8. Fundamentals of Charged Surfaces

1. 8. Fundamentals of Charged Surfaces

2. Moving the reagents Quickly and with Little energy Diffusion electric fields

3. + + + + Yo Y*o Charged Surface 1. Cations distributed thermally with respect to potential 2. Cations shield surface and reduce the effective surface potential X=0

4. + + + + + + + + + Yo Y*o Charged Surface Y**o Y***o X=0 * ** dx *** dx dx

5. Simeon-Denis Poisson 1781-1840 Surface Potentials Cation distribution has to account for all species, i Poisson-Boltzman equation Charge near electrode depends upon potential and is integrated over distance from surface - affects the effective surface potential Dielectric constant of solution Permitivity of free space

6. Solution to the Poisson-Boltzman equation can be simple if the initial surface potential is small: Potential decays from the surface potential exponentially with distance

7. Largest term Let Then:

8. General Solution of: Because Y goes to zero as x goes to infinity B must be zero Because Y goes to Y0 as x goes to zero (e0 =1) A must be Y0 thus

9. Potential decays from the surface potential exponentially with distance When k=1/x or x=1/k then The DEBYE LENGTH x=1/k

10. + + + + + + + + + Petrus Josephus Wilhelmus Debye 1844-1966 Yo What is k? Charged Surface Y=0.36 Yo X=1/k X=0

11. Debye Length Does not belong =1/cm Units are 1/cm

12. Debye Length Units are 1/cm

13. Simeon-Denis Poisson 1781-1840 Ludwig Boltzman 1844-1904 In the event we can not use a series approximation to solve the Poisson-Boltzman equation we get the following: Check as Compared to tanh By Bard

14. Set up excel sheet ot have them calc effect Of kappa on the decay

15. Example Problem A 10 mV perturbation is applied to an electrode surface bathed in 0.01 M NaCl. What potential does the outer edge of a Ru(bpy)33+ molecule feel? Debye length, x? Units are 1/cm Since the potential applied (10 mV) is less than 50 can use the simplified equation.

16. Radius of Ru The potential the Ru(bpy)33+ compound experiences is less than the 10 mV applied. This will affect the rate of the electron transfer event from the electrode to the molecule.

17. Surface Charge Density The surface charge distance is the integration over all the charge lined up at the surface of the electrode The full solution to this equation is: C is in mol/L

18. Yo + + + + + + + + + Charged Surface Y=0.36 Yo d X=1/k X=0 Can be modeled as a capacitor: d differential

19. For the full equation d d At 25oC, water Differential capacitance Ends with units of uF/cm2 Conc. Is in mol/L

21. Can be simplified if Specific Capacitance is the differential space charge per unit area/potential Specific Capacitance Independent of potential For small potentials

22. Flat in this region Gouy-Chapman Model

23. Henrik Jensen,David J. FermnandHubert H. Girault* Received 16th February 2001 , Accepted 3rd April 2001 Published on the Web 17th May 2001 Real differential capacitance plots appear to roll off instead of Steadily increasing with increased potential

24. + + + + + + + + + O. Stern Noble prize 1943 Hermann Ludwig Ferdinand von Helmholtz 1821-1894 Yo Linear drop in potential first in the Helmholtz or Stern specifically adsorbed layer Exponential in the thermally equilibrated or diffuse layer Charged Surface X=0 x2 Cdiffuse CHelmholtz or Stern

25. Capacitors in series Wrong should be x distance of stern layer

26. For large applied potentials and/or for large salt concentrations 1. ions become compressed near the electrode surface to create a “Helmholtz” layer. 2. Need to consider the diffuse layer as beginning at the Helmholtz edge Capacitance Due to Helmholtz layer Capacitance due to diffuse layer

27. Deviation Is dependent upon The salt conc. The larger the “dip” For the lower The salt conc.

28. Create an excel problem And ask students to determine the smallest Amount of effect of an adsorbed layer

29. Experimental data does not Correspond that well to the Diffuse double layer double capacitor model (Bard and Faulkner 2nd Ed)

30. Siv K. SiandAndrew A. Gewirth* Fig. 5 Capacitance�potential curve for the Au(111)/25 mM KI in DMSO interface with time. Received 8th February 2001 , Accepted 20th April 2001 Published on the Web 1st June 2001 Model needs to be altered to account For the drop with large potentials

31. This curve is pretty similar to predictions except where specific Adsorption effects are noted

33. Graphs of these types were (and are) strong evidence of the Adsorption of ions at the surface of electrodes. Get a refernce or two of deLevie here

34. + + + + + + + + + Introducing the Zeta Potential Imagine a flowing solution along this charged surface. Some of the charge will be carried away with the flowing solution. Yo Charged Surface

35. + + + + + + + + + Introducing the Zeta Potential, given the symbo lz Yo Shear Plane Flowing solution Charged Surface Sometimes assumed zeta corresponds to Debye Length, but Not necessarily true Yzeta

36. The zeta potential is dependent upon how the electrolyte concentration compresses the double layer. a, b are constants and sigma is the surface charge density.

37. Shear Plane can be talked about in two contexts + + + + + + + + + + + + + + + + + + + + + Yo Shear Plane Charged Surface In either case if we “push” the solution along a plane we end up with charge separation which leads to potential Shear Plane Particle in motion

38. Streaming Potentials From the picture on preceding slide, if we shove the solution Away from the charged surface a charge separation develops = potential

39. Sample problem here

40. Reiger- streaming potential apparatus. Can also make measurements on blood capillaries

42. In the same way, we can apply a potential and move ions and solution Anode Yo Jm Charged Surface Vapp + + + + + + + + + + Jo Jm X=0 Cathode

43. Movement of a charged ion in an electric field Electrophoretic mobility The force from friction is equal to the electric driving force The frictional drag comes about because the migrating ion’s atmosphere is moving in the opposite direction, dragging solvent with it, the drag is related to the ion atmosphere

44. Drag Force Electric Force Direction of Movement Ion accelerates in electric field until the electric force is equal and opposite to the drag force = terminal velocity

45. At terminal velocity The mobility is the velocity normalized for the electric field:

46. Sir George Gabriel Stokes 1819-1903 Stokes-Einstein equation r = hydrodynamic radius (Stokes Law) Typical values of the electrophoretic mobility are small ions 5x10-8 m2V-1s-1 proteins 0.1-1x10-8 m2V-1s-1 Reiger p. 97

47. Insert a sample calculation

48. When particles are smaller than the Debye length you get The following limit: Remember: velocity is mobility x electric field Reiger p. 98

49. What controls the hydrodynamic radius? - the shear plane and ions around it Compare the two equations for electrophoretic mobility Where f is a shape term which is 2/3 for spherical particles

50. Relation of electrophoretic mobility to diffusion Thermal “force”