Interchain periodicity

The interchain periodicity of 5.6 A can typically be visualized in all three common CM-AFM imaging modes, height, deflection and friction (latter one shows highest sensitivity with scan angles of 90°, see also Chap. 2) [34—36]. In the literature, some authors have reported that even the helical structure of the PTFE chains can be resolved in some cases [37], however, this is not obvious in the images shown here. For quantitative work, it is essential that the thermal drift is minimized, hence subsequent up and down scans should match and in particular the inclination angles of the periodic structure should be invariant with this capture direction. 

Preservation of a high density of interactions is ideally achieved when the substrate and deposit have identical periodicities. It is therefore of interest to search for substrates that match known periodicities of the polymer, in a one-dimensional or, better, a two-dimensional relationship. Epitaxy may also exist when the corresponding distances are multiple, for example, one substrate periodicity for two deposit periodicities. Larger multiples (1 for 3, or 2 for 3) appear very unlikely, and have been observed only occasionally in polymer epitaxy. Matching of polymer periodicities with that of the substrate may be rather complex. The simplest case is of course to match an interchain periodicity, as is the case for PE, considered in the next paragraphs. However, in polymers with a helical conformation, the heUx axis is not materialized by a string of atoms. The outer part of the helix interacts more closely with the substrate. In other words, the helical path may be involved in the epitaxy, or more exactly the distance between two successive helical paths, that is between parts of the helix located on its outer part. The orientation of the helix path relative to the helix axis differs for right-handed and left-handed helices (cf Fig. 8.9). Therefore, epitaxial deposition of polymers with helical conformation... 

In cellulose II with a chain modulus of 88 GPa the likely shear planes are the 110 and 020 lattice planes, both with a spacing of dc=0.41 nm [26]. The periodic spacing of the force centres in the shear direction along the chain axis is the distance between the interchain hydrogen bonds p=c/2=0.51 nm (c chain axis). There are four monomers in the unit cell with a volume Vcen=68-10-30 m3. The activation energy for creep of rayon yarns has been determined by Halsey et al. [37]. They found at a relative humidity (RH) of 57% that Wa=86.6 kj mole-1, at an RH of 4% Wa =97.5 kj mole 1 and at an RH of <0.5% Wa= 102.5 kj mole-1. Extrapolation to an RH of 65% gives Wa=86 kj mole-1 (the molar volume of cellulose taken by Halsey in his model for creep is equal to the volume of the unit cell instead of one fourth thereof). 

Fig. 4. Schematic diagram of segment IB in intermediate filament chains showing generally conserved features. These include the highly conserved residues L74, L81, and E95 the conserved intra- and interchain ionic interactions represented by solid and dotted lines, respectively the trigger motif (residues 79-91) that acts as a particularly stable region that nucleates coiled-coil formation the site at residue 40 (indicated by an asterisk) of a six heptad insertion in lamin molecules. The entire segment displays a regular disposition of acidic and basic residues, each with a period of about 9.54 residues. These periods are approximately out of phase with one another.

Epitaxial crystallization of helical polymers may involve three different features of the polymer chain or lattice. These are (a) the interchain distance (as for stretched out polymers), (b) the chain axis repeat distance, and (c) the interstrand distance - the distance between the exterior paths of two successive turns of the helix. The two former periodicities are normal and parallel to the chain axis direction, and are therefore not usually sensitive to the chirality of the helix (unless the substrate topography is asymmetric and favors a given helical hand). However, the interstrand distance is oblique to the helix axis (it is normal to the orientation of the outer chain path) and therefore has different, symmetric orientations relative to the helix axis for left-handed and right-handed helices (Fig. 2). In other words, epitaxies that involve the interstrand distances are discriminative with respect to helix chirality. This discrimination becomes visible if the crystal structure is based on whole layers of isochiral helices. Such a situation does indeed exist for isotactic poly(l-butene), Form I, that will be considered soon. 

Up to now, we have considered CPs (almost) exclusively as being perfectly periodic, infinite, and isolated one-dimensional chains. This is not what real materials are made of. In this and the following sections, we move closer to real materials by considering the effects of three-dimensional coupling and of disorder (both intrachain and interchain). Not surprisingly, less theoretical work has been done on these issues. On the other hand, considerable experimental effort has been devoted to characterizing the disorder, which is discussed in Chapter 12, where the structure of CPs is considered. 

Band Structure Calculations and Experimental Results The spectroscopic properties discussed above are related primarily to intrachain electronic structure. One exception is the stability of gap states (e.g., polarons) versus the three-dimensional interaction effects mentioned in Chapter 11, Section IV.D. Energy and charge transport are, of course, dependent on interchain transfers. So while there are only a few three-dimensional band structure calculations (e.g., for PA [184] and PPV [185]), there are many theoretical calculations concerning infinite perfectly periodic one-dimensinal chains, the effects of local perturbations, and the elementary excitations of these chains solitons, polarons, and bipolarons. Only a few hints of that work will be given here. It has been discussed and reviewed several times (see, e.g., Refs. 186 to 188). 

PDAs A Model of CPs Without Disorder In PDAs one would expect to have only two processes to consider transport along a really periodic chain, and all similar interchain hopping events. The case of PDAs illustrates the ambiguities of transport studies on CPs. Early time-of-flight experiments yielded mobilities ==5 cm2/V s along the chains, and 10 3 along the perpendicular directions [217]. A mobility of a few cm2/V s is typical of a molecular crystal, and the polymer character was not apparent. 

The plots give evidence of the interchain interactions which keep together the chains. The single-chain g(r) shows a set of sharp peaks starting at r=5 A which are attributable to the chain period, the broadened peak at about 4.7 A in the three-chain system accotmts for the carboxylic groups involved in interchain hydrogen bonding. 

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