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Nanotechnology for Materials Physical Chemistry for Nanotechnology

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Nanotechnology for Materials Physical Chemistry for Nanotechnology Nanotechnology for Materials Physical Chemistry for Nanotechnology 9 Overview of colloidal nanoparticles: principles, fabrication, characterization, sensors 9 Intermolecular forces ¾ Metallic colloidal nanoparticles: interaction with solvent and substrates, plasmon resonance • Physics of bottom‐up nanofabrication: wetting, dewetting, self‐assembled monolayers, micelles, liquid crystals • Surface microscopy techniques (TEM, SEM, AFM, STM, KPM ) • Molecular modeling and simulation: Molecular Dynamics and Monte Carlo methods and applications 1 Surface forces 2 Interactions in colloids In colloids and surface science we are interested in the interaction between macroscopic bodies constituted by thousands of atoms, typillicallysphilherical partilicles and flat surfaces. The dominant forces between the constituting atoms are: ‐ dispersion forces (van der Waals, depend on the density of atoms near the surface, ATTRACTIVE ) ‐ ionic forces (due to the surface charges, depend on the number of surface atoms and on the charge density at the surface, REPULSIVE) Assuming addit iv ity of forces, it is possibleto calculate the relevant interaction by integrating on the contribution of each atom. 3 PART 1 Van der Waals forces in collo ids 4 van der Waals forces between surfaces 5 6 Hamaker constant 7 Hamaker constant 8 Hamaker constant calculation: a microscopic approach For the van der Waals interaction the potential between two atoms or molecules 1 and 2 : where is the interaction constant as defined by London and is specific to the identity of the interacting atoms (C6 ∝ α1*α2. Hamaker then performed the integration of the interaction potential to calculate the total interaction between two macroscopic bodies. This then allows the total force between two arbitrarily shaped bodies to be given by: And the Hamaker constant is The Hamaker constant has units of energy and is the multiplicative factor of the distance‐dependent functions. Other geometrical constant often appears to make H (or A) transferable between the different possible geometries. 9 Hamaker constant calculation 1) Choose themathemati ca l form of the itintera tom ic/ ii/ionic/ molecular potential, w(r) (e.g. assume an arbitrary power law: w(r)=‐Cr ‐n ) 2) Set up the geometry of the particular interaction being derived 3) Assume "pairwise additivity"; i.e. the net interaction energy of a body is the sum of the individual interatomic/intermolecular interactions of the constituent atoms or molecules which make up that body 4) A solid continuum exists : the summation is replaced by an integration over the volumes of the interacting bodies assuming a number density of atoms/molecules/m3, ρ 5) Constant material properties : ρ and C are constant over the volume of the bodies→ volume integration : W12(D)= ∫∫∫w12(r) ρ1 ρ2 dV1dV2 10 Hamaker constant calculation: atom‐surface 11 Hamaker constant calculation: atom‐surface 12 Hamaker constant calculation: two planar surfaces 13 Hamaker constant calculation: two planar surfaces 14 Hamaker constant calculation: two spheres 15 Summary of common Hamaker interactions 16 Exercise U(a)=‐CH r/6 a = ‐CH d/12 a F(a) = ‐dU/da 17 Strength of VdW forces 2 V=‐AH/12π h per unit area 18 Strength of VdW forces: gecko 19 NATURE |VOL 405 | 8 JUNE 2000 |www.nature.com Geckos are exceptional in their ability to climb rapidly up smooth vertical surfaces. Microscopy has shown that a gecko's foot has nearly five hundred thousand keratinous hairs or setae. Each 30± 130μmlongsetaisonlyone‐ tenth the diameter of a human hair and contains hundreds of projections terminating in 0.2±0.5μmspatula‐shaped structures2. After nearly a century of anatomical description, here we report the first direct measurements of single setal force by using a two‐dimensional micro‐ electromechanical systems force sensor and a wire as a force gauge. Measurements revealed that a seta is ten times more effective at adhesion than predicted from maximal estimates on whole animals. Adhesive force values support the hypothesis that individual seta operate by van der Waals forces. Suitably orientated setae reduced the forces necessary to peel the toe by simply detaching above a critical angle with the substratum. 20 21 Gecko spatulae adhesion force Thesolid line representsasetawith spatltulae projtijecting tdtoward thesurface. The dashed line represents the setal force with spatulae projecting away from the surface 22 The structure similarity between the cross‐section views of the VA‐MWNTs (left) and gecko’s aligned elastic hairs (right). A book of 1480 g in weight suspended from a glass surface with use of vertically aligned‐MWNTs supported on a silicon wafer. The top right squared area shows the VA‐ MWNT array film, 4 mm by 4 mm 23 The effect of the liquid medium The medium between two interacting bodies has the net effect of reducing the attractive interaction with respect to vacuum. The extent depends on the dielectric properties of all themedia ildinvolved. 