Polymerization - curves kinetics

The primary cation CH20H is created in the cage reaction under photolysis of an impurity or y-radiolysis. The rate constant of a one link growth, found from the kinetic post-polymerization curves, is constant in the interval 4.2-12 K where = 1.6 x 10 s . Above 20K the apparent activation energy goes up to 2.3 kcal/mol at 140K, where k 10 s L... 

The situation is quite different when actin is polymerized under sonication in the presence of ATP. In this case, the polymerization curve cannot be described by equation (4). At a high actin concentration, overshoot polymerization kinetics are observed, with a maximum and subsequent decrease to a lower stable plateau (Carlier et al., 1985). The final amount of polymer is the same as that obtained when sonication is applied to F-actin that had polymerized spontaneously without sonication. Conversely, when sonication is stopped, repolymerization accompanies the spontaneous length redistribution to a population of less numerous, but longer filaments. 

The polymerization is kinetically controlled up to the vitrification time, for every cure temperature. Moreover, as in this range of temperatures, gelation arrives before vitrification, the passage through the gel point does not have any influence on the reaction rate this is a general experimental observation for stepwise polymerizations. After vitrification, a significant decrease in the reaction rate occurs, leading to the observed departure of experimental curves from the master curve. 

Kinetic polymerization curves show that autoacceleration takes place essentially from the beginning of the process. 

Figure 2.34. Kinetic polymerization curves of tetramethylene-dimetacrylate in a matrix of cis-polyisoprene at various values of Xex (I-IV) and ti 8 (1), 24 (2), 48 (3) and 240 (5) hour. Blackened markings show samples after secondary swelling. Explanation is provided in the text, see table 2.5.

The shape of the kinetic curves depends on the catalyst type and polymerization conditions (ethylene pressure, temperature, concentration of inhibitors in reaction medium) (89, 97, 98). The types of the kinetic curves obtained. at ethylene polymerization under various conditions are presented in Fig. 1. 

Fig. 1. Examples of the kinetic curves during ethylene polymerization by chromium oxide catalysts. Support—SiOs temperature—80°C polymerization at constant ethylene pressure in perfect mixing reactor. Curve 1—catalyst reduced by CO at 300°C. Curve 2— catalyst activated in vacuum (400°C) polymerization in the case of (1) and (2) in solvent (heptane) ethylene pressure 10 kg/cm2 02 content in ethylene 1 ppm, HsO 3 ppm. Curves 3, 4, 5, 6—catalyst activated in vacuum (400°C) polymerization without solvent ethylene pressure 19 (curve 3), 13 (curve 4), 4 (curve 5), and 2 (curve 6) kg/cm2 02 content in ethylene 1 ppm, HsO = 12 ppm.

However, when using supports with weak linkage between the primary particles of the catalyst, its splitting occurs quickly and it is unlikely to influence the shape of the kinetic curve. For example, in the case of chromium oxide catalyst reduced by CO supported on aerosil-type silica, steady-state polymerization with a very short period of increasing rate is possible (see curve 1, Fig. 1). 

The change of shape of the kinetic curves with monomer and inhibitor concentration at ethylene polymerization by chromium oxide catalysts may be satisfactory described 115) by the kinetic model based on reactions (8)-(14). 

It should be mentioned that the predicted curve at highest benzene level in Figure 13 agrees with classical kinetics (no diffusion-control). It is not clear therefore why measured data at even higher benzene concentrations do not agree with classical kinetics. There may be some subtle chemical interactions at these high solvent levels. Duerksen(lT) fomd similar effects with styrene polymerization in benzene and had to correct kp for solvent. 

This section is divided into three parts. The first is a comparison between the experimental data reported by Wisseroth (].)for semibatch polymerization and the calculations of the kinetic model GASPP. The comparisons are largely graphical, with data shown as point symbols and model calculations as solid curves. The second part is a comparison between some semibatch reactor results and the calculations of the continuous model C0NGAS. Finally, the third part discusses the effects of certain important process variables on catalyst yields and production rates, based on the models. 

Figure 5. Molecular weight-conversion contour map for various concentrations of a free-radical initiator operating in a tubular-addition polymerization reactor of fixed size. Curves were constructed using varying jacket temperatures (kinetic parameters for the initiator Ea = 32.921 Kcal/mol In k/ = 26.494 In sec f = 0.5 (------------------------) optimum operating line)...

When this resin was exposed as a thin film to the UV radiation of a medium pressure mercury lamp (80 W aiH), the crosslinking polymerization was found to develop extensively within a fraction of a second (18). The kinetics of this ultra-fast reaction can be followed quantitatively by monitoring the decrease of the IR absorption at 810 an-1 of the acrylic double bond (CHCH twisting). Figure 8 shows a typical kinetic curve obtained for a 20 pm thick film coated onto a NaCl disk and exposed in the presence of air to the UV radiation at a fluence rate of 1.5 x 10 6 einstein s-1 cm 2. 

