3.091 Summary Lecture Notes

3.091 Lecture Summary Notes Prepared by anonymous MIT students Disclaimer: Although these summary notes attempt to cover most of the main topics emphasized during each lecture, they should not be considered completely comprehensive. Material covered in assigned readings and/or homework are not necessarily covered by these notes. This document should be used as supplemental study material, in addition to reviewing your own notes and doing the assigned readings and homework questions. -1­ Lecture 1 – Sept 9:  Intro. Lecture 2 – Sept 11: PERIODIC TABLE, ATOMIC NOMECLATURE   History of the Periodic Table o Atoms - Dalton (1803) (nearly got it right) – pg 14-15  Dalton’s Atomic Theory o Mendeleyev (1869)  predicted “missing elements” and their properties Structure of the atom o Electron (e-), proton (p+), neutron (no) see table below Images by AhmadSherif and Xerxes314 on Wikipedia. o  A Method of labeling elements: Z X o A= mass # ~= # nucleons(protons + neutrons) o Z = proton # (defines chemical properties. An element’s “social security identification #”) o A,Z are integer numbers o      ex. 23 11 Na Ions = cation (“paws”itive = cat… meow) o positive (+): e- deficient = anion (extra ‘n’ = negative) o negative (-): e- rich Molar masses o ‘Relative’ masses of each element determined by mass spectroscopy, average elemental mass amongst its various isotopes Faraday’s const (F = 96,485 C/mol) o “Oil drop experiment” (Millikan)  e=1.6x10-19C o Electrochemistry: Ag+ + e-  Ago.  Count e- (=nAg). Weigh Ag. Determine mass per atoms  From ‘relative mass’ values, we now know atomic mass of each element Avogadro, NAv = 6.02 x 1023 moles : o Simply for convenience (easier units that 1023 atoms) o  Electrons are tiny (~1/1830 the mass of a proton), but their orbital’s take up a lot of space, the nucleus is tiny. Defined such that 1 mole of 12 6 C weighs 12g Chemical Reaction Equations 1. Write out a balanced equation 2. convert mass to moles 3. determine limiting reagent 4. calculate amount of product o ex. TiCl4 (g) + 2 Mg(l) = 2MgCl2(l) + Ti(s) Isotope calculations (iso=isotope) o X(miso1) + (1-X)(miso2) = mavg, solve for X. If X>0.5, iso1 is more abundant. -2­ Lecture 3 – Sept 14 – MORE HISTORY  Structure of atom o JJ Thomson (1904): “Plum Pudding”  e-‘s distributed uniformly throughout an atom o Ernest Rutherford (1911): “Nuclear Model”  Conclusion from gold foil expt  Majority of mass is found in the nucleus (rnucleus/ratom=1/10,000)  e- orbiting around nucleus o Niels Bohr (1913): introduces quantization condition  Needed to explain blackbody radiation and atomic spectra  Postulated  e- follow circular orbits around a nucleus  Orbital angular momentum is quantized, hence only certain orbits possible  e- in stable orbits do not radiate  e- change orbits by radiating or by absorbing radiation Lecture 4 – Sept 16: BOHR MODEL  Bohr Model o Developed for H-atom, applicable to any one electron system (e.g. Li3+, etc) o Quantized energy states (n=1,2,3…) o    1 1 Etransition  KZ 2  2  2   n f ni  Photons: o  hZ ao n 2 Z2 , E electron  K 2 , v(n)  Z 2mao n n o ao= Bohr radius = 0.529 Angstroms E=0 o Z = proton number E3 =-KZ2/9 o e = elementary charge ­ o m = mass of e E2 =-KZ2/4 o h= Planck’s constant o n = e- principal quantum number o K = a constant = 1.312MJ/mol = 13.6 eV/atom E1 =-KZ2 o 1eV = 1.6x10-19J Energy Level diagram o E=0 at n=infinity o E1 = ground state energy, when n=1 (e.g. E1 =-13.6 eV for H) o Spectrum from cathode ray tube with known gas Stimulated emission o Photons: Eincident = Etransition + Escattered o  r ( n)  E  hv  hc  o h=Planck’s constant, v = photon freq., = wavelength, c=speed of light Traveling Particle (in other words, particles with definite mass) o E 1 2 mv 2 -3­ n=infinity n=3 n=2 n=1 Lecture 5 – Sept 18: EMISSIONS SPECTRA, QUANTUM NUMBERS   Reading: Averill 6.5 Visible light: 400-700nm = 3.1-1.8eV Wavelength , ∗ (m) 10-12 10-11 10-10 Gamma 1020 (b) 10-9 10-8 X ray 1019 1018 10-7 10-6 10-5 Ultraviolet 1017 10-4 10-3 10-2 Infrared 1016 1015 1014 1013 10-1 100 Microwave 1012 1011 1010 109 101 Radio 108 Frequency , Α (Hz) (a) 400 450 500 550 600 Red Orange Yellow Green Blue Violet Visible Spectrum 650 700 Wavelength , ∗ (nm) Image by MIT OpenCourseWare.  