Copolymer, composition sequence

In Section 2.4 we consider copolymers. The determination, by MS techniques, of various quantities (such as copolymer composition, sequence distribution, composition heterogeneity, reactivity ratios, and bivariate distribution of chain compositions and chain lengths) are of major interest for the characterization of copolymers. 

Using either form of the equation, one can calculate the instantaneous comonomer feed composition as a function of the conversion, knowing the initial feed composition. This can then be used to calculate the copolymer composition, sequence distribution, and propagation rate using the corresponding instantaneous equations. 

Equations (7.40) and (7.41) suggest a second method, in addition to the copolymer composition equation, for the experimental determination of reactivity ratios. If the average sequence length can be determined for a feedstock of known composition, then rj and r2 can be evaluated. We shall return to this possibility in the next section. In anticipation of applying this idea, let us review the assumptions and limitation to which Eqs. (7.40) and (7.41) are subject ... 

Item (2) requires that each event in the addition process be independent of all others. We have consistently assumed this throughout this chapter, beginning with the copolymer composition equation. Until now we have said nothing about testing this assumption. Consideration of copolymer sequence lengths offers this possibility. 

These observations suggest how the terminal mechanism can be proved to apply to a copolymerization reaction if experiments exist which permit the number of sequences of a particular length to be determined. If this is possible, we should count the number of Mi s (this is given by the copolymer composition) and the number of Mi Mi and Mi Mi Mi sequences. Specified sequences, of any definite composition, of two units are called dyads those of three units, triads those of four units, tetrads those of five units, pentads and so on. Next we examine the ratio NmjMi/Nmi nd NmjMiMi/NmiMi If these are the same, then the mechanism is shown to have terminal control if not, it may be penultimate control. To prove the penultimate model it would also be necessary to count the number of Mi tetrads. If the tetrad/triad ratio were the same as the triad/dyad ratio, the penultimate model is proved. 

Methyl-2-furaldehyde gave a similar overall behaviour, but a penultimate effect was observed in its copolymerization with isopropenylbenzene whereby two molecules of the aldehyde could add together if the penultimate unit in the growing chain was from the olefin. This was borne out by the copolymers composition and spectra. The values of the reactivity ratios showed this interesting behaviour rx = 1.0 0.1, r2 = 0.0 0.1. An apparent paradox occurred the aldehyde, which could not homo-polymerize, had equal probability of homo- and copolymerization and the olefin, which homopolymerized readily, could only alternate. The structure arising from this situation was close to a regular sequence of the type ... 

Tire simplest model for describing binary copolyinerization of two monomers, Ma and Mr, is the terminal model. The model has been applied to a vast number of systems and, in most cases, appears to give an adequate description of the overall copolymer composition at least for low conversions. The limitations of the terminal model generally only become obvious when attempting to describe the monomer sequence distribution or the polymerization kinetics. Even though the terminal model does not always provide an accurate description of the copolymerization process, it remains useful for making qualitative predictions, as a starting point for parameter estimation and it is simple to apply. 

In traditional treatments of copolymerizaiion kinetics, the values of the ratios sA and % are implicitly set equal to unity (Section 7.3.1.2.2). Since they contain no terms from cross propagation, these parameters have no direct influence on either the overall copolymer composition or the monomer sequence distribution they only influence the rate of polymerization. 

Methods for evaluation of reactivity ratios comprise a significant proportion of the literature on copolymerization. There are two basic types of information that can be analyzed to yield reactivity ratios. These are (a) copolymer composition/convcrsion data (Section 7.3.3.1) and (b) the monomer sequence distribution (Section 7.3.3.2). The methods used to analyze these data are summarized in the following sections. 

The solvent in a bulk copolymerization comprises the monomers. The nature of the solvent will necessarily change with conversion from monomers to a mixture of monomers and polymers, and, in most cases, the ratio of monomers in the feed will also vary with conversion. For S-AN copolymerization, since the reactivity ratios are different in toluene and in acetonitrile, we should anticipate that the reactivity ratios are different in bulk copolymerizations when the monomer mix is either mostly AN or mostly S. This calls into question the usual method of measuring reactivity ratios by examining the copolymer composition for various monomer feed compositions at very low monomer conversion. We can note that reactivity ratios can be estimated for a single monomer feed composition by analyzing the monomer sequence distribution. Analysis of the dependence of reactivity ratios determined in this manner of monomer feed ratio should therefore provide evidence for solvent effects. These considerations should not be ignored in solution polymerization either. 

The effect of propagation-depropagation equilibrium on the copolymer composition is important in some cases. In extreme cases, depolymerization and equilibration of the heterochain copolymers become so important that the copolymer composition is no longer determined by the propagation reactions. Transacetalization, for example, cannot be neglected in the later stages of trioxane and DOL copolymerization111, 173. This reaction is used in the commercial production of polyacetal in which redistribution of acetal sequences increases the thermal stability of the copolymers. 

