Reactivity ratios differential

VEs do not readily enter into copolymerization by simple cationic polymerization techniques instead, they can be mixed randomly or in blocks with the aid of living polymerization methods. This is on account of the differences in reactivity, resulting in significant rate differentials. Consequendy, reactivity ratios must be taken into account if random copolymers, instead of mixtures of homopolymers, are to be obtained by standard cationic polymeriza tion (50,51). Table 5 illustrates this situation for butyl vinyl ether (BVE) copolymerized with other VEs. The rate constants of polymerization (kp) can differ by one or two orders of magnitude, resulting in homopolymerization of each monomer or incorporation of the faster monomer, followed by the slower (assuming no chain transfer). 

Copolymerization. The solid phase of the precipitation polymerization also influences copolymer composition, since differential monomer adsorption on the polymer particles considerably modifies the effective reactivity ratios of the comonomers. This problem has been discussed by several authors (22,23,24,25,26). 

Barrett and Thomas (10)proposed that these effects of differential monomer adsorption could be modeled by correcting homogeneous solution copolymerization reactivity ratios with the monomer s partition coefficient between the particles and the diluent. The partition coefficient is measured by static equilibrium experiments. Barrett s suggested equations are ... 

GPC is a promising method for examination of template polymerization, especially copolymerization. Copolymerization of methacrylic acid with methyl methacrylate in the presence of polyCdimethylaminoethyl methacrylate) can be selected as an example of GPC application for examination of template processes. The process was carried out in tetrahydrofurane as solvent at 65°C. After proper time of polymerization, the samples were cooled, diluted by THF, filtered, and injected to GPC columns. Two detectors on line UV and differential refractometer, DRI, were applied. UV detector was used to measure concentration of two monomers, while the template was recorded by DRI detector (Figure 11.3) The decrease in concentration ofboth monomers can be measured separately. It was found that a big difference in the rate of polymerization between template process and blank polymerization exists. The rate measured separately for methacrylic acid (decrease of concentration of methacrylic acid in monomers mixture) was much higher in the template process. Furthermore, the ratio ofboth monomers changes in a different manner. Reactivity ratios for both monomers can be computed. Decrease in concentration during the process is shown in Figure 11.4. 

In the alkyllithium initiated polymerizations of vinyl monomers, Lewis bases such as ethers and amines alter the kinetics, stereochemistry, and monomer reactivity ratios for copolymerization. In general, the magnitude of these effects has been directly or indirectly attributed to the extent or nature of the interaction of the Lewis base with the organolithium initiator or with the organolithium chain end of the growing polymer. Unfortunately, all of these observed effects are kinetic in nature, and therefore the observed effects of solvent represent a composite effect on the transition-state versus the ground state as shown below in Eq. (6), where 5 represents the differential... 

Another reason for errors of the reactivity ratio values are an exactitude in the course of the treatment of the experimental data using the differential or integrated form of the copolymer composition equation. In the first pase, the dependence of X(x°) on the monomer feed composition x° experimentally determined at low conversions is used. In the second case, one should use the data on the dependence of the copolymer composition on conversion p or the current values of x under the measurements of p. 

When r, r2 values are rather close to unity, one can use for their estimation the so-called approximation method [225, 256-258]. Its idea is based on the fact that if the copolymerization is carried out at low concentrations of one of the monomers, the instantaneous composition of the copolymer depends only on one reactivity ratio. In this case the composition equation in both differential and integrated forms is fairly simple. 

Fig. 2. (A) A schematic diagram of equine Cyt c from the front of the heme crevice. The approximate positions of the /8-carbons of the lysine residues are indicated by closed and dashed circles for residues located toward the front and back of the molecule, respectively. Differential chemical modification indicates that some residues are protected by both flavocytochrome c-552 and mitochondrial redox partners (cross-hatched), or only by flavocytochrome c-552 (hatched), or only by mitochondrial enzymes (stippled). (B) Comparison of reactivity ratios (R) obtained by differential chemical modification of equine Cyt c in the presence and absence of flavocytochrome c-552 (filled bars), mitochondrial Cyt foe, complex (left open bar) and mitochondrial Cyt c oxidase (right open bar). Data for mitochondrial redox partners are from Ref. 98. In the case of the mitochondrial redox partners, R values for lysines 55, 72 and 99 are average values for lysines 53-t-55, 72+73 and 99+100. The R values represent, after a series of corrections, the ratio of acetylation of a specific lysine residue in free Cyt c to the acetylation of the same residue in the Cyt c flavocytochrome c-552 complex. The larger the R value, the greater the extent of protection against acetylation.

Another important recent contribution is the provision of a good measurement of the precision of estimated reactivity ratios. The calculation of independent standard deviations for each reactivity ratio obtained by linear least squares fitting to linear forms of the differential copolymer equations is invalid, because the two reactivity ratios are not statistically independent. Information about the precision of reactivity ratios that are determined jointly is properly conveyed by specification of joint confidence limits within which the true values can be assumed to coexist. This is represented as a closed curve in a plot of r and r2- Standard statistical techniques for such computations are impossible or too cumbersome for application to binary copolymerization data in the usual absence of estimates of reliability of the values of monomer feed and copolymer composition data. Both the nonlinear least squares and the EVM calculations provide computer-assisted estimates of such joint confidence loops [15]. 

Various methods have been used to obtain monomer reactivity ratios from the copolymer composition data. Several procedures for extracting reactivity ratios from the differential copolymer equation [Eq. (7.11) or... 

