Segments of polymer molecules

By postulating that the primary factor determining the concentration and temperature dependence of viscosities of concentrated polymer solutions is the mobility of each flow unit or a segment of polymer molecule in solution, Fujita and Kishimoto (1961) have derived an equation for the viscosity of such solutions. If we denote byBj, the value of B corresponding to the minimum hole required for one flow unit to allow of a considerable displacement, their equation can be put in the form ... 

Fig. 2.18 A possible form of aggregation of parallel segments of polymer molecules during solidification requiring no chain folding, as conceived of by Fischer (from Fischer (1978) courtesy of the lUPAQ.

Fig. 4. Segments of polymer molecule on lattice sites in liquid.

In the case of polymer molecules where the dipoles are not directly attached to the main chain, segmental movement of the chain is not essential for dipole polarisation and dipole movement is possible at temperatures below the glass transition temperature. Such materials are less effective as electrical insulators at temperatures in the glassy range. With many of these polymers, e.g., poly(methyl methacrylate), there are two or more maxima in the power factor-temperature curve for a given frequency. The presence of two such maxima is due to the different orientation times of the dipoles with and without associated segmental motion of the main chain. 

The formation of the microstructure involves the folding of linear segments of polymer chains in an orderly manner to form a crystalline lamellae, which tends to organize into a spherulite structure. The SCB hinder the formation of spherulite. However, the volume of spherulite/axialites increases if the branched segments participate in their formation [59]. Heterogeneity due to MW and SCB leads to segregation of PE molecules on solidification [59-65], The low MW species are accumulated in the peripheral parts of the spherulite/axialites [63]. The low-MW segregated material is brittle due to a low concentration of interlamellar tie chains [65] and... 

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],... 

Heavily crosslinked polymers, by contrast, tend to be very brittle and, unlike thermoplastics, this brittleness cannot be altered much by heahng. Heavily crosslinked materials have a dense three-dimensional network of covalent bonds in them, with little freedom for motion by the individual segments of the molecules involved in such structures. Hence there is no mechanism available to allow the material to take up the stress, with the result that it fails catastrophically at a given load with minimal deformation. 

When a stress is applied to the bulk polymer melt, the mass flows in the direction that relieves the stress. At the molecular level, the probability of a molecular jump becomes higher in the direction of the stress than in any other direction and hence these stress-relieving motions predominate, leading to the observed pattern of flow. There is evidence that the molecular unit of flow is not the complete macromolecule but rather a segment of the molecule containing up to 50 carbon atoms. Viscous flow takes place by successive jumps of such segments until the entire macromolecule has shifted. 

This treatment, resting essentially on the assumed approximate interchangeability of molecules of solvent and solute in the solution, cannot possibly hold for polymer solutions in which the solute molecule may be a thousand or more times the size of the solvent. The long chain polymer may be considered to consist of x chain segTneTits each of which is equal in size to a solvent molecule x is, of course, the ratio of the molar volumes of the solute and solvent. A segment and a solvent molecule may replace one another in the liquid lattice. In other respects the assumptions required are equivalent to those used above. The polymer solution differs from that containing an equal proportion of monomeric solute in the one important respect that sets of x contiguous cells in the lattice are required for accommodation of polymer molecules, whereas no such restriction applies to the solution of the monomeric solute. The situation is illustrated in Fig. 110. 

The probability of finding the center of gravity of polymer molecule Z in a volume element dV far removed from any other polymer molecule naturally will be proportional to the size of the element. (This volume element should not be confused with the dV represented in Fig. 114 and employed above in the investigation of segment interactions in the vicinity of the pair kyL) Presuming pi — Ki to be positive, the probability that molecule Z is found near another molecule, such as fc, will be diminished to an extent depending on AFa for the pair. If we consider volume elements of the same size, one at a finite distance a from molecule k and the other far away from any polymer molecule, the relative probability that the center of molecule I will occur in the former compared with the latter is... 

There have been many attempts to describe the process of mixing and solubility of polymer molecules in thermodynamic terms. By assuming that the sizes of polymer segments are similar to those of solvent molecules, Flory and Huggins derived an expression for the partial molar Gibbs free energy of dilution that included the dimensionless Flory Higgins interaction parameter X = ZAH/RT, where Z is the lattice coordination number. It is now... 

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