Tacticity:

The tetrahedral bond of carbons can be thought of as a tripod with a bond sticking straight up. If a polymer chain is attached to the bond sticking straight up and the chain is attached to one of the legs of the tripod then substitutent groups attached to the other two legs have a choice of being placed to the right or left. This can be depicted in a Neuman projection along the chain back bone where the circle and three line apex are two carbons along the main chain connected by a bond.

The presence of the Cl substitutent group allows for the distinction of H_a and H_b. H_a is anti to Cl and H_b is gauche to the Cl group. For each mer unit in this polyvinylchloride molecule there will be an anti and a gauche methylene proton. The relationship between these mer unit stereo chemistries gives rise to tacticity. Because of this the smallest grouping for tacticity is a diad, two mer units.

Diad Tacticity:

For two substitutent groups in a three carbon sequence the substitutents can be located with the same handedness (Meso) or with opposite handedness (Racemic).

From an NMR perspective, Racemic diads give rise to two magnetically equivalent protons on the methylene group while Meso diads give rise to two magnetically different protons on the methylene group.

NMR can not sense diad tacticity because the proton on the substituted carbon can sense two diads (on either side). The smallest unit of tacticity which NMR can detect in polymers is a triad (3 mer units). Because of this triad tacticity is the usual way to refer to polymer stereochemistry. NMR can also sense higher odd number groupings of tactic mer units, with diminishing resolution, pentads (5), heptads (7) etc.

Note that the handedness, anti or gauche, is independent of rotation about the C-C bonds which occurs in all single bond chains. The particular arrangement shown above is merely for convenience of comparison between meso and racemic diads and does not reflect the actual conformation of the chains in a polymer which would be reflected by a distribution of rotational orientations reflecting the potential energy diagram for C-C bond rotation as show below for polyethylene (PE does not display tacticity),

A triad is composed of two diads which share a central mer unit. There are three possibilities for triad tacticity based on diad tacticity:

Isotactic, meso+meso mm 1

Syndiotactic, racemic+ racemic rr 1

Heterotactic, racemic + meso or meso + racemic rm or mr 2

A polymer with no preferred tacticity, an atactic polymer, has a random statistical distribution of diad tacticities so it would have 25% isotactic triads, 25% syndiotactic triads and 50% heterotactic triads. A polymer with 50% meso and 50% racemic diads does not necessarily have an atactic triad distribution, just as an atactic triad distribution does not necessarily have an atactic (random) pentad distribution. An atactic (random) pentad distribution does imply atactic triad and diad distributions.

Since syndiotactic is composed of two racemic units, and because the protons in a racemic diad are magnetically equivalent (see above), then syndiotactic triads will have the fewest number of magnetic types of protons and the fewest peaks and splittings. This is shown for PMMA in figure 6.6 of Campbell and White shown below (isotactic top, syndiotactic bottom):

PMMA was one of the first polymers studied in depth for tacticity using proton NMR (see texts by Bovey from the 1970's). For syndiotactic PMMA (bottom) 3 main absorptions are observed, a-CH₃ at 0.91, [beta]-CH₂ at 1.9 and a-COOCH₃ at 3.6. For isotactic polymer (top curve) the a-CH₃ is more deshielded 1.20, the [beta]-CH₂ becomes a quartet centered at 1.9 and the a-COOCH₃ remains a singlet at 3.6. The splittings of the [beta]-CH₂ in what should be a sequence of 1:1:1:1 is due to two types of methylene groups, termed erythro, e, (more deshielded) and threo, t, (less deshielded) corresponding to the bottom and top protons in the molecular sketch above. Each of these peaks are split into two peaks by the other leading to and expected splitting of 4 equal peaks, with a reported J coupling constant of about 0.2 ppm. The e and t protons are separated by 0.7 ppm which can be verified by molecular modeling.

A higher resolution NMR can resolve higher order stereosequences as shown below for isotactic and atactic PMMA. You should compare the information content of the 60 MHz spectrum above to the 500MHz spectra below. (Again, 60 MHz refers to the natural resonance frequency of a proton for a given magnetic field of the instrument, [nu] a B₀.)

A similar comparison of signal can be made for the 100 and 500 MHz spectra of polyvinyl chloride given below. [beta]-methylene protons occur at 1.5-2.5 range and the single a-methine proton is observed at about 4.6. In many polymers resolution of splittings for individual stereochemical peaks is not possible and this is illustrated by the PVC spectra. In such cases the tactic sequences can be identified with complicated NMR techniques such as 2-D NMR (see Campbell and White). Generally you will find a reference which has identified the peaks associated with certain tactic groupings for vinyl polymers and use the integrated areas of these peaks to determine the triad tacticity of a given polymer. (Note that the PMMA example given above is the best resolved spectra of commodity polymers, i.e. sharpest peaks, and this is related to the structure of PMMA).

The splittings of the tactic peaks in the proton NMR spectrum of PVC, shown above, are not resolvable on typical NMR spectrometers. Use of a different nucleus, ¹³C, can overcome problems with resolution of this type. The 125 MHz, ¹³C spectra for PVC is shown below. Notice the higher resolution even compared to the 500 MHz proton spectra shown above. (Note that spectrometer magnetic field strength is in reference to the proton resonance frequency even if a different nuclei is probed.)