m m lighter 'atom' dominates 2 INFRARED SPECTROSCOPY All modes of vibrations are not IR active.

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1 INFRARED SPECTROSCOPY Infrared spectroscopy probes the interaction of infrared radiation with covalent bonds in molecules. Absorption of IR radiation results in the transitions between vibrational energy levels (ground electronic state) of the various vibrational modes. The positions of atoms in a molecule with N atoms can be described with 3N coordinates. The center of mass of the molecule can be defined with 3 coordinates. Thus with respect to the center of mass (that does not move during vibrations) 3N-3 coordinates would be required. Also a molecule in general would require 3 more coordinates to describe its orientation in space making 3N-6 (for nonlinear) and 3N-5 (for linear) normal (fundamental) modes for a molecule. All modes of vibrations are not IR active. Those modes with changes in the dipole moment during vibrations are resonant, i.e. IR active, absorbs IR radiation. simplest example, heteronuclear diatomic Near-IR ( cm-1): poor in specific absorptions, overtones and combination bands of Mid-IR bands. Mid-IR (4-4 cm-1): useful structural information for most organic molecules (functional groups and fingerprint region). Far-IR (4-33 cm-1): used with inorganic molecules. + - Normal modes: Atom movements of a covalent molecule are well defined; periodic-harmonic. Such movements have well defined frequency values. The approximate model is mechanical viz., ball-spring; precise model - quantum mechanical. Model: Harmonic oscillator. Vibrational energy is quantized. diatomic m 1 m 2 k mm 1 2 m m k obs 2 mm 1 2 m m 1 2 ; m m 1 2 m1 m1 lighter 'atom' dominates 2 h E hvobs 2 k If the dipole moment changes at the same frequency as the IR radiation frequency, resonance condition is satisfied and absorption occurs. Normal Modes of CO 2 Normal Modes of H 2 O + _ + _ + _ The strength (extent) of absorption, absorbance is determined by their molar absorption coefficients ~ transition moment i.e. change in dipole moment during vibration. 1

2 Energy Vibrational energy levels, Harmonic oscillator Morse curve V=,1,2,.. Bond length Selection Rule; v =±1 allowed forbidden (v = ±1, ±2, ±3.. overtones) Because each structural entity may vibrate in several different motions (stretching rocking, or bending etc.), such molecules often absorb at many IR frequencies. Each vibrational mode can be treated as a harmonic oscillator with an effective k (bond strength) and reduced mass. 1 k obs 2 Bending and stretching vibrational modes for the CH 2 group Asymmetric stretch Symmetric stretch asym sym Rocking mm 1 2 ; m m m m m1 m1 lighter atom dominates 2 Scissoring Twisting Wagging Relative Values of Vibrational Energy Levels The observed IR bands are from (allowed transitions); a. normal modes b. overtones of vibrations. c. combination bands of vibrations d. Fermi doublets < 2 < 3 Energy h 1 h 2 h 3 Normal mode overtones 2

3 Combination bands: From simultaneous excitation of two fundamentals 1 and 2 by radiation frequency of ( 1 2 ). A Fermi resonance is the shifting of the energies anntensities of absorption bands in IR and Raman spectra, a consequence of quantum mechanical mixing. The strength (extent) of absorption, absorbance is determined by the peak molar absorption coefficient ~ transition moment change in dipole moment during vibration. Extent of absorption by IR bands, follows Beer s Law. All possible absorptions may not be observed due to low or zero transition moments, absorptions outside the observed IR range; 4cm -1 4 cm -1 and overlap of closer frequencies. 1%T %T %T 4cm -1 4cm -1 % Transmittance is often usen infrared spectroscopy. % T I 1 A2log(% T) I 7%T weak(w), 4%T medium (m), 5%T strong(s); absorptions The molecular IR spectra are unique to the atomic combinations in a molecule i.e. to the substance. The IR absorptions can be correlated to the bonds in a compound. From a broader context the spectrum can be viewen two regions fingerprint (<~15cm -1 ) and functional group absorption regions (>~15cm -1 ). Thus IR permits identification of functional groups (and substances) with the help of extensive tabulations. Absorption characteristics follow Beer s law, allowing quantification. Similar to UV, Fluorescence and Phosphorescence, it is a non-destructive technique. Functional group region 15cm -1 Fingerprint region Schematic diagram: double-beam infrared Dispersive spectrophotometer. Instrumentation: Conventional: double beam - dispersive instrument the components include; i. IR source ii. Cells iii. Chopper iv. Optical elements - monochromator v. Detector i. Blackbody radiator; Sources approaching blackbody radiator are Nernst glower (Globar) anncandescent wires. 3

