Dr ADK MSc Electrochemistry Elective Unit II B.pptx

2020 – 2021/2023-2024 REGULATION �MCH 34 A / DCH 34A/ 23PECH14 A
PART B
UNIT-I: ELECTRICAL DOUBLE LAYER
ELECTRICAL DOUBLE LAYER
Sources of interfacial charge
Electrostatic theory: The electrical double layer
3) Electro-kinetic Phenomena
4) Electrostatic forces

1. ELECTRO CHEMISTRY Dr.A.DINESH KARTHIK ASSOCIATE PROFESSOR &HEAD, RESEARCH SUPERVISOR, P G & RESEARCH DEPT. OF CHEMISTRY SHANMUGA INDUSTRIES ARTS & SCIENCE COLLEGE, TIRUVANNAMALAI-606603 . CELL : 9486887461 [email protected] .

2. UNIT-I: ELECTRICAL DOUBLE LAYER PART B 2020 – 2021/ 2023-2024 REGULATION MCH 34 A / DCH 34A/ 23PECH14 A Dr.A.DINESH KARTHIK ASSOCIATE PROFESSOR &HEAD, RESEARCH SUPERVISOR, P G & RESEARCH DEPT. OF CHEMISTRY SHANMUGA INDUSTRIES ARTS & SCIENCE COLLEGE, TIRUVANNAMALAI-606603 . CELL : 9486887461 [email protected] .

3. Dr.A.DINESH KARTHIK

4. Dr.A.DINESH KARTHIK

5. ELECTRICAL DOUBLE LAYER - The array of charged particles present at the electrode-solution interface - The ionic zones formed in a solution to compensate for the excess of charge on the electrode - A positively charged electrode attracts a layer of negative ions and vice versa - Interface must be neutral Charge on the electrode surface (q c ) = Charge of ions in the nearby solution ( q s ) Dr.A.DINESH KARTHIK

6. ELECTRICAL DOUBLE LAYER IHP OHP Positively Charged Electrode Surface Dr.A.DINESH KARTHIK

7. ELECTRICAL DOUBLE LAYER IHP OHP Compact (Stern) Layer Diffuse (Gouy) Layer Charged Surface Potential is - Constant within electrode - Linear until OHP - Exponential within diffuse layer Dr.A.DINESH KARTHIK

8. ELECTRICAL DOUBLE LAYER The Inner Layer - Known as the Inner Helmholtz Plane (IHP ) - Closest to the electrode surface - Contains solvent molecules and specifically adsorbed ions - The adsorbed ions are those not hydrated in aqueous solution (Br - , I - ) - Cations are less adsorbed because they are usually hydrated Dr.A.DINESH KARTHIK

9. ELECTRICAL DOUBLE LAYER The Outer Layer - Known as the Outer Helmholtz Plane (OHP) - The imaginary plane passing through the center of the solvated ions at their closest approach to the surface Thickness of OHP = half the diameter of solvated counter ion Dr.A.DINESH KARTHIK

10. ELECTRICAL DOUBLE LAYER Compact Layer - Comprises of both IHP and OHP - Known as the Stern Layer - Layer is strongly held by the electrode - Can exist even when electrode is pulled out of solution\ - Thermal motion of ions is not considered Dr.A.DINESH KARTHIK

11. ELECTRICAL DOUBLE LAYER Diffuse Layer - Known as the Gouy Layer ( Gouy -Chapman Layer ) - The three-dimensional layer beyond the OHP - The region of scattered ions (counter ions are more loosely bound ) - Total charge of the compact and diffuse layers equals (but opposite in sign) to the net charge on the electrode side - The thickness of the double layer depends on the ionic strength Dr.A.DINESH KARTHIK

12. Electrostatic Forces & The Electrical Double Layer 1) Sources of interfacial charge Electrostatic theory: The electrical double layer 3) Electro-kinetic Phenomena 4) Electrostatic forces Dr.A.DINESH KARTHIK

13. Charged Interfaces (see P.C. Hiemenz and R. Rajagopalan) Introduction origin and importance of surface charge The electrical double layer Parallel plate capacitor model Debye-Hückel approximation Gouy-Chapman theory Stern model: the inner layer Electrokinetic Theory Zeta Potential mobility (various models) Dr.A.DINESH KARTHIK

