In DMA, the N-methyl groups are magnetically nonequivalent, depending
on whether the group is cis or trans to the carbonyl. As a result
of DMA's rotational restrictions, protons on the N-methyl groups give rise
to two separate NMR peaks (near a d of 3.0)
at room temperature. For higher temperatures, rotation rates increase,
causing the two NMR peaks to widen due to shorter lifetimes (quicker exchange)
of the two conformers. As temperature is further increased (more rapid
rotation), the two peaks merge (at the coalescence temperature).
Above the coalescence temperature, the merged peak width decreases as temperature
increases. This continues until exchange effects no longer contribute
to spectral peak widths.
1. Slow Exchange: Below the coalescence temperature and for NMR temperatures at which the two peaks are well resolved (less than ~20% overlap), the rate constant can be calculated using :
2. Intermediate Exchange: Below the coalescence temperature and for NMR temperatures at which the two peaks overlap significantly (minimum between two peaks at least ~20% of peak intensity), the rate constant can be calculated using:
3. Coalescence: At the coalescence temperature, the peaks merge into a flat-topped peak and the rate constant can be found with:
4. Rapid Exchange: At temperatures at least 10-15 degrees above the coalescence point, the width of the merged peak may be used to calculate k:
The rate constant for the exchange of methyl groups (i.e. for rotation
about the amide bond) is:
From the linear plot of ln(k/T) vs 1/T, the entropy and enthalpy of
activation can be calculated:
where Ea is the activation energy and A is the pre-exponential
factor. From a plot of ln (k) vs 1/T, Ea can be calculated.
2. Use the cursers to find the both peak locations and the peak full-width at half maximum for the downfield peak.
3. Use the appropriate line shape analysis equations listed above to determine rate constants for the measured temperatures.
4. Create Eyring and Arrhenius plots and regressions of your data and calculate DG‡(298), DH‡, DS‡, and Ea.
5. Use these literature values for DMA rotation parameters: DH‡ = 83.68 kJ/mol, DS‡ = 19.6648 J / K-mol, and Ea = 86.1904kJ/mol.