Anionic polymerization polydispersity index

It may be shown that M > M. The two are equal only for a monodisperse material, in which all molecules are the same sise. The ratio MI /MI is known as the polydispersity index and is a measure of the breadth of the molecular weight distribution. Values range from about 1.02 for carefully fractionated samples or certain polymers produced by anionic polymerization, to 20 or more for some commercial polyethylenes. 

Consistently, Anderson and coworkers showed that the polymerization of MMA in THF at —78 °C is living when initiated by DPHLi (10), which is nothing but the model of the diphenylalkyl anion (9) of the PS macroinitiator used in the synthesis of PS-fcZock-PMMA (equation 21). It must be noted that DPHLi (10) results from the direct addition of DPE (8) to n-Buli (equation 22)". The molecular weight of PMMA is predetermined by the monomer-to-initiator molar ratio and the MMA conversion. The polydispersity index is low (1.04 < Mw/Mn < 1.16). The livingness of this polymerization was confirmed by the successful resumption of the polymerization of lauryl methacrylate (LMA), and formation of the parent PMMA-fc/ock-PLMA diblocks. The anionic polymerization of MMA in THF at —78°C is thus living , provided that sterically hindered initiators are used. 

One main difference between anionic polymerization and GTP has to be found in the amount of enolates active in polymerization. In anionic polymerization, all the chains are end-capped by an enolate, which is the case for only a small part of the chains in GTP consistent with the very good control of GTP even at room temperature. In this respect, Brittain and Dicker showed that prop/ term is by far higher in GTP (250) than in classical anionic polymerization ( prop/ term = 8) . In line with slow termination compared to propagation in GTP, Bandermann and coworkers found that the amount of the nucleophilic catalyst is essential to the polymerization control. Indeed, as far as the tris(piperidino)sulfonium bifluoride-mediated GTP of MMA in THF is concerned, the polydispersity index increases with the amount of catalyst . 

A truly monodisperse polymer has M /M equal to 1.0. Such materials have not been synthesized to date. The sharpest distributions that have actually been made are those of polystyrenes from very careful anionic polymerizations. These have Mw/A n ratios as low as 1.04. Since the polydispersity index is only 4% higher than that of a truly monodisperse polymer, these polystyrenes are sometimes assumed to be monodisperse. This assumption is not really justified, despite the small difference from the theoretical value of unity. 

Many addition polymerization reactions with very low concentrations of impurities have propagation rates much faster than initiation rates and have essentially no termination. Such reactions produce narrow molar mass distributions that can be approximated by the Poisson distribution. Comparison of the polydispersity index of anionically polymerized butadiene with Eq. (1.69) is shown in Fig. 1.20. 

Fig. 1.2 GPC data obtained from an attempt to form a styrene-acrylate diblock copolymer using anionic polymerization. Both the polydispersity index (2.96) and the shape of the curve suggest that the desired homogeneous product has not been formed.

The ratio M IMn approaches unity asymptotically as increases. Narrow molecular weight distributions should thus be obtained in living ionic polymerizations with fast initiation in the absence of depropagation, termination, and chain transfer reactions. Values of polydispersity index (PDI) below 1.1 -1.2 are indeed found for many living polymerizations. Molecular weight-standards for polystyrene, poly-isoprene, poly(a-methylstyrene), and poly (methyl methacrylate) are thus synthesized by living anionic polymerizations. However, the termination reactions in methyl methacrylate polymerizations and depropagation in or-methylstyrene polymerizations tend to broaden the PDI in these systems. 

One polydispersity index which measures the width of the distribution function is the ratio /. For many addition polymers, this polydispersity index lies in the range 1 5-2 0 but other polymers, especially those prepared by Ziegler-Natta catalysts, may have a polydispersity index that is an order of magnitude greater. The polydispersity index is 1-0 for a monodisperse (>ol3mier. Anionic polymerizations can lead to polydispersity indices close to unity. 

Pluronic block copolymers are S3mthesized by sequential addition of PO and EO monomers in the presence of an alkaline catalyst, such as sodium or potassimn hydroxide (3). The reaction is initiated by polymerization of the PO block followed by the growth of EO chains at both ends of the PO block. Anionic polymerization usually produces polymers with a relatively low polydispersity index (Mn/Mw). Fmrther chromatographic fractionation was employed in procedures for the manufacture of highly purified block copolymers (12,13). 

Anionic polymerization is used to produce the styrenic block copolymers and produces a polymer with an extremely narrow block and overall molecular weight distributions. The narrow molecular weight distributions are extremely useful in fundamental studies of polymers, and have led to a great deal of study of anionic polymerization, much more than justified by its commercial importance. In fact, the styrenic-block copolymers are the only polymers produced in large quantities via anionic polymerization. The extremely narrow polydispersity is evident in the following expression for the polydispersity index ... 

Typical polydispersity — index (M /Mn) Anionic polymerization active center sodium thiolates, tetrahydrofuran solvent 1.1-1.2 (13)... 

The synthesis of well-defined polymers and of complex polymer architectures has been greatly facilitated by recent developments in controlled radical polymerization, which has opened up new possibilities in the design and also in the preparation of functional nanostructures based on supramolecular assembly. Controlled radical polymerization is an attractive alternative to anionic polymerization for preparing polymeric building blocks of well-defined size and a low polydispersity index... 

If the termination reaction in chain polymerization is by disproportionation, then the polydispersity index, MJM , is 2. Termination by combination yields a polydispersity index of 1.5. Stepwise polymerizations, such as polyester formation, yield a value of 2. Anionic polymerizations yield surprisingly narrow distribution, with values sometimes less than 1.05. 

For reasonable values of n , the polydispersity index is nearly unity. This distribution is realized for carefully prepared anionic polymerizations. 

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