14. The electrical double layer Historical milestones The concept electrical double layer Quincke – 1862 Concept of two parallel layers of opposite charges Helmholtz 1879 and Stern 1924 Concept of diffuse layer Gouy 1910; Chapman 1913 Modern model Grahame 1947 Dr.A.DINESH KARTHIK

15. Immersion of some materials in an electrolyte solution. Two mechanisms can operate. (1) Direct Ionization of surface groups. (2) Specific ion adsorption + + + SOURCES OF INTERFACIAL CHARGE O - + H 2 O Dr.A.DINESH KARTHIK

16. (3) Differential ion solubility Some ionic crystals have a slight imbalance in number of lattice cations or anions on surface, eg . AgI, BaSO 4 , CaF 2 , NaCl, KCl (4) Substitution of surface ions eg. lattice substitution in kaolin SURFACE CHARGE GENERATION (cont.) Dr.A.DINESH KARTHIK

17. Hermann Ludwig Ferdinand von Helmholtz 1821-1894 O. Stern Noble prize 1943 Dr.A.DINESH KARTHIK

18. ELECTRICAL DOUBLE LAYERS Helmholtz (100+ years ago) proposed that surface charge is balanced by a layer of oppositely charged ions COUNTER IONS + + + + - - - + - CO IONS OHP - - - - - - - - SOLVENT MOLECULES Ψ x Dr.A.DINESH KARTHIK

19. The electrode-solution interface Electrical double layer Helmholtz layer model  Dr.A.DINESH KARTHIK

20. Gouy-Chapman Model (1910-1913) Assumed Poisson-Boltzmann distribution of ions from surface ions are point charges ions do not interact with each other Assumed that diffuse layer begins at some distance from the surface + + + + + - - - + - Diffusion plane Ψ x - - - - - - - - - Dr.A.DINESH KARTHIK

21. Gouy-Chapman Model This model explains why measurements of the dynamics of electrode processes are almost always done using a large excess of supporting electrolyte. Dr.A.DINESH KARTHIK

22. Gouy -Chapman Theory (1/4) Charge density r (x) is given by Poisson equation Charge density of the solution is obtained summarizing over all species in the solution Ions are distributed in the solution obeying Boltzmann distribution Dr.A.DINESH KARTHIK

23. Gouy -Chapman Theory (2/4) Previous eqs can be combined to yield Poisson-Boltzmann eq The above eq is integrated using an auxiliary variable p Dr.A.DINESH KARTHIK

24. Gouy -Chapman Theory (3/4) Integration constant B is determined using boundary conditions: i ) Symmetry requirement: electrostatic field must vanish at the midplane  d  / d x = ii) electroneutrality : in the bulk charge density must summarize to zero   = Thus x =0  Dr.A.DINESH KARTHIK

25. Gouy -Chapman Theory (4/4) Now it is useful to examine a model system containing only a symmetrical electrolyte The above eq is integrated giving potential on the electrode surface, x = 0 where (5.42) Dr.A.DINESH KARTHIK

26. Gouy -Chapman Theory – potential profile The previous eq becomes more pictorial after linearization of tanh 1:1 electrolyte 2:1 electrolyte 1:2 electrolyte linearized Dr.A.DINESH KARTHIK

27. Gouy -Chapman Theory – surface charge Electrical charge q inside a volume V is given by Gauss law In a one dimensional case electric field strength E penetrating the surface S is zero and thus E . d S is zero except at the surface of the electrode ( x = 0) where it is ( d f/ dx ) dS. Cosequently , double layer charge density is After inserting eq (5.42) for a symmetric electrolyte in the above eq surface charge density of an electrode is Dr.A.DINESH KARTHIK

28. Gouy -Chapman Theory – double layer capacitance (1/2) Capacitance of the diffusion layer is obtained by differentiating the surface charge eq 1:1 electrolyte 2:1 electrolyte 1:2 electrolyte 2:2 electrolyte Dr.A.DINESH KARTHIK

