How to measure the standard enthalpy of formation

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2 How to measure the standard enthalpy of formation PChem Thermodynamics class calculate H for ideal gas at real gas standard cond. standard cond. measure H for mixing the elements calculate H for real gas reaction standard cond. *) conditions measure by a calorimeter H of the reaction of the mixed elements calculate H for real gas reaction standard cond. conditions calculate H for ideal gas at real gas standard cond. standard cond. Do you Remember That one?

3 Problems with that scheme Data in thermodynamic tables are for standard conditions. But for the scheme we would need data for p 1 atm T 25C Solution A) Equations for T 1 T H H C dt z T2 T 1 p T PChem Thermodynamics class T 2 Kirchhoff s law =z Kirchhoff s law 1 B) Measure H at 25C somehow. Last missing step

4 Measuring H or U at standard conditions PChem Thermodynamics class Problem We need to measure H or U of the reaction at standard conditions. Solution Trick Using a cycle that is running the reaction virtually at 25C. That is the theory for one of your lab class experiments.

5 Step 1 PChem Thermodynamics class Reactants + calorimeter Step 1 Products + calorimeter 25 C T 25C + T U =? We have a calorimeter. Thus, w = 0 (no work on surroundings) q = 0 (dewar) U = q + w = 0 calorimeter

6 Step 2 PChem Thermodynamics class Reactants + calorimeter Step 1 Products + calorimeter 25 C T 25C + T U = 0 Products + calorimeter 25C Step 2 Cool down the system to 25C. Trick : That generates a reference system at 25 C (standard conditions). calorimeter

7 Step 3 PChem Thermodynamics class Reactants + calorimeter Step 1 Products + calorimeter 25 C T 25C + T U = 0 U el = VCt Step 3 Products + calorimeter 25C Step 2 Heat the system with an electrical heater. U el = Voltage * Current * time U el = VCt calorimeter

8 Step 4 PChem Thermodynamics class Reactants + calorimeter Step 1 Products + calorimeter 25 C T 25C + T U = 0 Step 4 U el = VCt Step 3 U(reaction, 25C) Products + calorimeter 25C Step 2 Ui is state t function Step 1 Step 4 Step 3 = + calorimeter U = U el + U(reaction, 25C) U el = U(reaction, 25C)

9 That s thermo bulls what about a real experiment? PChem Thermodynamics class Using an electrical heater is a little strange: it is experimentally difficult but has the advantage that we do not need to calibrate the system. The lab class experiment works a little differently. Not everybody y is in the lab class, I know. BUT that s thermodynamics. calorimeter

10 Experiment. T PChem Thermodynamics class Reactants + calorimeter 25 C Step 1 U = 0 Products + calorimeter 25C + T Step 4 putting heat in U q = heat = q Step 3 T U(reaction, 25C) Products + calorimeter 25C Step 2 U(reaction)=- U ) q =q=c Cal+Pr T calorimeter

11 Calibration PChem Thermodynamics class Disadvantage: we need C Cal+P Burning benzoic acid measuring T C Cal+P calorimeter

12 That s what you may copy for your notes. Or PChem Thermodynamics class Reactants + calorimeter Products + calorimeter 25 C U = 0 25C + T U el = VCt U(reaction, 25C) Products + calorimeter 25C U el = U(reaction, 25C) calorimeter

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14 How do we know that? I had to reduce the size of the file. Contact us if you are interested in a more complete version. Surface Chemistry How to determine the structure of a surface? I follow mostly Yip-Wah Chung, Practical Guide to Surface Science and Spectroscopy, Academic Press, 2001, Chapter 6, p

15 How to determine the surface structure? Surface Chemistry Reciprocal lattice Diffraction techniques LEED Low Energy Electron Diffraction HAS He Atom Scattering Real lattice Direct techniques Scanning probe techniques STM Scanning Tunneling Microscopy AFM Atomic Force Microscopy SCaM - Scanning capacitance microscope

16 Scanning Tunnelling Microscopy Surface Chemistry 1923 Q.M. theory of tunneling 1958 Tunnel diode, L. Esaki (IBM) nobel price 1981 Binnig & Rohrer (IBM) first STM paper Si(111)-7x Nobel price for STM for Binnig, Rohrer, Ruska 1983 AFM STM

17 Brief note solid state physics Surface Chemistry valence level Work function φ Vacuum level Fermi level single atom solid state solid state STM

18 Scanning Tunnelling Microscopy Surface Chemistry High-resolution imaging lateral (horizontal) vertical AND works in vacuum in air in liquids id STM used as a tool lithography atom manipulation atomic switching works with metals semiconductors metal oxides biological model surfaces If you know some tricks STM