Bohr model for hydrogen (1 electron system) resulted in quantized energy level 2 Generalized eqn.:   Z  o   1 o o   1 1   2 , 2    n f ni  o =wave number   Rydberg constant = 1.097 x 107 m-1 Berlin – Franck – Hertz: Hg (mercury vapor) experiment showed quantized energy levels applies to other elements/atoms as well. Limitations of Bohr model: o Fine structure (doublet) o Zeeman splitting (under an applied magnetic field (B) ) Image by Super_Rad! on Wikipedia.  Sommerfeld proposed ‘elliptical shape’ to the electron orbitals o Quantum numbers: n, l, m, s  ex. Ag metal beam split by magnetic field (atoms with spin-up e- go one way, atoms with spin-down e- go the other way).  Franck & Hertz Expt.: o Gas discharge tube, Hg vapor o Demonstrated existence of a threshold energy required to excite electrons in Hg atoms  electron energy levels are true to all atoms Image by Ahellwig on Wikipedia. -4­ Lecture 6 – Sept 21: QUANTUM NUMBERS, PARTICLE-WAVE DUALITY    Reading: Averill 6.4 Quantum numbers defining the ‘state’ of the electron o n = principle quantum number n=1,2,3…, (or K,L,M…) o l = angular momentum (“shape”), l = 0..n-1 (s,p,d,f,g…) o m = magnetic quantum number, m = -l..0..l o s = spin +/- ½ Examples of orbital shapes http://www.orbitals.com/orb/orbtable.htm : Courtesy of David Manthey. Used with permission. Source: http://www.orbitals.com/orb/orbtable.htm  Aufbau Principle 1. Pauli exclusion principle: in any atom, each e- has a unique set of quantum no.’s (n,l,m,s) 2. e- fill orbitals from lowest E to highest 3. Degenerate electrons (same energy level) strive to be unpaired  Filling electron states: o Ex. Carbon, C: 1s22s22p2  de Broglie – an electron can act as a wave o He asked: “if photons can behave as particles, can electrons behave as a wave?” o Geometric constraint: 2r = n, n=1,2,3… (circular wave path) o Wavelength of an electron: e=h/p=h/mv  mvr = nh/2 !  p=momentum = mv o Demonstration of diffraction of electron ‘beam’ using a crystal lattice o Particle-wave duality confirmed!  Heisenberg – uncertainty principle o (px)(x) >= h/2 o You can’t know the exact position and momentum of a particle at the same time o Deterministic models (billiard balls) turn into probabilistic models  Einstein: “God doesn’t play dice with the universe”  Bohr: “Einstein, stop telling God what to do!”  Schrodinger equation (NOT TESTED ON FINAL) o o o o o It’s a defining equation for quantum mechanics Think of it as equivalent to Newton’s equation: F=ma Complex equation that allows us to calculate measurable quantities, such as position, momentum, energy of microscopic systems. Well beyond the scope of this class… -5­ Lecture 7 – Sept 23: AUFBAU PRINCIPLE X-RAY PHOTON SPECTROSCOPY   Reading : Averill 8.1-8.2, 12.5, 8.3 n+l rule for filling orbitals. Fill in ascending n. o 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s…  Measurement of ionization energies (Einc = Ebinding + Ekin) o Peak height tells # of electrons in shell o Energy tells shell (n) Copyright © 2003 John Wiley & Sons, Inc. Reprinted with permission of John Wiley & Sons., Inc. Source: Spencer, J. N., G. M. Bodner, and L. H. Rickard. Chemistry: Structure and Dynamics. 2nd ed. New York, NY: John Wiley & Sons, 2003.  Average Valence Electron Energy (AVEE) o <11eV  e- weakly held = metals o >13ev  e- tightly bound = non-metals o >11ev, <13ev = semi-metals  Noble gases  filled valence shell  energy well = extremely stable  Electron transfer to achieve valence shell filling o Ion pair production o Na  Na+ + ­ e­ o Cl + e-  Cl o Agglomerate without limit due to coulombic attraction  Crystal! Image by MIT OpenCourseWare. -6- Lecture 8 – Sept 25 :   Reading : Averill 8.3-8.6, 8.8, 9.2 Energetics of pair attraction o  energy gained upon converting a gas of ion pairs, to a crystal array o Eattr   o b q1  q2 , Erep  n , Enet = Eattr + Erep 4 o r r b,n = constants, n~=6-12 Madelung constant, M  energy related term of a crystal, based on atomic geometry  Generally, an infinite sum  For a material with +1 and -1 charged species  Energy per mole of ions:  M  z   z   N AV  e 2  1  1   (sum of all ion interactions) 4 o ro  n  Eline     n = Born exponent, n~=6-12 If M > 1  a solid will form If M < 1  material will remain as a gas  Transparent materials: o If Ehv,incident<Etrans, visible light doesn’t have enough energy to promote electron excitation  the photon passes straight through material  Hess’s Law: energy change in a chemical rxn is path independent o Energy is a State Function o i.e. Na(s) + 1/2Cl2(g)  NaCl(xstal) o a) convert reactants to their independent gaseous forms (steps 1,2) o b) remove/add electrons (steps 3,4) o c) crystallize (step 5) 3. Na(g) Na+(g) + e 495.8 kJ/mol 2. 