4 The source consists of a rod or tube containing rare-earth oxides which is heated to C (bright 'orange heat') either directly by passing a current through it (as in the Nernst filament) or indirectly by means of a nichrome winding inside the tube. Radiation from the source is split into two beams by the mirrors comprising the 'source optics' which bring both beams to a focus in the sampling area, the sample being placed at the focus of the sample beam. ii. The sample and reference beams are then directed on to the entrance slit of the monochromator, ionic crystals used for transmitting components (not glass, absorb >4 ). Reflection gratings and mirrors (Au, Al coated) usen optics Schematic diagram: double-beam infrared Dispersive spectrophotometer. iii. Cells (windows) ionic materials. Solutions in (halo/hydro) hydrocarbons in crystal (ionic) cells. Specialty polymer cells in certain regions. Cell material : Refractive index close to that of air preferred; to minimize reflection. iv. Detectors (some) a. thermocouples b. bolometers c. Golay cells d. Solid State detectors (semiconductors p/n, MCT crystals, DTGS deuterated triglycine sulfate) IR Window Materials The detector converts the radiant energy it receives from the monochromator into an electric signal by sensing the heating effect of the infrared radiation. Material NaCl KCl KBr CsBr CsI LiF CaF2 BaF2 AgCl AgBr KRS 5 ZnS ZnSe Ge Si UV Quartz IR Quartz Polyethylene The simplest type of detector is the thermocouple which has an adequate sensitivity. Bolometer measures radiant energy by correlating the radiation induced change in electrical resistance of a blackened metal foil with the amount of radiation absorbed. The Golay detector senses a pressure change in the gas in a sealed container (caused by the heating effect) is more sensitive than the thermocouple but less robust. 4

5 Triglycine Sulfate (TGS) crystals are used for room-temperature infrared detectors, earth exploration, radiation monitoring and astronomical telescopes. TGS crystals are pyroelectric sensors. Pyroelectrics are materials where an electric potential difference is generated when they are heated or cooled. The change in temperature results in positive and negative charges moving to opposite ends. The crystal material polarized creating an electrical potential. Pyroelectric sensors based on TGS are uniformly sensitive to radiation in wavelength range from ultraviolet to far infrared and do not require cryogen cooling for operation. Dispersive IR slow (scans wave numbers sequentially) relatively large sample size dispersive (prism or grating) optics mechanically complex instrumentation low throughput (power of radiation reaching detector at a given time is low) inferior detection limits (high noise) low precision of wavelength requiring external calibration Using of deuterated Triglycine Sulfate (DTGS) crystals extends the temperature range of sensing due to their higher Curie temperature. Fourier Transform Infra Red (FTIR) Spectroscopy Double Beam Dispersive instrument Sample Source Chopper Reference/Bkg Monochromator Detector FTIR Source Interferometer 1. Reference/Bkg 2. Sample Detector single, weak beam reaches detector. all, high intensity beam An interferometer is a devise that superimposes two beams (here IR radiation) where light waves undergo interference to various degrees depending on phase differences of the two beams. The principle of superposition would explain the result of the interference level. The electromagnetic beams are travelling sinusoidal waves characterized by their amplitude and frequency. The main instrumental feature in FTIR is the Michelson interferometer. Interferometer takes advantage of the wave properties of electromagnetic radiation (here, IR). A wave Initial phase angle = /2 3/2 i Amplitude variation 3 at a point as a function A of time, for a monochromatic wave. y i Wavelength t i time initial phase angle y Asin t (at t i i i =) Phase angle The net effect two waves having the same frequency, if made to overlap in the same space, is determined by the Principle of Superposition. (A net =A 1 +A 2 ) The difference in their phases makes all the difference

