Conformation of the Polymer Chain

One of the great classic problems in polymer science has been the determination of the conformation of the polymer chain in space. The data in Table 

A more general equation yielding the average end-to-end distance of a random coil, Tq, is given by 

However, equation (5.13) stiU underestimates the end-to-end distance of the polymer chain, omitting such factors as excluded volume. This last arises from the fact that a chain cannot cross itself in space. 

The characteristic ratio C = rVl n varies from about 5 to about 10, depending on the foliage present on the individual chains (see Table 5.7). The values of Pn can be calculated by a direct consideration of the bond angles and energies of the various states and a consideration of longer-range interactions between portions of the chain (40). 

2 Kuhn Segments There are several approaches for dividing the polymer chain into specified lengths for conceptual or analytic purposes. For example, Section 4.2 introduced the blob, useful for semidilute solution 

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The transition state was shown to have a four-centered nonplanar structure and the product showed a strong jS-agostic interaction.59 Molecular-mechanics (MM) calculations based on the structure of the transition state indicated that the regioselectivity is in good agreement with the steric energy of the transition state rather than the stability of the 7r-complex. The MM study also indicated that the substituents on the Cp rings determine the conformation of the polymer chain end, and the fixed polymer chain end conformation in turn determines the stereochemistry of olefin insertion at the transition state.59... 

As discussed in Section 1, general requirements for the crystallizability of polymers are the regularity of the chemical constitution and of the configuration of long sequences of monomeric units. In these conditions the conformation of the chains is also regular (equivalence principle). However, some three-dimensional long-range (crystalline) order may be maintained even when disorder is present in the conformation of the polymer chains. 

The secondary structure describes the molecular shape or conformation of the polymer chain. For most linear polymers this shape approaches a helical or pleated skirt (or sheet) arrangement depending on the nature of the polymer, treatment, and function. Examples of secondary structures appear in Figure 2.13. 

The optical anisotropies y and molar Kerr constants mK of model compounds, and of polylp-chlorostyrene) and polyfp-bromostyrene), are determined. Averages and over all conformations of the polymer chains are calculated as functions of the fraction wm of the meso diads using the RIS model originally developed for PS. 

The authors prefered the latter explanation. They argue that the difference in the dielectric constant of the medium, when a hydrocarbon rich mixture is compared with that rich in sulfur dioxide, affects the ratio of gauche to trans conformations of the polymer chain. Such effects were observed in other systems, e.g. in 1,2 dichloroethane (38). Hence,... 

Figure 29-8 Configuration of atactic, isotactic, and syndiotactic poly-propene. These configurations are drawn here to show the stereochemical relationships of the substituent groups and are not meant to represent necessarily the stable conformations of the polymer chains.

Olefin Polymers Isotactic polymers of propylene and 1-butene obtained by optically active metallocene catalyst (145) have been reported to show large specific rotation in suspension ([a]D-123°, -250° for polypropylene [a]D+130° for polybutene), which was lost when the polymers were completely dissolved or heated [176,177]. The optical activity was ascribed to a helical conformation of the polymer chain with preferential screw sense. 

Figure 3.10 X-ray diffraction pattern obtained from a fiber of poly(dichlorophosphazene). The pattern of diffraction arcs is consistent with a near cis-trans-plama conformation of the polymer chains. 

When dendritic fragments are attached to polymer chains, the conformation of the polymer chain is strongly affected by the size and chemical structure of the dendritic wedges attached. Dense attachment of dendritic side chain converts a linear polymer into a cylindrically shaped, rigid and nanoscopic dimension. Frechet and Flawker [70] were one of the first to recognize these hybrid architectures . 

Comparable experiments were performed with DexP-coated macroporous polystyrene-divinylbenzene (PS-DVB) particles [264] and with DexP, labelled with 4-amino-TEMPO, using EPR spectroscopy to study the conformation of the polymer chains [265]. Low substituted DexP gave thicker layers with lower density than highly substituted derivatives due to the presence of more loops and tails. With increasing DS of DexP, the stiffness of the adsorbed layers and, therefore, the density increases and the non-specific interaction of BSA with the DexP-coated PS-DVB surfaces seems to be restricted to the top of the adsorbed layer. 

Adsorption of block copolymers onto a surface is another pathway for surface functionalization. Block copolymers in solution of selective solvent afford the possibility to both self-assemble and adsorb onto a surface. The adsorption behavior is governed mostly by the interaction between the polymers and the solvent, but also by the size and the conformation of the polymer chains and by the interfacial contact energy of the polymer chains with the substrate [115-119], Indeed, in a selective solvent, one of the blocks is in a good solvent it swells and does not adsorb to the surface while the other block, which is in a poor solvent, will adsorb strongly to the surface to minimize its contact with the solvent. There have been a considerable number of studies dedicated to the adsorption of block copolymers to flat or curved surfaces, including adsorption of poly(/cr/-butylstyrcnc)-ft/od -sodium poly(styrenesulfonate) onto silica surfaces [120], polystyrene-Woc -poly(acrylic acid) onto weak polyelectrolyte multilayer surfaces [121], polyethylene-Wocfc-poly(ethylene oxide) on alkanethiol-patterned gold surfaces [122], or poly(ethylene oxide)-Woc -poly(lactide) onto colloidal polystyrene particles [123],... 

