Polymers flexible-chain

Oscillatory shear experiments using, for example, cone-and-plate devices constitute the third main group of viscometric techniques. These techniques enable the complex dynamic viscosity rj ) to be measured as a function of the angular velocity (cu). The fundamental equations are presented in section 6.2 (eqs (6.22H6.27)). Another arrangement is two rotating parallel excentric discs by which the melt is subjected to periodic sinusoidal deformation. 

There are numerous other experimental methods that provide information about the rheological behaviour, including the molecular response to stresses and strains swell and shrinkage tests, flow-birefringence measurements (Chapter 9) and flow-infrared-dichroism measurements (Chapter 9) to mention but a few. 

Small-angle neutron scattering has confirmed that the radius of gyration of polymer chains has the same 

Both rjo and 7 show an abrupt change in their molar mass coefficients at certain critical molar mass values, denoted and M (Figs 6.13 and 6.14). The critical molar mass (M .) separating the two slopes in the plot of log rjo against log M is not the same as the other characteristic molar mass M. The low molar mass melts, with a molar mass lower than the critical M ( c)/ 3re characterized by few or no chain 

The so-called entanglement molar mass (Mg) is calculated from the plateau value of the shear modulus (Gg, Fig. 6.8) and, using classical rubber elasticity 

---

Properties. One of the characteristic properties of the polyphosphazene backbone is high chain dexibility which allows mobility of the chains even at quite low temperatures. Glass-transition temperatures down to —105° C are known with some alkoxy substituents. Symmetrically substituted alkoxy and aryloxy polymers often exhibit melting transitions if the substituents allow packing of the chains, but mixed-substituent polymers are amorphous. Thus the mixed substitution pattern is deUberately used for the synthesis of various phosphazene elastomers. On the other hand, as with many other flexible-chain polymers, glass-transition temperatures above 100°C can be obtained with bulky substituents on the phosphazene backbone. 

Elyashevich, G. K. Thermodynamics and Kinetics of Orientational Crystallization of Flexible-Chain Polymers. Vol. 43, pp. 207 — 246. 

Thermodynamics and Kinetics of Orientational Crystallization of Flexible-Chain Polymers... 

Thermodynamics of Crystallization of Flexible-Chain Polymers Under Conditions of Molecular Orientation. 217... 

Two approaches to the attainment of the oriented states of polymer solutions and melts can be distinguished. The first one consists in the orientational crystallization of flexible-chain polymers based on the fixation by subsequent crystallization of the chains obtained as a result of melt extension. This procedure ensures the formation of a highly oriented supramolecular structure in the crystallized material. The second approach is based on the use of solutions of rigid-chain polymers in which the transition to the liquid crystalline state occurs, due to a high anisometry of the macromolecules. This state is characterized by high one-dimensional chain orientation and, as a result, by the anisotropy of the main physical properties of the material. Only slight extensions are required to obtain highly oriented films and fibers from such solutions. 

These two different approaches for attaining an oriented state in flexible-chain and rigid-chain polymers indicate that the fundamental property of macromolecules - their flexibility - is of great importance to the orientation processes. However, the mechanism of the transition into the oriented state and the properties of highly oriented systems exhibit many features characteristic of both rigid- and flexible-chain polymers. 

Usually, dilute polymer solutions are isotropic systems, i.e. macromolecular chains can exist in these solutions independently of each other with a random distribution of orientations of the long axes of coils. The solutions of flexible-chain polymers remain isotropic when the solution concentration increases whereas in concentrated solutions of macromolecules of limited flexibility the chains can no longer be oriented arbitrarily and some direction of preferential orientations of macromolecular axes appears, i.e. the mutual orientations of the axes of neighboring molecules are correlated. This means that... 

In contrast, for flexible-chain polymers, the transition into the ordered state is possible only if the flexibility can be decreased to values below fcr (in the absence of external deformational fields, the crystallization of flexible-chain polymers occurs by the mechanism of chain folding). 

Hence, the main aim of the technological process in obtaining fibres from flexible-chain polymers is to extend flexible-chain molecules and to fix their oriented state by subsequent crystallization. The filaments obtained by this method exhibit a fibrillar structure and high tenacity, because the structure of the filament is similar to that of fibres prepared from rigid-chain polymers (for a detailed thermodynamic treatment of orientation processes in polymer solutions and the thermokinetic analysis of jet-fibre transition in longitudinal solution flow see monograph3. ... 

