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Chapter 16 Infrared Spectrometry Problems:1, 2, 3, 6, 11, 12 Intro Infrared 12,800-10 cm-1 .780-1000 :m 780-1,000,000nm Convenient to break into 3 somewhat arbitrary regions Near- .78-2.5:m use a vis spectrometer, maybe with a different source used in quantitation for industrial and agricultural process control Mid- 2.5-50 use to be a dispersive or diffraction monochrometer designed for IR, now use FT-IR machines. With older machines was used qualitatively only. With FTIR 10x better S/N so now quantitative as well + surface techniques far- 50-1000 used to be difficult, with FTIR now easier, so relatively new field Actually region most used is 2.5 to 15 Our machine 4000-500 cm-1 2.5-20 :m 16A Theory IR E corresponds to E for transitions between vibrational and rotational states Will focus on absorption, but emission and reflection also are important 16A-1 Introduction Figure 16-1 typical IR output Y is Transmittance X is usually wave # in cm-1 With modern computer driven machines don’t have to stick to this can do Absorbance vs wavelength, this is just holdover from earlier times X in a frequency unit it preferred because frequency directly proportional to E. Hz because exponents on numbers are so big. Remember cm-1 is not truly a frequency, it is just a number that is proportional to frequency. Note change in X scale about ½ way through spectrum. Right hand en of spectrum usually has more narrower peaks, to so this tends to spread the peaks out more. Not all machine do this. Our machine does not. Dipole changes during Vibrations and Rotations IR E not large enough for change molecule’s electron orbital Molecule only changes vibration or rotation state How does this allow E to be absorbed? 2 Molecule must undergo a net change in dipole moment Rotational Transitions How do EM radiation and a change in dipole interact? EM radiation Electric field alternating + then Rotation is easy - if molecule has a dipole, dipole will try to line up with electric field, If can rotate at same frequency as light, will do so. And will absorb that E to make the molecule rotate. (Note if molecule has do dipole will not absorb E!) E needed is slight 100cm-1, 8>100:m, only about 1000kJ/mol In gas phase many discrete, well defined lines In liquids or solids blur into a continuum Vibrational Transitions Let’s start with simplest vibration H-Cl Again EM radiation is alternating +/- electric field So will alternately want to push and pull the H (positive part of dipole) back and forth. Bond between atoms is like a spring There is a preferred position, but with just the right E you can get the spring to oscillate back an forth So when E of Em radiation matches E of bond, you get the atoms vibrating back and forth Also note each position also has a different dipole moment Lots of other motions are similar Atoms can rotate around single bonds Chair/boat conformations in cyclic compounds When have lots of atoms have lots of simultaneous changes and lots of different motions Break down into some general categories of motion Stretching (need 2 atoms) Continuous change in distance between atoms along a bond But direction of bond remains the same Dipole stays pointed same direction, but changes in magnitude Bending (need 3 or more atoms) Angle between 2 bonds changes 3 Scissoring Rocking Wagging Twisting (figure 16-2) Can also have complex coupling of all of the above with each other In next section will look at simplest model for this system, harmonic oscillators then at adjustments to this model 16A-2 Mechanical Model of a Stretching Vibration Nice, simple model 2 masses connected by a spring pull one of the masses along the axis of the spring (line connecting two masses) And release. What happens, atoms vibrate back and forth along the axis. The heaviest moves a little, the lightest mas moves the most Let’s make even simpler, eliminate one mass by hanging spring from a hook Figure 16-3 Back to physics Force of a spring determined by Hooke’s Law F=-ky spring force tends to restore mass to original position As distance Y increases + force will be increasing in opposite direction to restore to original position. As distance goes -, force will be positive, again to restore to original position. Potential E of a Harmonic oscillator skip differential and integral equations this year, may want to put back in for future dE= –Fdy -F=ky dE=kydy integrate E = ½ ky2 Show plot of E in figure 16-3 Higher E as spring is displaced from middle 0 E when weight is sitting still. Nice and symmetric 4 Vibrational Frequency Now that we know the E as a function id distance, we can look at motion F=ma (newton’s second law) A = acceleration = d2y/dt2 (Second derivative of y with respect to time Using F=-ky ma=-ky m d2y/dt2=-ky M times second derivative = y How can a function’s second derivative = the original function? This works for periodic functions