Upload
others
View
4
Download
0
Embed Size (px)
Citation preview
PChem – Thermodynamics class
How to measure the standard enthalpy of formation
y
calculate H forideal gas at real gasstandard cond. standard cond.
∆
measure H for mixing the elements∆
calculate H forreal gas reaction
∆ Do youRememberg
standard cond. conditions
measure by a calorimeter H of the reaction of thei d l t
∆
*) RememberThat one?
mixed elements
calculate H forreal gas reactionstandard cond. conditions
∆
calculate H forideal gas at real gasstandard cond. standard cond.
∆
PChem – Thermodynamics class
Problems with that scheme…
y
Data in thermodynamic tables are for standard conditions.But for the scheme we would need data for p ≠ 1 atm
T ≠ 25CT ≠ 25CSolution
A) Equations for T1 T2 ∆ ∆ ∆H H C dTT T
T20
10 0− = z Kirchhoff’s law∆ ∆ ∆H H C dTT T p
T2
1
1 z Kirchhoff s law
B) Measure ∆H at 25C somehow.
Last missing step
PChem – Thermodynamics class
Measuring ∆H or ∆U at standard conditions
y
Problem – We need to measure ∆H or ∆U of the reaction atstandard 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.
PChem – Thermodynamics class
Step 1
y
Reactants + calorimeter Products + calorimeterStep 125 C 25C + ∆T
∆T∆U = ?
We have a calorimeter. Thus, w = 0 (no work on surroundings)q = 0 (dewar) ∆U = q + w = 0
calorimeter
PChem – Thermodynamics class
Step 2
y
Reactants + calorimeter Products + calorimeterStep 125 C 25C + ∆T
∆T∆U = 0
P d l iProducts + calorimeter25C
Step 2
Cool down the system to 25C.“Trick”: That generates a reference system at 25 C (standard conditions).
calorimeter
PChem – Thermodynamics class
Step 3
y
Reactants + calorimeter Products + calorimeterStep 125 C 25C + ∆T
∆T∆U = 0
P d l i
Step 3∆Uel = VCt
Products + calorimeter25C
Step 2
Heat the system with an electrical heater. ∆Uel = Voltage * Current * time∆Uel = VCt
calorimeter
PChem – Thermodynamics class
Step 4
y
Reactants + calorimeter Products + calorimeterStep 125 C 25C + ∆T
∆T∆U = 0
P d l i
Step 3∆Uel = VCtStep 4
∆U(reaction, 25C)Products + calorimeter25C
Step 2
U i t t f tiU is state functionStep 1 Step 4 Step 3= +
∆U = ∆U + ∆U(reaction 25C) ∆U ∆U(reaction 25C)∆U = ∆Uel + ∆U(reaction, 25C) −∆Uel = ∆U(reaction, 25C)
calorimeter
PChem – Thermodynamics class
That’s thermo bulls… what about a real experiment?
y
Using an electrical heater is a little strange:it i i t ll “diffi lt”• 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 is in the lab class, I know.y y ,BUT that’s thermodynamics.
calorimeter
PChem – Thermodynamics class
“Experiment.”
y
Reactants + calorimeter Products + calorimeterStep 1
∆T
Reactants calorimeter25 C
Products + calorimeter25C + ∆T
Step 1
∆U = 0putting heat in
Step 3∆Uq = heat = qStep 4
∆U(reaction 25C)
∆Tp g
Products + calorimeter25C
Step 2∆U(reaction, 25C)
∆U( ti ) ∆U C ∆T∆U(reaction)=-∆Uq=q=CCal+Pr ∆T
calorimeter
PChem – Thermodynamics class
Calibration
y
Disadvantage: we need CCal+P
Burning benzoic acid measuring ∆T CCal+P
calorimeter
PChem – Thermodynamics class
That’s what you may copy for your notes.Or www…..
y
Reactants + calorimeter Products + calorimeter25 C 25C + ∆T
∆U = 0
P d l i
∆Uel = VCt
∆U(reaction, 25C)Products + calorimeter25C
−∆Uel = ∆U(reaction, 25C)
calorimeter
Surface Chemistry
How do we know that?y
I had to reduce the size of the file.Contact us if you are interested in a more complete version.
How to determine the structure of a surface?
