Copolymerization sequence length distribution

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

Fig. 6-8 Sequence length distribution for an ideal copolymerization with ri = r2 = 1 and/i =/2. After Vollmert (transl. Immergut) [1973] (by permission of Springer-Verlag New York, Inc., New York).

The sequence length distribution for an ideal copolymerization with r = 5, r2 = 0.2 for an equimolar feed composition is shown in Fig. 6-9. This copolymerization has pn — p2 0.8333 andp 2— p22 — 0.1667. Both M and M propagating centers have a 5 1 tendency to add Mi over M2, but Mi pentad sequences are not the most plentiful, although they are among the most plentiful. The most plentiful sequence is Mi at 16.7% with 14.0%, 11.6%, 9.7%, 8.1%, 6.7%, 5.6%, and 4.7%, respectively, of dyad, triad, tetrad, pentad, hexad, heptad, and octad Mi sequences. There are smaller amounts of longer sequences 3.2% of... 

Fig. 6-10 Sequence length distribution for an alternating copolymerization with r 0.1 and...

Copolymers are readily prepared by conducting polymerizations of a mixture of monomers. However, to obtain a product having any reasonable, structural homogeneity, it is necessary to take the reaction mechanism into account, and to perform the experiment under conditions consistent with classical, copolymerization theory. With properly controlled experiments, it is possible to determine the relative reactivities of the monomers, and the range of compositions and mer sequence-length distributions in any copolymer produced.81,82... 

It should be emphasized that copolymerizations that conform to the premises of binary-copolymerization theory produce copolymers of well defined structure. The kinetics of the competitive propagation-reactions determine not only the copolymer composition but also the sequence distribution. The mathematical procedures needed for calculating number-average sequence-lengths of mers, and sequence length-distributions of mers, are well known and have been... 

Statistical Models. Due to the difficulties involved in calculating the composition distributions by purely deterministic techniques, statistical methods have been developed from which not only the CCD can be obtained but also the sequence length distribution. These methods view the chain growth as an stochastic process having possible states resulting from the kinetic mechanisms. Early work on this approach was reported by Merz, Alfrey and Goldfinger (4) who derived the copolymerization equation and the SLD for the ultimate effect case. Alfrey Bohrer and Mark (19) and Ham (9) formalized this approach. 

Problem 7.12 The sequence length distribution for a copolymerization system can be described by the mole fractions of sequences with 1, 2, 3, 4, 5, 6,... 

Problem 7.13 Consider an alternating copolymerization with = V2 = 0.1 and fi = 0.5. What percentage of the alternating copolymer structure is made of M1M2 sequence Compare the sequence length distribution with that for the ideal copolymer in Problem 7.12(a) which has the identical overall composition. 

Problem 7.9 The sequence length distribution for a copolymerization system can be... 

Ttp 4 Chain microstructure and propagation reactions. Propagation reactions are mainly responsible for the development of polymer chain microstructure (and control chain composition and sequence length distribution in copolymerizations). In free radical polymerization, the stereoregularity of a high molecular weight homopolymer chain depends on polymerization temperature almost exclusively. It is usually independent of initiator type and monomer concentration. Calculations on stereoregularity... 

Fig. 6-9 Sequence-length distribution for an ideal copolymerization with rj = 5, rt = 0.2 and f = ft-...

Problem 7.9 The sequence length distribution for a copolymerization system can be described by the mole fractions of sequences with 1, 2, 3, 4, 5, 6, Mi or M2 units in a copolymer and plotting against sequence length in a bar graph. Describe such distribution for an ideal copolymerization with equimolar feed composition considering two cases (a) r = ri = I and (b) r = 5, ri = 0.2,... 

Figure 7.7 Sequence length distribution for an ideal copolymerization with (a) ri =r2 = 1. /i = and (b) ri =5, T2 = 0.2, /i = /2- [In (a) the distribution of M2 sequences is not shown as it is the same as for Mi sequences. In (b) the plots of W c(M2) (—) are shown slightly to the left of the actual sequence length for clarity] (After Vollmert, 1973.)...

We will introduce this approach in the case of the 2D CLD/DBD computation for mixed-metallocene polymerization of ethylene. Subsequently, we present applications of the approach to the 3D problems of radical polymerization of vinyl acetate (CLD/DBD/number of terminal double bonds distribution), AB radical copolymerization (CLD/comonomer composition distribution/sequence length distribution), and finally the 2D problem of radical polymerization of polyethylene, where random scission is a complicating factor. 

For the foUwing estimation of the copolymerization parameters it is useful to discern between the ovmaU or mixed parameters and the true oopolymerization parameters. First we assume that there are only uniform active centres located on the catalyst sur ce, (i.e., one centre model), and use ethene and comonomer peaks in the NMR spectrum of the polymer mixture for the estimation of the oopolymerization parameters according to the Mayo Lewis equqtion This evaluation, via the r versus diagram, leads to the overall or mixed copolymerization parameters. However, for the estimation of the true copolymerization parameters we now use the following considerations. The Mayo-Lewis equation describes the composition of the copolymer as a function of the initial monomers mixture and the oopolymerization parameters. If we know these and the monomers mixture we can calculate not only the copolymer composition but also, by means of statistical considerations, the sequence length distribution of Mj and M2 sequences in the copolymer... 

Recently, ACOMP capabilities were expanded to follow the evolution of different copolymer features during copolymerization reactions. A first study reported the online monitoring of the copolymerization of MMA and styrene [17]. Simultaneous, model-independent evolution of the average composition and mass distributions during free radical copolymerization reactions were determined. Also, model-dependent calculations of reactivity ratios and sequence length distributions were made. 

Ye YS, Schork FJ. Modeling and control of sequence length distribution for controlled radical (RAFT) copolymerization. Ind Eng Chem Res 2009 48 10827-10839. 

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