19 Tunneling effect Surface Chemistry potential distance classical mechanics quantum mechanics STM

20 Scattering problems in Q.M. PChem Quantum mechanics wave functions Ansatz ikx ψ 1 = Ae + Be ψ 3 ikx potential, size of the box = a α ψ = i x + 2 Ce De ψ 3 = iαx Ae ' ikx k = 2mE 2 2 α = 2mE ( E)/ 0 2 Result Transmission coefficient Remember that one: p exp( a m )

21 Tunneling effect more details Surface Chemistry Remember that one: p exp( a m ) STM

22 STM resolution Surface Chemistry Tunneling probability p: p exp( 2a 2mV ( 0 E) ) m: electron mass L surface tip step L P ( L ± L ) PL ( ) L = = 1± 001(1%) A for E = 0.1 V A = 0.5 V A = 0.9 V 0 STM

23 STM constant current mode Surface Chemistry p exp( 2a 2mV ( 0 E) ) h tunneling current Constant current constant a constant high above the surface STM

24 STM measuring mods Surface Chemistry moving Tip is moving up and down (fast feedback) constant height above the surface nt curre Constant current mode topography mode distance moving Tip follows the general surface morphology (but slow feedback) height above the surface not constant curre ent Constant height mode distance

25 What does the STM actually measure? Surface Chemistry Again remember quantum mechanics? golden rule of Q.M. Transition probabilities Selection rules Very general equation. as I told you in the Q.M. lecture. Application here I ψ ( tip position) 2 δ( E E ) surface s F LDOS E F : Fermi energy I: Tunneling current = Local density of states at the Fermi energy at the tip position. Constant current mode gives a contour of constant LDOS at E F. STM

26 What does the STM actually measure???? Surface Chemistry Remember: Constant current mode gives a contour of constant LDOS at E F. BUT 2a 2mV ( 0 E ) p exp( ) h tunneling current Tunneling through the Fermi level of metals. V 0 -E is related to the work function. p exp( Aφφ ) tunneling current If φ does not change along the surface. topography Otherwise (inhomogeneous surface) mixture of φ and topography Today: DFT calculations to simulate STM figures. STM

27 Why is an STM working in air? Surface Chemistry Tunneling volume approx. 0.1 nm 3 pv=nrt gas molecules in that volume 3.33 water molecules Small scattering probability of the electrons through the way from the tip to the surface. STM

28 Technical STM implementation moving the tip Surface Chemistry Coarse motion control Problem: long traveling distance of the tip with high precision Fine motion control Voltage 10 nm/v Is that so difficult? piezoelectric positioners At Actually not - consider: Conventional screw e.g. 80-pitch screw Z 80 turns = 1 inch (2.54 cm) 880 nm for 1deg screw rotation X Y piezoelectric tube scanner Inside completely metal coated Outside divided in 4 segments STM

29 Technical STM implementation vibration isolation Surface Chemistry How to minimize the coupling of the external vibrations with the STM? sp prings F STM f Remember physics.. againnn.. coupled harmonic oscillators F >> f f Result: 1) soft platform, small f 2) STM very rigid large F external vibrations F s resonance frequencies STM

30 Technical STM implementation typical set up Surface Chemistry T. Engel Quantum Chemistry & Spectroscopy ISBN X 3842 (2005)

31 STM Surface Chemistry

32 STM example surface structure Surface Chemistry Si(111) 7x7 reconstruction STM

33 STM example atomic manipulation Surface Chemistry Imaging mode: 5-6A ( MOhm) Manipulation mode: 1-3A (50-200kOhm)* tip tip tip D. Eigler, et al. Nature 344, 6266 (1990) Nature 417, 722 (2002) Science 254, 1319 (1991) Nature 352, 600 (1991) STM *R.J. Celotta, AVS-2005

34 STM example lithography Surface Chemistry The tunneling current is focused down to a diameter below a nm R Current density 1x10 6 A/cm 2 Distance Current That can induce chemical reactions. That can be used to produce patterns by decomposing molecules. (20A) Distance STM Phys. Rev. B 31 (1985) p. 2

35 STM spectroscopy Surface Chemistry variable tip A Mode: V 1) Keep tip-surface distance constant const 2) Change the tip-surface voltage (V). Remember: Tunneling samples LDOS (Local Density Of States). Therefore, the electronic states involved in the tunneling process depends on the voltage. Tunneling current bandgap Tip-surface voltage STM

