Chain-folded

In dilute polymer solutions, hydrodynamic interactions lead to a concerted motion of tire whole polymer chain and tire surrounding solvent. The folded chains can essentially be considered as impenneable objects whose hydrodynamic radius is / / is tire gyration radius defined as... 

Polymer crystals form by the chain folding back and forth on itself, with crystal growth occurring by the deposition of successive layers of these folded chains at the crystal edge. The resulting crystal, therefore, takes on a platelike structure, the thickness of which corresponds to the distance between folds. 

Both hollow pyramids and corrugated pyramids are thoroughly documented and fairly well understood. Such structures are consistent with the notion that successive layers of folded chains do not fold at the same place, but offset this fold stepwise to generate the pyramid face. The polymer chains are perpendicular to the planar faces of the pyramid and are therefore tilted at an angle relative to the base of the pyramid. 

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. 

Appropriately, this was called the Folded Chain Theory and is illustrated in Fig. A.ll. There are several proposals to account for the co-existence of crystalline and amorphous regions in the latter theory. In one case, the structure is considered to be a totally crystalline phase with defects. These defects which include such features as dislocations, loose chain ends, imperfect folds, chain entanglements etc, are regarded as the diffuse (amorphous) regions viewed in X-ray diffraction studies. As an alternative it has been suggested that crystalline... 

The single crystal of a polymer is a lamellar structure with a thin plateletlike form, and the chain runs perpendicular to the lamella. The crystal is thinner than the polymer chain length. The chain folds back and forth on the top and bottom surfaces. Since the fold costs extra energy, this folded chain crystal (FCC) should be metastable with respect to the thermodynamically more stable extended chain crystal (ECC) without folds. 

The actual experimental moduli of the polymer materials are usually about only % of their theoretical values [1], while the calculated theoretical moduli of many polymer materials are comparable to that of metal or fiber reinforced composites, for instance, the crystalline polyethylene (PE) and polyvinyl alcohol have their calculated Young s moduli in the range of 200-300 GPa, surpassing the normal steel modulus of 200 GPa. This has been attributed to the limitations of the folded-chain structures, the disordered alignment of molecular chains, and other defects existing in crystalline polymers under normal processing conditions. 

There is no unanimity in regard to the exact mechanism of ECC formation under high pressure. Wunderlich et al. [11-18] suggested that when a flexible polymer molecule crystallizes from the melt under high pressure, it does not grow in the form of a stable extended chain, rather it deposits as a metastable folded chain. 

It is known that elevating the crystallization temperature [42,49] or annealing above the crystallization temperature [50] of PE results in a thicker folded-chain lamella of up to —200 nm. In addition to the higher temperature, if high pressure is applied, crystals can grow as thick as several micrometers in the chain axis direction [2-4,51]. 

Sawada et al. [110] and the authors of this Chapter [104,111] have proposed another theory, the bundle-like nucleation theory, for the mechanism of ECC formation. Both groups of workers suggested that crystallization under high pressure starts from partially extended-chain nucleation rather than from the folded-chain nucleation as proposed by Hikosaka [103,104]. This theory was established on the basis of the following facts ... 

Extended- and folded-chain crystallization are mutually independent processes, and extended-chain crystallization can take place prior to folded-chain crystallization [6,19-25]. 

Figure 13 Schematic diagram of the dependence of <7 on pressure. (F) Denotes folded-chain nucleus, (B) denotes bundle-like nucleus and (B ) denotes addition of ethyl cellulose liquid crystal polymer. (From Refs. 104, 110, 111, and 117.)...

Usually, crystallization of flexible-chain polymers from undeformed solutions and melts involves chain folding. Spherulite structures without a preferred orientation are generally formed. The structure of the sample as a whole is isotropic it is a system with a large number of folded-chain crystals distributed in an amorphous matrix and connected by a small number of tie chains (and an even smaller number of strained chains called loaded chains). In this case, the mechanical properties of polymer materials are determined by the small number of these ties and, hence, the tensile strength and elastic moduli of these polymers are not high. 

Supramolecular structures formed during the crystallization of the melt under a tensile stress have already been described by Keller and Machin25. These authors have proposed a model for the formation of structures of the shish-kebab type according to which crystallization occurs in two stages in the first stage, the application of tensile stress leads to the extension of the molecules and the formation of a nucleus from ECC and the second stage involves epitaxial growth of folded-chain lamellae. 

A characteristic feature of the structure of samples obtained under the conditions of molecular orientation is the presence of folded-chain crystals in addition to ECC. Kawai22 has emphasized that the process of crystallization from the melt under the conditions of molecular orientation can be regarded as a bicomponent crystallization in which, just as in the case of fibrous structures in the crystallization from solutions, the formation of crystals of the packet type (ECC) occurs in the initial stage followed by the crystallization with folding . 

Wunderlich30 and Zubov33 suppose that ECC under high pressures occur as a result of an isothermal thickening of folded-chain lamellae. However, this contradicts the later data of Wunderlich and of Japanese authors31 who have shown that folded-chain crystals (FCC) are formed after ECC, when the melt is cooled. According to Kawai22, crystallization under hydrostatic compression can he considered as a variant of the bicomponent crystallization. 

Fig. 5 a, b. Models of the crystallization of flexible-chain polymers with the formation of a folded-chain crystals and b extended-chain crystals b... 

We will compare the change in the free energy per macromolecule in the formation of folded-chain (curve 1) and fibrillar (curve 2) crystals as a function of /J. Figure 8 b shows these curves calculated for the corresponding equilibrium values [a]. The increase... 

Fig. 8a-c. Dependence of the degree of crystallinity (a), free energy (b) and melting temperature (c) on fi. 1 folded-chain crystals, 2 fibrillar crystals the broken line corresponds tofi=fia... 

To avoid misunderstanding, it should be emphasized that if the transition from one type of crystallization to the other one is considered, this does not imply a transformation of crystals of one type into the other one during stretching. In contrast, if the molecule enters a folded-chain crystal, it is virtually impossible to extend it. In this case, we raise the question, which of the two crystallization mechanisms controls the process at each given value of molecular orientation in the melt (this value being kept constant in the crystallization process during subsequent cooling of the system). At /J < /3cr, only folded-chain crystals are formed whereas at / > only fibrillar crystals result at /8 /3cr, crystals of both types can be formed. 

If this sample contains also folded-chain crystals (reasons for their appearance during orientational crystallization were stated before), under isometric conditions they undergo melting at a higher temperature (at point 1 with respect to the oriented melt with transition to line A2) than under the conditions of free heating (point 1 with transition in the isotropic melt to line At). 

Finally we would like to draw attention to low molecular weight results and their analysis on the basis of surface nucleation theory. The theory was originally developed for infinitely long chains and cannot easily be applied to extended or once-folded chain crystallization. Therefore any discrepancies in this area would not be surprising and would not discredit the theory at higher molecular weights. 

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