like sin or cosine Y = A cos 2B<mt Where <m is called the natural harmonic frequency A is the amplitude of the motion The second derivative is: -4B2<m2A cos 2B<mt And substituting in we have m -4B2<m2A cos 2B<mt= -k A cos 2B<mt And cancelling out common terms m -4B2<m2= -k <m2= k/4B2m <m2=1/2B sqrt(k/m) Note the natural frequency depends only on the force constant of the spring and the mass, NOT on the energy! The only thing the energy changes is the amplitude of the vibration If we change the system to reflect 2 masses tied together by a spring we need to substitute a reduced mass for the original m : = m1m2/(m1+m2) 5 Then <m=1/2B sqrt[k(m1+m2)/m1m2] The last equation we can use in molecular systems. We can substitute the mass of the two atoms into the equation. Set < to the frequency of interest, and k becomes a measure of the ‘stiffness’ of the bond 16A-3 Quantum Treatment of vibrations If we really want to model an atom, then we have to shift to quantum mechanics to show the quantitized nature of the molecular vibrations. Using the harmonic oscillator couples with a quantum vibration we get: Where h is Planck’s constant v is the vibrational quantum number (positive integers 0,1,2...) And the rest is the same Note how similar ths is to the harmonic oscillator model Substituting one equation into the other to get rid of the common terms we have: E=(v+1/2)h<m At RT most of the molecules with be in the ground state so: E = 1/2h<m Promotion to the 1st excited state will be to E=3/2 h<m And the )E = 3/2-1/2 = h<m E=h< we then have h<=h<m = 1/2Bsqrt(k/:) 6 Since the frequency is usually in wavenumbers, and there are some other constants we can get lump together we can get the equation: < (bar) is the wavenumber of the absorption peak K is the force constant of the bond in Newtons/m : is the reduced mass in kg Using this equation we find that K is usually between 3 x102 and 8 x102 N/m, and is usually about 5x102 K for a double bond is about 2x as much (10x102 = 103) K for a triple bond is 3x About 1.5x103 Try a sample calculation A CH stretching frequency is 2900 cm-1 2900=5.3x10-12sqrt(k/:) :=m1m2/(m1+m2) m1=C = 12x10-3 kg/mol / 6.02x1023atom/mol = 2x10-26kg/atom m2 = H =1x10-3/6,02x1023 = 1.7x10-27 := 2x10-26 x 1.7x10-27 /(2x10-26 + 1.7x10-27) =3.4x10-53/3.7x10-27 =.9x10-26 2900=5.3x10-12sqrt(k/.9x10-26 ) 2900/5.3x10-12 = sqrt(k/0.9x10-26) 5.5x1014 = sqrt(k/0.9x10-26) (5.5x1014)2 = k/0.9x10-26 3x1029 = k/0.9x10-26 3x1029 x 0.9x10-26 = k 7 2.1x103 =k This is a little higher than expected, is there an error? Selection Rules Quantum theory indicates that only )v =+/- 1 are allowed So only ever see 1 absorption peak for a given vibration Anharmonic Oscillator Real atomic forces aren’t nice and symmetric like springs As the atoms get too close the inter atomic repulsion skyrockets, and as the atoms get too far away the bond force weakens. A more realistic E potential is shown in figure 16-3b. We can more properly model this system with more quantum theory, but at this point the math becomes very complex. If we use what is called an anharmonic oscillator model we can get a model that is simpler mathematically, and more realistic The anharmonic oscillator has some interesting ramifications 1. The E level between vibrations are no longer identical Because of this selection rules allow v=+/-2 or even +/- 3 transitions. This means that we can begin to see ’overtone’ vibrations These are weak lines and may not be observed 2. Two different frequencies can interact to give additional frequencies at sums and difference of the fundamental frequencies as well. 16A-4 Vibrational Modes for simple diatomic or triatomic molecules can figure out number and kinds of vibrations that will be present For more complicated molecules many different kinds of vibrations so can’t figure them all out Can figure out the total number of possible vibrations 3 coordinates needed to fix an atom in space (X, Y, Z) Each coordinate is one degree of freedom so with N atoms have 3N degrees of freedom Three kinds of motion to think about Translation of entire molecule through space Rotation of entire molecule around it’s center of gravity Individual vibrations within the molecule 8 The translation take up 3 degrees of freedom The rotation take up another 3 degrees of freedom So we are left with 3N-6 degrees of freedom (of possible different vibrations) Linear molecules are slightly different Since are linear, rotation about axis doesn’t cost a degree fo freedom So for linears have 3N-5 degrees of freedom 3N-6 or 3N-5 degrees of freedom, called the ‘normal modes’ of vibrations each normal mode will have a potential well like we developed earlier each will have its selection rules so if the vibration changes the dipole of the molecule, it will have an absorption Often will have less absorption peaks than normal modes 1. Symmetry of molecule is such that dipole of molecule doesn’t change 