1_ Cl2(g) 2 1. Na(g) _ _ _ 4. Cl(g) + e Cl (g) -348.6 kJ/mol _ Cl(g) Na(g) 5. Na+(g) + Cl (g) NaCl (s) -787 kJ/mol 122 kJ/mol 107.3 kJ/mol Net reaction _ Na(s) + 12 Cl2(g) NaCl (s) -411 kJ/mol A Born _ Haber Cycle for NaCl Image by MIT OpenCourseWare. -7­ Lecture 9 – Sept 28 : Reading : Averill 7.3, 8.9 Problems with ionic-bonding for diatomic molecules: H2, N2, O2  can’t be ionic G.N. Lewis (1916) – shell filling by electron sharing 1A(1) 3A(13) 4A(14) 2A(2) o Lewis Dot notation 1 ns ns2np1 ns2np2 ns2 o Cooperative use of valence e-‘s to achieve octet stability = Li Be B C 2 covalent bonds Period      Ionic Bond Covalent Bond  Carbon  only has 2 unpaired (bonding) electrons in p-orbital o s-orbitals ‘merge’ with p-orbitals  sp3 hybridized o Results in 4 unpaired e-, ready to bond 3 = e- transfer = e- sharing (directional) Na Mg Al Si 5A(15) 6A(16) 7A(17) 8A(18) ns2np3 ns2np4 ns2np5 ns2np6 N O F Ne P S Cl Ar Image by MIT OpenCourseWare. 2pz Four Tetrahedral sp3 Hybrid Orbitals Hybridization 2s An sp3 Hybrid Orbital 2py 2px  Image by MIT OpenCourseWare. Energy of heteronuclear bonds : o E AB  E AA  E BB  96.3  A   B  2 (in kJ/mol)   1 2  1  exp      100%   4   % ionic character =  Polar bonding  can lead to a polar molecule – but only if there’s asymmetry -8­    H2 (MOs) H (AO) Lecture 10 – Sept 30 : LCAO-MO Reading : Averill 9.2, 9.3, 9.4 LCAO-MO (Linear Combination of Atomic Orbitals – Molecular Orbitals) o Orbitals split into a bonding (lower) and anti-bonding (higher) orbitals. Electrons fill from lowest energy up. H (AO) - + � ν1s E 1s Types of bonds: o  = no nodal plane separates nuclei  eg. s + s, pz + pz, s + p o  = a nodal plane separates nuclei  eg. py + py, px + px o don’t need to worry about d or f orbitals 1s ν1s + Image by MIT OpenCourseWare. Copyright © 2003 John Wiley & Sons, Inc. Reprinted with permission of John Wiley & Sons., Inc. Source: Spencer, J. N., G. M. Bodner, and L. H. Rickard. Chemistry: Structure and Dynamics. 2nd edition. New York, NY: John Wiley & Sons, 2003.  Paramagnetism: from unpaired electrons in MO o eg. liquid oxygen is paramagnetic – can be held by a magnetic field 6 bonding electrons 2 anti bonding electrons => double bond O2 0=0 ν2p* αx* 498 kJ/mol αy* 2p 2p αx αy ν2p ν2s* 2s 2s ν2s Image by MIT OpenCourseWare. -9­ Lecture 11 – Oct 2 : HYBRIDIZED ORBITALS AND BONDING, SHAPES OF MOLECULES  Reading : Averill 9.1, Shackelford 2.5  Hybridized bonding in molecules o i.e. C2H4 (C=C double bond has one -bond, and one x -bond), and C-H bonds are from sp2 hybridized orbital in C. Sp2 Sp2 Sp2 Sp2 Sp2 Image by MIT OpenCourseWare.  VSEPR (Valence Shell Electron Pair Repulsion) o Electron Pair Geometry vs. Molecular Geometry Overview of molecular geometries 2 Electron pairs 3 4 5 6 90o Electron pairs geometry 120o Linear Trigonal planar Tetrahedral B Molecular geometry: Zero lone pairs B A B Linear AB2 B A B B B B A B A B B Trigonal planar AB3 B B B Tetrahedral AB4 .. Molecular geometry: One lone pair Trigonal bipyramidal Trigonal bipyramidal AB5 .. Octahedral B B B A B B B Octahedral AB .. .. B B A B B A B B Bent (V-shaped) AB2 Trigonal pyramidal AB3 .. B A .. .. .. Molecular geometry: Two lone pairs B A B B B Seesaw AB4 B Bent (V-shaped) AB2 B A B B T-shaped AB3 B A B B B Square pyramidal AB5 .. B B A B B .. Square planar AB4 .. .. B A B Molecular geometry: Three lone pairs .. Linear AB2 Image by MIT OpenCourseWare.  Elements that can undergo an expanded octet are: AlCl, GaKr, InXe, TlAt -10­ Lecture 12 – Oct 5 : SECONDARY BONDING Averill 12.5, 12.6; Shackelford 2-5, 2-4, 15-1, 15-2, 15-5 1. dipole-dipole:  applies to polar molecules (i.e. HCl)  Ed-d ~ 5 kJ/mol (vs. 780kJ/mol for an ionic bond)  Much weaker! H Cl H Cl Dipole - Dipole 2. induced dipole – induced dipole Image by MIT OpenCourseWare.  