NMR Spectroscopy for polymer chemists Rachel O’Reilly CH968 2-5pm 17 th February 2014 1 NMR Theory • Every nucleus has a magnetic moment given by: • For a nucleus with spin I there are 2I + 1 possible orientations. Most commonly used nuclei have I = ½ so there are 2 spin states. 2 π γIh μ Gyromagnetic ratio Nuclear spin Planck’s constant NMR Theory NMR Theory • The two spin states for I = ½ nuclei are m = ½ and m = -½. • When placed in a uniform magnetic field, B 0 , the spins align in one of two opposite directions. B 0 m = -½ m = ½ NMR Theory • The energy of each spin state is proportional to the magnetic moment and B 0 : • The selection rule is that m can only change by one in any transition... 0 μB E 2 π γhmB E 0 m = ½ or -½ NMR Theory • The transition energy is then: • The transition is induced by applying radiation with this energy, or this frequency: 2 π γhB ΔE 0 2 π γB ν h ν ΔE 0 NMR Theory • At the resonant frequency, the pulse’s energy is absorbed and nuclei are promoted to a higher energy level. • We try to measure this absorbance. N B N A kT ΔE A B e N N Very small! ∆E m = -½ m = ½ B 0 m = -½ m = -½ FT NMR • Because of the small difference between N A and N B every sample has net magnetisation , which is aligned with the applied field (B 0 ). • Instead of scanning the frequencies, a single pulse containing all of them is applied over time t • The length of the pulse is such that the magnetisation is tipped 90° ... B 0 π/2 pulse z y x FT NMR • The magnetisation now precesses like a top – the time for one revolution round the z axis is the same as the resonant frequency. • We measure this frequency by positioning a detector coil along the y axis, this gives us a cosine wave: y x y x y x FT NMR • Since all environments are simultaneously excited, we actually see a superposition of lots of cosines. • The magnetisation also decays over time (i.e. it returns to being along the z axis). • Both of these give us the Free Induction Decay (FID) spectrum: FT NMR • The FID is then converted to the spectrum with which we are familiar by a Fourier transform : A little demonstration... http://www.youtube.com/watch?v=7aRKAXD4dAg&feat ure=player_detailpage Things to bear in mind • Higher temperature lower sensitivity • High viscosity poor results • Try increasing the number of acquisitions rather than the concentration • Possible to use non-deuterated solvents, but you must add a small amount of deuterated to provide a lock for the machine Things to bear in mind • Magnetization of the nuclei by a pulse begins to return to its original equilm value along the z axis and the xy plane immediately after the pulse • Return of the Z-component (M z ) to equilm value is longitudinal relaxation • Return of M xy to zero is tranverse relaxation • Both are 1 st order processes, characterised by the times T 1 and T 2 Things to bear in mind • Good data depends on use of appropriate T 1 (spin lattice) and T 2 (spin-spin) relaxation times • Width of line in NMR spectra determined by T 2 • Short T 2 broad lines • Maximum repetition rate during NMR acquisition is given by T 1 (the delay time should be at least 5 times the longest T 1 ) T 1 always greater than or equal to T 2 In polymers T 1 much greater than T 2 For small molecules... Relaxation mechanisms • T 2 relaxation is caused by fluctuations in any direction • ie molecular motion • Define a correlation time ( t c ) for a molecule • This is the average time it takes one molecule to rotate by one radian Small molecule (M n < 1000 Da), t c ca. 10 -12 sec For a proton at 300 MHz u 0 = 10 8 (Larmor procession frequency) Small molecules move too fast to relax by spin-spin relaxation But polymers do not.... For small molecules... Chemical shift • Rapid rotation Brownian motion of small molecules averages out dipolar and other anisotropic magnetic interactions • Called molecular tumbling • Leads to narrow lines in the NMR spectra • If tumbling (or rotation) is slow relative to the timescale of the NMR then the signal is broadened • Because different chemical shifts are observed • Brownian motion of molecules decreases with increasing size • Line width of an NMR signal increases as size increases Polymers... NMR signals always broad in the 1D NMR of polymers (each monomer is similar to its neighbours, therefore signals overlap) Interactions usually broaden the NMR resonance lines of a spectrum. In (non-viscous) liquids these interactions are averaged by rapid isotropic motions of the molecules – in polymers by bond rotations of the backbone and the side- chain or groups. The fast isotropic motions average the interactions to zero or to a single finite value representing the average interaction. Line broadening due to slow relaxation as a result of larger mass, therefore slower tumbling How is NMR useful in polymer science • Measurement of polymerisation conversion • End group analysis • Molecular weight determination • Stereochemistry • CMC determination