Comonomer reactivity ratios

These structures are fictional in the sense that these sequences do not correspond to the actual statistical polymerization based on the comonomer reactivity ratio, although it was said that the results have significance with respect to Nafion structural optimization and guidance in the search for Nafion replacements. Also, the non-insignificant degree of crystallinity of Nafion was not accounted for in the model. 

After the demonstrations of preparation of stereoregular polymers having novel properties by means of special ionic methods, die possibilities of free radical methods were examined extensively. It must be concluded that in free radical systems the structures of homopolymers and copolymers can be little influenced by specific catalysts and other reaction conditions, but are determined largely by monomer structure. This is consistent with the relative uniformity of comonomer reactivity ratios in radical copolymerizations. However, it has been found possible to obtain somewhat more syndiotactic structure, dldl. than normally obtained by radical reactions, at low temperatures and by selecting solvents. Examples are polyvinyl chlorides of higher than usual crystallinity from polymerizations at low temperature e.g.. —50°C under ultraviolet light... 

From comonomer reactivity ratios, Wall (15) observed that certain critical monomer compositions were possible which he designated co-... 

The different reactivities of the olefins are important for the copolymerisation. The comonomer reactivity ratio, rj, in copolymerisation with ethylene appears to decrease with increasing steric hindrance around the double bond in the a-olefin in to the following order [250] ethylene > propylene > 1-butene > linear a-olefin > branched a-olefin. 

Otherwise, the method can be very misleading it failed badly when published data from certain copolymerizations were scrutinized by a specially developed analytical method for copolymerization data (52, 53). For these reasons, any published data on copolymerization reactivity ratios must be approached with caution, and the reader should be assured that the criteria just mentioned have been properly met. These precautions are especially true for siloxane copolymerizations, because reversibility can be established quickly, and rapid redistribution of comonomer units between rings and chains via equilibria 2 and 3 will confound any meaningful study of comonomer reactivity ratios. 

As mentioned in Chapter 1, ethylene is always the more reactive olefin in systems used to produce copolymers involving a-olefins (LLDPE and VLDPE). An important process consideration for copolymerizations is the reactivity ratio. This ratio may be used to estimate proportions needed in reactor feeds that will achieve the target resin. However, fine tuning is often required to obtain the density or comonomer content desired. Reactivity ratios were discussed previously (Chapter 2) in the context of free radical polymerization of ethylene with polar comonomers. Reactivity ratios are also important in systems that employ transition metal catalysts for copolymerization of ethylene with a-olefins to produce LLDPE. Discussions of derivations and an extensive listing of reactivity ratios for ethylene and the commonly used a-olefins are provided by Krentsel, et al. (1). 

Another aspect of free radical polymerizations under pressure which has been recently studied is the effect of pressure on comonomer reactivity ratios (5). In two copolymerization systems—styrene-acrylonitrile and methyl methacrylate-acrylonitrile—it was found that the product of the reactivity ratios, rif2, approaches unity as the pressure is increased. The monomer-polymer composition curves for these two copolymerizations at 1 and 1000 atm. are illustrated in Figures 1 and 2. The effect of pressure on the individual reactivity ratios and on the fit2 product is given in Table II. 

Simple propagation models discussed earlier fail to provide good fits when there is compositional heterogeneity in the polymer structure because of different comonomer reactivity ratios or deviations from the statistical combinations of comonomer placements on polymer chains. To overcome these drawbacks. 

Copolymerization of lactones allows the tuning of polymer properties while introducing new challenges to enzyme-catalyzed ROP such as understanding relationships between comonomer reactivity ratios, transesterification and copolymer microstructure (Scheme 4.20). 

An interesting trend is the increasing use of in situ NMR to study polymerization kinetics, curing reactions, or to determine the comonomer reactivity ratios (127). High-pressurCy high resolution NMR has been employed to study polymer/solvent interactions in poly(l,l-hydroperfluorooctyl acrylate) and its copolymer with styrene (128). 

