Nanostructures & Nanomaterials by Synthesis, Properties and Applications

1. Nanostructures & Nanomaterials by Synthesis, Properties and Applications Author : Guozhong Cao Instructor : Prof. Chie Gau

2. Chapter 2Physical Chemistry of Solid Surfaces

3. Percentage of surface atoms changes with cluster diameter

4. For 1 g of Sodium Chloride, the original 1 g cube is successively divided into smaller cubes.

5. Due to the vast surface area, all nanostructured materials possess a huge surface energy and, thus are thermodynamically unstable or metastable. • Goal: to overcome the surface energy, and to prevent the nanomaterials from growth in size, driven by the reduction of overall surface energy.

7. Surface Energy • Definition: energy required (or produced) to create a unit area of a new surface, therefore, γ= (∂G/ ∂A)ni, T, P • G: Gibs free energy of the surface • A: Surface area of the particles • Surface area can be increased by cutting a particle into two halves. The molecules of the newly created surface possess fewer nearest neighbors or coordination numbers, and thus have dangling or unsatisfied bonds. Due to the dangling bonds on the surface, surface atoms or molecules are under an inwardly directed force and the bond distance between molecules and the sub-surface molecules becomes smaller. An extra force or energy is required to pull the surface to its original positions.

8. Surface Energy This energy is defined as surface energy, γ • γ = Nbερa /2 (1) • Nb: number of broken bonds • ε: bond strength • ρa = number of atoms or molecules per unit surface area density • The above equation is very crude model and does not account for interactions between higher order neighbors.

10. Surface Energy • For FCC structure with lattice constant a, each atom will have a coordination number 12, and each atom on the surface {100} has 4 broken bonds, on {110} 5 broken bonds and on {111} 3 broken bonds. Therefore, • γ{100} = 2/a2．4．ε．1/2 • γ{110} = 2/20.5a2．5．ε．1/2 • γ{111} = 2/30.5εa2

11. According to Eqn (1), the lower Miller index facets have low surface energy. System is stable only when it is in a state with the lowest Gibbs free energy. Therefore, a crystal is often surrounded by low index surfaces.

12. Surface energy reduced by • Surface relaxation: surface atoms or ions shift inwardly. • Surface restructuring through combining surface dangling bonds into strained new chemical bonds • Surface adsorption through chemical or physical adsorption of terminal chemical species by forming chemical bonds or weak attraction forces such as electrostatic or van der Waals forces. • Composition segregation or impurity enrichment on the surface through solid-state diffusion.

13. Surface energy reduction by surface relaxation

14. Surface energy reduction by restructuring The restructured {100} faces have the lowest surface energy among {111}, {110} and {100} faces.

15. Surface energy reduction by chemical or physical adsorption

16. Reduction of surface energy for a nanoparticle: • One is to reduce the total surface area. That is, surface tends to become spherical. • For crystalline particle, facets forms because they have smaller surface energy than a spherical surface does. Since facets with a lower Miller Index have a lower surface energy than that with a higher Miller Index. Therefore, crystal is often surrounded by low index surfaces.

18. Wulff plot: using γi = Chi where C is the constant and hi is the perpendicular distance.

19. Crystal Grown with Nonfacets • At certain high temperature, the equilibrium crystal surfaces may not be smooth, and difference in surface energy of various crystal facets may disappear. Such a transition is called surface roughening or roughening transition. Most nanoparticles grown at elevated temperature are spherical in shape (not facets). • Kinetic factors (processing or crystal growth conditions) may also prevent formation of facets.

20. Mechanisms for reduction of overall surface energy • Combining individual nanostructures together to form large structures so as to reduce the overall surface area, which includes: • 1. sintering: individual structures merge together which occurs at 70% of Tm. Replacing solid-vapor interface by solid-solid interface and becomes polycrystalline. • 2. Ostwald ripening: A large one grows at the expense of the smaller one until the latter disappears completely, and becomes a single crystal. It occurs at relatively low temperature. • Agglomeration of individual nanostructures through chemical bonds and physical attraction forces at interfaces without altering the individual nanostructures. The smaller the particles, the greater the bonding forces are.

