Steady-state polymerization

In the case of reagents with a low content of inhibitors a steady-state polymerization rate may be set up. Steady-state kinetics are also observed... 

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). 

According to Demin et al. (125, 126) the steady-state polymerization of ethylene occurs at 5-70°C in the presence of Cr(7r-C3H6)3 and Zr (tt-CsHs) 4. In Ballard et al. (123) the induction period at ethylene polymerization using Zr (7r-C3H6)4 was observed the introduction of hydrogen... 

The steady-state polymerization in the presence of Cr (it-CsHb) was first order with respect to the monomer concentration (125) the effective activation energy was 4.7 0.5 kcal/mole. When the concentration of Crfir-CaHs was varied, first a linear rise of the polymerization rate occurred with an increase of tris-ir-allylchromium concentration to the upper limit then the rate does not depend on Crfx-CaHs concentration (126). The value of the upper limit of the polymerization rate increased with an increase in the water content of the solvent used. 

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). 

MICROTUBULE ASSEMBLY/DISASSEMBLY KINETICS. Cellular microtubules must undergo turnover, and nucleotide hydrolysis appears to play a central role in priming microtubules for their eventual disassembly. Two fundamentally different assembly/disassembly mechanisms persist during what has been termed steady-state polymerization both rely on GTP hydrolysis to provide a source of Gibbs free energy to sustain the steady-state condition . ... 

To obtain xs the steady-state polymerization rate (Rp)s is first measured at constant illumination (no pulsing). Then the average rate Rp is measured as a function of r and t. The data are plotted as the rate ratio Rp/(Rp)s versus log t. Alternately, one can plot the data as the rate ratio Rp/(Rp)QO since this ratio is related to Rpj (Rp)s through Eq. 3-159. The theoretical plot (e.g., Fig. 3-11) for the same r value is placed on top of the experimental plot and shifted on the abscissa (x axis) until a best fit is obtained. The displacement on the abscissa of one plot from the other yields log xs since the abscissa for the theoretical plot is log t — log xs. 

Compare Eq. 3-229 with 3-224. The decay in monomer concentration depends on the orders of both initiator and activator initial concentrations with no dependence on deactivator concentration and varies with t2/3 under non-steady-state conditions. For steady-state conditions, there are first-order dependencies on initiator and activator and inverse first-order dependence on deactivator and the time dependence is linear. Note that Eq. 3-229 describes the non-steady-state polymerization rate in terms of initial concentrations of initiator and activator. Equation 3-224 describes the steady-state polymerization rate in terms of concentrations at any point in the reaction as long as only short reaction intervals are considered so that concentration changes are small. 

Another kind of inhibitor often present in photopolymer systems is dissolved oxygen, which inhibits by producing stable species, incapable of initiation, after reaction with radicals. If inhibitors are present, either deliberately or adventitiously they must be depleted before normal polymerization can proceed. This results in observation of an inhibition period before onset of steady state polymerization. 

Assuming a non-steady state polymerization involving a long lived radical, the following equation is derived (9) ... 

The mechanism can be best understood within the framework of the conventional theory of radical chain kinetics, provided that certain of the usual simplifying assumptions are omitted. A solution is given to the problem of steady-state polymerization rate as a function of monomer and initiator concentration, taking into account termination reactions of primary radicals and recombination of geminate chains arising from the same initiation event. This model is shown to account for the kinetic data reported herein. With appropriate rate constants it should be generally applicable to radical polymerizations. 

Assuming 1 % catalyst efficiency Ep refers to steady state polymerization. 

Styrene is capable of forming moderately stable Co-C bonds.370 The formation and decomposition of adducts between the CCT catalysts and the propagating radicals results in reversible inhibition .123-271 In this case, an induction period is observed at the beginning of polymerization. This induction period is characterized by the steady growth of the rate of polymerization similar to the classic kinetics of a polymerization inhibited by a weak inhibitor. Depending upon conditions, the time required to reach steady-state polymerization kinetics (eq 42) may require tens of minutes. 

In order to determine the factors that control the rate, r, and the chain length, Vp, of the polymerization, it is important to determine the rate of the separate reactions involved, namely initiation, propagation and termination, as well as the rates of any other processes that may compete with them. These rate equations will contain reactive intermediates (i.e. radical concentrations [R-]) that cannot be explicitly determined. The process of solution requires the steady-state approximation, which states that there is no net change in radical population with time during the steady-state polymerization, i.e. d[R ]/df = 0, in order to... 

