Kinetics with specific initiators

2 Kinetics with specific initiators (a) Triethyloxonium tetrafluoroborate 

Vofsi and Tobolsky [86] reported the first careful kinetic study of THF polymerization. They used Et3 0 BF4 as initiator and carried out the polymerizations at 0°C in dichloroethane. By using C labelled catalyst, they were able to show that initiation was fast but not immediate. The rate of initiator disappearance was measured. The initial propagation rate was directly proportional to initial monomer concen- 

Rozenberg et al. [87] generated their catalyst in situ from ECH and BFj. EtjO. They carried out their polymerizations in bulk and in EtjO solution. The experimental data are reported to fit eqn. (6). They define [I] 0 in terms of the catalyst components charged, assuming instantaneous and quantitative conversion to catalyst, but do not make any direct measurements of active centres. Their kinetic parameters are given in Table 6. 

Before leaving Et3 0 BF4 initiated polymerizations of THE one other study needs to be mentioned. In polymerizations of thietanes above we saw that free sulphonium ions did not propagate very much more rapidly than ion pairs (Section 3.2.1). Sangster and Worsfold [88] have found that in THE polymerizations with BE4 counter-ions in CH2CI2 the free ion rate is only a factor of 7 greater than that of the ion pair rate. 

Lyudvig et al. [89] studied the kinetics of bulk THE polymerizations initiated by EtsO SbClg at 20°C. In another study using this initiator, Stejny [90] examined the effect of simultaneous polymerization and crystallization of THE. He found that at his reaction temperatures, —25° and —45°C, at the onset of crystallization the polymerization rate was somewhat Accelerated. 

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Measurements of overall reaction rates (of product formation or of reactant consumption) do not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield—time data does not always lead to a unique reaction model but, in favourable systems, the rate parameters, considered with reference to quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (a)—time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. 

The desired product is P, while S is an unwanted by-product. The reaction is carried out in a solution for which the physical properties are independent of temperature and composition. Both reactions are of first-order kinetics with the parameters given in Table 5.3-2 the specific heat of the reaction mixture, c, is 4 kJ kg K , and the density, p, is 1000 kg m . The initial concentration of /I is cao = 1 mol litre and the initial temperature is To = 295 K. The coolant temperature is 345 K for the first period of 1 h, and then it is decreased to 295 K for the subsequent period of 0.5 h. Figs. 5.3-13 and 5.3-14 show temperature and conversion curves for the 63 and 6,300 litres batch reactors, which are typical sizes of pilot and full-scale plants. The overall heat-transfer coefficient was assumed to be 500 W m K. The two reactors behaved very different. The yield of P in a large-scale reactor is significantly lower than that in a pilot scale 1.2 mol % and 38.5 mol %, respectively. Because conversions were commensurate in both reactors, the selectivity of the process in the large reactor was also much lower. 

In recent years the Coal Research Laboratory has been investigating the kinetics and isotherm behavior of methanol sorption on coal (6, 7, 10) along with the sorption of other vapors on coal (6) and of polar vapors on swelling gels (9, 10). Methanol sorption was shown to be reversible on coal, and its sorption behavior supports the model of coal as a gel or mixture of gels in its physical structure. All indications (I, 6, 7) are that its interaction is with specific and a fixed number of sites for a particular coal sample. Although the sorption of methanol is reversible, coal exhibits sorption behavior which is interpreted in terms of an irreversible swelling of the coal gel upon initial exposure to methanol vapor. As a result of these studies, an isotherm and experimental rate equation for the sorption and desorption were derived that fit the observed data. The isotherm derived for methanol sorption on coal was ... 

In this section of the research, the aim is to investigate the optimal composition of the Ni(II)-containing solution as a function of the Ni(II) reduction rate, the total amount of Ni reduced, the fraction of NiS formed and PAN-hbre properties, such as specific electrical resistance. In Fig. 11.2, data are shown for the variation of Ni(II) and rongalite concentration as a function of time and temperature starting from a constant initial Ni(II) concentration, while the initial rongalite concentration was increased. It must be pointed out that in this section of the research, no fibre was immersed in the solution, so the pure kinetic parameters of the reduction reaction of Ni(II) by rongalite is studied. Similar experiments were performed with different initial Ni(II) concentrations. 

Active centres of ionic polymerizations do not usually decay by mutual collisions as the radical centres. The stationary state, when it exists at all, results from quite different causes, mostly specific to the given system. Therefore the kinetics of ionic polymerizations is more complicated and its analysis more difficult. The concentration of centres cannot usually be calculated. On the other hand, ionic systems with rapid initiation give rise to the kinetically very simple living polymerizations (see Chap. 5, Sect. 8.1). 

There is no evidence in any of the gas phase systems for initial multiple bond rupture (i.e., fragmentation reactions). Because of the low reaction temperatures, the alkoxy radical intermediates of the bond fission reactions (or radicals resulting from alkoxy radicals) are mainly involved in radical-radical termination processes ( 0) rather than participating in hydrogen abstraction from the parent peroxide E oi 6-8). Thus it has been commonly believed that the peroxide decompositions were classic examples of free radical non-chain processes. Identification of the rate coefficients and the overall decomposition Arrhenius parameters with the initial peroxide bond fission kinetics were therefore made. However, recent studies indicate that free radical sensitized decompositions of some peroxides do occur, and that the low Arrhenius parameters obtained in many of the early studies (rates measured by simple manometric techniques) were undoubtedly a result of competitive chain processes. The possible importance of free radical reactions in peroxide decompositions is illustrated below with specific regard to the dimethyl peroxide decomposition. 

The specific role of pyrite (FeS2) as a catalyst has been under investigation since pyrite was identified as the most active inherent mineral for coal liquefaction. Under liquefaction conditions, FeS2 is transformed into a nonstoichiometric iron sulfide, Fei-x (0 X 0.125). Thomas et al. (15) studied the kinetics of this decomposition under coal liquefaction conditions, and concluded that the catalytic activity of FeS2 is associated with radical initiation resulting from the... 

The steady-state assumption that is helpful in simplifying the analysis of free-radical kinetics is not valid in many, if not most, cationic polymerizations, which proceed so rapidly that steady-state is not achieved. Some of these reactions (e.g., isobutylene polymerization by AICI3 at -100°C) are essentially complete in a matter of seconds or minutes. Even in slower polymerizations, the steady-state may not be achieved if > Rt- The expressions given above can only be employed if there is assurance that steady-state conditions exist, at least during some portion of the overall reaction. Steady state is implied if Rp is constant with conversion, except for changes due to decreased monomer and initiator concentrations. A more rapid decline in Rp with time than what is expected or an increase in Rp with time would signify a nonsteady state. Thus many of the experimental expressions reported in the literature to describe the kinetics of specific cationic polymerizations are not valid since they are based on data where steady-state conditions do not apply. 

The approach is, of course, not restricted to the rate expressions of chemical kinetics, and can be applied to a great variety of differential equations. We have used chemical kinetics here because these are important in chemical analysis, and provide a specific topic to illustrate the method. If one can write down the differential equation of a problem, one can also solve it numerically on the spreadsheet. It can be done the quick (but somewhat crude) explicit way illustrated in section 9.2, or more precisely (but with more initial effort) through the implicit method of sections 9.3 and 9.4. 

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