Equilibrium monomer concentration determination

In the copolymerization of five- and six-membered oxacyclic monomers, the effective monomer concentration in the propagation reaction decreases because only the monomer in excess of equilibrium is available for copolymerization. However, it is not easy to determine the equilibrium monomer concentration in a copolymerization system. The following equilibrium is expected to exist in the copolymerization of THF. 

In this paper we formulated and solved the time optimal problem for a batch reactor in its final stage for isothermal and nonisothermal policies. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and optimum time was studied. It was shown that the optimum isothermal policy was influenced by two factors the equilibrium monomer concentration, and the dead end polymerization caused by the depletion of the initiator. When values determine optimum temperature, a faster initiator or higher initiator concentration should be used to reduce reaction time. 

Fig. 7-1 Determination of the equilibrium monomer concentration [M]c for the (CiHs O1 (Blvi) initiated polymerization of tetrahydrofuran in dichloroethane at 0°C. After Vofsi and Tobolsky [1965] (by...

PTHF does not behave ideally in solution and the equilibrium monomer concentration varies with both solvent and temperature. Kinetics of THF polymerizations fit equation 2, provided that the equilibrium monomer concentration is determined for the conditions used. 

The reversibility of propagation, or more specifically, the position of the equilibrium as determined by the ratio of the rate constants of propagation and depropagation is also independent of the mechanism. The equilibrium monomer concentration of monosubstituted alkenes such as styrenes and vinyl ethers are so low ([M] < 10-6 mol/L) at temperatures used for carbocationic polymerizations that the reversibility of polymerization can be neglected. 

However, the equilibrium monomer concentrations of disubstituted alkenes is measurable. The equilibrium constants for dimerization, tri-merization, and polymerization of a-methylstyrene have been determined as a function of temperature under anionic conditions [12] similar values should be obtained under cationic conditions. Unfortunately, the equilibrium position can t be determined directly under cationic conditions due to the irreversible side reactions of isomerization and indan and spirobiindan formation (Section II. A). The equilibrium monomer concentrations of isobutene and isopropenyl vinyl ethers should also be relatively high, albeit lower than those of a-methylstyrenes. However, the true equilibrium can t be reached with these monomers due to irreversible side reactions, and reliable data are therefore not available. Nevertheless, the ceiling temperature of isobutene polymerization is apparently between 50 and 150° C. 

Thus, measuring the concentration of initiator as a function of time, the rate constant of initiation can be determined. In a few systems, when the equilibrium monomer concentration is relatively high (THF, DXL), initiation has been studied under conditions at which propagation is excluded ([M]o < lM]e). 

The polymerization of THF approaches an equilibrium between monomer and polymer at every temperature. That is, for every temperature there is an equilibrium monomer concentration, [M]e, that is thermodynamically determined. Also there is a temperature,, above which no polymerization will occur. A value for of 85 2°C was derived for bulk polymerization of THF using PFg counter-ion [72, 73]. Dainton and Ivin [74] have related [M] to the absolute temperature, T, and to the enthalpy change, Affss, and entropy change, AS°, upon the conversion of... 

Equation 11 refers to equilibrium swelling conditions. Now, Flory (24) concludes from theoretical considerations that monomer is easily supplied to the polymer particles at the required rate even in the case of monomers which are little soluble in water, such as styrene. That equilibrium swelling is maintained during emulsion polymerization is supported by a comparison of values of the monomer concentrations determined in equilibrium swelling measurements with those found to prevail during polymerization and determined by analysis of reaction kinetics (see below). The results obtained by both methods are plotted in Figure 10. 

Equations (10.33) and (10.35) can be used to determine the propagation rate constant. The equilibrium monomer concentration [M]e is obtained by direct analysis or as the intercept of a plot of polymerization rate versus initial monomer concentration (see Problem 10.4). The polymerization data are then plotted, in accordance with Eq. (10.36), as the left side of that equation versus time to yield a staright line where slope is A [M ]. Since [M ] for a living polymer can be obtained from measurements of the number-average molecular weight, one can determine the propagation rate constant. 

Figure 10.2 Determination of the equilibrium monomer concentration [M]e from initial rate (Rj,) versus initial monomer concentration ([M] ) data. (Problem 10.4.)...

