Heterogeneity compositional

The existence of an azeotropic composition has some practical significance. By conducting a polymerization with the monomer feed ratio equal to the azeotropic composition, a high conversion batch copolymer can be prepared that has no compositional heterogeneity caused by drift in copolymer composition with conversion. Thus, the complex incremental addition protocols that arc otherwise required to achieve this end, are unnecessary. Composition equations and conditions for azeotropic compositions in ternary and quaternary eopolymerizations have also been defined.211,21... 

The copolymer composition equation only provides the average composition. Not all chains have the same composition. There is a statistical distribution of monomers determined by the reactivity ratios. When chains are short, compositional heterogeneity can mean that not all chains will contain all monomers. 

In early work, while compositional heterogeneity was recognized and could be predicted, it was difficult to measure. Now, methods such as GPC combined with NMR and/or MALDI,238 239 GPC coupled with FTIR240 and two dimensional HPLC or GPC241"245 can provide a direct measure of the composition distribution. 

Chain compositional heterogeneity is of particular relevance to functional copolymers which find widespread use in the coalings and adhesives industries.13,240,246 In these applications, the functional copolymer and a crosslinking agent are applied together and are cured to form a network polymer. The functional copolymers are based on functional monomers with reactive groups (e.g. OH), it is desirable that all copolymer molecules have a functionality of at least two. Nonfunctional polymer will not be incorporated and could plasticize the network or be exuded from the polymer. Monofunctional polymers are not involved in crosslink formation and will produce dangling ends. 

The influence of selectivity in the initiation, termination or chain transfer steps on the distribution of monomer units within the copolymer chain is usually neglected. Galbraith et a .u provided the first detailed analysis of these factors. They applied Monte Carlo simulation to examine the influence of the initiation and termination steps on the compositional heterogeneity and molecular weight distribution of binary and ternary copolymers. Spurting et a/.250 extended this... 

The effect of the initiation and termination processes on compositional heterogeneity can be seen in data presented in Figure 7.3 and Figure 7.4. The data come from a computer simulation of the synthesis of a hydroxy functional oligomer prepared from S, BA, and HEA with a thiol chain transfer agent. The recipe is similar to those used in some coatings applications. 

It is possible to exercise control over this form of compositional heterogeneity (i. e. the functionality distribution) by careful selection of the functional monomer and/or the transfer agent taking into account the reactivities of the radical species, monomers, and transfer agents, and their functionality.11 250 Relative reactivities of initiator and transfer agent-derived radicals towards monomers are summarized in Section 3.4. Some values for transfer constants are provided in Chapter 6. 

This polymeric oxocarbenium salt readily initiates the cationic ring opening polymerization of oxolane to produce a polystyrene-polyTHF block copolymer. Molecular weight control is provided, polydispersity is narrow and compositional heterogeneity is small59). 

The synthesis of well defined block copolymers exhibiting controlled molecular weight, low compositional heterogeneity and narrow molecular weight distribution is a major success of anionic polymerization techniques 6,7,14-111,112,113). Blocks of unlike chemical nature have a general tendency to undergo microphase separation, thereby producing mesomorphic phases. Block copolymers therefore exhibit unique properties, that prompted numerous studies and applications (e.g. thermoplastic elastomers). 

Miller J.A., Speckhard T.A., Homan J.G., and Cooper S.L. Monte Carlo simulation study of the pol3mier-ization of polyurethane block co-polymers. 4. ModeUng of experimental data. Polymer, 28, 758, 1987. Speckhard T.A., Miller J.A., and Cooper S.L., Monte Carlo simulation study of polymerization of polyurethane block co-pol3miers. 1. Natural compositional heterogeneity under ideal polymerization condition, Macromolecules, 19, 1550, 1986. 

Copolymers synthesized under conversion of less than ten percent exhibit composition heterogeneity substantially exceeding that predicted by the traditional theories. 