I follow mostlyYip-Wah Chung, Practical Guide to Surface Science and Spectroscopy,Academic Press 2001 Chapter 6 p 101-118Academic Press, 2001, Chapter 6, p. 101-118
How to determine the surface structure?Surface Chemistryy
Real latticeDirect techniquesScanning probe techniques
Reciprocal latticeDiffraction techniques
Scanning probe techniques
LEED – Low Energy ElectronDiffraction STM – Scanning Tunneling
AFM – Atomic ForceMicroscopy
HAS – He Atom Scattering
Microscopy
Microscopy
SCaM - Scanning capacitance microscope
Scanning Tunnelling MicroscopySurface Chemistryy
1923 Q.M. theory of tunneling1958 Tunnel diode L Esaki (IBM) nobel price1958 Tunnel diode, L. Esaki (IBM) nobel price1981 Binnig & Rohrer (IBM) first STM paper Si(111)-7x71986 Nobel price for STM for Binnig, Rohrer, Ruska1983 AFM1983 AFM
STM
Brief note – solid state physicsSurface Chemistryy
Work function φVacuum level
valence Work function φFermi level
level
single atomsolid state solid state
STM
Scanning Tunnelling MicroscopySurface Chemistryy
High-resolution imaging lateral (horizontal)vertical
AND
works withmetals
worksin vacuumin airi li id
metalssemiconductorsmetal oxidesbiological model surfaces
STM used as a toollithography
in liquids If you know some tricks…atom manipulationatomic switching
STM
Tunneling effectSurface Chemistryy
potential
distance
STM
classical mechanics quantum mechanics
PChem – Quantum mechanics
Scattering problems in Q.M.Q
wave functions
ψ 3 =−A e ikx'Ansatz
potential, size of the box = a
ψ α α2 = + −Ce Dei x i x
ψ 3
k mEm E E
2 2
02
22=
= −α ( ) /
ψ 1 = + −Ae Beikx ikx
Result
0
Transmission coefficient
( )Remember that one:
p a m≈ −exp( )
Tunneling effect – more detailsSurface Chemistryy
( )Remember that one:
STM
p a m≈ −exp( )
STM resolutionSurface Chemistryy
Tunneling probability p:
pa m V E
≈ −−
exp(( )
)2 2 0
l tm: electron mass
P L L( )± ∆tip P L LP L
( )( )
.±= ±
∆ 1 0 01 (1%)
fL
∆L
∆L =0.02 A for E = 0.1 V00.03 A = 0.5 V00.06A = 0.9 V0
∆L
surface step
STM
STM – constant current modeSurface Chemistryy
pa m V E
≈ −−
≈exp(( )
)2 2 0
h tunneling current
h
Constant current constant aConstant current constant aconstant high above the surface
STM
STM – measuring modsSurface Chemistryy
movingTip is moving up and down (fast feedback)
constant height above the surface
nt Constant current mode
distance
curr
e Constant current modetopography mode
movingTip follows the general surface morphology (but slow feedback)
height above the surface not constant
ent
distance
curr
e “Constant” height mode
What does the STM actually measure?Surface Chemistryy
Again remember quantum mechanics ? – golden rule of Q.M.
Transition probabilitiesTransition probabilitiesSelection rules Very general equation …. as I told you in the Q.M. lecture.Application here …
I E ELDOS
surface s F≈ − tip position)|2| ( ( )ψ δEF: Fermi energyI: Tunneling current
LDOS≈ = Local density of states at the Fermi energy at the tip position.
Constant current mode gives a contour of constant LDOS at EF.
STM
What does the STM actually measure????Surface Chemistryy
Constant current mode gives a contour of constant LDOS at EF.Remember:
a m V E−(
( ))
2 2 0 li
BUT
Tunneling through the Fermi level of metals
p ≈ − ≈exp(( )
)0
htunneling current
Tunneling through the Fermi level of metals.V0-E is related to the work function.
p A≈ − ≈exp( )φ tunneling currentp A≈ ≈exp( )φ tunneling current
If φ does not change along the surface. topography Otherwise (inhomogeneous surface) mixture of φ and topography
STM
Otherwise (inhomogeneous surface) mixture of φ and topographyToday: DFT calculations to simulate STM figures.
Why is an STM working in air?Surface Chemistryy
Tunneling volume approx. 0.1 nm3
pV=nRT 0.003 gas molecules in that volume
3 3 water molecules3.3 water molecules
Small scattering probability of the electronsSmall scattering probability of the electronsthrough the way from the tip to the surface.
