Chain segment stiffness

In a real chain segment-segment correlations extend beyond nearest neighbour distances. The standard model to treat the local statistics of a chain, which includes the local stiffness, would be the rotational isomeric state (RIS) [211] formalism. For a mode description as required for an evaluation of the chain motion it is more appropriate to consider the so-called all-rotational state (ARS) model [212], which describes the chain statistics in terms of orthogonal Rouse modes. It can be shown that both approaches are formally equivalent and only differ in the choice of the orthonormal basis for the representation of statistical weights. In the ARS approach the characteristic ratio of the RIS-model becomes mode dependent. 

When polymer melts, rubbers, or elastomers are cooled down below Tg, they may freeze to glasses (noncrystalline amorphous phases). The rotations motions of the chain segments (micro-Brownian motions) are almost stopped now, and the transparent materials become stiff and (in most cases) brittle. 

Permeation is dependent on the segmental motion of the polymer chains and the free volume of chain segments. The free volume decreases, whereas the chain stiffness increases, as the temperature of the polymeric membrane is lowered toward the glass transition temperature Tf. The free volume is similar for all polymers at the Tf. 

The coils are mutually entangled, this fact is largely responsible for the special behaviour of polymers Between chain segments relatively weak interaction forces are present chain segments can move with respect to each other under the influence of relatively small external stresses. Consequently, the stiffness of polymers is rather low. 

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... 

A = xoK/Ky /(4jr/- y) is the angular-independent strength of the dipolar coupling [Coh2, Brel]. The average distance r// of the coupling spins I and J is contained in A, and the effective number of fictitious chain segments depends on the chain stiffness,... 

Some important properties of polymer chains in dilute solutions [steric hindrance parameter, characteristic ratio, persistence length, radius of gyration, statistical chain segment length (introduced earlier, in Chapter 11), intrinsic viscosity, and viscosity at small but finite concentrations] will be discussed, and new correlations will be presented for the steric hindrance parameter and the molar stiffness function, in Chapter 12. 

There have been several attempts to relate Kg to the critical molecular weight (Mcr, which is discussed in Chapter 13) based on considerations of the effects of polymer chain entanglements on the large-scale cooperative motions of chain segments involved in the glass transition for example, see references [97-99]. It was also suggested [100,101], from considerations of chain stiffness and the statistics of chain conformations, that Kg should be proportional to a power of... 

Although a higher tendency to crystallise and form LC-phases was expected for disubstituted hydroquinones reacted with the same diacid, in fact amorphous isotropic PEIs were generally obtained. Since there is no reason why a second bulky substituent should reduce chain stiffness it seemed more likely that extra bulky side substituents interfere with electronic interactions between neighbouring chain segments. 

A method of internal homogeneous nucleation utilizes the tendency of chainlike molecules to chain-fold. Stiff macromolecules do not fold easily. If flexible segments are polymerized into the macromolecule, these segments will preferentially reside in the fold surface, and homogeneous nucleation is facilitated by chain folding. 

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