Atomic Structure and Cohesion

Size: px

Start display at page:

Download "Atomic Structure and Cohesion"

Felix Mills
5 years ago
Views:

1 Nanotechnology for engineers Winter semester Atomic Structure and Cohesion Chemical bonds Absorption and adsorption of particles on a surface Microscopic and Macroscopic Van der Waals (VdW) forces Wetting Self-assembled monolayer (SAM) Nanotechnology for engineers Winter semester Chemical bond - From atomic orbitals (AO) to molecular orbitals (MO) - From covalent bond to ionic bond 1

2 Molecules why? Energy Geometry Symmetry Probability A system minimizes its total free energy Pairing electrons filling shells (Schrödinger equation) Atoms orient in simple geometries, tetrahedron, octahedron, cubes, icosahedron, etc. As more symmetry elements as more stable will be the system (Group theory) The more different distributions of electrons exist in a molecule the higher is its stability (Statistical thermodynamics) (resonance structures aromats) Wave mechanics quantum number, relations, and their physical meaning The quantum mechanical model needs 4 quantum numbers to describe atomic structure principle quantum number n = 1, 2, 3, angular momentum quantum number l = 0, 1,, n-1 magnetic quantum number m l = l,l-1,,0,,-l+1,-l sp + spin quantum number for electrons (not obtained by theory) Physical properties are related to quantum numbers: E n me = 8πε 4 e h 1 2 n L = ll ( +1) h Lz = m h Energy Eigenvalue Orbital angular momentum Magnetic quantum number 2

Principle: e - s are added to atoms into

available - Pauli s Exclusion Principle:

3 Solutions of the Schrödinger equation : the orbitals Electronic structure of polyelectronic atoms - Aufbau Principle: e - s are added to atoms into the lowest energy level & sub-level available - Pauli s Exclusion Principle: no 2 e - in the same atom may have the same set of 4 quantum numbers - Hund s First Rule: as e - s fill a multiple orbital sublevel, one e - goes to each orbital with parallel spin until the sublevel is half filled. Then they pair up. E 3

Linear Combination of Atomic Orbitals (LCAO) Rules for orbital combinations Rules

functions 2 large overlap integral S 3 ϕ a and ϕ b must have identical symmetry

function) S > 0 S < 0 Application of LCAO MO model on light diatomic http://www.

4 Linear Combination of Atomic Orbitals (LCAO) Rules for orbital combinations Rules for covalent bonds: 1 close values of the corresponding energies of the wave functions 2 large overlap integral S 3 ϕ a and ϕ b must have identical symmetry along bond axis Orbital combinations (different colors for different sign of wave function) S > 0 S < 0 Application of LCAO MO model on light diatomic try/chang7/esp/folder_structure/bo/m 1/s2/assets/real/bom1s2_2.rm 4

5 Application of LCAO MO model on light diatomic Light absorption/emission of simple diatomic molecules (H 2 ) Overlap integral S of hydrogen molecule: 0.68 Biggest known value for S E Lowest Unoccupied Molecular Orbital (LUMO) σ AO Highest Occupied Molecular Orbital (HOMO) hν MO σ AO Light absorption / emission in a gaseous molecule 5

function) Application of LCAO MO model on light diatomics energies and graph S has generally values of about 0.

6 Application of LCAO MO model on light diatomics - higher orbitals S > 0 S = 0 S < 0 s - s σ g σ u s - p z z z z p z -p z z z p x -p x z z p y -p y p x -p y z Orbital combinations (different colors for different sign of wave function) Application of LCAO MO model on light diatomics energies and graph S has generally values of about 0.25 σ g and σ u of the oxygen 1s orbitals result in an S of 10-5 The reason is the strong contraction of the s-orbitals 6

7 MO diagram of O 2 and related gases LUMO HOMO LUMO HOMO Bond order, bond distance, and dissociation energy for diatomics Definition of bond order: BO = 1/2( N# of e - in bonding orbital N# of e - in anti-bonding orbitals) H 2 + H 2 He 2 + He 2 BO R [pm] D e [ev] Li 2 Be 2 B 2 C 2 N 2 + N 2 O 2 + O 2 O 2 - O 2 2- F 2 Ne 2 BO R [pm] D e [ev]

adsorption of particles on a surface - Physisorption and

8 From covalent band to ionic bond Nanotechnology for engineers Winter semester Absorption and adsorption of particles on a surface - Physisorption and chimisorption - Isotherm of Langmuir - Example: water on silica surface 8

