NMR
NMR takes advantage of the fact that some nuclei have access to two or more energy levels when they are subjected to an external magnetic field.
The experiment induces transitions of the nuclei between these energy levels.
Number and spacing of the energy levels
The number of energy levels in the presence of an applied magnetic field is 2I+1, where I is the nuclear spin quantum number.
- The common isotopes of two important elements in polymers, 12C and 16O, have I = 0.
Therefore these two isotopes have only a single energy level, and transitions involving these nuclei are not observed in NMR.
- Several important isotopes in polymers, 1H (natural abundance 99.98%) 13C (natural abundance 1.11%) and 19F (natural abundance 100%), have I = 1/2.
In the presence of the applied magnetic field H0, each of these two nuclei has two states, with energies of + muH0 and - muH0, where mu is the magnetic moment.
Transitions between these two energy levels involve an energy of 2 muH0.
For the muH0 encountered in nmr meassurements with polymers, this energy is in the radiowave region of the spectrum.
- Some other elements have larger values of I, but they will not be discussed here.
Chemical Shift
The local field sensed by a nucleus is dominated by muH0.
However, it can be modified slightly by shielding by nearby electrons.
This slight affect is exploited in nmr spectroscopy.
The modification is proportional to muH0, but this proportionality is removed from the data when the frequencies are converted to chemical shifts, d, using a standard substance.
d = (Hreference - Hsample)/Hreference
The protons in tetramethylsilane (TMS) are frequently used as a reference in proton nmr.
Since the effect is small, d is usually quoted in parts per million, ppm.
The range covered depends on the type of nucleus examined, being larger for 13C (~600 ppm) than for 1H (~10 ppm).
With proton nmr, the areas under the peaks in the spectrum are proportional to the number of protons in a given magnetic environment.
Therefore ethanol, at low resolution, shows three peaks, with areas in the ratio of 3:2:1, for the protons in the methyl:methylene:hydroxyl groups.
Ring currents in aromatic rings (such as those found in polystyrene) can produce important changes in d for protons closeby, with the size of the effect depending on distance from the aromatic ring, and orientation with respect to the normal to the plane of that ring.
Spin-Spin Interactions
When ethanol is examined at higher resolution, fine structure is revealed in the methyl and methylene peaks.
- The single methyl peak observed at low resolution splits into three equally spaced peaks, with intensities in the ratio 1:2:1, at higher resolution
- The single methylene peak observed at low resolution splits into four equally spaced peaks, with intensities in the ratio 1:3:3:1, at higher resolution
- The hydroxyl peak remains as a single peak.
The splittings arise from interaction of the spins on hydrogens bonded to neighboring carbon atoms.
The multiplicity from n hydrogen atoms is n + 1, with the intensities being 1:1 for doublets, 1:2:1 for triplets, 1:3:3:1 for quadruplets, etc.
The spacing, determined by the spin-sping coupling constant J, is independent of H0.
The value of J in the fragment H-C-C-H depends on the torsion angle at the C-C bond, but this dependence is not apparent in ethanol, because rotation about this bond is rapid on the nmr time scale.
If rotation about the C-C` bond is slow (which can occur if this bond is incorporated into a ring), then measurement of the size of J gives information about the conformation at that bond.
Some distinguishing features of 13C nmr
- Spin-spin interactions are usually of little importance, due to the low natural abundance of 13C (but these interactions can become important if the material is enriched in this isotope).
Therefore the 13C nmr spectra often have a simpler appearance than proton nmr spectra.
- The range for d is nearly two orders of magnitude larger for 13C than for protons.
- The signals tend to be weaker in 13C nmr, due to its low natural abundance.
- In contrast to proton nmr, the signals in 13C nmr do not have intensities proportional to the number of nuclei involved.
For a recent brief review of nmr of polymers, see Tonelli Physical Properties of Polymers Handbook Mark, J. E., Ed., American Institute of Physics, 1996, p 271.
An excellent book on nmr is Bovey, F. A. Nuclear Magnetic Resonance Spectroscopy Academic Press, New York, 1988.
The technique can be used to determine tacticity and sequence isomerization.
A good online source for more extensive fundamental information on nmr can be found under Basics of NMR at the web site maintained by Prof. Hornak.
http://www.cis.rit.edu/people/faculty/hornak/index.html
Return to the index
October 8, 1999
Wayne L. Mattice: wlm@polymer.uakron.edu