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. 

The minimum polydispersity index from a free-radical polymerization is 1.5 if termination is by combination, or 2.0 if chains ate terminated by disproportionation and/or transfer. Changes in concentrations and temperature during the reaction can lead to much greater polydispersities, however. These concepts of polymerization reaction engineering have been introduced in more detail elsewhere (6). 

The MWD is the ratio of Mw Mn and is called the polydispersity index. This largely varies from one grade of polymer to the other, depending on the polymerization conditions and the type of catalyst used. Figure 14 shows different types of MWD for the polymers. 

Assuming that no intramolecular or side reactions take place and that all groups are equireactive, the polydispersity index, 7P, of hyperbranched polymers obtained by step-growth polymerization of ABX monomers is given by Eq. (2.2), where pA is die conversion in A groups.196 Note that the classical Flory relationship DPn = 1/(1 — pa) holds for ABX monomer polymerizations ... 

To run the residence time distribution experiments under conditions which would simulate the conditions occurring during chemical reaction, solutions of 15 weight percent and 30 percent polystyrene in benzene as well as pure benzene were used as the fluid medium. The polystyrene used in the RTD experiment was prepared in a batch reactor and had a number average degree of polymerization of 320 and a polydispersity index, DI, of 1.17. 

This trend is illustrated by the curves for the micro-mixed reactor in Figures 8 through 14. Also characteristic of the seeded, micro-mixed reactor is the convergence of the polydispersity index to 2 for a high degree of polymerization. This trend is illustrated to some extent in Table VI which presents the calculated degrees of polymerizations. 

A micro-mixed, seeded reactor will produce a broad polymer distribution with a high molecular weight tail and polydispersity index that approaches 2 at large degrees of polymerization. 

Our theoretical studies [38] showed that the hyperbranched polymers generated from an SCVP possess a very wide MWD which depends on the reactivity ratio of propagating and initiating groups, r=kjk. For r=l, the polydispersity index where P is the number-average degree of polymerization. 

A way to narrow the MWD and to approach the structure of dendrimers is the addition of a small fraction of a/-functional initiator, to inimers [40,71]. In this process the obtainable degree of polymerization is limited by the ratio of inimer to initiator. It can be conducted in two ways (i) inimer molecules can be added so slowly to the initiator solution that they can only react with the initiator molecules or with the already formed macromolecules, but not with each other (semi-batch process). Thus, each macromolecule generated in such a process will contain one initiator core but no vinyl group. Then, the polydispersity index is quite low and decreases with / M /Mn l-i-l//. (ii) Alternatively, initiator and monomer molecules can be mixed instantaneously (batch process). Here, the normal SCVP process and the process shown above compete and both kinds of macromolecules will be formed. For this process the polydispersity index also decreases with/,but is higher than for the semi-batch process, M /Mn=Pn//. ... 

Living polymerization of lactones has been successfully performed by catalysis of rare earth metal complexes to obtain Mw/Mn of 1.07-1.08 [8]. The lowest polydispersity index attained so far with the AlEt3/H20 system is 1.13. 

In general, syndiotacticity (rr%) increases with a reduction of the polymerization temperature. In the case of SmH(C5Me5)2, it increased from 78 to 95.2% as the polymerization temperature was reduced from 25 to — 95 °C, but the polydispersity index remained low [3]. Extrapolating the data suggests that syndiotacticity over 97% may be obtained at — 115°C. Polymerization of MMA in both THF and toluene using the organolanthanide initiators produced syndiotactic polymers, despite the fact that the RMgX initiator in toluene led to isotactic polymers [15]. 

These observations require a detailed explanation. After several unsuccessful attempts a satisfying answer was finally found. A first step was made by the ingenious derivation of the molar mass distributions of randomly branched or randomly cross-linked materials [14]. The equation, that was later rederived by Elory [13], will be given in the next section. Here it suffices to point out that the width of the distribution, or the polydispersity index MJM , increases asymptotically with the weight average degree of polymerization... 

At 24 °C and 15-60 bar ethylene, [Rh(Me)(0H)(H20)Cn] catalyzed the slow polymerization of ethylene [4], Propylene, methyl acrylate and methyl methacrylate did not react. After 90 days under 60 bar CH2=CH2 (the pressure was held constant throughout) the product was low molecular weight polyethylene with Mw =5100 and a polydispersity index of 1.6. This is certainly not a practical catalyst for ethylene polymerization (TOP 1 in a day), nevertheless the formation and further reactions of the various intermediates can be followed conveniently which may provide ideas for further catalyst design. For example, during such investigations it was established, that only the monohydroxo-monoaqua complex was a catalyst for this reaction, both [Rh(Me)3Cn] and [Rh(Me)(H20)2Cn] were found completely ineffective. The lack of catalytic activity of [Rh(Me)3Cn] is understandable since there is no free coordination site for ethylene. Such a coordination site can be provided by water dissociation from [Rh(Me)(OH)(H20)Cn] and [Rh(Me)(H20)2Cn] and the rate of this exchange is probably the lowest step of the overall reaction.The hydroxy ligand facilitates the dissociation of H2O and this leads to a slow catalysis of ethene polymerization. 

The degree of polymerization depends on the duration of the process. After 7 min, the molecular mass is equal to 9400 (the polydispersity index is 5.30). When the reaction is carried out for 15 min, the molecular mass of the polymer increases to 37,000 and the polydispersity index reaches 7.31 (Bauld et al. 1996). Depending on whether cation-radical centers arise at the expense of intramolecular electron transfer or in a stepwise intermolecular lengthening, polymerization can occur, respectively, through a chain or a step-growth process (Bauld and Roh 2002). In the reaction depicted in Scheme 7.17, both chain and step-growth propagations are involved. 

Hence, cation-radical copolymerization leads to the formation of a polymer having a lower molecular weight and polydispersity index than the polymer got by cation-radical polymerization— homocyclobutanation. Nevertheless, copolymerization occnrs nnder very mild conditions and is regio-and stereospecihc (Bauld et al. 1998a). This reaction appears to occnr by a step-growth mechanism, rather than the more efficient cation-radical chain mechanism proposed for poly(cyclobutanation). As the authors concluded, the apparent suppression of the chain mechanism is viewed as an inherent problem with the copolymerization format of cation-radical Diels-Alder polymerization. ... 

All these limitations were overcome by implementing a third approach based on the ROP of lactones [7, 8]. Indeed, many examples of living or/and controlled polymerization with fast initiation are reported using this technique. High molar mass aliphatic polyesters with low polydispersity indexes can be thus be synthesized. In terms of the availability of the monomers, this approach occupies... 

Fig. 3-22 Dependence of number-average molecular weight ( ) and polydispersity index (A) on monomer conversion for ATRP polymerization of bulk styrene at 110°C with CuBr, 1-phenylethyl bromide (I), and 4,4-di-5-nonyl-2,2 -bipyridine (L). [M] = 0.087M [CuBr]0 = [L]0/2 = [I] = 0.087 M. After Matyjaszewski et al. [1997] (by permission of American Chemical Society, Washington, DC) an original plot, from which this figure was drawn, was kindly supplied by Dr. K. Matyjaszewski.

For polymerizations carried out to high conversions where the concentrations of propagating centers, monomer, and transfer agent as well as rate constants change, the polydispersity index increases considerably. Relatively broad molecular-weight distributions are generally encountered in cationic polymerizations. 

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