Various approximations for describing electrons in metals, starting with the simplest: E=0 jellium model = particle in a box

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Allen Dennis
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1 ) Metallic Bond The outer electrons are weakly bound. They roam freely in the space between the atoms and thus are able to conduct electricity. They can be approximated by free electrons in a constant, attractive inner potential V 0 (typically 15 ev). Isotropic bonding. Examples: Alkali metals, aluminum. Various approximations for describing electrons in metals, starting with the simplest: E=0 V 0 ellium model = particle in a box muffin tin potential valence levels core level equivalent singleelectron pseudopotential full potential Wave functions of the outer electrons versus distance (in Å = 0.1 nm) for nickel, a transition metal. The 4s electrons are truly metallic, extending well beyond the nearest neighbor atoms (at r 1, r 2, r ). The d electrons are concentrated at the central atom and behave almost like a core level. 1

2 Electronegativity The goal: Find a simple number for each element that tells us the type of bonding (covalent, ionic, metallic). The electronegativity quantifies the ability of an atom to bind electrons. There are various definitions. The simplest is: = (I A) I = ionization energy, A = electron affinity (in ev) The electron affinity is the binding energy of an added electron (= ionization energy of the negative ion). An atom with high ionization energy is able to keep its electrons, and an atom with high electron affinity is able to attract more electrons. The electronegativities A, B of two atoms A, B and their difference Δχ = A B can be used to qualitatively predict the type of bonding in the compound AB : Ionic: Δχ large Cs F ( = 0.8, 4.0) Covalent: Δχ 0 χ medium large C C ( = 2.5) Metallic: Δχ 0 χ small Al Al ( = 1.5) In an ionic bond, atom A holds electrons weakly, and atom B holds them strongly. In a covalent bond, both atoms hold electrons strongly. In a metallic bond, both atoms hold electrons weakly. The transitions between the three types of bonding are continuous, since the electronegativities vary gradually (see the table below). The charge transfer between the two atoms in an ionic bond is proportional to Δχ. The absolute charge transfer is hard to define and often subect to controversy. It depends on how one defines the volume of each atom/ion. Electronegativity Table H 2.1 Li 1.0 Be 1.5 B 2.0 C 2.5 N.0 O.5 F 4.0 Na 0.9 Mg 1.2 Al 1.5 Si 1.8 P 2.1 S 2.5 Cl.0 K 0.8 Ca 1.0 Ga 1.8 Ge 1.8 As 2.0 Se 2.4 Br 2.8 Rb 0.8 Sr 1.0 In 1.8 Sn 1.8 Sb 1.9 Te 2.1 I 2.5 Cs 0.8 Ba 0.9 Tl 1.6 Pb 2. Bi 2.0 The overall trend is an increase of the electronegativity from the lower left to the upper right of the Periodic Table. 2

3 4) Hydrogen Bond Attraction between static dipoles; polar molecules (containing electric dipoles). A shared proton is attracted to two negative ions (e.g. oxygens from two H 2 O molecules). 2 Can be symmetric or asymmetric. (Compare the covalent bond in H 2 : A shared electron is attracted to two protons ) 5) Molecular (van der Waals) Bond Attraction between dynamic (oscillating) dipoles; nonpolar molecules. A temporary electric dipole is created at molecule i by zero point oscillations at its optical resonance i frequency (h E gap, in the ultraviolet). This dipole creates an electric field E at a neighbor molecule. The dipole lowers its energy by lining up parallel to the electric field. Electric dipole field: E 1/r i Induced dipole moment on molecule : E 1/r i Energy of the induced dipole in the electric field: 6 U C E 1/r i

4 Hydrogen Bonding in Ice O 2 H Tetrahedral arrangement of the oxygens. Each oxygen has two short and two long OH bonds. That leads to many possible combinations (N) and a large entropy S = k B ln(n). Hydrogen Bonding between Base Pairs in DNA 4

5 Hydrophilic versus Hydrophobic The hydrogen bond and the van der Waals bond are mutually exclusive, since they have opposite requirements (polar vs. nonpolar molecules). This leads to the distinction between hydrophilic (charged) and hydrophobic (neutral) groups of atoms, for example OH and CH. Hydrophilic groups bond to other hydrophilic groups, and likewise hydrophobic to hydrophobic, but there is no bonding between hydrophilic and hydrophobic. This competition leads to intricate selfassembled structures which are discussed in the next lecture. Amphiphilic Molecules, Surfactants Hydrophilic and hydrophobic groups can be stitched together by covalent bonds, leading to amphiphilic molecules (= surfactants). An example is the class of phospholipids, which consist of a charged phosphate group stitched to neutral alkane chains (right side). They form the cell walls of all living beings. Block Copolymers The same effect can be achieved in blockcopolymers by stitching a hydrophilic polymer block to a hydrophobic block. A common combination is PMMA (=Plexiglas) Polystyrene, as shown below. Block copolymers are used in nanolithography for fabricating patterns with molecular precision. 5

Chemical Bonding polarity & Dipole Moments. Chapter 8 Part III

Chemical Bonding polarity & Dipole Moments Chapter 8 Part III Exercise Arrange the following bonds from most to least polar: a) N F O F C F b) C F N O Si F c) Cl Cl B Cl S Cl Exercise a) C F, N F, O F