Theory of Nucleation- Thermodynamics

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1 Colloid Science Nanochemistry UIO 1 Theory of Nucleation- Thermodynamics Theory of Nucleation ΔG = free energy of particle with radius r, ΔG s = surface tension of particle with radius r, Δ G v = bulk or volume energy of particle with radius r, particles with r < r * dissolve again; particles with r > r* grow on nucleation growth Ostwald ripening Stable nucleus Nanochemistry UIO 2

2 Nucleation Nucleation nucleation growth Ostwald ripening Nanochemistry UIO 3 Theory of Nucleation Nanochemistry UIO 4

3 G homogeneous nucleation Free Enthalpy (ΔG) as Function of Nucleus Radius (r) + ΔG 0 G - +ΔG O = 4π r 2 γ G 0 = 4 r 2 ΔG* r* r - G V = 4 r 3 g V - ΔG V = 4/3π r 3 Δg v r G = - G V + G 0 ΔG= - ΔG V + ΔG O Nanochemistry UIO 5 Critical Nucleus Critical Nucleus and Nucleation Rate - - γ = surface tension Δg v = energy difference of liquid and solid phase r* = critical radius of nucleus J = nucleation rate S = c(r) / c* c* = equilibrium concentration v = molecular volume r* = critical radius of nucleus Nanochemistry UIO 6

4 Super Saturation Nanochemistry UIO 7 Rate of Nucleation (I) and of Crystallization (V) I, V 0 2/3 Tg I V 1 T l T/T l OM Nanochemistry UIO 8

5 Volume Nucleation a) b) c) nucleation Crystal growth Glas ceramics Nanochemistry UIO 9 Surface crystallization a) b) c) crystallization without volume nucleation Nanochemistry UIO 10

6 Heterogeneous Nucleation 2 L H L = liquid, mother phase S = nucleus, FK H = heterogeneous substrate, catalyst δ = contact angel S δ ΔG H * = ΔG* f (δ) f (δ) = (2 + cos δ) (1-cos δ ) 2 / Nanochemistry UIO 11 Epitaxial Growth 2 (010) LP (120) (120) LS (200) (110) Growth of Li 2 SiO 3 (LS) on Li 3 PO 4 (LP) (110) (1 10) LS (010) 10 4 LP (120) Growth of Li 2 Si 2 O 5 (LS2) on Li 3 PO 4 (LP) Nanochemistry UIO 12

7 Micelles and Vesicles Nanochemistry UIO 13 Micelles and Vesicles Micelles and Vesicles Nanochemistry UIO 14

8 Forms and Transforms Nanochemistry UIO 15 Vesicles - Classification Nanochemistry UIO 16

9 Micelle and Vesicle Forms Nanochemistry UIO 17 Micelles Microscopic Construction Nanochemistry UIO 18

10 LC forms Bilayer Arrangements in Space Nanochemistry UIO 19 Template Template / Tenside / Tenside Solutions Nanochemistry UIO 20

11 Liquid Crystal Structures 3D-Structures Nanochemistry UIO 21 Liquid Crystal Structures Nanochemistry UIO 22

12 Overview General Forms Nanochemistry UIO 23 Mesoporous Silicates: MCM41 / MCM48 Liquid crystal systems Nanochemistry UIO 24

13 Selfassembled Selfassembled Domain Domain Patterns Nanochemistry UIO 25 Multi Component Multi Component Systems Systems Nanochemistry UIO 26

14 ZeolitesMulti Component Systems Nanochemistry UIO 27 Mesoporous Multi Component Systems The body-centered cubic (Im-3m) mesostructured silica (S2) 0.80 g F127 and g AOT were dissolved in a mixture of 31.0 g water and 9.0 g H 2 SO 4 (2.0 M) at 45 uc to obtain a clear solution. After 3.80 g TEOS was added to the solution under vigorous stirring, the mixture was continuously stirred at 45 o C for 1 day. The precipitate together with the solution was transferred into a Teflon autoclave and then heated at 100 o Cfor 24 h. J. Mater. Chem., 2006, 16, Nanochemistry UIO 28