As the coupling constants, especially between two protons on adjacent carbon atoms, are very sensitive to rotational changes, one can also derive from them the preferred conformation of the polymer chain (see Diehl et al., 1971). 

The secondary structure, such as a conformation, is studied mainly by solid-state NMR.2 In the solid state, NMR chemical shift is characteristic of specific conformations because the internal rotation around the chemical bonds is restricted. This shows that the NMR chemical shift can be used for elucidating the conformation of polymers in the solid state. In the amorphous phase, the conformation of the polymer chain is not fixed above Tg. Even in such a case, NMR chemical shift and the relaxation parameters can give us useful information such as the averaged conformation or the dynamics of the exchange. Solid-state NMR can also provide information about the crystalline structures, which are classified under the higher order structures through NMR chemical shift, since for most polymers, different crystalline structures accompany conformational changes which affect their NMR chemical shift. 

The conformation of the polymer chain in a crystal is approximately the same as that corresponding to one of the minima of the potential energy of the isolated chain, with only small deviations possible. 

Data of intrinsic viscosity indicate that the conformation of the polymer chain is affected by the sort of solvent. As the polymer is soluble in DMSO but insoluble EG, addition of EG to DMSO may cause shrinkage of the polymer chain. A decrease in intrinsic viscosity (Table 12) appears to correspond to an increase in the hypochromi-city (Table 11). 

Polymer Conformation and Crystallinity. Beyond the stereoregularity and tacticity, the geometrical conformation of the polymer chain in the solid material could influence its electronic structure, through a modification of its valence band molecular orbitals. Indeed, a few years ago, very characteristic band structures were calculated for T, G, TG, and TGTG polyethylenes ( ). More recently. Extended Huckel crystal orbital calculations showed that for isotactic polypropylene, a zig-zag planar or a helical conformation resulted in significant changes in the theoretical valence band spectra, supporting the idea that conformation effects could be detected experimentally by the XPS method ( ). 

The polysilane a-a absorption wavelength, kmax. depends on the nature of the substituents, and depends quite strongly on the conformation of the polymer chain. The absorption band is shifted to a longer wavelength as the length of all-trans segments in the polymer chain increases. The number of trans junctions often increases with decreasing temperature. 

The optical rotation of such imprinted polymers after template removal is clearly not caused by individual chiral centres, as is usually the case, but by the boundaries of the empty cavities as a whole. Their chiral construction is stabilised by means of the cross-linking of the polymer chains. This type of chirality can arise from the asymmetric configuration of the cross-linking points as well as from asymmetric conformations of the polymer chains which are stabilised by cross-linking. The extent to which these two factors contribute is not known. 

The expoimental data on the non-steady state Ken effect of flexible-chain polymers dissolved in solvents with moderate viscosities reveal that at frequences up to lO Hz no dispersion of B is observed (just as in solutions of low molecular weight substances and monomers). This is also an indication of mutually independent orientation of single monomer units in the electric field which is only sightly related to the structure and conformation of the polymer chain as a whole. 

The method of preparation also influences the properties of the film. Cast films of varying properties can be prepared by variation inter alia of the solvent power of the casting solution containing the polymer, although the complex processes involved in film formation are not yet fully understood. It is clear, however, that the conformation of the polymer chains in concentrated solution just prior to solvent evaporation will determine the density of the film, and the number and size of pores and voids. Dmg flux through dense (nonporous) polymer membranes is by diffusion flux through porous membranes will be by diffusion and by transport in solvent through pores in the film. With... 

Dextran forms crystalline, spherulitic complexes with Ca " ", Ba, and La, but not with Mg " and Na. The optical rotation of dextran in aqueous solution is considerably increased by the addition of La and Ba, but only slightly by Ca, Mg, and Na" " acetates. Complex-formation appears to ter the conformation of the polymer chain. A 20% solution of dextran will dissolve — 5% of Fe this solution is used for the treatment of anemia. ... 

The adsorption of polymers is more complex than surfactant adsorption, since the various interactions (chain-surface, chain-solvent and surface-solvent) must be considered, as well as the conformation of the polymer chain on the surface... 

Some isotactic polymers such as polychloral and poly(triphenylmethyl methacrylate)289 are known to exist only in purely helical conformation. The helical structure of the polymers is rigid even in solution, owing to the bulkiness of the side-groups. This has been demonstrated by the measurement of high optical activity of the polymers prepared by asymmetric polymerizations the optical activity is based on a one-handed helical conformation of the polymer chain. 

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