operative in non-polar species  explains why non-polar species can exists as a liquid or solid (i.e. N2 bp = 77k)  Van der Waals bond or London Dispersion forces  EVdW    Force is larger for larger atoms  higher bp for larger atoms 2 r6 Induced Dipole - Induced Dipole Image by MIT OpenCourseWare. 3. Hydrogen Bonding  Between exposed proton side of H, and e- on other atom  Only applies between H+ F, O, or N. (i.e. HCl does not have a “H-bonding”)  i.e. (H-F) … (H-F) Courtesy of John Wiley & Sons. Used with permission. Source: Fig. 8.18 in Spencer, James N., George M. Bodner, and Lyman H. Rickard. Chemistry: Structure and Dynamics. New York, NY: John Wiley & Sons, 2003. ISBN: 0471419214. -11­ Lecture 13 – Oct 9: E- BAND STRUCTURE: METALS, CONDUCTORS, INSULATORS Averill 12.6  Drude model: o “Free e- gas” model  e- in valence shell can move  some success o Couldn’t explain insulators vs. metals  needed quantum mechanics!  Quantum mechanics  LCAO-MO applied to many atoms (solids) o Energy levels turn into bands Courtesy of Daniel Nocera. Used with permission.   Electrons can only move (e- conduction) if they are in an energy level adjacent to unoccupied states Metals (Eg=0), Insulators (Eg>3eV), Semiconductors (1ev (h k l) o Plane1: {h k l} o Family of planes1:  1 direction [h k l] is normal to plane (h k l)  1h,k,l are reciprocal of axial intercepts   Distance between adjacent planes with miller indices (h k l) a o d hkl  o a = lattice spacing of unit cell h2  k 2  l 2 X-ray Spectra o e- discharge tube (vacuum tube with a large voltage (~35,000V’s) applied between two electrodes (cathode and anode (target)) o accelerate e- through a vacuum o e- ‘crash’ into anode (target), ejecting bound e- from core shells o e- from higher orbitals ‘cascade down’, releasing high energy photons  x-rays o K, K, L, L, etc.  i.e. K = final shell number of transition (if n=1K, 2L, 3M, 4N...)  i.e.  = n of falling electron (1=, 2=, 3=) o Underlying whale-like shape from continuous e- deflections  Bremsstrahlung o Shortest wavelength of Bremsstrahlung curve -15­  SWL  hc eV Lecture 17 – Oct 19: MOSELEY FIT OF X-RAY SPECTRA Averill pp. 305, 535, 536; Cullity pp. 1E-11E, 19E-22E.  X-ray spectra data fitted to Rydberg-type equation   1 1  2  2   Z    2 n  ni   f    o o  =1/ = inverse frequency  = screening factor  =1 for K, and =7.4 for L  Results of Moseley’s work: o A plot of  vs. Z2 demonstrated a linear relationship o Corrected Mendeleyev: periodic table should be arranged via Z, and not A (atomic mass number) o Placed Lanthenides in periodic table  Improvements to x-ray spectra apparatus by W. D. Coolidge, MIT alum o Lead-shielding o Beryllium window o Water-cooled anode (target) o Heated cathode Hot Cathode o Better vacuum e- X - rays Vacuum Water Therefore: We can now accurately identify relative amounts of elemental species within a sample! e­ Anode Pb shielding Be window Image by MIT OpenCourseWare. -16­ Lecture 18 – Oct 21: PROBING ATOMIC ARRANGEMENT BY X-RAYS, BRAGGS LAW Shackelford 3-7.  See ‘lecture notes’ for Lecture 18 on steps to determine crystal structure  X-Ray Diffraction (XRD)  A means to determine crystal structure! 1. Model atoms as mirrors 2. Apply interference criterion – constructive or destructive  Parallel monochromatic x-rays (i.e. K line from a specific target) are sent to sample.  X-rays reflect off of various planes, constructively or destructively interfering, based on extra distance traveled by ray reflecting off of lower atomic plane.  n  2d sin     2   4a 2 P O For 3.091, n=1 d=interplanar spacing (Lect 16)  ∗ P' O' sin   const h  k2  l2 P'' 2 2 (hkl) Can determine appropriate values of h,k,l, based on (handout) a λ λ B (hkl)  λ E � d d D C d  Can also determine ‘a’:  Image by MIT OpenCourseWare. Determine different crystal types by values of h2+k2+l2 o sc: 1,2,3,4,5,6,8,9 (no 7!) o bcc: 2,4,6,8,10,12,14,16 (would appear as 1,2,3,4,5,6,7,8  there is a 7!) o fcc: 3,4,8,11,12… (the first two terms are a ¾ ratio, not ½)  Two XRD Techniques: 1. Diffractometry (fixed , variable ) (hkl) 2 const (111) Intensity (arbitrary units) 100 ∗ = 0.1542 nm (Cu K�-radiation) 80 60 (200) 40 (220) 20 0 20 2. Laue (variable , fixed )  Spot pattern  atomic symmetry (311) (222) 30 40 50 60 70 2λ (degrees) 80 (400) (331) (420) 90 100 110 120 Image by MIT OpenCourseWare. Therefore, we can now determine crystal structure! Image by MIT OpenCourseWare. -17­ Lecture 19,20 - Oct 23,26: DEFECTS o Reading : Averill 12.4; Shackelford 4-1, 4-2, 4-3, 4-4, 5-1. Point Defects (0-D):  i)Self interstitial, ii) Interstitial impurity, iii) substitution impurity, iv) vacancy  Vacancies: i) Schotty, ii) Frenkel, iii) F-center o Should be able to calculate vacancy fraction based on enthalpy of vacancy formation. o fv   H v nv  A  exp  N  k BT    Also be able to show ‘reaction’ equation for forming a vacancy. (i.e. null  VZr’’’’ + 2Vooo) Line Defect (1-D):  Edge disclocation – extra half-plane of atoms.  