Reactivity ratios, r and

GopolymeriZation. The importance of VDC as a monomer results from its abiHty to copolymerize with other vinyl monomers. Its Rvalue equals 0.22 and its e value equals 0.36. It most easily copolymerizes with acrylates, but it also reacts, more slowly, with other monomers, eg, styrene, that form highly resonance-stabiHzed radicals. Reactivity ratios (r and r, with various monomers are Hsted in Table 2. Many other copolymers have been prepared from monomers for which the reactivity ratios are not known. The commercially important copolymers include those with vinyl chloride (VC),... 

The relative monomer reactivity ratios, r and r2, for ethylene/cycloolefin copolymerisation with zirconocene-methylaluminoxane catalysts are presented in Table 3.6 [468],... 

Styrene undergoes copolymerisation with ethylene and various a-olefins in the presence of heterogeneous Ziegler-Natta catalysts. Its reactivity in the copolymerisation is quite low, which is illustrated by the values of the relative reactivity ratios, r and r2, presented in Table 4.5 [118]. One may note, however, a considerably high relative reactivity of styrene in copolymerisation with vinyl-cyclohexane. The copolymerisation of styrene with small amounts of a-olefin, such as 1-octene or 1-decene, yields copolymers of reduced crystallinity and thus reduced brittleness compared with the homopolymer of styrene. 

Copolymerization can occur through any of the chain reaction polymerization mechanisms described above however, the reactivity of a given monomer toward the second monomer can vary. Thus, not all combinations of monomers may be copolymerized. Each active end will exhibit different reactivity toward each monomer, which can be expressed as reactivity ratios, r and r2.35 These reactivity ratios rl in this example) show the tendency of a given active end, for example Mj, to add its own monomer (Mt) over the other monomer (M2). The copolymer composition at any instant can be determined by the composition of the feedstock and the reactivity ratios by... 

To solve these equations and eliminate the reactive intermediates, we note the stationary-state approximation and the definition of the reactivity ratios r and r2 above. Then... 

Table 1.14. Sequence-length distributions (W )xfor copoiymerization of monomers Mi and M2 with reactivity ratios r, and T2 and feed compositions f, and 2...

Block copolymers were defined above, and it was noted that there was a tendency for blocks to form when both of the reactivity ratios, r and r2, were greater than unity. This approach results in a random copolymer with extended blocks of Mj and M2 rather than a pure block copolymer with well-defined block length and composition. More precise control can be achieved through living polymerization, since on exhaustion of the first monomer added, Mj,... 

All the above factors controlling monomer and radical reactivities contribute to the rate of polymerization, but in a manner which makes it difficult to distinguish the magnitude of each effect. Attempts to correlate copolymerization tendencies based on these factors are thus mainly of a semiempirical nature and can, at best, be treated as useful approximations rather than rigorous relations. However, a generally useful scheme was proposed by Alfrey and Price [23] to provide a quantitative description of the behavior of diferent monomers in radical polymerization, with the aid of two parameters, for each monomer rather than for a monomer pair. These parameters are denoted by Q and e and the method has been called the Q — e scheme. It allows calculation of monomer reactivity ratios r and T2 from properties of monomers irrespective of which pair is used. The scheme assumes that each radical or monomer can be classified according to its reactivity or resonance effect and its polarity so that the rate constant... 

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. ... 

TaUe 2. Copolymerization reactivity ratios (r, and r,) of activated (meth)acrylates (M,) and structural monomers (M,)... 

Tip 12 Copolymerization, reactivity ratios, and estimation of reactivity ratios. In a binary copolymerization of monomers and M2, reactivity ratios r and r2 are important parameters for calculating polymerization rate, copolymer composition, and comonomer sequence length indicators (see Chapter 6 for basic equations and further information). 

Some Reactivity Ratios r, and f2 for Free Radical Initiated Copolymerizations... 

According to the terminal model, the composition of binary copolymers is determined by the reactivity ratios r and by the composition of the monomer mixture via Eq. (4) [33] ... 

Random copolymers are always found if the product rjxr2 = 1, i.e., both monomers have the same preference for monomer 1 over 2 (kn/ki2 = k2i/k22). The examples 3a and 3b are two possible random copolymers with opposite reactivity-ratios r, and tj. A typical random copolymer can be made of 1,3-butadiene, CH2=CH-CH=CH2, and styrene, CH2=CH-CgH5). 

The relative reactivity of comonomers during copolymerization is usually expressed through the reactivity ratios r and The reactions involved in a copolymerization are shown in Figure 12.6. 

The way in which ethylene and propylene distribute themselves along the macromolecular chain is expressed by the product of the reactivity ratios r and C2 (Figure 12.7). In particular, if the comonomer insertion ... 

This represents a lower limit of regioirregular units, because sequences containing six or more methylenes are indistinguishable from those formed by sequences of at least three ethylene units. Since the reactivity ratios r and r2 are obtained only from triads containing regioregular propylene units, the presence of a relatively large amount of regioirregular propylene placements introduces uncertainties in their evaluation. 

By de ning two parameters (called monomer reactivity ratios), r and r2, as... 

Two types of copoly.merization, SFC and CPC, were carried out at 30°C with the catalyst system, MgCl2/TiCU/EB/Al(02115)3. For reference, homopolymerization of each olefin was conducted under similar conditiona The monomer reactivity ratios r and rp(K = ethylene, P = propylene) were calculated according to the Fineman-Ross method and Helen—Tudos method, where the necessary parameters are defined as follows ... 

Many researches on random copolymers in the presence of metallocene catalyst have been undertaken. Reactivity ratios r and T2 in the copolymerization of ethylene (1) or with propylene (2) performed in the... 

Table 8.13. Reactivity ratios r and rz) of some couples of ethylenic monomers...

The occurring in the equation ratios of the reaction rate constants are defined as the monomer reactivity ratios r and r ... 

The selected reactivity ratios r and r for different monomers are given in Table 8.18. 

---