Polymerization kinetic rate

The simple approach discussed above is valid for steady-state Monte Carlo simulations, but dynamic simulations are also possible. In this case, the model probabilities must be updated frequently, generally after every iteration. A detailed discussion of these methods would be too lengthy to be included herein the most common algorithm for dynamic Monte Carlo simulation follows the approach proposed by Gillespie, which requires the discretization of the polymerization reactor with small control volumes and the conversion of the polymerization kinetic rates into molecular collision frequencies [97, 98],... 

Studies of the copolymerization of VDC with methyl acrylate (MA) over a composition range of 0—16 wt % showed that near the intermediate composition (8 wt %), the polymerization rates nearly followed normal solution polymerization kinetics (49). However, at the two extremes (0 and 16 wt % MA), copolymerization showed significant auto acceleration. The observations are important because they show the significant complexities in these copolymerizations. The auto acceleration for the homopolymerization, ie, 0 wt % MA, is probably the result of a surface polymerization phenomenon. On the other hand, the auto acceleration for the 16 wt % MA copolymerization could be the result of Trommsdorff and Norrish-Smith effects. 

Polymerization Kinetics of Mass and Suspension PVC. The polymerization kinetics of mass and suspension PVC are considered together because a droplet of monomer in suspension polymerization can be considered to be a mass polymerization in a very tiny reactor. During polymerization, the polymer precipitates from the monomer when the chain size reaches 10—20 monomer units. The precipitated polymer remains swollen with monomer, but has a reduced radical termination rate. This leads to a higher concentration of radicals in the polymer gel and an increased polymerization rate at higher polymerization conversion. 

An alternating copolymer of a-methyl styrene and oxygen as an active polymer was recently reported [20]. When a-methyl styrene and AIBN are pressurized with O2, poly-a-methylstyreneperoxide is obtained. Polymerization kinetic studies have shown that the oligoperoxides mentioned above were as reactive as benzoyl peroxide, which is a commercial peroxidic initiator. Table 1 compares the overall rate constants of some oligoperoxides with that of benzoyl peroxide. 

The kinetics of ethylene polymerization at temperatures below 90°C (the slurry process) were studied in Bukatov el al. (157, 159). The steady-state polymerization rate was observed the first order in the polymerize tion rate with respect to ethylene and the catalyst concentration was found. The polymerization rate increased on increasing the polymerization temperature from 20° to 80°C (Eeu = 7.5 0.5 kcal/mole). 

Knowledge of kui/kii is also important in designing polymer syntheses. For example, in the preparation of block copolymers using polymeric or multifunctional initiators (Section 7.6.1), ABA or AB blocks may be formed depending on whether termination involves combination or disproportionation respectively. The relative importance of combination and disproportionation is also important in the analysts of polymerization kinetics and, in particular, in the derivation of rate parameters. 

For less polar monomers, the most extensively studied homopolymerizations are vinyl esters (e.g. VAc), acrylate and methacrylate esters and S. Most of these studies have focused wholly on the polymerization kinetics and only a few have examined the mierostructures of the polymers formed. Most of the early rate data in this area should be treated with caution because of the difficulties associated in separating effects of solvent on p, k and initiation rate and efficiency. 

Continuous stirred-tank reactors can behave very differently from batch reactors with regard to the number of particles formed and polymerization rate. These differences are probably most extreme for styrene, a monomer which closely follows Smith-Ewart Case 2 kinetics. Rate and number of particles in a batch reactor follows the relationship expressed by Equation 13. 

In the study, the kinetic rate constants applicable to the polymerization of ethylene (, ) were used with an assumed activation volume. These values appear to be a reasonably consistent set of constants for the polymerization of ethylene and, as shown... 

The fixed variables used in the computer simulation are shown in Table 1 along with the kinetic rate constants for the polymerization reactions. 

The effect of media viscosity on polymerization rates and polymer properties is well known. Analysis of kinetic rate data generally is constrained to propagation rate constant invarient of media viscosity. The current research developes an experimental design that allows for the evaluation of viscosity dependence on uncoupled rate constants including initiation, propagation and macromolecular association. The system styrene, toluene n-butyllithium is utilized. 

The molar rate of change of polymeric species of degree of polymerization n in a well-mixed, continuous flow tank reactor is related to the kinetic rate of propagation of unassociated polystyryl anions plus their withdrawal rate in the reactor s effluent. Feed streams are void of polymeric substances, but contain monomer initiator and solvent. 

