Nonideal polymerization

A given polymerization conforming strictly to the reaction scheme (6.3) to (6.10) is commonly considered as an ideal polymerization. Any system deviating from this pattern of reaction is to be considered as a case of nonideal polymerization. The ideal behavior prescribes constancy of the term / [l] [M] ), according to Eq. (6.26) expressed as... 

Barnes and co-workers have studied mixed-monolayer systems [278,281,283,284] and found some striking nonidealities. Mixed films of octadecanol and cholesterol, for example, show little evaporation resistance if only 10% cholesterol is present [278] apparently due to an uneven granular microstructure in films with cholesterol [284]. Another study of cellulose decanoate films showed no correlation between holes in the monolayer and permeation rate [285]. Polymerized surfactants make relatively poor water evaporation retarders when compared to octadecanol [286]. There are problems in obtaining reproducible values for r [287] due to impurities in the monolayer material or in the spreading solvent. 

Because of this parallel with liquid-vapor equilibrium, copolymers for which ri = l/r2 are said to be ideal. For those nonideal cases in which the copolymer and feedstock happen to have the same composition, the reaction is called an azeotropic polymerization. Just as in the case of azeotropic distillation, the composition of the reaction mixture does not change as copolymer is formed if the composition corresponds to the azeotrope. The proportion of the two monomers at this point is given by Eq. (7.19). 

Those involving solution nonideality. This is the most serious approximation in polymer applications. As we have already seen, the large differences in molecular volume between polymeric solutes and low molecular weight solvents is a source of nonideality even for athermal mixtures. 

Our primary objective in this section is the discussion of practical osmometry, particularly with the goal of determining the molecular weight of a polymeric solute. We shall be concerned, therefore, with the design and operation of osmometers, with the question of units, and with circumventing the problem of nonideality. The key to these points is contained in the last section, but the details deserve additional comment. 

In continuation of this series, Saini et al. [24] studied the initiation effect of a-PCPY on the polymerization of MMA [28] and MA [29]. The systems followed nonideal kinetics in both cases, which was explained in terms of... 

More recent studies, particularly with slower hafnium complexes, have provided more detailed mechanistic insight As a step polymerization, the reaction is "nonideal" in that inequivalent reactivities for different Si-H functional groups in the system are observed. For exaniple, disilanes tend to be more reactive than monosilanes. Beyond disilane formation, the preferred dehydrocoupling reaction appears to involve addition of one silicon at a time to the growing chain, via M-S1H2R intermediates (n = 1 above). The Si-Si bond-forming reactions are also reversible. 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

Because of the highly nonideal behavior of polymer-solvent solutions, polymer-vapor equilibrium relations account for the third major difference found in stripping operations with polymeric solutions. The appro-... 

The problem at hand with Equation 74 is how to deal with the quantity , and this complication is what has stymied sedimentation equilibrium work with nonideal solutions containing polymeric solutes. This problem has been discussed by Goldberg (29), Wales (6), and Fujita (17). One way to overcome the problem is to assume that... 

Here BLS is the second virial coefficient of the polymeric solute in the original solution before ultracentrifugation. BLs is a quantity which can be obtained in light-scattering experiments (17, 25, 30) or in Archibald experiments (31), provided it is calculated from a plot of l/MWapp° vs. c. Here 1/Mw pp° is obtained from values of Mw pp (at rm or rb) that have been extrapolated to zero time. The reason for using Equation 75 is that it leads to a simple method of estimating the MWD in nonideal solutions. 

But Leonard and Ivin point out, Tc is not given by A HlcjA Slc since this takes no account of the partial molar free energies of the monomer and polymer. This can be seen in Fig. 4 which shows that AFlcjRT is positive above 37° C, suggesting that polymerization will not occur above this temperature. Experimentally (Fig. 1) at 37° C approximately 65 % conversion to polymer is obtained and in fact polymerization continues to occur up to about 85° C. Practically, it would seem that either THF behaves ideally enough to justify the use of equation (1) for the derivation of meaningful heat and entropy terms for the derivation of Te or nonidealities fortuitously cancel out. It should be understood that terms derived from equation 1 will include terms for the removal of monomer and addition of polymer to the polymer-monomer mixture. 

The free radical polymerization of DADMAC (M,) with vinyl acetate (M2) in methanol proceeds as a nonideal and nonazeotropic copolymerization with monomer reactivity ratios rx=1.95 and r2=0.35 were obtained [75]. The resulting low molar mass copolymers were reported to be water soluble over their whole range of composition. Modification of the vinyl acetate unit by hydrolysis, ace-talization, and acylation resulted in DADMAC products with changed hydrophilic or polyelectrolyte properties [75]. For the copolymerization of DADMAC and AT-methyl-AT-vinylacetamide (NMVA) a nearly ideal copolymerization behavior could be identified [45]. The application properties of the various copolymer products will be discussed in Sect. 8. 

A nonideal network may be obtained as in the previous case but using different nonstoichiometric molar ratios or arresting the polymerization at different conversions, to modify the structure. In these cases, the presence of a sol fraction and dangling chains will introduce an additional plasticization effect, surimposed on the new architecture (Vallo et al., 1993). 

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