Crystals deform via. dislocation motion. Courtesy of John Wiley & Sons. Used with permission. Image by MIT OpenCourseWare. Interfacial Defects (2-D) - Grain Boundaries, surfaces Bulk Defects (3-D) – Amorphous regions in crystal, voids, inclusions, precipitates Courtesy of David Roylance. Used with permission. Image removed due to copyright restrictions. Please see Fig. 12.16 in Averill, Bruce, and Patricia Eldredge. Chemistry: Principles, Patterns, and Applications. San Francisco, CA: Pearson/Benjamin Cummings, 2007. ISBN: 080538039. -18­ Lecture 21 – Oct 30: GLASSES o o o Volume vs. Temperature heating/cooling curves for glasses.  Know: excess volume, effect of different cooling rates, Tg, Tm. Energy comparison: xstal has lower energy than glass ) stal Properties of oxide glasses: cry ( 3 1. Chemically inert B 2O 2. Electrically insulating 3. Mechanically brittle 4. Optically transparent   but high melting point  tough to process  add modifiers to lower Tg Net work formers: have bridging oxygens, i.e. SiO2, B2O3, Network modifiers (lower Tg): ionic bonds  O2­ breaks bridging –O– bonds  i.e. CaO, Na2O, Li2O…  i.e. CaO  Ca2+ + O2­ Intermediates: Courtesy of John Wiley & Sons. Used with permission.  A glass that has a cation that makes a different number of oxygen bonds than the majority glass former. It breaks up the network, results in poorer packing, and increases the thermal shock resistance (i.e. Al2O3 in a SiO2 glass) o o o bo rat e o o gla s s o Atomistic model of Hooke’s law (E vs. r  F vs. r graphs) Factors promoting glass formation:  (viscosity) x (complexity of xtal structure) x (cooling rate)  The larger each of these values, the more likely it is to form a glass instead of a crystal Silicate glasses  Bridging oxygens, –O–  Chemical formula: SiO2  Structural formula: SiO44­ -19­ Lecture 22,23 – Nov 2, 4: GLASS STRENGTHENING MECHANISMS o Two assumptions: i) Glasses break by crack formation and propagation, which starts at the surface. ii) Glasses are strong under compression, but fail because their weak under tension. Solution: create internal stresses that place the surface layer under compression, thereby increasing its strength.  Thermal treatment  tempering  Air jets cool outside of glass faster  larger volume, compressed by slower-cooled internal region  surface under compression yields higher strength  Vouter > Vbulk  Chemical Treatment  Ion exchange. A larger ion replaces a smaller ion in the glass (i.e. K+ (from KCl salt bath) replaced Na+ from the glass). K+ is larger  puts a compressive strain on surface region  increases strength o KINETICS:  Reaction rates, including nuclear decay.  Rate of reaction is proportional to concentration of reactant.  Reaction: aA + bB  cC + dD  Rate Equation:      dC  kC n dt  E  k  Aexp  a   k BT  r ‘k’ is related to MaxwellBoltzmann distribution of energy  Arrhenius relationship Solution depends on value of n (rate of reaction = sum of exponents in reaction equation) Solutions to rate equation: o n=1  ln C  ln C o  kt  1/ C o  kt o n=2  1/ C o  t1/2 = ln(2) / k n=other  plot log(r) vs. log (C)  slope = n, intercept = log(k) -20­ Substitutional (vacancy) Lecture 24 – Nov 6: DIFFUSION o o o o o o o Random movement of particles, resulting in a ‘spreading out’ of particles tending towards equal Qv concentration. Rate Process “d/dt” Rate at which atoms vibrate. = 1013 Hz Jump Freq = 108 Hz  very fast!! Diffusion occurs only if there is a free space to move into (vacancy for self or substitutional diffusion) Diffusion (D) is proportional to the concentration of Image by MIT OpenCourseWare. Adapted from Fig. 5-4 in Askeland, free sites. D also increases with a looser packed atomic Donald R. The Science and Engineering of Materials. 