Also known as the method of intersections, the method first described by Mayo and Lewis [3] has been widely used for computing reactivity ratios from data fitted to the differential copolymer equation. In this procedure, Eq. (7.11) is recast to the form... 

The monomer reactivity ratios r and r2 can be determined from the experimental conversion-composition data of binary copolymerization using both the instantaneous and integrated binary copolymer composition equations, described previously. However, in the former case, it is essential to restrict the conversion to low values (ca. < 5%) in order to ensure that the feed composition remains essentially unchanged. Various methods have been used to obtain monomer reactivity ratios from the instantaneous copolymer composition data. Several procedures for extracting reactivity ratios from the differential copolymer equation [Eq. (7.11) or (7.17)] are mentioned in the following paragraphs. Two of the simpler methods involve plotting of r versus r2 or F versus f. ... 

Because of the ease of synthesis and industrial importance of diallyl esters much of the research has dealt with the behavior of the isomeric phthalates. Some other dicarboxylic acid esters have been studied by Simpson and Holt [41]. The kinetics of the poljmierization of the diallyl esters of oxalic, malonic, succinic, adipic, and sebacic acid have also been considered. In previous kinetie studies, no differentiation was made between the behavior of the uncyclized monomer (or its free radical) and of the cyclic free-radicals. A priori, differences should have been presumed, but evidently Matsumoto and Oiwa [46] were the first seriously to attempt a kinetic analysis based on the concept that the linear and the cyclic units are two different species. In effect, these two species copolymerize with each other. However, the analysis has not been carried so far as to determine reactivity ratios. 

Copolymers are made to produce unique or functional properties in the polymeric product. The properties of step copolymers can be understood and, in some cases, predicted from an analysis of the chain length and functional groups in the monomers. The composition and composition-dependent properties of a free radical, chain reaction copolymer can be predicted from monomer reactivity ratios, a property first correctly quantified in 1944 (11-14). These ratios have been extensively measured and tabulated (15). They allow, by use of differential equations, the calculation of the monomer content in a copolymer as a function of time during the reaction. Reactivity ratios have also been measured for cationic chain reactions (16). Anionic chain reactions in monomer mixtures are generally so fast and indiscriminate that reactivity ratios are meaningless. 

It is immaterial here which monomer is termed 1 or 2. Both growing ends participate in the competition for a monomer, so that both reactivity ratios have to be discussed together. The reactivity ratios, however, depend on the probability of addition. In order to differentiate between the various types of copolymerization, therefore, it is necessary to consider the product of the reactivity ratios r r2-... 

In by far the largest number of cases of free radical copolymerization, the reactivity ratios are practically independent of the nature of the starting reaction (thermal, photochemical, radical-forming type) and the site of propagation (bulk, solution, emulsion). Ionic copolymerization, by contrast, leads to quite different parameters (Table 22-13). Thus copolymerizations can be employed as a diagnostic tool for initiators whose mode of action is unknown, differentiating between free radical copolymerization and the nonradical mechanism (Table 22-14). On such evidence, boron alkyls appear to be free radical initiators in the copolymerization of methyl methacrylate with acrylonitrile, whereas lithium alkyls are anionic initiators. 

Using HRTOF crossed molecular beam technique, we studied the F( P) + D2 DF + D reaction systematically. The differential cross sections and the relative integral cross sections in this reaction were provided. We measured the F( P3/2)/ F ( Pi/2) r tio in the F atom beam and thus got the F( P3/2)/F ( Pi/2) reactivity ratio, which is in perfect agreement with the theoretical results. In Sect. 4.1 of this chapter, we review non-adiabatic efifects in the F -b H2 system the measurement of the F( P3/2)/F ( Pi/2) ratio in the F atom beam is described in Sects. 4.2, 4.3 presents the crossed molecular beam experimental results and discussion summary is given in the last section. 

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... 

Several procedures for extracting reactivity ratios from differential forms of the copolymer equation are mentioned in the following paragraphs. These methods are arithmetically correct, but they do not give reliable results because of the nature of the experimental uncertainties in reactivity ratio measurements. 

During the polymerisation the heat released by the polymerisation reaction can be determined online from temperature measurements, see these references for details about reaction calorimetry - MacGregor (1986), Bonvin et al (1989), Moritz (1989), Schuler and Schmidt (1992). Calorimetric measurements can be used to infer the free amount of monomers in the copolymerisation and also the overall conversion (Urretabizkaia et al, 1993 Gugliotta etal, 1995c Hammouri etal, 1999 Saenz de Buruaga etal, 2000) by means of an observer/estimator. Basically the estimator solves the monomer material balance differential equations using the heat of reaction as input variable instead of the theoretical polymerisation rate. Therefore, the estimator uses the enthalpies of polymerisation of the monomers and the reactivity ratios as parameters. This information is compared with the... 

The ratio of palmitic acid to stearic acid (P/S) can be used to differentiate between drying oils, since these two saturated monocarboxylic acids are less subject to chemical reactions during treatment and ageing. Also, they have a similar chemical reactivity, so their ratio can be hypothesized to be relatively unaltered during ageing. The P/S ratio approach was pioneered by Mills [10], and has been subsequently adopted in a number of studies [7 9]. Typical values of the P/S ratio are 1 2 for linseed oil, 2 3 for walnut oil, 3 8 for poppy seed oil and 2.5 3.5 for egg. 

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