Concentration of monomer in the polymer

Considering that one particle from a certain class is representative of the whole class and that Mp, the concentration of monomer in the polymer particles, is the same for the whole class (for a different approach see (20)), equation (III-l) becomes ... 

Addition of small amounts of to solutions of polymers has been shown to facilitate formation of aqueous emulsions of-such solutions. A very recent application involves the addition of Z2 to the monomer phase in an ordinary emulsion polymerization. This results in a decrease in the concentration of monomer in the polymer particles and thereby in a change in the kinetics of polymerization. 

Allen and Gill [154] considered the effect of this on change of polymerization rate with time for two models distinguished by either a steady concentration of monomer in the polymer layer or by a falling concentration of monomer through the polymer coating, viz. 

As the polymerization proceeds, the presence of hydrophobe in the non-ini-tiated monomer droplets reduces the concentration of monomer in the polymer particles. 

Stage in —At an advanced stage of the polymerization (50 to 80% conversion), the supply of excess monomer becomes exhausted due to the disappearance of the monomer droplets. The polymer particles contain all the unreacted monomers. As the concentration of monomer in the polymer particles decreases, the rate of polymerization decreases steadily and deviates from linearity. The characteristics of various stages of emulsion polymerization are summarized in Table 10.4. 

The inner boundary condition at the surface of the catalyst fragment. Equation 2.135, states that the diffusional flux at the surface of the fragment (rp = R ) is equal to the rate of reaction R. The outer boimdary condition at the interface of the microparticle (rp = R ic) states that the concentration of monomer in the polymer layer at the interface is in equilibrium with the monomer concentration in the pores of the macroparticle at the position imder consideration. If a partition coefficient (K ) is used between the concentrations of monomer in the pores of the macroparticle and absorbed in the polymer layer surrounding the microparticle, then ... 

For gas-phase or liquid propylene bulk reactors, the bulk monomer concentration in the reactor must be converted to concentration in the polymer phase surrounding the active sites with a thermodynamic relationship. Generally, a simple partition coefficient such as the one used in Equation 2.136a is used. For diluent slurry reactors, where the monomer is introduced in the gas phase, a partition coefficient such as Herny s law constant must also be used to calculate the concentration of monomer in the diluent which, in turn, is used to estimate the concentration of monomer in the polymer phase surrounding the active sites. Evidently, more sophisticated thermodynamic relationships relating the concentration of monomer in the gas phase, diluent and polymer can be used but, from a practical point of view, are only justified when the polymerization kinetic constants are very well known. Similar considerations apply to calculate the concentrations of comonomers, hydrogen and any other reactant in the system. 

Consequently, the molecular weight increases with the number of polymer particles and the concentration of monomer in the polymer particles, and decreases as initiator concentration increases. In addition, because the activation energy of the initiator decomposition rate constant is greater than that of propagation (see Section 3.2.1.2), the molecular weights decrease with temperature. 

Taking into account the 4, values in (2.145) we can easily determine the ratio between the concentrations of monomers in the polymer ... 

Ryabova et al. have presented evidence for believing that the rate of diffusion of styrene into reaction loci is considerably higher than the rate of polymerization, and that, in consequence, the concentration of monomer in the reaction locus is little affected by the occurrence of polymerization. On the other hand, Gritskova et al. believe that the concentration of monomer in the polymer-monomer particles is variable, depending upon the reaction conditions. 

Conventional emulsion polymerization occurs in a three-phase system (polymer particles, aqueous phase, and monomer droplets) and polymerization may, in principle, occur in any phase. However, the concentrations of both monomer and radicals in the polymer particles are much higher than those in the aqueous phase (see below), and hence the extent of the polymerization in the aqueous phase is in most cases negligible. On the other hand, the concentration of the radicals in the monomer droplets is very low because the monomer droplets are not efficient at capturing the radicals formed in the aqueous phase. The polymerization in the polymer particles follows the same mechanisms as in bulk polymerization and the rate of polymerization per polymer particle Rpp is given by Eq. (1), where kp is the propagation rate constant [m mol s ], [M] the concentration of monomer in the polymer particles [mol m ], h the average number of radicals per particle and Na Avogadro s number. 

