Monomer fugacity

During the whole duration of polymerization process, the three phases (four in the case of VCM polymerization) are assumed to be in thermodynamic equilibrium. As a result, the monomer fugacities in the three (four) phases will be equal ... 

By contrast, in the system propionic acid d) - methyl isobutyl ketone (2), (fi and are very much different when y 1, Propionic acid has a strong tendency to dimerize with itself and only a weak tendency to dimerize with ketone also,the ketone has only a weak tendency to dimerize with itself. At acid-rich compositions, therefore, many acid molecules have dimerized but most ketone molecules are monomers. Acid-acid dimerization lowers the fugacity of acid and thus is well below unity. Because of acid-acid dimerization, the true mole fraction of ketone is signi-... 

The estimation of the two parameters requires not only conversion and head space composition data but also physical properties of the monomers, e.g. reactivity ratios, vapor pressure equation, liquid phase activity coefficients and vapor phase fugacity coefficients. 

For the monomers in the polymerization under consideration the fugacity coefficients were estimated by Redlich-Kwong equation of state and were found to be close to unity. The activity coefficients (8) for the monomers were estimated by Scatchard-Hildebrand s method (5) for the most volatile monomer there was a temperature dependence but none for the other monomer. These were later confirmed by applying the UNIFAC method (6). The saturation vapor pressures were calculated by Antoine coefficients (5). 

In 1977 De Santis et al. (J5) as well as Heidemann et al. ( ) calculated the gas-phase fugacities in the systems HjO-air and H2O-N2-CO2 by equation of state in these calculations the liquid phase was not included. One of the authors (7J showed in 1978 that aqueous systems with some inert gases and alkanes as well as H2S and C02 could be represented by an equation of state if the molecular weight of water was artificially increased. An extension of this method applied to alcohols was found to be only partially successful. Gmehling et al. (8) treated polar fluids such as alcohols, ketones and water as monomer-dimer mixtures using Donohue s equation of state (9) various systems including water-methanol and water-ethanol were succussfully represented. 

The one-field model gives a description of the approximate grand canonical ensembles introduced in Chapter 11, Section 5. These ensembles, called equilibrium ensembles , depend on only two fugacities, which determine respectively the average number of polymers and the average number of monomers (constituting the polymers). In the continuous case, a connected partition function J(/, a) can be associated with this ensemble it is defined by... 

Here/and e are the two fugacities determining the ensemble. This equation is analogous to (11.5.1) (since S oc N and e-" oc < ). When J(/, a) is known, the osmotic pressure II can be expressed, in parametric form, as a function of the average number C of polymers per unit volume and of the average total area per unit volume ((< can be considered as proportional to the monomer concentration). 

So fur we have only considered the behavior of apparently pure" acetic acid vapor. Dimerization aleo occurs in vapor mixtures containing carboxylic acide. The effect on component fugacity coefficients is easily illustrated for binary vapor mixtures containing acetic acid aed en inert substneee I. For Ibis example, the true mixture contains three species monomer, dimer, and inert. A development similar to that just preseined produces a similar expression for the dimensionless extent of reaction ... 

In [79] a SAW model of this transition was introduced. Cause et al. [79] considered pairs of SAW on the simple cubic lattice, with a common origin, which are allowed to overlap only at the same monomer position along each chain. That is to say, if one numbers the monomers from the common origin 0,1,2,... i,... n, the two chains arc mutually and individually self-avoiding except possibly where site i of the first monomer coincides with site i of the second monomer. Such overlaps are encouraged by a fugacity e, associated with such contacts. As the temperature increases, there is a transition temperature T,n above... 

The term in the brackets corresponds to the monomer fugadty in the monomer-rich phase in the case of the powder suspension polymerization (i.e., VCM polymerization). For the EPS process, the fugacities of the -pentane in the three phases should also be equal ... 

Now the addition of (J0 ) - gives a collection of chains with L links as in Fig. 47. These expressions can be more easily handled by fugacities with the result that the soup of monomers, polymers and network is contained in the expression... 

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