Physical Chemistry II CHEM 3340 Solids 2024 PDF

Physical Chemistry II CHEM 3340 Bonds in Solid Phase Bonds in Solids Various kinds of bonds: ◊ Metallic solid: electrons are delocalized over arrays of identical cations ◊ Ionic solid: ions held together by Coulombic interactions ◊ Covalent solid: covalent bonds in definite spatial orientation link...

Physical Chemistry II CHEM 3340 Bonds in Solid Phase Bonds in Solids Various kinds of bonds: ◊ Metallic solid: electrons are delocalized over arrays of identical cations ◊ Ionic solid: ions held together by Coulombic interactions ◊ Covalent solid: covalent bonds in definite spatial orientation link the atoms in a network ◊ Molecular solid: discrete molecules attracted each other by molecular interactions (e.g., dipole-dipole) Electrical Properties Metallic conductor: generally high conductivity that decreases with temperature Semiconductor: generally lower conductivity than that of metals, but conductivity increases with temperature Insulators: very low conductivity Superconductivity: solid that conducts electricity without resistance (low temperature, special material) Band Theory of Metals MO theory for metals For n atoms: n orbitals When n is very large: it looks almost continuous The orbitals form a ‘band’ Band Structure s orbitals form s band p orbitals form p band The two bands might: ◊ separate: there exists a band gap (when the energy of atomic p orbitals is very different from the energy of s orbitals ◊ overlap (e.g., in Mg2+) Occupation of Orbitals Assumption: N alkali metal atom, each atom contributes one electron At T=0, lowest N/2 orbitals are occupied. HOMO: Fermi level When potential is applied, the electron can jump to an orbital just above the Fermi level: the electron is very mobile -> Metals conduct electricity Mg: s2 but s and p bands overlap Effect of temperature: more vigorous thermal motion of electrons -> more collisions between the electrons and atoms -> less efficient transfer of charge Semi-conductors There is ◊ Filled valence band ◊ large band gap At large temperature some of the electrons can get thermally excited into the empty band and they can effectively conduct electricity there The conductivity increases with temperature as more and more electrons can get thermally excited Doping Semi-conductivity can be enhanced by dopants ◊ p-type (In or Ga in Si): they can withdraw electrons from the filled band, freeing up MO for the electrons to move in the valence band ◊ n-type (P in Ge): excess electrons form an additional band (donor band) and contribute to temperature dependent conductivity The Ionic Model of Bonding MO theory: for two atoms (e.g., Na 3s and Cl 3p the bonding wavefunction is mostly on Cl because of lower energy): Cl- and Na+ ions Na 3s For N atoms ◊ banding is narrow: overlap between orbitals (of the same atom) is less important because of larger distance ◊ Valence band is full (N positive + N negative atoms -> 2N electrons in the bonding p band Cl 3p Na 3s nonbonding s band No electric conductance: insulator Cl 3p We can treat as positive and negative ions: like elementary picture of ionic bonding fully occupied bonding p band Lattice Energy Work required to disassemble one mole of ionic crystal: ◊ constant volume: lattice energy (difficult) ◊ constant pressure: lattice enthalpy Work required to separate all the ions of solid from each other NaCl(s) → Na+ (g) + Cl- (g) HL = 786kJ/mol This work is purely Coulombic, and thus can be evaluated Lattice Energy: linear arrangement Each ion experiences electrostatic interactions with the others Attraction (V = -z2e2/(4πε0r)) and repulsion (V = z2e2/(4πε0r)): let’s sum the potential energy for one ion Attraction comes from ions in distances: d, 3d, 5d, etc. 1 V = ⇥ 4⇥ 0 1 ⇥ V = 4⇥ 0 z 2 e2 + d z 2 e2 z 2 e2 + + d 2d Repulsion comes from ions in distances: 2d, 4d, 6d, etc. ⇥ z 2 e2 +... 