29. Gouy -Chapman Theory – double layer capacitance (1/2) Dr.A.DINESH KARTHIK

30. Inner layer effect on the capacity (1/2) + + + - + + + - + + x = 0 f OHL x = x 2 f ( x 2 ) = f 2 + If the charge density at the inner layer is zero potential profile in the inner layer is linear: x = x 2 f ( x 2 ) = f 2 f ( ) = f x = Dr.A.DINESH KARTHIK

31. Inner layer effect on the capacity (2/2) Surface charge density is obtained from the Gauss law r elative permeability in the inner layer r elative permeability in the bulk solution f 2 is solved from the left hand side eqs and inserted into the right hand side eq and C dl is obtained after differentiating Dr.A.DINESH KARTHIK

32. Surface charge density C dl E C dl,min s m ( E ) C dl ( E ) E pzc Dr.A.DINESH KARTHIK

33. Effect of specific adsorption on the double layer capacitance (1/2) + + + p hase a p hase b x = x = x 2 q d From electrostatistics , continuation of electric field, for a|b phase boundary Specific adsorbed species are described as point charges located at point x 2 . Thus the inner layer is not charged and its potential profile is linear Dr.A.DINESH KARTHIK

34. Effect of specific adsorption on the double layer capacitance (2/2) So the total capacitance is Dr.A.DINESH KARTHIK

35. Stern (1924) / Grahame (1947) Model Gouy/Chapman diffuse double layer and layer of adsorbed charge. Linear decay until the Stern plane. + + + + + Shear Plane Gouy Plane Difusion layer + - - - + - Bulk Solution Stern Plane - - - - - - - - - - - - - - - Ψ x Ψ ζ Dr.A.DINESH KARTHIK

36. Stern (1924) / Grahame (1947) Model In different approaches the linear decay is assumed to be until the shear plane, since there is the barrier where the charges considered static. In this courese however we will assume that the decay is linear until the Stern plane. + + + + + Shear Plane Gouy Plane Difusion layer + - - - + - Bulk Solution OHP - - - - - - - - - - - - - + + Ψ Ψ ζ x Dr.A.DINESH KARTHIK

37. The Stern model of the electrode-solution interface The Helmholtz model overemphasizes the rigidity of the local solution. The Gouy-Chapman model underemphasizes the rigidity of local solution. The improved version is the Stern model. Dr.A.DINESH KARTHIK

38. The electric potential at the interface Outer potential Inner potential Surface potential The potential difference between the points in the bulk metal (i.e. electrode) and the bulk solution is the Galvani potential difference which is the electrode potential discussed in chapter 7. Dr.A.DINESH KARTHIK

39. The origin of the distance-independence of the outer potential Dr.A.DINESH KARTHIK

40. POISSON-BOLTZMANN DISTRIBUTION 1 st Maxwell law (Gauss law): “ The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity ” Electric field is the differential of the electric potential → → → → Combining the two equations we get: Which for one dimension becomes: Assuming Boltzmann ion distribution: Boltzmann ion distribution Definitions E: Electric filed Ψ : Electric potential ρ : Charge density E Q : Energy of the ion x, r : Distance Dr.A.DINESH KARTHIK

41. POISSON-BOLTZMANN DISTRIBUTION Z = electrolyte valence, e = elementary charge (C) n = electrolyte concentration(#/m 3 )  r = dielectric constant of medium  = permittivity of a vacuum (F/m) k = Boltzmann constant (J/K) T = temperature (K) Poisson-Boltzmann distribution describes the EDL Defines potential as a function of distance from a surface ions are point charges ions do not interact with each other Simeon-Denis Poisson 1781-1840 Ludwig Boltzman 1844-1904 Dr.A.DINESH KARTHIK

42. POISSON-BOLTZMANN DISTRIBUTION Debye-Hückel approximation For then: The solution is a simple exponential decay (assuming Ψ (0)= Ψ and Ψ ( ∞ )=0): Debye-Hückel parameter (  ) describes the decay length Dr.A.DINESH KARTHIK

43. DOUBLE LAYER FOR MULTIVALENT ELECTROLYTE: DEBYE LENGTH Debye-Hückel parameter (  ) describes the decay length Z i = electrolyte valence e = elementary charge (C) C i = ion concentration (#/m 3 ) n = number of ions  r = dielectric constant of medium  = permittivity of a vacuum (F/m) k = Boltzmann constant (J/K) T = temperature (K)  -1 (Debye length) has units of length Dr.A.DINESH KARTHIK