STM
Technical STM implementation – moving the tipSurface Chemistryy
Coarse motion control Fine motion control
Problem: long traveling distanceof the tip with high precision Voltage
10 nm/V
Is that so difficult?
A t ll t id
piezoelectric positioners
Actually not - consider:Conventional screwe.g. 80-pitch screw
80 turns = 1 inch (2.54 cm)
Z piezoelectrictube scanner
( )880 nm for 1deg screw rotation X Y
STM
Inside completely metal coatedOutside divided in 4 segments
Technical STM implementation – vibration isolationSurface Chemistryy
How to minimize the coupling of theexternal vibrations with the STM ?
prin
gs
Remember physics .. againnn..
coupled “harmonic” oscillatorsF fSTMsp coupled harmonic oscillators
F >> f’
Result:Result:1) soft platform, small f2) STM very rigid large Ff’
external vibrations
STM
F’s resonance frequencies
Technical STM implementation –typical set up
Surface Chemistryy
T. EngelQuantum Chemistry & SpectroscopyISBN 0 8053 3842 XISBN 0-8053-3842-X(2005)
Surface Chemistryy
STM
Surface Chemistry
STM example – surface structurey
Si(111) 7x7 reconstruction
STM
http://www.almaden.ibm.com/vis/stm/corral.html
Surface Chemistry
STM example – atomic manipulationy
Imaging mode: 5-6A (10-100 MOhm)Manipulation mode: 1-3A (50-200kOhm)*
tiptip
tip
D Eigler et alD. Eigler, et al.Nature 344, 6266 (1990)Nature 417, 722 (2002)Science 254, 1319 (1991)N 352 600 (1991)
STM*R.J. Celotta, AVS-2005
Nature 352, 600 (1991)
Surface Chemistry
STM example – lithographyy
The tunneling current is focused down to a diameter below a nm
Current density 1x106 A/cm2R
Distance
• That can induce chemical reactions.• That can be used to produce patterns
by decomposing molecules. (20A)Cur
rent
Distance
STMPhys. Rev. B 31 (1985) p. 2
STM – spectroscopySurface Chemistryy
Mode:1) Keep tip-surface distance constant
tip
tvariable
A
V ) p p2) Change the tip-surface voltage (V).constvariable V
Remember: Tunneling samples LDOS (Local Density Of States).
Therefore, the electronic states involved in the tunneling process depends on the voltage.
Tunneling currentbandgap
Tip-surface voltage
STM
Tip surface voltage
STM – insulating samplesSurface Chemistryy
Typical tunneling conditions:Tip-surface gap resistance 10 MOhms
Resistance of sample must be smaller than
Tunneling current 1 nATip-surface voltage (bias) 10 mV
must be smaller than approx. 10 MOhms.
Cover the surface with a metal.Heat the surface.Doping the surface.AC li
Solution
AC tunneling.
STM
Surface Chemistryy
AFM Atomic Force MicroscopeAFM – Atomic Force MicroscopePSTM – Photon Scanning Tunneling MicroscopeSCM -- Scanning Capacitance MicroscopeNFTM – Near Field Thermal MicroscopeSICM – Scanning Ion Conductance MicroscopeTAM – Tunneling Acoustic MicroscopePCM – Point Contact MicroscopeBEEM – Ballisic Electron Emission Microscope
STM
BEEM Ballisic Electron Emission MicroscopeIETS – Inelastic Electron Tunneling Spectroscopy
Scanning Capacitance MicroscopeSurface Chemistryy
Physics (again) - sorry
ε AC = 0ε Ad
q CV=q
Idea: Capacitance (tip – sample) correlated with tip-sample distance.
