Copolymer composition instantaneous

The reversibility of supramolecular polymers adds new aspects to many of the principles that are known from condensation polymerizations. A mixture of different supramolecular monomers, for example, will yield copolymers, but it is extremely simple to adjust the copolymer composition instantaneously by adding an additional monomer. Moreover, the use of monomers with a functionality of three or more, will give rise to a network formation. However, in contrast to condensation networks, the self-healing supramolecular network can reassemble to form the thermodynamically most favorable state, thus forming denser networks.121... 

FIGURE 16.1 Copolymer composition. Instantaneous copolymer composition (Fj) as a function of monomer composition (/, ) for random copolymerization with r =l/r as indicated. This material is reprodnced with permission of John Wiley Sons, Inc from Billmeyer FW. Textbook of Polymer Science. 3rd ed. New York Wiley 1984. 

This equation relates the (instantaneous) copolymer composition with the monomer feed of M and M2. Values for and are usually determined by graphical methods (9,10). Today, with the prevalence of powerful desktop computers, numerical minimisa tion methods are often used (11—14). 

The ratio of these equations provides an expression for the instantaneous copolymer composition (eq. 3). 

Figure 7.1 Plot of the instantaneous copolymer composition (FA) v.s monomer feed...

The instantaneous copolymer composition is described by the following equation (eq. 12) ... 

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. 

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... 

In order to obtain the expression for the components of the vector of instantaneous copolymer composition it is necessary, according to general algorithm, to firstly determine the stationary vector ji of the extended Markov chain with the matrix of transitions (13) which describes the stochastic process of conventional movement along macromolecules with labeled units and then to erase the labels. In this particular case such a procedure reduces to the summation ... 

Upon expressing from the equilibrium condition the complex concentration M12 through the concentrations of monomers, and substituting the expression found into relationship (21) we obtain, invoking the formalism of the Markov chains, final formulas enabling us to calculate instantaneous statistical characteristics of the ensemble of macromolecules with colored units. A subsequent color erasing procedure is carried out in the manner described above. For example, when calculating instantaneous copolymer composition, this procedure corresponds to the summation of the appropriate components of the stationary vector jt of the extended Markov chain ... 

By virtue of the conditions xi+X2 = 1>Xi+X2 = 1, only one of two equations (Eq. 98) (e.g. the first one) is independent. Analytical integration of this equation results in explicit expression connecting monomer composition jc with conversion p. This expression in conjunction with formula (Eq. 99) describes the dependence of the instantaneous copolymer composition X on conversion. The analysis of the results achieved revealed [74] that the mode of the drift with conversion of compositions x and X differs from that occurring in the processes of homophase copolymerization. It was found that at any values of parameters p, p2 and initial monomer composition x° both vectors, x and X, will tend with the growth of p to common limit x = X. In traditional copolymerization, systems also exist in which the instantaneous composition of a copolymer coincides with that of the monomer mixture. Such a composition, x =X, is known as the azeotrop . Its values, controlled by parameters of the model, are defined for homophase (a) [1,86] and interphase (b) copolymerization as follows... 

When deriving this expression for the average composition distribution, authors of paper [74] entirely neglected its instantaneous constituent, having taken (as is customary in the quantitative theory of radical copolymerization [3,84]) the Dirac delta-function < ( -X) as the instantaneous composition distribution. Its averaging over conversions, denoted hereinafter by angular brackets, leads to formula (Eq. 101). Note, this formula describes the composition distribution only provided copolymer composition falls in the interval between X(0) and X(p). Otherwise, this distribution function vanishes at all values of composition lying outside the above-mentioned interval. 

Fig. 8 Dependencies on conversion p of monomer mixture composition x (a), instantaneous X (b) and average X) (c) copolymer composition as well as dispersion a2 (d) of the composition distribution calculated at different values of the initial compositions of monomers x°. The calculations have been carried out at values of parameters a and a2 = 1 - fli (Eq. 100) equal to 0.3 and 0.7, respectively... 

Figure 6. Variation of the instantaneous copolymer composition with conversion for a starting monomer composition of 20 mol% of...

