi-neutral region in semiconductors

17 in polar solvents, all charged surfaces possess a common structure 973 (IHP) (AKA compact, Helmholtz, or Stern layer) anion (e.g. Cl ) q M < 0 specifically adsorbed anion; also called contact adsorption; polarized with δ + near the electrode + water

18 cations have strongly coordinated waters that exchange slowly 974 (OHP) cation (e.g. Na + )

19 the layer of solution extending from the OHP that has a composition perturbed from bulk is called the diffuse layer 975 follows a Poisson Boltzmann distribution

20 the layer of solution extending from the OHP that has a composition perturbed from bulk is called the diffuse layer 976 follows a Poisson Boltzmann distribution Akin to the Debye Hückel equation, which was used to derive activity coefficients based on the ionic strength the main idea was that you balance thermal motion (Boltzmann) with electrostatics (Poisson/Gauss)

21 Notice particularly the following: 1. A layer of oriented water covers the surface its orientation (O or H) is dictated by the charge on the surface 2. Anions shed their primary hydration layers and directly adsorb on the surface. This is called specific adsorption with an exception being F 3. Cations don t do this in general; their primary hydration layers are are too strongly attached (by the ion dipole interaction) to be shed at room temperature. This is an example of nonspecific adsorption with an exception being (CH3)4N + 977

22 the persistence of water molecules within the first hydration layer is illustrated by the exchange rate 978 Girault, Analytical and Physical Electrochemistry, Marcel Dekker, 2004, Figure 3.13

23 the persistence of water molecules within the first hydration layer is illustrated by the exchange rate > I Cl Br Girault, Analytical and Physical Electrochemistry, Marcel Dekker, 2004, Figure 3.13

24 the electrode carries a charge, q M, and a surface change density σ M (σ M = q M /A). The total charge (density) of the system is zero, and so 980 σ M = σ S charge (density) on metal excess charge (density) in solution

25 the electrode carries a charge, q M, and a surface change density σ M (σ M = q M /A). The total charge (density) of the system is zero, and so 981 σ M = σ S q M < 0 q M > 0 Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure 1.2.2

26 now, what is this excess solution stuff? There is a technical name for this. It is called the (Gibbs) Surface Excess, Γ 982 (mol cm -2 ) Bockris and Reddy, Vol. 2, Plenum Publishing, 1977, Figure 7.46

27 now put it all together, and what do we have? 983 where R is in a reference system, and S is in the actual system

28 now put it all together, and what do we have? 984 where R is in a reference system, and S is in the actual system and at constant temperature and constant pressure differential excess free energy γ = G A surface tension

29 now put it all together, and what do we have? 985 where R is in a reference system, and S is in the actual system and at constant temperature and constant pressure total differential

30 now put it all together, and what do we have? 986 and setting the two forms of the differential equal to each other dγ = Γ i d μ i surface i excess = Gibbs Adsorption Isotherm total differential

31 now put it all together, and what do we have? we won t derive it, but the electrocapillary equation follows (pp ) 987 dγ = σ M de + Γ i μ i i the surface tension (units: energy/area, typically J m -2 or N m -1 these are identical) γ = G A

32 now put it all together, and what do we have? we won t derive it, but the electrocapillary equation follows (pp ) 988 dγ = σ M de + Γ i μ i i the surface excess concentration of species i (units: moles/area), and sometimes called the Gibbs surface excess

33 now put it all together, and what do we have? we won t derive it, but the electrocapillary equation follows (pp ) 989 dγ = σ M de + Γ i μ i i the chemical potential of species i Where is the electric potential term?

34 now put it all together, and what do we have? we won t derive it, but the electrocapillary equation follows (pp ) 990 dγ = σ M de + Γ i μ i i the change in potential between the WE and the RE

35 now put it all together, and what do we have? we won t derive it, but the electrocapillary equation follows (pp ) 991 dγ = σ M de + Γ i μ i so measurement of the surface tension of the electrode as a function of its potential is a direct way to get at its surface charge (density), σ M. This is called Lippmann's Equation: We want to know this i σ M = dγ de μi

36 now put it all together, and what do we have? we won t derive it, but the electrocapillary equation follows (pp ) 992 dγ = σ M de + Γ i μ i so measurement of the surface tension of the electrode as a function of its potential is a direct way to get at its surface charge (density), σ M. This is called Lippmann's Equation: We want to know this or better yet, q M or better yet, q S σ M = dγ de i μi

37 now put it all together, and what do we have? we won t derive it, but the electrocapillary equation follows (pp ) 993 dγ = σ M de + Γ i μ i so measurement of the surface tension of the electrode as a function of its potential is a direct way to get at its surface charge (density), σ M. This is called Lippmann's Equation: i σ M = We want to know this or better yet, q M or better yet, q S it s all the same dγ de Key Point: Measuring γ is easy if the electrode is a liquid μi

38 thus, our window into double layer structure is the dropping mercury electrode (DME) Seriously! 994 m = mass flow rate (kg/s) 2rc Hg where the drop is largest when F γ = F g (recall that γ has units of N m -1 ) acceleration due to gravity

39 now, in a dropping mercury electrode, as the name implies glass 995 Hg

40 now, in a dropping mercury electrode, as the name implies glass 996 Hg

41 now, in a dropping mercury electrode, as the name implies glass 997 Hg

42 what do we measure during this process? glass 998 Hg r = 1 mm suppose the electrode is at a potential where σ M = q M /A = 25 µc/cm 2 what is the surface charge, q M?