24 Medium effect: like particles 25 Medium effect: unlike particles Lorentz‐Berthelot rule 26 Summary of Vdw forces between colloids • Van der Waals forces in solvents are always attractive for particles of the same material • Approximate macroscopic interaction equations can be derived for different geometries (particle/surface 1 – medium 2‐ particle/surface 3) n • Equations have the form Energy = A123 * f / r A: Hamaker constant, depends on materials 1,2,3 f: geometric factor; n lower than 6 (typically 1 or 3) • The medium (2) has a strong influence on A: higher dielectric constant <‐>lowerHamakerconstant (even negative if 1/=3) • Tabulated Hamaker constants and equations can be useful in understanding the forces acting between your nanoparticles and substrates 27 PART 2 Dielectric permittivity (the medium between the nanopp)articles) 28 Dielectric constant (permittivity) 29 The effect of the liquid medium VACUUM VACUUM 30 The effect of the liquid medium 31 The effect of the liquid medium 32 The effect of the liquid medium Molecular permanent and induced dipoles DIELECTRIC produce local fields in the opposite direction εD > ε0 wrt the applied field 33 Contributions to permittivity: polarization 34 Dipoles in electric field • Thestrengthofthefieldatagivenpointisdefinedasthe force that would be exerted on a positive test charge of +1 coulblomb pldlaced at tha t poitint; the direc tion of the field is given by the direction of that force. • The definition of dipole orientation is instead from the negative to the positive charge From Coulomb’s law and theabove definitions, it follows that Energy = ‐ E • μ = ‐ E μ cos θ where θ is the angle μ between the two vectors 35 Polarization/2 36 Polarization/3 37 Polarization/4 38 Polarizability Let’s consider a spherical atom. In absence of external field the average charge density has a spherical symmetry centered at the nucleus. Appl yin g a field E the electron cloud will be distorted and attracted to the positive pole of the field, while the nucleus to the negative one, giving rise to the so called induced dipole. 39 Origin of polarizability/1 The nucleus has a point charge +Ze, while the electrons with total charge –Ze are uniformly distributed on the atomic volume, Electron density: We try now to evaluate quantitatively the equal and opposite forces that act on electrons and nuclei when they separate of a distance d in presence of an external field. 40 Origin of polarizability/2 Force acting on the nucleus due to the field: At the equilibrium distance d, this force will be balanced by the force exerted by the electrons on the nucleus. As the field due to a hollow charged sphere is 0 (cf Faraday cage/shield), only the electron charge inside the sphere of radius d has to be taken into account: A spherical charge distribution can be treated as a point charge, hence from Coulomb’ s law: 41 Origin of polarizability/3 Now we can equalize the two forces: The law obtained is the electrical analogous to Hooke’s law: F=‐kd ‐> F = (Drude oscillator) the distance of equilibrium is: and the induce dipole is μ∗ The total polarization (total dipole per unit of volume) for such a material is therefore ∗ 3 P = Σ μ /V = (Natoms/V)4πε0 R E = (Natoms/V)αE 3 where α= 4πε0 R is the atomic polarizability and E is the LOCAL field 42 Summary of polarization effects DIPOLE POLARIZABILITY Electronic polarization (polarizability) Orientational polarization (permanent dipoles) Ionic polarization (ionic solids) 43 The response to electric fields The electric displacement field,denotedasD, is a vector field that appears in Maxwell's equations. It accounts for the effects of free charges within materials. "D" stands for "displacement," as in the related concept of displacement current in dielectrics. In a linear, homogeneous, isotropic dielectric with instantaneous response to changes in the electric field, the polarization P depends linearly on the electric field, P = ε0 (εr‐1) E, D= ε0 εr E As opposed to the response of a vacuum, the response of normal materials to external fields generally depends on the frequency of the field. This frequency dependence reflects the fact that a material's polarization does not respond instantaneously to an applied field. 44 Micro‐macro equations for static permittivity “Lorentz local field:” Eloc =(εr+2)/3 Eext (takes into account that the field inside the dielectric is different from the external field) Macro: P = ε0 (εr‐1) Eext Micro: P = (N/V)αEloc = (N/V)α (εr+2)/3 Eext Combining the two equations: Clausius‐Mossotti: (εr‐1)/(εr+2) = (N/V)αelectronic /(3ε0) 2 Debye: (εr‐1)/(εr+2) = (N/V)(αelectronic +μ permanent/3kT)/ (3ε0) ‐> εr=(2k+1)/(1‐k) with k depending on molecular properties More complex and accurate: Onsager, Kirkwood and Fröhlich 45 Dielectric constants of common materials 46 Dielectric constants of organic solvents 47 Exercise: the effect of polarizability Calculate the dielectric constant for nitrogen gas (N2), composed by atoms with radius=0.8 Å, having a density = 1.251 g/L, and molllecular weihtight 28 g/l/mol.
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