Uncoupled Rate Constants. An initial evaluation of polymerization kinetics is presented in Figure (2), constrained by viscosity invariant rate constants K. The slopes of these straight lines give initial estimates of Rgg/Kp according to Equation (14). Figure 3 presents graphically a power law relationship between K g/Kp and viscosity at 21°C and at 16.6 C. More scatter In Yu s data may be attributed to the use of an older GPC instrument of relatively low resolution. The ratio Kgq/Kp is temperature-sensitive a change of the order or five times is observed if the temperature is reduced by 4.4°C and viscosity is kept constant. 

In this paper, the pseudo-kinetic rate constant method in which the kinetic treatment of a multicomponent polymerization reduces to that of a hcmopolymerization is extensively applied for the statistical copolymerization of vinyl/divinyl monomers and applications to the pre- and post-gelation periods are illustrated. 

The pseudo-kinetic rate constant method for multicomponent polymerization has been applied in some copolymerization studies (3-5), and its derivation and specific approximations have been made clear (6,7). The pseudo-kinetic rate constants basically... 

Applying the pseudo-kinetic rate constants, the explicit formulation of the kinetics of a multicomponent polymerization reduces to that of a homopolymerization. 

Both kjn and kd, which are the kinetic rate constants of this model, are functions of temperature and Arrhenius dependence is assumed for each (Equations 8 and 9.) In this model, kj is the net polymerization rate constant. 

The study of polymerization kinetics allows us to understand how quickly a reaction progresses and the role of temperature on the rate of a reaction. It also provides tools for elucidating the mechanisms by which polymerization occurs. In addition, we are able to study the effect of catalysts on the rates of polymerization reactions, allowing us to develop new and better catalysts based on the measured performance. 

The several kinetic rates are a consequence of Reactions 2-5 The first two represent monomeric additions the third describes all rates by which two polymeric molecules smaller than j form a molecule of size j. The molecule A AC contains a carboxylic anion the second molecule P. supplies aS oxirane and, in general, is any polymeric molecule of iSze j-n. 

The formation of inter- and intrapolymer complexes has also been shown to affect the polymerization kinetics. For example, Ferguson and Shah (1968) investigated the influence of intrapolymer complexation on the kinetics of AA in the presence of copolymer matrices composed of either A-vinylpyrrolidone and acrylamide or A--vi nyl pyrrol idone and styrene. The polymerization rate reaches a maximum in the vicinity of AA to VP ratio equal to one for the VP/AAm matrix. This maximum in the polymerization rate is most pronounced in the presence of copolymer with the highest content of VP. When the hydrophilic acrylamide is replaced with the more hydrophobic styrene monomer in the copolymer matrix, the observed maximum in AA polymerization rate occurred at a lower than equimolar ratio of AA to VP. The hydrophilic groups of VP were interacting with the hydrophobic nucleus consisting of the styrene units in the VP/St copolymer, and were thus unable to participate in the formation of the complex unlike in the case of VP/AAm copolymer matrix. 

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 Effect of Crosslinker Concentration on the Rate of Polymerization. Ethylene glycol dimethacrylate is used most frequently as the crosslinker for HEMA formulations useful in contact lens manufacturing. To demonstrate the effect of crosslinker concentration on the curing rate, formulations derived from HEMA/Glycerine/BME at 85/15/0.17, while varying EGDMA (from 0.34 to 0.68), the peak times were about the same (3.73 and 3.61 minutes respectively). This is reasonable due to the similarity in molecular structure of the crosslinker and the monomer, and the low amount of crosslinker used. The possible presence of other crosslinker, such as the dimerization product of HEMA, is even less a factor to be considered in polymerization kinetics, due to low concentration (normally much less than 0.1 %, in-house information). 

The objective of the present work was to determine the influence of the light intensity on the polymerization kinetics and on the temperature profile of acrylate and vinyl ether monomers exposed to UV radiation as thin films, as well as the effect of the sample initial temperature on the polymerization rate and final degree of cure. For this purpose, a new method has been developed, based on real-time infrared (RTIR) spectroscopy 14, which permits to monitor in-situ the temperature of thin films undergoing high-speed photopolymerization, without introducing any additive in the UV-curable formulation 15. This technique proved particularly well suited to addressing the issue of thermal runaway which was recently considered to occur in laser-induced polymerization of divinyl ethers 13>16. 

The effect of the nitrone stmcture on the kinetics of the styrene polymerization has been reported. Of all the nitrones tested, those of the C-PBN type (Fig. 2.29, family 4) are the most efficient regarding polymerization rate, control of molecular weight, and polydispersity. Electrophilic substitution of the phenyl group of PBN by either an electrodonor or an electroacceptor group has only a minor effect on the polymerization kinetics. The polymerization rate is not governed by the thermal polymerization of styrene but by the alkoxyamine formed in situ during the pre-reaction step. The initiation efficiency is, however, very low, consistent with a limited conversion of the nitrone into nitroxide or alkoxyamine. 

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