3d 1 V = 4⇥ 0 ⇥ z 2 e2 z 2 e2 + +... = 3d 4d 1 z 2 e2 ⇥ 4⇥ 0 d 1 1 1 + 2 3 ⇥ z 2 e2 z 2 e2 + +... 2d 4d ⇥ 1 +... 4 1-1/2+1/3-1/4+... = ln 2 Lattice Energy: linear arrangement V = z 2 e2 ⇥ ln 2 4⇥ 0 d This equation counts only ions to the right -> to get the effect of the ions to the left, x2 V = z 2 e2 ⇥ 2 ln 2 4⇥ 0 d For one mole of ions: V = z 2 e2 NA ⇥ 2 ln 2 4⇥ 0 d d = rcat + ranion Lattice energy: Madelung Constant General equation for a lattice of ions with charges z1 and z2 V = |z1 z2 |e2 NA A 4⇥ 0 d A: Madelung Constant For each crystal structure it can be obtained Further modification takes into account electron-electron repulsion between two ions at very small distances d*=34.5pm V = |z1 z2 |e2 NA A ⇥ (1 4⇥ 0 d d /d) Born-Mayer Equation Lattice Energy, EL =-V Lattice Energy (Enthalpy) EL = |z1 z2 |e2 NA A ⇥ (1 4⇥ 0 d The lattice energy (enthalpy) depends: ◊charges: large charge: larger enthalpy ◊ distance between the ions: small distance gives larger enthalpy d /d) Solid: Covalent Networks Covalent bonds in a definite spatial orientation link the atoms in a network extending through crystals Examples: silicon, red phosphorous, boron nitride, diamond, graphite, carbon nanotubes Diamond: sp3 hybridized carbon Graphite: sp2 hybridized carbon is bonded tetrahedrally to its four neighbors is bonded hexagonally to its three neighbors forming sheets Very hard Very soft because sheets can move Buckyball and Carbon Nanotubes Kroto Smalley Curl Nobel prize: 1996 Molecular Solids How does ice form? Molecules interact with each other! Intermolecular forces ◊ Van der Waals Forces ◊ Hydrogen bonding ◊ Hydrophobic interaction: pseudo interaction (lack of interaction) Van der Waals Forces Intermolecular interactions ◊ attractive and repulsive interactions -between partial charges on atoms of polar molecules - polar groups on macromolecules ◊ repulsive interactions that prevent closed shell orbitals to overlap (repulsion of nuclei) Potential energies often vary as 1/r6: Van der Waals Interaction Partial charges play an important role through dipoles Electric Dipole Moment Each molecule has distribution of charges Simplest: heteronuclear molecule, one atom has a charge +q the other -q Dipole moment: μ Vector of length qR pointing from the negative to the positive charge If q=e, R=100 pm μ = 1.6x10-29 Cm = 4.8D Non SI unit: Debye, D 1D = 3.33564x10-30 Cm Nonpolar molecules: μ =0 (e.g., homonuclear molecules) Polar Molecules: μ > 0 (e.g., HCl: 1.08 D) Electric Dipole Moment When you have more atom, we sum the vectors corresponding to the dipole moments of neighboring atoms μ=0 µ= µ21 + µ22 + 2µ1 µ2 cos Molecular symmetry is important Dipole Moment For a large molecule with many atoms there is a simpler method using the charges (qJ) on the atoms (J) with positions (xJ, yJ, zJ) Amide group (in peptides) μ=2.7 D µx = qJ xJ J µy = q J yJ J µz = q J zJ J µ= µ2x + µ2y + µ2z Dipole-Dipole Interaction Coulombic potential energy between two dipole molecules: same way as for ions q1 l1 q2 l2 V = ⇥ (1 3 4⇤ 0 r 3 cos2 ⇥) µ2 = q2 l2 µ1 = q1 l1 µ1 µ2 V = ⇥ (1 3 4⌅ 0 r 3 cos2 ⇥) Typical value: -20 kJ/mol This energy falls quickly with r: from large distance it looks like there is no separation Rotating dipoles When two molecules are rotating, they will interact