44. POISSON-BOLTZMANN DISTRIBUTION Exact Solution For 0.001 M 1-1 electrolyte Surface Potential (mV) Surface Potential (mV) Dr.A.DINESH KARTHIK

45. E l e c t r o l y t e C o n c e n t r a t i o n ( M ) 1 - 5 1 - 4 1 - 3 1 - 2 1 - 1 1 1 1 Debye Length  -1 , (nm) 1 2 3 4 5 6 7 8 9 1 1 - 1 e l e c t r o l y t e 2 - 2 e l e c t r o l y t e 3 - 3 e l e c t r o l y t e DEBYE LENGTH AND VALENCY Ions of higher valence are more effective in screening surface charge. Dr.A.DINESH KARTHIK

46. ZETA POTENTIAL Point of Zero Charge (PZC) - pH at which surface potential = 0 Isoelectric Point (IEP) - pH at which zeta potential = 0 Question : What will happen to a mixed suspension of Alumina and Si 3 N 4 particles in water at pH 4, 7 and 9? Dr.A.DINESH KARTHIK

47. ZETA POTENTIAL -- Effect of Ionic Strength -- p H 1 2 3 4 5 6 7 8 9 1 1 1 Zeta Potential (mV) - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 A l u m i n a Increasing I.S. Dr.A.DINESH KARTHIK

48. Free energy decrease upon adsorption greater than predicted by electrostatics Have the ability to shift the isoelectric point v and reverse zeta potential Multivalent ions: Ca +2 , Mg +2 , La +3 , hexametaphosphate, sodium silicate Self-assembling organic molecules: surfactants, polyelectrolytes SPECIFIC ADSORPTION +2 + - - - - - + + + + + + + + + + + + + Dr.A.DINESH KARTHIK

49. SPECIFIC ADSORPTION Multivalent cations shift IEP to right (calcite supernatant) Multivalent anions shift IEP to left (apatite supernatant) pH Amankonah and Somasundaran, Colloids and Surfaces , 15, 335 (1985). PO 4 3- Ca 2+ Dr.A.DINESH KARTHIK

50. ELECTROKINETIC PHENOMENA Electrophoresis - Movement of particle in a stationary fluid by an applied electric field. Electro-osmosis - Movement of liquid past a surface by an applied electric field Streaming Potential - Creation of an electric field as a liquid moves past a stationary charged surface Sedimentation Potential - Creation of an electric field when a charged particle moves relative to stationary fluid Dr.A.DINESH KARTHIK

51. Electrophoresis -  determined by the rate of diffusion (electrophoretic mobility) of a charged particle in an applied DC electric field. PCS -  determined by diffusion of particles as measured by photon correlation spectroscopy (PCS) in applied field Acoustophoresis -  determined by the potential created by a particle vibrating in its double layer due to an acoustic wave Streaming Potential -  determined by measuring the potential created as a fluid moves past macroscopic surfaces or a porous plug ZETA POTENTIAL MEASUREMENT Dr.A.DINESH KARTHIK

52. ZETA POTENTIAL MEASUREMENT Electrophoresis Smoluchowski Formula (1921) assumed a >> 1  = Debye parameter a = particle radius - electrical double layer thickness much smaller than particle v = velocity,  r = media dielectric constant  = permittivity of free space  = zeta potential, E = electric field  = medium viscosity  E = electrophoretic mobility Dr.A.DINESH KARTHIK

53. ZETA POTENTIAL MEASUREMENT Electrophoresis Henry Formula (1931) expanded for arbitrary a, assumed E field does not alter surface charge - low  v = velocity  r = media dielectric constant  = permittivity of free space  = zeta potential  = medium viscosity E = electric field  E = electrophoretic mobility Hunter, Foundations of Colloid Science, p. 560 Dr.A.DINESH KARTHIK

54. ZETA POTENTIAL MEASUREMENT Streaming Potential  = Debye parameter a = particle radius  = zeta potential  = Potential over capillary (V)  r = media dielectric constant  = permittivity of free space (F/m)  = medium viscosity (Pa·s) K E = solution conductivity (S/m) p = pressure drop across capillary (Pa) Dr.A.DINESH KARTHIK

