Equilibrium polymerization, kinetic

The actual SFE extraction rate is determined by the slowest of these three steps. Identification of the ratedetermining step is an important aspect in method development for SFE. The extraction kinetics in SFE may be understood by changing the extraction flow-rate. Such experiments provide valuable information about the nature of the limiting step in extraction, namely thermodynamics (i.e. the distribution of the analytes between the SCF and the sample matrix at equilibrium), or kinetics (i.e. the time required to approach that equilibrium). A general strategy for optimising experimental parameters in SFE of polymeric materials is shown in Figure 3.10. 

The equilibrium constant for ATRP, XATRp= k/kd, provides critical information about the position of dynamic equilibrium between dormant and active species during polymerization (Scheme 4). The relative magnitude of KATRp can be easily accessed from the polymerization kinetics using ln([M]0/[M]t) vs.t plots, which provide values... 

The polymerization kinetics have been intensively discussed for the living radical polymerization of St with the nitroxides,but some confusion on the interpretation and understanding of the reaction mechanism and the rate analysis were present [223,225-229]. Recently, Fukuda et al. [230-232] provided a clear answer to the questions of kinetic analysis during the polymerization of St with the poly(St)-TEMPO adduct (Mn=2.5X 103,MW/Mn=1.13) at 125 °C. They determined the TEMPO concentration during the polymerization and estimated the equilibrium constant of the dissociation of the dormant chain end to the radicals. The adduct P-N is in equilibrium to the propagating radical P and the nitroxyl radical N (Eqs. 60 and 61), and their concentrations are represented by Eqs. (62) and (63) in the derivative form. With the steady-state equations with regard to P and N , Eqs. (64) and (65) are introduced, respectively ... 

The kinetic expression generally applicable to reversible equilibrium polymerizations is ... 

Figure 12. Model graphs for a kinetic analysis of an equilibrium polymerization (definition of variables of Equation 11)...

Although reversible or equilibrium polymerizations would almost always be carried out in an irreversible manner, it is interesting to consider the kinetics of polymerization for the case in which the reaction was allowed to proceed in a reversible manner. (The kinetics of reversible ring-opening polymerizations are discussed in Sec. 7-2b-5). 

The first interval is the interval of particle nucleation (interval I) and describes the process to reach an equilibrium radical concentration within every droplet formed during emulsification. The initiation process becomes more transparent when the rate of polymerization is transferred into the number of active radicals per particle n, which slowly increases to n 0.5. Therefore the start of the polymerization in each miniemulsion droplet is not simultaneous, so that the evolution of conversion in each droplet is different. Every miniemulsion droplet can be perceived as a separate nanoreactor, which does not interact with others. After having reached this averaged radical number, the polymerization kinetics is slowing down again and follows nicely an exponential kinetics as known for interval III in emulsion polymerization or for suspension polymer-... 

On a macroscopic level the polymerization kinetics will follow the usual relationship where equilibrium, as described above, exists (Equation 1). 

As demonstrated by the association rate constants listed in Table 10, association is relatively fast and has low activation energies. Table 10 also tabulates the equilibrium constants for reaction of a variety of nucleophiles with carbenium ions. Most of the equilibrium constants involving trityl carbenium ions were obtained from UV studies, whereas those of me-thoxymethylium carbenium ions with both dimethyl ether and methylal were calculated using dynamic NMR [64]. Values for isobutoxy alkyl derivatives have been estimated from polymerization kinetics. The data presented in Table 10 demonstrate that the equilibrium constants are lower for weaker nucleophiles and more stable carbenium ions. For example, carbenium ions react faster with diethyl ether than with the less nucleo-... 

The value of fcprop of the associated species is at least two orders of magnitude lower than fcprop of the nonassodated ion parrs . Consistently, nonassodated ion pairs can be considered as dormant and can be omitted in kinetic equations. Table 4 compares the values of various equilibrium and kinetic parameters for the polymerization of MMA, tBuMA and tBuA. Association is less important for tBMA than for MMA, more likely as a result of the buUdness of the ester groups. In the same line, aggregation is less extensive in the polymerization of tBuMA than tBuA, because of the steric hindrance of the a-methyl subsituent . Values of kf and ko in Table 4 were calculated according to equations 15 and 27, where a denotes the fraction of nonassociated ion pairs. 

TABLE 4. Equilibrium and kinetic parameters for the anionic polymerization of MMA, tBuMA and tBuA in THE, at —65°C, with a Li+ counter-ion... 

Some readers will be interested in the fact that Huang and Wang [75] in 1972 presented a newer theoretical treatment of the reaction kinetics of reversible polymerization in which this classic derivation of Dainton and Ivin is a special case. The thermodynamics of equilibrium polymerizations have recently been reviewed by Sawada [76]. 

The kinetics of THF polymerization are expressed in terms of the rate of reaction for an equilibrium polymerization without termination viz. 

The composition of the copolymer formed at the beginning of polymerization is generally different from the composition of the equilibrium polymerization product [167, 173, 174]. Whereas kinetic factors are decisive for the former, the heat and entropy of polymerization determine the composition of the equilibrium copolymer. 

Wallace and Morrow used halogenated alcohols, such as 2,2,2-trichloroethyl, to activate the acyl donor and thereby improve the polymerization kinetics [53, 56], They also removed by-products periodically during reactions to further shift the equilibrium toward chain growth instead of chain degradation. They copolymerized bis(2,2,2-trichloroethyl) tmns-3,4-epoxyadipate and 1,4-butanediol using porcine pancreatic lipase as the catalyst. After 5 days, an enantioenriched polyester with Mw = 7900 g mol-1 and an optical purity in excess of 95% was formed (Scheme 4.6). 

Moreover, if polyoxymethylene is recrystallized from nitrobenzene and the usual chain-folded lamellae of ca. 100 A thickness is treated with TXN in the presence of BF3, more perfect extended-chain-type crystals are formed. These facts confirm the conclusion formulated -by Wunderlich, that post-crystallization leads to chain-folded crystals because of kinetic restrictions, while crystallization in the polymerizing system gives thermodynamically more stable extended-chain crystals77). The formation of the thermodynamic product in polymerization is due to the growth of crystals at equilibrium polymerization conditions. Thermodynamically less stable crystals may redissolve as a result of depropagation, and crystals may thus grow further under equilibrium conditions. This (at least partly) eliminates kinetic restric-... 

The thermodynamics of TXN polymerization also influences the polymerization kinetics. Kern 92) has proposed that induction periods, frequently observed in the cationic polymerization of TXN, are due to the build up of the equilibrium formaldehyde concentration, which has to occur before polymer can be formed. According to other authors, it is not formaldehyde but TTXN that must be formed prior to polymerization 93). We conclude that formation of polymer may require that the equilibrium concentration of any monomeric species which is in equilibrium with polymer is reached first. 

This study revealed that under microwave conditions polymerization phenomena such as polymerization selectivity, polymerization temperature shift, and polymerization temperature shift as a result of the microwave power setting, can be observed when products are compared with those obtained under conventional conditions. To explain these phenomena it was proposed that a new dipole partition function is present in the microwave field, so values of thermodynamic properties such as internal energy and Gibbs free energy of materials with permanent dipole moments change under microwave conditions, which in turn leads to shifts in the reaction equilibrium and kinetics compared with conventional conditions at the same temperature [46]. 

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