Polymerization kinetics, pseudo first order

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

Example 4.3 Suppose a pure monomer polymerizes in a CSTR with pseudo-first-order kinetics. The monomer and pol5Tner have different... 

The relative kinetic importance of the reactions we have outlined would be expected to change throughout the course of a polymerization. This is illustrated by the following considerations. The reactivity of the 5-CO of an oxazolidine-2,5-dione system depends markedly on whether the 3-posi-tion is unsubstituted or acylated (as in (VI), (VII), (VIII), etc.) electron-withdrawal by the acyl substituent activates the 5-CO to nucleophilic attack. Thus the rate coefficient of (18a) is less than that of (20a) and the rate coefficient of (19a) is less than that of (19b). In all but the very earliest and latest stages of polymerization reaction (20a) appears to predominate and gives rise to pseudo first-order kinetics in [NCA] until... 

A ten- to twenty-fold concentration excess of pol3nneric imidazole residues over that of substrate molecules was usually employed. This allowed a pseudo first-order presentation of the kinetic data.. In many cases, curvature in the plots of In versus time was found. Observation of complex kinetics in hydrolysis of functional groups on polymer chains is not uncommon. (30,31) Letsinger and Klaus(32) have observed some phenomena in the study of synthetic polymeric catalysts and substrates. In treating the data, they used the empirical relation... 

Repeat Example 2.8 assuming that the polymerization is second order in monomer concentration. This assumption is appropriate for a binary polycondensation with good initial stoichiometry while the pseudo-first-order assumption of Example 2.8 is typical of an addition polymerization. As in Example 2.8, find the rate constant for the reaction assuming that the monomer content is reduced to 20% of its initial value after 2 h, now by second-order kinetics. Also determine the monomer content predicted after 4 h. 

The situation is less clear-cut for RAFT systems. For a dithiocarbonate-mediated styrene polymerization studied by Goto and co-workers, the steady-state kinetic analysis applied both in the presence and absence of a BPO initiator (Figure 3.10). Similarly, for the solution polymerization of methyl methacrylate, mediated by dithioesters containing a-cyanobenzyl groups in the presence of AIBN initiator, pseudo-first-order plots were obtained although a significant induction period was detected. 

Figure 17, Pseudo first order kinetic plot for 2-vinylnaphthalene polymerized under SFRP and thermal conditions (black=SFRP, gray=thermal).

Examination of the observed rate constants determined by pseudo first order kinetics illustrates a large variance in the thermal polymerization of... 

Fe Oj, FejO, nanocomposites, oxidation polymerization, Langmuir adsorption isotherm, Freundlich adsorption isotherm, Dubinin-Radushkevich adsorption isotherm, Tempkin adsorption isotherm, pseudo-first-order kinetic. Pseudo-second-order kinetic, removal efficiency, adsorption capacity... 

Like many other exothermic reactions in stirred tanks, three steady stages are possible for polymerizations beginning with monomer a lower one where there is essentially zero conversion an intermediate, metastable condition and an upper, runaway condition where conversion to polymer is nearly complete. It is usually desired to operate at the intermediate, metastable condition. To illustrate this, assume that the polymerization kinetics are pseudo-first order and write material and energy balances based on perfect mixing in the reactor. A material balance on monomer gives... 

Polymerization of diallg l vinylphosphonate monomers was nevertheless efficiently carried out in the presence of lanthanide derivatives and especially cyclopentadienyl lanthanide complexes, used both as initiators and catalysts. Very recently, Shen et al performed the synthesis of poly (diethyl vinylphosphonate) using a lanthanide tris(borohydride) below 50 °C. The authors showed that the polymerization eould be controlled and proceeds under pseudo-first-order kinetics, giving rise to high molecular weight polymers, i.e. ranging from 20 to 40 kDa with molecular weight dispersity below 1.7. 

Pseudo-first-order kinetic curves for RAFT polymerization of MA mediated by Si-MPPA in the presence of MPPA. Polymerization conditions [MA]o [SI-MPPA]o [MPPA]o [AIBN]o = 40o i i o.i, [MA]o = 3.o mol/L, in toluene at 60 °C. 

In weakly polar solvents such as dioxane (a = 2.21), the kinetics of styrene propagation exhibit pseudo-first-order kinetics as illustrated in equation 34, where obs is the observed pseudo-first-order rate constant, kp is the propagation rate constant, and [PS Mt+] represents the concentration of carbanionic chain ends that does not change for a living polymerization. 

As a first approach, we studied the epoxidation of the exocychc double bond of 1 by weto-chloroperbenzoic acid (mCPBA) in dichloromethane. IR spectra provided evidence for a fluorescent epoxide [94]. Eater on, surface-catalyzed epoxidation was ascribed to the formation of further fluorescent BODIPY derivatives [54]. The bimolecular rate constant had been determined beforehand, and pointed to the concentration range of mCPBA for maintaining useful pseudo-first-order kinetics. Immobilization turned out to be a major issue because, while the oxidizing species should have free access to the double bond, the translational mobility of the substrate must be widely suppressed. Introduction of a further terminal double bond permitted subsequent immobilization on polymeric sihcone [102-104]. 

The relationship between degree of polymerization, DP, and reaction time varies according to the mechanism of reaction. For chain reaction kinetics, DP is approximately constant as the reaction time increases. Conversely, in stepwise kinetics DP increases steadily throughout the reaction. First order or pseudo-first order reactions give a linear relationship for plots of In(DP) vs. reaction time second order re-... 

The rate of an ideal living polymerization process free from termination and transfer reactions should follow pseudo-first-order kinetics. In such a process, the number of active centers, [P ], remains constant provided the polymerization proceeds with a single active species, or faster interconverting species and the rate of initiation should be faster or at least equal to the rate of propagation, that is, fe, 2 kp. 

Butadiene is polymerized by rhodium compounds in aqueous or alcoholic solution [178]. It is generally accepted that the active species is a TT-allyl rhodium complex of low valency [28, 179] which is not rapidly terminated by reaction with water or alcohol. No clear kinetic pattern was observed in the earlier papers but a recent investigation [180] has shown the rate and molecular weight data to be accommodated by a scheme involving monomer transfer and physical immobilization of the active centres in precipitated polymer. In the initial stages the polymerization is first order in rhodium and, at constant monomer concentration, is (pseudo) zero order E = 14.8 kcal mole" ). This is followed by a declining rate which is almost independent of temperature. Molecular weights rise slowly to a maximum value with time (ca. 4000 after 22 h at 70°C). 

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