1. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 1 Nanostructures & Nanomaterials by Synthesis, Properties and Applications Author : Guozhong Cao Instructor : Prof. Chie Gau

2. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 2 Chapter 2 Physical Chemistry of Solid Surfaces

3. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 3 Percentage of surface atoms changes with cluster diameter

4. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 4 For 1 g of Sodium Chloride, the original 1 g cube is successively divided into smaller cubes.

5. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 5 Due to the vast surface area, all nanostructured materials possess a huge surface energy and, thus are thermodynamically unstable or metastable. 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. Goal: to overcome the surface energy, and to prevent the nanomaterials from growth in size, driven by the reduction of overall surface energy.

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7. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 7 Surface Energy Definition: energy required (or produced) to create a unit area of a new surface, therefore, Definition: energy required (or produced) to create a unit area of a new surface, therefore, γ= (∂G/ ∂A) ni, T, P γ= (∂G/ ∂A) ni, T, P G: Gibs free energy of the surface G: Gibs free energy of the surface A: Surface area of the particles 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. 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. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 8 Surface Energy This energy is defined as surface energy, γ This energy is defined as surface energy, γ γ = N b ερ a /2 (1) γ = N b ερ a /2 (1) N b : number of broken bonds N b : number of broken bonds ε: bond strength ε: bond strength ρ a = number of atoms or molecules per unit surface area density ρ a = 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. The above equation is very crude model and does not account for interactions between higher order neighbors.

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10. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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, 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/a 2 ． 4 ． ε ． 1/2 γ {100} = 2/a 2 ． 4 ． ε ． 1/2 γ {110} = 2/2 0.5 a 2 ． 5 ． ε ． 1/2 γ {110} = 2/2 0.5 a 2 ． 5 ． ε ． 1/2 γ {111} = 2/3 0.5 εa 2 γ {111} = 2/3 0.5 εa 2

11. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 12 Surface energy reduced by Surface relaxation: surface atoms or ions shift inwardly. Surface relaxation: surface atoms or ions shift inwardly. Surface restructuring through combining surface dangling bonds into strained new chemical bonds 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. 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. Composition segregation or impurity enrichment on the surface through solid-state diffusion.

13. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 13 Surface energy reduction by surface relaxation

14. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 14 Surface energy reduction by restructuring The restructured {100} faces have the lowest surface energy among {111}, {110} and {100} faces.

15. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 15 Surface energy reduction by chemical or physical adsorption

16. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 16 Reduction of surface energy for a nanoparticle: One is to reduce the total surface area. That is, surface tends to become spherical. 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. 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.

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18. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 18 Wulff plot: using γ i = Ch i where C is the constant and h i is the perpendicular distance.

19. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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). 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. Kinetic factors (processing or crystal growth conditions) may also prevent formation of facets.

20. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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: 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 T m. Replacing solid-vapor interface by solid-solid interface and becomes polycrystalline. 1. sintering: individual structures merge together which occurs at 70% of T m. 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. 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. 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. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 21 Sintering and Ostwald ripening process

22. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 22 Chemical Potential as a Function of Surface Curvature

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24. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 24 Note From definition of chemicalμ and surface energy γ: From definition of chemicalμ and surface energy γ: Therefore, Therefore,

25. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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. 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. An atom on a convex surface possesses the highest chemical potential, whereas an atom on a concave surface has the lowest chemical potential.

26. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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. 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.

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29. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 29 For the case of ideal gas, integrate Eqn (2.111), one obtains For the case of ideal gas, integrate Eqn (2.111), one obtains μ = μ o + RT ln p/p o μ = μ o + RT ln p/p o Similarly, one obtains solubility Sc Similarly, one obtains solubility Sc μ = μ o + RT ln Sc/Sc o μ = μ o + RT ln Sc/Sc o

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34. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 34 Ostwald Ripening Process

35. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 35 Ostwald Ripening Process Results in Results in 1. abnormal grain growth (in the sintering of polycrystalline materials) which leads to inhomogeneous microstructure and inferior mechanical properties of the products. 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. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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. 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. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 37 Stabilization of Nanoparticles Electrostatic stabilization: kinetically stable Electrostatic stabilization: kinetically stable Steric stabilization: thermodynamically stable Steric stabilization: thermodynamically stable

38. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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: 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. 1. preferential adsorption of ions due to dissolution. 2. dissociation of surface charged species. 2. dissociation of surface charged species. 3. Isomorphic substitution 3. Isomorphic substitution 4. Accumulation or depletion of electrons at the surface. 4. Accumulation or depletion of electrons at the surface. 5. Physical adsorption of charged species onto the surface. 5. Physical adsorption of charged species onto the surface.

39. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 39 Surface charge density Therefore, a electrode potential is established as Nernst eqn Therefore, a electrode potential is established as Nernst eqn E = E o + R g T ． lna i /n i F E = E o + R g T ． lna i /n i F where E o is the standard electrode potential when the concentration of the ions is unity, where E o is the standard electrode potential when the concentration of the ions is unity, n i is the valence state of ions, n i is the valence state of ions, a i is the activity of ions a i is the activity of ions R g is the gas constant R g is the gas constant F is the Faraday’s constant F is the Faraday’s constant

40. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 40 For oxide in water Typical charge determining ions are Typical charge determining ions are protons or hydroxyl groups, their concentrations are described by protons or hydroxyl groups, their concentrations are described by pH (pH = -log [H + ]) 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 (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. When pH>pzc (neutral), OH - is the charge determining ions and the surface is negatively charged.

41. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 41 Counter ions Surface charge determining ions

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43. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 43 A is Hamaker constant

44. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 44 For S/r <<1, Φ A = -Ar/12S For van der Waals attraction between two molecules, Φ A ～ -S -6

45. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 45 Interaction between two particles Φ = Φ A + Φ B Repulsion attraction

46. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 46 Occurance of 2ndary min leads to flocculation. repulsion attraction

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

49. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 49 Steric Stabilization or Polymeric Stabilization It is thermodynamic stabilization method, so that particles are always redispersible. 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. A very high concentration can be accommodated, and the dispersion medium can be completely depleted. It is not electrolyte sensitive. It is not electrolyte sensitive. It is suitable to multiple phase system. It is suitable to multiple phase system.

50. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 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. 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.

51. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 51 Good or Poor Solvent When polymer dissolved in a solvent tends to expand to reduce the overall Gibbs free energy of the system, such a solvent is called good solvent. When polymer dissolved in a solvent tends to expand to reduce the overall Gibbs free energy of the system, such a solvent is called good solvent. When polymer in solvent tends to coil up or collapse to reduce the Gibbs free energy, such a solvent is called poor solvent. When polymer in solvent tends to coil up or collapse to reduce the Gibbs free energy, such a solvent is called poor solvent.

52. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 52 Different Kinds of Polymer Interacting with Solid Wall or (c) non-absorbing polymer or diblock polymer

53. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 53 Interaction between Polymer Layers, Coverage of polymer on the solid surface less than 50%, -- interpenetration of polymer layer -- freedom reduction of polymer -- reduction of entropy -- increase of Gibbs free energy

54. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 54 Interaction between Polymer Layers Coverage of polymer on the solid surface approaching 100%, -- compressed of two polymer layers -- coil up of polymer in both layers -- increase of Coverage of polymer on the solid surface approaching 100%, -- compressed of two polymer layers -- coil up of polymer in both layers -- increase of ΔG. Poor solvent and low coverage, interpenetra- tion leads to further coil up of polymer, decrease in ΔG.

55. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 55 Absorbing Polymer Absorbing Polymer For full coverage, the situation for absorbing polymer is the same as the anchored polymer. For full coverage, the situation for absorbing polymer is the same as the anchored polymer. For a partial coverage, situation for absorbing polymer in good solvent can lead to increase in For a partial coverage, situation for absorbing polymer in good solvent can lead to increase in ΔG, while in poor solvent it can lead to decrease in ΔG for L<H<2L, and lead to increase in ΔG for H<L.

56. Department of Aeronautics and Astronautics NCKU NANO AND MEMS Technology LAB. 56 Mixed Steric and Electric Interactions