Ideal copolymer

Preference for reaction with the unlike monomer occurs when ri is less than 1. When r and T2 are approximately equal to 1, the conditions are said to be ideal, with a random (not alternating) copolymer produced, in accordance with the Wall equation. Thus, a random copolymer (ideal copolymer) would be produced when chlorotrifluoroethylene is copolymerized with tetrafluoroethylene (Table 7.1). 

When Fj = 1/f2, the copolymer composition curve will be either convex or concave when viewed from the Fj axis, depending on whether Fj is greater or less than unity. The further removed from unity rj is, the farther the composition curve will be displaced from the 45° line. This situation is called ideal copolymerization. The example below explores the origin of this terminology. 

There is a parallel between the composition of a copolymer produced from a certain feed and the composition of a vapor in equilibrium with a two-component liquid mixture. The following example illustrates this parallel when the liquid mixture is an ideal solution and the vapor is an ideal gas. 

An ideal gas obeys Dalton s law that is, the total pressure is the sum of the partial pressures of the components. An ideal solution obeys Raoult s law that is, the partial pressure of the ith component in a solution is equal to the mole fraction of that component in the solution times the vapor pressure of pure component i. Use these relationships to relate the mole fraction of component 1 in the equilibrium vapor to its mole fraction in a two-component solution and relate the result to the ideal case of the copolymer composition equation. 

Because of this parallel with liquid-vapor equilibrium, copolymers for which ri = l/r2 are said to be ideal. For those nonideal cases in which the copolymer and feedstock happen to have the same composition, the reaction is called an azeotropic polymerization. Just as in the case of azeotropic distillation, the composition of the reaction mixture does not change as copolymer is formed if the composition corresponds to the azeotrope. The proportion of the two monomers at this point is given by Eq. (7.19). 

Some cast (unoriented) polypropylene film is produced. Its clarity and heat sealabiUty make it ideal for textile packaging and overwrap. The use of copolymers with ethylene improves low temperature impact, which is the primary problem with unoriented PP film. Orientation improves the clarity and stiffness of polypropylene film, and dramatically increases low temperature impact strength. BOPP film, however, is not readily heat-sealed and so is coextmded or coated with resins with lower melting points than the polypropylene shrinkage temperature. These layers may also provide improved barrier properties. 

VEs can also copolymerize by free-radical initiation with a variety of comonomers. According to the and rvalues of 0.023 and —1.77 (isobutyl vinyl ether), VEs are expected to form ideal copolymers with monomers of similar and e values or alternating copolymers with monomers such as maleic anhydride (MAN) that have high values of opposite sign (Q = 0.23 e = 2.25). 

Serious deviations of the polymer network structure from the ideal one can have several causes. One of them is the crosslinking agent involvement in intramolecular cycle formation. The contribution of this reaction grows with the system dilution as well as when the crosslinker units in the chain are close one to the other, i.e. its fraction in the copolymer increases. All this is in good agreement with the observed trend. 

It is also possible to process copolymer composition data to obtain reactivity ratios for higher order models (e.g. penultimate model or complex participation, etc.). However, composition data have low power in model discrimination (Sections 7.3.1.2 and 7.3.1.3). There has been much published on the subject of the design of experiments for reactivity ratio determination and model discrimination.49 "8 136 137 Attention must be paid to the information that is required the optimal design for obtaining terminal model reactivity ratios may not be ideal for model discrimination.49... 

The value of the reachvity rahos is crihcal in determining the composition of the copolymer. If the reactivity raho is greater than 1, the radical prefers to react with chains having the same kind of terminal unit, e.g. A- with A. On the other hand, if the reactivity ratio is less than 1, the monomer prefers to react with chains which end in the other kind of monomer. In the special case that r r2 = 1, the reaction is described as ideal copolymerisation because it results in a truly random copolymer whose composition is the same as the composition of the reaction mixture from which polymerisation took place. 

Copolymerizations. The uniform chemical environment of a CSTR makes it ideally suited for the production of copolymers. If the assumption of perfect mixing is justified, there will be no macroscopic composition distribution due to monomer drift, but the mixing time must remain short upon scaleup. See Sections 1.5 and 4.4. A real stirred tank or loop reactor will more closely... 

It is also apparent that the sequence of monomer units in an ideal copolymer must necessarily be random. That is to say, the likelihood of occurrence of an Mi unit immediately following an M2 unit is the same as for an Mi to follow an Mi unit. The probability of either unit at any place in the chain is always equal to its mole fraction in an ideal copolymer. ... 

Controlling the exact architectnre of polymers has always attracted attention in macromolecular chemistry. Snccessfnl synthesis of alternating copolymers nsing ring opening metathesis polymerisation is of great interest also from a mechanistic perspective. NHC ligands were fonnd to be ideal to tune the selectivity of the metathesis initiators. 

This closure property is also inherent to a set of differential equations for arbitrary sequences Uk in macromolecules of linear copolymers as well as for analogous fragments in branched polymers. Hence, in principle, the kinetic method enables the determination of statistical characteristics of the chemical structure of noncyclic polymers, provided the Flory principle holds for all the chemical reactions involved in their synthesis. It is essential here that the Flory principle is meant not in its original version but in the extended one [2]. Hence under mathematical modeling the employment of the kinetic models of macro-molecular reactions where the violation of ideality is connected only with the short-range effects will not create new fundamental problems as compared with ideal models. 

The instantaneous composition of a copolymer X formed at a monomer mixture composition x coincides, provided the ideal model is applicable, with stationary vector ji of matrix Q with the elements (8). The mathematical apparatus of the theory of Markov chains permits immediately one to wright out of the expression for the probability of any sequence P Uk in macromolecules formed at given x. This provides an exhaustive solution to the problem of sequence distribution for copolymers synthesized at initial conversions p l when the monomer mixture composition x has had no time to deviate noticeably from its initial value x°. As for the high-conversion copolymerization products they evidently represent a mixture of Markovian copolymers prepared at different times, i.e. under different concentrations of monomers in the reaction system. Consequently, in order to calculate the probability of a certain sequence Uk, it is necessary to average its instantaneous value P Uk over all conversions p preceding the conversion p up to which the synthesis was conducted. 

An exhaustive statistical description of living copolymers is provided in the literature [25]. There, proceeding from kinetic equations of the ideal model, the type of stochastic process which describes the probability measure on the set of macromolecules has been rigorously established. To the state Sa(x) of this process monomeric unit Ma corresponds formed at the instant r by addition of monomer Ma to the macroradical. To the statistical ensemble of macromolecules marked by the label x there corresponds a Markovian stochastic process with discrete time but with the set of transient states Sa(x) constituting continuum. Here the fundamental distinction from the Markov chain (where the number of states is discrete) is quite evident. The role of the probability transition matrix in characterizing this chain is now played by the integral operator kernel ... 

Most widely used is the two-dimensional combination of SEC and HPLC for copolymer characterization. The typical HPLC instrument is very similar to an SEC apparatus. While the ideal SEC separation is exclusively determined by entropy changes, in HPLC or adsorption chromatography it is assumed that no... 

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