Chains stiffness

As we have already seen in Chapter 1 for butane and polyethylene, steric repulsions impose restrictions on bond rotation. This means that Equation 10.5 has to be modified further, and now becomes 

The freely jointed dimensions are now more realistic when restricted by the skeletal factor composed of the two terms. 

For more complex chains containing rings or heteroatomic chains, e.g., polydienes, polyethers, polysaccharides, and proteins, an estimate of o is obtained from 

Values of the imperturbed dimension can be obtained experimentally from dilute solution measurements made either directly in a theta solvent (see Chapter 9, Section 9.7) or by using indirect measurements in nonideal solvents and employing an extrapolation procedure. The geometry of each chain allows the calculation of ( and results are expressed either as o or as the characteristic ratio = (r )o/ F. Both provide a measure of chain stiffness in dilute solution. The range of values normally foimd for o is from about 1.5 to 2.5, as shown in Table 10.1. 

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Polyamides. The next two compounds are the amide counterparts of the esters listed under item (4). Although the values of AH j are less for the amides than for the esters, the values of T j, are considerably higher. This is a consequence of the very much lower values of AS j for the amides. These, in turn, are attributed to the low entropies of the amide in the liquid state owing to the effects of hydrogen bonding and chain stiffness arising from the contribution of the resonance form... 

The presence of two substituents rather than one (compare methyl methacrylate with methyl acrylate) increases chain stiffness, decreases V -, and increases Tg. 

The combination of strong intermolecular forces and high chain stiffness accounts for the high melting points of polyamides through application of Eq.(4.5). 

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

The wide variety of ketomethylene and amino ketone monomers that could be synthesized, and the abiUty of the quinoline-forming reaction to generate high molar mass polymers under relatively mild conditions, allow the synthesis of a series of polyquinolines with a wide stmctural variety. Thus polyquinolines with a range of chain stiffness from a semirigid chain to rod-like macromolecules have been synthesized. Polyquinolines are most often prepared by solution polymerization of bis(i9-amino aryl ketone) and bis (ketomethylene) monomers, where R = H or C H, in y -cresol with di-y -cresyl phosphate at 135—140°C for a period of 24—48 h (92). 

The glass transition temperature of a random copolymer usually falls between those of the corresponding homopolymers since the copolymers will tend to have intermediate chain stiffness and interchain attraction. Where these are the only important factors to be considered a linear relationship between Tg and copolymer composition is both reasonable to postulate and experimentally verifiable. One form of this relationship is given by the equation... 

Polyolefins with branched side chains other than P4MP1 have been prepared Figure 11.14). Because of their increased cohesive energy, ability for the molecules to pack and the effect of increasing chain stiffness some of these polymers have very high melting points. For example, poly-(3-methylbut-l-ene) melts at about 240°C and poly-(4,4-dimethylpent-l-ene) is reported to have a melting point of between 300 C and 350°C. Certain cyclic side chains can also... 

As a class the aliphatic polyalkenamers have low values due to a combination of low chain stiffness and low interchain attraction. The presence of double bonds has the effect of increasing the flexibility of adjacent single bonds (see Chapter 4) and overall this leads to a reduction in. Thus in the sequence from polydecenamer down to polypentenamer an increase in the double bond concentration leads to a lowering of Tg. On the other hand the Tg of polybutenamer, i.e. poly butadiene, is somewhat higher than that of polypentenamer, presumably because the proportion of stiff links, i.e. double bonds, becomes sufficiently high to override the flexibilising effect on adjacent chains. Consequently the polypentenamers have the lowest Tg values known for hydrocarbon polymers (cis- -114°C, trans- -97°C). 

It has already been shown (e.g. Chapters 20 and 21) that the insertion of a p-phenylene into the main chain of a linear polymer increased the chain stiffness and raised the heat distortion temperature. In many instances it also improved the resistance to thermal degradation. One of the first polymers to exploit this concept commercially was poly(ethylene terephthalate) but it was developed more with the polycarbonates, polysulphone, poly(phenylene sulphides) and aromatic polyketones. 

On the other hand, it has also become clear that a materials-oriented synthesis of conjugated poly(phenylene)s cannot narrow its attention to properties of molecules only in solution, but has to include aspects of processing and supramolecu-lar ordering as well. The rigid-rod character of PPPs therefore suggests the use of chain stiffness as a structure-forming principle in the design of supramolecular motifs. 

The results presented up to here concern only one-dimensional oligomers and polymers of the PPP-lype. This section is mainly focussed on the electronic properties of extended re-chains and on the morphology of solid PPPs using chain-stiffness as a structure-forming principle for supramolecular architectures. 

High degree of chain-to-chain attraction as a result of polarity (high cohesive energy density) results in chain stiffness and immobility... 

FIGURE 21.8 The behavior of (a) chain stiffness, kz and (b) viscosity of the chain, tj2 against the extension. The values of 2 and -172 were calculated by a double-Voigt model. 

An experimental test of the scaling model requires a selective variation of the two scaling variables of the model, i.e. the lateral chain distance and the chain stiffness. The Kuhn length /K depends on temperature via the characteristic ratio Cw the lateral chain distance s can be varied via the volume fraction 4>. 

The measurements of chain stiffness of denatured proteins are made in the presence of a strong denaturant, such as 8 M urea or 6 M GdmCl, in which peptide H-bonds are weak and peptide helices unfold (Scholtz et al., 1995 Smith and Scholtz, 1996), and the possible presence of (/-helices or /3-hairpins is not an issue in these denaturants. The careful and thorough measurements of intrinsic viscosities made by Tanford and co-workers (1968), discussed above, yield a substantially lower estimate for chain stiffness than the work of Flory and co-workers. A comparison is made by Tanford (1968) between the proportionality coefficient... 

In general, the factor by which G is reduced depends on Me, f, chain stiffness, and the initial concentrations of reactive groups obtainable in bulk, in a manner which still needs to be resolved in detail. However, for bulk reaction mixtures, the moduli of networks with relatively flexible chain structures can be reduced by a factor of five below those expected for network formation in the absence of pre-gel intramolecular reaction. 

Several factors related to chemical structure are known to affect the glass transition tempera lure. The most important factor is chain stiffness or flexibility of the polymer. Main-chain aliphatic groups, ether linkages, and dimethylsiloxane groups build flexibility into a polymer and lower Tg Aliphatic side chains also lower Tg, (he effect of the length of aliphatic groups is illustrated by the methacrylate series (4,38) ... 

Although the origin of the PM transition remains obscure, the differences in potential energy curves and main-chain stiffness between 16 and 17 may be critical. Figure 4.14 shows the main-chain dihedral angle dependence on the... 

Chain stationary insertion, 16 110 Chain stiffness, of fiber polymers, 11 175 Chain-stopped alkyds, 2 152 Chain structure of PVDC, 25 699... 

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