Equilibrium monomer concentration copolymers

Derive an expression for ceiling temperature of copolymer in terms of the equilibrium monomer concentration, entropy of copolymerization, and enthalpy of copolymerization. 

Tognacci et al. [ 183] discussed various methods for measuring the monomer concentration in the polymer particles. The method proposed by the authors is a direct estimation of the solvent activity by the GC (gas chromatography) measurement of its partial pressure in the gas phase at equilibrium with the polymer particle, monomer droplet (if any) and aqueous phase in the latex. They proposed an original measuring technique and carried out measurements for different monomers (St, MMA, and VAc) and polymeric matrices (PSt and MMA-VAc copolymer), both above and below saturation conditions (corresponding to Intervals II and III). They compared the experimental data with that predicted by the monomer partitioning relationships derived by Maxwell et al. [166,170] and Noel et al. [172]. 

DSC has also been used to evaluate the surfactant monomer concentration in equilibrium with micelles and its temperature dependence for triblock copolymers [160]. 

Upon expressing from the equilibrium condition the complex concentration M12 through the concentrations of monomers, and substituting the expression found into relationship (21) we obtain, invoking the formalism of the Markov chains, final formulas enabling us to calculate instantaneous statistical characteristics of the ensemble of macromolecules with colored units. A subsequent color erasing procedure is carried out in the manner described above. For example, when calculating instantaneous copolymer composition, this procedure corresponds to the summation of the appropriate components of the stationary vector jt of the extended Markov chain ... 

In contrast to the kinetic approach, deviations from the terminal model have also been treated from a thermodynamic viewpoint [Kruger et al., 1987 Lowry, 1960 Palmer et al., 2000, 2001]. Altered copolymer compositions in certain copolymerizations are accounted for in this treatment in terms of the tendency of one of the monomers (M2) to depropagate. An essential difference between the kinetic and thermodynamic treatments is that the latter implies that the copolymer composition can vary with the concentrations of the monomers. If the concentration of monomer M2 falls below its equilibrium value [M]c at the particular reaction temperature, terminal M2 units will be prone to depropagate. The result would be a... 

In hydrocarbon solvents it is known that most of the growing chains are associated and it is necessary to enquire what effect this has on the copolymerization mechanism. The reactivity ratios measured from copolymer composition are unaffected because they refer to a common ion-pair. The equilibrium constants for association cancel and the reactivity ratios measured give a true measure of the relative propagation constants of the two monomers. No assessment can be made of the real reactivity of two types of active chain with the same monomer, however. In this case the observed rates are a function of the relative reactivities of the free ion-pairs and also of the relative extents of association. For example in hydrocarbon solvents polystyryllithium reacts with butadiene much more rapidly than does polybutadienyllithium. Until we know the two equilibrium constants for self-association we cannot find out if the increased rate is due to greater intrinsic reactivity or to a higher concentration of free polystyryllithium. In polar solvents or in hydrocarbon solvents in the presence of small amounts of ethers, these difficulties do not arise as self-association is no longer important. 

In the copolymerization of trioxane with dioxolane, reactivity ratios of dissolved copolymer cations are quite different from those of active centers in the crystalline phase. The former strongly prefer addition of dioxolane. The difference in reactivity ratios between dissolved and precipitated active centers is attributed to the fact that in the solid phase, polymerization and crystallization of the copolymer are simultaneous. The cationic chain ends are assumed to be directly on the crystal surface. Determination of the equilibrium concentrations of formaldehyde confirms this conclusion dissolved copolymer has a higher tendency to cleave formaldehyde than crystalline polyoxymethylene. In the latter stages of copolymerization the soluble copolymer is degraded gradually to the dioxolane monomer which is incorporated into the crystalline copolymer in an almost random distribution. 

On the other hand copolymer with a trioxane unit at the cationic chain end (Pi+) may be converted intp P2+ by cleavage of several formaldehyde units. These side reactions change the nature of the active chain ends without participation of the actual monomers trioxane and dioxo-lane. Such reactions are not provided for in the kinetic scheme of Mayo and Lewis. In their conventional scheme, conversion of Pi+ to P2+ is assumed to take place exclusively by addition of monomer M2. Polymerization of trioxane with dioxolane actually is a ternary copolymerization after the induction period one of the three monomers—formaldehyde— is present in its equilibrium concentration. Being the most reactive monomer it still exerts a strong influence on the course of copolymerization (9). This makes it impossible to apply the conventional copolymerization equation and complicates the process considerably. 

When the equilibrium (83) is shifted sufficiently to the right, zwitterion concentration in the medium is so high that the end groups of opposite charge react before the monomer has had a chance to become attached to a suitable ion. A strictly alternating copolymer is formed (see also Chap. 5, Sect. 5.8)... 

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