Monomer mass balances

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

The experiments were carried out with two initiators. According to published data (B.), at the base temperature, Tb, the fast initiator, II, has a half-life of 3.5 minutes, and the slow initiator, 12, has a half-life of 95 minutes. A minor modification of the monomer mass balance (Equation 7) is required for the case of two initiators. 

Dense emulsion-phase monomer mass-balances Here the mass-balance equation is... 

To calculate the reactor pressure and the polymerization rates in the monomer- and polymer-rich phases, the monomer distribution in the different phases in the system must be known. Assuming that all the phases in the system (i.e., three for PS and four for VCM) are in thermodynamic equilibrium, the following pseudo-steady-state monomer mass balance... 

The SimuSolv program (Program B) which was written to simulate the reaction finishing process with extra initiator addition is similar to Program A and uses the monomer and initiators mass balance equations with optimized values of the kinetic parameters. The semibatch step had been experimentally optimized for obtaining... 

Thus, the initial value of the initiator concentrations, [Il]° and [I2]°, are calculated with Equation 15, for given values of the initial loading, feed rates, temperature, and time for the main semi-batch step, and [M]° is fixed according to experimental data from the base case semi-batch step. The nonlinear differential equation for [M] in terms of [II] and [I2] is given by Equation 16. Equation 10, with a redefinition of terms, is the differential equation mass balance for [II] and [12]. In the finishing step, only one of the initiators would be added for residual monomer reduction. Thus, Qm = 0,... 

Improved co-monomer incorporation. Metallocene catalysts are very efficient at co-monomer incorporation, which means that co-monomer use can be reduced by a factor of ten or more. This has some cost advantages but, more importantly, there is less unincorporated comonomer in the final product, improving efficiency and mass balance and reducing VOCs. 

The concentration of monomer present at any concentration of inhibitor is given by SC, and the concentration of dimer is given, considering mass balance, by (1 - 8)C. When an enzyme is treated simultaneously with two inhibitors, / and J, that bind in a mutually exclusive fashion, the fractional activity is given by (Copeland, 2000)... 

If we introduce the monomer-complexation by means of equation (1) and write the new charge and mass balances as... 

We begin by writing the mass balance on aU species in batch (t) or PFTR (t). For monomer [M] we obtain... 

Again we have an infinite set of coupled equations. For the PFTR or batch reactor we can write these mass balances for condensation polymerizatioa The monomer A[ is lost by reacting with all the polymeis,... 

The amount of a reagent consumed in the reactor is given by the mass balance, i.e. by the difference between the amounts flowing in and out, thus enabling the calculation of the required rate constants. For monomer, the mass balance becomes ... 

The mass balance on the inactive bubble phase for the monomer is given by... 

On the basis of the above assumptions one can write the following transient mass balances for gaseous propylene oxide, adsorbed propylene oxide monomer and sites covered by i-mer respectively ... 

Each zone of the tubular reactor is simulated as a sequence of N perfectly mixed elementary volumes, as shown in Figure 2. Each volume can receive a feed side-stream, and exchanges heat with a corresponding volume in the oil jacket. For volume i and chemical species j (either initiator, oxygen, radicals or monomer) the mass balance is written as ... 

The mass balance is written using as state variables the amount of initiator I (kmol), monomer M (kg) and polymer P (kg). The reaction rates are in kmol/s, and kmol/m3, respectively. Subscripts 1 and 2 refer to the monomer-rich and polymer-rich phases, respectively. For clarity, we will use symbols as cKj to denote the concentration (kmol/m3) of species FCin phase j. 

As seen in Equation (7.118), the copolymer and the feed compositions vary with the conversion during the polymerization process. The drift of a feed composition with the conversion favors the less reactive monomer. To obtain F, at different conversions, it is necessary to integrate the copolymer composition equation. Assume that the system contains a total of M moles of monomers and F, > f,. After dM moles of monomers have been polymerized, the copolymer contains F,dM moles of Mj. The feed then contains (M - dM)(fj - dl",) moles of M where the first term is the total monomer concentration and the second term is the mole fraction of M, in the feed. The mass balance of Mj reacted in the system is given by ... 

By combining thermodynamically-based monomer partitioning relationships for saturation [170] and partial swelling [172] with mass balance equations, Noel et al. [174] proposed a model for saturation and a model for partial swelling that could predict the mole fraction of a specific monomer i in the polymer particles. They showed that the batch emulsion copolymerization behavior predicted by the models presented in this article agreed adequately with experimental results for MA-VAc and MA-Inden (Ind) systems. Karlsson et al. [176] studied the monomer swelling kinetics at 80 °C in Interval III of the seeded emulsion polymerization of isoprene with carboxylated PSt latex particles as the seeds. The authors measured the variation of the isoprene sorption rate into the seed polymer particles with the volume fraction of polymer in the latex particles, and discussed the sorption process of isoprene into the seed polymer particles in Interval III in detail from a thermodynamic point of view. 

It is desirable to obtain an a priori predictio of the total equilibrium monomer concentration (CAC ) at set levels of adsorption based on the mixture feed mole fractions, instead of the equilibrium monomer mole fractions (Y.). The equilibrium monomer mole fractions will differ from the feed mole fractions because of the preferential adsorption of some of the surfactants in the mixture. A mass balance on component i in the feed, equilibrium solution, and adsorbed phase is solved for the equilibrium monomer mole fraction to obtain Equation 4 ... 

Table 10.13 PS flash pyrolysis mass balance including the yield of monomer, styrene...

For the flash pyrolysis of PS, the results in mass balance are presented in Table 10.13. The yield of monomer is added because styrene is the major component during the carbonization of PS. 

As a check on the results of this calculation we can make use of the fact that the number of molecules, /V, left in the system at an extent of conversion p is equal to the original number of moles of monomer minus the number of linkages formed. From a mass balance, the number of linkages that have been formed is p times the number of moles of deficient groups and equals 2/z = 2 in the present... 

The schematic diagram of CAP principle is shown in Figure 10.1. In this scheme, four major processes are necessary to complete the mass balance in the reactor (1) monomer feed in (2) ablation (3) material deposition and (4) escape from the system (pump out). The formation of reactive species is an ablation process because considerable fragmentation of the monomer (starting material) occurs in general cases. 

There are two factors that infiuence the particle formation conditions the adsorption of emulsifier on the droplets, which baves less emulsifier in the aqueous phase to facilitate particle formation-there, and the rate of radical absorption in monomer droplets. The former factor may be evaluated by talcing into account the adsorption isotherm of emulsifier on monomer droplets. Using a modified Langmuir adsorption isotherm in combination with a mass balance gives an expression for the aqueous phase concentration of emulsifier C... 

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