It is unfortunate that many workers have not appreciated how essential a clue to the kinetics can be provided by the kinetic order of the whole reaction curve. The use of initial rates was carried over from the practice of radical polymerisation, and it can be very misleading. This was in fact shown by Gwyn Williams in the first kinetic study of a cationic polymerization, in which he found the reaction orders deduced from initial rates and from analysis of the whole reaction curves to be signfficantly different [111]. Since then several other instances have been recorded. The reason for such discrepancies may be that the initiation is neither much faster, nor much slower than the propagation, but of such a rate that it is virtually complete by the time that a small, but appreciable fraction of the monomer, say 5 to 20%, has been consumed. Under such conditions the overall order of the reaction will fall from the initial value determined by the consumption of monomer by simultaneous initiation and propagation, and of catalyst by initiation, to a lower value characteristic of the reaction when the initiation reaction has ceased. 

Poly(acrylic acid) is not soluble in its monomer and in the course of the bulk polymerization of acrylic acid the polymer separates as a fine powder. The conversion curves exhibit an initial auto-acceleration followed by a long pseudo-stationary process ( 3). This behaviour is very similar to that observed earlier in the bulk polymerization of acrylonitrile. The non-ideal kinetic relationships determined experimentally in the polymerization of these two monomers are summarized in Table I. It clearly appears that the kinetic features observed in both systems are strikingly similar. In addition, the poly(acrylic acid) formed in bulk over a fairly broad range of temperatures (20 to 76°C) exhibits a high degree of syndiotacticity and can be crystallized readily (3). 

The authors [1] studied kinetics of poly (amic acid) (PAA) solid phase imidization in the presence of nanofiller (Na+-montmorillonite) and in its absence. It was found out, that the kinetic curves conversion (imidization) degree Q versus reaction duration t were have typical for polymerization reactions shape with autodeceleration showing imidization rate reduction as time is passing. As it is known [2], such curves Q(t) are specific for reaction passing in heterogeneous medium and are described by the simple relationship ... 

The polymerization temperature, through its effects on the kinetics of polymerization, is a particularly effective means of control, allowing the preparation of macroporous polymers with different pore size distributions from a single composition of the polymerization mixture. The effect of the temperature can be readily explained in terms of the nucleation rates, and the shift in pore size distribution induced by changes in the polymerization temperature can be accounted for by the difference in the number of nuclei that result from these changes [61,62]. For example, while the sharp maximum of the pore size distribution profile for monoliths prepared at a temperature of 70 °C is close to 1000 nm, a very broad pore size distribution curve spanning from 10 to 1000 nm with no distinct maximum is typical for monolith prepared from the same mixture at 130°C [63]. 

Kinetic curves relative to polymerization reactions in the solid state commonly show a sigmoidal shape with a slow initiation step followed by a steep increase, even by two orders of magnitude, of the reaction rate. A reaction with this kind of kinetic curve is said to have an autocatalytic behavior. 

At Van Sickle s conditions of low temperatures and low conversions, branching routes A and B appear to be dominant since there is little alkenyl hydroperoxide decomposition. In our work above 100°C., the branching routes are supported by the nearly linear initial portions at low conversions for alkenyl hydroperoxide and polymeric dialkyl peroxide curves (see Figures 2, 3, and 4). The polymeric dialkyl peroxides formed under our reaction conditions include those formed by the branching mechanism postulated by Van Sickle (routes A and B) and those formed by the reaction of the alkenoxy and hydroxy radicals from alkenyl hydroperoxide thermal decomposition reacting further and alternately with olefin and oxygen (step C). The importance and kinetic fit of the sequential route A to C appears to increase with temperature and extent of olefin conversion owing to the extensive thermal decomposition of the alkenyl hydroperoxides above 100°C. 

Solutions of Eqns. 32 through 35 on an analog computer are shown in Fig. 6 for the case of polymerization in a closed system. The plots of rp(t) and p(t) are seen to be in qualitative agreement with the experimental observations shown in Fig. 7. The model of polymerization kinetics was also found to provide curves of rp versus discharge current density and monomer flow rate which were consistent qualitatively with the experimentally observed results. 

Kinetics of multimethacrylate polymerization was examined only with limited interest. Conversion in this case was measured by IR spectroscopy. The kinetic curves for three concentrations of multimonomer are presented in Figure 8.15. 

At 273 and s 9.02 the polymerization followed first order kinetics. At 225 (Figure 4) the conversion curve was indistinguishable from a zero-order plot up to 40 percent conversion but if the whole curve was examined the internal order was seen to lie between zero and one. At 250 the internal order also lay between zero and one but the fit was nearer to the first-order plot in monomer. The kinetics are consistent with a Bateup-Yerusalimskii mechanism. At low temperatures the limiting condition of Equation 3 is approached. As the temperature rises the stationary state concentration of the complex decreases and the mechanism shifts to its other limit... 

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