Steady-state conditions, styrene

A detailed analysis of an asymmetric process coupling styrene synthesis through dehydrogenation of ethylbenzene with combustion of hydrogen has been presented in [23]. Figure 1.9 shows typical periodic steady-state conditions of the process. One... 

This equation shows that the radical concentration and consequently the rate of consumption of alkene in ATRA ( aid[alkene][R ], Scheme 4) under steady state conditions are dependent only on the AIBN concentration and its decomposition and termination rate constants. In other words, radical concentration in this system should not be governed by the choice of ATRA catalyst (which regulates the equilibrium constant for atom transfer, KATRA=kJk or the initial concentrations of copper(II) species. Indeed, these predictions have been shown to be in excellent agreement with experimental observations where apparent rates of polymerization in ICAR ATRP of styrene mediated by copper(II) bromide complexes with MeeTREN, TPMA, PMDETA and dNbpy... 

Isomerization probably occurs primarily via i Rh(CO)L2 prior to capture by CO in step 9. After i CORh(CO)2L2 forms by further steps 10 and 14, getting back to i Rh(CO)L2 by the reverse of steps 14, 10, and 9 seems unlikely, especially under CO and H2 pressure. This conclusion is supported by isotopic-labeling studies by Pino. If steps 9 and 4 are essentially irreversible, then the RCHO/R CHO ratio will primarily depend on the steady-state concentration ratio of i Rh(CO)L2 to i Rh(CO)L2. If 4 and kg are similart, then fcs, kg, and the relative stabilities (K /Kg) of i Rh(CO)L2 and R Rh(CO)L2 will determine the aldehyde product distribution. Steric crowding in the branched alkyl complex is no doubt a major factor in destabilizing it compared to the linear alkyl as early recognized by Evans, Osborn, and Wilkinsonthe increased crowding of phosphines relative to carbonyls accounts for the increased yields of desired linear products in both the Rh and Co hydroformylation systems. Electronic factors no doubt also play a role, and in fact most dominate the product distribution with styrene, where R Rh(CO)L2 capture by CO is favored over R Rh(CO)L2. The question is, to what extent is the ratio [R Rh(CO)L2]/[R Rh(CO)L2] kinetically or thermodynamically controlled under steady-state conditions ... 

An optimum model-based predictive controller was developed to allow for control of molecular weight averages (intrinsic viscosities) and reactor temperatures in solid-state PET polymerizations, through manipulation of the inert gas temperatures and flowrates [ 199]. Simulation studies also showed that predictive controllers might lead to significant improvement of process operation in PVC suspension reactors, when temperatures are allowed to vary along the batch time [200]. Simulation studies performed for continuous styrene solution polymerizations showed that the closed-loop predictive control can also be used to stabilize the reactor operation at unstable open-loop steady-state conditions [201]. 

Figure 4.10.28 shows the graphical solution for the example of styrene polymerization based on the data given in Table 4.10.5. For steady-state conditions, the reaction temperature is 436 K (163 °C) and the concentration and conversion of styrene are 540 mol m and 94%, respectively. 

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,... 

The existence of three steady states, two stable and one metastable, is common for exothermic reactions in stirred tanks. Also common is the existence of only one steady state. For the styrene polymerization example, three steady states exist for a limited range of the process variables. For example, if Ti is sufficiently low, no reaction occurs, and only the lower steady state is possible. If Tin is sufficiently high, only the upper, runaway condition can be realized. The external heat transfer term, UAextiTout — Text in Equation (5.28) can also be used to vary the location and number of steady states. 

The behavior shown in Figure 5.5 is typical of systems that have two stable steady states. The realized steady state depends on the initial conditions. For this example with a() = 1, the upper steady state is reached if T0 is greater than about 398 K, and the lower steady state is reached if T0 is less than about 398 K. At the lower steady state, the CSTR acts as a styrene monomer storage vessel with Tout Tin and there is no significant reaction. The upper steady state is a runaway where the reaction goes to near completion with Tout Tin + ATadiabatic- (In actuality, the styrene polymerization is reversible at very high temperatures, with a ceiling temperature of about 625 K.)... 