36 STM insulating samples Surface Chemistry Typical tunneling conditions: Tip-surface gap resistance 10 MOhms Tunneling current 1 na Tip-surface voltage (bias) 10 mv Resistance of sample must be smaller than approx. 10 MOhms. Solution Cover the surface with a metal. Heat the surface. Doping the surface. AC tunneling. STM

37 Surface Chemistry AFM Atomic Force Microscope PSTM Photon Scanning Tunneling Microscope SCM -- Scanning Capacitance Microscope NFTM Near Field Thermal Microscope SICM Scanning Ion Conductance Microscope TAM Tunneling Acoustic Microscope PCM Point Contact Microscope BEEM Ballisic Electron Emission Microscope IETS Inelastic Electron Tunneling Spectroscopy STM

38 Scanning Capacitance Microscope Surface Chemistry Physics (again) - sorry ε A C= 0 d q = CV Idea: Capacitance (tip sample) correlated with tip-sample distance. Disadvantage: Change in capacitance is very small (25 nm resolution) Advantage: 1) works for insulators 2) can be chemically specific STM

39 Idea - Atomic Force Microscope Surface Chemistry Idea: LASER cantilever surface Advantage: -) works for insulators -) magnetic cantilever (magnetic surfaces) STM Surface Science Reports vol. 59 (2005) p Force measurements with the atomic force microscope: Techniques, interpretation and applications Hans-Jürgen Butt, Brunero Cappella and Michael Kappl

40 STM - Literature Surface Chemistry Yip-Wah Chung, Practical Guide to Surface Science and Spectroscopy, Academic Press, 2001 C. Hamann, M. Hietschold, Raster-Tunnel-Microscopy, Akademie Verlag, STM

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42 FT NMR setup (idea) PChem Quantum mechan 1) Static and large B 0 field along z axis 2) Small oscillation B 1 field along y axis B 0 (Effectively linear polarized field.) B 1 3) Detector coil (not shown) wound around sample NMR

43 FT NMR setup that s how it really looks like PChem lab class experiment PChem Quantum mechan Inside a NMR Magnet NMR Flow Chart 90 degree pulse NMR NMR magnets made from a coil of super conducting wire. Superconducting wire needs to be cooled to 4K (-269C). Liquid helium is used as coolant. Liquid nitrogen is used as a secondary coolant. Static magnetic field strengths above 20T are possible. Excite the system by turning on an oscillating current in excitation coil (pulse). Nuclear macroscopic magnetization flips from Z direction to XY (90 o ). In the XY plane magnetization precesses creating an oscillating signal. Oscillating current detected in receiver coil. Convert the resulting signal from analogue to digital. Fig. from John Bagu

44 Circular polarized field B 1 cc B = B[ xcos( ωt) + ysin( ωt)] 1 1 counterclockwise c B = B[ xcos( ωt) ysin( ωt)] 1 1 clockwise PChem Quantum mechan B c + B = cc 1 1 x oscillating y zero (no net effect) NMR Only cc component rotates with M and can induce transition. Thus, circular polarized field has the same effect as a linear polarized filed.

45 FT NMR lab frame & rotating frame (vector model) PChem Quantum mechan z: Static field x-y: Circularly polarized field rotating Σ: total filed processes along z axis M processes about the total field which is processing by itself Coordinate system rotates about z axis B and B 1 are stationary. Σ: Total field B = B B 1 along z axis M processes about B At resonance M tilts and processes in xy plane. NMR

46 FT NMR dephasing spins PChem Quantum mechan The pulse tilts the magnetization M in the xy plane. After the pulse: z: relaxes back to equilibrium along z axis with T 1 xy: different spins rotate at different frequency dephasing spins with T 2 NMR

47 FT NMR Bloch equation PChem Quantum mechan d dt F GH 1 < s x > T > < 1 2 < s s > x B + < s y > T2 s0 < sz > T 1 I JK Works for electron and nuclear spins. NMR

48 FT NMR-free induction decay PChem Quantum mechan Detector coil along gy axis. z: M z decreases no effect on detector xy: M xy decreases free induction decay seen in detector NMR

49 FT NMR more than one resonance PChem Quantum mechan Chemical shifts & field heterogeneities result in more than one resonance frequency Recovering the information. I( ω) = I( t)[cos( ωt) + isin( ωt)] dt z0 Why does that work? pulse consits of many frequency components f () t = ( cnsin( nωt) + dncos( nωt)) Analog: Like a bell struck with a hammer. It will ring with its resonance frequency independent d of the kind of hammer. NMR