The Phillips and Ziegler-Natta catalyst systems are actually believed to possess more than one type of catalyst "site," with each site having distinct ratios of chain-transfer to propagation rates and different comonomer reactivity ratios. 

The comonomer reactivity ratios are especially useful characteristics for a pair of monomers since a knowledge of their values allows polymer composition and microstructure to be predicted over the full range of monomer feeds. It can be shown that the monomer addition probabilities of the first-order Markov model are related to the reactivity ratios by the following expressions ... 

In a number of the examples discussed in the preceding section, comonomer reactivity ratios were used to predict sequence distributions. A number of procedures exist for deriving reactivity ratios based on copolymer/comonomer composition data. Recently, a new method for determining reactivity ratios, based on in situ NMR measurements has been derived. This method is described. In addition, some of the mathematical techniques available to calculate sequence distributions using reactivity ratios are mentioned briefly, since their use can impinge on a number of the NMR studies of sequence distributions. 

The terms A and B represent the number of moles of the two comonomers in the feed at any given instant, and and are the comonomer reactivity ratios defined earlier. The differential dA/dB is sometimes termed the instantaneous copolymer composition since it represents the composition of polymer chains forming at any instant. A variety of methods have been developed to determine the reactivity ratios. Most of these methods are based on the assumption that for conversions up to approximately 5%, the ratio of the two monomers in the feed does not change appreciably. Thus, equation (2.24) can be rewritten as... 

A new method has recently been devised for determining comonomer reactivity ratios [45], following a suggestion by Maitland that proton NMR spectroscopy can be used as a convenient monitor of free-radical copolymerisation reactions performed in situ in an NMR tube [46]. From the... 

In batch polymerisation (399), the components of the emulsion are charged into a stirred reactor, which is then heated to begin polymerisation. No material is added or removed during the entire polymerisation. Since most polymerisations are highly exothermal, the rate of heat generation can easily exceed the heat removal capabilities, and a mnaway reaction is possible. The batch polymerisation method offers little or no control over the copolymer composition, but depends upon the comonomer reactivity ratios and the partitioning of the comonomers in the latex particles (288, 340). 

In copolymerisations (70, 408), the copolymer composition may be controlled by the relative rates of monomer addition. In this way, any large differences in the comonomer reactivity ratios or water solubilities can be overcome to produce a copolymer with uniform composition. In order to maintain control of the monomer concentration in the polymer particles, the polymerisation may have to be performed under monomer-starved conditions. This means that the polymer particles are not saturated with monomer, but are being polymerised at an instantaneous conversion of 90% or greater. If the monomer addition rate is greater than the polymerisation rate, the reactor will be operating under flooded conditions, and control over the copolymer composition is lost. 

Comonomer reactivity ratios for AMD and NaAMPS are given in Table 5 (147). AMD/AMPS copolymers and AMD/NaAMPS copolymers maintain their anionic charge at low pH and have a high tolerance to many divalent cations. They are used as flocculants for phosphate slimes, uranium leach residues, and coal refuse. There are also many oilfield applications. 

Copolymerization. In free-radical copolymerization (qv), the composition of the copolymer is controlled by the comonomer reactivity ratios (23). The monomer reactivity ratio is defined as the quotient of the rate constants for chain homopropagation to the rate constant for chain cross-propagation. 

Digressing for a moment, it should be recognized that the sequence propagation probability, p, in the melt can be related to the comonomer reactivity ratio for addition type copolymerization. Formulating copolymerization kinetics in the classical manner(5), we let Fa represent the fraction of monomer Ma in the increment of copolymer formed at a given stage of the polymerization. Then one can write... 