2. Energies of 2 or more vibrations are nearly the same so they overlap 3. absorption is so low that it can’t be observed 4. Vibrational wavelength outside the range of the instrument Occasionally more absorption bands than expected 1. Overtones (as discussed earlier) 2. Combination bands - a photon excites 2 different vibration modes simultaneously 16A-5 Vibrational Coupling The E of a vibration (frequency or wavelength of a vibration) may be coupled (influenced) by other vibrators in the molecule 1. Strong coupling between stretching vibrations where one atoms is common to both stretches 2. Interactions between bending vibrations involving a common bond between vibrating groups 3. Stretching and bending can couple if the bond that is stretching forms one side of the angle that is bending 4. Interactions are greater when the E of the 2 energies are about equal 5. Little or no interactions between groups separated by 2 or more bond 6. Coupling requires that vibrations must be of the same symmetry species What does this all mean? Let’s look at CO2 O=C=O 9 3 atoms, linear, 3N-5, 9-5, expect 4 normal modes or bands Diagrams page 388&389 Since contains C=O bonds, expect vibration like C=O in other carbonyls (Like ketones) 1700 cm-1 6:m Actually observe 2 bands 2330 cm-1 (4.3 :m) 677 cm-1 (15 :m) Can see 2 stretching vibrations Symmetric - non change in dipole - no absorption Asymmetric change in dipole should absorb this is the 2330 cm-1 band 2 remaining modes are scissoring , either in plane or out of plane Since same motion, but in different directions, the E’s are the same If the E’s are the same, the quantum states are degenerate This is the 677 cm-1 band So you have accounted for all normal modes of vibrations! Look at non-linear SO2 (lone pair on the S makes sp2 hybridization) Again 3 atoms, but nonlinear so 3N-6 for 9-6 = 3 vibrational modes (Shown in diagram) Here symmetric stretching does change dipole so does absorb 3650 cm-1 Asymmetric stretching 3760 cm-1 Because 3 atoms are non-linear they define the scissoring plane, so have only 1 scissoring motion, so only 1 vibration For water this is at 1595 cm-1 I don’t see what it is for SO2 Note, the presence of 1 or 2 scissoring can be used to determine molecular structure, linear or nonlinear, so there is structural information here Coupling of vibrations can shift things around as well C-O Stretch Methanol 1034 cm-1 Ethanol 1053 cm-1 2 butanol 1105 cm-1 Changed due to C-H, C-C-OH or C-COH-C coupled motions So assignment of frequencies to specific groups can have some uncertainties 10 16B Infrared Sources and Transducers Need a continuum source of IR radiation and a sensitive detector. Discussed briefly in earlier chapter, now here are details 16B-1 Sources Inert solid heated to 1500-2200 K where produce blackbody continuum radiation At these temps max intensity 5000-5900 cm-1 See figure 6-18 page 134 To long 8 side falls off smoothly, to about 1% at 670cm-1 To short 8 side decreases more rapidly, 1% at 10,000 cm-1 Note: most organic IR 650-4000 cm-1 Nernst Glower Cylinder f rare earth oxides 1-2 mm diameter, 20 mm length Platinum leads Pass current through to heat to 1200-2200 K Large negative T coefficient of electrical resistance IE high resistance when cold, can’t pass enough current through it to make it hot, so need an external heat source. Once is it warm enough, now lower resistance, so it lets more current through, and it stays warm. Electronic design problem. Must limit current. If you don’t as more current passes gets warmer, resistance decreases, to lets more current through, that will make warmer, etc until the machine burns out! Spectral output at 2200K. General blackbody like, small peaks and dips due to composition Globar Silicon carbide rod 5 mm diameter, 50 mm length Again heat with electrical current + coefficient of resistance So current limits itself, no fancy electronics Need to water cool contacts, otherwise will arc Energy similar to Nernst, but has better output <5:m Incandescent wire Lower intensity but longer life Tightly wound Nichrome wire Again pass current to heat until glows about 1100K Mercury Arc 11 The above 3 don’t put out much when 8>50:m (far IR) Here high pressure Hg Arc works Current causes arc that forms plasma that yields IR continuum Tungsten Filament Ordinary bulb, good in near IR 4000-12,800 cm-1 CO2 Laser 100 closely spaced lines between 900 and 1100 cm-1 (about 1/10 of usual IR range) Can tune laser to any 1 line Use in instrument designed to monitor a specific compound. Very bright, several orders of magnitude brighter than other sources, but not flexible 16B-2 IR Transducers 3 main types 1. Thermal transducers 2. Pyroelectric transducer (very specialized thermal transducer) 3. Photoconducting transducer Thermal Transducers response depends on heating effect of radiation radiation is absorbed by a small amount of material, measure temperature