50 FT NMR advantage of the technique PChem Quantum mechan N 2 e E / = kt N 10 N 1. Bad signal-to-noise ratio in NMR Average many scans by keeping measuring time reasonable. FT-IR is faster The whole spectral range is accessed at all time (in one pulse). In contrast: cw NMR individual resonances are measures serially. NMR

51 FT NMR spin echo experiment PChem Quantum mechan Measuring T 2 Intro to 2D NMR Effect of the pulse M x M x M y -M y Similar idea is used for 2D NMR Next week. NMR

52 FT NMR -- setup PChem Quantum mechan Figures from Quantum Chemistry and Spectroscop T. Engel Ch 18 - NMR ISBN X Cool web sites: edu/biophysics/lecture6 ppt# (e.g. lecture 3 PowerPoint) NMR

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54 Infrared spectroscopy -- classification PChem Quantum mechan Transmission Infrared spectroscopy RAIS Reflection-absorption Infrared spectroscopy HREELS High Resolution Electron Energy Loss Spectroscopy Spectroscopy

55 Infrared spectroscopy -- setup PChem Quantum mechan Sometimes called dispersion IR spectrometer since it includes a prism or grating to disperse the electro.mag. radiation Idea of operation, briefly: The chopper splits the beam that consecutive the reference cell or the sample cell signal will reach the detector The mirror acts as a diffraction gratings selects a partition of the spectra. If the sample does not adsorb at the selected frequency then the reference beam and sample beam have the same intensity and the amplifier will yield a zero signal Typically lock-in technique is use i.e. the amplifier is a little more sophisticated than shown in the scheme above.

56 AES Lock In technique input AC amplifier band pass filters Phase sensitive amplifier Low pass filter output Surface Chemistry Phase shifter Modulator Reference Lock in idea: Input signal - modulated with ω and zero phase lag with respect to the refe Output signal - constant voltage level. All other signals will be averaged out by the phase sensitive amplifier. A lock in amplifier is a filter with an extremely narrow band width. Side effects Nyquist equation: Signal-to-noise noise ratio ~ sqrt(band width) Background not modulated: it will be subtracted Spectroscopy

57 Infrared spectroscopy setup ---FTIR Fourier-transform IR spectrometer PChem Quantum mechan Idea of operation: The source beam will be split. One part arrives at the detector directly. The other one will be delayed by going a longer way. The difference in the traveling path length of these two beams will be modulated by a movable mirror. (That s the clue.) The interference of these two beams will be analyzed at the detector. The spectra (intensity vs. wave number) is the Fourier transformation of the interference signal (intensity vs. position of the mirror). Spectroscopy

58 Infrared spectroscopy Michelson interferometer PChem Quantum mechan The interferogram is a sum of cos waves, each has an amplitude and frequency proportional to the source intensity at a particular infrared frequency. Recovering ering this information is done by a Fourier transformation.

59 More than one frequency of the source PChem Quantum mechan Main idea: We measure an intensity as a function of time (i.e. as a function of the position of the 2 nd mirror which is changing with time) that is the interference of the sample and reference beam. This intensity vs. time signal is converted in an intensity vs, frequency signal by means of a Fourier transformation.

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61 HREELS

62 O C O C O C

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64 Emission/Absorption spectra of gases PChem Quantum mechan Emission spectra Absorption spectra Lyman series Balmer series

65 Emission/Absorption spectra of gases H atom PChem Quantum mechan

66 Electronic absorption spectrum of gas-phase benzene PChem Quantum mechan Vibrational and rotational levels are broadened at larger gas pressures which leads to the detection of continuous spectra.

67 Potential energy diagram diatomic molecule PChem Quantum mechan ground state excited state D 0, D 0 dissociation energies E at, E at separated atoms >E at continuous absorption

68 LIF Laser induced Fluorescence PChem Quantum mechan LIF has a much better sensitivity than absorption spectroscopy.

69 Potential energy diagram more details but same story PChem Quantum mechan

70 Set-up -- cf., PChem lab class -- spectrofluorimeter Excitation spectra excitation wavelength scanned emission wavelength fixed Excitation monochromator Emission monochromator Emission spectra emission wavelength scanned excitation wavelength fixed

71 Emission / Excitation spectra PChem Quantum mechan Excita ation spect tra Emiss sion spectr ra Excitation spectra excitation wavelength scanned emission wavelength fixed Emission spectra emission wavelength scanned excitation wavelength fixed

72 Spectrofluorimeter PChem Quantum mechan

73 Examples PChem Quantum mechan