Disadvantage: Change in capacitance is very small (25 nm resolution)
Advantage: 1) works for insulators2) can be chemically specific
STM
2) can be chemically specific
Idea - Atomic Force MicroscopeSurface Chemistryy
LASERIdea:
surfacecantileversurface
Advantage:-) works for insulators)-) magnetic cantilever (magnetic surfaces)
STM
Surface Science Reports vol. 59 (2005) p.1-152Force measurements with the atomic force microscope: Techniques, interpretation and applicationsHans-Jürgen Butt, Brunero Cappella and Michael Kappl
STM - LiteratureSurface Chemistryy
Yip-Wah Chung, “Practical Guide to Surface Science and Spectroscopy”, Academic Press, 2001
C. Hamann, M. Hietschold, “Raster-Tunnel-Microscopy”, Akademie Verlag, 1991
http://www.lassp.cornell.edu/ardlouis/dissipative/atom_manip.html
http://www.almaden.ibm.com/vis/stm/corral.html
http://www.research.ibm.com/topics/popups/serious/nano/html/sresearchers.html
http://www.lanl.gov/mst/SPML/ssqcnanolith.htmlhttp://www.lanl.gov/mst/SPML/ssqcnanolith.html
STM
PChem – Quantum mechan
FT NMR – setup (idea)
1) Static and large B0 field along z axis2) Small oscillation B1 field along y axis
(Effectively linear polarized field.) B1
B0
3) Detector coil (not shown) wound around sample
NMR
PChem – Quantum mechan
FT NMR – setup – that’s how it really looks likePChem lab class experiment
Inside a NMR Magnet NMR Flow Chart
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
Excite the system by turning on an oscillating current in excitation coil (pulse).Nuclear macroscopic magnetization flips from Z direction to XY (90o).In the XY plane magnetization precesses creating an oscillating signal.Oscillating current detected in receiver coil.
90 degree pulse
NMR
Liquid nitrogen is used as a secondary coolant.Static magnetic field strengths above 20T are possible.
gConvert the resulting signal from analogue to digital.
Fig. from John Bagu
PChem – Quantum mechan
Circular polarized field B1
B B x t y tcc1 1= +[ cos( ) sin( )]ω ω
counterclockwiseB B x t y tc
1 1= −[ cos( ) sin( )]ω ωclockwise
B Bxy
cc c1 1+ =
→→
oscillating zero (no net effect)
Only cc component rotates with M and can induce transition
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.
PChem – Quantum mechan
FT NMR lab frame & rotating frame (vector model)
C di b iz: Static fieldx-y: Circularly polarized field rotatingΣ: total filed processes along z axis
Coordinate system rotates about z axis
B and B1 are stationary.Σ: Total field ∆B = B – B1 along z axisΣ: total filed processes along z axis
M processes about the total fieldwhich is processing by itself
Σ: Total field ∆B B B1 along z axis
M processes about ∆BAt resonance M tilts and processes i l
NMR
in xy plane.
PChem – Quantum mechan
FT NMR – dephasing spins
The pulse tilts the magnetization M in the xy plane.After the pulse:z: relaxes back to equilibrium along z axis with T1
NMR
z: relaxes back to equilibrium along z axis with T1xy: different spins rotate at different frequency dephasing spins with T2
PChem – Quantum mechan
FT NMR – Bloch equation
F I1
d s s B
Ts
s
x
< >≈< > +
− < >
− < >
FGGGG
IJJJJx 1
2
dts s B
Ts
s sT
y
z
< > < > + < >
− < >H
GGGG K
JJJJ
x 2
0
TH K1
Works for electron and nuclear spinsWorks for electron and nuclear spins.
NMR
PChem – Quantum mechan
FT NMR-free induction decay
Detector coil along y axis.g y
z: Mz decreasesno effect on detector
xy: Mxy decreasesfree induction decay seen in detector
NMR
PChem – Quantum mechan
FT NMR – more than one resonance
Chemical shifts & field heterogeneities result in more than one resonance frequency
∞Recovering the information.
I I t t i t dt( ) ( )[cos( ) sin( )]ω ω ω= +∞z0
pulse consits of many frequency components
Why does that work?
frequency components
f t c n t d n tn n( ) ( sin( ) cos( ))= +∑ ω ω
Analog:Like a bell struck with a hammer.It will ring with its resonance frequencyi d d t f th ki d f h
NMR
independent of the kind of hammer.
PChem – Quantum mechan
FT NMR – advantage of the technique
NN
e E kt2 10= ≈−∆ / . Bad signal-to-noise ratio in NMRN1
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
PChem – Quantum mechan
FT NMR – spin echo experiment
Measuring T2Intro to 2D NMR
Effect of the pulseMx MxMy -My
Similar idea is usedfor 2D NMR Next week.
