Branches per polymer molecule

N = average number of long chain branches per polymer molecule N+2 = average number of end groups per polymer molecule... 

At 60 C with a conversion of 60% in a single CSTR, Bf, — 4J86 long branches per polymer molecule. Increasing the number of equal-sized CSTRs in series so as to approach plug flow (or batch reactor) behavior, one would obtain a of about 1.5 long branches per polymer mol ule. In... 

The development takes into account transfer to monomer, transfer to polymer, and terminal double bond polymerization. For the vinyl acetate system where transfer to monomer is high, the generation of radicals by transfer to monomer is much greater than the generation of radicals by initiation, so that essentially all radicals present have terminal double bonds hence, effectively all dead polymer molecules also have a terminal double bond. Thus, for vinyl acetate polymerization, the terminal double bond polymerization can be significant, and has been built into the development. The equations for the moments of the molecular weight distribution and the average number of branches per polymer molecule are as follows ... 

Fig. 109. Reciprocal gel-melting temperature vs logvi (V2 - polymer volume fraction) for low density polyethy-lenes of various long brandies content (O), (A) and 7.18, 4.07, and 0 branch points of long branches per polymer molecule, respectively. Reproduced from Polym J [Rdt 19] by the courtesy of die authors and The Sodtty of Polymer Sdence, Japan...

A branched macromolecule forms a more compact coil than a linear polymer with the same molecular weight, and the flow properties of the two types can differ significantly in the melt as well as in solution. Controlled introduction of relatively long branches into diene rubbers increases the resistance of such materials to flow under low loads without impairing processability at commercial rates in calenders or extruders. The high-speed extrusion of linear polyethylene is similarly improved by the presence of a few long branches per average molecule. 

Figure 2b. Average number of branch points per polymer molecul t> number average particle diameter, Dp (X), versus number of residf °K.(Q), and single CSTR. Conditions 0 = 3600 s, [I] = 0.01 mol/L, [SI — n e dmes for a...

Figure 12-3 Plots of the degree of polymerization versus the cumulative number of synthetic steps for various repetitive syntheses (a) conventional linear solid-phase synthesis (b) nonlinear straight-chain sequence synthesis (c) dendrimer synthesis (branching multiplicity of three) (d) double exponential den-drimer synthesis (branching multiplicity of three). In all cases, the degree of polymerization is defined as the total number of monomer units per polymer molecule.

Measurement of the number of end-grouj in AIBN initiated PS utilizing CNMR [138] and a radiochemical technique [126] are in agreement that there are more than two end-groups per polymer molecule (indicates branching). The mechanism of the branching reaction is uncertain, especially in light of the relatively poor ability of CIP radicals to abstract H-atoms from the polymer backbone [138]. 

Prediction and control of molecular weight averages, the number of short-and long-chain branches, and termimal double bonds per polymer molecule is of... 

As a rule, LLDPE resins do not contain long-chain branches. However, some copolymers produced with metallocene catalysts in solution processes can contain about 0.002 long-chain branches per 100 ethylene units (1). These branches are formed in auto-copolymerisation reactions of ethylene with polymer molecules containing vinyl double bonds on their ends (2). 

Investigation has shown that chain transfer to polymer occurs predominantly on the acetate methyl group in preference to the chain backbone one estimate of the magnitude of the predominance is 40-fold (92,93). The number of branches per molecule of poly(vinyl acetate) polymerised at 60°C is ca 3, at 80% conversion. It rises rapidly thereafter and is ca 15 at 95% conversion and 1-2 x lO" number-average degrees of polymerisation. 

As follows from the comparison of the rates of oxidation and destruction of linear and branched polyalkenes, the branched form possesses more susceptible tertiary C—H bonds and oxidizes more rapidly (but degrade more slowly) than the linear form. This was observed for PS, PE, PP, polyfrt-isopropyl styrene), polymethylene, and polymers produced by the decomposition of diazomethane-diazoethane and diazomethane-diazobutane mixtures [125], The number of cleavages per oxygen molecule consumed at 403 K amounts to 0.25 for PE and to 0.04 for PP. 

The quantitative nature of the silylamine-phenol reaction has been demonstrated for several different polymer systems (7). In our case, the charged PDMSX content was low to ensure that <1 phenolic group per novolac molecule reacted. This was done primarily to prevent extensive branching or crosslinking, and problems of insolubility and reproducibility associated with network formation... 

In some processes, a diluent, like benzene or chlorobenzene are used as the solvent. At high pressure and temperature, both the polyethylene and the monomers dissolve in these solvents so that the reaction occur in a solution phase. In a typical process, 10-30 per cent of the monomer is converted to polymer per cycle. Rest of monomer is recycled. Extensive chain transfer reactions take place during polymerisation to yield a branched polyethylene. Apart from long branches it is also having a large number of short branches of unto 5 carbon atoms formed by intramolecular chain transfer reactions. A typical molecule of Low density polyethylene is having a short branch for about every 50 carbon atoms and one or two long branches per molecule. 

The discussions until this point have been concerned with the polymerization of bifunctional monomers to form linear polymers. When one or more monomers with more than two functional groups per molecule are present the resulting polymer will be branched instead of linear. With certain monomers crosslinking will also take place with the formation of network structures in which a branch or branches from one polymer molecule become attached to other molecules. The structures of linear, branched, and crosslinked polymers are compared in Fig. 1-2. 

HDPE is alinear polymer with the chemical composition ofpolymethylene, (CII2V Depending on application, HDPE molecules either have no branches at all. as in certain injection molding and blow molding grades, or contain a small number of branches which are introduced by copolymerizing ethylene with o-olefins, e g., ethyl branches in the case of 1-butene and -butyl branches in the case of 1-hexene. The number of branches in HDPE resins is low, at most 5 to 10 branches per 1000 carbon atoms in the chain. 

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