Rigid chain polymers parameters

Figure 16 shows a schematic diagram of phase transformations for rigid-chain polymers separated from isotropic solutions by introducing a nonsolvent into the system (this is a usual method of obtaining fibres and films) (cf. >). The initial isotropic solution with the polymer concentration V2 and the value of the Huggins-Flory parameter is in the monophase region. The critical concentration of the transition into liquid crystalline state for this system is v. When a nonsolvent is introduced, i.e. when x is increased up to the value >0.5 (x ), two routes of the phase transition... 

Equations (4) and (5) show that when the parameter x = 2 L/A changes from 0 to the hydrodynamic properties of a worm-like chain change from those of a thin straight tod to those of an undrained Gaussian coil. In accordance with this the dependence of intrinsic viscosity (nl and diffusion coefficient D on molecular weight M of a rigid-chain polymer cannot be described by the usual Mark-Kuhn dependence... 

Tables 1—3 give the values of molecular parameters characterizing the equilibrium rigidity and hydrodynamic properties of molecules of some rigid-chain polymers obtained from viscometric and diffusion-sedimentation measurements of their dilute solutions.

Table 9. Parameters characterizing the equilibrium rigidity and optical anisotropy of some rigid-chain polymer molecules according to the data of flow birefringence in their a luttons... 

As it has been shown in Ref [227], increase from 1 up to 4 leads to essential growth of PSD macromolecules equilibrium rigidity Kuhn segment lengthincreases from 3.9 up to 23.3 nm. The authors [56] received the relationships (54) and (55) between stmctural/) and molecular 4 macromolecule parameters for flexible- and rigid-chain polymers, respectively. In Fig. 113 the similar dependence D A) for the considered polymers PSD is adduced, which, as earlier, has shown reduction at growth and is described analytically by the following empirical correlation [240] ... 

Shogenov, V. N. Kozlov, G. V. Mikitaev, A. K. The prediction of failure process parameters of rigid-chain polymers. High-Molecular Compounds. B, 1989, 31(11), 809-811. 

Special attention should be turned to the sharp transition from a narrow concentration corridor to a broad heterophase region, mentioned above, which takes place for low positive values of parameter x- It is int esting to compare the appearance of this broad region with the phenomenon of decomposition of solutions of flexible-chain polymers into two phases with the formation of two liquid (amorphous) phases with values of x in the limit (with infinitely high molecular weight of the polymer) of 0.5. TTie phase equilibrium diagrams (in coordinates v-x) for a rigid-chain polymer with an axial ratio of x = 150 and 350... 

Precipitation of the polymer on addition of a nonsolvent or with any changes in the thermodynamic parameters in solutions whose conc tration is below the critical point of the transition to the liquid-crystalline state is the most typical case of the intermediate phase equilibrium in rigid-chain polymer-solvent systems. Instead of the anticipated establishment of isotropic-anisotrqric phase equilibrium, equilibrium of two amorphous (isotropic) phases initially arises if the parameter x attains values greater than +0.5. 

In going to semidilute solutions of both flexible-chain and rigid-chain polymers, it is thus necessary to find a new parameter which describes the properties of such a network. The ratio (c/c ) can be used as such a parameter [18, 19], where is the concentration corresponding to the formation of a system of intermolecular contacts, and P is the exponent in the equation i] c. In view of this, Martin s equation should be updated ... 

When the salt of PMAA is formed the rigidity of polymer chain is increased a little that leads to little increase of values of mean-square length of monomer unit and distance between polymer chain ends. The result obtained under addition to polymer salt solvent in methanol (40 vol. % of water, at large content of water the solution is not vitrificated, but is crystallized) represents special interest at that the macromolecule in solid state keeps conformation of Gauss ball (Figure 2), however, as we should expect, rigidity (parameter a) and sizes of ball are increased (Table 1). 

This system of rigid blocks with flexible spacers may serve as a model of polymers with a limited flexibih ty. In his early work Flory considered the behavior of semiflexible chain polymers by introducing the flexibility parameter / which represents the fraction of bonds which are not in a colhnear position in the... 

As already mentioned, for polymers with high equilibrium chain rigidity the experimental dependence of [n]/[t ] on molecular we t agrees with the theoretical relation (59) for kinetically rigid chains. Thhi equation can be utilized for the determination of the parameters A and 0 from experimental data on flow birefringence of polymer or fraction of varying molecular we t. 

For all ring-containing aromatic polymers the parameters of hindrance to rotation are close to each other and are lower than the values which are characteristic of typical flexible-chain polymers This means that, in contrast to cellulose derivatives, the high equilibrium chain rigidity of these aromatic polymers is caused by the peculiarities of the geometrical structure of their molecules rather than by hindrance to intra-molecular rotation. 

Thus, analysis of hydrodynamic properties of native lignins reveals that their behaviour in dilute solutions is different from that of linear polymers, both flexible- and rigid-chain, in any of the known conformations. Apparently, the macromolecules of soluble lignins are randomly branched chains. Branchings in a chain are known to reduce the hydrodynamic dimensions, (i.e., reduce [q]), and increase the diffusion mobility compared to the linear analog, theoretical value of b, in a 0-solvent is 0.25. The branching of the polymer also reduces the hydrodynamic invariant by 15-20% compared to the standard value 3.2 x 10 erg/(K mol ) and results in anomalous values of the Huggins parameter. 

The necessary for ealculations parameters (a and A) for flexible-ehain pol5miers aceepted aeeording to the data of Ref. [65], for rigid-chain ones—according to the data of Ref [66]. As it has been noted above, in Ref. [63] the empirieal relationships between D and A were obtained. For flexible-ehain polymers the indicated relationship has a look like [63] ... 

For a chain with completely free rotation, (cos 0 > = 0 and Equation (4-26) becomes Equation (4-25). An dAVtrans chain is a rigid chain with 6 = 0, which is, however, physically absurd with regard to Equation (4-26). Thus, o is a measure of the hindrance to rotation it is often called the steric hindrance parameter. With tactic polymers, the relationship between 0 and a is more complicated. One can, however, always use an equation analogous to Equation (4-26) ... 

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