Siloxy substitution at the 3-position of the indenyl ligand (17) was found to remarkably improve the 1-olefin copolymerization ability, whereas substitution at the 2-position (15) slightly reduced the copolymerization ability as compared to the unsubstituted 5. The reason for this was suggested to be mainly the increased coordination gap aperture of the 3-siloxy-substituted complexes. Table 1 summarizes the ethylene reactivity ratio data obtained for the siloxy-substituted complexes 15, 16, and 17 The large difference in the ethylene and comonomer reactivity ratio values, the product of which is much below unity, emphasizes the prevailing tendency of the catalysts to produce copolymers with isolated comonomer units. The reason for the 15 0% lower incorporation of 1-hexadecene than 1-hexene was explained by the higher steric bulk and lower rate of diffusion of the longer a-olefin. 

Brar and Sunita [58] described a method for the analysis of acrylonitrile-butyl acrylate (A/B) copolymers of different monomer compositions. Copolymer compositions were determined by elemental analyses and comonomers reactivity ratios were determined using a non-linear least squares errors-in-variables model. Terminal and penultimate reactivity ratios were calculated using the observed distribution determined from C( H)-NMR spectra. The triad sequence distribution was used to calculate diad concentrations, conditional probability parameters, number-average sequence lengths and block character of the copolymers. The observed triad sequence concentrations determined from C( H)-NMR spectra agreed well with those calculated from reactivity ratios. 

Under these conditions, the 1-hexene/ethylene vapor ratio is 0.126 and the hydrogen/ethylene vapor ratio is 0.366. This information is sufficient for determining kinetic data, comonomer reactivity ratios and the effect of hydrogen on polyethylene molecular weight. 

Online H NMR measurements were r rted by Abdollahi et al. [171] in a recent study of the free-radical copolymerization of vinyl acetate (VA) and Me acrylate (MA) in ben-zene-d at 60°C, with benzoyl peroxide (BPO) as initiator. A significant composition drift in the comonomer mixture was observed as the reaction progressed. The comonomer reactivity ratios were calculated using the data collected only from one sample via online monitoring of the comonomer mixture and copolymer compositions at different reaction time intervals up to medium overall monomer conversions. The results were in good agreement with the fiteratme data reported for this system, indicating the accuracy of the monomer reactivity ratios calculated by the procedme developed in the study. 

Ethene high-pressure copolymerization smdies have also been carried out for the systems E-MMA, E-BMA, E-acrylic acid, and E-methacrylic acid. Whereas the comonomer reactivity ratios turn out to be slightly different, the ethene reactivity ratios for the entire set of (meth)acrylates and for (meth) acrylic acid are remarkably close to each other. The similarity of rE = feEE/ Ex is probably due to the crosstermination propagation rate coefScient rate ftEx being dominated by the highly reactive ethene-terminated radical. ... 

Arrhenius equations such as eqns [25]-[28] and/or the corresponding expressions presented in References 96 and 99 allow for estimating ethene and comonomer reactivity ratios... 

The sequence propagation probability p can be related to the comonomer reactivity ratio in a straightforward manner. The problem can be further generalized to the case where p is influenced by the penultimate group. ... 

Kapur and Brar [179] prepared acrylonitrile-ethyl methacrylate (A/E) copolymers of different monomer concentrations in bulk by free radical initiation. Copolymer composition was determined by nitrogen analysis and the comonomer reactivity ratios were determined by the method of Kelen-Tiidos. C-NMR spectra of several A/E copolymers are discussed in terms of their triad monomer sequence and cotacticity. Terminal and penultimate reactivity ratios were calculated using the observed monomer triad sequence distribution determined from C-NMR spectroscopy for individual samples. Triad sequence distribution was used to calculate dyad concentrations, probability parameters, number average sequence lengths, and the comonomer mole fractions in the copolymers. The configurational sequence distributions in terms of all the 10 A-centred and 10 E-centred triad cotactic sequences have been determined and found to be in excellent agreement with those obtained using various cotactic probability parameters. 

Instractive example of the copolymerization involving monomer propagating reversibly comes from the L,L-lactide (LA)/ecopolymerization system, by means of the numerical integration method [183], revealed that the comonomers reactivity ratios can be controlled by the configuration of the active species [184]. Thus, using initiator of various stereochemical compositions a broad spectrum of copolymers... 

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