Deviations from Terminal Model

Klumperman and coworkers [259] observed that while it is lately quite common to treat living radical copolymerization as being completely analogous to its radical counterpart, small deviatiOTis in the copolymerization behavior do occur. They interpret the deviations on the basis of the reactions being specific to controlled/living radical polymerization, such as activation—deactivation equilibrium in ATRP. They observed that reactivity ratios obtained from atom transfer radical copolymerization data, interpreted according to the conventional terminal model deviate from the true reactivity ratios of the propagating radicals. 

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

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... 

Another model used to describe deviations from the terminal model involves the participation of a comonomer complex (Sec. 6-3b-3) [Cais et al., 1979 Coote and Davis, 2002 Coote et al., 1998 Seiner and Litt, 1971]. The comonomer complex competes with each of the individual monomers in propagation. The monomer complex participation model involves eight... 

An alternative view of the polysilane structure is depicted using the worm-like model as proposed for poly(diacetylene)s59, where the linear chain has a large number of small twists without sharp twists playing a special role60-62. In this model, a Gaussian distribution of site energies and/or exchange interactions and the coherence of the excitation is terminated by any of the numerous usual random deviations from perfect symmetry. 

Exponents 0.6 and 0.8 deviate from both the homogeneous nucleation and micellar models. Thus the bimolecular termination between the growing radicals is suppressed. This behavior may also result from the surface activity of the graft copolymer formed. The higher the surface activity of graft copolymer the higher the particle number. This behavior would indicates that the graft copolymer formed within the particles (with DBP) is more efficient. 

The model in Fig. 3.2 is sufficient to predict the general features of N E), but much more detailed calculations are needed to obtain an accurate density of states distribution. Present theories are not yet as accurate as the corresponding results for the crystalline band structure. The lack of structural periodicity complicates the calculations, which are instead based on specific structural models containing a cluster of atoms. A small cluster gives a tractable numerical computation, but a large fraction of the atoms are at the edge of the cluster and so are not properly representative of the real structure. Large clusters reduce the problem of surface atoms, but rapidly become intractable to calculate. There are various ways to terminate a cluster which ease the problem. For example, a periodic array of clusters can be constructed or a cluster can be terminated with a Bethe lattice. Both approaches are chosen for their ease of calculation, but correspond to structures which deviate from the actual a-Si H network. 

All quantitative theories based on micellar nucleation can be developed from balances of the number concentrations of particles, and of the concentrations of aqueous radicals. Smith and Ewart solved these balances for two limiting cases (i) all free radials generated in the aqueous phase assumed to be absorbed by surfactant micelles, and (ii) micelles and existing particles competing for aqueous phase radicals. In both cases, the number of particles at the end of Interval I in a batch macroemulsion polymerization is predicted to be proportional to the aqueous phase radical flux to the power of 0.4, and to the initial surfactant concentration to the power of 0.6. The Smith Ewart model predicts particle numbers accurately for styrene and other water-insoluble monomers. Deviations from the SE theory occur when there are substantial amounts of radical desorption, aqueous phase termination, or when the calculation of absorbance efficiency is in error. 

A kinetic model based on homogeneous polymerization was developed to describe the polymerization in CO2 [51, 54]. A model based on the reaction scheme in Fig. 3 adequately described the polymerization rates and the poly-dispersity of the polymer. Monomer inhibition was incorporated into the model to account for the observed deviation from first-order kinetics. However, imperfect mixing of the higher viscosity medium is an alternative explanation. It was concluded that termination was by combination, for three reasons. First, there was no existing literature to support termination by disproportionation for PVDF. Second, the polydispersity was approximately 1.5 at low monomer concentrations. Third, NMR studies showed no evidence of unsaturation. 

Tsividis, Y.P. Operation and modeling of the MOS transistor, 2nd ed., Oxford University Press, New York, 1999. The classical model also includes capacitances to a fourth MOSFET terminal, the body, which does not exist for a TFT, which has only three terminals. An accurate TFT capacitance model is therefore expected to deviate from an accurate four-terminal MOSFET model. 

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