In conjunction with molecular weight sensitive detection systems, SEC can be used for determining various molecular weight parameters, such as molecular size, conformation and branching, as a function of MW. Furthermore, by interfacing SEC with spectrometry, polymer compositional heterogeneity can be determined. 

Applications Applications of SEC-FTIR include quantitative analysis of copolymers [701] product deformulation of hot melt adhesives characterisation of polymer compositional heterogeneity analysis of complex mixtures of urethane oligomers and eventually also the identification and quantitative analysis of polymer additives... 

Partially Crystalline Transition Metal Sulphide Catalysts. Chiannelli and coworkers (6, 7, 8) have shown how, by precipitation of metal thio-molybdates from solution and subsequent mild heat-treatment many selective and active hydrodesulphurization catalysts may be produced. We have shown (18) recently that molybdenum sulphide formed in this way is both structurally and compositionally heterogeneous. XRES, which yields directly the variation in Mo/S ratio shows up the compositional nonuniformity of typical preparations and HREM images coupled to SAED (see Figure 2) exhibit considerable spatial variation, there being amorphous regions at one extreme and highly crystalline (18, 19) MoS at the other. 

Figure 2. These high-resolution micrographs show how a so-called x-ray amorphous, nonstoichiometric molybdenum sulfide catalyst exhibits structural (as well as compositional) heterogeneity. Amorphous, quasi-crystalline, and crystalline regions coexist at the ultramicro level (18,).

N and 0, in solid material. The second point is that EXELFS is especially suitable for the study of inhomogeneous samples (structurally and compositionally heterogeneous in the sense discussed in section 2.2 above) because the primary electron beam can be focussed to a diameter of ca 20. Other advantages of EXELFS have been discussed elsewhere (60, 61). The limitations of the technique include (i) the need to select an optimal thickness of sample so as to minimize multiple scattering and (ii) the susceptibility of the samples to suffer radiation damage. 

The alternating tendency of the copolymers is advantageous in that the polymerizations can be carried out to high conversions with little or no compositional drift. For random copolymerizations in which there is preferential incorporation of one monomer due to a mismatch in reactivity ratios, the compositional variations with conversion can be substantial. Such compositional heterogeneities in resist materials can lead to severe problems during image development. 

The use of simultaneous equations with at least three sets of experimental data can, however, be applied to Eq. (101) or (102) to yield M, MA and MB. This is especially useful, if the specific co-ordinates of the whole parabola cannot be realised experimentally as is often the case. The data159-1 in Table 14 relate to a random copolymer of styrene (A)/di-n-butyl itaconate (B) in which WA = 0.169. Solution of simultaneous equations [Eq. (101)] yields M = 67300, MA = 56800 and MB =64700. The compositional heterogeneity is such that the data conform to the required theoretical relationship149 ... 

On the assumption of some finite compositional heterogeneity, Eq. (101) reveals the following criteria necessary for the most sensitive determination of the relevant molecular weights152 ... 

Characterisation of A/B/C terpolymers is still in its infancy, but there are already clear indications that, in a compositionally heterogeneous terpolymer, the determination of molecular weights MA, MB, Mc and M may prove an intractable problem in the general case. Apart from some semi-quantitative studies, most effort in this direction has been made by Kambe, Kambe and collaborators162,163, who extended the original approach of Bushuk and Benoit164. ... 

The existence of compositional heterogeneity may be evidenced by the dependence of the measured v on the extent of conversion of monomers to terpolymer for a random terpolymer163) (Fig. 56). Other data on the same diagram demonstrate that composition and v remain sensibly constant with conversion for a partial azeotrope. These observations are corroborated by the LS results in Table 15, which show that for the random terpolymer, M varies between 2.63 x 10s and 4.05 x 10s (that is, by about 50%) according to the solvent used. In contrast, for the partial... 

Solvent M x 10-4 Partially azeotropic terpolymer Compositionally heterogeneous terpolymer... 

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