Polydispersity minimum

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 MALDI-TOF spectrum of [G-3] poly(benzyl ether) dendrimer-po-ly(ethylene glycol) triblock copolymer shows a broad band of peaks between 4300 and 6100 D with resolution of the individual ethyleneoxide (44 D) units. The MALDI-TOF spectrum of a [G-3] dendrimer with two polystyrene blocks (molecular peak=8073 D) shows material with 6000-11,000 D and a broad band corresponding to material with 2 M+Ag+. SEC can be used to prove that the latter species is indeed an artifact of the mass spectroscopic method. The authors claim almost exact agreement between the polydispersities derived from MALDI-TOF and SEC [40]. This does, however, not leave any room for the unavoidable column spreading in the latter method. Furthermore, anionically prepared low MW polymers have a minimum polydispersity given by (1 + 1/DP) [41]. 

Concerning the production of narrow MWD polyethylene, suitable for injection molding, the most commonly used method seems to be that based on catalyst chemical composition control (often by introducing electron-releasing ligands, i.e. alkoxides, on the transition metal compound). In this way minimum polydispersity values could be obtained (Q approximately 3 or even lower), a rather noteworthv result if one remembers that the catalytic systems dealt with are heterogeneous. 

The theoretical minimum polydispersity of the dead polymer assuming termination by disproportionation and combination are 2.0 and 1.5, respectively ... 

Thus, for termination by combination, the polydispersity of the dead chains will have a minimum polydispersity of 1.5. For systems with both disproportionation and combination, the minimum polydispersity will be somewhere between 1.5 and 2.0, depending on the relative rates of the two termination mechanisms. In both cases, the minimum values of polydispersity are absolute minima, and not likely to be attained in practice. The derivations of the minima assume constant temperature, constant monomer concentration (clearly not possible in a batch reactor), constant radical flux, and perfect mixing. For these reasons, actual polydispersities will always be greater than the appropriate minimum. 

Recall that in the earlier batch the right-hand side of Equation 17.40 was assumed to be constant. This was strictly incorrect and resulted in the minimum polydispersity. Eor the CSTR we can assume steady state the right-hand side of Equation 17.39 really is constant. Thus, what was a minimum polydispersity for the batch case is a realistic polydispersity for the CSTR case. 

Cmd Chemicals is producing a polymer with minimum polydispersity by homogeneous, free-radical polymerization in a CSTR. The polymer terminates inherently by disproportionation. To maintain and control the desired average chain length, they... 

In some applications, narrow molecular weight distributions are desirable. Polydispersity indexes in the range of 3-4 have been reported for systems in which the catalyst is supported on MgCl2 (selective promotion of certain types of sites ) or when additives are used (selective poisoning of certain types of sites ). Single-site (EXXPOL) catalysts have recently been announced, They are reportedly capable of producing polyolefins with a minimum polydispersity index of 2. As this is written, the tot is being commercialized. ... 

Analysis of the 1D Correlation Function. Several publications describe the search for a simple graphical analysis [22,159,162-164] of the ID correlation function by means of a geometrical construction. It is the drawback of all such methods that polydispersity and heterogeneity are not considered. The methods are derived from the general generation principle of correlation functions (Fig. 8.20), resulting in equations (cf. Eqs. (8.23), (8.70) and (8.64)) for the first off-origin maximum, the depth of the first minimum or the initial slope iid (0) of ideal correlation functions. For the simplified case of a lamellar system we obtain... 

The simplest measure of the breadth of a distribution is the ratio of two different types of average molecular weight. Specifically the ratio of Mw to Mn is by far the most widely used for this purpose, and is called the polydispersity index. It has a minimum value of unity (for a monodisperse material in which all the chains have exactly the same length). The extent to which it exceeds unity is a measure of the breadth of the distribution. Typical values are in the range 1.5-2.0, but many polymerizations yield considerably larger values. 

The barrier factor, i.e. the expression before the bracket, decreases exponentially with increasing stem length l and the driving force factor (the term in brackets) increases with l (see Fig. 6). The product G has a maximum at an l value which is considered as the kinetically determined lamellar crystal thickness in polydisperse polymers. G becomes positive at the minimum stable fold length /mjn ... 

The minimum fluidisation velocity represents the lower limit of the range of operative conditions at which a fluid-bed process can be operated, while the particle terminal fall velocity represents the upper limit beyond which the particles will start leaving or elutriating from the bed. To avoid or reduce carryover of particles from a fluidised bed, gas velocity has to be kept between um( and ut. For polydisperse systems, in calculating wmr, the mean diameter dvs is used for the particle size distribution present in the bed. In calculating nt, the smallest size of solids present in appreciable quantity in the bed is used. 

For the catalyst system NdV/EASC/DIBAH the impact of water on monomer conversion, Mw, polydispersity and cis- 1,4-content was systematically studied (Table 16) [191], With increasing amounts of water catalyst activity passes through a maximum whereas Mw and Mw/Mn pass through a minimum. It has to be mentioned, however, that the overall effect of water on reaction rate and polymer properties are relatively small. In this study it is also shown that water has no influence on cis-1,4-contents [ 191],... 

The measurement technique already contains the possibility of calculating the minimum fluidization velocity Mmf. The pressure drop in flow through the polydisperse fixed bed at the point u = mf, given for example by the Ergun relation [20], is set equal to the... 

In living polymerization processes it is in fact possible to adjust the final degree of polymerization by simply tuning the initiator amount while keeping narrow the chain length distribution (CLD), i.e. with polydispersity values lower than 1.3 (this quantity reflects the broadness of the final CLD typical minimum values in FRP range from 1.5 to 2). Also, by suitable selection of chemistry and structure... 

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