Usually, crystallization of flexible-chain polymers from undeformed solutions and melts involves chain folding. Spherulite structures without a preferred orientation are generally formed. The structure of the sample as a whole is isotropic it is a system with a large number of folded-chain crystals distributed in an amorphous matrix and connected by a small number of tie chains (and an even smaller number of strained chains called loaded chains). In this case, the mechanical properties of polymer materials are determined by the small number of these ties and, hence, the tensile strength and elastic moduli of these polymers are not high. 

We carried out thermodynamic studies on the crystallization from melts of flexible-chain polymers uniaxially stretched at various degrees of molecular orientation in the melt and studied the effect of the stretching stress on thermodynamic parameters such as degree of... 

Fig. 5 a, b. Models of the crystallization of flexible-chain polymers with the formation of a folded-chain crystals and b extended-chain crystals b... 

Figure 4 (curve 1) shows that in the absence of extension the distribution function W(fi) lies in the range 0 < /S < 0.2 for relatively long chains. In other words, in the absence of external forces, crystallization of flexible-chain polymers always proceeds with the formation of FCC since in the unperturbed melt the values of /3 are lower than /3cr. For short chains, the function W(/3) is broader (at the same structural flexibility f) (Fig. 4, curve 2) and the chains are characterized by the values of > /3cr, i.e. they can crystallize with the formation of ECC. Hence, at the same crystallization temperature, a... 

In the foregoing discussion, flexible-chain polymers with f close to unity were considered. The limitation of flexibility (decrease in f), just as the lowering of N, leads, according to Flory1, to a decreas in /3... 

This model of the structure of orientationally crystallized samples based on experimental data is in good agreement with the results of the foregoing thermodynamic analysis which resulted in relationships describing the formation of two structures, FCC and ECC, during the crystallization of strongly oriented melts of flexible-chain polymers. 

Fig. 21 a-c. Schematic representation supramolecular structure of a crystalline rigid-chain polymer (a), an idealized ECC of a flexible-chain polymer (b) and an orientationally crystallized sample with a spatial ECC framework (c)... 

At present, it is known that the structures of the ECC type (Figs 3 and 21) can be obtained in principle for all linear crystallizable polymers. However, in practice, ECC does not occur although, as follows from the preceding considerations, the formation of linear single crystals of macroscopic size (100% ECC) is not forbidden for any fundamental thermodynamic or thermokinetic reasons60,65). It should be noted that the attained tenacities of rigid- and flexible-chain polymer fibers are almost identical. The reasons for a relatively low tenacity of fibers from rigid-chain polymers and for the adequacy of the model in Fig. 21 a have been analyzed in detail in Ref. 65. 

In conclusion, the fundamental features of various methods for obtaining high strength systems from flexible-chain polymers should also be mentioned. Since the presence of ECC leads to an increase in the fraction of tie chains in crystallized samples (their number can be increased by other methods not related to a direct formation of ECC, e.g. by orientational drawing investigated by Marikhin and Myasnikova4)), the main tech-... 

Klenin VJ (1999) Thermodynamics of systems containing flexible chain polymers. 

An alkali halide (NaCl, KCl, KBr, etc.) which has a freshly cleaved (001) face is introduced into a polymer solution and then the pol5nner is to be crystallized epitaxially onto the face of the alkali halide. In general, flexible-chain polymers are apt to be crystallized as rod-like crystals on such an alkali halide these rod-like crystals are edge-on lamellae with their lateral surface being mostly in contact with the (001) face of the alkali halide. A given polymer deposited on an alkali halide can be melted and subsequently crystallized there in an epitaxial fashion. 

Figure 8. The reduced excess free energy of mixing x versus the volume fraction of solute for a) flexible chain polymers (18) a and b) rodlike chains (17). The chains have 100 segments in both cases.

Eisner, G., Riekel, Ch. and Zachmann, H. G. Synchrotron Radiation Physics. Vol. 67, pp. 1-58. Elyashevich, G. KThermodynamics and Kinetics of Orientational Crystallization of Flexible-Chain Polymers. Vol. 43, pp. 207-246. 

---