Emulsion Polymerization in a CSTR. Emulsion polymerization is usually carried out isothermally in batch or continuous stirred tank reactors. Temperature control is much easier than for bulk or solution polymerization because the small (. 5 Jim) polymer particles, which are the locus of reaction, are suspended in a continuous aqueous medium as shown in Figure 5. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. Gerrens and coworkers at BASF seem to be the first to report these phenomena both computationally and experimentally. Figure 6 (taken from ref. (253)) plots the autocatalytic behavior of the reaction rate for styrene polymerization vs. monomer conversion in the reactor. The intersection... 

Matsuura and Kato (3 ) predict the possibility of multiple steady states under isothermal conditions because of the gel effect, and Gerrens et al (20) experimentally verified these predictions with styrene emulsion polymerization. 

It is important to note that the true steady state deposition rate that is independent of the mixing modes (method A or B) was obtained only after more than 100 min operation in the case of styrene-N2. Without monomer adsorption in the case of acetylene-N2 system, the steady-state deposition rate is established much sooner than that in the styrene-N2 system. However, even in this case, it took more than 30 min to reach the steady-state deposition rate under the conditions of method B. 

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. 

H2 into the nmr tube gave a mixture of aldehydes in a similar ratio. The RCHO/R CHO ratio of >2 in the nmr experiment was much larger than observed under any catalytic hydroformylation conditions, where the maximum value with styrene was about 0.6. This indicates that under the conditions of stepwise addition in the nmr experiments, where the alkyls and acyls presumably had time to equilibrate, the RRh/R Rh and R CORh/R CORh ratios were higher than at steady state. Thus with styrene K3 > Kg but kg > ks. 

Jaisinghani and Ray (40) also predicted the existence of three steady states for the free-radical polymerization of methyl methacrylate under autothermal operation. As their analysis could only locate unstable limit cycles, they concluded that stable oscillations for this system were unlikely. However, they speculated that other monomer-initiator combinations could exhibit more interesting dynamic phenomena. Since at that time there had been no evidence of experimental work for this class of problems, their theoretical analysis provided the foundation for future experimental work aimed at validating the predicted phenomena. Later studies include the investigations of Balaraman et al. (43) for the continuous bulk copolymerization of styrene and acrylonitrile, and Kuchanov et al. (44) who demonstrated the existence of sustained oscillations for bulk copolymerization under non-isothermal conditions. Hamer, Akramov and Ray (45) were first to predict stable limit cycles for non-isothermal solution homopolymerization and copolymerization in a CSTR. Parameter space plots and dynamic simulations were presented for methyl methacrylate and vinyl acetate homopolymerization, as well as for their copolymerization. The copolymerization system exhibited a new bifurcation diagram observed for the first time where three Hopf bifurcations were located, leading to stable and unstable periodic branches over a small parameter range. Schmidt, Clinch and Ray (46) provided the first experimental evidence of multiple steady states for non-isothermal solution polymerization. Their... 

The polymerisation of styrene in miniemnlsions stabilised with anionic sodium dodecyl sulphate or nonionic Lntensol AT50 results in stable polymer dispersions with particle diameters between 30 and 480 nm and narrow particle size distributions. Steady-state mini-emulsification results in a system with critical stability , i.e. the droplet size is the prodnct of a rate equation of fission by ultrasound and fusion by collisions, and the mini-droplets are as small as possible for the timescales involved. The droplet growth by monomer exchange, or the T1 mechanism, is effectively suppressed by addition of a very hydrophobic material, whereas droplet growth by collisions, or the T2 mechanism, is subject to the critical conditions. The growth of the critically stabilised miniemulsion droplets is usually slower than the polymerisation time therefore, in ideal cases, a 1 1 copy of droplets to particles is obtained, and the critically stabilised state is frozen. 6 refs. 

Based on the kinetic results from the previous subsections, Dar (1999) estimated interior particle temperatures for FRRPP of styrene in ether. He used the same approach as the quasi-steady-state approximation in Section 2.2, which resulted in the use of the same differential equation and boundary conditions (Eqs. 2.2.1 and 2.2.2). The difference is that he employed a temperature-independent energy source term wherein the rate of reaction was based on the calculated derivative of monomer concentration with respect to time within a certain population of polymer-rich particles thus. 

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