Bauer et al. describe the use of a noncontact probe coupled by fiber optics to an FT-Raman system to measure the percentage of dry extractibles and styrene monomer in a styrene/butadiene latex emulsion polymerization reaction using PLS models [201]. Elizalde et al. have examined the use of Raman spectroscopy to monitor the emulsion polymerization of n-butyl acrylate with methyl methacrylate under starved, or low monomer [202], and with high soUds-content [203] conditions. In both cases, models could be built to predict multiple properties, including solids content, residual monomer, and cumulative copolymer composition. Another study compared reaction calorimetry and Raman spectroscopy for monitoring n-butyl acrylate/methyl methacrylate and for vinyl acetate/butyl acrylate, under conditions of normal and instantaneous conversion [204], Both techniques performed well for normal conversion conditions and for overall conversion estimate, but Raman spectroscopy was better at estimating free monomer concentration and instantaneous conversion rate. However, the authors also point out that in certain situations, alternative techniques such as calorimetry can be cheaper, faster, and often easier to maintain accurate models for than Raman spectroscopy, hi a subsequent article, Elizalde et al. found that updating calibration models after... 

The instantaneous copolymer composition—the composition of the copolymer formed at very low conversions (about <5%)—is usually different from the composition of the comonomer feed from which the copolymer is produced, because different monomers have differing tendencies to undergo copolymerization. It was observed early that the relative copolymerization tendencies of monomers often bore little resemblance to their relative rates of homopolymerization [Staudinger and Schneiders, 1939]. Some monomers are more reactive in copolymerization than indicated by their rates of homopolymerization other monomers are less reactive. Further, and most dramatically, a few monomers, such as maleic... 

Fig. 6-1 Dependence of the instantaneous copolymer composition F on the initial comonomer feed composition/i for the indicated values of ri, where rir2 — 1. After Walling [1957] (by permission of Wiley, New York) from plot in Mayo and Walling [1950] (by permission of American Chemical Society, Washington, DC).

A few examples will illustrate the utility of Eqs. 6-33 and 6-34. Figure 6-3 shows the behavior observed in the radical copolymerization of styrene and methyl methacrylate. F and h i are the instantaneous copolymer compositions for the instantaneous feed... 

Even with the Kelen Tudos refinement there are statistical limitations inherent in the linearization method. The independent variable in any form of the linear equation is not really independent, while the dependent variable does not have a constant variance [O Driscoll and Reilly, 1987]. The most statistically sound method of analyzing composition data is the nonlinear method, which involves plotting the instantaneous copolymer composition versus comonomer feed composition for various feeds and then determining which theoretical plot best fits the data by trial-and-error selection of r and values. The pros and cons of the two methods have been discussed in detail, along with approaches for the best choice of feed compositions to maximize the accuracy of the r and r% values [Bataille and Bourassa, 1989 Habibi et al., 2003 Hautus et al., 1984 Kelen and Tudos, 1990 Leicht and Fuhrmann, 1983 Monett et al., 2002 Tudos and Kelen, 1981]. 

Detector Technology. For copolymer composition analysis the new diode array UV/vis detectors are extremely attractive the absorption at many wavelengths are instantaneously recorded there is only a single spectrophotometer cell so that transport time delays between detectors and axial mixing in detector cells do not confound comparison of detector response at different wavelengths and for styrene copolymers, extremely low concentrations of polymer can be detected. 

In homogeneous copolymerization, the instantaneous composition of copolymer is decided only by monomer reactivity ratio. On the contrary, in emulsion copolymerization, the copolymer composition depends not only on the monomer reactivity ratio but also on the distribution of monomers between oil (polymer-monomer particles) and aqueous phases (18). 

Table IV - Instantaneous and average copolymer composition versus conversion (run Mj)...

An alternative rationale for the unusual RLi (hydrocarbon) copolymerization of butadiene and styrene has been presented by O Driscoll and Kuntz (71). Rather than invoking selective solvation, these workers stated that classical copolymerization kinetics is sufficient to explain this copolymerization. They adapted the copolymer-composition equation, originally derived from steady-state assumptions for free-radical copolymerizations, to the anionic copolymerization of butadiene and styrene. Equation (20) describes the relationship between the instantaneous copolymer composition c/[M,]/rf[M2] with the concentrations of the two monomers in the feed, M, and M2, and the reactivity ratios, rt, r2, of the monomers. The rx and r2 values are measures of the preference of the growing chain ends for like or unlike monomers. 

A number of copolymerizations involving macromonomer(s) have been studied and almost invariably treated according to the terminal model, Mayo-Lewis equation, or its simplified model [39]. The Mayo-Lewis equation relates the instantaneous compositions of the monomer mixture to the copolymer composition ... 

FIGURE 7.18 Instantaneous copolymer composition vs. feed composition for an ideal copolymerization with values of r =l/r2. 

Equation (7.113b) gives the instantaneous copolymer composition in terms of the feed composition and the reactivity ratio. Figure 7.18 shows the copolymer composition for an ideal copolymerization (r,r2 = 1). In this case, the copolymer composition equation becomes ... 

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