2nd ed. structure. Boston, MA: PWS-Kent, 1989. ISBN: 0534916570.  i.e. # vacancies, or other defects, such as grain boundaries Surface, brain boundary, and volume diffusion occur at different rates  proportional to # of free sites! Energy o Fick’s First Law (FFL)  Flux is proportional to the concentration gradient dC dx  J  D    Use if in stead-state In steady-state, this results in a linear concentration gradient (i.e. straight line) through a material D=diffusivity, units = cm2/s,    Q  D  Do exp   , R  kB N A  RT   Maxwell-Boltzmann distribution again o Fick’s Second Law (FSL)  Introduce time-varying concentration profile. dC d 2C   D 2 ,  one solution is:  dt dx  x  C(x,t)  Cs  erf   Co  Cs  2 Dt     lattice or bulk Courtesy of John Wiley & Sons. Used with permission. Note: solution is for semi-infinite system with constant surface concentration erf = special function. erf (0) = 0, erf(infinity) = 1, erf (x) ~= x for 0 0.1 M, insoluble if Csolute < 0.001 M Equilibrium Constant, K: aA + bB  cC + dD  K = [A]a[B]b / [C]c[D]d  Most other “K’s” are based on the form of this ‘K’, but exclude one term. Solubility Product AaBb  aAb+ + bBa- (i.e. MgCl2  Mg2+ + 2Cl-)  Coefficients become the exponents in Ksp eqn.  Ksp = [Ab+]a[Ba-]b = K[AaBb] Common Ion Effect:  If [Ba-] added via another compound, Ksp must remain the same, therefore, [Ab+] must decrease. o o -22­ Lecture 26 – Nov 13: ACIDS AND BASES o o o pH = -log10[H+], pOH = -log10[OH-], pH + pOH = 14 Definitions: Arrhenius Acid: p+ donor Base: OH- donor Bronsted-Lowry p+ donor p+ acceptor Lewis e- pair acceptor e- pair donor o General Rxn: HA + B  BH+ + A­  Conjugate acid-base pairs  HA & A­  B & BH+  For an acid, B can equal [H2O] o Ka and Kb describe the degree of dissociation of an acid/base, respectively. o In aqueous systems, with B = [H2O]:  Ka = K [H2O] = [H3O+][A-] / [HA] o Amphiprotic: can act as an acid or a base (i.e. H2O) Strong acids  complete dissociation (Ka >> 1) o ACID STRENGTH HF < HCl < HBr < HI To solve some of these problems, 1. write out reaction equation 2. set up chart: initial, change, and final concentrations, with ‘x’ as the change the concentration of the base or acid. 3. solve for x and Ka or Kb are related, using formula above. 567 431 366 299 H-A BOND STRENGTH (kJ/mol) Image by MIT OpenCourseWare. -23­ Lecture 27 – Nov 16: ORGANIC CHEMISTRY o o o o o Naming Nomenclature Prefix (# of carbons in chain)  1 = meth  2 = eth  3 = prop  4 = but  5 = pent  6 = hex  7 = hept  8 = oct Add ‘-ane’ or ‘-ene’, or ‘-yne’ based on bond type. Isomer: same chemical formula, but different configuration  Constitutional Isomers: Same chemical formula, but atoms bonded together in a different order (different side-groups)  (i.e butane vs. 2-methyl propane)  Stereoisomers: Same chemical formula, same sidegroups, but different configuration (i.e. left-hand vs. right-hand). cis- vs. transAromatic compounds:  Double and single bonds ‘share’ delocalized -bond  e- conductivity. cis - 2- Butene (methyl groups on the same side) H3C C Top View H H H3C H C H C C CH3 trans - 2- Butene (methyl groups on the opposite side) C ν C Side View α C CH3 Isomers of Butene C Image by MIT OpenCourseWare. Image by MIT OpenCourseWare. -24­   Diffracted intensity Lecture 28 – Nov 18: POLYMERS I Applied organic chem => polymers Polymers are macromolecules – long chains of molecules with repeating chemical structure. Poly = “many” mer = “repeat unit”  Can be xtalline, amorphous, or a combination of both  XRD can verify this (a) Crystalline 12 30 (b) Amorphous Tailoring Molecular Architecture: I. Composition:  Random copolymer (AABBBABBAAA…)  Regular copolymer (ABABA…)  Block copolymer (AAAAAABBBBBBB…)  Graft copolymer (BBBBBBBBB… with AAA…and S side chains) (c) Partially Crystalline 12 15 20 25 30 Angle of diffraction (o) II. Tacticity  Polymer can also be classified by side-group orientation o atactic, syndiotactic, isotactic Polyethelene Image by MIT OpenCourseWare. III. Backbone:  Linear chain  Branched chain: harder to xtalize  Crosslinked: Enabled by sulfur. Rubbery! Partially crystallized polyethylene Synthesis:  Addition polymerization o Need free radicals and double bonds to carry synthesis Source: Hayden, H. W., W. G. Moffatt, and J. Wulff. The Structure and Condensation