Flexible-chain polymers models

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... 

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. 

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. 

The points in Fig. 24 represent the experimental values of A for a ladder poly-dichlorophenylsfloxane and cellulose carbanilate For both polymers the experimental data are in agreement with theoretical Curve 4 corresponding to the value of d/A = 0.5 for a kinetically flexible chain polymer. This qualitatively demonstrates that the hydrodynamic properties of the molecules of these two polymers at low X differ from those of an infinitely thin worm-like model. However, to obtain quantitative agreement between theory and experimental data according to Curve 4 in Fig. 24, A/d should be equal to 2 — a reasonable value for many flexible-chain polymers not realistic for such r d-chain polymers as ladder polysiloxanes or cellulose ethers and esters. 

Table 8). This permits the interpretation of experimental data by using the electro-optical properties of flexible-chain polymers in terms of a worm-like chain model However, EB in solutions of polyelectrolytes is of a complex nature. The high value of the observed effect is caused by the polarization of the ionic atmosphere surrounding the ionized macromolecule rather than by the dipolar and dielectric structure of the polymer chain. This polarization induced by the electric field depends on the ionic state of the solution and the ionogenic properties of the polymer chain whereas its dependence on the chain structure and conformation is slight. Hence, the information on the optical, dipolar and conformational properties of macromoiecules obtained by using EB data in solutions of flexible-chain polyelectrolytes is usually only qualitative. Studies of the kinetics of the Kerr effect in polyelectrolytes (arried out by pulsed technique) are more useful since in these... 

The study of catalytic and inhibitory effects in solutions of flexible chain polymers and micelles is of sufficient intrinsic interest, so that no special justification should be required for investigations of this tyj)e. Nevertheless, many of the workers active in this field insist on emphasizing the utility of such systems as enzyme models and we should, therefore, try to answer two crucial questions. What has been learned so far from these studies about the nature of enzymic catalysis What is the probability that studies of this type will contribute to the clarification of the enzyme problem in the future ... 

Hence, the perfonned within the framewoik of fractal approach analysis of behavior of polystirene, modified by Dendron s, in diluted solutions gave the same conclusions, as the analysis within the fiamewoik of classical approaches. The main distinction of the indicated approaches is the fact, that the structural model, allowing to describe quantitatively macromolecules structural state and conformation, was placed in the fractal approach base. Other characteristics (gyration radius, Kuhn segment length and so on) are the function of the indicated structural state of a macromolecule. The fractal analysis methods, used for the description of linear flexible-chain polymers behavior, can be applied successfiilly also in case of polymers with more complex macromolecular architecture. 

Although such a model satisfactorily describes complexation with proteins or DNA, its use for flexible chain polymers is restricted because there are no definite binding sites - one metal ion coordinates with a few arbitrarily located functional groups. 

In the modelling of industrial processing of flexible chain polymer melts we often need physically sensible description of the crystallization kinetics. Usually, the melt is subjected to time-dependent deformation rates (fibre spinning,... 

The expression for P f( q,0) for the monodisperse random-flight chain model, with Rl = dM / (where M =MIL), is widely used for the conformation of flexible chain polymers. Expansion of this expression in the limit of small u=(qR y gives [13,66] ... 

It is important to emphasize that the types of polymer dealt with in this chapter have flexible chains. Rigid-rod polymers forming mesomorphic phases are not discussed here. Most of the material presented comes from extensive studies of polyethylene. This polymer should be considered as a model for other flexible-chain polymers and not as a special case. 

The model of -relaxation in flexible-chain polymers [111, 112, 114] under discussion implies, in addition to rotation through different angles of the adjacent monomeric units, also the participation of a one-barrier transogauche... 

This kind of perfect flexibility means that C3 may lie anywhere on the surface of the sphere. According to the model, it is not even excluded from Cj. This model of a perfectly flexible chain is not a realistic representation of an actual polymer molecule. The latter is subject to fixed bond angles and experiences some degree of hindrance to rotation around bonds. We shall consider the effect of these constraints, as well as the effect of solvent-polymer interactions, after we explore the properties of the perfectly flexible chain. Even in this revised model, we shall not correct for the volume excluded by the polymer chain itself. 

At the beginning of this section we enumerated four ways in which actual polymer molecules deviate from the model for perfectly flexible chains. The three sources of deviation which we have discussed so far all lead to the prediction of larger coil dimensions than would be the case for perfect flexibility. The fourth source of discrepancy, solvent interaction, can have either an expansion or a contraction effect on the coil dimensions. To see how this comes about, we consider enclosing the spherical domain occupied by the polymer molecule by a hypothetical boundary as indicated by the broken line in Fig. 1.9. Only a portion of this domain is actually occupied by chain segments, and the remaining sites are occupied by solvent molecules which we have assumed to be totally indifferent as far as coil dimensions are concerned. The region enclosed by this hypothetical boundary may be viewed as a solution, an we next consider the tendency of solvent molecules to cross in or out of the domain of the polymer molecule. 

G. Guillot, L. Leger, F. Rondelez. Diffusion of large flexible polymer chains through model porous membranes. Macromolecules 5 2531-2537, 1985. 

Diffusion of flexible macromolecules in solutions and gel media has also been studied extensively [35,97]. The Zimm model for diffusion of flexible chains in polymer melts predicts that the diffusion coefficient of a flexible polymer in solution depends on polymer length to the 1/2 power, D N. This theoretical result has also been confirmed by experimental data [97,122]. The reptation theory for diffusion of flexible polymers in highly restricted environments predicts a dependence D [97,122,127]. Results of various... 

The main parameters used to describe a polymer chain are the polymerization index N, which counts the number of repeat units or monomers along the chain, and the size of one monomer or the distance between two neighboring monomers. The monomer size ranges from a few Angstroms for synthetic polymers to a few nanometers for biopolymers. The simplest theoretical description of flexible chain conformations is achieved with the so-called freely-jointed chain (FJC) model, where a polymer consisting of N + I monomers is represented by N bonds defined by bond vectors r/ with j= Each bond vector has a fixed length r,j = a corresponding to the... 

Figure 7 presents z as a function of the reduced temperature variable 87a T — 7a /7a- The different curves of Fig. 7 refer to the F-F and F-S polymer classes and the same M as in Fig. 6. Evidently, the calculated z grows much faster with 87a for the F-S polymer class and increases somewhat with M within each polymer class. These trends, taken in conjunction with the AG model, again translate into the prediction that polymer chains with bulky stiff side groups (F-S class) have a stronger dependence of the relaxation time on temperature (i.e., they are more fragile) than flexible chains with...

---