Polymerization, activation statistics

DP E F f f. Ha He AG Degree of polymerization Activation energy, enhancement factor for gas-liquid mass transfer with reaction, electrochemical cell potential Faraday constant, F statistic Efficiency of initiation in polymerization Ca/CaQ or na/nao, fraction of A remaining unconverted Hatta number Henry constant for absorption of gas in liquid Free energy change kj/kgmol Btu/lb-mol... 

The theoretical model simulates the reaction scheme of the intermittent propagation of Fig. 7 on the basis of a statistical distribution of the polymerization activity onto all molecules (C ) present in the reactor. In other words, the possibility to become an active species is again distributed newly after each insertion step, because the concentration of the different alkyl chains is changed after each insertion step. Figure 14 shows the binomial distribution formula or, more precisely, the Bernoulli scheme for two incompatible events. In this formula, a is the probabiUty for the event, 1—a the non-probability for the event, and v the number of times that the event occurs. 

Decolorization of polymeric dyes Poly R-478 (polyanthraquinone-based) and Poly S-l 19 (azo dye) by immobibzed white rot fungus Crysosporium lignorum CL1 on circular plastic packing material in 2L air-lift fermenter was studied by Buckley and Dobson [47]. They also examined the relationship between polymeric dye decolorization and the production of LiP and MnP activity in its statistically growth... 

A single polymer particle contains a statistically large number of polymers, of the order of 1013. The corresponding MWD can be described with the Flory-Schulz equation only if the single-site type is guaranteed, and under constant reaction conditions, i.e., constant temperature, pressure, and concentrations near the active sites. However, in an industrial polymerization process, a particle often encounters different conditions over its lifetime. In... 

A single step of the polymerization is analogous to a diastereoselective synthesis. Thus, to achieve a certain level of chemical stereocontrol, chirality of the catalytically active species is necessary. In metallocene catalysis, chirality may be associated with the transition metal, the ligand, or the growing polymer chain (e.g., the terminal monomer unit). Therefore, two basic mechanisms of stereocontrol are possible (145,146) (i) catalytic site control (also referred to as enantiomorphic site control), which is associated with the chirality at the transition metal or the ligand and (ii) chain-end control, which is caused by the chirality of the last inserted monomer unit. These two mechanisms cause the formation of microstructures that may be described by different statistics in catalytic site control, errors are corrected by the (nature (chirality) of the catalytic site (Bernoullian statistics), but chain-end controlled propagation is not capable of correcting the subsequently inserted monomers after a monomer has been incorrectly inserted (Markovian statistics). 

The thermodynamic approach considers micropores as elements of the structure of the system possessing excess (free) energy, hence, micropore formation processes are described in general terms of nonequilibrium thermodynamics, if no kinetic limitations appear. The applicability of the thermodynamic approach to description of micropore formation is very large, because this one is, in most cases, the result of fast chemical reactions and related heat/mass transfer processes. The thermodynamic description does not contradict to the fractal one because of reasons which are analyzed below in Sec. II. C but the nonequilibrium thermodynamic models are, in most cases, more strict and complete than the fractal ones, and the application of the fractal approach furnishes no additional information. If no polymerization takes place (that is right for most of processes of preparation of active carbons at high temperatures by pyrolysis or oxidation of primary organic materials), traditional methods of nonequilibrium thermodynamics (especially nonequilibrium statistical thermodynamics) are applicable. 

When 1,3-dioxolane was added to the solution of living (nontermi-nated) poly(l,3-dioxepane) or vice versa, further polymerization ensued and the increase of molecular weight indicated that polymerization of added monomer proceeded exclusively on living active species of the former monomer. The isolated copolymer was analyzed by l3C NMR spectroscopy and it was found that, instead of a block copolymer, the copolymer with nearly statistical distribution of DXL and DXP units was formed practically from the beginning of the process. This is a clear indication that chain transfer to polymer leads to branched oxonium ions, which participate in further reactions with a rate comparable to the rate of propagation. 

Thus, in sequential polymerization of two different cyclic acetals, 1,3-dioxolane and 1,3-dioxepane, the sequential polymerization (i.e., polymerization of added second monomer initiated by active species of the first monomer polymerization) may be easily achieved as evidenced by increase of molecular weight [130]. The isolated polymer is not a block copolymer, however, having nearly statistical distribution of both types... 

Random hydrocarbon copolymers can also be produced by this new equilibrium polymerization method. Copolymers containing octenylene and butenylene linkages in a statistical array based on feed ratio result from the cocondensation of the two respective monomers or by the reaction of diene with unsaturated polymer. More controlled polymer stmctures have also been prepared by the slow addition of a diene solution to an unsaturated polymer containing active catalyst. Substituent effects were shown to dictate the polymerizability of monomers and in some cases selective polymerization of speciflc aUcenes in the monomer resulted in what appears as perfectly alternating copolymers. ... 

Methacrylates with pendant oxyethylene units (FM-19) were polymerized in a controlled way with metal catalysts in the bulk or in water. The catalytic systems include a bromide initiator coupled with Ni-2 for n = 2 (bulk, 80 °C)319 and CuCl for n = 7-8.246-320 The latter polymerization proceeded very fast in aqueous media at 20 °C to reach 95% conversion in 30 min and gave very narrow MWDs (MJMn =1.1 — 1.3). The fast reaction is attributed to the formation of a highly active, monomeric copper species com-plexed by the oxyethylene units. A statistical copolymerization of FM-19 (n = 7—8) and FM-20, a methacrylate with a oligo (propylene oxide) pendant group, led to hydrophilic/hydrophobic copolymers with narrow MWDs (MwIMn = 1.2).320... 

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