Bundle of chains

If the ordered, crystalline regions are cross sections of bundles of chains and the chains go from one bundle to the next (although not necessarily in the same plane), this is the older fringe-micelle model. If the emerging chains repeatedly fold buck and reenter the same bundle in this or a different plane, this is the folded-chain model. In either case the mechanical deformation behavior of such complex structures is varied and difficult to unravel unambiguously on a molecular or microscopic scale. In many respects the behavior of crystalline polymers is like that of two-ph ise systems as predicted by the fringed-micelle- model illustrated in Figure 7, in which there is a distinct crystalline phase embedded in an amorphous phase (134). 

For the transformation of the macrocomposite model to a molecular composite model for the ultimate strength of the fibre the following assumptions are made (1) the rods in the macrocomposite are replaced by the parallel-oriented polymer chains or by larger entities like bundles of chains forming fibrils and (2) the function of the matrix in the composite, in particular the rod-matrix interface, is taken over by the intermolecular bonds between the chains or fibrils. In order to evaluate the effect of the chain length distribution on the ultimate strength the monodisperse distribution, the Flory distribution, the half-Gauss and the uniform distribution are considered. 

Fig. 23. Schematic representation of different possible types of ion channel structures (from left to right) stack, string, rack, pipe of macrocycles, helical strand, two half-channel units, self-aggregated and macrocycle core bearing bundles of chains.

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. 

In the glassy state (below Tg) the critical stress required to plastically deform the amorphous molecular network (H) involves displacement of bundles of chain segments against the local restraints of secondary bond forces and internal rotations. The intrinsic stiffness of these polymers below Tg leads to H values which are 3-4... 

These properties have been explained213 in terms of the residual crystallinity that, from x-ray diffraction studies,157 is known to survive the (carboxymethyl)ation of cellulose. Bundles of chains (see Fig. 8) therefore exist. It is to be expected that some chains extend through... 

The above results have obvious implications for the biosynthesis of cellulose mlcrofIbrlls. The parallel chain structure of cellulose I rules out any kind of regularly folded chain structure, and reveals the mlcrofibrils to be extended chain polymer single crystals, which leads to optimum tensile properties. Work by Brown and co-workers (22) on the mechanism of biosynthesis points to synthesis of arrays of cellulose chains from banks of enzyme complexes on the cell wall. These complexes produce a bundle of chains with the same sense, which crystallize almost immediately afterwards to form cellulose I mlcroflbrlls there is no opportunity to rearrange to form a more stable anti-parallel cellulose II structure. Electron microscopy by Hleta et al. (23) confirms the parallel sense of cellulose chains within the individual mlcroflbrlls stains reactive at the reducing end of the cellulose molecule stain only one end of the mlcroflbrll. 

Kargin and his school in a large number of papers, have discussed the structural features of polymers as revealed by examination under the electron microscope. It is suggested that, even in amorphous glasses, aggregation into long, thin bundles of chains is possible. 

Corradini, De Rosa et al [245] have evaluated in explicit manner the effect of various kinds of disorder on the X-ray diffraction intensity distribution, performing Fourier transform calculations on model bundles of chains of finite size containing specific kind of disorder. Disorder due to the presence of random translational displacements of chains along the chain axes, random rotational displacements around their axes with respect to an average position (already treated by Clark and Muus [11]), random placement of left- and right-handed helices in the positions of the pseudo-hexagonal lat-... 

This discrepancy can be explained by taking into account the effect of the finite width of the chains. In conjuction with the rotation there has to be some relative displacement or slip of adjacent chains (or bundles of chains) parallel to the chain axis. This is easily visualized by a row of books that is slowly falling over. Using this model it can be shown that this slip contribution to the fibre strain increases with decreasing orientation angles of the chains, as occurs when the creep stress is increased. 

A Monte Carlo method employed by Vacatello et al. upon a liquid of 31 C,o chains to model amorphous polyethylene found no tendency towards the formation of bundles of chains as judged by the reproduction of experimental JT-ray scattering curves and other measures of chtiin direction correlations. ... 

A bundle of chain molecules, all of which may slide past each other when stressed, can probably be stretched without breaking, more easily than molecules with bridges between them, as in a rope ladder. This behavior is evident in the stress-strain curves of Young s modulus (see Table 4.1). Everything else being... 

In the third paragraph we shall discuss the results of some Monte-Carlo calculations related to the structure of "liquid" polyethylene preliminary evidence will be given that bundles of chains are not present at equilibrium in the melt of polyeth lene and their existence is not required to explain the X-ray diffraction data with its characteristic 4.5 X halo. 

Thus, from our model calculations, it seems that, contrary to previous objections to the random coil model of liquid hydrocarbons, the correct density may be achieved by Monte-Carlo filling of the space and the X-ray amorphous halo ( -which many of us considered as an evidence for the presence of bundles of chain molecules) may be fairly well reproduced in intensity, while no evidence of chain parallelism is present. 

Sandberg, D.J., Carrillo, J.-M.Y., Dobrynin, A.V. Molecular dynamics simulations of polyelectrolyte brushes from single chains to bundles of chains. Langmuir 23, 12716-12728 (2007). doi 10.1021/la702203c... 

The mathematical representation of the elastic behavior of oriented heterogeneous solids can be somewhat improved through a more appropriate choice of the boundary conditions such as proposed by Hashin and Shtrikman [66] and Stern-stein and Lederle [86]. In the case of lamellar polymers the formalisms developed for reinforced materials are quite useful [87—88]. An extensive review on the experimental characterization of the anisotropic and non-linear viscoelastic behavior of solid polymers and of their model interpretation had been given by Hadley and Ward [89]. New descriptions of polymer structure and deformation derive from the concept of paracrystalline domains particularly proposed by Hosemann [9,90] and Bonart [90], from a thermodynamic treatment of defect concentrations in bundles of chains according to the kink and meander model of Pechhold [10—11], and from the continuum mechanical analysis developed by Anthony and Kroner [14g, 99]. 

Fig. 2.18. Kink-model representation of (a) bundles of chains and (b) oriented fibers with sandwich-like structure (after [10, 111).

A chain molecule as part of a thermoplastic body is in thermal contact with other chains and — at room temperature — constantly in motion. The atoms vibrate and take part in the more or less hindered rotations of groups and even of chain segments. With no external forces acting all molecular entities try to approach — and fluctuate around — the most stable positions attainable to them. The action of external forces causes — or maintains — displacements of the chain from those positions and evokes retractive forces. Let us consider a chain or a bundle of chains in thermal contact with the surrounding and at constant volume. The condition of thermodynamic stabihty of such a system is that the free energy... 

---