55. DLVO Theory DLVO – Derjaguin, Landau, Verwey and Overbeek Combined Effects of van der Waals and Electrostatic Forces Based on the sum of van der Waals attractive potential and a screened electrostatic repulsion potential arising between the “double layer potential” screened by ions in solution. The total interaction energy U of the system is: Van der Waals (Attractive force) Electrostatics (Repulsive force) Dr.A.DINESH KARTHIK

56. DLVO Theory A = Hamakar’s constant R = Radius of particle x = Distance of Separation k = Boltzmann’s constant T = Temperature n = bulk ion concentration = Debye parameter z = valency of ion e = Charge of electron Ψ = Surface potential Dr.A.DINESH KARTHIK

57. DLVO Theory For short distances of separation between particles 100 nm Alumina, 0.01 M NaCl,  zeta =-20 mV Dr.A.DINESH KARTHIK

58. Primary Minimum Secondary Minimum Energy Barrier Hard Sphere Repulsion (< 0.5 nm) J/m x (distance) DLVO Theory (Flocculation) (Coagulation) No Salt added Dr.A.DINESH KARTHIK

59. Discussion: Flocculation vs. Coagulation The DLVO theory defines formally (and distinctly), the often inter-used terms flocculation and coagulation Flocculation: Corresponds to the secondary energy minimum at large distances of separation The energy minimum is shallow (weak attractions, 1-2 kT units) Attraction forces may be overcome by simple shaking Coagulation: Corresponds to the primary energy minimum at short distances of separation upon overcoming the energy barrier The energy minimum is deep (strong attractions) Once coagulated, particle separation is almost impossible Dr.A.DINESH KARTHIK

60. Primary Minimum Secondary Minimum Energy Barrier Hard Sphere Repulsion (< 0.5 nm) J/m x (distance) Effect of Salt (Flocculation) (Coagulation) No Salt added Upon Salt addition Addition of salt reduces the energy barrier of repulsion. How? Dr.A.DINESH KARTHIK

61. Secondary Minimum: Real System 100 nm Alumina,  zeta =-30 mV Dr.A.DINESH KARTHIK

62. Discussion on the Effect of Salt The salt reduces the EDL thickness by charge screening Also increases the distance at which secondary minimum occurs (aids flocculation) Reduces the energy barrier (may induce coagulation) Since increased salt concentration decreases  -1 (or decreases electrostatics), at the Critical Salt Concentration U(x) = 0 Dr.A.DINESH KARTHIK

63. Effect of Salt Concentration and Type H: Distance of separation at critical salt concentration At critical salt concentration, H = 1. Upon simplification, we get: Schultz – Hardy Rule: Concentration to induce rapid coagulation varies inversely with charge on cation n: Concentration Z: Valence Dr.A.DINESH KARTHIK

64. For As 2 S 3 sol, KCl: MgCl 2 : AlCl 3 required to induce flocculation and coagulation varies by a simple proportion 1: 0.014: 0.0018 Effect of Salt Concentration and Type The DLVO theory thus explains why alum (AlCl 3 ) and polymers are effective (functionality and cost wise) to induce flocculation and coagulation Dr.A.DINESH KARTHIK

65. pH and Salt Concentration Effect Stability diagram for Si 3 N 4 (M11) particles as produced from calculations (IEP 4.4) assuming 90% probability of coagulation for solid formation. Dispersion Dispersion Agglomerate Dr.A.DINESH KARTHIK

66. REMARKS -- hydrophobic and solvation forces -- Due to the number of fitting parameters ( y , A 132 , spring constant, I.S.) and uncertainty in force laws (C.C. vs C.P., retardation) hydrophobic forces often invoked to explain differences between theory and experiment. Because hydrophobic forces involve the structure of the solvent, the number of molecules to be considered in the interaction is large and computer simulation has only begun to approach this problem. Widely accepted phenomenological models of hydrophobic forces still need to be developed. Dr.A.DINESH KARTHIK

67. Dr.A.DINESH KARTHIK [email protected]