Statistical copolymers melting/crystallization

Figure 11.9 Poly(ET-c6>-EN) statistical copolymer melting point and unit-cell data, shown as a function of composition (a) copolymer melting temperature, (b) projection of the a unit cell length onto the plane normal to the chain axis, a (c) projection of the b unit cell length onto the plane normal to the chain axis, b(d) c unit-cell length. In panels (b-d), filled symbols indicate a PEN-like crystal structure, while open symbols correspond to a PET-like structure. Reprinted from Reference [86] with permission of Elsevier, Copyright 1995.

Statistical copolymers of the types described in Chapter 8 tend to have broader glass transition regions than homopolymers. The two comonomers usually do not fit into a common crystal lattice and the melting points of copolymers will be lower and their melting ranges will be broader, if they crystallize at all. Branched and linear polyethylene provide a case in point since the branched polymer can be regarded as a copolymer of ethylene and higher 1-olefins. 

Nonregularity of structure first decreases the melting temperature and finally prevents crystallinity. Mers of incorrect tacticity (see Chapter 2) tend to destroy crystallinity, as does copolymerization. Thus statistical copolymers are generally amorphous. Blends of isotactic and atactic polymers show reduced crystaUinity, with only the isotactic portion crystallizing. Under some circumstances block copolymers containing a crystallizable block will crystallize again, only the crystallizable block crystallizes. 

The melting point of a polymer will also be affected by copolymerization. In the case of random or statistical copolymers (Section 1.2.3) the structure is very irregular and so crystallization is normally suppressed and the copolymers are usually amorphous. In contrast, in block and graft copolymers crystallization of one or more of the blocks may take place. It is possible to analyse the melting behaviour for a copolymer system in which there are a small number of non-crystallizable comonomer units incorporated in the chain, using Equation (4.39). These units will act as impurities (cf. chain ends) and so the melting point of the copolymer will be given by... 

In semicrystalline block copolymers, the crystallization behavior is often more complex than that observed in statistical copolymers because the solid-state morphology adopted by block copolymers can be driven either by block incompatibility or by crystallization of one or more blocks [5-8]. In this chapter, we will cover only block copolymers with homogeneous or weakly segregated melts, such that crystallization is always the dominant factor in determining solid-state morphology. Crystallization of block copolymers from strongly segregated melts is covered in Chapter 12. Furthermore, the... 

Statistical copolymers refer to a class of copolymers in which the distribution of the monomer counits follows Markovian statistics [1,2]. In these polymeric materials, since the different chemical units are joined at random, the resulting polymer chains would be expected to encounter difficulties in packing into crystaUine structures with long-range order however, numerous experiments have shown that crystallites can form in statistical copolymers under suitable conditions [2], In this section, we will discuss the effects of counit incorporation on the solid-state structure and the crystallization kinetics in statistical copolymers. A number of thermodynamic models, which have been proposed to describe the equilibrium crystallization/melting behavior in copolymers, vill also be highlighted, and their applicability to describing experimental observations will be discussed. 

However, there are also aspects of the crystallization process that are particular to statistical copolymers [16, 69, 71-76]. In a series of studies on the crystallization and melting behavior of ethylene-butene statistical copolymers, it was observed that after isothermal crystallization, while polyethylene homopolymer exhibited a single-peak melting endotherm, all the copolymers showed bimodal melting behavior [16,71]. Each melting peak of the copolymer endotherm was determined to represent a distinct crystal population because its shape... 

Statistical copolymers of ethylene terephthalate (ET) and 1,4-cyclohexylene dimethylene terephthalate (CT) were also found to co-crystallize over a limited composition range [84, 85]. The copolymers rich in ET were found to form a crystalline phase that contained only ET units, while in the copolymers rich in CT, the crystalline phase contained both ET and CT units. The transition between these two crystal phases, as a function of composition, corresponded to a minimum in both copolymer melting temperature and heat of crystallization. It was speculated that the transition occurs at a composition where the energy difference between the melt and the crystal is identical for the two comonomers [85]. 

