Termination kinetics molecular weight averages

A mathematical model for styrene polymerization, based on free-radical kinetics, accounts for changes in termination coefficient with increasing conversion by an empirical function of viscosity at the polymerization temperature. Solution of the differential equations results in an expression that calculates the weight fraction of polymer of selected chain lengths. Conversions, and number, weight, and Z molecular-weight averages are also predicted as a function of time. The model was tested on peroxide-initiated suspension polymerizations and also on batch and continuous thermally initiated bulk polymerizations. 

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

GPC-derived weight average molecular weights are often less prone to error than number average molecular weights. When termination is wholly hy disproportionation or chain transfer and chains are long (>10 units), classical kinetics predicts Xn = XJ2 (Section 5.2.1.3). It follows that Cit can be obtained from the slope of a plot of 21 Xw vs [T]0/[M]t>."4 "5 The errors introduced even when the dominant process for radical-radical termination is combination (e.g. S polymerization) are small as long as X n is small in relation to... 

If the degree of polymerization is controlled principally by chain termination so that Xn is proportional to the kinetic chain length, the temperature coefficient of the average molecular weight will depend... 

These initial investigations also included kinetic studies on catalyst initiation, polymer chain propagation and termination rates and the time dependence of the number-average molecular weight, using isotopic labelling with ( " CH3)2A1C1 [10]. 

The molecular weight distribution and the average molecular weight in a free-radical polymerization can be calculated from kinetics. The kinetic chain length v is defined as the average number of monomers consumed per number of chains initiated during the polymerization. It is the ratio of the propagation rate to the initiation rate (or the termination rate with a steady-state approximation) ... 

The "ideal" concept of emulsion polymerization was built on the assumption that the monomer was water insoluble and that in the absence of chain transfer, the number average degree of polymerization, Xj can be related to the rate processes of initiation and propagation by the steady-state relationship Xjj = 2 Rp/Rj. Since Ri and Rp are both constant and termination is assumed to be Instantaneous during the constant rate period described by Smith-Ewart kinetics, the above equation predicts the generation of constant molecular weight polymer. Data has been obtained which agrees with Smith-Ewart but there is... 

The term zero-one designates that all latex particles contain either zero or one active free radical. The entry of a radical in a particle that already contains a free radical will instantaneously cause termination. Thus, the maximum value of the average number of radicals per particle, n, is 0.5. In a zero-one system, compartmentalization plays a crucial role in the kinetic events of emulsion polymerization processes. In fact, a radical in one particle will have no access to a radical in another particle without the intervention of a phase transfer event. Two radicals in proximity will terminate rapidly however, the rate of termination will be reduced in the process because of compartmentalization, as the radicals are isolated as separate particles. Consequently, the propagation rate is higher and the molecular weight of the polymer formed is larger than in the corresponding bulk systems. Which model is more appropriate depends primarily on the particle size. Small particles tend to satisfy the zero-one model, as termination is likely to be instantaneous. ... 

It is of course realized that several different Ions and Ion pairs may be present under these conditions (8,10). Indeed, In precise work, one needs to address the kinetic parameters in terms of their exact Ionic nature (e.g., k , k-, etc.) and not simply in terms of a "global rate constant. In any event, it is possible to prepare low molecular weight (2,000-4,000) polymers that are predominately hydroxyl terminated with one primary and one secondary group. This general approach has been widely utilized for some years as a route for the Important intermediates used In polyurethane foams. Since it Is often desired that these foams be chemically crossllnked, one must consider methods that can produce average functionalities higher than 2 in order to generate the desired network behavior. 

Ionic-polymerization Kinetics. The kinetics of ionic polymerization share some common principles with that of the free-radical reaction. Both are based on the basic steps of initiation, propagation, termination, and chain transfer, and in both the ultimate average molecular weight depends on the ratio of the reaction rates of propagation and termination. There are, however, important differences. In ionic polymerization the termination step appears to be unimolecular, while it is bimolecular in free-radical type polymerization. The dependence of the kinetic scheme of the reaction on the various parameters is therefore different in the two reactions. Likewise, the fact that a cocatalyst has to be brought into the ionic reaction scheme has to be taken into account. 

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