NMR
PChem – Quantum mechan
FT NMR -- setup
Figures from Quantum Chemistry and SpectroscopFigures from Quantum Chemistry and SpectroscopT. EngelCh 18 - NMRCh 18 NMRISBN 0-8053-3842-X
Cool web sites:1. http://www.le.ac.uk/biochem/mp84/teaching/lecture2.html 2 http://www life uiuc edu/biophysics/Lecture6 ppt#2562. http://www.life.uiuc.edu/biophysics/Lecture6.ppt#2563. http://ascaris.health.ufl.edu/classes/bch6746 (e.g. lecture 3 PowerPoint)
NMR
PChem – Quantum mechan
Infrared spectroscopy -- classification
Transmission
RAISReflection-absorptionInfrared spectroscopy
HREELSHigh ResolutionTransmission
Infrared spectroscopy Electron Energy Loss SpectroscopySpectroscopy
Spectroscopy
PChem – Quantum mechan
Infrared spectroscopy -- setup
Sometimes called “dispersion IR spectrometer” since it includes a prism or grating to disperse theprism or grating to disperse theelectro.mag. radiation
Idea of operation, briefly:p , y•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.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 sophisticatedthan shown in the scheme above.
Surface Chemistry
AES – Lock In techniquey
AC amplifierband pass filters
Phase sensitiveamplifier
Low passfilter
input output
Phase shifter
ModulatorReference
Lock in idea: Input signal - modulated with ω and zero phase lag with respect to the refeOutput signal - constant voltage level. All other signals will be averaged out by the phase sensitive amplifier.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 ratio sqrt(band width)
Spectroscopy
Side effects Nyquist equation: Signal-to-noise ratio ~ sqrt(band width)Background not modulated: it will be subtracted
PChem – Quantum mechan
Infrared spectroscopy – setup ---FTIR – Fourier-transform IR spectrometer
Idea of operation:
Th b ill b lit• The source beam will be split. • One part arrives at the detector “directly”.• The other one will be “delayed” by going
a longer way. g y
The difference in the traveling path length of these two beams will be modulated by a movable mirror. y(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
signal (intensity vs. position of the mirror).
PChem – Quantum mechan
Infrared spectroscopy – Michelson interferometer
The interferogram is a sum of cos waves,The interferogram is a sum of cos waves, each has an amplitude and frequency proportional to the source intensity at a particular infrared frequency.Reco ering this information is done b aRecovering this information is done by aFourier transformation.
PChem – Quantum mechan
More than one frequency of the source
Main idea:
We measure an intensity as a function of time(i.e. as a function of the position of the 2nd
mirror which is changing with time)mirror which is changing with time)that is the interference of the sample and reference beam.
This intensity vs. time signal is converted in anintensity vs, frequency signal by means of a Fourier transformation.
HREELS
OC
O
C
O
C
PChem – Quantum mechan
Emission/Absorption spectra of gases
Emission spectra
Absorption spectraLyman series
Balmer series
PChem – Quantum mechan
Emission/Absorption spectra of gases – H atom
PChem – Quantum mechan
Electronic absorption spectrum of gas-phase benzene
Vibrational and rotational levels are broadened at larger gas pressures which leads to the detection of continuous spectra.which leads to the detection of continuous spectra.
PChem – Quantum mechan
Potential energy diagram – diatomic molecule
‘’ ground state ‘ excited state excited stateD0’’, D0’ dissociation energiesE’’at, Eat’ separated atoms>Eat’ continuous absorption
PChem – Quantum mechan
LIF – Laser induced Fluorescence
LIF has a much better sensitivity than absorption spectroscopy.
PChem – Quantum mechan
Potential energy diagram – more details but same story
Set-up -- cf., PChem lab class -- spectrofluorimeter
Excitation monochromator
Excitation spectraexcitation wavelength scannedscannedemission wavelength fixed
Emission monochromatorEmission monochromator
Emission spectra emission wavelength scannedexcitation wavelength fixed
PChem – Quantum mechan
Emission / Excitation spectra
traat
ion
spec
tExcitation spectra excitation wavelength scanned emission wavelength fixed
Exc
itara
g
sion
spe
ctr
Emission spectra emission wavelength scannedexcitation wavelength fixed
Em
iss excitation wavelength fixed
PChem – Quantum mechan
Spectrofluorimeter
PChem – Quantum mechan
Examples