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

In analysis of homopolymers the critical interpretation problems are calibration of retention time for molecular weight and allowance for the imperfect re >lution of the GPC. In copolymer analysis these interpretation problems remain but are ven added dimensions by the simultaneous presence of molecular weight distribution, copolymer composition distribution and monomer sequence length distribution. Since, the GPC usu y separates on the basis of "molecular size" in solution and not on the basB of any one of these particular properties, this means that at any retention time there can be distributions of all three. The usual GPC chromatogram then represents a r onse to the concentration of some avera of e h of these properties at each retention time. 

V. Copolvmerization Kinetics. Qassical copolymerization kinetics commonly provides equations for instantaneous property distributions (e.g. sequence length) and sometimes for accumulated instantaneous (i.e. for high conversion samples) as well (e.g. copolymer composition). These can serve as the basis upon whkh to derive nations which would reflect detector response for a GPC separation based upon properties other than molecular weight. The distributions can then serve as c bration standards analagous to the use of molecular weight standards. 

When calculating the average copolymer composition and the probabilities P Uk] of the sequences of monomeric units it is possible to set Ta=0 in the expressions in (7), that is to neglect the finiteness of the size of the macromolecules. In this case the absorbing Markov chain (7) is replaced by the ergodic Markov chain with transition matrix Q whose elements ... 

A user-friendly computer program has been developed (A.S.Yakovlev, S.LKuch-anov Copolymerization for Windows ) which makes it possible at any values of conversion to calculate for m=2-6 along with the composition of monomer mixture x, such statistical characteristics as instantaneous X and average (x j copolymer composition as well as the fractions (P Uk of sequences Uk with k=2-4 and... 

The spectra of copolymers of MMA and MAA are poorly resolved, and although the 0-methylene and o-methyl signals show structure, very little quantitative information is available. The butyl resonances at 0.8, 1.2, 1.3, and 1.6 ppm overwhelm the useful proton signals at the 0-methylene and o-methyl psoitions, i.e., the resolution is poor because of compositional sequencing. 

Butadiene-Styrene Copolymers from Ba-Mg-Al Catalyst Systems. Figure 13 shows the relationship between copolymer composition and extent of conversion for copolymers of butadiene and styrene (25 wt.7. styrene) prepared in cyclohexane with Ba-Mg-Al and with n-BuLi alone. Copolymerization of butadiene and styrene with barium salts and Mg alkyl-Al alkyl exhibited a larger initial incorporation of styrene than the n-BuLi catalyzed copolymerization. A major portion of styrene placements in these experimental SBR s are more random however, a certain fraction of the styrene sequences are present in small block runs. 

The value in units of incident dose per unit area for either a positive or negative resist system is of little value unless accompanied by a detailed description of the conditions under which it was measured. This description should include, at the minimum, the initial film thickness, the characteristics of the substrate, the temperature and time of the post- and pre-bake, the characteristics of the exposing radiation, and the developer composition, time and temperature. The structure, copolymer ratio, sequence distribution, molecular weight, and dispersity of polymers included in the formulation should also be provided. 

The implicit penultimate model was proposed for copolymerizations where the terminal model described the copolymer composition and monomer sequence distribution, but not the propagation rate and rate constant. There is no penultimate effect on the monomer reactivity ratios, which corresponds to... 

Figure 2 Property distributions in a linear copolymer composition distribution, molecular weight distribution and sequence length distribution of poly styrene-co-n-butyl methacrylate). (Styrene units are represented by "A and n-butyl methacrylate units by B".)...

Anionic polymerizations initiated with alkyllithium compounds enable us to prepare homopolymers as well as copolymers from diene and vinylaromatic monomers. These polymerization systems are unique in that they have precise control over such polymer properties as composition, microstructure, molecular weight, molecular weight distribution, choice of functional end groups and even copolymer monomer sequence distribution. Attempts have been made in this paper to survey these salient features with respect to their chemistry and commercial applications. 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

It should be emphasized that copolymerizations that conform to the premises of binary-copolymerization theory produce copolymers of well defined structure. The kinetics of the competitive propagation-reactions determine not only the copolymer composition but also the sequence distribution. The mathematical procedures needed for calculating number-average sequence-lengths of mers, and sequence length-distributions of mers, are well known and have been... 

Wu, Ovenall and Hoehn have published a detailed study of the H- ajid 13C-NMR spectra of the QH —CO copolymers with varied QH /CO ratios, comparing them with appropriate model compounds 48). Based on their work, it is possible to determine copolymer compositions, comonomer sequence distributions, end groups, branching and conformational transitions in these copolymers. 

The problem of predicting copolymer composition and sequence in the case of chain copolymerizations is determined by a set of differential equations that describe the rates at which both monomers, Ma and MB, enter the copolymer chain by attack of the growing active center. This requires a kinetic model of the copolymerization process. The simplest one is based on the assumption that the reactivity of a growing chain depends only on its active terminal unit. Therefore when the two monomers MA and MB are copolymerized, there are four possible propagation reactions (Table 2.17). 

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