Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 431	Biochemistry Laboratory	Fall 2008
Lab Lecture Notes	© R. Paselk 1999

Characterization of Macromolecules

Introduction to Spectrochemical Methods

Introduction: Spectroscopy traditionally has referred to techniques based on electromagnetic radiation (originally just visible light). More recently the definition expanded to include other forms of energy such as electrons or neutrons (after all, at the quantum level the distinctions between photons and particles becomes somewhat artificial since both are characterized by momentums and wavelengths). Modern usage includes essentially any distributed energy function, such as acoustic energy involving energy vs. wavelength, particle speed etc. In our studies we will restrict ourselves largely to "light" in its more classical definition, that is UV-Vis-IR.

Electromagnetic Radiation

Recall that EM radiation has both wave-like and particle-like phenomena associated with it. Both sets of properties are utilized in spectroscopic methods.

• Wave phenomena: v = = c; c = 3.00 x 10⁸ m sec^-1 for EM in vacuo. Note that EM is slowed in matter due to its interactions with electrons. Th us since the frequency of light in matter stays constant its wavelength must shorten. For example, visible light's wavelength shortens by nearly 30% upon entering glass. Note that the two components of EM, the electric and magnetic fields, oscillate at right angles to each other (they are perpendicular). (Common spectroscopists unit, wavenumber = 1 / wavelength, so proportional to frequency and energy).
• Quantum (particle) Properties: Photoelectric effect. E = h. Note that you can't explain the photoelectric effect in terms of waves! The energy of a photon depends on frequency, the number depends on intensity. No way to get this response from a wavefront-need packets.

Absorption of Radiation

Matter can absorb radiant energy in quantized fashion by raising electrons from ground to excited states. Notice that there must generally be an exact match between the energy of a transition and the energy of a photon (current tech can add photons). Species goes to an excited state:

M + M*

After a short period (10^-9 to 10^-6 sec) the excited species relaxes (returns) back to a ground state:

M* M + heat

Can also get relaxation via the emission of a photon:

M* M + h + heat

to give fluorescence or phosphorescence. Finally can get photochemical decomposition to form new species.

M* P + Q + heat

Absorption Spectra

a plot of the attenuation (reduction) of a beam of radiation as a function of wavelength, frequency, or wavenumber. The attenuation is commonly described by either Transmittance:

or Absorbance:

• Atomic Absorption Spectra: Line spectra (half-widths of about 0.005 nm) due to electron transitions between orbitals (l values must be different). UV-Vis spectra are due to outer electron transitions only (lo energy), while X-rays come from inner electron transitions (hi energy).
• Molecular Absorption Spectra: Get absorption bands instead of lines (half-widths up to hundreds of nm). Why the difference? Three contributions:
  • Outer electron transitions
  • Vibrational transitions
  • Rotational transitions

Absorption Spectroscopy

Molecular Absorption

Get absorption bands. Three components to give overall energy: E = E_electronic + E_vibrational + E_rotational [overhead 35]:

• Outer Electron orbital transitions (E_electronic): these would give line spectra as seen in atoms, except that we have additional energy levels due to vibration and rotation
• Vibrational transitions (E_vibrational): these are due to the vibration of atoms in a molecule. Note that there are two major type of vibration. 1) stretching (symmetric and asymmetric), and 2) bending (rocking, scissoring, wagging, and twisting)
• Rotational transitions (E_rotational): due to quantized rate of rotation around a bond (very low energies).

When add all of these up get band structure due to superposition. Note also broadening due to solvent. [overhead 43]

Emission of Radiation

Again can get continuous or discontinuous spectra:

• Discontinuous or Line Spectra: this type of emission will result from atoms in the gaseous state behaving as independent emitters, as in the line spectra of hydrogen in the visible region show here:
  
• Continuous Spectra: all wavelengths are represented over a range, or lines are unresolved, as seen in the continuous comparison spectra above. Occurs under a variety of circumstances.
  • Solids or liquids where emitters can't behave independently
  • Complicated molecules with many closely spaced energies
  • non-quantized kinetic energies for particles (thermal radiation--note that this radiation is characterized by the temperature of the object rather than the nature of the substance {blackbody radiation}. Thermal radiation exhibits a spectral maximum varying width 1/T. The total energy in thermal system varies as the fourth power of temperature, and the emission power at a given temperature varies as the fifth power of the wavelength.)
• Fluorescence and Phosphorescence: Can be resonant (emission and absorption wavelength identical) or non-resonant (emission wavelength longer than absorption) Phosphorescence due to long-lived triplet state where electrons share same spin state.

Beer-Lambert Law, or Beer's Law

For monochromatic (single color or wavelength) radiation the absorbance is directly related to the pathlength through the medium and the concentration of the absorbing substance for a given material:

where A = absorbance, a = absorptivity, a constant which is specific to the substance and the wavelength of light; b = pathlength through the material; and c = concentration. Note that a has units which cancel b and c, thus A is unitless. For the commonly defined conditions using molarity for concentration and cm for length can define:

A = bc

where is the molar absorptivity and has the units of L mol^-1 cm^-1.

Lambert's Law relates absorbance to pathlength: A = kb. We can rationalize by looking at how a series of identical filters would cut down teh light in a light beam. If we start with an intensity I_o, and a filter cuts it to I_o/2, then an additional filter would cut it to I_o/4 etc. If we now plot pathlength (number of filters) vs. I/I_o we see an exponential decay curve which can be linearized by taking the log of I/I_o. Thus A=-log I/I_o=kb with the negative sign being added to give a positive correlation bwetween concentration and A. This law is followed for all values of b.

Beer's Law may be similarly understood if we consider that k must include concentration within k, that is the color intensity includes a component of concentration. Now if we think of each filter as having a certain number of absorbers, then adding filters is the same as just adding more absorbers to the same filter, or, in other words, increasing the concentration. Beer's Law, however is not followed always, there are limitations:

• Real limitations: these are limits due to physical phenomena.
  • First, as concentration increases there will be a consequent change in refractive index, since each substance has a characteristic value for n. This in turn will cause a non-linear response of A vs. c.
  • Second, as concentration increases the solute begins to have a significant influence on the local electromagnetic environment (which was initially due solely to the solvent), which again leads to non-linearities.
• Chemical limitations: equilibria can shift and thus lead to non-linearities.
• Instrumental limitations: due to the fact that frequently the bandpass of the instrument is not narrow enough to provide sufficiently monochromatic light to give a linear response.
  • One last problem is stray radiation in instruments. Stray radiation is radiation that is not part of the selected radiation, but which still gets to the detector. Note that it may not be the proper wavelength, but still pass through sample etc, and result in breakdown of Beer's law.

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Last modified 4 September 2008