rise E hitting transducer 10-7 to 10-9 W Need very small amount of material so T rise is maximal Make detector as small as possible Focus light as tightly as possible T rise still only.001 K or so Detecting heat is also a problem because fo thermal noise (Everything else is warm so has make thermal noise) House transducer in vacuum, so other heat can’t get to it Use chopper electronics to minimize drift Keep detector at constant T Thermocouples 2 junction at 2 metals A potential difference develops when 2 junctions are at different T’s 12 Use either ver fine wires or metals evaporated onto nonconducting support Again, seal in vacuum to shield from outside heat House both junctions in same spot, but only shine IR radiation on one Again chop signal and compare one to the other But don’t need to keep at a constant T Can put several thermocouple in series for better sensitivity -called a thermopile Well designed can detect )T of 10-6K Bolometers Not used as much in mid IR, but good in 5-400 cm-1 region Strips of metal like Pt or Ni, or semiconducting thermisters Resistance has large change with heat Measure resistance of circuit Pyroelectric Transducers Single crystals of pyroelectric materials Insulators with special thermal and electrical properties Most common triglycine sulfate (NH2CH2COOH)3 @ H2SO4 Usually deuteratred, with a few alanines Is a dielectric material, does not conduct E, but material within dielectric will orient with external electric field Usually polarization disappears when field removed In pyroelectric substance polarization remains for a while And polarization is T dependent So use like a capacitor, Charge it up and watch current flow out of it Very fast response So used in most FTIR machines Photoconducting Transducers Thin film of semiconducting material sealed in vacuum to protect from air When light hits, moves electrons into conducting orbitals, starts to conduct E PbS widely used in near IR (10,000-333 cm-1) operates at RT 13 In mid and far IR use Hg/Cd Te, cooled under liquid N2 (77K) Also has fast response for FT machine Probably best overall detector, if you can afford the liquid N2 16C Infrared Instruments First IR machines were dispersive, used until 1980's now largely replaced by FTIR machines 16C-1 FTIR Spectrometers Actually two different designs the interference design and the Hadamard design. The latter isn’t used much so will stick to the interference Original FT machines big, bulky >100,000 and some mechanical adjustments Now 15-20K and largely maintenance free Components Figure 7-42 page 186 Figure 16-6 Drive For interferometer need to know speed and position of moving mirror at all time to within a fraction of a 8 In far IR (50-1000 :m, 200-10 cm-1) This can be accomplished with a motor driven micrometer screw Near and mid IR need more precision Mirror floated on an air bearing Held in close fitting stainless steel sleeve DC coil pushes plunger back and forth Drive length 1 to 20 cm-1 Scan rate .01 to 10 cm/s Need to sample signal at precise intervals Need to know zero retardation point exactly One way to do this is to have 3 interferometers built into same moving mirror 1st system is the IR sampling system 14 2nd system uses a helium/neon laser Has a single frequency Creates a simple sine wave pattern Use to keep track of mirror speed Used to trigger sampling electronics Called laser-fringe reference system 3rd system called the white-light system Tungsten source and visible transducer Polychromatic source so largest signal is at zero position As get off zero, some light interferes and intensity decreases Look for max signal, know where zero position is Triple system extremely accurate and reproducible Current instruments use a single interferometer with a laser, and get zero position from max of IR signal Beam Splitters IR transparent material with refractive materials that reflect 50% of light and transmit 50% Usually thin film of Mylar between 2 plates Sources Already covered Designs Single beam 16-20K Since single beam need a reference run Usually stable so only need occasional reference runs Performance Characteristics Less expensive 7800-350 cm-1 Resolution of 4 cm-1 (Check specs on our machine) More expensive Interchangeable splitters, sources, transducers For IR through vis Resolution from 8 to .01 cm-1 15 Advantages 10x better S/N than dispersive machines Gets even better with signal averaging High resolution and highly accurate frequency determination Much higher E throughput because not using classical monochrometer A bit of a trade off is that high speed e\detector is not as sensitive as other detectors No equivalent of stray light problems Has really been useful in 1. high resolution work on gases 2. study of samples with high absorbance 3. study of samples with weak absorbance 4. fast kinetic studies 5. small sample 6. IR emission studies 16C-2 Dispersive - skip 16C-3 Non dispersive - skip