polymerization  of Materials; Vol. III, Mechanical Behavior. John Wiley and o Formed by rxns between the start and ends of mers Properties Sons, Inc., 1965. © John Wiley and Sons. All rights reserved. o Polymer looses mass when synthesized (e.g. the condensation) Thermoplastic: only Van der Waals acting between neighboring polymers, liquefies upon melting and are easy to recycle. CH3 CH3 ... CH2 CH CH2 CH3 CH CH2 CH CH2 CH CH2 CH3 CH ... CH3 Atactic Polypropylene Thermoset: caused by the cross linking of polymers with disulfide bonds. There are covalent bonds between polymers, so the material strengthens but as a result is extremely hard to recycle. ... CH2 CH CH2 CH CH2 CH CH2 CH CH2 CH ... CH2 CH ... Syndiotactic Polystyrene ... CH2 CH Cl CH2 CH Cl CH2 CH CH2 CH Cl Cl Cl Isotactic Poly(vinyl chloride) Image by MIT OpenCourseWare. -25­ Lecture 29 – Nov 20: POLYMERS II: Polymer Synthesis: 1. Addition Polymerization  Uses an initiator (R radical) to break a double or triple C-C bond (of a mer unit)  i.e. R* + CHn=CHn  R-CHn-CHn*  growth by subsequent mer attachment 2. Condensation Polymerization  Uses the reaction between an H and an OH on two separate molecules to form an amide or peptide both, and releasing H2O  i.e. R1H + R2OH  R1-R2 + H2O  mass polymer < Sum (mass of reactants) Plastics can have zones of random configuration and zones of crystallization, which can make the material stronger and denser. Factors favoring crystallization: 1. composition - homopolymer over copolymer) 2. tacticity – isotactic attractive 3. conformation – linear over branched Properties of polymers  e- insulating, transparent to visible light, low density, solid at room temp. Recall:  Nylon pull-out video  glass transition temperature of different polymers -26­ Lecture 30 – Nov 25: BIOCHEMISTRY: Amino Acids:    Contain an amine group, carboxylic acid group, and a side chain, R. R can be anything. But in our bodies, there are just 20 different R’s, giving rise to twenty different amino acids R can be 1) nonpolar, 2) polar, 3) hydrophilic + acidic, 4) hydrophilic + basic  3) and 4) can be ‘titratable’ (i.e. can accept or give off a H+, depending on the local pH) Image by Yassine Mrabet on Wikipedia. Amino acids are usually Chiral (i.e. Left (L) or Right (D) handedness  L- or D-enantiomers) Image by MIT OpenCourseWare. Amino acids are Zwitterions:  In water at neutral pH, COOH group gives up an H+, and the amine group accepts an H+, causing the molecule to be net neutral, but have local +’ive and –‘ive charges  At high pH (low [H+]), H+ are stripped off of NH3+  At low pH (high [H+]), H+ are added to COOFor titratable groups on the amino acid (i.e. a group that can gain or lose a H+): HA + H+  HAH+ K1 = [H+][HA]/[A-] (K is basically the equilibrium constant) pK1 = pH + log10([HAH+]/[HA]) Similarly, at high pH A­ + H+  HA+ K2 = [H+][A-]/[HA] (K is basically the equilibrium constant) pK1 = pH + log10([HA]/[A-]) pI = isoelectric point. When net charge of all molecule is zero (i.e. [HA] >> [HAH+],[A-]) It happens ½ way between pK1 and pK2. pI = (pK1 + pK2)/2 -27­ Lecture 31 – Nov 30: PROTEIN STRUCTURE: Titration Curve for Alanine Plot of pH as a function of ‘extent of reaction’: “Equivalents of OH-” is the same as the negative of [H+]. i.e. the number of [H+] in the system (both free, and bound to the Zwitterion) increases from right to left. CH3 12 pK2 H2N CH (anion) COO 10 H H pIAla 8 CH3 pH Gel Electrophoresis: Apply a voltage across a gel tube with varying pH. Amino acids (zwitterions) introduced at one end. Zwitterions are propelled to migrate in the electric field as long as they have charge. When they reach the pH equivalent to their pI, they no longer have net charge, so they stop. This allows researchers to measure the pI 6 H3N pK1 4 H H CH3 2 H3N 0 of an amino acid / zwitterion. CH COO (zwitterion) 0 0.5 1.0 1.5 CH (cation) COOH 2.0 Equivalents of OH Proteins formed by condensation reaction between amides, forming polyamides. Image by MIT OpenCourseWare. Protein exhibiting secondary structures:  regions: -helix, -sheets, random coils Courtesy of John Wiley & Sons. Used with permission. Source: Spencer, J. N., G. M. Bodner, and L. H. Rickard. Chemistry: Structure and Dynamics. 