9 Mie Potential : a r b r () = + m n Ur Absorption and adsorption physisorption attraction repulsion Energie (kj/mol) (for Lennard-Jones potential: m=6, n=12) Enthalpy of physisorption: H P r o Distance r (Å) Répulsion Attraction Lennard-Jones H P : H P is negative (exothermic process) l H P l < 20 kj / mol Similar to the enthalpy of liquefaction Equilibrium distance: R e : 4-6 Å Absorption and adsorption chimisorption U(r) Enthalpy of chimisorption: H c is negative (exothermic process) - l H c l > 100 kj / mol - can be estimated theoretically Equilibrium distance: R e < 3 Å Hc r - Model of covalent bond (ex- H 2 +metal) - Model of ionic bond (ex- Na on W) 9

10 Physisorption and chimisorption comparison Orogin of interaction Enthalpy Equilibrium distance N# of adsorbed layers Specific Dependance on the temperature Physisorption Van der Waals bonds (no common molecular orbitals) Exothermic l H p l < 20 kj/mol 4 to 6 Å (long range interaction) > 1 Non-specific High close to boiling point Chimisorption Chemical bonds (common electronic orbitals) Exothermic l H c l>100 kj/mol < 3 Å (short range interaction, formation of moleculars) 1 Specific Depend on the activation energy U(r) Physisorption and chimisorption comparison Quantity of absorped gas Chimisorption Chimisorption Physisorption E act Physisorption Hp r Temperature of the solid Hc r ep The physical absorption happens before the chemical adsorption usually. E act is the necessary activation energy for the chemical adsorption. r ec Depending on the relative positions of the 2 curves, the process can be either activated or not. 10

11 Experimental studies on the adsorption process, isotherm of adsorption Important: - The quantity of the adsorbed gas - The nature of adsorption (physical or chemical) - Adsorption enthalpy - The type of chemical bonds (ionic, covalent, etc ) quantity of adsorbed gas An isotherm of adsorption gives the quantity of gas adsorbed as a fonction of its pressure at a fixed temperature Pressure of gas Isotherm of Langmuir (1916) Isotherm of Langmuir: -1 st developed theory - valid for the chemical adsorption and physical absorption at the same time - based on a kinetic and thermodynamic approach Hypothesis: 1- Surface is a uniform array of adsorption sites 2- Monolayer adsorption 3- No interaction between species on adjacent sites (i.e., random occupancy) 11

12 Demonstration of the isotherm of Langmuir Γ: occupation ratio of the surface, P: pressure of the gas Adsorption rate: vads= kads P (1 Γ) Desorption rate: v des = kdes Γ Equilibrium: v des = v ads We pose: G 1 k b = k ads des b P Γ= 1 + b P P Langmuir equation With a combination of the kinetic theory of gas, we can obtain: H b α exp[ ] RT - b increases when l Hl increases - b depends exponentiellement on the temperature Γ=0.3 12

Knözinger, in «The Hydrogen Bond, recent developments in theory and experiments», Eds. P.

13 Example: water adsorbed on a silica surface SiO air SiO H SiO H... H O 2 2 T T, hum., p T Geminal silica surface silanol sites and vicinal Energies H 2nd - nth layer = 44 kj/mol H 1st layer = 25 kj/mol H. Knözinger, in «The Hydrogen Bond, recent developments in theory and experiments», Eds. P. Schuster, North-Holland 1976, Chapter 27 Example: water adsorbed on a silica surface Absorption spectra of water over SiO 2 Free silanol group: 3750 cm -1 Lower energies : water with hydrogen bonds H. Knözinger, in «The Hydrogen Bond, recent developments in theory and experiments», Eds. P. Schuster, North-Holland 1976, Chapter 27 13

14 Nanotechnology for engineers Winter semester Microscopic and Macroscopic Van der Waals (VdW) Forces - Microscopic VdW forces: London dispersion, Debye induction and Keesom orientation - Example of dipole-dipole interaction: hydrogen bond - Macroscopic VdW forces and Hamaker constant Microscopic VdW forces The Van der Waals force is composed of 3 different forces: London dispersion: induced dipole induced dipole Debye induction: dipole induced dipole Keesom orientation: dipole - dipole Israelachvili, page: 60, 75,83 14

15 Microscopic VdW forces London dispersion London dispersion forces: induced dipole induced dipole interaction -Main contribution in the Van der Waals forces -Interaction distance: 2 Ǻ until 10 nm The dispersion force stands for the electronic interaction between the atoms or molecules. e- Be e- e- e- Neutral dipole moment e- - e- Be + e- e- At certain time - charged Induced dipole induced dipole interaction Israelachvili, page: 60, 75,83 Microscopic VdW forces Debye induction Debye forces: dipole induced dipole interaction between a permanent dipole and a polarizable molecule. - + dipole - + rotation Averaged value with time = Angular average of the induced dipole moment is 0 Electric field Induced dipole Israelachvili, page: 60, 75,83 15