21. Sintering and Ostwald ripening process

22. Chemical Potential as a Function of Surface Curvature

24. Note • From definition of chemicalμ and surface energy γ: • Therefore,

25. Conclusions • For a convex surface, the curvature is positive, and thus the chemical potential of an atom on such a surface is higher than that on a flat surface. • An atom on a convex surface possesses the highest chemical potential, whereas an atom on a concave surface has the lowest chemical potential.

26. Definition of Chemical Potential • The difference of chemical potential may be regarded as the cause of a chemical reaction or of the tendency of a substance to diffuse from one phase into another. The chemical potential is thus a kind of chemical pressure and is an intensive property of system.

29. For the case of ideal gas, integrate Eqn (2.111), one obtains μ = μo + RT ln p/po Similarly, one obtains solubility Sc μ = μo + RT ln Sc/Sco

34. Ostwald Ripening Process

35. Ostwald Ripening Process • Results in 1. abnormal grain growth (in the sintering of polycrystalline materials) which leads to inhomogeneous microstructure and inferior mechanical properties of the products. 2. Eliminating smaller particles and the size distribution becomes narrower during growth of nanoparticles.

36. Triggering and Stopping of Ostwald Ripening Process • Ostwald ripening process can be triggered after initial nucleation and subsequent growth by raising the temperature. That is, the concentration of solid in solvent falls below the equilibrium solubility of small nanoparticles, and the small ones dissolve into the solvent. Once a nanoparticle starts to dissolve into the solvent, the dissolution process never stops until the nanoparticle is dissolved completely. The large particles will grow until the concentration of solid in the solvent equals the equilibrium solubility of these large nanoparticles.

37. Stabilization of Nanoparticles • Electrostatic stabilization: kinetically stable • Steric stabilization: thermodynamically stable

38. Electrostatic Stabilization-surface charge density • When a solid emerges in a polar solvent or an electrolyte solution, a surface charge will be developed due to: • 1. preferential adsorption of ions due to dissolution. • 2. dissociation of surface charged species. • 3. Isomorphic substitution • 4. Accumulation or depletion of electrons at the surface. • 5. Physical adsorption of charged species onto the surface.

39. Surface charge density • Therefore, a electrode potential is established as Nernst eqn E = Eo + RgT．lnai/niF where Eo is the standard electrode potential when the concentration of the ions is unity, ni is the valence state of ions, ai is the activity of ions Rg is the gas constant F is the Faraday’s constant

40. For oxide in water • Typical charge determining ions are protons or hydroxyl groups, their concentrations are described by pH (pH = -log [H+]) When pH<pzc (corresponds to a neutral surface), H+ is the charge determining ions and the surface is positively charged. When pH>pzc (neutral), OH- is the charge determining ions and the surface is negatively charged.

41. Counter ions Surface charge determining ions

43. A is Hamaker constant

44. For S/r <<1, ΦA = -Ar/12S For van der Waals attraction between two molecules, ΦA～ -S-6

45. Interaction between two particles Φ = ΦA + ΦB Repulsion attraction

46. repulsion Occurance of 2ndary min leads to flocculation. attraction

48. Limitations of the electrostatic stabilization • Electrostatic stabilization is a kinetic stabilization method. • It is only applicable to dilute system. • It is almost not possible to redisperse the agglomerated particles • It is difficult to apply to multiple phase systems, since in a given condition, different solids develop different surface charge and electric potential.

49. Steric Stabilization or Polymeric Stabilization • It is thermodynamic stabilization method, so that particles are always redispersible. • A very high concentration can be accommodated, and the dispersion medium can be completely depleted. • It is not electrolyte sensitive. • It is suitable to multiple phase system.

50. Polymeric Stabilization Leads to Monosized nanoparticles • Polymeric stabilization leads to narrow size distribution. Polymer layer absorbed on the surface of nanoparticles serves as a diffusion barrier to the growth species, resulting in a diffusion limited growth. Diffusion limited growth would reduce the size distribution of the initial nuclei, leading to monosized nanoparticles.