Crystalline polymers lamellae

Polymer crystals most commonly take the form of folded-chain lamellae. Figure 3 sketches single polymer crystals grown from dilute solution and illustrates two possible modes of chain re-entry. Similar stmctures exist in bulk-crystallized polymers, although the lamellae are usually thicker. Individual lamellae are held together by tie molecules that pass irregularly between lamellae. This explains why it is difficult to obtain a completely crystalline polymer. Tie molecules and material in the folds at the lamellae surfaces cannot readily fit into a lattice. 

Crystalline structures have a much greater degree of molecular packing and the individual lamellae can be considered as almost impermeable so that diffusion can occur only in amorphous zones or through zones of imperfection. Hence crystalline polymers will tend to resist diffusion more than either rubbers or glassy polymers. 

The fringed micelle theory has been less favoured recently following research on the subject of polymer single crystals. This work has led to the suggestion that polymer crystallisation takes place by single molecules folding themselves at intervals of about 10 nm to form lamellae as shown in Figure 3.3b. These lamellae appear to be the fundamental structures of crystalline polymers. 

It has proved difficult to decide which of these two theories of polymer crystallisation is correct, since both are consistent with the observed effects of crystallinity in polymers. These effects include increased density, increased stiffness, and higher softening point. However, the balance of opinion among those working with crystalline polymers favours the latter theory, based on lamellae formed by the folding of single molecules. 

Figure 3.3 Arrangements of molecules in crystalline polymers according to (a) fringed micelle and (b) lamellae theories...

Many polymers solidify into a semi-crystalline morphology. Their crystallization process, driven by thermodynamic forces, is hindered due to entanglements of the macromolecules, and the crystallization kinetics is restricted by the polymer s molecular diffusion. Therefore, crystalline lamellae and amorphous regions coexist in semi-crystalline polymers. The formation of crystals during the crystallization process results in a decrease of molecular mobility, since the crystalline regions act as crosslinks which connect the molecules into a sample spanning network. 

It is well known that the stacked lamellae of semi-crystalline polymers result in the long period which usually gives two (or three) diffuse Bragg reflections. We will focus on the first reflection (named LI) and the secondary reflection (named L2) at two (/-ranges, denoted as qu and qu, respectively [30,31]. 

The structure of crystalline polymers may be significantly modified by the introduction of fillers. All aspects of the structure change on filling, crystallite and spherulite size, as well as crystallinity, are altered as an effect of nucleation [9]. A typical example is the extremely strong nucleation effect of talc in polypropylene [10,11], which is demonstrated also in Fig. 2. Nucleating effect is characterized by the peak temperature of crystallization, which increases significantly on the addition of the filler. Elastomer modified PP blends are shown as a comparison crystallization temperature decreases in this case. Talc also nucleates polyamides. Increasing crystallization temperature leads to an increase in lamella thickness and crystallinity, while the size of the spherulites decreases on... 

For a semi-crystalline polymer the solidification model of Fischer [11] predicts that the chain dimensions are frozen in at Tm if crystallization occurs sufficiently fast so as to prevent the disentanglement of chains by unravelling and/or their segregation according to their mass. For a series of polyethylene samples Michler [12] has accomplished an instructive comparison between the dimensions of molecular coils and the thickness of crystalline lamellae (Fig. 4). 

Crystallization is an inherently time-dependent process the nucleation and growth of crystalline structures, the degree of crystallinity, the phase structure and quality of crystal lamellae, and their connectedness strongly influence the mechanical properties of semi-crystalline polymers. It is for this... 

Fig. 6 Micromechanical model of a section of a semi-crystalline polymer with lamellae oriented perpendicular to the principal stress direction showing the long period L and the thicknesses of crystalline (Lc) and amorphous layers (La) the latter are composed of loose segments, entangled chains and more or less extended tie molecules. Large forces can be transferred at those points (o) where highly extended tie molecules (eTM) enter crystalline lamellae...

Deformed crystals. If a semi-crystalline polymer is deformed while undergoing crystallization, oriented lamellae form instead of spherulites. 

The lamellar habit adopted by crystalline polymers adds surface terms to the specific Gibbs function (chemical potential), most importantly the fold surface free energy, ae, which contributes 2ae/Xg for a lamella of thickness k and crystalline density q. In consequence melting points are lowered from T, for infinite thickness, to Tm according to the Hoffman-Weeks equation... 

The concept Tie molecules" was introduced by Peterlin (1973), see Chap. 2. Tie molecules are part of chains or bundles of chains extending from one crystallite (or plate or lamella) to another in fibres they even constitute the core of the stretched filament. They concentrate and distribute stresses throughout the material and are therefore particularly important for the mechanical properties of semi-crystalline polymers. Small amounts of taut tie molecules may give a tremendous increase in strength and a decrease in brittleness of polymeric materials. 

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