16 Microscopic VdW forces Keesom orientation Keesom forces: dipole dipole interaction between a permanent dipole and a polarizable molecule - + dipole - + rotation Averaged value with time = Angular average of the induced dipole moment is 0 Electric field permanent dipole Example of dipole-dipole interaction: hydrogen bond Hydrogen-bonding: a special type of dipole-dipole interaction in which a hydrogen atom bonded to a highly electronegative atom with lone pair electrons interacts with another electronegative atom with lone pair electrons. Hydrogen bonding occurs when hydrogen is attached to N, O, and F, because 1) N, O, and F are electronegative enough to polarize the covalent bond with H 2) Lone pair electrons on N, O, and F can come in close contact with an adjacent H. H H O H H O H H O 16

Macroscopic VdW forces When applied to large

integrated over the volume of the bodies.

Number density of molécules in sphere D C = Force

interaction energy W(D) and interaction force

Interaction energies for some simple geometries:

17 Macroscopic VdW forces When applied to large bodies the van der Waal s potential must be integrated over the volume of the bodies. R 2 2 π Cρ R WD ( ) = 6D Hamaker constant A ρ = Number density of molécules in sphere D C = Force constant (attractive) Relation between the interaction energy W(D) and interaction force F(D): WD ( ) FD ( ) = D Macroscopic VdW forces Interaction energies for some simple geometries: 2 spheres 2 surfaces 2 cylinders Sphere - surface 2 perpendicular cylinders 17

18 Macroscopic VdW forces Some values Material Hamaker constant [10-20 J] PTFE 3.8 Polystyrene 6.6 Quartz 6.5 Metals (Ag, Au, Cu) N.A. of the interaction of a sphere of PTFE with a surface in function of the distance D: W = -A*R / 6D F = W / D For a radius R of 50 nm and a distance of 5nm: W = J, F = For the same sphere and a distance of 10nm: W = J, F = N 11 N Nanotechnology for engineers Winter semester Wetting - Surface energies - Wetting phenomena, contact angle, Young s equation, and Zismann plot - Capillary forces 18

19 Surface energies interaction liquid gas/liquid Attractive energy +E Internal molecules - sur un atome en surface s exerce une force d attraction vers l intérieur du matériau - on doit fournir de l énergie pour déplacer une molécule ou un atome de l intérieur du matériau vers une interface. La surface de celle-ci augmente. - l énergie nécessaire pour augmenter la surface de 1 cm 2 est par définition l énergie libre de surface F [J/cm 2 ] Surface energies - tout système tend à minimiser son énergie, donc aussi son énergie de surface. - c est la raison pour laquelle les gouttes (ou bulles de gaz dans un liquide) ont une forme sphérique car la sphère est la forme qui a le plus grand rapport volume surface. - un liquide à tendance à se contracter : tension Force/longueur [N/m] 19

20 Application of surface energies: calculation of the pressure in a droplet r r Il y a équilibre entre la pression interne et la tension de surface de la gouttelette. Démonstration : supposons une augmentation isobare du volume de la goutte : W = PA r W : travail r : rayon de la goutte P : différence de pression int/ext A : surface de la goutte g : tension de surface da = d(4πr 2 ) = 8πrdr P = 2γ r = 2 P4πr dr γ8πrdr γ = W A W = γ A Loi de Laplace pour la capillarité Surface tension of water in function of the temperature concentration of NaCl T en sio n su p erficielle (m J/m 2) Température ( C) T e n s io n s u p e rfic ie lle (m J /m 2 ) Masse sel (% )..and of the pressure: pressure surface tension 20

21 Wetting on a homogeneous, smooth and rigid solid, Young s equation Thermodynamic expression of the surface energies for a system at thermal and mechanical equilibrium F = free energy γ 12 F = A 12 T, µ i A 12 = contacting interface between phase 1 and 2 (cm 2 ) γ 12 = Interface energy 12 = SL (Solid / Liquid) = SG (Solid / Gas) = LG (Liquid / Gas) = LL (Liquid / Liquid) Vapor Liquid(Soid) Vapor Solid γ SV γ LV Θ γsl Liquid Horizontal balance of forces Young s equation γ SV = γ SL + γ LV cos Θ Wetting contact angle Contact angle: Θ cos Θ Spreading Complete wett. Partial wetting γ SL = γ SV Negligible wett. Non-wett. Θ depends on chemical constitution of both S and L 1) hard solids - covalent, ionic, metallic => high energy surfaces γ SO 500 to 5000 mn/m 2) weak molecular crystals - VdW, H bonds => low energy surfaces γ SO 50 mn/m 21

