How to measure the standard enthalpy of formation

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