Statistical copolymers crystallization

On the topic of statistical copolymer crystallization, the scope of the review will be limited to composition-ally homogeneous statistical copolymers. In many studies, anionic polymerization of butadiene, followed by hydro-... 

In what follows, we use simple mean-field theories to predict polymer phase diagrams and then use numerical simulations to study the kinetics of polymer crystallization behaviors and the morphologies of the resulting polymer crystals. More specifically, in the molecular driving forces for the crystallization of statistical copolymers, the distinction of comonomer sequences from monomer sequences can be represented by the absence (presence) of parallel attractions. We also devote considerable attention to the study of the free-energy landscape of single-chain homopolymer crystallites. For readers interested in the computational techniques that we used, we provide a detailed description in the Appendix. ... 

Statistical co-crystallization of different constitutional repeating units, which may either belong to the same copolymer chains (copolymer isomorphism) or originate from different homopolymer chains (homopolymer isomorphism). 

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. 

Inclusion compounds allow the realization of copolymerization in the crystal state (1-6). This is a further difference with respect to typical solid state reactions. Both block- and statistical copolymers can be obtained the former involves a two-step process, with subsequent inclusion and polymerization of two different monomers (21) the latter requires the simultaneous inclusion of two guests. This phenomenon has a much wider occurrence than thought at first, especially when a not very selective host such as PHTP is used. Research with this host started with mixtures of 2-methylpentadiene and 4-methylpentadiene, two almost exactly superimposable molecules (22), but was successfully extended to very dissimilar monomers, such as butadiene and 2,3-dimethylbutadiene. 

Moreover, some polymers cannot be crystallized even in principle. Indeed, crystallization may only appear if there is long-scale order in the molecules positions (as in Figure 4.1 b). However, say, for a statistical copolymer whose chains consist of two types of units, A and B, long-scale order is impossible. (This is simply because the sequences of A and B along the chains are totally random.) Such copolymers can never crystalhze on cooling. 

This kind of sequence defect occurs in the statistical copolymers, where the species of monomers can crystallize. On the backbone of polyethylene chains, the short branches can be regarded as the non-crystallizable comonomers. In high-density polyethylene (HOPE), the branching probability is about 3 branches/1,000 backbone carbon atoms, and its crystallinity can reach levels as high as 90 % while in low-density polyethylene (LDPE), the branching probability is about 30 branches/ 1,000 backbone carbon atoms, and its crystallinity reaches only 50 %. The most common industry product is actually linear low-density polyethylene (LLDPE), and its branching probability is determined by the copolymerization process of CH2 = CH2 and CH2 = CHR (R means side alkane groups for short branches). 

Polymers that cannot crystallize usually have some irregularity in their structure. Examples include the atactic vinyl polymers and statistical copolymers. 

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. 

It is useful to divide the polymers into two main classes the fully amorphous and the semicrystal-line. The fully amorphous polymers show no sharp, crystalline Bragg reflections in the X-ray diffracto-grams taken at any temperature. The reason why these polymers are unable to crystallize is commonly their irregular chain structure. Atactic polymers, statistical copolymers and highly branched polymers belong to this class of polymers (Chapter 5). 

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... 

Copolymers are macromolecules composed of two or more chemically distinct monomer units, covalently joined to form a common polymer chain [1,2], In these materials, the sequence distribution of the monomer counits plays a critical role in determining the copolymer s crystallization behavior, and consequently influences its solid-state morphology and material properties [1,2], At one extreme, different types of monomer units may be randomly incorporated into the polymer chain, resulting in a statistical copolymer. At the other extreme, blocks of homopolymer sequences of different chemical nature and chain length may be joined together to form what is known as a block copolymer. In this chapter, we wiU review the key effects of comonomer incorporation on the solid-state morphology and crystallization kinetics in both statistical and block copolymers. 

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. 

Besides its influence on the crystal unit cell dimension, the presence of noncrystallizable counits can also stabilize crystalline phases that are not commonly observed in homopolymers crystallized at atmospheric pressure [46,47]. X-ray diffraction on a compositionally uniform ethylene statistical copolymer containing... 

Figure 11.6 Schematic illustration of the morphological and mechanical behavior of ethyl-ene-octene statistical copolymers. With increasing counit content, the copolymer morphology transitions from lamellar crystals to bundle-like crystals, and its mechanical behavior transitions from semicrystalline thermoplastic to elastomeric. Reprinted from Reference [62] with permission of John Wiley Sons, Inc., Copyright 1996.

The tensile properties of homogeneous ethylene-alkene statistical copolymers were further explored by Kennedy et al. [64]. It has been shown that the yield stress of a semicrystalline polymer is dependent on its crystal thickness [65, 66]. During uniaxial compression, the yield stress of polyethylene was observed to increase with crystal thickness up to 40 nm, whereas for thicker crystals it leveled off [66]. Since the crystal thickness in homogeneous copolymers decreases with increasing counit concentration, not surprisingly, an inverse correlation was also found between yield stress and counit content [64]. 

In many ways, crystallization of statistical copolymers resembles that of homopolymers [65, 68-70]. For example, hydrogenated polybutadienes of different branch content and molecular weight show sigmoidal crystallization isotherms, similar to those seen in polyethylene homopolymer crystallization. In addition, at a given isothermal crystallization temperature, the degree of copolymer crystallinity drops above a critical molecular weight, also qualitatively similar to polyethylene homopolymer [69]. 

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... 

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