6 Relative movement of with respect to the other (both waves meeting in the same space ) changes the direction of movement of the electrical (and magnetic) vector. Consider two waves of same frequency in the same space, one wave moved with respect to the other, at every n path reinforcement occur, Amplitude doubles. y i 2 4 = or 2n Consider two waves of same frequency in the same space, one moved with respect to the other, at every (n+1/2) path annihilation occur. Amplitude zero. y i y i = =/2 y i y i =3/2 =2 Consider two waves of same frequency in the same space, one moved with respect to the other, at path differences not equal to n or (n+1/2) there will be a nonzero amplitude. y i 2 4 = y i 2 4 =5/2. 6

7 y i y i y i x= x=/8 y i x=/4 y i 2 4 y i d x = physical displacement of mirror from i ZPD x=3/8 x=/2 x=5/8 The annihilation (amplitude =) or reinforcement (amplitude =maximum) when the optical path-length difference equals (n+1/2) or n respectively. For path-length differences in between, n and (n+1/2) the intensity will be between intensity of maximum and zero. For path-length differences in between, the intensity will be between intensity of non-zero and maximum (Another point of view phase difference = n - reinforcement, phase difference = (n+1/2) - annihilation.) Michelson Interferometer To Detector IR radiation from IR source Michelson Interferometer Zero Path Difference Michelson Interferometer Fixed mirror ZPD Mirror speed=v I I 2A A A x x > Monochromatic beam Beam Splitter Moving mirror Detector Video GUC 1 Video GUC 2 I() Path length difference= = 2x x= Detector 7

8 The relative path difference,, retardation of one wave with respect to the other changes with the position of the moving mirror with respect to the beam splitter. Therefore the intensity sensed by the detector changes with. i.e. intensity of light reaching the detector, I = I() is a function of position, x, of the moving mirror from ZPD. In the system, the mirror is moved at a constant speed. Therefore x and is a function of time (directly proportional). i.e. I= I() = I(x) = I(t) Where t = time to move the mirror to x from ZPD. The difference in the distance traveled by the two beams = retardation= = 2(OM-OS). For a single, intensity variation with relative position of the moving mirror is sinusoidal. I(t) Detector signal Fourier Transform intensity B ZPD t = x = Looking from the reverse point of view, if the intensity of light, I(t), reaching the detector is sinusoidal with respect to t, then the radiation is monochromatic. t time Time domain signal Interferogram frequency Frequency domain signal For monochromatic radiation, the conversion of this time domain data to the frequency domain data would generate a single (point) in the I vs plot. Fourier Theorem: A mathematical theorem stating that a function which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which has specific amplitude and phase coefficients known as Fourier coefficients. I( ) [ A sin(2 ) B cos(2 )] The application of this theorem is known as Fourier analysis and Fourier synthesis. The theorem was developed by the French mathematician J.B. Fourier around 18. 8

9 Fourier Analysis: According to the Fourier Theorem any function can be expressed as a sum of sine and cosine functions, Fourier series. y [ a sin( nx) b cos( nx)] n 2 2 x x 1 n 2 1 n Note: frequency increases with n. x More terms improves the Fourier series fit to y = f(x). amplitudes Monochromatic beam n = number of terms in Fourier summation The objective of the Fourier analysis is to find the n, a n and b n of the Fourier series for the corresponding frequencies. Detector signal as a function of /x/t The magnitude of coefficients (amplitude) is a measure of the contribution by respective sine/cosine function. Two monochromatic beam Polychromatic beam Lorentzian shape ZPD 9

10 Polychromatic beam Lorentzian shape Polychromatic beam ZPD ZPD Interferometer interferogram Output of a Laser interferometer Laser beam shifted for clarity. The He-Ne laser is used as an internal reference. It follows the same path as the IR beam starting from the interferometer unit. Diagram is modified from a Nicolet brochure. Primary interferometer interferogram that was sampled Optical path difference x 1

11 1x < x > P P%T=PP 11

12 P %transmission P P %transmission wave number wave number P %T 1 P P %transmission P wave number Noise is inevitable in all instrumental measurements. The objective of any experimental data collection is to increase the S/N ratio. N S baseline Noise is random. Adding series of n random signals will increase the net noise as n where as adding signals will increase the signal value as n. Thus adding a series of spectra where the background/ baseline is essentially noise and spectral absorption/ emission is the signal will result in the enhancement of the signal relative to the noise; improving the S/N ratio. For n = #spectra added, improvement of S/N ratio n. ( S / N) n n 1 1 ( S / N) n n2 2 12