22 Zismann plot critical surface tension γ C Typical Zisman plot - cos Θ vs. γ LV for homologous series of liquids and low energy solid surface (ex. polymers) critical surface tension γ c = surface energy of a liquid that just spread on the surface not the surface free energy of the solid but only an empirical parameter closely related to this quantity 1.00 linear relation between cos Θ and γ LV 0.90 γ C (γ LV, γ SV ) but for simple molecular liquids (VdW interactions are dominant) => γ C (γ SV )! COSINE θ Surface Tension at 20 C [mn/m] Zismann plot critical surface tension γ C Zismann plot (experiments) C8H18 on glass 22

23 Zismann plot critical surface tension γ C Zismann plot (experiments) C8H18 on silane Zismann plot critical surface tension γ C Zismann plot (experiments) C10H22 C11H24 C16H34 C12H26 C8H18 on silane 23

24 Zismann plot critical surface tension γ C Zismann plot 1.00 (experiments) C8H18 COSINE θ C10H22 C11H24 Contact angle (Θ) ,6 44,7 45,0 C x H y on silane cos Θ 0,81 0,71 0,70 Surface tension (20 C) 21,14 mn/m 23,74 mn/m 24,65 mn/m C12H ,0 0,66 25,58 mn/m C16H ,0 0,60 27,48 mn/m Surface Tension at 20 C [mn/m] Capillary effects in circular tubes γcosθ γ r h θ h θ Capillary rise of a wetting phase Capillary depression of a non-wetting phase 24

25 Capillary Pressure Equations At equilibrium (no movement of interface): Force Up = Force Down Force Up = 2πrγ cos θ Force Down = πr ρgh Capillary Pressure is defined as Force per Unit Area (πr 2 ): 2 P P c c 2πγ r cos = θ 2γ = π 2 r 2 cos r πr ρhg = = ρh g π 2 r θ and cos So: Pc = 2γ θ r = ρ g h Nanotechnology for engineers Winter semester Self Assembled Monolayers - Lotus effect - Langmuir-Blodgett, Self-assembly and Silanisation and their thermal stability 25

contamination Water droplet on lotus leaf,

26 The lotus effect: correlation between ultrastructure, wettability and contamination Water droplet on lotus leaf, with adhering particles Contaminating stain powder (Sudan III) removed by rinsing with water The Lotus Effect is based on surface roughness caused by different microstructures together with the hydrophobic properties of the epicuticular wax. The lotus effect: correlation between ultrastructure, wettability and contamination 26

Monolayer Oleo and hydrophobic surfaces Chen W., Fadeev A.Y.,Hsieh M.C., Oener D.

Lotus Effect as an extremely effective biological system only bases on

Therefore, it serves as a model for the development of artificial

27 Monolayer Oleo and hydrophobic surfaces Chen W., Fadeev A.Y.,Hsieh M.C., Oener D., Youngblood J., McCarthy T.J., Langmuir, 15, 1999, The lotus effect auto-clean effect The Lotus Effect as an extremely effective biological system only bases on physical-chemical principles. Therefore, it serves as a model for the development of artificial surfaces. Many fields for applications are possible (roofs, facades, paints) where such surfaces are advantageous. Reducing the use of cleansing agent the Lotus Effect is beneficial to the environment. 27

28 Surface mono-layer Non-polar Substrat polar Langmuir-Blodgett, Self-assembly, Silanisation Langmuir-Blodgett assembly 28

29 Langmuir-Blodgett assembly Langmuir-Blodgett assembly 29

30 Self-assembly Ethanol solution with a thiol(r-s-h) sample covered by gold From some minutes to 24 hours at RT Silanisation the ideal reaction RnSiX 4 n + SiOH SiOSiRn + 4 nhx n = 1 3 X Cl, OR, NH2, NR2 = R=Alkyl, functional chain R Si R R X + H O -HX Si O R STRONG COVALENT BOND 30

electrostatic 0.52 ev = 50 kj/mol Self Assembly R- SH on gold Covalent, d-d 1.

31 Silanisation the result Ideal and risk O Si O Si O O O O H Si HO O OH SAM s LB, SA, Sil thermal stability SAM type Bonding type Energy Langmuir-Blodgett ionic, electrostatic 0.52 ev = 50 kj/mol Self Assembly R- SH on gold Covalent, d-d 1.87 ev = 177 kj/mol Silanization Covalent (Si-O) Covalent (Si-C) 4.59 ev = 443 kj/mol 3.17 ev = 306 kj/mol 31

Self Assembled Monolayers

Nanotechnology for engineers Winter semester 2005-2006 Plastic Electronics - Self Assembled Monolayers - Organic Materials Based Devices - Organic photovoltaic devices Nanotechnology for engineers Winter