is composed of a racemo diad adjacent to a meso 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, the triad composition can be calculated from the probability Pm of a diad being meso. For example, when this probability is 0.25 then the probability of finding: 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 with a total probability of 1. Similar relationships with diads exist for tetrads. 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: Polymers 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 polymerization, is crystalline with a melting point of 161 °C. Gutta percha is also an example for Syndiotactic polymer. 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 polyvinyl chloride are usually atactic. Due to their random nature atactic polymers are usually amorphous. In hemi isotactic macromolecules every other repeat unit has a random substituent. Atactic