Other statistical copolymers that have been found to exhibit isodimorphic behavior include poly()3-hydroxybutyrate-co-)3-hydroxyvalerate) [87, 88], poly (butylene terephthalate-co-butylene-2,6-naphthalate) [89], poly(butylene terephthalate-co-l,4-cyclohexane dimethylene terephthalate) [90], and poly(butylene terephthalate-co-cyclopentane dimethylene terephthalate) [90]. In all cases, measurable crystallinity was observed over the entire copolymer composition range. An abrupt transition in the crystal structure was detected at some intermediate composition and was correlated with a eutectic-Uke minimum in the melting temperature [87-90]. 

Thus far, we have discussed a number of key experimental observations regarding the effects of counit incorporation on the solid-state structure and the crystallization kinetics in statistical copolymers. In order to better quantify these experimental observations, various thermodynamic models have been proposed. Rory s model, as outlined in Section 11.2.1, correctly describes the equilibrium melting behavior of copolymers in the limit of complete comonomer exclusion however, it is often found to be inadequate at predicting experimentally accessible copolymer melting temperatures [11-14]. An alternative was proposed by Baur [91], where each polymer sequence is treated as a separate molecule with an average sequence length in the melt given by [91] ... 

Besides Baur s model, other relationships, both theoretical and empirical, have been proposed to describe the experimentally observed crystallization and melting behavior of statistical copolymers [94-96]. In one study, Pakula presented two models for determining copolymer crystallinity as a function of critical nucleus size [94]. In model one, crystallizable sequences longer than the critical nucleus are allowed to participate in the formation of stable crystallites however, chain folding is assumed to be absent, so any portion of the crystallizable sequence longer than the critical nucleus size must be rejected to the amorphous phase. In model two. 

The Sanchez-Eby and Wendling-Suter models, which differ mainly in the limit of large e, have been successfully applied to describe experimental copolymer crystallization data, especially when counit inclusion in the crystal unit cell is substantial (i.e., e is small) [88,101]. In one such example, Marchessault and colleagues studied the isodimorphic crystallization behavior in poly(j8-hydroxybutyrate-C(9-/3-hydroxyvalerate) statistical copolymers [87, 88]. The experimentally measured copolymer melting temperatures were found to be well described by Sanchez and Eby s model with the assumptions that the crystals were of finite thickness (i.e., Eq. 11.12) and defect inclusion was uniform (i.e., Xcb = b) [88]. 

There is also the special case where two crystallizable units are incorporated into a statistical copolymer. If the two units are structurally similar, in some cases these copolymers can be isodimorphic and show a high degree of crystallinity over the entire range of copolymer compositions. The abrupt transition between the two limiting crystal structures, each characteristic of one of the homopolymers, occurs at a composition that corresponds to a minimum in both melting temperature and heat of fusion. 

Besides its effects on morphology, comonomer sequence distribution also affects copolymer crystallization kinetics. In statistical copolymers, due to the broad distribution of crystaUizable sequence lengths, bimodal melting endotherms are typically observed. In block copolymers, the dynamics of crystallization have features characteristic of both homopolymer crystallization and microphase separation in amorphous block copolymers. In addition, the presence of order in the melt, even if the segregation strength is weak, hinders the development of the equihbrium spacing in the block copolymer solid-state structure. 

The principles of polymer fractionation by solubility or crystallization in solution have been extensively reviewed on the basis of Hory-Huggins statistical thermodynamic treatment [58,59], which accounts for melting point depression by the presence of solvents. For random copolymers the classical Flory equation [60] applies ... 

This study was followed by a series of papers that examined the effect of the distance between the pendant fluorine [96], chlorine [97], or bromine [98] atoms. Later, a series of ethylene/vinyl halide polymers containing fluorine, chlorine, and bromine were created via ADMET copolymerization of a halogen-containing (x,K)-diene and 1,9-decadiene [99]. Thermal analysis of these statistically random copolymers showed a distinct difference between their crystallization behavior and that of their compositionally matched precise analogs. The sharp melting... 

---