Stiff-flexible polymers

Insertion of flexible blocks into the stiff polymer chain of PAN ensures the possibility of raising the resistance of modified PAN fibres to multiple deformations and, especially, increases significantly the abrasive resistance of fibres made of block copolymers. 

Subsequent work by Johansson and Lofroth [183] compared this result with those obtained from Brownian dynamics simulation of hard-sphere diffusion in polymer networks of wormlike chains. They concluded that their theory gave excellent agreement for small particles. For larger particles, the theory predicted a faster diffusion than was observed. They have also compared the diffusion coefficients from Eq. (73) to the experimental values [182] for diffusion of poly(ethylene glycol) in k-carrageenan gels and solutions. It was found that their theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. Equation (73) is an example of the so-called stretched exponential function discussed further later. 

Our principal concern is often the polymer s mechanical properties. For instance, the requirements of the handle of an electrician s screwdriver are very different from those of wire insulation. In the former application, we are free to choose stiff polymers of many types, including glassy amorphous polymers. In contrast, wire insulation must be flexible, which limits our choice to ductile polymers. 

Table 5.2 lists polymers and their tendency toward crystallinity. Yield stress and strength, and hardness increase with an increase in crystallinity as does elastic modulus and stiffness. Physical factors that increase crystallinity, such as slower cooling and annealing, also tend to increase the stiffness, hardness, and modulus of a polymeric material. Thus polymers with at least some degree of crystallinity are denser, stiffer, and stronger than amorphous polymers. However, the amorphous region contributes to the toughness and flexibility of polymers. 

Flexible pendant groups also promote flexibility in polymers. Thus polyoctyl methacrylate is much more flexible than PMMA, Stiffness resulting from crystallinity may be overcome by copolymerization which reduces the tendency to crystallize. Thus although hdpe is relatively stiff, EP is flexible. 

For a polydisperse polymer, analysis of sedimentation equilibrium data becomes complex, because the molecular weight distribution significantly affects the solute distribution. In 1970, Scholte [62] made a thermodynamic analysis of sedimentation equilibrium for polydisperse flexible polymer solutions on the basis of Flory and Huggins chemical potential equations. From a similar thermodynamic analysis for stiff polymer solutions with Eqs. (27) for IT and (28) for the polymer chemical potential, we can show that the right-hand side of Eq. (29) for the isotropic solution of a polydisperse polymer is given, in a good approximation, by Eq. (30) if M is replaced by Mw [41],... 

Then there are flexible linear polymers which curl up in solution to give a random cell. If the chain is stiff, such as in cellulose or in DNA, the coil becomes highly expanded. 

By building - in combinations of aromatic rings into the polymer chains, chemists are able to produce polymer chains with very low chain flexibility. In the limit they reach rigid-rod-type op polymers. Such polymers show substantial temperature - pressure -concentration regions in which the stiff polymer chains arrange in some form of orientation. This phase behaviour gave them the name Liquid Crystalline Polymers (LCP) and LCP have unique properties. 

Changes in the flexibility of polymer coils owing to concentration - variation may effect the entropy. Huggins [21] introduced two corrections for the athermal entropy of mixing, that take into account the influence a second polymer has on the stiffness of the other polymer... 

Using the matrix notation approach [13 15] that was introduced to describe multicomponent (here also consider n components) flexible polymer systems, the RPA equations are reviewed here for an incompressible stiff polymer mixture. As before, the idea is to isolate a matrix component (denoted component M) from the rest of the blend (denoted R). The various correlations are described through a scalar part XjiM(Q), a vector part Xmr(Q) and a matrix part XRR(Q), and similarly for potentials W s. The RPA equations for the n-vector fluctuating densities are ... 

From Ciferri s equation it follows that for flexible polymers the exponent n is larger than for stiff polymers (see, e.g. Fig. 16.29). 

Flexibility, for example, can be imparted to stiff polymers through the addition of a compatible liquid or solid that permits spillage of polymer... 

More recently Morse produced a complete microscopic tube theory for stiff polymers that successfully interpolates between the rigid-rod and flexible chain limits. This theory explains many features of semiflexible polymer rheology, including the two mechanisms for plateau moduli described above (which depend on a comparison of timescales), with the tube diameter being the sole fitting parameter as in the Doi-Edwards theory. More recently, Morse successfully computed a tube diameter from two different approaches (self-consistent binary collision and continuum effective medium) that give similar results, e.g. modulus G p and respectively). An elastic network approximation... 

More recently Morse produced a complete microscopic tube theory for stiff polymers that successfully interpolates between the rigid-rod and flexible chain... 

The worm-like chain model (sometimes called the Kratky-Porod model) is a special case of the freely rotating chain model for very small values of the bond angle. This is a good model for very stiff polymers, such as double-stranded DNA for which the flexibility is due to fluctuations of the contour of the chain from a straight line rather than to trans-gauche bond rotations. For small values of the bond angle ( < 1), the cos 9 in Eq. (2.23) can be expanded about its value of unity at = 0 ... 

The subject of polymer size or chain dimensions is concerned with relating the sizes and shapes of individual polymer molecules to their chemical structure, chain length, and molecular environment. The shape of the polymer molecule is to a large extent determined by the effects of its chemical structure upon chain stiffness. Polymers with relatively flexible backbones tend to be highly coiled and can be represented as random coils. But as the backbone becomes stiffer, e.g., in polymers with more aromatic backbone chain, the molecules begin to adopt a more elongated wormlike shape and ultimately become rodlike. However, the theories which are presented below are concerned only with the chain dimensions of linear flexible polymer molecules. More advanced texts should be consulted for treatments of wormlike and rodlike chains. 

Since, ligand accessibility and template definition are maximal in stiff polymers, whilst good kinetics and rapid equilibration are favoured in flexible polymers, the choice of cross-linker must inevitably be a compromise [47], It should be pointed out that, in addition to the type and proportion of cross-linker involved, the porogenic solvent and method of polymerisation both also affect the macro structure of the polymer in terms of porosity and internal surface area. 

Flexible (as opposed to stiff) polymer chain ends and loops in the material interface lower the thrombogenic potential of the foreign surface. 

A 0.1 mm thick bag will be flexible whatever polymer is used consider the flexibility of a 0.13 mm thick OHP sheet, the PET has Young s modulus E = 3 GPa. Thin films, made from low crystallinity PE copolymers or plasticised PVC have < 0.1 GPa, and are much more flexible. The tubing, of typical inner and outer diameters 3 and 4 mm, respectively, has a higher bending stiffness than the bags. 

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