Ordered Chain Conformations

let s revisit chain conformations. We ve mentioned that although there is a minimum energy conformation, one where all the bonds are trans in polyethylene, for example, a statistical distribution of conformations will be found in the melt. Upon cooling, however, ordered structures are formed as a result of crystallization (for reasons we consider later). So, the initial questions we want to answer are first, what is the shape or conformation of the chains in the crystal and second, how are they arranged relative to one another  

If we now look at the diffractogram of a sample of a low molecular weight analog of 

FIGURE 8-40 Schematic diagram of the scattering of X-rays by single crystals (top) and a crystalline powder (bottom). 

According to the phase rule, this should not be. A single component material should be either crystalline or amorphous at a given temperature, not both at the same time. Now all crystalline materials have defects, but we re not talking about grain boundaries here. Some polymers are barely 50% crystalline. Thus polymers had laid upon them the curse of not obeying thermodynamics, as Hoffman18 put it Of course, this invocation of the phase rule assumes the material can 

An X-ray of one of your authors artificial hip (Courtesy Dr. Wayne Sebastianelli). 

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FIGURE 8-15 Schematic diagram depicting ordered chain conformations. 

The conductivity values of the PAM salts measured as pellets are given in Table 4.12. The conductivity of the PAM salts are in the range of 0.3-0.9 S/cm. The higher conductivity of PAM obtained by the inverted emulsion method could be due to a more homogenous protonation of the imine nitrogen and a more ordered chain conformation of the polymer. The conductivity of the PAM-camphor sulfonic acid was found to be higher than the other salts (see Table 4.12). 

In the other type, termed isodimorphism, the system consists of two different crystalline structures. The formation of one or the other depends on the sequence distribution (composition) of the crystalline phase. Examples of these types of replacements are found in virtually all types of copolymer, including copolyamides [97-103], synthetic and natural copolyesters [89, 90, 104-107], vinyl copolymers [29,94, 108, 109], diene polymers [110], poly(olefins) [111-114], poly(aryl ether ether ketones) [115], andpoly(phenyls) [116]. A detailed summary of other copolymers in which co-crystallization occurs can be found in [117]. There appear to be two underlying principles that govern isomorphic replacement [117]. These are that the two repeating units should have the same shape and volume and that the new ordered chain conformation be compatible with both types. In many of these examples the melting temperatures are essentially a linear function of the composition, whereas in others there is a smooth monotonic change. 

Heparin and i-carrageenan (segments) should have relatively stiff backbones with an essentially regular structure, and therefore liable (in principle) to assume ordered chain conformations in solution. ... 

An example of cocrystallization among vinyl copolymers can be found in copoly(styrene/ p-fluorostyrene). The stable crystal modifications of the homopolymers polystyrene and poly (p-fluorostyrene) are quite different. In the former case the ordered chain conformation is a threefold helix while in the latter it is a four-fold one. Nevertheless, the copolymers are crystalline over the complete composition range, and the melting temperature is essentially a linear function of composition. These data by themselves provide adequate evidence of cocrystallization. 

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

In order to examine whether this sequence gave a fold similar to the template, the corresponding peptide was synthesized and its structure experimentally determined by NMR methods. The result is shown in Figure 17.15 and compared to the design target whose main chain conformation is identical to that of the Zif 268 template. The folds are remarkably similar even though there are some differences in the loop region between the two p strands. The core of the molecule, which comprises seven hydrophobic side chains, is well-ordered whereas the termini are disordered. The root mean square deviation of the main chain atoms are 2.0 A for residues 3 to 26 and 1.0 A for residues 8 to 26. 

Plotting U as a function of L (or equivalently, to the end-to-end distance r of the modeled coil) permits us to predict the coil stretching behavior at different values of the parameter et, where t is the relaxation time of the dumbbell (Fig. 10). When et < 0.15, the only minimum in the potential curve is at r = 0 and all the dumbbell configurations are in the coil state. As et increases (to 0.20 in the Fig. 10), a second minimum appears which corresponds to a stretched state. Since the potential barrier (AU) between the two minima can be large compared to kBT, coiled molecules require a very long time, to the order of t exp (AU/kBT), to diffuse by Brownian motion over the barrier to the stretched state at any stage, there will be a distribution of long-lived metastable states with different chain conformations. With further increases in et, the second minimum deepens. The barrier decreases then disappears at et = 0.5. At this critical strain rate denoted by ecs, the transition from the coiled to the stretched state should occur instantaneously. 

As an example of the third case, we may have conformationally ordered chains, parallel among themselves, with short-range order in the lateral packing. Fiber spectrum features are well-defined layer lines, with diffuse reflections only. 

Besides crystalline order and structure, the chain conformation and segment orientation of polymer molecules in the vicinity of the surface are also expected to be modified due to the specific interaction and boundary condition at the surface between polymers and air (Fig. 1 a). According to detailed computer simulations [127, 128], the chain conformation at the free polymer surface is disturbed over a distance corresponding approximately to the radius of gyration of one chain. The chain segments in the outermost layers are expected to be oriented parallel to the surface and chain ends will be enriched at the surface. Experiments on the chain conformation in this region are not available, but might be feasible with evanescent wave techniques described previously. Surface structure on a micrometer scale is observed with IR-ATR techniques [129],... 

While thin polymer films may be very smooth and homogeneous, the chain conformation may be largely distorted due to the influence of the interfaces. Since the size of the polymer molecules is comparable to the film thickness those effects may play a significant role with ultra-thin polymer films. Several recent theoretical treatments are available [136-144,127,128] based on Monte Carlo [137-141,127, 128], molecular dynamics [142], variable density [143], cooperative motion [144], and bond fluctuation [136] model calculations. The distortion of the chain conformation near the interface, the segment orientation distribution, end distribution etc. are calculated as a function of film thickness and distance from the surface. In the limit of two-dimensional systems chains segregate and specific power laws are predicted [136, 137]. In 2D-blends of polymers a particular microdomain morphology may be expected [139]. Experiments on polymers in this area are presently, however, not available on a molecular level. Indications of order on an... 

Polypeptide chains exist in an equilibrium between different conformations as a function of environment (solvent, other solutes, pH) and thermodynamic (temperature, pressure) conditions. If a polypeptide adopts a structurally ordered, stable conformation, one speaks of an equilibrium between a folded state, represented by the structured, densely populated conformer, and an unfolded state, represented by diverse, sparsely populated conformers. Although this equilibrium exists for polypeptide chains of any size, its thermodynamics and kinetics are typically different for oligopeptides and proteins. This can be broadly explained with reference to the different dimensionalities of the free-energy hypersurfaces of these two types of molecules. 

In addition to quantitative crystallinity data, IR and Raman have been proven valuable tools to extract information on chain conformation in the three major phases [112-114], local order in amorphous polymers [115,116] high throughput characterization [117] and structural and polymorphic changes on heating and cooling semi-crystalline polymers [118-120]. 

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