43 what do we measure during this process? glass 999 Hg r = 2 mm

44 what happens as the electrode grows? glass 1000 Hg r = 2 mm so even though the potential is constant, and even though there is no Faradaic electrochemistry going on, the Hg droplet grows, and current flows to its surface and this current is proportional to q M

45 what happens as the electrode grows? glass 1001 Hg after it falls, off, the current drops to a small value and then the process repeats

46 okay, so let s do an experiment scan the potential (E) while we measure the current in 0.1 M HCl 1002 Question: Why do the current oscillations stop at -0.60V? t max Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure 7.1.5

47 okay, so let s do an experiment scan the potential (E) while we measure the current in 0.1 M HCl 1003 the potential at the point of zero charge (pzc) t max Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure 7.1.5

48 okay, so let s do an experiment scan the potential (E) while we measure the current in 0.1 M HCl 1004 notice also that the phase of the current oscillation inverts as E crosses the PZC Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure 7.1.5

49 a linear scan voltammogram acquired with a DME (and therefore called a polarogram) DMEs are "self-cleaning" 1005 CrO e - + 4H 2 O Cr(OH) 3 + 5OH - il

50 look familiar? It s just this: 1006

51 okay, now going back to the case of 0.10 M HCl, let s measure the drop time, tmax, as a function of potential 1007 the potential at the point of zero charge (pzc) t max Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure 7.1.5

52 take the tmax versus E data, plot it up, and voila 1008 clearly proportional to γ and recall σ M = dγ de μi

53 take the tmax versus E data, plot it up, and voila σ M = dγ de μi = pzc

54 take the tmax versus E data, plot it up, and voila σ M = dγ de μi = 0 Why is the surface tension largest when the surface charge is smallest? 1010 pzc

55 take the tmax versus E data, plot it up, and voila σ M = dγ de μi = 0 Why is the surface tension largest when the surface charge is smallest? 1011 pzc because the cohesive forces between solvent molecules is large but like charges repel!

56 okay, what can we do with this information? Well, a plot of charge (q) versus potential (E) has a slope of What? 1012

57 okay, what can we do with this information? Well, a plot of charge (q) versus potential (E) has a slope of the capacitance (C): 1013 but this is the integral / total capacitance the capacitance that applies for a given applied potential versus the pzc. For a real capacitor, C is virtually E-independent, but that may not be (and in fact, is not) true for an electrical double layer. In anticipation of this, let s define a differential capacitance (C d ), which is the correct term to use, as follows: C d = σm E = 2 γ E 2 μ i

58 Let s compare total capacitance (C) and differential capacitance (C d ) as follows: 1014 E z = pzc

59 if we can measure γ, we can determine σ M and if we can determine σ M, we can determine C and all of this only works for liquid electrodes 1015 σ M = dγ de μi

60 if we can measure γ, we can determine σ M and if we can determine σ M, we can determine C and all of this only works for liquid electrodes 1016 σ M = dγ de μi ASIDE: You can find the pzc of a solid electrode using the capacitance

61 here s what the C vs. E data actually look like as a function of concentration, for KF 1017 H.H. Girault, Analytical and Physical Electrochemistry, EPFL Press, 2004, Figure 5.13

62 data for NaF from B&F is qualitatively similar 1018 Flat? Eh. Why were both of these measured using fluoride salts? Grahame, Chem. Rev., 1947, 41, 441

63 data for NaF from B&F is qualitatively similar 1019 Flat? Eh. Why were both of these measured using fluoride salts? In order to minimize specific adsorption! Grahame, Chem. Rev., 1947, 41, 441

64 1020 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 quasi-constant at potentials well positive and well negative of the pzc. c) This quasi-constant 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.

65 do you want to understand the details of C d away from the pzc? Do you want to understand the hump? There is a book for that 1021 John Bockris Bockris, J. Chem. Educ., 1983, 60, 265

66 1022 Three traditional models for double layer structure: 1) Helmholtz 2) Gouy Chapman (GC) 3) Gouy Chapman Stern (GCS)

67 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

68 so the Helmholtz model says: Hey, the electrical double layer acts like a parallel plate capacitor 1024 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?

69 recall, here s what the double layer really looks like 1025

70 and here s what the double layer looks like, in the Helmholtz approximation 1026

71 and here s what the double layer looks like, in the Helmholtz approximation 1027 now, what s ε r? 4Å = 0.4 x 10-9 m

72 first, what s ε r for water? Well, that depends can it rotate? 1028 for water at 20 o C

73 first, what s ε r for water? Well, that depends can it rotate? 1029 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

74 and here s what the double layer looks like, in the Helmholtz approximation 1030 Answer: ε r 78 (static relative permittivity) 4Å = 0.4 x 10-9 m

75 and here s what the double layer looks like, in the Helmholtz approximation 1031 Is this what is observed? OK, now what? 4Å = 0.4 x 10-9 m

76 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!

77 if the Helmholtz model is correct, we d get this exactly: 1033 σ M = dγ de μi

78 here are electrocapillary data for various electrolytes. Hey, you can already see that the Helmholtz Model fails mostly on the left 1034