Stiffness of the chain

Molecular flexibility depends on the freedom of rotation around single bonds in the main chain of the polymer molecule, restrictions in this free rotation reduce the flexibility [2], 

In linear aliphatic chains having C-C-C-C-C- bonds, free rotation around the C-C bonds is characteristic but this is restricted by the electropositive repulsion between adjacent H 

The Tg is connected with the flexibility of polymeric chains. A low Tg of the oligo-polyol segment in polyurethanes is very important because it conserves the high elasticity at lower temperatures. 

Polymer Repeat unit Glass transition temperature, Ts (°C) 

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Few sets of K,a parameters were given in references 17 and 22 K and a are parameters which may depends on the fine structure i.e. rhamnose content, DE... when they play on the stiffness of the chain. Nevertheless, it seems that the viscometry must be used in carefully defined conditions to avoid aggregation which often surestimates the viscosity in that conditions, [ti] is related to the physical properties of the solution (tickening properties) but not directly to My. 

As discussed in the last 3 years, polysaccharides behave in solution under a worm like chain [26] the local stiffness of the chain is characterized by a persistance length (Ip) the larger Ip is, the larger the chain deviates from the gaussian behaviour in the usual molecular weight range of these natural polymers [27], This makes difficult to use the relations given in litterature for synthetic... 

As explained above, towards shorter scales a more realistic description of the chain dynamics must include the stiffness of the chain. The influence of the stiffness that can be expected from the characteristic ratio of PIB was calculated according to both the ARS model and bending force models. For the mode... 

Theoretical conformational analysis provides a basis for understanding the unique features of double-stranded DNA In terms of its chemical architecture. The well-known stiffness of the chain as a whole derives from the sequence of heterocyclic bases, while the local mobility of the constituent nucleotides reflects the structural complexity of the sugar-phosphate backbone. 

The stiffness of the chains, represented by the term Hi) in Eq. (2), together with the electrical and van der Waals interactions determine the conformation of the polyelectrolyte chains and hence their charge and segment concentration distributions in solution. The chains become more extended with increasing stiffness. As a result, at short distances, the force between plates is repulsive for... 

As noted above, the first study of the problem of partial chain flexibility has been done by Flory (1) - one more problem in polymer science which he was the first to tackle. Flory has assumed the existence of a favorable arrangement of a number of consecutive base units. The configurational free energy of this arrangement differs by an amount e from other possible sequences. Apparently, these other arrangements do not have to be all identical thus e represents an average value. Flory points out that the stiffness of the chain is involved. He places the chains and solvent molecules on a lattice, a convenient although not a necessary step. 

An aspect ratio T=a/V1/3 has been introduced [213], characterizing an effective stiffness of the chain and reflecting an interchain packing ability. The real more linear (low x) olefinic copolymers are described as the more stiff chains (with large T and a), while the more branched polyolefines (high x) as the more flexible blend components (with small r and a). 

A large number of linear aromatic poly(imide)s are highly intractable and cannot be processed due to the inherent stiffness of the chains and, more importantly, due to strong interactions between aromatic rings on adjacent polymer chains. An approach to improve the processability of such stiff macromolecules is to attach flexible alkoxy chains to the aromatic rings (see, for example. Refs. [63-65]). 

The details of the molecular structure of polymers profoundly influence the observed Tg s, as illustrated by Table 5-2, where we may contrast the Tg of polydimethyl siloxane, -123 °C, with that of poly(calcium phosphate), + 525 °C. At least approximately, we may separate the observed effects into intermolecular and intramolecular parts. The latter refer to structural parameters affecting the stiffness of the chain backbone we shall examine these first. 

Although it had been appreciated since the early studies of Meyer and Lotmar 11 in the 1930 s that there was a substantial gap between the theoretical stiffness of the chain in several commercially available polymers and the achievement of stiffness by existing processes, it was not until the 1970 s that this gap was bridged. It is in polyethylene that the results have been most dramatically realised, and oriented fibres and rods have been produced with room temperature Young s moduli in the range from 50-100 GPa 2-7). Solution spun fibres have even been prepared with a Young s modulus at low temperatures of 288 GPa 8), which is very close to the highest theoretical estimate of 324 GPa 9). 

Physicochemical studies have also been performed on carboxymethyl-ated 0-methyl- and 0-(2-hydroxyethyl)-cellulose. As with other car-boxymethylated polysaccharides, the degree of substitution and the distribution of substituents play a dominant role in the viscosity of aqueous solutions of O-(carboxymethyl)starch. Viscosimetric "" and other measurements indicate that 0-(carboxymethyl)amylose exists as a random coil in solution, " and that the chains are stiffer than the corresponding cel-lulosic chains whereas the stiffness of the chains of 0-(carboxy-methyl)dextran is little different from that of other charged ether derivatives of dextran and dextran sulfate. Fractional precipitation is a useful procedure for obtaining homogeneous fractions of carboxymethylated polysaccharides, as with other polysaccharide ethers. Acetylated O-(carboxymethyl) cellulose provides a useful basis for the formation of desalination membranes. ... 

Terylene is an important polyester. It exhibits high resilience, durability, and low moisture absorption, properties that contribute to its desirable wash and wear characteristics. The harsh feel of the fiber, caused by the stiffness of the chain, is overcome by blending it with wool and cotton. 

Link 4. Comparison to Experiment for Liquid Crystals Liquid crystals and polymer glasses are really two faces of the same coin. In both cases e transition occurs because of a geometrical frustration arising from the stiffness of the chain. 

According to Equation (4-27), the chain end-to-end distance depends on parameters independent of the constitution and configuration, such as the number of bonds, as well as on parameters which are dependent, like bond length, valence angle, and steric hindrance parameter. A certain stiffness of the chain can be caused by increased bond length and valence angle, as well as... 

Up to this point we have confined ourselves to ideally flexible chains. Thus, the theories developed on the models of such chains (for example, the spring-bead chain) should no longer be adequate for polymers whose chemical stmcture suggests considerable stiffness of the chain backbone. Many cheiin models may be used to formulate a theory of stiff or semi-flexible polymers in solution, but the most frequently adopted is the wormlike chain mentioned in Section 1.3 of Chapter 1 it is sometimes called the KP chain. This physical model was introduced long ago by Kratky and Porod [1] to represent cellulosic polymers. However, significant progress in the study of its dilute solution properties, static and dynamic, has occurred in the last two decades. 

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