The graph shows that the region of polymer/monomer ratio below 3 1 (concentration of monomer in the polymer particles higher than [MJ = 2.90 mol L ) will not be safe. In other words, if higher monomer concentrations are used in the process and the cooling system fails, there is a risk of exceeding the Tu it tempera-... 

Another consequence of the existence of micelles during the whole process is that the concentration of monomer in the polymer particles continuously decreases during the process due to its partitioning between polymer particles and micelles. The combination of an increasing number of particles and a decreasing monomer concentration leads to a maximum in the evolution of the polymerization rate during the process. 

The actual concentration of monomer in the polymer particles (gels) in a diffusion controlled polymerization (at subsaturation pressure and at low agitation speed) equals the equilibrium value given by the value P/Po [133]. The apparent P/Pq values, as well as the corresponding concentrations of monomer in the polymer gel are related to different agitation speeds. For example, with increasing the agitation speed from 500 to 1500 rmp, the monomer concentration increases from 6.1 to 25 g VC/100 g PVC [134]. 

These assumptions then lead to a scenario that, at any moment, the monomer-swollen polymer particles contain either only one free radical (active) or none (idle). Under these circumstances, a value of n equal to 0.5 is achieved for the polymerization systems that follow the Smith-Ewart Case 2 kinetics. In addition, the concentration of monomer in the polymer particles does not vary to any extent with the progress of polymerization in the presence of monomer droplets. As a result, a steady polymerization rate is attained during Interval II. Furthermore, the polymerization kinetics is strictly controlled by the population of polymer particles available for consuming monomer. Smith-Ewart Case 2 kinetics has been successfully applied to emulsion polymerizations of relatively water-insoluble monomers such as styrene and butadiene. 

One potential method developed to predict the concentration of monomer in polymer particles in emulsion polymerization is the thermodynamic approach [77-80], Morton et al. [77] proposed the following equation for calculating the equilibrium concentration of monomer in the polymer particles ... 

The concentration of monomer in the polymer particles depends on relative time constants for mass transfer and polymerisatiou Except for poorly emulsified highly water-insoluble monomers, the time constant for mass transfer is negligible with respect to the time constant for polymerisation. Hence the concentrations of the monomers in the different phases are given by the thermodynamic equilibrium ... 

Figure 4.8 Simulated data for the seeded batch emulsion copolymerisation of MMA and BA, initial molar ratio of BA and MMA is one (a) instantaneous and cumulative copolymer composition (b) ratio of the concentration of monomer in the polymer particles referred to BA, %a = [BA]p/([BA]p + (MMA]p) (c) partial and overall conversions (d) rates of polymerisation.

Figure 4.15 shows the master curves necessary to produce a homogeneous BA-MMA copolymer containing 50 mol% BA and 50 mol% MMA at a temperature of 70°C. The master curves are calculated for two different monomer swelling values (constraint 2). The master curves show the amounts of monomer BA and MMA that must be added into the reactor as a function of conversion. The values at zero conversion represent the monomer that must be initially present in the reactor. The plot also shows that the addition of the less reactive monomer must end at a lower conversion than the more reactive monomer. This difference in the optimal monomer addition profiles calculated for case (a) (a limit is imposed in the free amount of BA in the particles) and case (b) (saturation limit) show that the complete addition of the monomers can be achieved at lower overall conversion (in less process time) when a higher limit is imposed in the concentration of monomer in the polymer particles. 

Calculation of the concentration of monomer in the polymer particles depends on the reaction interval. The polymer particles are nucleated in interval I and grow by consuming monomer during interval 11. Particles are assumed to be saturated with monomer during this last interval and the excess of monomer is stored in the monomer droplets. In interval III, monomer droplets disappear and all the monomer is supposed to be in the polymer particles (this assumes... 

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