Tacticity

Tacticity (from Greek 'taktikos': of or relating to arrangement or order) is the relative stereochemistry of adjacent chiral centers within a macromolecule. The practical significance of tacticity rests in the link between tacticity and the physical properties of the polymer. The regularity of the macromolecular structure influences the degree to which it has rigid, crystalline long range order or flexible, amorphous long range disorder. Precise knowledge of tacticity of a polymer also helps understanding at what temperature a polymer melts, how soluble it is in a solvent and its mechanical properties.

A tactic macromolecule in the IUPAC definition is a macromolecule in which essentially all the configurational (repeating) units are identical. Tacticity is particularly significant in vinyl polymers of the type -H2C-CH(R)- where each repeating unit with a substituent R on one side of the polymer backbone is followed by the next repeating unit with the substituent on the same side as the previous one, the other side as the previous one or positioned randomly with respect to the previous one. In a hydrocarbon macromolecule with all carbon atoms making up the backbone in a tetrahedral molecular geometry, the zigzag backbone is in the paper plane with the substituents either sticking out of the paper or retreating into the paper. This projection is called the Natta projection after Giulio Natta. Monotactic macromolecules have one stereoisomeric atom per repeat unit, ditactic to n-tactic macromolecules have more than one stereoisomeric atom per unit.

Diads
Two adjacent structural units in a polymer molecule constitute a diad. If the diad consists of two identically oriented units, the diad is called a meso diad reflecting similar features as a meso compound. If the diad consists of units oriented in opposition, the diad is called a racemo diad as in a racemic compound. In the case of vinyl polymer molecules, a meso diad is one in which the substituent carbon chains are oriented on the same side of the polymer backbone.

Triads
The stereochemistry of macromolecules can be defined even more precisely with the introduction of triads. An isotactic triad (mm) is made up of two adjacent meso diads, a syndiotactic triad (rr) consists of two adjacent racemo diads and a heterotactic triad (rm) is composed of a meso diad adjacent to a racemo diad. The mass fraction of isotactic (mm) triads is a common quantitative measure of tacticity.

When the stereochemistry of a macromolecule is considered to be a Bernoulli process, triad composition can be calculated from the probability of finding meso diads (Pm). When this probability is 0.25 then the probability of finding: with a total probability of 1. Similar relationships with diads exist for tetrads.
 * an isotactic triad is Pm2 or 0.0625
 * an heterotactic triad is 2Pm(1-Pm) or 0.375
 * a syndiotactic triad is (1-Pm)2 or 0.5625

Tetrads, Pentads, etc.
The definition of tetrads and pentads introduce further sophistication and precision to defining tacticity, especially when information on long-range ordering is desirable. Tacticity measurements obtained by Carbon-13 NMR are typically expressed in terms of the relative abundance of various pentads within the polymer molecule, e.g. mmmm, mrrm.

Other conventions for quantifying tacticity
The primary convention for expressing tacticity is in terms of the relative weight fraction of triad or higher-order components, as described above. An alternative expression for tacticity is the average length of meso and racemo sequences within the polymer molecule. The average meso sequence length may be approximated from the relative abundance of pentads as follows:

$$MSL = \frac{mmmm+ \tfrac{3}{2} mrrr + 2 rmmr + \tfrac{1}{2} rmrm + \tfrac{1}{2} rmrr}{\tfrac{1}{2} mmmr + rmmr + \tfrac{1}{2}rmrm + \tfrac{1}{2}rmrr}$$

Isotactic Polymers
Isotactic polymers are composed of isotactic macromolecules (IUPAC definition). In isotactic macromolecules all the substituents are located on the same side of the macromolecular backbone. An isotactic macromolecule consists of 100% meso diads. Polypropylene formed by Ziegler-Natta catalysis is an isotactic polymer. Isotactic polymers are usually semicrystalline and often form a helix configuration.



Syndiotactic polymers
In syndiotactic or syntactic macromolecules the substituents have alternate positions along the chain. The macromolecule consists 100% of racemo diads. Syndiotactic polystyrene, made by metallocene catalysis polymerisation, is crystalline with a melting point of 270 °C.



Atactic polymers
In atactic macromolecules the substituents are placed randomly along the chain. The percentage of meso diads is between 1 and 99%. With the aid of spectroscopic techniques such as NMR it is possible to pinpoint the composition of a polymer in terms of the percentages for each triad.

Polymers that are formed by free-radical mechanisms such as polyvinylchloride are usually atactic. Due to their random nature atactic polymers are usually amorphous. In hemiisotactic macromolecules every other repeat unit has a random substituent.

Head/tail configuration
In vinyl polymers the complete configuration can be further described by defining polymer head/tail configuration. In a regular macromolecule all monomer units are normally linked in a head to tail configuration so that all β-substituents are separated by three carbon atoms. In head to head configuration this separation is only by 2 carbon atoms and the separation with tail to tail configuration is by 4 atoms. Head/tail configurations are not part of polymer tacticity but should be taken into account when considering polymer defects.

Techniques for measuring tacticity
Tacticity may be measured directly using proton and carbon-13 nuclear magnetic resonance, especially two-dimensional techniques. NMR techniques enable a quantitative assignment of degree of tacticity by quantifying the relative abundance of diad, triad, and higher order polymer subunits (%rr, %mm, %mrm etc.). Other techniques sensitive to tacticity include x-ray powder diffraction, secondary ion mass spectroscopy (SIMS) and vibrational spectroscopy. Tacticity may also be inferred by measuring another physical property, such as melting temperature, when the relationship between tacticity and that property is well-established.