2nd ed., supplement. New York, NY: John Wiley & Sons, 2003. Tertiary structure of proteins (“random” coils): - “random” structure determined by secondary bonding, ie. 1) disulfide bonds, 2) H-bonding, 3) columbic, 4) hydrophobic regions © source unknown. All rights reserved. Underlying image © source unknown. All rights reserved. -28­ Lecture 32 – Dec 2: LIPIDS, NUCLEIC ACIDS, DNA Proteins can be denatured (i.e. breaking secondary bonding) by changes in:  1) Temperature, 2) pH, 3) oxidizing/reducing agents to create/destroy -S-S- bonds), 4) detergents Lipids: defined by their properties – soluble in solvents of low polarity – includes fats, oils, cholesterol, hormones.  Some have a hydrophilic head and a hydrophilic tail (amphipathic molecules)  can arrange in a lipid bilayer in a polar solvent  Cell wall! Nucleic acids  Building block of nucleotides  DNA  DNA contain sugar (amine link) and a phosphate backbone, with one of four of five amine groups that make up the ‘code’ (AGCU for RNA, and AGCT for DNA)  A pairs with T (2 H bonds), C pairs with G (3 H bonds). Spacing is important.  These chains makeup a double-helix structure  DNA Generalized Structure of Nucleic Acid DNA Double Helix Phosphate Sugar-phosphate backbones 5' end sugar Base O C G C G GC _ P O O CH2 Base O A T A 3' Position Base O CG _ P O O CH2 T T O sugar A 5' Position O Major groove G Base C C G A G Phosphate Base pair 3' end 0.33 nm C T T O Base sugar 3.40 nm Phosphate Minor groove T T A 2.37 Images by MIT OpenCourseWare. H N H O N H N O H N N Cytosine Guanine N N N Backbone Hydrogen bond Backbone H H O CH3 Thymine H N N H N O N N Adenine N Hydrogen bond N Backbone Backbone -29- Lecture 33 – Dec 4: PHASE DIAGRAMS, ONE COMPONENT - UNARY o o o Triple point is where the three lines meet, a region where three phases coexist in equilibrium Slope of solid/liquid interface (2 phase region) characterized the density of the material in either phase Super critical fluid is a one phase regime “Normal” conditions means 1 atm of pressure more examples Supercritical fluid Carbon dioxide (CO2) 73.0 Pressure (atm) o Liquid Solid Gas 5.11 1 -78.5 -56.4 31.1 Temperature (oC) Image by MIT OpenCourseWare. Source: Bergeron, C., and S. Risbud. Introduction to Phase Equilibria in Ceramics. American Ceramic Society, 1984. Reprinted with permission of The American Ceramic Society, www.ceramics.org. Some rights reserved. -30­ Lecture 34 – Dec 7: PHASE DIAGRAMS – BINARY – LENTICULAR/IMMISCIBILITY o Sadoway’s system classification o Type 1  Complete solubility as solids and liquids  Isomorphism – lens shape  Properties include:  Identical crystal structures  Similar atomic volumes  Small electronegativity differences  When (c) > 1, impossible to move from one single phase field to another single phase field  Liquidus: lowest temperature at which all liquid is stable  Solidus: highest temperature at which all solids are stable o LEVER RULE  (P) = 2  Used to compute percentages of the relevant phases in equilibrium  For the example on the right:  Held at c2 (you can do the same for c1) c*s  c2 c*s  c*l  %liquid   %solid   c*l is the equilibrium concentration in the L c2  c*l c*s  c*l liquid phase  c*s is the equilibrium concentration in the solid phase Polystyrene - Polybutadiene phase diagram o Type 2  partial or limited solubility of both components in each other  no change of state – always solid or always liquid  generates “Synclinal” coexistence curve Images: top © Cengage Learning/PWS-Kent, bottom © source unknown. All rights reserved. -31­ Lecture 35 – Dec 9: PHASE DIAGRAMS – BINARY – LIMITED SOLUBILITY o Type 3  Partial solubility of A and B  Change of state  “hybrid between lens and syncline”  Freezing point depression of both components  Eutectic: composition and temperature where three phases coexist in equilibrium.  APPLY LEVER RULE TO TWO PHASE REGIONS!!!   ,  L, L  Top example:   is a Pb-rich phase   is a Sn-rich phase  You can tell a lot about the history of a material by looking at the microstructure © Cengage Learning/PWS-Kent. All rights reserved. Source: Source: Fig. 10-6 in Askeland, Donald R. The Science and Engineering of Materials. 2nd ed. Boston, MA: PWS-Kent, 1989. Courtesy of John Wiley & Sons. Used with permission. Fig. 9.14 in Callister, Materials Science and Engineering. 6th ed. John Wiley and Sons, 2002. -32­