with each other: they prefer orientations with low energy Thermal motion tries to disrupt this orientation V = 2µ21 µ22 3(4⇤ 0 )2 kT r6 Keesom interaction: ◊always negative ◊ depends on distance with r6 ◊ larger dipole, larger energy ◊ larger temperature: lower energy ◊ typical value: 298.15 K, μ=1D, r=0.5 nm, V=-0.07 kJ/mol (energy in ’thermal’ motion: 3/2 RT= 3.7 kJ/mol) Polarizability, α When a nonpolar molecule is put into electric field (E), the field induces dipole moment, μ* µ = E ◊ If the molecule has few electrons that are tightly controlled by nuclear charges: small α (e.g., N2) ◊ Molecule with loose electrons: large α (e.g., I2) ◊ In tables often give: polarizability volume α’=α/(4πε0) [m3] The value is often close to the volume of the molecule Dipole - Induced Dipole Interaction ◊ Polar molecule (μ1) can induce dipole moment in a nonpolar molecule (polarizability α2) ◊ The interaction of dipoles and induced dipole has interaction energy: µ21 2 V = 4 ⌅⇥0 r 6 Proportional to 1/r6, thus Van der Waals interaction Typical value: -0.8 kJ/mol(μ=1D, α’=1x10-31m3, r=0.3 nm) Dispersion Interaction Even nonpolar molecules interact Fluctuations in the instantaneous motion of the particles (electron, nucleus) causes transient dipole to form: this transient dipole interacts with other molecules through dipole-induced dipole interactions V = 2/3 1 2 r6 I1 I2 ⇥ I1 + I2 ◊ 1/r6 dependence ◊ I1,2: ionization energies ◊ Typical values: -5 kJ/mol ◊ This interaction is responsible for solid He, H2, etc. Hydrogen bonding General type of bonding, but most important for interaction of two molecules ◊In molecule #1: a H atom that bonds to a highly electronegative atom (e.g., O, N, F) ◊ In molecule #2 there is a highly electronegative atom with lone pairs of electron (O, N, F) The two molecules can be ◊the same: H2O, NH3, HF ◊ different: CHCl3 + CH3CHO Notation: A-H ---B H is usually closer to atom A, but can be in the middle F-H-F- MO interpretation Three atoms-> three orbitals 4 electrons (H: 1, A: 1; atom with lone pair of electrons: 2) Anti-bonding Non-bonding Bonding The energy level of this nonbonding orbital will determine the stability of A-H---B If it is low enough: stabilizing (20 kJ/mol) Can be quite strong: responsible for ◊vaporization enthalpy of water ◊ rigidity of ice, sucrose ◊ Structure of DNA Hydrophobic Effect It is a pseudo (apparent) interaction Water molecules have strong interactions through hydrogen bonds When a large hydrocarbon molecule is put in water, it tries to minimize the surface so that more water molecules can interact with other water molecules: the molecule is hydrophobic The result is like non-charged, non-polar surfaces of the molecule attract each other Important in shapes of bio-macromolecules Total Interaction: attraction Attractive forces: Van der Waals forces V = -C6/r6 ◊ dipole-dipole ◊ dipole-induced dipole ◊ dispersion C6 depends on the identity of the molecule Total Interactions: repulsion When molecules/atoms get really close to each other the nuclei charges impose a strong repulsive force I.V = Cn/rn n=12 simulate a largely increasing trend II. Exponential: V = exp(-r/r0) Lennard-Jones Potential Attraction: Van der Waals Repulsion: n=12 V =4 (r0 /r) 12 (r0 /r) 6 ε: well depth r0: separation at which V=0 Well minimum: re = 21/6 r0 Motion in Lennard-Jones potential is an important concept of interacting molecules: bridge between macro and micro world Example: motion of gas molecules: attractive forces or repulsive forces dominate depending on distance (pressure): deviation from perfect gas law ⇥