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Chapter 16 Infrared Absorption Spectroscopy An IR spectrum contains information about the functional groups in a molecule, and this is used to uniquely identify the compound. UV Vis 400 nm Near IR 780 nm Mid IR Far IR 2500 nm 50,000 nm or 4000 cm-1 or 200 cm-1 Wavenumbers (cm-1) are used since they are directly proportional to energy – E hν hc λ e.g. convert 2.5 µm to wavenumbers (cm-1) Typical Infrared Spectrum “overtones” C-H C=O Higher energy vibrations C-C Mechanical Model of a Stretching Vibration in a Diatomic Molecule Treats the vibrating bond like a spring with a given “stiffness” -- ν 1 k 2π μ = frequency of vibration k = force constant (spring “stiffness”) µ = “reduced mass” m 1m 2 m1 m 2 Quantum Mechanical Treatment of Normal Modes 1. Only certain vibrations are “allowed” 2. The vibrational quantum number v = 0, 1, 2, 3…… 3. Only transitions between adjacent energy levels are possible, i.e. v = 1 4. The frequency of the photon has to equal the frequency of the vibration (see next slide) 5. The molecule must have a change in “dipole moment” as a result of the vibration Dipole moment = charge difference X separation distance - + Homonuclear diatomics never have an Infrared spectrum. Why? Frequency of absorbed light frequency of vibration + + + + - S1 + v = 1 - IR Absorption if the vibration results in a change in dipole moment So Common Types of Vibrations (“Normal Modes”) Higher energy modes Lower energy modes The number of normal modes = 3N-6 For linear molecules it’s 3N-5 Example – predict the normal modes of CO2 Which normal modes are Infrared active? Example 16-1, p.436 Calculate the approximate wavenumber and wavelength of the fundamental absorption peak due to the stretching vibration of a C=O group (k = 1.0 x 103 N/m) ν 1 k 2π μ Force Constants increase with Bond Strength Bond Type* Force Constant, k (N/m) Wavenumber (cm-1) Bond Energy (kJ/mol) C-C 5 x 102 800-1200 347 C=C 10 x 102 1600 620 CΞC 15 x 102 2100 812 Bond Type* Reduced mass (kg) Wavenumber (cm-1) Bond Energy (kJ/mol) C-H 1.55 x 10-27 3000 414 C-N 1.07 x 10-26 1000-1350 [email protected] C-O 1.14 x 10-26 1000-1300 [email protected] (a). (b) (a).as then frequency (b) When masses approx. equal, then see peak at same wavenumbers * all bonds are stretches @ consider these as being approx. equal IR Sources Output from a Nernst Glower 1. Nichrome – Ni/Cr alloy, resistively heats up and emits IR, 1100 K 2. Globar – SiC rod, 1500 K 3. Nernst Glower – electrically heated rare earth-oxide ceramic, 2000 K cm-1 Optics – IR spectra are measured in the mid-IR, so have to use halides such as NaCl and KBr UV Vis 400 nm Near IR 780 nm Mid IR Far IR 2500 nm 50,000 nm or 4000 cm-1 or 200 cm-1 Never use aqueous samples, or water to clean salt plates Sample Handling – a few drops of “neat” sample between “salt plates” Solutions Detectors for the Mid-IR – 200-4000cm-1 1. Pyroelectric – crystal of DTGS (Deuterated Triglyceine Sulfate) Nice link: http://www.doitpoms.ac.uk/tlplib/pyroelectricity/printall.php?question=2&type=1 1. DTGS maintains polarization when heated to just below the Curie Point 2. Above the Curie Point, the permanent polarization of the DTGS crystal disappears. 3. The closer to the Curie Point, the more responsive the detector 4. Much faster response so can take a spectrum much more quickly (FTIR) Detectors for the Mid-IR – 200-4000cm-1 2. Photoconduction - Mercury-Cadmium-Tellurium (MCT) 1. Semiconductor-based Liquid N2 @ 77K 2. Cooled to 77 K using liquid N2 3. Much faster response so can take a spectrum much more quickly (FTIR) http://www.newport.com http://www.boselec.com/pdf/Laser_Focus_World.PDF Definition of the Fourier Transform () ( ) f ( t ) f (t )e i t i dt 1 2f The Inverse Fourier Transform f (t ) 1 ( ) 1 2 ( ) e i t d The functions f(t) and () are called "transform pairs" f(t) () time (t) frequency (s-1, Hz) e.g. FTIR distance (cm) wavenumber (cm-1) background interferogram sample interferogram background spectrum = Po sample spectrum = P P/Po = IR spectrum e.g. FT-NMR time (s) ppm (Hz) Free Induction Decay (FID) Signal (time) NMR Spectrum (ppm, Hz) Fourier Transforms "invert dimensionality" – signal domain FT domain Instrument time (t) frequency (s-1, Hz) oscilloscope mirror distance (cm) wavenumber (cm-1) FTIR free induction decay (t) ppm (from Hertz) FT-NMR Fast Fourier Transform (FFT) on computers - •Cooley-Tukey algorithm •very efficient on a PC fixed mirror ¼ IR source + + + - - movable mirror → 50/50 beamsplitter D interferogram /4 2 /4 3/4 4/4 mirror distance, x (cm) → If polychromatic radiation enters the interferometer, then each wavelength produces a separate interferogram. The output from the interferometer will therefore be a superposition of all wavelengths - 1 1 2 2 3 3 ←mirror distance (-x, cm) mirror distance (+x, cm) → signal at detector S(x) A ( 1 ) cos 4 x 1 A ( 2 ) cos 4 x 2 A ( 3 ) cos 4 x 3 .... N A ( i ) cos 4 x i i 1 A ( i ) cos 4 x i d this term contains the IR spectrum Taking the Fourier Transform of S(x) results in the IR spectrum, A() - A ( ) S ( x ) cos 4 x i dx Depends on the distance the mirror moves in the Michelson Interferometer – the further it moves, the greater the resolution. 1 2x 1 "retardation“ = 2x minimum detectable difference in wavenumber x = distance mirror moves e.g. What length of mirror drive in a Michelson Interferometer is required to separate 20.34 and 20.35 m? Fourier Transform Infrared (FTIR) Spectrometers The Multiplex (Fellgett's) Advantage - entire spectrum obtained virtually instantaneously; results in a higher S/N because during the time a scanning instrument is slowly obtaining the spectrum, a multiplex instrument such as an FTIR can acquire 100’s pf spectra. Averaging these extra spectra causes the increased S/N (see next slide) and allows quantitative IR. S/N increases as N where N = number of "resolution elements" e.g. scan range 400 - 4000 cm-1 at a resolution of 2 cm-1 2 cm-1 4000 cm-1 400 cm-1 N ( 4000 400 cm 2 cm 1 1 ) 1800 "resolution elements" so the S/N increases by 1800 40 X IF the FTIR can obtain the entire spectrum for the same amount of time a slower, scanning instrument requires to acquire only one resolution element. Signal-to-Noise Ratio (S/N) Single-Beam – run background first (see next slide) and store in memory (Po) Higher energy throughput (Jacquinot’s Advantage) and no stray light problems Typical IR background spectrum (Po) inexpensive (~ $25K) range = 350 – 7800 cm-1 (29 to 1.3 m) max resolution = 4 cm-1 scan time = as fast as 1 sec detector = DTGS expensive (~ $100K) range = 10 – 50,000 cm-1 (1000 m to 200 nm) max resolution < 0.01 cm-1 scan time = can be minutes at high-res detector(s) = DTGS, MCT Advantages over Scanning Instruments 1. fast scan times 2. higher S/N because of signal averaging 3. higher resolution 4. because there are no slits, there’s a higher energy throughput (Jacquinot’s Advantage); means larger signals for the same concentration (therefore lower LODs) 5. no stray light problems Disadvantages 1. higher cost than scanning instruments 2. difficult to align the interferometer (automation helps) 3. IR optics water soluble (beamsplitter made of KBr) Chapter 17 Applications of IR Spectrometry 1. Qualitative Analysis "group frequency region" "fingerprint region" 2. Quantitative Analysis Much less sensitive (i.e. higher LODs) in the IR compared to the UV-Vis because of 1. lower source powers than in UV-Vis (in FTIR Jacquinot's Advantage partially offsets) 2. detectors suffer from thermal noise (i.e. larger backgrounds or blank) 3. salt plates have a very short path length (A = bc) Signal averaging with FTIR's has improved the S/N enough to allow more sensitive quantitative work in the IR. 3. Diffuse Reflectance Accessory Typically used for powdered samples, i.e. forensic drug analyses Kubelka-Munk Units = converts the reflectance spectrum to the equivalent of an absorbance spectrum. R’ = sample refectivity/KBr reflectivity f(R’) = (1 - R’)2/2 R’ = k/S k = 2.303 C = the molar absorptivity C is the sample concentration S = "scattering coefficient" For a sample to follow a linear relationship between f(R’) and concentration, the following criteria must be met: 1. the sample must be diluted in a non-absorbing matrix such as KBr or KCl. 2. the scattering coefficient S must remain constant over the entire spectrum. 3. there must be no specular, or regular reflectance off the surface of the sample. 4. Attenuated Total Internal Reflectance (ATR) Accessory Samples - conventional (solutions, liquids, etc) as well as powders, pastes, suspensions, colloids Total Internal Reflection and the "evanescent wave" - 5. Infrared Microscopy