A special case of Eq. (6.148) is of interest. Consider polymerization in the absence of a solvent or added chain transfer agent, so that [S] = 0. For steady-state polymerization, Eq. (6.25) can be used to express in terms of i p as... 

The overall rate equation, describing the steady-state polymerization period is thus given by... 

The induction period can also be shortened or even eliminated by the addition of reducing agents either to the catalyst or to the reactor. Particularly effective are the alkyls or hydrides of aluminum, boron, zinc, lithium, magnesium, etc. When added in ppm quantities, they can eliminate the induction time of Cr(VI)/silica and also raise the steady-state polymerization rate. Some metal alkyls can remove poisons and redox byproducts. All metal alkyls no doubt help reduce the Cr(VI), perhaps to Cr(IV). And some may even help alkylate the chromium, similar to the chemistry of Ziegler catalysts. Figure 16 shows how triethylaluminum cocatalyst can be used to shorten the induction time [52],... 

Derive expressions for (i) overall rate of steady state polymerization and (ii) number average degree of polymerization DPn- Predict the mode of variation of DPn with reaction conditions. 

The overall rate equation for the period of steady-state polymerization is thus given by (Burfield et al., 1972)... 

O Driscoll has proposed that the auto-acceleration can be modeled by recognizing that the termination reaction is diffusion controlled but will also depend on the size of the chain involved. The critical chain length for entanglement then becomes an important parameter, and two termination rate constants can also be defined, one for chains smaller than and one for large entangled chains. These are, respectively, and k. If v is the kinetic chain length and Vp is the conventional steady-state polymerization, then the observed rate v is given by... 

Average Degree of Polymerization. To calculate the number-average degree of polymerization, P , of a polymer produced by a steady-state polymerization. 

The Full Chain Length Distribution. So far, only the average degree of polymerization has been considered. To calculate the distribution function itself for a steady-state polymerization it is convenient to choose a statistical approach based on kinetic parameters. A probability factor a of propagation is defined as the probability that a radical will propagate rather than terminate. The factor a is the ratio of the rate of propagation over the sum of the rates of all possible reactions the macroradical can undergo. 

Experimental equipment that is useful for the rapid screening of catalysts in support of the global polyethylene business must meet two critical requirements (1) The polymerization reactor needs to be properly designed so that an experiment can be carried out imder steady-state polymerization conditions for a minimum of about 20 minutes in order to provide important catalyst activity data and sufficient polymer for complete characterization. (2) A process model is needed in order to quantitatively determine important kinetic parameters of an experimental catalyst. 

In addition, steady-state polymerization conditions are required in order to determine meaningful kinetic data from an experimental catalyst such as catalyst activity, catalyst decay rates and catalyst reactivity ratios for comonomers such as 1-butene, 1-hexene and 1-octene. 

In a classic 1978 paper [5,6], L.L. Bohm reported on the experimental parameters needed to establish steady-state polymerization conditions in order to eliminate monomer transport phenomena from the experimental results. As pointed out by Bohm, suspension or slurry polymerization takes place if the polymerization temperature is lower than the polyethylene solubility temperature and, therefore, the semicrystalline polymer precipitates from the suspension medium as the polymerization proceeds. The important physical process is the mass transfer of ethylene, comonomer and hydrogen (chain transfer reagent used to control polymer molecular weight) from the gas phase through the suspension medium and into the growing polymer particle to the active site. In order to obtain correct kinetic results, concentration gradients and temperature gradients within the polymer particle need to be removed from the polymerization process to achieve the necessary steady-state polymerization conditions. 

The first goal in achieving steady-state polymerization conditions is to determine the stirring rate that eliminates the stirring rate of the suspension medium (usually a saturated hydrocarbon) from affecting the... 

Some prelimarily work to illustrate this last point is reported below. This work, by Lee and Poehlein (18), is based on the analysis of the data published by Berens (19) for the emulsion polymerization of vinyl chloride in a seed-fed CSTR. Berens reported both the seed and effluent PSD s for steady-state polymerization in a CSTR, These data are shown in Figure 7. Since the seed latex is not monodisperse the model presented previously was modified by subdiving the seed distribution into twelve parts which were considered to be monodisperse with the mean diameter of the part. The previous model was applied to each part and the results added to predict the effluent PSD. Since the volume of the seed particles were distributed, the mean seed particle volume, , was used in the appropriate dimensionless groups. 

Stationary Polymerization The most classic kinetic treatment for the rate of polymerization is the quasi steady-state polymerization, which assumes a constant free radical polymerization throughout the course of the polymerization [52] ... 

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