13 The difference in the optical distance traveled by the two beams = retardation. The difference in the optical distance traveled by the two beams = retardation. Retardation interval of between two consecutive data points; The recording of the interferogram is done digitally at discrete intervals. Closer the data points in the interferogram greater the wave number range (span) of the spectrum; For maximum retardation interval of ; 1 span; 2 ' a span of 4cm -1 needs a = m = 1-6 m, i.e. for every 1cm the mirror travels (2cm. retardation) the number of data points that must be collected = 16. (21-2 m/1-6 m = 16) For v =.2 cm/sec, it means 32 points/sec. (time=1/.2=5s) (16/5s = 32s -1 ) Resolution, R: The resolution of the spectrum ~ 1/, where is the maximum retardation. R ~ 1/(2 mirror movement distance) [mirror movement distance ~ 1/(2R)] e.g. for a displacement of ± 2cm =±4 cm retardation, leading to a.25 cm -1 resolution. Advantages of FTIR: Speed: simultaneous measurement of all in a few seconds (Felgett Advantage). Better S/N: fast scans (speed of acquisition) allow coadditions of several scans improving S/N ratio Sensitivity: FTIR detectors are very sensitive, high optical throughput (Jacquinot advantage) yields lower noise. mechanical simplicity internal calibration uses a HeNe laser as an internal wavelength calibration standard (Connes advantage) 13

14 ATR r Low refractive index Attenuated total reflectance (ATR), or frustrated multiple internal reflectance (FMIR) is generated when IR radiation is passed through an internal reflection element (IRE) ans internally reflected. i High refractive index, sinr sin i Low refractive index Evanescent wave d p High refractive index D High refractive index > c The ray penetrates a fraction of a wavelength d p beyond the reflecting surface ans displaced by D upon reflection. P The reflective wave penetrates some distance into the sample, in the IRE (Internal Reflection Element) ans either reflected or partly absorbed by the sample. Path of a ray of light for total internal reflection. 14

15 Direct the IR beam without a sample on the substrate into the detector, generate the interferogram, perform FT to obtain the background transform. P Direct the IR beam with a sample on the substrate into the detector, generate the interferogram, perform FT to obtain the absorption transform. If the sample absorbs the radiation it will be attenuated before re-entering the IRE. Multiple reflections result in an increasing absorption of the IR beam. Linear Dynamic Range and Limit of Detection P Instrument response to analytes usually are proportional to the concentration/amount of analyte under study. C l C u P P %T 1 P R = mc+b m = sensitivity LDR C u Cl Concentration Distinguishing of Signals from the background. If the signal is very large compared to the background (instrument noise), peak height from the mean base line is the signal. Distinguishing Signals from the background noise. If the signal is nearly comparable to the background, there will be a peak height limiting value of the signal that can distinguish itself from the base line noise. Signal + Background Signal + Background 15

16 background Signal Signal + Background =output The mean of the background (noise) data points is the base line. Each maximum, minimum or shoulder is an instrument reading i.e. data point, (with no analyte present) for the background (noise). 3 bkg bkg Baseline related to background noise The mean of the background data points is the base line. Analysis of the data point distribution from the baseline shows a Gaussian distribution. 3 bkg Signal Any data point 3 bkg above the baseline is considered a legitimate data point (considered determine to be statistically different from an analytical blank). 3 bkg Baseline Note: Zero instrument response line 3 bkgcontains 99% of noise points (either side of base) 16

17 3 bkg y = mx + b b < here Instrumental Limit of Detection, LOD (IUPAC) The limit of detection of an instrumental technique is a number expressen units of concentration (or amount) of an analyte that describes the lowest concentration (or amount) that an analyst can determine to be statistically different from an analytical blank. Base line = bkg = Mean of noise 3 bkg Note: Zero instrument response line Baseline/background bkg Baseline = Mean of background noise. Noise level can be expressen terms of, bkg. baseline Calibration plot after zero intercept. y = mc Baseline 3 bkg y More sensitive signal y C m Only signals > 3 are considered true signals (convention). Signals equal to 3 therefore is the detection limit of the instrument. Signal The detection limit expressen terms of concentration; C D 3 m bkg m = sensitivity (slope) of calibration curve = rise/run, Better C D 3 bkg 3 CD m bkg C baseline Calibration plot after non-zero intercept. y = mc + b y More sensitive signal y b C m Signal b, 3 bkg 3 C D m bkg C baseline 17