chemistry 311: topic 3b - ftir basicschemistry 311: topic 3b - ftir basics michelson interferometer:...

Chemistry 311: Topic 3b - FTIR basics

Infrared Absorption Spectroscopy: Examination of the energy associated with transitions between vibrational or rotational energy states of a molecule. Wavelength associated with these types of transitions 0.78 to 1000 µm, or in other words 7.8 x 10-7 m (780 nm) to 1.0 x 10-3 m (1,000,000 nm). Wavelength indicated by wavenumber (ν) expressed as cm-1 ie.,

2.5 µm = 2.5 x 10-6 m ; 1/2.5 x 10-6 m = 400000 m-1 = 4000 cm-1 Wavenumber is directly proportional to energy and frequency. In fact wavenumbers in cm-1 is often referred to as frequency in the plotting of IR data (see Skoog Figure 16-1, Table 16-1)


Typical IR Spectra (mid-region): Note:

Change of scale at 2000 cm-1 Frequency is actually wavenumber


Absorption of Radiation: In order for a molecule to absorb IR radiation a net change of dipole moment must occur. The frequency of radiation must match the natural vibration frequency of the vibration. Rotational Transitions are of the order of 100 cm-1 or less. These are associated with vibrations and lead to broadening of peaks, especially in solutions. Types of Vibrations: (see Skoog, Figure 16-2)


Mechanical model - Simple Harmonic Motion: (see Skoog, Figure 16-3)

ν =1

2 πk

m√


Classical Treatment of Vibration Frequency: Natural Frequency: Modified to describe system with 2 masses by introducing concept of reduced mass (µ). In Quantum mechanical treatment:

Where; ν is vibrational quantum number k is the force constant µ is the reduced mass

ν =1

2 πk

m√

µ = m1m2

m1 + m2

νm = 1

2 π k

µ √ νm =1

2 πk (m1m2)

m1 + m2 √

E = (ν + ½) h

2 π k

µ√


The relationship between the Classical and quantum energy relationship is ∴

Where; ν is vibrational quantum number NOT Frequency (integers 0, 1, 2, …) νm is observed vibrational frequency Energy of ground vibrational state (E0) and first excited state (E1) is ∴; Observed frequency is then;

Where; k = force constant For single bonds; k ≈ 3 x 102 to 8 x 102 N/m

kave = 5 x 102 N/m to estimate For double bond use 2 x kave For triple bond use 3 x kave

∆E = (3/2 h νm) – (½ h νm) = h νm =h

2 πk

µ √

E = (ν + ½) h νm

E0 = ½ h νm E1 = 3/2 h νm

νm = 1

2 π k

µ √ ν = = 5.3 x 10-12

1

2 c π k

µ √ k

µ√


Selection Rules: Permitted transitions ∆ν = ± 1 For true Harmonic Oscillator all vibration levels are identical so only a single transition can be observed. In a real bond get Anharmonic Oscillations. When atoms too close coulombic repulsion increases in a non-linear manner. Similarly, when atoms get too far apart the distance approaches bond breaking, ∴ relationships more complex (see Skoog Figure 16-3 (b)) Because of anharmonic oscillations, spacing of energy states much closer nearer to the dissociation limit. Can also get transitions ∆ν = ± 2 or 3 which leads to overtone lines (frequencies 2 – 3 times the fundamental line) In polyatomic molecules may also get interaction between vibrations such that either sum or difference frequencies are observed. As is the case with overtones, these interaction frequencies have low intensities.


Number of Vibrational Modes: For a linear molecule; # Vibrational modes = 3N – 5 For a non-linear molecule; # Vibrational modes = 3N – 6 Related to concept of degree’s of freedom: A molecule with N atoms has 3N degree’s of freedom, ie., one for each Cartesian coordinate (x,y,z) To define translations or movement of the molecule through space, 3 values are required x,y,z (base movement on changes in center of gravity) To define rotation motion an additional 3 values are required. However, in the special case of linear molecules only 2 values are required. (rotations occur around the molecules center of gravity) The remaining variables are used to describe inter-atomic motion and thus vibrations. A unique frequency could be observed for each vibration that involves a change in dipole


Fewer peaks are found when: No change in dipole results from a particular vibration;

The energies of two or more vibrations are identical or nearly identical;

The absorption intensity is so low as to be undetectable by ordinary means

Vibrational energy in a wavelength region beyond range of the instrument

More peaks are found when:

Occurrence of overtone peaks (2 to 3) times the frequency of fundamental

A photon excites two vibrational modes simultaneously.

Combination band at the sum or difference of two fundamental frequencies

Vibrational Coupling

The energy of a vibration, and thus the wavelength of its absorption peak, may be influenced by (or coupled with) other vibrators in the molecule.


Vibrational Coupling influenced by;

Strong coupling between stretching vibrations occurs only when there is an atom common to the two vibrations.

Interaction between bending vibrations requires a common bond between the vibrating groups

Coupling between a stretching and a bending vibration can occur if the stretching bond forms one side of the angle that varies in the bending vibration

Interaction is greatest when the coupled groups have individual energies that are approximately equal

Little interaction observed between groups separated by two or more bonds

Coupling requires that the vibrations be of the same symmetry species


Multiplex instrument: Spectral information is obtained by measuring a time-domain signal, which is then converted to desired domain such as the frequency domain commonly used for spectroscopy. Spectrum modulated and then collected simultaneously. Signal decoded mathematical using a Fourier Transform (FT) function. Advantages: 1) Throughput (Jaquinot) advantage: no slits, ∴ more signal though. 2) High resolving power and λ reproducibility. 3) Simultaneous data collection (Fellgett’s advantage), leads to very fast spectrum collection 1 sec or less. In typical scanning instrument high resolution means multiple “steps” and narrow slits, typically 5 to 15 minutes per spectra. To improve S/N take multiple spectra, can take 1 hour or more. Hugh number of spectra can be collected in short time by FT instruments. Note: In UV and Visible range Shot and Flicker noise dominate, these reduce advantage of FT. (See Skoog, Figure 7-40) Measured time based signal “contains” Frequency signal and these can be interconverted by very complex mathematical treatments.


P(t) = k cos (2πν1t) + k cos (2πν2t) Time vs Frequency Domain Plots: (See Skoog Figure 7-40)

P(t) = k cos (2πν1t) + k cos (2πν2t)


Time vs Frequency Domain Plots: (See Skoog Figure 7-43)


Michelson Interferometer: (See Skoog Figure 7-42)


Michelson Interferometer: Used to modulate radiation in the optical region Horizontal motion of the movable mirror causes the power of the radiation to fluctuate in a manner related to the distance and velocity that the mirror oscillates as well as the radiation wavelength. The resulting time domain interferogram is a complex combination of wavelength dependent cosine functions that can be mathematically converted to a frequency domain spectra using a Fourier Transform algorithm. The retardation, δ, is defined as the twice the difference in the path length between the split and the fixed mirror compared to the splitter and the movable mirror. The magnitude of the mirror motion is equal to ½ the retardation. The resolution of a Michelson Interferometer is inversely related to the retardation, ie., ∆ ν = ν2 - ν1 = δ-1 Where; ν is the wavenumbers of two barely resolved lines.

chemistry 311: topic 3b - ftir basicschemistry 311: topic 3b - ftir basics michelson interferometer:...

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