Tacticity

Tacticity is the relative stereochemistry of adjacent chiral centers within a macromolecule. The practical significance of tacticity rests on the effects on 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, as well as its mechanical properties.
A tactic macromolecule in the IUPAC definition is a macromolecule in which essentially all the configurational units are identical. 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. Tacticity is particularly significant in vinyl polymers of the type -, where each repeating unit contains a substituent R attached to one side of the polymer backbone. The arrangement of these substituents can follow a regular pattern- appearing on the same side as the previous one, on the opposite side, or in a random configuration relative to the preceding unit. Monotactic macromolecules have one stereoisomeric atom per repeat unit, ditactic to n-tactic macromolecules have more than one stereoisomeric atom per unit.

Definition

Diads

Two adjacent structural units in a polymer molecule constitute a diad. Diads overlap: each structural unit is considered part of two diads, one diad with each neighbor. If a diad consists of two identically oriented units, the diad is called an '. If a diad consists of units oriented in opposition, the diad is called an '. In the case of vinyl polymer molecules, an is one in which the substituents are oriented on the same side of the polymer backbone; in the Natta projection, they both point into the plane or both point out of the plane.

Triads

The stereochemistry of macromolecules can be defined even more precisely with the introduction of triads. An isotactic triad is made up of two overlapping m diads, a syndiotactic triad consists of two overlapping, and a heterotactic triad is composed of an overlapping an. The mass fraction of isotactic 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 P_m of a diad being. For example, when this probability is 0.25 then the probability of finding:

an isotactic triad is P_m², or 0.0625
an heterotactic triad is 2P_m, or 0.375
a syndiotactic triad is 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 m and r sequences within the polymer molecule. The average m-sequence length may be approximated from the relative abundance of pentads as follows:

Polymers

Isotactic polymers

Isotactic polymers are composed of isotactic macromolecules. In isotactic macromolecules, all the substituents are located on the same side of the macromolecular backbone. An isotactic macromolecule consists of 100%, though IUPAC also allows the term for macromolecules with at least 95% if that looser usage is explained. Polypropylene formed by Ziegler–Natta catalysis is an example of an isotactic polymer. Isotactic polymers are usually semicrystalline and generally crystallize in a helical configuration.

Syndiotactic polymers

In syndiotactic or syntactic macromolecules the substituents have alternate positions along the chain. The macromolecule comprises 100%, though IUPAC also allows the term for macromolecules with at least 95% if that looser usage is explained. Syndiotactic polystyrene, made by metallocene catalysis polymerization, is crystalline with a melting point of 161 °C. Gutta percha is also an example syndiotactic polymer.

Atactic polymers

In atactic macromolecules the substituents are placed randomly along the chain. The percentage of is understood to be between 45 and 55% unless otherwise specified, but it could be any value other than 0 or 100% if that usage is clarified. 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 polymers such as polystyrene are technologically very important. It is possible to obtain syndiotactic polystyrene using a Kaminsky catalyst, but most industrial polystyrene produced is atactic. The two materials have very different properties because the irregular structure of the atactic version makes it impossible for the polymer chains to stack in a regular fashion: whereas syndiotactic PS is a semicrystalline material, the more common atactic version cannot crystallize and forms a glass instead. This example is quite general in that many polymers of economic importance are atactic glass formers.

Eutactic polymers

In eutactic macromolecules, substituents may occupy any specific sequence of positions along the chain. Isotactic and syndiotactic polymers are instances of the more general class of eutactic polymers, which also includes heterogeneous macromolecules in which the sequence consists of substituents of different kinds.

Effect on polymer properties

Tacticity has a significant effect on polymer crystallinity, and thus affects other properties that depend on crystallinity such as strength, melting point, and solubility. Isotactic and syndiotactic polymers have a more ordered structure and can form semicrystalline materials, while atactic polymers are generally amorphous because their lack of order prevents them from packing into a crystal lattice. Crystallinity generally leads to better mechanical strength, solvent resistance, and barrier properties, but amorphous polymers do not necessarily have poor mechanical properties and can have other advantages such as optical clarity. As an example, atactic polypropylene is an amorphous polymer with a glass-transition temperature, T_g, of -27 °C, while isotactic polypropylene is crystalline with a T_g of -26 °C and a melting temperature, T_m, of 160 °C and syndiotactic polypropylene is also crystalline with a higher T_g of -4.3 °C and a lower T_m of 126 °C. Isotactic polypropylene is strong and high-melting and so is widely used in a range of applications, while atactic polypropylene is soft and waxy and sees only limited use in adhesives and as an asphalt additive.

Stereocontrolled polymerization

Polymers with controlled tacticity must be produced via some type of stereocontrolled polymerization. Stereocontrolled polymerizations have been demonstrated with a variety of chain-growth polymerization mechanisms, although stereocontrolled radical and cationic polymerizations are less common than stereocontrolled coordination and anionic polymerizations due to a lack of stereochemical definition at the propagating chain end. Stereocontrolled polymerization of chiral monomers can also be enantioselective, meaning that one enantiomer of the monomer is selectively polymerized to give an isotactic polymer. Depending on the origin of stereoselectivity, stereocontrolled polymerizations can be classified as polymer chain-end control or enantiomorphic site control.

Polymer chain-end control

In polymer chain-end control, the stereochemistry of the most recent monomer added to the polymer chain determines the stereochemistry of the next monomer added. In an isoselective polymerization, the next monomer to be inserted will have the same stereochemistry as the previous monomer, while in a syndioselective polymerization it will be the opposite. The stereoselectivity of a polymerization with polymer chain-end control is quantified by P_m and P_r, the probabilities of forming an m and r diad, respectively. An isoselective polymerization has a P_m approaching 1, while a syndioselective polymerization has a P_r approaching 1. When a stereoerror occurs, it is propagated, meaning that in an isoselective polymerization the substituents would switch from all being on one side of the polymer chain to all being on the other side.

Enantiomorphic site control

In enantiomorphic site control, the stereochemistry of the next monomer added is instead determined by the stereochemistry of the catalyst. The stereoselectivity of a polymerization with enantiomorphic site control is often quantified by the site control selectivity α, the probability of adding a monomer with a certain absolute configuration. For an isoselective polymerization, an α value of 0 or 1 indicates a fully isotactic polymer while an α value of 0.5 indicates an atactic polymer. When a stereoerror occurs, it is corrected, meaning that substituents will return to being on the same side of the polymer chain that they were on before the error.