Determine (a) the equilibrium monomer concentration and (b) the propagation rate constant /t at0°C. 

The solution headspace approach is applicable to a much wider range of samples than the solid approach. When working with sample solutions, headspace equilibrium is more readily attained and the calibration procedure is simplified. The sensitivity of the solution method depends upon the vapor pressure of the constituent to be analysed and its solubility in the solvent phase. Vinyl chloride, butadiene, and acrylonitrile, are readily transferred from polymer solutions into the headspace by heating to 90 °C. The headspace/solution partitioning for these constituents is not appreciably affected by changes in the solvent phase (namely, addition of water) since the more volatile materials favonr the headspace at 90 °C. Less volatile monomers such as styrene (bp = 145 "C) and 2-ethylhexyl acrylate (bp = 214 °C) may not be determined using headspace techniques with the same sensitivities realised for the more volatile monomers. By altering the composition of the solvent phase to decrease the monomer solubility, the equilibrium monomer concentration in the headspace can be increased. This resulted in a dramatic increase in the detection sensitivity for styrene and 2-ethylhexyl acrylate. 

By changing the polymerization temperature from -20 C to 30 C, thermodynamic parameters for the polymerization of ll-CF-4 were determined by plotting the logarithms of the equilibrium monomer concentration against reciprocal temperature to fit the Dainton s equation (7 ). H ... 

It was observed in the polymerization of THF in benzene solvent that the equilibrium monomer concentration [THF]e depends linearly on [THF]q. A method was elaborated to determine AicH and from the experimental data for such... 

ROP of aliphatic cyclic esters is a continuously and dynamically developing research field. Initially, fundamental aspects of polymerization, such as thermodynamics, kinetics, and mechanisms of the elementary reactions, were explored. The best understood systems encompass polymerization of lactones and LAs. Determination of the standard thermodynamics parameters of polymerization for a majority of the most important monomers now allows the estimation of the equilibrium monomer concentration at given polymerization conditions. For a few polymerizing systems, such as anionic polymerization of PL, CL, or coordinated (proceeding on polarized covalent bonds) polymerizations of CL and LAs, the absolute rate constants have been determined. However, in a majority of the polymerizations, only the net reactivities have usually been determined which does not provide direct access to absolute rate constants of propagation. Nonetheless, the ROP of cyclic esters seems to be a convenient model system for studies of mechanism of cyclic monomers, in general. 

Equation 44 shows the equilibrium monomer concentration [M] as a function of the reaction or the ceiling temperature T. The heat of polymerization was obtained in earlier studies from the slope of a plot of In [M] versus HT. This procedure, however, is not quite correct. The volume fraction of the pol3uner increases with decreasing temperature, and in bulk polymerization approaches unity at sufficiently low temperatures. This affects the activity coefficient of the monomer. The heat of polymerization should be determined from the slope of a plot of AGIRT versus 1/T (44). 

As already discussed in Chapter 1, the relative tendency of a surfactant component to adsorb on a given surface or to form micelles can vary greatly with surfactant structure. The adsorption of each component could be measured below the CMC at various concentrations of each surfactant in a mixture. A matrix could be constructed to tabulate the (hopefully unique) monomer concentration of each component in the mixture corresponding to any combination of adsorption levels for the various components present. For example, for a binary system of surfactants A and B, when adsorption of A is 0.5 mmole/g and that of B is 0.3 mmole/g, there should be only one unique combination of monomer concentrations of surfactant A and of surfactant B which would result in this adsorption (e.g., 1 mM of A and 1.5 mM of B). Uell above the CMC, where most of the surfactant in solution is present as micelles, micellar composition is approximately equal to solution composition and is, therefore, known. If individual surfactant component adsorption is also measured here, it would allow computation of each surfactant monomer concentration (from the aforementioned matrix) in equilibrium with the mixed micelles. Other processes dependent on monomer concentration or surfactant component activities only could also be used in a similar fashion to determine monomer—micelle equilibrium. 

A multi-component gas solubility model and a multi-component surface adsorption model are generally required to estimate the monomer concentration at active sites. If the latter equilibrium can be neglected then the gas-solubility in the suspending agent determines the monomer concentration near the active site, which changes significantly with temperature and pressure. 

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