Steady-State Polymerization Conditions

Soon after the discovery of the first generation Ziegler catalysts and the chromium-based Phillips catalysts in the mid-1950s, the need developed 

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. 

1 Determination of Steady-State Conditions During Polymerization 

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 

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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. 

The summations extend from n = 2 to n. = oo.) Keii [Kinetics of Ziegler-Natta Polymerization, Kodansha, Tokyo, 1972] has noted that under steady-state reaction conditions, the number of polymer molecules with degree of polymerization n desorbing per unit catalyst surface area in unit time may be written as... 

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 . ... 

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. 

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. 

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. 

Figure 9.12 Molecular weight distribution function for situations in which the duration of the growth stage is short compared to the residence time in the reactor (e.g., free-radical polymerization). The steady-state operating conditions in CSTR A and CSTR B correspond to relative monomer concentrations of 0.1 and 0.354, respectively. The conditions in the batch reactor involve a transition from a relative monomer concentration of 1.0 to one of 0.1. [Adapted with permission of The Royal Society of Chemistry from the contribution of K. G. Denbigh to Trans. Faraday Soc., 43,648 (1947). Copyright 1947, The Royal Society of Chemistry.]...

Polymerization processes have adopted a character of continuous multiproduct plants, in response to the current demand for polymers. Precisely, the variability observed in the polymer market demand, in terms of product quality specifications, calls upon frequent grade transition policies on the polymerization plants, with legitimate consequences on process economics, due to the regular necessary disturbances from steady-state operating conditions. Therefore, the issue of how to operate such process as continuous multiproduct plants, in a global polymer industry environment with intense competitive pressures, emerges nastily. 

Itis worth mentioning that there is a fair amount of information on computer simulation to achieve steady-state reaction conditions [39]. These simulations use artificial neural networks, [40] advances in computational fluid dynamics (CFD) [41], as well as combination of new experimental and modeling techniques, whence the apphcation of these techniques can lead to improved models of polymerization systems as well as the discovery of new kinetic mechanisms that control polymerization rate and properties. 

Photoinitiation is an excellent method for studying the pre- and posteffects of free radical polymerization, and from the ratio of the specific rate constant (kx) in non-steady-state conditions, together with steady-state kinetics, the absolute values of propagation (kp) and termination (k,) rate constants for radical polymerization can be obtained. 

Traditionally, measurement of kp has required determination of the rate of polymerization under steady state (to give kpi k,7) and non-steady state conditions... 

From this we can see that knowledge of k f and Rf in a conventional polymerization process readily yields a value of the ratio kp fkt. In order to obtain a value for kf wc require further information on kv. Analysis of / , data obtained under non-steady state conditions (when there is no continuous source of initiator radicals) yields the ratio kvlkx. Various non-stcady state methods have been developed including the rotating sector method, spatially intermittent polymerization and pulsed laser polymerization (PLP). The classical approach for deriving the individual values of kp and kt by combining values for kp kx. with kp/k, obtained in separate experiments can, however, be problematical because the values of kx are strongly dependent on the polymerization conditions (Section... 

In summary, then, polymerization of ATP-actin under conditions of sonication displays two characteristic deviations from the simple law described by equation (4), which is only valid for reversible polymerization. These are (a) overshoot polymerization kinetics, and (b) the steady-state amount of polymer formed decreases, or the steady-state monomer concentration increases, with the number of filaments. These two features are the direct consequence of ATP hydrolysis accompanying the polymerization of ATP-actin, as will be explained now. 

Because ATP hydrolysis on F-actin takes place with a delay following the incorporation of ATP-subunits, and because in the transient F-ATP state filaments are more stable than in the final F-ADP state, polymerization under conditions of sonication can be complete, within a time short enough for practically all subunits of the filaments to be F-ATP. At a later stage, as Pj is liberated, the F-ADP filament becomes less stable and loses ADP-subunits steadily. The G-ADP-actin liberated in solution is not immediately converted into easily polymerizable G-ATP-actin, because nucleotide exchange on G-actin is relatively slow, and is not able to polymerize by itself unless a high concentration (the critical concentration of ADP-actin) is reached. Therefore, G-ADP-actin accumulates in solution. A steady-state concentration of G-ADP-actin is established when the rate of depolymerization of ADP-actin (k [F]) is equal to the sum of the rates of disappearance of G-ADP-actin via nucleotide exchange and association to filament ends. [G-ADP]ss in this scheme is described by the following equation (Pantaloni et al., 1984) ... 

There is a middle steady state, but it is metastable. The reaction will tend toward either the upper or lower steady states, and a control system is needed to maintain operation around the metastable point. For the styrene polymerization, a common industrial practice is to operate at the metastable point, with temperature control through autorefrigeration (cooling by boiling). A combination of feed preheating and jacket heating ensures that the uncontrolled reaction would tend toward the upper, runaway condition. However,... 

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